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Purpose ------- This directory contains example drivers that call ARPACK subroutines __aupd.f and __eupd.f to solve various eigenvalue problems using regular, shift-invert or other special modes (such as Cayley, Bucking etc.) These drivers illustrate how to set various ARPACK parameters to solve different problems in different modes. They provide a guideline on how to use ARPACK's reverse communication interface. The user may modify any one of these drivers, and supply his/her own matrix vector multiplication routine to solve the problem of his/her own interest. These drivers are installed in the following subdirectories. SIMPLE --- simple drivers for beginners. SYM --- drivers for symmetric eigenvalue problems NONSYM --- drivers for nonsymmetric eigenvalue problems COMPLEX --- drivers for eigenvalue problem with complex matrices BAND --- drivers for eigenvalue problem with BANDED matrices SVD --- drivers for computing singular values and vectors of a m by n matrix. 2. Getting started --------------- If you have never used ARPACK before, it might be a good idea to go into the subdirectory SIMPLE, and read one of the simple drivers [s,d]ssimp.f, [s,d]nsimp.f [c,z]nsimp.f first. The documentation explains how to use ARPACK in considerable detail. To run these drivers, you may use the makefile in that directory and issue, for example, "make sssimp", and then execute using "sssimp" The output should look like: _saupd: number of update iterations taken ----------------------------------------- 1 - 1: 5 _saupd: number of "converged" Ritz values ----------------------------------------- 1 - 1: 4 _saupd: final Ritz values ------------------------- 1 - 4: 8.912E+02 9.198E+02 9.198E+02 9.484E+02 _saupd: corresponding error bounds ---------------------------------- 1 - 4: 4.686E-11 1.905E-08 1.050E-10 5.700E-19 ========================================== = Symmetric implicit Arnoldi update code = = Version Number: 2.1 = = Version Date: 11/15/95 = ========================================== = Summary of timing statistics = ========================================== Total number update iterations = 5 Total number of OP*x operations = 78 Total number of B*x operations = 0 Total number of reorthogonalization steps = 78 Total number of iterative refinement steps = 0 Total number of restart steps = 0 Total time in user OP*x operation = 0.066667 Total time in user B*x operation = 0.000000 Total time in Arnoldi update routine = 1.166667 Total time in ssaup2 routine = 1.166667 Total time in basic Arnoldi iteration loop = 0.216667 Total time in reorthogonalization phase = 0.066667 Total time in (re)start vector generation = 0.000000 Total time in trid eigenvalue subproblem = 0.050000 Total time in getting the shifts = 0.000000 Total time in applying the shifts = 0.900000 Total time in convergence testing = 0.000000 Ritz values and relative residuals ---------------------------------- Col 1 Col 2 Row 1: 8.91167E+02 6.95597E-07 Row 2: 9.19781E+02 3.30156E-07 Row 3: 9.19781E+02 4.25717E-07 Row 4: 9.48395E+02 3.20519E-07 _SSIMP ====== Size of the matrix is 100 The number of Ritz values requested is 4 The number of Arnoldi vectors generated (NCV) is 20 What portion of the spectrum: LM The number of converged Ritz values is 4 The number of Implicit Arnoldi update iterations taken is 5 The number of OP*x is 78 The convergence criterion is 5.96046E-08 3. Convention ---------- The naming convention for each driver is explained in the README file in each subdirectory. 4. LAPACK & BLAS routines ---------------------- All ARPACK codes assume the use of LAPACK version 2.0 codes. LAPACK and BLAS routines needed for each driver program are listed at the beginning of the documentation in each driver program. arpack-0.92.1/EXAMPLES/SVD/0000755000175000017500000000000010776001577011731 500000000000000arpack-0.92.1/EXAMPLES/SVD/dsvd.f0000644000175000017500000005260410776001577012767 00000000000000 program dsvd c c This example program is intended to illustrate the c the use of ARPACK to compute the Singular Value Decomposition. c c This code shows how to use ARPACK to find a few of the c largest singular values(sigma) and corresponding right singular c vectors (v) for the the matrix A by solving the symmetric problem: c c (A'*A)*v = sigma*v c c where A is an m by n real matrix. c c This code may be easily modified to estimate the 2-norm c condition number largest(sigma)/smallest(sigma) by setting c which = 'BE' below. This will ask for a few of the smallest c and a few of the largest singular values simultaneously. c The condition number could then be estimated by taking c the ratio of the largest and smallest singular values. c c This formulation is appropriate when m .ge. n. c Reverse the roles of A and A' in the case that m .le. n. c c The main points illustrated here are c c 1) How to declare sufficient memory to find NEV c largest singular values of A . c c 2) Illustration of the reverse communication interface c needed to utilize the top level ARPACK routine DSAUPD c that computes the quantities needed to construct c the desired singular values and vectors(if requested). c c 3) How to extract the desired singular values and vectors c using the ARPACK routine DSEUPD. c c 4) How to construct the left singular vectors U from the c right singular vectors V to obtain the decomposition c c A*V = U*S c c where S = diag(sigma_1, sigma_2, ..., sigma_k). c c The only thing that must be supplied in order to use this c routine on your problem is to change the array dimensions c appropriately, to specify WHICH singular values you want to c compute and to supply a the matrix-vector products c c w <- Ax c y <- A'w c c in place of the calls to AV( ) and ATV( ) respectively below. c c Further documentation is available in the header of DSAUPD c which may be found in the SRC directory. c c This codes implements c c\Example-1 c ... Suppose we want to solve A'A*v = sigma*v in regular mode, c where A is derived from the simplest finite difference c discretization of the 2-dimensional kernel K(s,t)dt where c c K(s,t) = s(t-1) if 0 .le. s .le. t .le. 1, c t(s-1) if 0 .le. t .lt. s .le. 1. c c See subroutines AV and ATV for details. c ... OP = A'*A and B = I. c ... Assume "call av (n,x,y)" computes y = A*x c ... Assume "call atv (n,y,w)" computes w = A'*y c ... Assume exact shifts are used c ... c c\BeginLib c c\Routines called: c dsaupd ARPACK reverse communication interface routine. c dseupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c dnrm2 Level 1 BLAS that computes the norm of a vector. c daxpy Level 1 BLAS that computes y <- alpha*x+y. c dscal Level 1 BLAS thst computes x <- x*alpha. c dcopy Level 1 BLAS thst computes y <- x. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: svd.F SID: 2.4 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c----------------------------------------------------------------------- c c %------------------------------------------------------% c | Storage Declarations: | c | | c | It is assumed that A is M by N with M .ge. N. | c | | c | The maximum dimensions for all arrays are | c | set here to accommodate a problem size of | c | M .le. MAXM and N .le. MAXN | c | | c | The NEV right singular vectors will be computed in | c | the N by NCV array V. | c | | c | The NEV left singular vectors will be computed in | c | the M by NEV array U. | c | | c | NEV is the number of singular values requested. | c | See specifications for ARPACK usage below. | c | | c | NCV is the largest number of basis vectors that will | c | be used in the Implicitly Restarted Arnoldi | c | Process. Work per major iteration is | c | proportional to N*NCV*NCV. | c | | c | You must set: | c | | c | MAXM: Maximum number of rows of the A allowed. | c | MAXN: Maximum number of columns of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %------------------------------------------------------% c integer maxm, maxn, maxnev, maxncv, ldv, ldu parameter (maxm = 500, maxn=250, maxnev=10, maxncv=25, & ldu = maxm, ldv=maxn ) c c %--------------% c | Local Arrays | c %--------------% c Double precision & v(ldv,maxncv), u(ldu, maxnev), & workl(maxncv*(maxncv+8)), workd(3*maxn), & s(maxncv,2), resid(maxn), ax(maxm) logical select(maxncv) integer iparam(11), ipntr(11) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, m, n, nev, ncv, lworkl, info, ierr, & j, ishfts, maxitr, mode1, nconv logical rvec Double precision & tol, sigma, temp c c %------------% c | Parameters | c %------------% c Double precision & one, zero parameter (one = 1.0D+0, zero = 0.0D+0) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & dnrm2 external dnrm2, daxpy, dcopy, dscal c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------------------------% c | The following include statement and assignments | c | initiate trace output from the internal | c | actions of ARPACK. See debug.doc in the | c | DOCUMENTS directory for usage. Initially, the | c | most useful information will be a breakdown of | c | time spent in the various stages of computation | c | given by setting msaupd = 1. | c %-------------------------------------------------% c include 'debug.h' ndigit = -3 logfil = 6 msgets = 0 msaitr = 0 msapps = 0 msaupd = 1 msaup2 = 0 mseigt = 0 mseupd = 0 c c %-------------------------------------------------% c | The following sets dimensions for this problem. | c %-------------------------------------------------% c m = 500 n = 100 c c %------------------------------------------------% c | Specifications for ARPACK usage are set | c | below: | c | | c | 1) NEV = 4 asks for 4 singular values to be | c | computed. | c | | c | 2) NCV = 20 sets the length of the Arnoldi | c | factorization | c | | c | 3) This is a standard problem | c | (indicated by bmat = 'I') | c | | c | 4) Ask for the NEV singular values of | c | largest magnitude | c | (indicated by which = 'LM') | c | See documentation in DSAUPD for the | c | other options SM, BE. | c | | c | Note: NEV and NCV must satisfy the following | c | conditions: | c | NEV <= MAXNEV, | c | NEV + 1 <= NCV <= MAXNCV | c %------------------------------------------------% c nev = 4 ncv = 10 bmat = 'I' which = 'LM' c if ( n .gt. maxn ) then print *, ' ERROR with _SVD: N is greater than MAXN ' go to 9000 else if ( m .gt. maxm ) then print *, ' ERROR with _SVD: M is greater than MAXM ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _SVD: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _SVD: NCV is greater than MAXNCV ' go to 9000 end if c c %-----------------------------------------------------% c | Specification of stopping rules and initial | c | conditions before calling DSAUPD | c | | c | abs(sigmaC - sigmaT) < TOL*abs(sigmaC) | c | computed true | c | | c | If TOL .le. 0, then TOL <- macheps | c | (machine precision) is used. | c | | c | IDO is the REVERSE COMMUNICATION parameter | c | used to specify actions to be taken on return | c | from DSAUPD. (See usage below.) | c | | c | It MUST initially be set to 0 before the first | c | call to DSAUPD. | c | | c | INFO on entry specifies starting vector information | c | and on return indicates error codes | c | | c | Initially, setting INFO=0 indicates that a | c | random starting vector is requested to | c | start the ARNOLDI iteration. Setting INFO to | c | a nonzero value on the initial call is used | c | if you want to specify your own starting | c | vector (This vector must be placed in RESID.) | c | | c | The work array WORKL is used in DSAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. | c %-----------------------------------------------------% c lworkl = ncv*(ncv+8) tol = zero info = 0 ido = 0 c c %---------------------------------------------------% c | Specification of Algorithm Mode: | c | | c | This program uses the exact shift strategy | c | (indicated by setting IPARAM(1) = 1.) | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 1 of DSAUPD is used | c | (IPARAM(7) = 1). All these options can be changed | c | by the user. For details see the documentation in | c | DSAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = n mode1 = 1 c iparam(1) = ishfts c iparam(3) = maxitr c iparam(7) = mode1 c c %------------------------------------------------% c | M A I N L O O P (Reverse communication loop) | c %------------------------------------------------% c 10 continue c c %---------------------------------------------% c | Repeatedly call the routine DSAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call dsaupd ( ido, bmat, n, which, nev, tol, resid, & ncv, v, ldv, iparam, ipntr, workd, workl, & lworkl, info ) c if (ido .eq. -1 .or. ido .eq. 1) then c c %---------------------------------------% c | Perform matrix vector multiplications | c | w <--- A*x (av()) | c | y <--- A'*w (atv()) | c | The user should supply his/her own | c | matrix vector multiplication routines | c | here that takes workd(ipntr(1)) as | c | the input, and returns the result in | c | workd(ipntr(2)). | c %---------------------------------------% c call av (m, n, workd(ipntr(1)), ax) call atv (m, n, ax, workd(ipntr(2))) c c %-----------------------------------------% c | L O O P B A C K to call DSAUPD again. | c %-----------------------------------------% c go to 10 c end if c c %----------------------------------------% c | Either we have convergence or there is | c | an error. | c %----------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message. Check the | c | documentation in DSAUPD. | c %--------------------------% c print *, ' ' print *, ' Error with _saupd, info = ', info print *, ' Check documentation in _saupd ' print *, ' ' c else c c %--------------------------------------------% c | No fatal errors occurred. | c | Post-Process using DSEUPD. | c | | c | Computed singular values may be extracted. | c | | c | Singular vectors may also be computed now | c | if desired. (indicated by rvec = .true.) | c | | c | The routine DSEUPD now called to do this | c | post processing | c %--------------------------------------------% c rvec = .true. c call dseupd ( rvec, 'All', select, s, v, ldv, sigma, & bmat, n, which, nev, tol, resid, ncv, v, ldv, & iparam, ipntr, workd, workl, lworkl, ierr ) c c %-----------------------------------------------% c | Singular values are returned in the first | c | column of the two dimensional array S | c | and the corresponding right singular vectors | c | are returned in the first NEV columns of the | c | two dimensional array V as requested here. | c %-----------------------------------------------% c if ( ierr .ne. 0) then c c %------------------------------------% c | Error condition: | c | Check the documentation of DSEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _seupd, info = ', ierr print *, ' Check the documentation of _seupd. ' print *, ' ' c else c nconv = iparam(5) do 20 j=1, nconv c s(j,1) = sqrt(s(j,1)) c c %-----------------------------% c | Compute the left singular | c | vectors from the formula | c | | c | u = Av/sigma | c | | c | u should have norm 1 so | c | divide by norm(Av) instead. | c %-----------------------------% c call av(m, n, v(1,j), ax) call dcopy(m, ax, 1, u(1,j), 1) temp = one/dnrm2(m, u(1,j), 1) call dscal(m, temp, u(1,j), 1) c c %---------------------------% c | | c | Compute the residual norm | c | | c | || A*v - sigma*u || | c | | c | for the NCONV accurately | c | computed singular values | c | and vectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance). | c | Store the result in 2nd | c | column of array S. | c %---------------------------% c call daxpy(m, -s(j,1), u(1,j), 1, ax, 1) s(j,2) = dnrm2(m, ax, 1) c 20 continue c c %-------------------------------% c | Display computed residuals | c %-------------------------------% c call dmout(6, nconv, 2, s, maxncv, -6, & 'Singular values and direct residuals') end if c c %------------------------------------------% c | Print additional convergence information | c %------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, ' _SVD ' print *, ' ==== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %-------------------------% c | Done with program dsvd. | c %-------------------------% c 9000 continue c end c c ------------------------------------------------------------------ c matrix vector subroutines c c The matrix A is derived from the simplest finite difference c discretization of the integral operator c c f(s) = integral(K(s,t)x(t)dt). c c Thus, the matrix A is a discretization of the 2-dimensional kernel c K(s,t)dt, where c c K(s,t) = s(t-1) if 0 .le. s .le. t .le. 1, c t(s-1) if 0 .le. t .lt. s .le. 1. c c Thus A is an m by n matrix with entries c c A(i,j) = k*(si)*(tj - 1) if i .le. j, c k*(tj)*(si - 1) if i .gt. j c c where si = i/(m+1) and tj = j/(n+1) and k = 1/(n+1). c c------------------------------------------------------------------- c subroutine av (m, n, x, w) c c computes w <- A*x c integer m, n, i, j Double precision & x(n), w(m), one, zero, h, k, s, t parameter ( one = 1.0D+0, zero = 0.0D+0 ) c h = one / dble(m+1) k = one / dble(n+1) do 5 i = 1,m w(i) = zero 5 continue t = zero c do 30 j = 1,n t = t+k s = zero do 10 i = 1,j s = s+h w(i) = w(i) + k*s*(t-one)*x(j) 10 continue do 20 i = j+1,m s = s+h w(i) = w(i) + k*t*(s-one)*x(j) 20 continue 30 continue c return end c c------------------------------------------------------------------- c subroutine atv (m, n, w, y) c c computes y <- A'*w c integer m, n, i, j Double precision & w(m), y(n), one, zero, h, k, s, t parameter ( one = 1.0D+0, zero = 0.0D+0 ) c h = one / dble(m+1) k = one / dble(n+1) do 5 i = 1,n y(i) = zero 5 continue t = zero c do 30 j = 1,n t = t+k s = zero do 10 i = 1,j s = s+h y(j) = y(j) + k*s*(t-one)*w(i) 10 continue do 20 i = j+1,m s = s+h y(j) = y(j) + k*t*(s-one)*w(i) 20 continue 30 continue c return end c arpack-0.92.1/EXAMPLES/SVD/makefile0000644000175000017500000000055010776001577013351 00000000000000# # makefile to run simple examples of the reverse communication # protocol. # # Modify if ARPACK library was built somewhere else. # #\SCCS Information: @(#) # FILE: makefile SID: 2.2 DATE OF SID: 9/24/96 RELEASE: 2 # include ../../ARmake.inc ssvd: ssvd.o $(FC) $(FFLAGS) ssvd.o $(ALIBS) -o ssvd dsvd: dsvd.o $(FC) $(FFLAGS) dsvd.o $(ALIBS) -o dsvd arpack-0.92.1/EXAMPLES/SVD/README0000644000175000017500000000112410776001577012527 000000000000001. Purpose ------- This directory contains simple example drivers that call ARPACK subroutine [s,d]saupd.f and [s,d]seupd.f to compute the Singular Value Decomposition of a matrix A. These drivers illustrate how to use ARPACK in considerable detail. 2. Naming Convention ----------------- The name for each driver has the form 'Xsvd.f', where X - is 's' (single precision) or 'd' (double precision) 3. Usage ----- To run these drivers, you may use the makefile in this directory and issue, for example, "make ssvd". Then execute using "ssvd". arpack-0.92.1/EXAMPLES/SVD/debug.h0000644000175000017500000000135110776001577013110 00000000000000c c\SCCS Information: @(#) c FILE: debug.h SID: 2.3 DATE OF SID: 11/16/95 RELEASE: 2 c c %---------------------------------% c | See debug.doc for documentation | c %---------------------------------% integer logfil, ndigit, mgetv0, & msaupd, msaup2, msaitr, mseigt, msapps, msgets, mseupd, & mnaupd, mnaup2, mnaitr, mneigh, mnapps, mngets, mneupd, & mcaupd, mcaup2, mcaitr, mceigh, mcapps, mcgets, mceupd common /debug/ & logfil, ndigit, mgetv0, & msaupd, msaup2, msaitr, mseigt, msapps, msgets, mseupd, & mnaupd, mnaup2, mnaitr, mneigh, mnapps, mngets, mneupd, & mcaupd, mcaup2, mcaitr, mceigh, mcapps, mcgets, mceupd arpack-0.92.1/EXAMPLES/SVD/ssvd.f0000644000175000017500000005247410776001577013013 00000000000000 program ssvd c c This example program is intended to illustrate the c the use of ARPACK to compute the Singular Value Decomposition. c c This code shows how to use ARPACK to find a few of the c largest singular values(sigma) and corresponding right singular c vectors (v) for the the matrix A by solving the symmetric problem: c c (A'*A)*v = sigma*v c c where A is an m by n real matrix. c c This code may be easily modified to estimate the 2-norm c condition number largest(sigma)/smallest(sigma) by setting c which = 'BE' below. This will ask for a few of the smallest c and a few of the largest singular values simultaneously. c The condition number could then be estimated by taking c the ratio of the largest and smallest singular values. c c This formulation is appropriate when m .ge. n. c Reverse the roles of A and A' in the case that m .le. n. c c The main points illustrated here are c c 1) How to declare sufficient memory to find NEV c largest singular values of A . c c 2) Illustration of the reverse communication interface c needed to utilize the top level ARPACK routine SSAUPD c that computes the quantities needed to construct c the desired singular values and vectors(if requested). c c 3) How to extract the desired singular values and vectors c using the ARPACK routine SSEUPD. c c 4) How to construct the left singular vectors U from the c right singular vectors V to obtain the decomposition c c A*V = U*S c c where S = diag(sigma_1, sigma_2, ..., sigma_k). c c The only thing that must be supplied in order to use this c routine on your problem is to change the array dimensions c appropriately, to specify WHICH singular values you want to c compute and to supply a the matrix-vector products c c w <- Ax c y <- A'w c c in place of the calls to AV( ) and ATV( ) respectively below. c c Further documentation is available in the header of DSAUPD c which may be found in the SRC directory. c c This codes implements c c\Example-1 c ... Suppose we want to solve A'A*v = sigma*v in regular mode, c where A is derived from the simplest finite difference c discretization of the 2-dimensional kernel K(s,t)dt where c c K(s,t) = s(t-1) if 0 .le. s .le. t .le. 1, c t(s-1) if 0 .le. t .lt. s .le. 1. c c See subroutines AV and ATV for details. c ... OP = A'*A and B = I. c ... Assume "call av (n,x,y)" computes y = A*x c ... Assume "call atv (n,y,w)" computes w = A'*y c ... Assume exact shifts are used c ... c c\BeginLib c c\Routines called: c ssaupd ARPACK reverse communication interface routine. c sseupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c snrm2 Level 1 BLAS that computes the norm of a vector. c saxpy Level 1 BLAS that computes y <- alpha*x+y. c sscal Level 1 BLAS thst computes x <- x*alpha. c scopy Level 1 BLAS thst computes y <- x. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: svd.F SID: 2.4 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c----------------------------------------------------------------------- c c %------------------------------------------------------% c | Storage Declarations: | c | | c | It is assumed that A is M by N with M .ge. N. | c | | c | The maximum dimensions for all arrays are | c | set here to accommodate a problem size of | c | M .le. MAXM and N .le. MAXN | c | | c | The NEV right singular vectors will be computed in | c | the N by NCV array V. | c | | c | The NEV left singular vectors will be computed in | c | the M by NEV array U. | c | | c | NEV is the number of singular values requested. | c | See specifications for ARPACK usage below. | c | | c | NCV is the largest number of basis vectors that will | c | be used in the Implicitly Restarted Arnoldi | c | Process. Work per major iteration is | c | proportional to N*NCV*NCV. | c | | c | You must set: | c | | c | MAXM: Maximum number of rows of the A allowed. | c | MAXN: Maximum number of columns of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %------------------------------------------------------% c integer maxm, maxn, maxnev, maxncv, ldv, ldu parameter (maxm = 500, maxn=250, maxnev=10, maxncv=25, & ldu = maxm, ldv=maxn ) c c %--------------% c | Local Arrays | c %--------------% c Real & v(ldv,maxncv), u(ldu, maxnev), & workl(maxncv*(maxncv+8)), workd(3*maxn), & s(maxncv,2), resid(maxn), ax(maxm) logical select(maxncv) integer iparam(11), ipntr(11) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, m, n, nev, ncv, lworkl, info, ierr, & j, ishfts, maxitr, mode1, nconv logical rvec Real & tol, sigma, temp c c %------------% c | Parameters | c %------------% c Real & one, zero parameter (one = 1.0E+0, zero = 0.0E+0) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & snrm2 external snrm2, saxpy, scopy, sscal c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------------------------% c | The following include statement and assignments | c | initiate trace output from the internal | c | actions of ARPACK. See debug.doc in the | c | DOCUMENTS directory for usage. Initially, the | c | most useful information will be a breakdown of | c | time spent in the various stages of computation | c | given by setting msaupd = 1. | c %-------------------------------------------------% c include 'debug.h' ndigit = -3 logfil = 6 msgets = 0 msaitr = 0 msapps = 0 msaupd = 1 msaup2 = 0 mseigt = 0 mseupd = 0 c c %-------------------------------------------------% c | The following sets dimensions for this problem. | c %-------------------------------------------------% c m = 500 n = 100 c c %------------------------------------------------% c | Specifications for ARPACK usage are set | c | below: | c | | c | 1) NEV = 4 asks for 4 singular values to be | c | computed. | c | | c | 2) NCV = 20 sets the length of the Arnoldi | c | factorization | c | | c | 3) This is a standard problem | c | (indicated by bmat = 'I') | c | | c | 4) Ask for the NEV singular values of | c | largest magnitude | c | (indicated by which = 'LM') | c | See documentation in SSAUPD for the | c | other options SM, BE. | c | | c | Note: NEV and NCV must satisfy the following | c | conditions: | c | NEV <= MAXNEV, | c | NEV + 1 <= NCV <= MAXNCV | c %------------------------------------------------% c nev = 4 ncv = 10 bmat = 'I' which = 'LM' c if ( n .gt. maxn ) then print *, ' ERROR with _SVD: N is greater than MAXN ' go to 9000 else if ( m .gt. maxm ) then print *, ' ERROR with _SVD: M is greater than MAXM ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _SVD: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _SVD: NCV is greater than MAXNCV ' go to 9000 end if c c %-----------------------------------------------------% c | Specification of stopping rules and initial | c | conditions before calling SSAUPD | c | | c | abs(sigmaC - sigmaT) < TOL*abs(sigmaC) | c | computed true | c | | c | If TOL .le. 0, then TOL <- macheps | c | (machine precision) is used. | c | | c | IDO is the REVERSE COMMUNICATION parameter | c | used to specify actions to be taken on return | c | from SSAUPD. (See usage below.) | c | | c | It MUST initially be set to 0 before the first | c | call to SSAUPD. | c | | c | INFO on entry specifies starting vector information | c | and on return indicates error codes | c | | c | Initially, setting INFO=0 indicates that a | c | random starting vector is requested to | c | start the ARNOLDI iteration. Setting INFO to | c | a nonzero value on the initial call is used | c | if you want to specify your own starting | c | vector (This vector must be placed in RESID.) | c | | c | The work array WORKL is used in SSAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. | c %-----------------------------------------------------% c lworkl = ncv*(ncv+8) tol = zero info = 0 ido = 0 c c %---------------------------------------------------% c | Specification of Algorithm Mode: | c | | c | This program uses the exact shift strategy | c | (indicated by setting IPARAM(1) = 1.) | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 1 of SSAUPD is used | c | (IPARAM(7) = 1). All these options can be changed | c | by the user. For details see the documentation in | c | SSAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = n mode1 = 1 c iparam(1) = ishfts c iparam(3) = maxitr c iparam(7) = mode1 c c %------------------------------------------------% c | M A I N L O O P (Reverse communication loop) | c %------------------------------------------------% c 10 continue c c %---------------------------------------------% c | Repeatedly call the routine SSAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call ssaupd ( ido, bmat, n, which, nev, tol, resid, & ncv, v, ldv, iparam, ipntr, workd, workl, & lworkl, info ) c if (ido .eq. -1 .or. ido .eq. 1) then c c %---------------------------------------% c | Perform matrix vector multiplications | c | w <--- A*x (av()) | c | y <--- A'*w (atv()) | c | The user should supply his/her own | c | matrix vector multiplication routines | c | here that takes workd(ipntr(1)) as | c | the input, and returns the result in | c | workd(ipntr(2)). | c %---------------------------------------% c call av (m, n, workd(ipntr(1)), ax) call atv (m, n, ax, workd(ipntr(2))) c c %-----------------------------------------% c | L O O P B A C K to call SSAUPD again. | c %-----------------------------------------% c go to 10 c end if c c %----------------------------------------% c | Either we have convergence or there is | c | an error. | c %----------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message. Check the | c | documentation in SSAUPD. | c %--------------------------% c print *, ' ' print *, ' Error with _saupd, info = ', info print *, ' Check documentation in _saupd ' print *, ' ' c else c c %--------------------------------------------% c | No fatal errors occurred. | c | Post-Process using SSEUPD. | c | | c | Computed singular values may be extracted. | c | | c | Singular vectors may also be computed now | c | if desired. (indicated by rvec = .true.) | c | | c | The routine SSEUPD now called to do this | c | post processing | c %--------------------------------------------% c rvec = .true. c call sseupd ( rvec, 'All', select, s, v, ldv, sigma, & bmat, n, which, nev, tol, resid, ncv, v, ldv, & iparam, ipntr, workd, workl, lworkl, ierr ) c c %-----------------------------------------------% c | Singular values are returned in the first | c | column of the two dimensional array S | c | and the corresponding right singular vectors | c | are returned in the first NEV columns of the | c | two dimensional array V as requested here. | c %-----------------------------------------------% c if ( ierr .ne. 0) then c c %------------------------------------% c | Error condition: | c | Check the documentation of SSEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _seupd, info = ', ierr print *, ' Check the documentation of _seupd. ' print *, ' ' c else c nconv = iparam(5) do 20 j=1, nconv c s(j,1) = sqrt(s(j,1)) c c %-----------------------------% c | Compute the left singular | c | vectors from the formula | c | | c | u = Av/sigma | c | | c | u should have norm 1 so | c | divide by norm(Av) instead. | c %-----------------------------% c call av(m, n, v(1,j), ax) call scopy(m, ax, 1, u(1,j), 1) temp = one/snrm2(m, u(1,j), 1) call sscal(m, temp, u(1,j), 1) c c %---------------------------% c | | c | Compute the residual norm | c | | c | || A*v - sigma*u || | c | | c | for the NCONV accurately | c | computed singular values | c | and vectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance). | c | Store the result in 2nd | c | column of array S. | c %---------------------------% c call saxpy(m, -s(j,1), u(1,j), 1, ax, 1) s(j,2) = snrm2(m, ax, 1) c 20 continue c c %-------------------------------% c | Display computed residuals | c %-------------------------------% c call smout(6, nconv, 2, s, maxncv, -6, & 'Singular values and direct residuals') end if c c %------------------------------------------% c | Print additional convergence information | c %------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, ' _SVD ' print *, ' ==== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %-------------------------% c | Done with program ssvd. | c %-------------------------% c 9000 continue c end c c ------------------------------------------------------------------ c matrix vector subroutines c c The matrix A is derived from the simplest finite difference c discretization of the integral operator c c f(s) = integral(K(s,t)x(t)dt). c c Thus, the matrix A is a discretization of the 2-dimensional kernel c K(s,t)dt, where c c K(s,t) = s(t-1) if 0 .le. s .le. t .le. 1, c t(s-1) if 0 .le. t .lt. s .le. 1. c c Thus A is an m by n matrix with entries c c A(i,j) = k*(si)*(tj - 1) if i .le. j, c k*(tj)*(si - 1) if i .gt. j c c where si = i/(m+1) and tj = j/(n+1) and k = 1/(n+1). c c------------------------------------------------------------------- c subroutine av (m, n, x, w) c c computes w <- A*x c integer m, n, i, j Real & x(n), w(m), one, zero, h, k, s, t parameter ( one = 1.0E+0, zero = 0.0E+0 ) c h = one / real(m+1) k = one / real(n+1) do 5 i = 1,m w(i) = zero 5 continue t = zero c do 30 j = 1,n t = t+k s = zero do 10 i = 1,j s = s+h w(i) = w(i) + k*s*(t-one)*x(j) 10 continue do 20 i = j+1,m s = s+h w(i) = w(i) + k*t*(s-one)*x(j) 20 continue 30 continue c return end c c------------------------------------------------------------------- c subroutine atv (m, n, w, y) c c computes y <- A'*w c integer m, n, i, j Real & w(m), y(n), one, zero, h, k, s, t parameter ( one = 1.0E+0, zero = 0.0E+0 ) c h = one / real(m+1) k = one / real(n+1) do 5 i = 1,n y(i) = zero 5 continue t = zero c do 30 j = 1,n t = t+k s = zero do 10 i = 1,j s = s+h y(j) = y(j) + k*s*(t-one)*w(i) 10 continue do 20 i = j+1,m s = s+h y(j) = y(j) + k*t*(s-one)*w(i) 20 continue 30 continue c return end c arpack-0.92.1/EXAMPLES/SYM/0000755000175000017500000000000010776001577011745 500000000000000arpack-0.92.1/EXAMPLES/SYM/dsdrv5.f0000644000175000017500000004125010776001577013245 00000000000000 program dsdrv5 c c Program to illustrate the idea of reverse communication c in Buckling mode for a generalized symmetric eigenvalue c problem. The following program uses the two LAPACK subroutines c dgttrf.f and dgttrs.f to factor and solve a tridiagonal system of c equations. c c We implement example five of ex-sym.doc in DOCUMENTS directory c c\Example-5 c ... Suppose we want to solve K*x = lambda*KG*x in Buckling mode c where K and KG are obtained by the finite element of the c 1-dimensional discrete Laplacian c d^2u / dx^2 c on the interval [0,1] with zero Dirichlet boundary condition c using piecewise linear elements. c ... OP = (inv[K - sigma*KG])*K and B = K. c ... Use mode 4 of DSAUPD. c c\BeginLib c c\References: c 1. R.G. Grimes, J.G. Lewis and H.D. Simon, "A Shifted Block Lanczos c Algorithm for Solving Sparse Symmetric Generalized Eigenproblems", c SIAM J. Matr. Anal. Apps., January (1993). c c\Routines called: c dsaupd ARPACK reverse communication interface routine. c dseupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c dgttrf LAPACK tridiagonal factorization routine. c dgttrs LAPACK tridiagonal solve routine. c daxpy Level 1 BLAS that computes y <- alpha*x+y. c dcopy Level 1 BLAS that copies one vector to another. c dscal Level 1 BLAS that scales a vector by a scalar. c dnrm2 Level 1 BLAS that computes the norm of a vector. c av Matrix vector multiplication routine that computes A*x. c mv Matrix vector multiplication routine that computes M*x. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: sdrv5.F SID: 2.5 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c---------------------------------------------------------------------- c c %-----------------------------% c | Define leading dimensions | c | for all arrays. | c | MAXN: Maximum dimension | c | of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %-----------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=10, maxncv=25, & ldv=maxn) c c %--------------% c | Local Arrays | c %--------------% c Double precision & v(ldv,maxncv), workl(maxncv*(maxncv+8)), & workd(3*maxn), d(maxncv,2), resid(maxn), & ad(maxn), adl(maxn), adu(maxn), adu2(maxn), & ax(maxn), mx(maxn) logical select(maxncv) integer iparam(11), ipntr(11), ipiv(maxn) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nev, ncv, lworkl, info, j, ierr, & nconv, maxitr, ishfts, mode logical rvec Double precision & h, sigma, r1, r2, tol c c %------------% c | Parameters | c %------------% c Double precision & zero, one, two, four, six parameter (zero = 0.0D+0, one = 1.0D+0, & four = 4.0D+0, six = 6.0D+0, & two = 2.0D+0 ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & dnrm2 external daxpy, dcopy, dscal, dnrm2, dgttrf, dgttrs c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable statements | c %-----------------------% c c %--------------------------------------------------% c | The number N is the dimension of the matrix. A | c | generalized eigenvalue problem is solved (BMAT = | c | 'G'.) NEV is the number of eigenvalues to be | c | approximated. Since the buckling mode is used, | c | WHICH is set to 'LM'. The user can modify NEV, | c | NCV, SIGMA to solve problems of different sizes, | c | and to get different parts of the spectrum. | c | However, The following conditions must be | c | satisfied: | c | N <= MAXN, | c | NEV <= MAXNEV, | c | NEV + 1 <= NCV <= MAXNCV | c | | c | The shift SIGMA cannot be zero!!! | c %--------------------------------------------------% c n = 100 nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _SDRV5: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _SDRV5: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _SDRV5: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' sigma = one c c %-----------------------------------------------------% c | The work array WORKL is used in DSAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in DSAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = ncv*(ncv+8) tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | This program uses exact shifts with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 4 specified in the | c | documentation of DSAUPD is used (IPARAM(7) = 4). | c | All these options may be changed by the user. For | c | details, see the documentation in DSAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 4 c iparam(1) = ishfts iparam(3) = maxitr iparam(7) = mode c c %------------------------------------------------------% c | Call LAPACK routine to factor the tridiagonal matrix | c | (K-SIGMA*KG). The matrix A is the 1-d discrete | c | Laplacian on the interval [0,1] with zero Dirichlet | c | boundary condition. The matrix M is the associated | c | mass matrix arising from using piecewise linear | c | finite elements on the interval [0, 1]. | c %------------------------------------------------------% c h = one / dble(n+1) r1 = (four / six) * h r2 = (one / six) * h do 20 j=1,n ad(j) = two / h - sigma * r1 adl(j) = -one / h- sigma * r2 20 continue call dcopy (n, adl, 1, adu, 1) call dgttrf (n, adl, ad, adu, adu2, ipiv, ierr) if (ierr .ne. 0) then print *, ' ' print *, ' Error with _gttrf in _SDRV5.' print *, ' ' go to 9000 end if c c %-------------------------------------------% c | M A I N L O O P (Reverse communication) | c %-------------------------------------------% c 10 continue c c %---------------------------------------------% c | Repeatedly call the routine DSAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call dsaupd ( ido, bmat, n, which, nev, tol, resid, & ncv, v, ldv, iparam, ipntr, workd, workl, lworkl, & info ) c if (ido .eq. -1) then c c %-------------------------------------------% c | Perform y <--- OP*x = inv[K-SIGMA*KG]*K*x | c | to force starting vector into the range | c | of OP. The user should provide his/her | c | matrix vector multiplication routine and | c | a linear system solver here. The matrix | c | vector multiplication routine (K*x) takes | c | workd(ipntr(1)) as the input vector. The | c | final result is returned to | c | workd(ipntr(2)). | c %-------------------------------------------% c call av (n, workd(ipntr(1)), workd(ipntr(2))) c call dgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv, & workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print *, ' ' print *, ' Error with _gttrs in SDRV5.' print *, ' ' go to 9000 end if c c %-----------------------------------------% c | L O O P B A C K to call DSAUPD again. | c %-----------------------------------------% c go to 10 c else if (ido .eq. 1) then c c %------------------------------------------% c | Perform y <-- OP*x=inv(K-sigma*KG)*K*x. | c | K*x has been saved in workd(ipntr(3)). | c | The user only needs the linear system | c | solver here that takes workd(ipntr(3)) | c | as input, and returns the result to | c | workd(ipntr(2)). | c %------------------------------------------% c call dcopy ( n, workd(ipntr(3)), 1, workd(ipntr(2)), 1) call dgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv, & workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print *, ' ' print *, ' Error with _gttrs in _SDRV5.' print *, ' ' go to 9000 end if c c %-----------------------------------------% c | L O O P B A C K to call DSAUPD again. | c %-----------------------------------------% c go to 10 c else if (ido .eq. 2) then c c %---------------------------------------------% c | Perform y <--- K*x | c | Need matrix vector multiplication routine | c | here that takes workd(ipntr(1)) as input | c | and returns the result to workd(ipntr(2)). | c %---------------------------------------------% c call av (n, workd(ipntr(1)), workd(ipntr(2))) c c c %-----------------------------------------% c | L O O P B A C K to call DSAUPD again. | c %-----------------------------------------% c go to 10 c end if c c %-----------------------------------------% c | Either we have convergence, or there is | c | an error. | c %-----------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message, check the | c | documentation in DSAUPD. | c %--------------------------% c print *, ' ' print *, ' Error with _saupd, info = ',info print *, ' Check the documentation of _saupd ' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using DSEUPD. | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may also be computed now if | c | desired. (indicated by rvec = .true.) | c %-------------------------------------------% c rvec = .true. c call dseupd ( rvec, 'All', select, d, v, ldv, sigma, & bmat, n, which, nev, tol, resid, ncv, v, ldv, & iparam, ipntr, workd, workl, lworkl, ierr ) c if (ierr .ne. 0) then c c %------------------------------------% c | Error condition: | c | Check the documentation of DSEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _seupd, info = ',ierr print *, ' Check the documentation of _seupd ' print *, ' ' c else c nconv = iparam(5) do 30 j=1, nconv c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c call av(n, v(1,j), ax) call mv(n, v(1,j), mx) call daxpy (n, -d(j,1), mx, 1, ax, 1) d(j,2) = dnrm2(n, ax, 1) d(j,2) = d(j,2) / abs(d(j,1)) c 30 continue c call dmout(6, nconv, 2, d, maxncv, -6, & 'Ritz values and relative residuals') c end if c c c %------------------------------------------% c | Print additional convergence information | c %------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, ' _SDRV5 ' print *, ' ====== ' print *, ' ' print *, ' Size of the matrix is', n print *, ' The number of Ritz values requested is', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program dsdrv5. | c %---------------------------% c 9000 continue c end c c------------------------------------------------------------------------ c Matrix vector subroutine c where the matrix is the 1-dimensional mass matrix c arising from using piecewise linear finite elements on the c interval [0,1]. c subroutine mv (n, v, w) integer n, j Double precision & v(n),w(n), one, four, six, h parameter (one = 1.0D+0, four = 4.0D+0, & six = 6.0D+0) c w(1) = four*v(1) + v(2) do 100 j = 2,n-1 w(j) = v(j-1) + four*v(j) + v(j+1) 100 continue j = n w(j) = v(j-1) + four*v(j) c c Scale the vector w by h. c h = one / (six*dble(n+1)) call dscal(n, h, w, 1) return end c------------------------------------------------------------------------ c Matrix vector subroutine c where the matrix is the stiffness matrix obtained from the c finite element discretization of the 1-dimensional discrete Laplacian c on the interval [0,1] with zero Dirichlet boundary condition c using piecewise linear elements. c subroutine av (n, v, w) integer n, j Double precision & v(n), w(n), one, two, h parameter (one = 1.0D+0, two = 2.0D+0) c w(1) = two*v(1) - v(2) do 100 j = 2,n-1 w(j) = - v(j-1) + two*v(j) - v(j+1) 100 continue j = n w(j) = - v(j-1) + two*v(j) c c Scale the vector w by (1/h) c h = one / (n+1) call dscal(n, one/h, w, 1) return end arpack-0.92.1/EXAMPLES/SYM/ssdrv1.f0000644000175000017500000003406310776001577013264 00000000000000 program ssdrv1 c c Simple program to illustrate the idea of reverse communication c in regular mode for a standard symmetric eigenvalue problem. c c We implement example one of ex-sym.doc in SRC directory c c\Example-1 c ... Suppose we want to solve A*x = lambda*x in regular mode, c where A is derived from the central difference discretization c of the 2-dimensional Laplacian on the unit square [0,1]x[0,1] c with zero Dirichlet boundary condition. c c ... OP = A and B = I. c c ... Assume "call av (n,x,y)" computes y = A*x. c c ... Use mode 1 of SSAUPD. c c\BeginLib c c\Routines called: c ssaupd ARPACK reverse communication interface routine. c sseupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c snrm2 Level 1 BLAS that computes the norm of a vector. c saxpy Level 1 BLAS that computes y <- alpha*x+y. c av Matrix vector multiplication routine that computes A*x. c tv Matrix vector multiplication routine that computes T*x, c where T is a tridiagonal matrix. It is used in routine c av. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: sdrv1.F SID: 2.5 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c----------------------------------------------------------------------- c c %-----------------------------% c | Define leading dimensions | c | for all arrays. | c | MAXN: Maximum dimension | c | of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %-----------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=10, maxncv=25, $ ldv=maxn ) c c %--------------% c | Local Arrays | c %--------------% c Real & v(ldv,maxncv), workl(maxncv*(maxncv+8)), & workd(3*maxn), d(maxncv,2), resid(maxn), & ax(maxn) logical select(maxncv) integer iparam(11), ipntr(11) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nev, ncv, lworkl, info, ierr, j, & nx, nconv, maxitr, mode, ishfts logical rvec Real & tol, sigma c c %------------% c | Parameters | c %------------% c Real & zero parameter (zero = 0.0E+0) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & snrm2 external snrm2, saxpy c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c %----------------------------------------------------% c | The number NX is the number of interior points | c | in the discretization of the 2-dimensional | c | Laplacian on the unit square with zero Dirichlet | c | boundary condition. The number N(=NX*NX) is the | c | dimension of the matrix. A standard eigenvalue | c | problem is solved (BMAT = 'I'). NEV is the number | c | of eigenvalues to be approximated. The user can | c | modify NEV, NCV, WHICH to solve problems of | c | different sizes, and to get different parts of the | c | spectrum. However, The following conditions must | c | be satisfied: | c | N <= MAXN, | c | NEV <= MAXNEV, | c | NEV + 1 <= NCV <= MAXNCV | c %----------------------------------------------------% c nx = 10 n = nx*nx nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _SDRV1: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _SDRV1: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _SDRV1: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'I' which = 'SM' c c %--------------------------------------------------% c | The work array WORKL is used in SSAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in SSAUPD to start the Arnoldi | c | iteration. | c %--------------------------------------------------% c lworkl = ncv*(ncv+8) tol = zero info = 0 ido = 0 c c %---------------------------------------------------% c | This program uses exact shifts with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 1 of SSAUPD is used | c | (IPARAM(7) = 1). All these options may be | c | changed by the user. For details, see the | c | documentation in SSAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 1 c iparam(1) = ishfts iparam(3) = maxitr iparam(7) = mode c c %-------------------------------------------% c | M A I N L O O P (Reverse communication) | c %-------------------------------------------% c 10 continue c c %---------------------------------------------% c | Repeatedly call the routine SSAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call ssaupd ( ido, bmat, n, which, nev, tol, resid, & ncv, v, ldv, iparam, ipntr, workd, workl, & lworkl, info ) c if (ido .eq. -1 .or. ido .eq. 1) then c c %--------------------------------------% c | Perform matrix vector multiplication | c | y <--- OP*x | c | The user should supply his/her own | c | matrix vector multiplication routine | c | here that takes workd(ipntr(1)) as | c | the input, and return the result to | c | workd(ipntr(2)). | c %--------------------------------------% c call av (nx, workd(ipntr(1)), workd(ipntr(2))) c c %-----------------------------------------% c | L O O P B A C K to call SSAUPD again. | c %-----------------------------------------% c go to 10 c end if c c %----------------------------------------% c | Either we have convergence or there is | c | an error. | c %----------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message. Check the | c | documentation in SSAUPD. | c %--------------------------% c print *, ' ' print *, ' Error with _saupd, info = ', info print *, ' Check documentation in _saupd ' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using SSEUPD. | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may also be computed now if | c | desired. (indicated by rvec = .true.) | c %-------------------------------------------% c rvec = .true. c call sseupd ( rvec, 'All', select, d, v, ldv, sigma, & bmat, n, which, nev, tol, resid, ncv, v, ldv, & iparam, ipntr, workd, workl, lworkl, ierr ) c %----------------------------------------------% c | Eigenvalues are returned in the first column | c | of the two dimensional array D and the | c | corresponding eigenvectors are returned in | c | the first NEV columns of the two dimensional | c | array V if requested. Otherwise, an | c | orthogonal basis for the invariant subspace | c | corresponding to the eigenvalues in D is | c | returned in V. | c %----------------------------------------------% c if ( ierr .ne. 0) then c c %------------------------------------% c | Error condition: | c | Check the documentation of SSEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _seupd, info = ', ierr print *, ' Check the documentation of _seupd. ' print *, ' ' c else c nconv = iparam(5) do 20 j=1, nconv c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c call av(nx, v(1,j), ax) call saxpy(n, -d(j,1), v(1,j), 1, ax, 1) d(j,2) = snrm2(n, ax, 1) d(j,2) = d(j,2) / abs(d(j,1)) c 20 continue c c %-------------------------------% c | Display computed residuals | c %-------------------------------% c call smout(6, nconv, 2, d, maxncv, -6, & 'Ritz values and relative residuals') end if c c %------------------------------------------% c | Print additional convergence information | c %------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, ' _SDRV1 ' print *, ' ====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program ssdrv1. | c %---------------------------% c 9000 continue c end c c ------------------------------------------------------------------ c matrix vector subroutine c c The matrix used is the 2 dimensional discrete Laplacian on unit c square with zero Dirichlet boundary condition. c c Computes w <--- OP*v, where OP is the nx*nx by nx*nx block c tridiagonal matrix c c | T -I | c |-I T -I | c OP = | -I T | c | ... -I| c | -I T| c c The subroutine TV is called to computed y<---T*x. c subroutine av (nx, v, w) integer nx, j, lo, n2 Real & v(nx*nx), w(nx*nx), one, h2 parameter ( one = 1.0E+0 ) c call tv(nx,v(1),w(1)) call saxpy(nx, -one, v(nx+1), 1, w(1), 1) c do 10 j = 2, nx-1 lo = (j-1)*nx call tv(nx, v(lo+1), w(lo+1)) call saxpy(nx, -one, v(lo-nx+1), 1, w(lo+1), 1) call saxpy(nx, -one, v(lo+nx+1), 1, w(lo+1), 1) 10 continue c lo = (nx-1)*nx call tv(nx, v(lo+1), w(lo+1)) call saxpy(nx, -one, v(lo-nx+1), 1, w(lo+1), 1) c c Scale the vector w by (1/h^2), where h is the mesh size c n2 = nx*nx h2 = one / real((nx+1)*(nx+1)) call sscal(n2, one/h2, w, 1) return end c c------------------------------------------------------------------- subroutine tv (nx, x, y) c integer nx, j Real & x(nx), y(nx), dd, dl, du c Real & one parameter (one = 1.0E+0 ) c c Compute the matrix vector multiplication y<---T*x c where T is a nx by nx tridiagonal matrix with DD on the c diagonal, DL on the subdiagonal, and DU on the superdiagonal. c c dd = 4.0E+0 dl = -one du = -one c y(1) = dd*x(1) + du*x(2) do 10 j = 2,nx-1 y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1) 10 continue y(nx) = dl*x(nx-1) + dd*x(nx) return end arpack-0.92.1/EXAMPLES/SYM/ssdrv4.f0000644000175000017500000004135610776001577013272 00000000000000 program ssdrv4 c c Program to illustrate the idea of reverse communication c in shift and invert mode for a generalized symmetric eigenvalue c problem. The following program uses the two LAPACK subroutines c sgttrf.f and sgttrs to factor and solve a tridiagonal system of c equations. c c We implement example four of ex-sym.doc in DOCUMENTS directory c c\Example-4 c ... Suppose we want to solve A*x = lambda*M*x in inverse mode, c where A and M are obtained from the finite element discretrization c of the 1-dimensional discrete Laplacian c d^2u / dx^2 c on the interval [0,1] with zero Dirichlet boundary condition c using piecewise linear elements. c c ... OP = (inv[A - sigma*M])*M and B = M. c c ... Use mode 3 of SSAUPD. c c\BeginLib c c\Routines called: c ssaupd ARPACK reverse communication interface routine. c sseupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c sgttrf LAPACK tridiagonal factorization routine. c sgttrs LAPACK tridiagonal solve routine. c saxpy Level 1 BLAS that computes y <- alpha*x+y. c scopy Level 1 BLAS that copies one vector to another. c sscal Level 1 BLAS that scales a vector by a scalar. c snrm2 Level 1 BLAS that computes the norm of a vector. c av Matrix vector multiplication routine that computes A*x. c mv Matrix vector multiplication routine that computes M*x. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: sdrv4.F SID: 2.5 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c---------------------------------------------------------------------- c c %-----------------------------% c | Define leading dimensions | c | for all arrays. | c | MAXN: Maximum dimension | c | of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %-----------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=10, maxncv=25, & ldv=maxn) c c %--------------% c | Local Arrays | c %--------------% c Real & v(ldv,maxncv), workl(maxncv*(maxncv+8)), & workd(3*maxn), d(maxncv,2), resid(maxn), & ad(maxn), adl(maxn), adu(maxn), adu2(maxn) logical select(maxncv) integer iparam(11), ipntr(11), ipiv(maxn) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nev, ncv, lworkl, info, j, ierr, & nconv, maxitr, ishfts, mode logical rvec Real & sigma, r1, r2, tol, h c c %------------% c | Parameters | c %------------% c Real & zero, one, two, four, six parameter (zero = 0.0E+0, one = 1.0E+0, & four = 4.0E+0, six = 6.0E+0, & two = 2.0E+0 ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & snrm2 external saxpy, scopy, sscal, snrm2, sgttrf, sgttrs c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable statements | c %-----------------------% c c %----------------------------------------------------% c | The number N is the dimension of the matrix. A | c | generalized eigenvalue problem is solved (BMAT = | c | 'G'.) NEV is the number of eigenvalues (closest to | c | the shift SIGMA) to be approximated. Since the | c | shift-invert mode is used, WHICH is set to 'LM'. | c | The user can modify NEV, NCV, SIGMA to solve | c | problems of different sizes, and to get different | c | parts of the spectrum. However, The following | c | conditions must be satisfied: | c | N <= MAXN, | c | NEV <= MAXNEV, | c | NEV + 1 <= NCV <= MAXNCV | c %----------------------------------------------------% c n = 100 nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _SDRV4: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _SDRV4: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _SDRV4: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' sigma = zero c c %--------------------------------------------------% c | The work array WORKL is used in SSAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in SSAUPD to start the Arnoldi | c | iteration. | c %--------------------------------------------------% c lworkl = ncv*(ncv+8) tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | This program uses exact shifts with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 3 specified in the | c | documentation of SSAUPD is used (IPARAM(7) = 3). | c | All these options may be changed by the user. | c | For details, see the documentation in SSAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 3 c iparam(1) = ishfts iparam(3) = maxitr iparam(7) = mode c c %-------------------------------------------------------% c | Call LAPACK routine to factor the tridiagonal matrix | c | (A-SIGMA*M). The matrix A is the 1-d discrete | c | Laplacian. The matrix M is the associated mass matrix | c | arising from using piecewise linear finite elements | c | on the interval [0, 1]. | c %-------------------------------------------------------% c h = one / real(n+1) r1 = (four / six) * h r2 = (one / six) * h do 20 j=1,n ad(j) = two/h - sigma * r1 adl(j) = -one/h - sigma * r2 20 continue call scopy (n, adl, 1, adu, 1) call sgttrf (n, adl, ad, adu, adu2, ipiv, ierr) if (ierr .ne. 0) then print *, ' Error with _gttrf in _SDRV4.' go to 9000 end if c c %-------------------------------------------% c | M A I N L O O P (Reverse communication) | c %-------------------------------------------% c 10 continue c c %---------------------------------------------% c | Repeatedly call the routine SSAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call ssaupd ( ido, bmat, n, which, nev, tol, resid, & ncv, v, ldv, iparam, ipntr, workd, workl, & lworkl, info ) c if (ido .eq. -1) then c c %--------------------------------------------% c | Perform y <--- OP*x = inv[A-SIGMA*M]*M*x | c | to force the starting vector into the | c | range of OP. The user should supply | c | his/her own matrix vector multiplication | c | routine and a linear system solver here. | c | The matrix vector multiplication routine | c | takes workd(ipntr(1)) as the input vector. | c | The final result is returned to | c | workd(ipntr(2)). | c %--------------------------------------------% c call mv (n, workd(ipntr(1)), workd(ipntr(2))) c call sgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv, & workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print *, ' ' print *, ' Error with _gttrs in _SDRV4. ' print *, ' ' go to 9000 end if c c %-----------------------------------------% c | L O O P B A C K to call SSAUPD again. | c %-----------------------------------------% c go to 10 c else if (ido .eq. 1) then c c %-----------------------------------------% c | Perform y <-- OP*x = inv[A-sigma*M]*M*x | c | M*x has been saved in workd(ipntr(3)). | c | the user only needs the linear system | c | solver here that takes workd(ipntr(3) | c | as input, and returns the result to | c | workd(ipntr(2)). | c %-----------------------------------------% c call scopy ( n, workd(ipntr(3)), 1, workd(ipntr(2)), 1) call sgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv, & workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print *, ' ' print *, ' Error with _gttrs in _SDRV4.' print *, ' ' go to 9000 end if c c %-----------------------------------------% c | L O O P B A C K to call SSAUPD again. | c %-----------------------------------------% c go to 10 c else if (ido .eq. 2) then c c %-----------------------------------------% c | Perform y <--- M*x | c | Need the matrix vector multiplication | c | routine here that takes workd(ipntr(1)) | c | as the input and returns the result to | c | workd(ipntr(2)). | c %-----------------------------------------% c call mv (n, workd(ipntr(1)), workd(ipntr(2))) c c %-----------------------------------------% c | L O O P B A C K to call SSAUPD again. | c %-----------------------------------------% c go to 10 c end if c c %-----------------------------------------% c | Either we have convergence, or there is | c | an error. | c %-----------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message, check the | c | documentation in SSAUPD. | c %--------------------------% c print *, ' ' print *, ' Error with _saupd, info = ',info print *, ' Check the documentation of _saupd ' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using SSEUPD. | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may also be computed now if | c | desired. (indicated by rvec = .true.) | c %-------------------------------------------% c rvec = .true. c call sseupd ( rvec, 'All', select, d, v, ldv, sigma, & bmat, n, which, nev, tol, resid, ncv, v, ldv, & iparam, ipntr, workd, workl, lworkl, ierr ) c c %----------------------------------------------% c | Eigenvalues are returned in the first column | c | of the two dimensional array D and the | c | corresponding eigenvectors are returned in | c | the first NEV columns of the two dimensional | c | array V if requested. Otherwise, an | c | orthogonal basis for the invariant subspace | c | corresponding to the eigenvalues in D is | c | returned in V. | c %----------------------------------------------% c if ( ierr .ne. 0 ) then c c %------------------------------------% c | Error condition: | c | Check the documentation of SSEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _seupd, info = ', ierr print *, ' Check the documentation of _seupd ' print *, ' ' c else c nconv = iparam(5) do 30 j=1, nconv c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c call av(n, v(1,j), workd) call mv(n, v(1,j), workd(n+1)) call saxpy (n, -d(j,1), workd(n+1), 1, workd, 1) d(j,2) = snrm2(n, workd, 1) d(j,2) = d(j,2) / abs(d(j,1)) c 30 continue c call smout(6, nconv, 2, d, maxncv, -6, & 'Ritz values and relative residuals') c end if c c %------------------------------------------% c | Print additional convergence information | c %------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, ' _SDRV4 ' print *, ' ====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program ssdrv4. | c %---------------------------% c 9000 continue c end c c------------------------------------------------------------------------ c matrix vector subroutine c The matrix used is the 1 dimensional mass matrix c on the interval [0,1]. c subroutine mv (n, v, w) integer n, j Real & v(n),w(n), one, four, six, h parameter (one = 1.0E+0, four = 4.0E+0, & six = 6.0E+0) c w(1) = four*v(1) + v(2) do 100 j = 2,n-1 w(j) = v(j-1) + four*v(j) + v(j+1) 100 continue j = n w(j) = v(j-1) + four*v(j) c c Scale the vector w by h. c h = one / ( six*real(n+1)) call sscal(n, h, w, 1) return end c------------------------------------------------------------------------ c matrix vector subroutine c where the matrix is the finite element discretization of the c 1 dimensional discrete Laplacian on [0,1] with zero Dirichlet c boundary condition using piecewise linear elements. c subroutine av (n, v, w) integer n, j Real & v(n), w(n), two, one, h parameter (one = 1.0E+0, two = 2.0E+0) c w(1) = two*v(1) - v(2) do 100 j = 2,n-1 w(j) = - v(j-1) + two*v(j) - v(j+1) 100 continue j = n w(j) = - v(j-1) + two*v(j) c c Scale the vector w by (1/h) c h = one / real(n+1) call sscal(n, one/h, w, 1) return end arpack-0.92.1/EXAMPLES/SYM/makefile0000644000175000017500000000322010776001577013362 00000000000000# # makefile to run simple examples of the reverse communication # protocol. # # Modify if ARPACK library was built somewhere else. # We assume that the required BLAS and LAPACK routines # are in the version of libarpack.a built. If not, you # will need to modify the link step below and link to them. # #\SCCS Information: @(#) # FILE: makefile SID: 2.1 DATE OF SID: 11/19/95 RELEASE: 2 # include ../../ARmake.inc # # Issue "make sym" to make all 12 symmetric drivers # Issue "make ssdrv" to make 6 single precision symmetric drivers # Issue "make dsdrv" to make 6 double precision symmetric drivers # sym: ssdrv dsdrv # # simple symmetric problem using single precision # ssdrv: ssdrv1 ssdrv2 ssdrv3 ssdrv4 ssdrv5 ssdrv6 ssdrv1: ssdrv1.o $(FC) $(FFLAGS) ssdrv1.o $(ALIBS) -o ssdrv1 # ssdrv2: ssdrv2.o $(FC) $(FFLAGS) ssdrv2.o $(ALIBS) -o ssdrv2 # ssdrv3: ssdrv3.o $(FC) $(FFLAGS) ssdrv3.o $(ALIBS) -o ssdrv3 # ssdrv4: ssdrv4.o $(FC) $(FFLAGS) ssdrv4.o $(ALIBS) -o ssdrv4 # ssdrv5: ssdrv5.o $(FC) $(FFLAGS) ssdrv5.o $(ALIBS) -o ssdrv5 # ssdrv6: ssdrv6.o $(FC) $(FFLAGS) ssdrv6.o $(ALIBS) -o ssdrv6 # #----------------------------------------------------------------------- # simple symmetric problem using double precision # dsdrv: dsdrv1 dsdrv2 dsdrv3 dsdrv4 dsdrv5 dsdrv6 dsdrv1: dsdrv1.o $(FC) $(FFLAGS) dsdrv1.o $(ALIBS) -o dsdrv1 # dsdrv2: dsdrv2.o $(FC) $(FFLAGS) dsdrv2.o $(ALIBS) -o dsdrv2 # dsdrv3: dsdrv3.o $(FC) $(FFLAGS) dsdrv3.o $(ALIBS) -o dsdrv3 # dsdrv4: dsdrv4.o $(FC) $(FFLAGS) dsdrv4.o $(ALIBS) -o dsdrv4 # dsdrv5: dsdrv5.o $(FC) $(FFLAGS) dsdrv5.o $(ALIBS) -o dsdrv5 # dsdrv6: dsdrv6.o $(FC) $(FFLAGS) dsdrv6.o $(ALIBS) -o dsdrv6 arpack-0.92.1/EXAMPLES/SYM/ssdrv2.f0000644000175000017500000003320410776001577013261 00000000000000 program ssdrv2 c c Program to illustrate the idea of reverse communication c in shift and invert mode for a standard symmetric eigenvalue c problem. The following program uses the two LAPACK subroutines c sgttrf.f and sgttrs.f to factor and solve a tridiagonal system of c equations. c c We implement example two of ex-sym.doc in DOCUMENTS directory c c\Example-2 c ... Suppose we want to solve A*x = lambda*x in shift-invert mode, c where A is derived from the central difference discretization c of the 1-dimensional Laplacian on [0,1] with zero Dirichlet c boundary condition. c ... OP = (inv[A - sigma*I]) and B = I. c ... Use mode 3 of SSAUPD. c c\BeginLib c c\Routines called: c ssaupd ARPACK reverse communication interface routine. c sseupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c sgttrf LAPACK tridiagonal factorization routine. c sgttrs LAPACK tridiagonal solve routine. c saxpy saxpy Level 1 BLAS that computes y <- alpha*x+y. c snrm2 Level 1 BLAS that computes the norm of a vector. c av Matrix vector multiplication routine that computes A*x. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: sdrv2.F SID: 2.5 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c---------------------------------------------------------------------- c c %-----------------------------% c | Define leading dimensions | c | for all arrays. | c | MAXN: Maximum dimension | c | of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %-----------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=10, maxncv=25, & ldv=maxn ) c c %--------------% c | Local Arrays | c %--------------% c Real & v(ldv,maxncv), workl(maxncv*(maxncv+8)), & workd(3*maxn), d(maxncv,2), resid(maxn), & ad(maxn), adl(maxn), adu(maxn), adu2(maxn), & ax(maxn) logical select(maxncv) integer iparam(11), ipntr(11), ipiv(maxn) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nev, ncv, lworkl, info, j, ierr, & nconv, maxitr, ishfts, mode logical rvec Real & sigma, tol, h2 c c %------------% c | Parameters | c %------------% c Real & zero, one, two parameter (zero = 0.0E+0, one = 1.0E+0, & two = 2.0E+0) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & snrm2 external saxpy, snrm2, sgttrf, sgttrs c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c %----------------------------------------------------% c | The number N is the dimension of the matrix. A | c | standard eigenvalue problem is solved (BMAT = 'I'. | c | NEV is the number of eigenvalues (closest to | c | SIGMA) to be approximated. Since the shift-invert | c | mode is used, WHICH is set to 'LM'. The user can | c | modify NEV, NCV, SIGMA to solve problems of | c | different sizes, and to get different parts of the | c | spectrum. However, The following conditions must | c | be satisfied: | c | N <= MAXN, | c | NEV <= MAXNEV, | c | NEV + 1 <= NCV <= MAXNCV | c %----------------------------------------------------% c n = 100 nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _SDRV2: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _SDRV2: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _SDRV2: NCV is greater than MAXNCV ' go to 9000 end if c bmat = 'I' which = 'LM' sigma = zero c c %--------------------------------------------------% c | The work array WORKL is used in SSAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in SSAUPD to start the Arnoldi | c | iteration. | c %--------------------------------------------------% c lworkl = ncv*(ncv+8) tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | This program uses exact shifts with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 3 of SSAUPD is used | c | (IPARAM(7) = 3). All these options may be | c | changed by the user. For details, see the | c | documentation in SSAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 3 c iparam(1) = ishfts iparam(3) = maxitr iparam(7) = mode c c %-----------------------------------------------------% c | Call LAPACK routine to factor (A-SIGMA*I), where A | c | is the 1-d Laplacian. | c %-----------------------------------------------------% c h2 = one / real((n+1)*(n+1)) do 20 j=1,n ad(j) = two / h2 - sigma adl(j) = -one / h2 20 continue call scopy (n, adl, 1, adu, 1) call sgttrf (n, adl, ad, adu, adu2, ipiv, ierr) if (ierr .ne. 0) then print *, ' ' print *, ' Error with _gttrf in SDRV2.' print *, ' ' go to 9000 end if c c %-------------------------------------------% c | M A I N L O O P (Reverse communication) | c %-------------------------------------------% c 10 continue c c %---------------------------------------------% c | Repeatedly call the routine SSAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call ssaupd ( ido, bmat, n, which, nev, tol, resid, & ncv, v, ldv, iparam, ipntr, workd, workl, & lworkl, info ) c if (ido .eq. -1 .or. ido .eq. 1) then c c %----------------------------------------% c | Perform y <-- OP*x = inv[A-sigma*I]*x. | c | The user only need the linear system | c | solver here that takes workd(ipntr(1)) | c | as input, and returns the result to | c | workd(ipntr(2)). | c %----------------------------------------% c call scopy (n, workd(ipntr(1)), 1, workd(ipntr(2)), 1) c call sgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv, & workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print *, ' ' print *, ' Error with _gttrs in _SDRV2. ' print *, ' ' go to 9000 end if c c %-----------------------------------------% c | L O O P B A C K to call SSAUPD again. | c %-----------------------------------------% c go to 10 c end if c c %----------------------------------------% c | Either we have convergence or there is | c | an error. | c %----------------------------------------% c if ( info .lt. 0 ) then c c %----------------------------% c | Error message. Check the | c | documentation in SSAUPD | c %----------------------------% c print *, ' ' print *, ' Error with _saupd, info = ',info print *, ' Check documentation of _saupd ' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using SSEUPD. | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may also be computed now if | c | desired. (indicated by rvec = .true.) | c %-------------------------------------------% c rvec = .true. c call sseupd ( rvec, 'All', select, d, v, ldv, sigma, & bmat, n, which, nev, tol, resid, ncv, v, ldv, & iparam, ipntr, workd, workl, lworkl, ierr ) c c %----------------------------------------------% c | Eigenvalues are returned in the first column | c | of the two dimensional array D and the | c | corresponding eigenvectors are returned in | c | the first NEV columns of the two dimensional | c | array V if requested. Otherwise, an | c | orthogonal basis for the invariant subspace | c | corresponding to the eigenvalues in D is | c | returned in V. | c %----------------------------------------------% if ( ierr .ne. 0 ) then c c %------------------------------------% c | Error condition: | c | Check the documentation of SSEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _seupd, info = ', ierr print *, ' Check the documentation of _seupd ' print *, ' ' c else c nconv = iparam(5) do 30 j=1, nconv c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c call av(n, v(1,j), ax) call saxpy(n, -d(j,1), v(1,j), 1, ax, 1) d(j,2) = snrm2(n, ax, 1) d(j,2) = d(j,2) / abs(d(j,1)) c 30 continue c c %-------------------------------% c | Display computed residuals | c %-------------------------------% c call smout(6, nconv, 2, d, maxncv, -6, & 'Ritz values and relative residuals') end if c c %------------------------------------------% c | Print additional convergence information | c %------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, ' _SDRV2 ' print *, ' ====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program ssdrv2. | c %---------------------------% c 9000 continue c end c c------------------------------------------------------------------------ c Matrix vector subroutine c where the matrix is the 1 dimensional discrete Laplacian on c the interval [0,1] with zero Dirichlet boundary condition. c subroutine av (n, v, w) integer n, j Real & v(n), w(n), one, two, h2 parameter (one = 1.0E+0, two = 2.0E+0) c w(1) = two*v(1) - v(2) do 100 j = 2,n-1 w(j) = - v(j-1) + two*v(j) - v(j+1) 100 continue j = n w(j) = - v(j-1) + two*v(j) c c Scale the vector w by (1 / h^2). c h2 = one / real((n+1)*(n+1)) call sscal(n, one/h2, w, 1) return end arpack-0.92.1/EXAMPLES/SYM/README0000644000175000017500000000413510776001577012550 000000000000001. Purpose ------- This directory contains example drivers that call ARPACK subroutines [s,d]saupd.f and [s,d]seupd.f to solve SYMMETRIC eigenvalue problems using regular, inverse, shift-invert or other special modes (such as Cayley, Bucking etc.) These drivers illustrate how to set various ARPACK parameters to solve different problems in different modes. They provide a guideline on how to use ARPACK's reverse communication interface. The user may modify any one of these drivers, and provide his/her own matrix vector multiplication routine to solve the problem of his/her own interest. 2. Naming convention ----------------- The name for each driver has the form 'XsdrvN.f', where X - is 's' (single precision) or 'd' (double precision) N - is a number between 1 and 6. If N = 1, the driver solves a STANDARD eigenvalue problem in REGULAR mode N = 2, the driver solves a STANDARD eigenvalue problem in SHIFT-INVERT mode. N = 3, the driver solves a GENERALIZED eigenvalue problem in INVERSE mode N = 4, the driver solves a GENERALIZED eigenvalue problem in SHIFT-INVERT mode. These are 4 commonly used drivers. For shift-invert (N=2,4) mode the user needs to supply a linear system solver to perform y=inv[A-sigma*B]*x. When N > 4, a special mode is used. If N = 5, the driver solves a GENERALIZED eigenvalue problem in BUCKLING mode. N = 6, the driver solves a GENERALIZED eigenvalue problem in CAYLEY mode. These two drivers require the user to provide linear system solvers also. For more information on Cayley and Buckling mode, see the following reference: R.G. Grimes, J.G. Lewis and H.D. Simon, "A Shifted Block Lanczos Algorithm for Solving Sparse Symmetric Generalized Eigenproblems", SIAM J. Matr. Anal. Apps., January (1993). 3. Usage ----- To run these drivers, you may use the makefile in this directory and issue, for example, "make ssdrv1". Then execute using "ssdrv1". arpack-0.92.1/EXAMPLES/SYM/ssdrv5.f0000644000175000017500000004114010776001577013262 00000000000000 program ssdrv5 c c Program to illustrate the idea of reverse communication c in Buckling mode for a generalized symmetric eigenvalue c problem. The following program uses the two LAPACK subroutines c sgttrf.f and sgttrs.f to factor and solve a tridiagonal system of c equations. c c We implement example five of ex-sym.doc in DOCUMENTS directory c c\Example-5 c ... Suppose we want to solve K*x = lambda*KG*x in Buckling mode c where K and KG are obtained by the finite element of the c 1-dimensional discrete Laplacian c d^2u / dx^2 c on the interval [0,1] with zero Dirichlet boundary condition c using piecewise linear elements. c ... OP = (inv[K - sigma*KG])*K and B = K. c ... Use mode 4 of SSAUPD. c c\BeginLib c c\References: c 1. R.G. Grimes, J.G. Lewis and H.D. Simon, "A Shifted Block Lanczos c Algorithm for Solving Sparse Symmetric Generalized Eigenproblems", c SIAM J. Matr. Anal. Apps., January (1993). c c\Routines called: c ssaupd ARPACK reverse communication interface routine. c sseupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c sgttrf LAPACK tridiagonal factorization routine. c sgttrs LAPACK tridiagonal solve routine. c saxpy Level 1 BLAS that computes y <- alpha*x+y. c scopy Level 1 BLAS that copies one vector to another. c sscal Level 1 BLAS that scales a vector by a scalar. c snrm2 Level 1 BLAS that computes the norm of a vector. c av Matrix vector multiplication routine that computes A*x. c mv Matrix vector multiplication routine that computes M*x. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: sdrv5.F SID: 2.5 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c---------------------------------------------------------------------- c c %-----------------------------% c | Define leading dimensions | c | for all arrays. | c | MAXN: Maximum dimension | c | of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %-----------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=10, maxncv=25, & ldv=maxn) c c %--------------% c | Local Arrays | c %--------------% c Real & v(ldv,maxncv), workl(maxncv*(maxncv+8)), & workd(3*maxn), d(maxncv,2), resid(maxn), & ad(maxn), adl(maxn), adu(maxn), adu2(maxn), & ax(maxn), mx(maxn) logical select(maxncv) integer iparam(11), ipntr(11), ipiv(maxn) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nev, ncv, lworkl, info, j, ierr, & nconv, maxitr, ishfts, mode logical rvec Real & h, sigma, r1, r2, tol c c %------------% c | Parameters | c %------------% c Real & zero, one, two, four, six parameter (zero = 0.0E+0, one = 1.0E+0, & four = 4.0E+0, six = 6.0E+0, & two = 2.0E+0 ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & snrm2 external saxpy, scopy, sscal, snrm2, sgttrf, sgttrs c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable statements | c %-----------------------% c c %--------------------------------------------------% c | The number N is the dimension of the matrix. A | c | generalized eigenvalue problem is solved (BMAT = | c | 'G'.) NEV is the number of eigenvalues to be | c | approximated. Since the buckling mode is used, | c | WHICH is set to 'LM'. The user can modify NEV, | c | NCV, SIGMA to solve problems of different sizes, | c | and to get different parts of the spectrum. | c | However, The following conditions must be | c | satisfied: | c | N <= MAXN, | c | NEV <= MAXNEV, | c | NEV + 1 <= NCV <= MAXNCV | c | | c | The shift SIGMA cannot be zero!!! | c %--------------------------------------------------% c n = 100 nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _SDRV5: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _SDRV5: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _SDRV5: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' sigma = one c c %-----------------------------------------------------% c | The work array WORKL is used in SSAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in SSAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = ncv*(ncv+8) tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | This program uses exact shifts with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 4 specified in the | c | documentation of SSAUPD is used (IPARAM(7) = 4). | c | All these options may be changed by the user. For | c | details, see the documentation in SSAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 4 c iparam(1) = ishfts iparam(3) = maxitr iparam(7) = mode c c %------------------------------------------------------% c | Call LAPACK routine to factor the tridiagonal matrix | c | (K-SIGMA*KG). The matrix A is the 1-d discrete | c | Laplacian on the interval [0,1] with zero Dirichlet | c | boundary condition. The matrix M is the associated | c | mass matrix arising from using piecewise linear | c | finite elements on the interval [0, 1]. | c %------------------------------------------------------% c h = one / real(n+1) r1 = (four / six) * h r2 = (one / six) * h do 20 j=1,n ad(j) = two / h - sigma * r1 adl(j) = -one / h- sigma * r2 20 continue call scopy (n, adl, 1, adu, 1) call sgttrf (n, adl, ad, adu, adu2, ipiv, ierr) if (ierr .ne. 0) then print *, ' ' print *, ' Error with _gttrf in _SDRV5.' print *, ' ' go to 9000 end if c c %-------------------------------------------% c | M A I N L O O P (Reverse communication) | c %-------------------------------------------% c 10 continue c c %---------------------------------------------% c | Repeatedly call the routine SSAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call ssaupd ( ido, bmat, n, which, nev, tol, resid, & ncv, v, ldv, iparam, ipntr, workd, workl, lworkl, & info ) c if (ido .eq. -1) then c c %-------------------------------------------% c | Perform y <--- OP*x = inv[K-SIGMA*KG]*K*x | c | to force starting vector into the range | c | of OP. The user should provide his/her | c | matrix vector multiplication routine and | c | a linear system solver here. The matrix | c | vector multiplication routine (K*x) takes | c | workd(ipntr(1)) as the input vector. The | c | final result is returned to | c | workd(ipntr(2)). | c %-------------------------------------------% c call av (n, workd(ipntr(1)), workd(ipntr(2))) c call sgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv, & workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print *, ' ' print *, ' Error with _gttrs in SDRV5.' print *, ' ' go to 9000 end if c c %-----------------------------------------% c | L O O P B A C K to call SSAUPD again. | c %-----------------------------------------% c go to 10 c else if (ido .eq. 1) then c c %------------------------------------------% c | Perform y <-- OP*x=inv(K-sigma*KG)*K*x. | c | K*x has been saved in workd(ipntr(3)). | c | The user only needs the linear system | c | solver here that takes workd(ipntr(3)) | c | as input, and returns the result to | c | workd(ipntr(2)). | c %------------------------------------------% c call scopy ( n, workd(ipntr(3)), 1, workd(ipntr(2)), 1) call sgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv, & workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print *, ' ' print *, ' Error with _gttrs in _SDRV5.' print *, ' ' go to 9000 end if c c %-----------------------------------------% c | L O O P B A C K to call SSAUPD again. | c %-----------------------------------------% c go to 10 c else if (ido .eq. 2) then c c %---------------------------------------------% c | Perform y <--- K*x | c | Need matrix vector multiplication routine | c | here that takes workd(ipntr(1)) as input | c | and returns the result to workd(ipntr(2)). | c %---------------------------------------------% c call av (n, workd(ipntr(1)), workd(ipntr(2))) c c c %-----------------------------------------% c | L O O P B A C K to call SSAUPD again. | c %-----------------------------------------% c go to 10 c end if c c %-----------------------------------------% c | Either we have convergence, or there is | c | an error. | c %-----------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message, check the | c | documentation in SSAUPD. | c %--------------------------% c print *, ' ' print *, ' Error with _saupd, info = ',info print *, ' Check the documentation of _saupd ' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using SSEUPD. | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may also be computed now if | c | desired. (indicated by rvec = .true.) | c %-------------------------------------------% c rvec = .true. c call sseupd ( rvec, 'All', select, d, v, ldv, sigma, & bmat, n, which, nev, tol, resid, ncv, v, ldv, & iparam, ipntr, workd, workl, lworkl, ierr ) c if (ierr .ne. 0) then c c %------------------------------------% c | Error condition: | c | Check the documentation of SSEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _seupd, info = ',ierr print *, ' Check the documentation of _seupd ' print *, ' ' c else c nconv = iparam(5) do 30 j=1, nconv c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c call av(n, v(1,j), ax) call mv(n, v(1,j), mx) call saxpy (n, -d(j,1), mx, 1, ax, 1) d(j,2) = snrm2(n, ax, 1) d(j,2) = d(j,2) / abs(d(j,1)) c 30 continue c call smout(6, nconv, 2, d, maxncv, -6, & 'Ritz values and relative residuals') c end if c c c %------------------------------------------% c | Print additional convergence information | c %------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, ' _SDRV5 ' print *, ' ====== ' print *, ' ' print *, ' Size of the matrix is', n print *, ' The number of Ritz values requested is', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program ssdrv5. | c %---------------------------% c 9000 continue c end c c------------------------------------------------------------------------ c Matrix vector subroutine c where the matrix is the 1-dimensional mass matrix c arising from using piecewise linear finite elements on the c interval [0,1]. c subroutine mv (n, v, w) integer n, j Real & v(n),w(n), one, four, six, h parameter (one = 1.0E+0, four = 4.0E+0, & six = 6.0E+0) c w(1) = four*v(1) + v(2) do 100 j = 2,n-1 w(j) = v(j-1) + four*v(j) + v(j+1) 100 continue j = n w(j) = v(j-1) + four*v(j) c c Scale the vector w by h. c h = one / (six*real(n+1)) call sscal(n, h, w, 1) return end c------------------------------------------------------------------------ c Matrix vector subroutine c where the matrix is the stiffness matrix obtained from the c finite element discretization of the 1-dimensional discrete Laplacian c on the interval [0,1] with zero Dirichlet boundary condition c using piecewise linear elements. c subroutine av (n, v, w) integer n, j Real & v(n), w(n), one, two, h parameter (one = 1.0E+0, two = 2.0E+0) c w(1) = two*v(1) - v(2) do 100 j = 2,n-1 w(j) = - v(j-1) + two*v(j) - v(j+1) 100 continue j = n w(j) = - v(j-1) + two*v(j) c c Scale the vector w by (1/h) c h = one / (n+1) call sscal(n, one/h, w, 1) return end arpack-0.92.1/EXAMPLES/SYM/dsdrv6.f0000644000175000017500000004305710776001577013255 00000000000000 program dsdrv6 c c Program to illustrate the idea of reverse communication c in Cayley mode for a generalized symmetric eigenvalue c problem. The following program uses the two LAPACK subroutines c dgttrf.f and dgttrs.f to factor and solve a tridiagonal system of c equations. c c We implement example six of ex-sym.doc in DOCUMENTS directory c c\Example-6 c ... Suppose we want to solve A*x = lambda*M*x in inverse mode, c where A and M are obtained by the finite element of the c 1-dimensional discrete Laplacian c d^2u / dx^2 c on the interval [0,1] with zero Dirichlet boundary condition c using piecewise linear elements. c c ... OP = (inv[A-sigma*M])*(A+sigma*M) and B = M. c c ... Use mode 5 of DSAUPD. c c\BeginLib c c\References: c 1. R.G. Grimes, J.G. Lewis and H.D. Simon, "A Shifted Block Lanczos c Algorithm for Solving Sparse Symmetric Generalized Eigenproblems", c SIAM J. Matr. Anal. Apps., January (1993). c c\Routines called: c dsaupd ARPACK reverse communication interface routine. c dseupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c dgttrf LAPACK tridiagonal factorization routine. c dgttrs LAPACK tridiagonal solve routine. c daxpy Level 1 BLAS that computes y <- alpha*x+y. c dcopy Level 1 BLAS that copies one vector to another. c dscal Level 1 BLAS that scales a vector by a scalar. c dnrm2 Level 1 BLAS that computes the norm of a vector. c av Matrix vector multiplication routine that computes A*x. c mv Matrix vector multiplication routine that computes M*x. c c\Author c Danny Sorensen c Richard Lehoucq c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: sdrv6.F SID: 2.5 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c------------------------------------------------------------------------ c c %-----------------------------% c | Define leading dimensions | c | for all arrays. | c | MAXN: Maximum dimension | c | of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %-----------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=10, maxncv=25, & ldv=maxn) c c %--------------% c | Local Arrays | c %--------------% c Double precision & v(ldv,maxncv), workl(maxncv*(maxncv+8)), & workd(3*maxn), d(maxncv,2), resid(maxn), & ad(maxn), adl(maxn), adu(maxn), adu2(maxn), & temp(maxn), ax(maxn), mx(maxn) logical select(maxncv) integer iparam(11), ipntr(11), ipiv(maxn) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nev, ncv, lworkl, info, j, ierr, & nconv, maxitr, ishfts, mode logical rvec Double precision & sigma, r1, r2, tol, h c c %------------% c | Parameters | c %------------% c Double precision & zero, one, two, four, six parameter (zero = 0.0D+0, one = 1.0D+0, & four = 4.0D+0, six = 6.0D+0, & two = 2.0D+0 ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & dnrm2 external daxpy, dcopy, dscal, dnrm2, dgttrf, dgttrs c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable statements | c %-----------------------% c c %--------------------------------------------------% c | The number N is the dimension of the matrix. A | c | generalized eigenvalue problem is solved (BMAT = | c | 'G'.) NEV is the number of eigenvalues to be | c | approximated. Since the Cayley mode is used, | c | WHICH is set to 'LM'. The user can modify NEV, | c | NCV, SIGMA to solve problems of different sizes, | c | and to get different parts of the spectrum. | c | However, The following conditions must be | c | satisfied: | c | N <= MAXN, | c | NEV <= MAXNEV, | c | NEV + 1 <= NCV <= MAXNCV | c %--------------------------------------------------% c n = 100 nev = 4 ncv = 20 if ( n .gt. maxn ) then print *, ' ERROR with _SDRV6: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _SDRV6: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _SDRV6: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' sigma = 1.5D+2 c c %--------------------------------------------------% c | The work array WORKL is used in DSAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in DSAUPD to start the Arnoldi | c | iteration. | c %--------------------------------------------------% c lworkl = ncv*(ncv+8) tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | This program uses exact shifts with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 5 specified in the | c | documentation of DSAUPD is used (IPARAM(7) = 5). | c | All these options may be changed by the user. For | c | details, see the documentation in DSAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 5 c iparam(1) = ishfts iparam(3) = maxitr iparam(7) = mode c c %------------------------------------------------------% c | Call LAPACK routine to factor (A-sigma*M). The | c | stiffness matrix A is the 1-d discrete Laplacian. | c | The mass matrix M is the associated mass matrix | c | arising from using piecewise linear finite elements | c | on the interval [0, 1]. | c %------------------------------------------------------% c h = one / dble(n+1) r1 = (four / six) * h r2 = (one / six) * h do 20 j=1,n ad(j) = two / h - sigma * r1 adl(j) = -one / h - sigma * r2 20 continue call dcopy (n, adl, 1, adu, 1) call dgttrf (n, adl, ad, adu, adu2, ipiv, ierr) if (ierr .ne. 0) then print *, ' ' print *, ' Error with _gttrf in _SDRV6.' print *, ' ' go to 9000 end if c c %-------------------------------------------% c | M A I N L O O P (Reverse communication) | c %-------------------------------------------% c 10 continue c c %---------------------------------------------% c | Repeatedly call the routine DSAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call dsaupd ( ido, bmat, n, which, nev, tol, resid, ncv, & v, ldv, iparam, ipntr, workd, workl, lworkl, & info ) c if (ido .eq. -1) then c c %-------------------------------------------------------% c | Perform y <--- OP*x = (inv[A-SIGMA*M])*(A+SIGMA*M)*x | c | to force starting vector into the range of OP. The | c | user should provide his/her matrix vector (A*x, M*x) | c | multiplication routines and a linear system solver | c | here. The matrix vector multiplication routine takes | c | workd(ipntr(1)) as the input vector. The final | c | result is returned to workd(ipntr(2)). | c %-------------------------------------------------------% c call av (n, workd(ipntr(1)), workd(ipntr(2))) call mv (n, workd(ipntr(1)), temp) call daxpy(n, sigma, temp, 1, workd(ipntr(2)), 1) c call dgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv, & workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print *, ' ' print *, ' Error with _gttrs in _SDRV6.' print *, ' ' go to 9000 end if c c %-----------------------------------------% c | L O O P B A C K to call DSAUPD again. | c %-----------------------------------------% c go to 10 c else if (ido .eq. 1) then c c %----------------------------------------------------% c | Perform y <-- OP*x = inv[A-SIGMA*M]*(A+SIGMA*M)*x. | c | M*x has been saved in workd(ipntr(3)). The user | c | need the matrix vector multiplication (A*x) | c | routine and a linear system solver here. The | c | matrix vector multiplication routine takes | c | workd(ipntr(1)) as the input, and the result is | c | combined with workd(ipntr(3)) to form the input | c | for the linear system solver. The final result is | c | returned to workd(ipntr(2)). | c %----------------------------------------------------% c call av (n, workd(ipntr(1)), workd(ipntr(2))) call daxpy(n, sigma, workd(ipntr(3)), 1, workd(ipntr(2)), 1) call dgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv, & workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print *, ' ' print *, ' Error with _gttrs in _SDRV6. ' print *, ' ' go to 9000 end if c c %-----------------------------------------% c | L O O P B A C K to call DSAUPD again. | c %-----------------------------------------% c go to 10 c else if (ido .eq. 2) then c c %--------------------------------------------% c | Perform y <--- M*x. | c | Need matrix vector multiplication routine | c | here that takes workd(ipntr(1)) as input | c | and returns the result to workd(ipntr(2)). | c %--------------------------------------------% c call mv (n, workd(ipntr(1)), workd(ipntr(2))) c c %-----------------------------------------% c | L O O P B A C K to call DSAUPD again. | c %-----------------------------------------% c go to 10 c end if c c %-----------------------------------------% c | Either we have convergence, or there is | c | an error. | c %-----------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message, check the | c | documentation in DSAUPD | c %--------------------------% c print *, ' ' print *, ' Error with _saupd, info = ',info print *, ' Check the documentation of _saupd. ' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using DSEUPD. | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may also be computed now if | c | desired. (indicated by rvec = .true.) | c %-------------------------------------------% c rvec = .true. c call dseupd ( rvec, 'All', select, d, v, ldv, sigma, & bmat, n, which, nev, tol, resid, ncv, v, ldv, & iparam, ipntr, workd, workl, lworkl, ierr ) c c %----------------------------------------------% c | Eigenvalues are returned in the first column | c | of the two dimensional array D and the | c | corresponding eigenvectors are returned in | c | the first NEV columns of the two dimensional | c | array V if requested. Otherwise, an | c | orthogonal basis for the invariant subspace | c | corresponding to the eigenvalues in D is | c | returned in V. | c %----------------------------------------------% c if ( ierr .ne. 0 ) then c c %------------------------------------% c | Error condition: | c | Check the documentation of DSEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _seupd, info = ', ierr print *, ' Check the documentation of _seupd ' print *, ' ' c else c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c nconv = iparam(5) do 30 j=1, nconv call av(n, v(1,j), ax) call mv(n, v(1,j), mx) call daxpy (n, -d(j,1), mx, 1, ax, 1) d(j,2) = dnrm2(n, ax, 1) d(j,2) = d(j,2) / abs(d(j,1)) 30 continue c call dmout(6, nconv, 2, d, maxncv, -6, & 'Ritz values and relative residuals') c end if c c %------------------------------------------% c | Print additional convergence information | c %------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, ' _SDRV6 ' print *, ' ====== ' print *, ' ' print *, ' Size of the matrix is', n print *, ' The number of Ritz values requested is', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program dsdrv6. | c %---------------------------% c 9000 continue c end c c------------------------------------------------------------------------ c Matrix vector subroutine c where the matrix used is the 1 dimensional mass matrix c arising from using the piecewise linear finite element c on the interval [0,1]. c subroutine mv (n, v, w) integer n, j Double precision & v(n), w(n), one, four, six, h parameter (one = 1.0D+0, four = 4.0D+0, & six = 6.0D+0) c w(1) = four*v(1) + v(2) do 100 j = 2,n-1 w(j) = v(j-1) + four*v(j) + v(j+1) 100 continue j = n w(j) = v(j-1) + four*v(j) c c Scale the vector w by h. c h = one / (six*dble(n+1)) call dscal(n, h, w, 1) return end c c------------------------------------------------------------------------ c Matrix vector subroutine c where the matrix is the stiffness matrix obtained from the c finite element discretization of the 1-dimensional discrete Laplacian c on the interval [0,1] with zero Dirichlet boundary condition c using piecewise linear elements. c subroutine av (n, v, w) integer n, j Double precision & v(n), w(n), one, two, h parameter (one = 1.0D+0, two = 2.0D+0) c w(1) = two*v(1) - v(2) do 100 j = 2,n-1 w(j) = - v(j-1) + two*v(j) - v(j+1) 100 continue j = n w(j) = - v(j-1) + two*v(j) c c Scale the vector w by (1/h). c h = one / dble(n+1) call dscal(n, one/h, w, 1) return end arpack-0.92.1/EXAMPLES/SYM/dsdrv2.f0000644000175000017500000003330010776001577013237 00000000000000 program dsdrv2 c c Program to illustrate the idea of reverse communication c in shift and invert mode for a standard symmetric eigenvalue c problem. The following program uses the two LAPACK subroutines c dgttrf.f and dgttrs.f to factor and solve a tridiagonal system of c equations. c c We implement example two of ex-sym.doc in DOCUMENTS directory c c\Example-2 c ... Suppose we want to solve A*x = lambda*x in shift-invert mode, c where A is derived from the central difference discretization c of the 1-dimensional Laplacian on [0,1] with zero Dirichlet c boundary condition. c ... OP = (inv[A - sigma*I]) and B = I. c ... Use mode 3 of DSAUPD. c c\BeginLib c c\Routines called: c dsaupd ARPACK reverse communication interface routine. c dseupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c dgttrf LAPACK tridiagonal factorization routine. c dgttrs LAPACK tridiagonal solve routine. c daxpy daxpy Level 1 BLAS that computes y <- alpha*x+y. c dnrm2 Level 1 BLAS that computes the norm of a vector. c av Matrix vector multiplication routine that computes A*x. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: sdrv2.F SID: 2.5 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c---------------------------------------------------------------------- c c %-----------------------------% c | Define leading dimensions | c | for all arrays. | c | MAXN: Maximum dimension | c | of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %-----------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=10, maxncv=25, & ldv=maxn ) c c %--------------% c | Local Arrays | c %--------------% c Double precision & v(ldv,maxncv), workl(maxncv*(maxncv+8)), & workd(3*maxn), d(maxncv,2), resid(maxn), & ad(maxn), adl(maxn), adu(maxn), adu2(maxn), & ax(maxn) logical select(maxncv) integer iparam(11), ipntr(11), ipiv(maxn) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nev, ncv, lworkl, info, j, ierr, & nconv, maxitr, ishfts, mode logical rvec Double precision & sigma, tol, h2 c c %------------% c | Parameters | c %------------% c Double precision & zero, one, two parameter (zero = 0.0D+0, one = 1.0D+0, & two = 2.0D+0) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & dnrm2 external daxpy, dnrm2, dgttrf, dgttrs c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c %----------------------------------------------------% c | The number N is the dimension of the matrix. A | c | standard eigenvalue problem is solved (BMAT = 'I'. | c | NEV is the number of eigenvalues (closest to | c | SIGMA) to be approximated. Since the shift-invert | c | mode is used, WHICH is set to 'LM'. The user can | c | modify NEV, NCV, SIGMA to solve problems of | c | different sizes, and to get different parts of the | c | spectrum. However, The following conditions must | c | be satisfied: | c | N <= MAXN, | c | NEV <= MAXNEV, | c | NEV + 1 <= NCV <= MAXNCV | c %----------------------------------------------------% c n = 100 nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _SDRV2: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _SDRV2: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _SDRV2: NCV is greater than MAXNCV ' go to 9000 end if c bmat = 'I' which = 'LM' sigma = zero c c %--------------------------------------------------% c | The work array WORKL is used in DSAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in DSAUPD to start the Arnoldi | c | iteration. | c %--------------------------------------------------% c lworkl = ncv*(ncv+8) tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | This program uses exact shifts with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 3 of DSAUPD is used | c | (IPARAM(7) = 3). All these options may be | c | changed by the user. For details, see the | c | documentation in DSAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 3 c iparam(1) = ishfts iparam(3) = maxitr iparam(7) = mode c c %-----------------------------------------------------% c | Call LAPACK routine to factor (A-SIGMA*I), where A | c | is the 1-d Laplacian. | c %-----------------------------------------------------% c h2 = one / dble((n+1)*(n+1)) do 20 j=1,n ad(j) = two / h2 - sigma adl(j) = -one / h2 20 continue call dcopy (n, adl, 1, adu, 1) call dgttrf (n, adl, ad, adu, adu2, ipiv, ierr) if (ierr .ne. 0) then print *, ' ' print *, ' Error with _gttrf in SDRV2.' print *, ' ' go to 9000 end if c c %-------------------------------------------% c | M A I N L O O P (Reverse communication) | c %-------------------------------------------% c 10 continue c c %---------------------------------------------% c | Repeatedly call the routine DSAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call dsaupd ( ido, bmat, n, which, nev, tol, resid, & ncv, v, ldv, iparam, ipntr, workd, workl, & lworkl, info ) c if (ido .eq. -1 .or. ido .eq. 1) then c c %----------------------------------------% c | Perform y <-- OP*x = inv[A-sigma*I]*x. | c | The user only need the linear system | c | solver here that takes workd(ipntr(1)) | c | as input, and returns the result to | c | workd(ipntr(2)). | c %----------------------------------------% c call dcopy (n, workd(ipntr(1)), 1, workd(ipntr(2)), 1) c call dgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv, & workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print *, ' ' print *, ' Error with _gttrs in _SDRV2. ' print *, ' ' go to 9000 end if c c %-----------------------------------------% c | L O O P B A C K to call DSAUPD again. | c %-----------------------------------------% c go to 10 c end if c c %----------------------------------------% c | Either we have convergence or there is | c | an error. | c %----------------------------------------% c if ( info .lt. 0 ) then c c %----------------------------% c | Error message. Check the | c | documentation in DSAUPD | c %----------------------------% c print *, ' ' print *, ' Error with _saupd, info = ',info print *, ' Check documentation of _saupd ' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using DSEUPD. | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may also be computed now if | c | desired. (indicated by rvec = .true.) | c %-------------------------------------------% c rvec = .true. c call dseupd ( rvec, 'All', select, d, v, ldv, sigma, & bmat, n, which, nev, tol, resid, ncv, v, ldv, & iparam, ipntr, workd, workl, lworkl, ierr ) c c %----------------------------------------------% c | Eigenvalues are returned in the first column | c | of the two dimensional array D and the | c | corresponding eigenvectors are returned in | c | the first NEV columns of the two dimensional | c | array V if requested. Otherwise, an | c | orthogonal basis for the invariant subspace | c | corresponding to the eigenvalues in D is | c | returned in V. | c %----------------------------------------------% if ( ierr .ne. 0 ) then c c %------------------------------------% c | Error condition: | c | Check the documentation of DSEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _seupd, info = ', ierr print *, ' Check the documentation of _seupd ' print *, ' ' c else c nconv = iparam(5) do 30 j=1, nconv c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c call av(n, v(1,j), ax) call daxpy(n, -d(j,1), v(1,j), 1, ax, 1) d(j,2) = dnrm2(n, ax, 1) d(j,2) = d(j,2) / abs(d(j,1)) c 30 continue c c %-------------------------------% c | Display computed residuals | c %-------------------------------% c call dmout(6, nconv, 2, d, maxncv, -6, & 'Ritz values and relative residuals') end if c c %------------------------------------------% c | Print additional convergence information | c %------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, ' _SDRV2 ' print *, ' ====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program dsdrv2. | c %---------------------------% c 9000 continue c end c c------------------------------------------------------------------------ c Matrix vector subroutine c where the matrix is the 1 dimensional discrete Laplacian on c the interval [0,1] with zero Dirichlet boundary condition. c subroutine av (n, v, w) integer n, j Double precision & v(n), w(n), one, two, h2 parameter (one = 1.0D+0, two = 2.0D+0) c w(1) = two*v(1) - v(2) do 100 j = 2,n-1 w(j) = - v(j-1) + two*v(j) - v(j+1) 100 continue j = n w(j) = - v(j-1) + two*v(j) c c Scale the vector w by (1 / h^2). c h2 = one / dble((n+1)*(n+1)) call dscal(n, one/h2, w, 1) return end arpack-0.92.1/EXAMPLES/SYM/ssdrv3.f0000644000175000017500000003734610776001577013275 00000000000000 program ssdrv3 c c Program to illustrate the idea of reverse communication in c inverse mode for a generalized symmetric eigenvalue problem. c The following program uses the two LAPACK subroutines sgttrf.f c and sgttrs.f to factor and solve a tridiagonal system of equations. c c We implement example three of ex-sym.doc in DOCUMENTS directory c c\Example-3 c ... Suppose we want to solve A*x = lambda*M*x in inverse mode, c where A and M are obtained by the finite element of the c 1-dimensional discrete Laplacian c d^2u / dx^2 c on the interval [0,1] with zero Dirichlet boundary condition c using piecewise linear elements. c c ... OP = inv[M]*A and B = M. c c ... Use mode 2 of SSAUPD. c c\BeginLib c c\Routines called: c ssaupd ARPACK reverse communication interface routine. c sseupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c sgttrf LAPACK tridiagonal factorization routine. c sgttrs LAPACK tridiagonal solve routine. c saxpy Level 1 BLAS that computes y <- alpha*x+y. c sscal Level 1 BLAS that scales a vector by a scalar. c scopy Level 1 BLAS that copies one vector to another. c snrm2 Level 1 BLAS that computes the norm of a vector. c av Matrix vector multiplication routine that computes A*x. c mv Matrix vector multiplication routine that computes M*x. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: sdrv3.F SID: 2.5 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c-------------------------------------------------------------------------- c c %-----------------------------% c | Define leading dimensions | c | for all arrays. | c | MAXN: Maximum dimension | c | of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %-----------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=10, maxncv=25, & ldv=maxn ) c c %--------------% c | Local Arrays | c %--------------% c Real & v(ldv,maxncv), workl(maxncv*(maxncv+8)), & workd(3*maxn), d(maxncv,2), resid(maxn), & ad(maxn), adl(maxn), adu(maxn), adu2(maxn), & ax(maxn), mx(maxn) logical select(maxncv) integer iparam(11), ipntr(11), ipiv(maxn) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nev, ncv, lworkl, info, j, ierr, & nconv, maxitr, ishfts, mode logical rvec Real & sigma, r1, r2, tol, h c c %------------% c | Parameters | c %------------% c Real & zero, one, four, six parameter ( zero = 0.0E+0 , one = 1.0E+0 , & four = 4.0E+0 , six = 6.0E+0 ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & snrm2 external saxpy, scopy, sscal, snrm2, sgttrf, sgttrs c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable statements | c %-----------------------% c c %----------------------------------------------------% c | The number N is the dimension of the matrix. A | c | generalized eigenvalue problem is solved (BMAT = | c | 'G'.) NEV is the number of eigenvalues to be | c | approximated. The user can modify NEV, NCV, WHICH | c | to solve problems of different sizes, and to get | c | different parts of the spectrum. However, The | c | following conditions must be satisfied: | c | N <= MAXN, | c | NEV <= MAXNEV, | c | NEV + 1 <= NCV <= MAXNCV | c %----------------------------------------------------% c n = 100 nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _SDRV3: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _SDRV3: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _SDRV3: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' c c %--------------------------------------------------% c | The work array WORKL is used in SSAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in SSAUPD to start the Arnoldi | c | iteration. | c %--------------------------------------------------% c lworkl = ncv*(ncv+8) tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | This program uses exact shifts with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 2 of SSAUPD is used | c | (IPARAM(7) = 2). All these options may be | c | changed by the user. For details, see the | c | documentation in SSAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 2 c iparam(1) = ishfts iparam(3) = maxitr iparam(7) = mode c c %------------------------------------------------% c | Call LAPACK routine to factor the mass matrix. | c | The mass matrix is the tridiagonal matrix | c | arising from using piecewise linear finite | c | elements on the interval [0, 1]. | c %------------------------------------------------% c h = one / real (n+1) c r1 = (four / six) * h r2 = (one / six) * h do 20 j=1,n ad(j) = r1 adl(j) = r2 20 continue call scopy (n, adl, 1, adu, 1) call sgttrf (n, adl, ad, adu, adu2, ipiv, ierr) if (ierr .ne. 0) then print *, ' ' print *, ' Error with _gttrf in _SDRV3. ' print *, ' ' go to 9000 end if c c %-------------------------------------------% c | M A I N L O O P (Reverse communication) | c %-------------------------------------------% c 10 continue c c %---------------------------------------------% c | Repeatedly call the routine SSAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call ssaupd ( ido, bmat, n, which, nev, tol, resid, & ncv, v, ldv, iparam, ipntr, workd, workl, & lworkl, info ) c if (ido .eq. -1 .or. ido .eq. 1) then c c %--------------------------------------% c | Perform y <--- OP*x = inv[M]*A*x. | c | The user should supply his/her own | c | matrix vector multiplication (A*x) | c | routine and a linear system solver | c | here. The matrix vector | c | multiplication routine takes | c | workd(ipntr(1)) as the input vector. | c | The final result is returned to | c | workd(ipntr(2)). The result of A*x | c | overwrites workd(ipntr(1)). | c %--------------------------------------% c call av (n, workd(ipntr(1)), workd(ipntr(2))) call scopy(n, workd(ipntr(2)), 1, workd(ipntr(1)), 1) call sgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv, & workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print *, ' ' print *, ' Error with _gttrs in _SDRV3.' print *, ' ' go to 9000 end if c c %-----------------------------------------% c | L O O P B A C K to call SSAUPD again. | c %-----------------------------------------% c go to 10 c else if (ido .eq. 2) then c c %-----------------------------------------% c | Perform y <--- M*x. | c | Need the matrix vector multiplication | c | routine here that takes workd(ipntr(1)) | c | as the input and returns the result to | c | workd(ipntr(2)). | c %-----------------------------------------% c call mv (n, workd(ipntr(1)), workd(ipntr(2))) c c %-----------------------------------------% c | L O O P B A C K to call SSAUPD again. | c %-----------------------------------------% c go to 10 c end if c c c c %-----------------------------------------% c | Either we have convergence, or there is | c | an error. | c %-----------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message, check the | c | documentation in SSAUPD | c %--------------------------% c print *, ' ' print *, ' Error with _saupd, info = ',info print *, ' Check the documentation of _saupd ' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using SSEUPD. | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may also be computed now if | c | desired. (indicated by rvec = .true.) | c %-------------------------------------------% c rvec = .true. c call sseupd ( rvec, 'All', select, d, v, ldv, sigma, & bmat, n, which, nev, tol, resid, ncv, v, ldv, & iparam, ipntr, workd, workl, lworkl, ierr ) c c %----------------------------------------------% c | Eigenvalues are returned in the first column | c | of the two dimensional array D and the | c | corresponding eigenvectors are returned in | c | the first NEV columns of the two dimensional | c | array V if requested. Otherwise, an | c | orthogonal basis for the invariant subspace | c | corresponding to the eigenvalues in D is | c | returned in V. | c %----------------------------------------------% c if (ierr .ne. 0) then c c %------------------------------------% c | Error condition: | c | Check the documentation of SSEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _seupd, info = ', ierr print *, ' Check the documentation of _seupd' print *, ' ' c else c nconv = iparam(5) do 30 j=1, nconv c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*M*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c call av(n, v(1,j), ax) call mv(n, v(1,j), mx) call saxpy(n, -d(j,1), mx, 1, ax, 1) d(j,2) = snrm2(n, ax, 1) d(j,2) = d(j,2) / abs(d(j,1)) c 30 continue c c %-----------------------------% c | Display computed residuals. | c %-----------------------------% c call smout(6, nconv, 2, d, maxncv, -6, & 'Ritz values and relative residuals') end if c c %------------------------------------------% c | Print additional convergence information | c %------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, ' _SDRV3 ' print *, ' ====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program ssdrv3. | c %---------------------------% c 9000 continue c end c c------------------------------------------------------------------------ c Matrix vector subroutine c where the matrix is the 1 dimensional mass matrix c on the interval [0,1]. c subroutine mv (n, v, w) integer n, j Real & v(n),w(n), one, four, six, h parameter (one = 1.0E+0 , four = 4.0E+0 , & six = 6.0E+0 ) c w(1) = four*v(1) + v(2) do 100 j = 2,n-1 w(j) = v(j-1) + four*v(j) + v(j+1) 100 continue j = n w(j) = v(j-1) + four*v(j) c c Scale the vector w by h. c h = one / (real (n+1)*six) call sscal(n, h, w, 1) return end c c-------------------------------------------------------------------- c matrix vector subroutine c c The matrix used is the stiffness matrix obtained from the finite c element discretization of the 1-dimensional discrete Laplacian c on the interval [0,1] with zero Dirichlet boundary condition using c piecewise linear elements. c subroutine av (n, v, w) integer n, j Real & v(n),w(n), two, one, h parameter ( one = 1.0E+0 , two = 2.0E+0 ) c w(1) = two*v(1) - v(2) do 100 j = 2,n-1 w(j) = - v(j-1) + two*v(j) - v(j+1) 100 continue j = n w(j) = - v(j-1) + two*v(j) c c Scale the vector w by (1 / h). c h = one / real (n+1) call sscal(n, one/h, w, 1) return end arpack-0.92.1/EXAMPLES/SYM/dsdrv4.f0000644000175000017500000004146610776001577013255 00000000000000 program dsdrv4 c c Program to illustrate the idea of reverse communication c in shift and invert mode for a generalized symmetric eigenvalue c problem. The following program uses the two LAPACK subroutines c dgttrf.f and dgttrs to factor and solve a tridiagonal system of c equations. c c We implement example four of ex-sym.doc in DOCUMENTS directory c c\Example-4 c ... Suppose we want to solve A*x = lambda*M*x in inverse mode, c where A and M are obtained from the finite element discretrization c of the 1-dimensional discrete Laplacian c d^2u / dx^2 c on the interval [0,1] with zero Dirichlet boundary condition c using piecewise linear elements. c c ... OP = (inv[A - sigma*M])*M and B = M. c c ... Use mode 3 of DSAUPD. c c\BeginLib c c\Routines called: c dsaupd ARPACK reverse communication interface routine. c dseupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c dgttrf LAPACK tridiagonal factorization routine. c dgttrs LAPACK tridiagonal solve routine. c daxpy Level 1 BLAS that computes y <- alpha*x+y. c dcopy Level 1 BLAS that copies one vector to another. c dscal Level 1 BLAS that scales a vector by a scalar. c dnrm2 Level 1 BLAS that computes the norm of a vector. c av Matrix vector multiplication routine that computes A*x. c mv Matrix vector multiplication routine that computes M*x. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: sdrv4.F SID: 2.5 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c---------------------------------------------------------------------- c c %-----------------------------% c | Define leading dimensions | c | for all arrays. | c | MAXN: Maximum dimension | c | of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %-----------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=10, maxncv=25, & ldv=maxn) c c %--------------% c | Local Arrays | c %--------------% c Double precision & v(ldv,maxncv), workl(maxncv*(maxncv+8)), & workd(3*maxn), d(maxncv,2), resid(maxn), & ad(maxn), adl(maxn), adu(maxn), adu2(maxn) logical select(maxncv) integer iparam(11), ipntr(11), ipiv(maxn) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nev, ncv, lworkl, info, j, ierr, & nconv, maxitr, ishfts, mode logical rvec Double precision & sigma, r1, r2, tol, h c c %------------% c | Parameters | c %------------% c Double precision & zero, one, two, four, six parameter (zero = 0.0D+0, one = 1.0D+0, & four = 4.0D+0, six = 6.0D+0, & two = 2.0D+0 ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & dnrm2 external daxpy, dcopy, dscal, dnrm2, dgttrf, dgttrs c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable statements | c %-----------------------% c c %----------------------------------------------------% c | The number N is the dimension of the matrix. A | c | generalized eigenvalue problem is solved (BMAT = | c | 'G'.) NEV is the number of eigenvalues (closest to | c | the shift SIGMA) to be approximated. Since the | c | shift-invert mode is used, WHICH is set to 'LM'. | c | The user can modify NEV, NCV, SIGMA to solve | c | problems of different sizes, and to get different | c | parts of the spectrum. However, The following | c | conditions must be satisfied: | c | N <= MAXN, | c | NEV <= MAXNEV, | c | NEV + 1 <= NCV <= MAXNCV | c %----------------------------------------------------% c n = 100 nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _SDRV4: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _SDRV4: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _SDRV4: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' sigma = zero c c %--------------------------------------------------% c | The work array WORKL is used in DSAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in DSAUPD to start the Arnoldi | c | iteration. | c %--------------------------------------------------% c lworkl = ncv*(ncv+8) tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | This program uses exact shifts with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 3 specified in the | c | documentation of DSAUPD is used (IPARAM(7) = 3). | c | All these options may be changed by the user. | c | For details, see the documentation in DSAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 3 c iparam(1) = ishfts iparam(3) = maxitr iparam(7) = mode c c %-------------------------------------------------------% c | Call LAPACK routine to factor the tridiagonal matrix | c | (A-SIGMA*M). The matrix A is the 1-d discrete | c | Laplacian. The matrix M is the associated mass matrix | c | arising from using piecewise linear finite elements | c | on the interval [0, 1]. | c %-------------------------------------------------------% c h = one / dble(n+1) r1 = (four / six) * h r2 = (one / six) * h do 20 j=1,n ad(j) = two/h - sigma * r1 adl(j) = -one/h - sigma * r2 20 continue call dcopy (n, adl, 1, adu, 1) call dgttrf (n, adl, ad, adu, adu2, ipiv, ierr) if (ierr .ne. 0) then print *, ' Error with _gttrf in _SDRV4.' go to 9000 end if c c %-------------------------------------------% c | M A I N L O O P (Reverse communication) | c %-------------------------------------------% c 10 continue c c %---------------------------------------------% c | Repeatedly call the routine DSAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call dsaupd ( ido, bmat, n, which, nev, tol, resid, & ncv, v, ldv, iparam, ipntr, workd, workl, & lworkl, info ) c if (ido .eq. -1) then c c %--------------------------------------------% c | Perform y <--- OP*x = inv[A-SIGMA*M]*M*x | c | to force the starting vector into the | c | range of OP. The user should supply | c | his/her own matrix vector multiplication | c | routine and a linear system solver here. | c | The matrix vector multiplication routine | c | takes workd(ipntr(1)) as the input vector. | c | The final result is returned to | c | workd(ipntr(2)). | c %--------------------------------------------% c call mv (n, workd(ipntr(1)), workd(ipntr(2))) c call dgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv, & workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print *, ' ' print *, ' Error with _gttrs in _SDRV4. ' print *, ' ' go to 9000 end if c c %-----------------------------------------% c | L O O P B A C K to call DSAUPD again. | c %-----------------------------------------% c go to 10 c else if (ido .eq. 1) then c c %-----------------------------------------% c | Perform y <-- OP*x = inv[A-sigma*M]*M*x | c | M*x has been saved in workd(ipntr(3)). | c | the user only needs the linear system | c | solver here that takes workd(ipntr(3) | c | as input, and returns the result to | c | workd(ipntr(2)). | c %-----------------------------------------% c call dcopy ( n, workd(ipntr(3)), 1, workd(ipntr(2)), 1) call dgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv, & workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print *, ' ' print *, ' Error with _gttrs in _SDRV4.' print *, ' ' go to 9000 end if c c %-----------------------------------------% c | L O O P B A C K to call DSAUPD again. | c %-----------------------------------------% c go to 10 c else if (ido .eq. 2) then c c %-----------------------------------------% c | Perform y <--- M*x | c | Need the matrix vector multiplication | c | routine here that takes workd(ipntr(1)) | c | as the input and returns the result to | c | workd(ipntr(2)). | c %-----------------------------------------% c call mv (n, workd(ipntr(1)), workd(ipntr(2))) c c %-----------------------------------------% c | L O O P B A C K to call DSAUPD again. | c %-----------------------------------------% c go to 10 c end if c c %-----------------------------------------% c | Either we have convergence, or there is | c | an error. | c %-----------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message, check the | c | documentation in DSAUPD. | c %--------------------------% c print *, ' ' print *, ' Error with _saupd, info = ',info print *, ' Check the documentation of _saupd ' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using DSEUPD. | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may also be computed now if | c | desired. (indicated by rvec = .true.) | c %-------------------------------------------% c rvec = .true. c call dseupd ( rvec, 'All', select, d, v, ldv, sigma, & bmat, n, which, nev, tol, resid, ncv, v, ldv, & iparam, ipntr, workd, workl, lworkl, ierr ) c c %----------------------------------------------% c | Eigenvalues are returned in the first column | c | of the two dimensional array D and the | c | corresponding eigenvectors are returned in | c | the first NEV columns of the two dimensional | c | array V if requested. Otherwise, an | c | orthogonal basis for the invariant subspace | c | corresponding to the eigenvalues in D is | c | returned in V. | c %----------------------------------------------% c if ( ierr .ne. 0 ) then c c %------------------------------------% c | Error condition: | c | Check the documentation of DSEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _seupd, info = ', ierr print *, ' Check the documentation of _seupd ' print *, ' ' c else c nconv = iparam(5) do 30 j=1, nconv c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c call av(n, v(1,j), workd) call mv(n, v(1,j), workd(n+1)) call daxpy (n, -d(j,1), workd(n+1), 1, workd, 1) d(j,2) = dnrm2(n, workd, 1) d(j,2) = d(j,2) / abs(d(j,1)) c 30 continue c call dmout(6, nconv, 2, d, maxncv, -6, & 'Ritz values and relative residuals') c end if c c %------------------------------------------% c | Print additional convergence information | c %------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, ' _SDRV4 ' print *, ' ====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program dsdrv4. | c %---------------------------% c 9000 continue c end c c------------------------------------------------------------------------ c matrix vector subroutine c The matrix used is the 1 dimensional mass matrix c on the interval [0,1]. c subroutine mv (n, v, w) integer n, j Double precision & v(n),w(n), one, four, six, h parameter (one = 1.0D+0, four = 4.0D+0, & six = 6.0D+0) c w(1) = four*v(1) + v(2) do 100 j = 2,n-1 w(j) = v(j-1) + four*v(j) + v(j+1) 100 continue j = n w(j) = v(j-1) + four*v(j) c c Scale the vector w by h. c h = one / ( six*dble(n+1)) call dscal(n, h, w, 1) return end c------------------------------------------------------------------------ c matrix vector subroutine c where the matrix is the finite element discretization of the c 1 dimensional discrete Laplacian on [0,1] with zero Dirichlet c boundary condition using piecewise linear elements. c subroutine av (n, v, w) integer n, j Double precision & v(n), w(n), two, one, h parameter (one = 1.0D+0, two = 2.0D+0) c w(1) = two*v(1) - v(2) do 100 j = 2,n-1 w(j) = - v(j-1) + two*v(j) - v(j+1) 100 continue j = n w(j) = - v(j-1) + two*v(j) c c Scale the vector w by (1/h) c h = one / dble(n+1) call dscal(n, one/h, w, 1) return end arpack-0.92.1/EXAMPLES/SYM/dsdrv3.f0000644000175000017500000003752710776001577013257 00000000000000 program dsdrv3 c c Program to illustrate the idea of reverse communication in c inverse mode for a generalized symmetric eigenvalue problem. c The following program uses the two LAPACK subroutines dgttrf .f c and dgttrs .f to factor and solve a tridiagonal system of equations. c c We implement example three of ex-sym.doc in DOCUMENTS directory c c\Example-3 c ... Suppose we want to solve A*x = lambda*M*x in inverse mode, c where A and M are obtained by the finite element of the c 1-dimensional discrete Laplacian c d^2u / dx^2 c on the interval [0,1] with zero Dirichlet boundary condition c using piecewise linear elements. c c ... OP = inv[M]*A and B = M. c c ... Use mode 2 of DSAUPD . c c\BeginLib c c\Routines called: c dsaupd ARPACK reverse communication interface routine. c dseupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c dgttrf LAPACK tridiagonal factorization routine. c dgttrs LAPACK tridiagonal solve routine. c daxpy Level 1 BLAS that computes y <- alpha*x+y. c dscal Level 1 BLAS that scales a vector by a scalar. c dcopy Level 1 BLAS that copies one vector to another. c dnrm2 Level 1 BLAS that computes the norm of a vector. c av Matrix vector multiplication routine that computes A*x. c mv Matrix vector multiplication routine that computes M*x. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: sdrv3.F SID: 2.5 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c-------------------------------------------------------------------------- c c %-----------------------------% c | Define leading dimensions | c | for all arrays. | c | MAXN: Maximum dimension | c | of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %-----------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=10, maxncv=25, & ldv=maxn ) c c %--------------% c | Local Arrays | c %--------------% c Double precision & v(ldv,maxncv), workl(maxncv*(maxncv+8)), & workd(3*maxn), d(maxncv,2), resid(maxn), & ad(maxn), adl(maxn), adu(maxn), adu2(maxn), & ax(maxn), mx(maxn) logical select(maxncv) integer iparam(11), ipntr(11), ipiv(maxn) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nev, ncv, lworkl, info, j, ierr, & nconv, maxitr, ishfts, mode logical rvec Double precision & sigma, r1, r2, tol, h c c %------------% c | Parameters | c %------------% c Double precision & zero, one, four, six parameter ( zero = 0.0D+0 , one = 1.0D+0 , & four = 4.0D+0 , six = 6.0D+0 ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & dnrm2 external daxpy , dcopy , dscal , dnrm2 , dgttrf , dgttrs c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable statements | c %-----------------------% c c %----------------------------------------------------% c | The number N is the dimension of the matrix. A | c | generalized eigenvalue problem is solved (BMAT = | c | 'G'.) NEV is the number of eigenvalues to be | c | approximated. The user can modify NEV, NCV, WHICH | c | to solve problems of different sizes, and to get | c | different parts of the spectrum. However, The | c | following conditions must be satisfied: | c | N <= MAXN, | c | NEV <= MAXNEV, | c | NEV + 1 <= NCV <= MAXNCV | c %----------------------------------------------------% c n = 100 nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _SDRV3: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _SDRV3: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _SDRV3: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' c c %--------------------------------------------------% c | The work array WORKL is used in DSAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in DSAUPD to start the Arnoldi | c | iteration. | c %--------------------------------------------------% c lworkl = ncv*(ncv+8) tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | This program uses exact shifts with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 2 of DSAUPD is used | c | (IPARAM(7) = 2). All these options may be | c | changed by the user. For details, see the | c | documentation in DSAUPD . | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 2 c iparam(1) = ishfts iparam(3) = maxitr iparam(7) = mode c c %------------------------------------------------% c | Call LAPACK routine to factor the mass matrix. | c | The mass matrix is the tridiagonal matrix | c | arising from using piecewise linear finite | c | elements on the interval [0, 1]. | c %------------------------------------------------% c h = one / dble (n+1) c r1 = (four / six) * h r2 = (one / six) * h do 20 j=1,n ad(j) = r1 adl(j) = r2 20 continue call dcopy (n, adl, 1, adu, 1) call dgttrf (n, adl, ad, adu, adu2, ipiv, ierr) if (ierr .ne. 0) then print *, ' ' print *, ' Error with _gttrf in _SDRV3. ' print *, ' ' go to 9000 end if c c %-------------------------------------------% c | M A I N L O O P (Reverse communication) | c %-------------------------------------------% c 10 continue c c %---------------------------------------------% c | Repeatedly call the routine DSAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call dsaupd ( ido, bmat, n, which, nev, tol, resid, & ncv, v, ldv, iparam, ipntr, workd, workl, & lworkl, info ) c if (ido .eq. -1 .or. ido .eq. 1) then c c %--------------------------------------% c | Perform y <--- OP*x = inv[M]*A*x. | c | The user should supply his/her own | c | matrix vector multiplication (A*x) | c | routine and a linear system solver | c | here. The matrix vector | c | multiplication routine takes | c | workd(ipntr(1)) as the input vector. | c | The final result is returned to | c | workd(ipntr(2)). The result of A*x | c | overwrites workd(ipntr(1)). | c %--------------------------------------% c call av (n, workd(ipntr(1)), workd(ipntr(2))) call dcopy (n, workd(ipntr(2)), 1, workd(ipntr(1)), 1) call dgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv, & workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print *, ' ' print *, ' Error with _gttrs in _SDRV3.' print *, ' ' go to 9000 end if c c %-----------------------------------------% c | L O O P B A C K to call DSAUPD again. | c %-----------------------------------------% c go to 10 c else if (ido .eq. 2) then c c %-----------------------------------------% c | Perform y <--- M*x. | c | Need the matrix vector multiplication | c | routine here that takes workd(ipntr(1)) | c | as the input and returns the result to | c | workd(ipntr(2)). | c %-----------------------------------------% c call mv (n, workd(ipntr(1)), workd(ipntr(2))) c c %-----------------------------------------% c | L O O P B A C K to call DSAUPD again. | c %-----------------------------------------% c go to 10 c end if c c c c %-----------------------------------------% c | Either we have convergence, or there is | c | an error. | c %-----------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message, check the | c | documentation in DSAUPD | c %--------------------------% c print *, ' ' print *, ' Error with _saupd, info = ',info print *, ' Check the documentation of _saupd ' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using DSEUPD . | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may also be computed now if | c | desired. (indicated by rvec = .true.) | c %-------------------------------------------% c rvec = .true. c call dseupd ( rvec, 'All', select, d, v, ldv, sigma, & bmat, n, which, nev, tol, resid, ncv, v, ldv, & iparam, ipntr, workd, workl, lworkl, ierr ) c c %----------------------------------------------% c | Eigenvalues are returned in the first column | c | of the two dimensional array D and the | c | corresponding eigenvectors are returned in | c | the first NEV columns of the two dimensional | c | array V if requested. Otherwise, an | c | orthogonal basis for the invariant subspace | c | corresponding to the eigenvalues in D is | c | returned in V. | c %----------------------------------------------% c if (ierr .ne. 0) then c c %------------------------------------% c | Error condition: | c | Check the documentation of DSEUPD . | c %------------------------------------% c print *, ' ' print *, ' Error with _seupd, info = ', ierr print *, ' Check the documentation of _seupd' print *, ' ' c else c nconv = iparam(5) do 30 j=1, nconv c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*M*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c call av(n, v(1,j), ax) call mv(n, v(1,j), mx) call daxpy (n, -d(j,1), mx, 1, ax, 1) d(j,2) = dnrm2 (n, ax, 1) d(j,2) = d(j,2) / abs(d(j,1)) c 30 continue c c %-----------------------------% c | Display computed residuals. | c %-----------------------------% c call dmout (6, nconv, 2, d, maxncv, -6, & 'Ritz values and relative residuals') end if c c %------------------------------------------% c | Print additional convergence information | c %------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, ' _SDRV3 ' print *, ' ====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program dsdrv3 . | c %---------------------------% c 9000 continue c end c c------------------------------------------------------------------------ c Matrix vector subroutine c where the matrix is the 1 dimensional mass matrix c on the interval [0,1]. c subroutine mv (n, v, w) integer n, j Double precision & v(n),w(n), one, four, six, h parameter (one = 1.0D+0 , four = 4.0D+0 , & six = 6.0D+0 ) c w(1) = four*v(1) + v(2) do 100 j = 2,n-1 w(j) = v(j-1) + four*v(j) + v(j+1) 100 continue j = n w(j) = v(j-1) + four*v(j) c c Scale the vector w by h. c h = one / (dble (n+1)*six) call dscal (n, h, w, 1) return end c c-------------------------------------------------------------------- c matrix vector subroutine c c The matrix used is the stiffness matrix obtained from the finite c element discretization of the 1-dimensional discrete Laplacian c on the interval [0,1] with zero Dirichlet boundary condition using c piecewise linear elements. c subroutine av (n, v, w) integer n, j Double precision & v(n),w(n), two, one, h parameter ( one = 1.0D+0 , two = 2.0D+0 ) c w(1) = two*v(1) - v(2) do 100 j = 2,n-1 w(j) = - v(j-1) + two*v(j) - v(j+1) 100 continue j = n w(j) = - v(j-1) + two*v(j) c c Scale the vector w by (1 / h). c h = one / dble (n+1) call dscal (n, one/h, w, 1) return end arpack-0.92.1/EXAMPLES/SYM/ssdrv6.f0000644000175000017500000004274710776001577013301 00000000000000 program ssdrv6 c c Program to illustrate the idea of reverse communication c in Cayley mode for a generalized symmetric eigenvalue c problem. The following program uses the two LAPACK subroutines c sgttrf.f and sgttrs.f to factor and solve a tridiagonal system of c equations. c c We implement example six of ex-sym.doc in DOCUMENTS directory c c\Example-6 c ... Suppose we want to solve A*x = lambda*M*x in inverse mode, c where A and M are obtained by the finite element of the c 1-dimensional discrete Laplacian c d^2u / dx^2 c on the interval [0,1] with zero Dirichlet boundary condition c using piecewise linear elements. c c ... OP = (inv[A-sigma*M])*(A+sigma*M) and B = M. c c ... Use mode 5 of SSAUPD. c c\BeginLib c c\References: c 1. R.G. Grimes, J.G. Lewis and H.D. Simon, "A Shifted Block Lanczos c Algorithm for Solving Sparse Symmetric Generalized Eigenproblems", c SIAM J. Matr. Anal. Apps., January (1993). c c\Routines called: c ssaupd ARPACK reverse communication interface routine. c sseupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c sgttrf LAPACK tridiagonal factorization routine. c sgttrs LAPACK tridiagonal solve routine. c saxpy Level 1 BLAS that computes y <- alpha*x+y. c scopy Level 1 BLAS that copies one vector to another. c sscal Level 1 BLAS that scales a vector by a scalar. c snrm2 Level 1 BLAS that computes the norm of a vector. c av Matrix vector multiplication routine that computes A*x. c mv Matrix vector multiplication routine that computes M*x. c c\Author c Danny Sorensen c Richard Lehoucq c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: sdrv6.F SID: 2.5 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c------------------------------------------------------------------------ c c %-----------------------------% c | Define leading dimensions | c | for all arrays. | c | MAXN: Maximum dimension | c | of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %-----------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=10, maxncv=25, & ldv=maxn) c c %--------------% c | Local Arrays | c %--------------% c Real & v(ldv,maxncv), workl(maxncv*(maxncv+8)), & workd(3*maxn), d(maxncv,2), resid(maxn), & ad(maxn), adl(maxn), adu(maxn), adu2(maxn), & temp(maxn), ax(maxn), mx(maxn) logical select(maxncv) integer iparam(11), ipntr(11), ipiv(maxn) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nev, ncv, lworkl, info, j, ierr, & nconv, maxitr, ishfts, mode logical rvec Real & sigma, r1, r2, tol, h c c %------------% c | Parameters | c %------------% c Real & zero, one, two, four, six parameter (zero = 0.0E+0, one = 1.0E+0, & four = 4.0E+0, six = 6.0E+0, & two = 2.0E+0 ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & snrm2 external saxpy, scopy, sscal, snrm2, sgttrf, sgttrs c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable statements | c %-----------------------% c c %--------------------------------------------------% c | The number N is the dimension of the matrix. A | c | generalized eigenvalue problem is solved (BMAT = | c | 'G'.) NEV is the number of eigenvalues to be | c | approximated. Since the Cayley mode is used, | c | WHICH is set to 'LM'. The user can modify NEV, | c | NCV, SIGMA to solve problems of different sizes, | c | and to get different parts of the spectrum. | c | However, The following conditions must be | c | satisfied: | c | N <= MAXN, | c | NEV <= MAXNEV, | c | NEV + 1 <= NCV <= MAXNCV | c %--------------------------------------------------% c n = 100 nev = 4 ncv = 20 if ( n .gt. maxn ) then print *, ' ERROR with _SDRV6: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _SDRV6: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _SDRV6: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' sigma = 1.5E+2 c c %--------------------------------------------------% c | The work array WORKL is used in SSAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in SSAUPD to start the Arnoldi | c | iteration. | c %--------------------------------------------------% c lworkl = ncv*(ncv+8) tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | This program uses exact shifts with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 5 specified in the | c | documentation of SSAUPD is used (IPARAM(7) = 5). | c | All these options may be changed by the user. For | c | details, see the documentation in SSAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 5 c iparam(1) = ishfts iparam(3) = maxitr iparam(7) = mode c c %------------------------------------------------------% c | Call LAPACK routine to factor (A-sigma*M). The | c | stiffness matrix A is the 1-d discrete Laplacian. | c | The mass matrix M is the associated mass matrix | c | arising from using piecewise linear finite elements | c | on the interval [0, 1]. | c %------------------------------------------------------% c h = one / real(n+1) r1 = (four / six) * h r2 = (one / six) * h do 20 j=1,n ad(j) = two / h - sigma * r1 adl(j) = -one / h - sigma * r2 20 continue call scopy (n, adl, 1, adu, 1) call sgttrf (n, adl, ad, adu, adu2, ipiv, ierr) if (ierr .ne. 0) then print *, ' ' print *, ' Error with _gttrf in _SDRV6.' print *, ' ' go to 9000 end if c c %-------------------------------------------% c | M A I N L O O P (Reverse communication) | c %-------------------------------------------% c 10 continue c c %---------------------------------------------% c | Repeatedly call the routine SSAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call ssaupd ( ido, bmat, n, which, nev, tol, resid, ncv, & v, ldv, iparam, ipntr, workd, workl, lworkl, & info ) c if (ido .eq. -1) then c c %-------------------------------------------------------% c | Perform y <--- OP*x = (inv[A-SIGMA*M])*(A+SIGMA*M)*x | c | to force starting vector into the range of OP. The | c | user should provide his/her matrix vector (A*x, M*x) | c | multiplication routines and a linear system solver | c | here. The matrix vector multiplication routine takes | c | workd(ipntr(1)) as the input vector. The final | c | result is returned to workd(ipntr(2)). | c %-------------------------------------------------------% c call av (n, workd(ipntr(1)), workd(ipntr(2))) call mv (n, workd(ipntr(1)), temp) call saxpy(n, sigma, temp, 1, workd(ipntr(2)), 1) c call sgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv, & workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print *, ' ' print *, ' Error with _gttrs in _SDRV6.' print *, ' ' go to 9000 end if c c %-----------------------------------------% c | L O O P B A C K to call SSAUPD again. | c %-----------------------------------------% c go to 10 c else if (ido .eq. 1) then c c %----------------------------------------------------% c | Perform y <-- OP*x = inv[A-SIGMA*M]*(A+SIGMA*M)*x. | c | M*x has been saved in workd(ipntr(3)). The user | c | need the matrix vector multiplication (A*x) | c | routine and a linear system solver here. The | c | matrix vector multiplication routine takes | c | workd(ipntr(1)) as the input, and the result is | c | combined with workd(ipntr(3)) to form the input | c | for the linear system solver. The final result is | c | returned to workd(ipntr(2)). | c %----------------------------------------------------% c call av (n, workd(ipntr(1)), workd(ipntr(2))) call saxpy(n, sigma, workd(ipntr(3)), 1, workd(ipntr(2)), 1) call sgttrs ('Notranspose', n, 1, adl, ad, adu, adu2, ipiv, & workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print *, ' ' print *, ' Error with _gttrs in _SDRV6. ' print *, ' ' go to 9000 end if c c %-----------------------------------------% c | L O O P B A C K to call SSAUPD again. | c %-----------------------------------------% c go to 10 c else if (ido .eq. 2) then c c %--------------------------------------------% c | Perform y <--- M*x. | c | Need matrix vector multiplication routine | c | here that takes workd(ipntr(1)) as input | c | and returns the result to workd(ipntr(2)). | c %--------------------------------------------% c call mv (n, workd(ipntr(1)), workd(ipntr(2))) c c %-----------------------------------------% c | L O O P B A C K to call SSAUPD again. | c %-----------------------------------------% c go to 10 c end if c c %-----------------------------------------% c | Either we have convergence, or there is | c | an error. | c %-----------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message, check the | c | documentation in SSAUPD | c %--------------------------% c print *, ' ' print *, ' Error with _saupd, info = ',info print *, ' Check the documentation of _saupd. ' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using SSEUPD. | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may also be computed now if | c | desired. (indicated by rvec = .true.) | c %-------------------------------------------% c rvec = .true. c call sseupd ( rvec, 'All', select, d, v, ldv, sigma, & bmat, n, which, nev, tol, resid, ncv, v, ldv, & iparam, ipntr, workd, workl, lworkl, ierr ) c c %----------------------------------------------% c | Eigenvalues are returned in the first column | c | of the two dimensional array D and the | c | corresponding eigenvectors are returned in | c | the first NEV columns of the two dimensional | c | array V if requested. Otherwise, an | c | orthogonal basis for the invariant subspace | c | corresponding to the eigenvalues in D is | c | returned in V. | c %----------------------------------------------% c if ( ierr .ne. 0 ) then c c %------------------------------------% c | Error condition: | c | Check the documentation of SSEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _seupd, info = ', ierr print *, ' Check the documentation of _seupd ' print *, ' ' c else c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c nconv = iparam(5) do 30 j=1, nconv call av(n, v(1,j), ax) call mv(n, v(1,j), mx) call saxpy (n, -d(j,1), mx, 1, ax, 1) d(j,2) = snrm2(n, ax, 1) d(j,2) = d(j,2) / abs(d(j,1)) 30 continue c call smout(6, nconv, 2, d, maxncv, -6, & 'Ritz values and relative residuals') c end if c c %------------------------------------------% c | Print additional convergence information | c %------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, ' _SDRV6 ' print *, ' ====== ' print *, ' ' print *, ' Size of the matrix is', n print *, ' The number of Ritz values requested is', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program ssdrv6. | c %---------------------------% c 9000 continue c end c c------------------------------------------------------------------------ c Matrix vector subroutine c where the matrix used is the 1 dimensional mass matrix c arising from using the piecewise linear finite element c on the interval [0,1]. c subroutine mv (n, v, w) integer n, j Real & v(n), w(n), one, four, six, h parameter (one = 1.0E+0, four = 4.0E+0, & six = 6.0E+0) c w(1) = four*v(1) + v(2) do 100 j = 2,n-1 w(j) = v(j-1) + four*v(j) + v(j+1) 100 continue j = n w(j) = v(j-1) + four*v(j) c c Scale the vector w by h. c h = one / (six*real(n+1)) call sscal(n, h, w, 1) return end c c------------------------------------------------------------------------ c Matrix vector subroutine c where the matrix is the stiffness matrix obtained from the c finite element discretization of the 1-dimensional discrete Laplacian c on the interval [0,1] with zero Dirichlet boundary condition c using piecewise linear elements. c subroutine av (n, v, w) integer n, j Real & v(n), w(n), one, two, h parameter (one = 1.0E+0, two = 2.0E+0) c w(1) = two*v(1) - v(2) do 100 j = 2,n-1 w(j) = - v(j-1) + two*v(j) - v(j+1) 100 continue j = n w(j) = - v(j-1) + two*v(j) c c Scale the vector w by (1/h). c h = one / real(n+1) call sscal(n, one/h, w, 1) return end arpack-0.92.1/EXAMPLES/SYM/dsdrv1.f0000644000175000017500000003420710776001577013245 00000000000000 program dsdrv1 c c Simple program to illustrate the idea of reverse communication c in regular mode for a standard symmetric eigenvalue problem. c c We implement example one of ex-sym.doc in SRC directory c c\Example-1 c ... Suppose we want to solve A*x = lambda*x in regular mode, c where A is derived from the central difference discretization c of the 2-dimensional Laplacian on the unit square [0,1]x[0,1] c with zero Dirichlet boundary condition. c c ... OP = A and B = I. c c ... Assume "call av (n,x,y)" computes y = A*x. c c ... Use mode 1 of DSAUPD. c c\BeginLib c c\Routines called: c dsaupd ARPACK reverse communication interface routine. c dseupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c dnrm2 Level 1 BLAS that computes the norm of a vector. c daxpy Level 1 BLAS that computes y <- alpha*x+y. c av Matrix vector multiplication routine that computes A*x. c tv Matrix vector multiplication routine that computes T*x, c where T is a tridiagonal matrix. It is used in routine c av. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: sdrv1.F SID: 2.5 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c----------------------------------------------------------------------- c c %-----------------------------% c | Define leading dimensions | c | for all arrays. | c | MAXN: Maximum dimension | c | of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %-----------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=10, maxncv=25, $ ldv=maxn ) c c %--------------% c | Local Arrays | c %--------------% c Double precision & v(ldv,maxncv), workl(maxncv*(maxncv+8)), & workd(3*maxn), d(maxncv,2), resid(maxn), & ax(maxn) logical select(maxncv) integer iparam(11), ipntr(11) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nev, ncv, lworkl, info, ierr, j, & nx, nconv, maxitr, mode, ishfts logical rvec Double precision & tol, sigma c c %------------% c | Parameters | c %------------% c Double precision & zero parameter (zero = 0.0D+0) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & dnrm2 external dnrm2, daxpy c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c %----------------------------------------------------% c | The number NX is the number of interior points | c | in the discretization of the 2-dimensional | c | Laplacian on the unit square with zero Dirichlet | c | boundary condition. The number N(=NX*NX) is the | c | dimension of the matrix. A standard eigenvalue | c | problem is solved (BMAT = 'I'). NEV is the number | c | of eigenvalues to be approximated. The user can | c | modify NEV, NCV, WHICH to solve problems of | c | different sizes, and to get different parts of the | c | spectrum. However, The following conditions must | c | be satisfied: | c | N <= MAXN, | c | NEV <= MAXNEV, | c | NEV + 1 <= NCV <= MAXNCV | c %----------------------------------------------------% c nx = 10 n = nx*nx nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _SDRV1: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _SDRV1: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _SDRV1: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'I' which = 'SM' c c %--------------------------------------------------% c | The work array WORKL is used in DSAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in DSAUPD to start the Arnoldi | c | iteration. | c %--------------------------------------------------% c lworkl = ncv*(ncv+8) tol = zero info = 0 ido = 0 c c %---------------------------------------------------% c | This program uses exact shifts with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 1 of DSAUPD is used | c | (IPARAM(7) = 1). All these options may be | c | changed by the user. For details, see the | c | documentation in DSAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 1 c iparam(1) = ishfts iparam(3) = maxitr iparam(7) = mode c c %-------------------------------------------% c | M A I N L O O P (Reverse communication) | c %-------------------------------------------% c 10 continue c c %---------------------------------------------% c | Repeatedly call the routine DSAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call dsaupd ( ido, bmat, n, which, nev, tol, resid, & ncv, v, ldv, iparam, ipntr, workd, workl, & lworkl, info ) c if (ido .eq. -1 .or. ido .eq. 1) then c c %--------------------------------------% c | Perform matrix vector multiplication | c | y <--- OP*x | c | The user should supply his/her own | c | matrix vector multiplication routine | c | here that takes workd(ipntr(1)) as | c | the input, and return the result to | c | workd(ipntr(2)). | c %--------------------------------------% c call av (nx, workd(ipntr(1)), workd(ipntr(2))) c c %-----------------------------------------% c | L O O P B A C K to call DSAUPD again. | c %-----------------------------------------% c go to 10 c end if c c %----------------------------------------% c | Either we have convergence or there is | c | an error. | c %----------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message. Check the | c | documentation in DSAUPD. | c %--------------------------% c print *, ' ' print *, ' Error with _saupd, info = ', info print *, ' Check documentation in _saupd ' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using DSEUPD. | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may also be computed now if | c | desired. (indicated by rvec = .true.) | c %-------------------------------------------% c rvec = .true. c call dseupd ( rvec, 'All', select, d, v, ldv, sigma, & bmat, n, which, nev, tol, resid, ncv, v, ldv, & iparam, ipntr, workd, workl, lworkl, ierr ) c %----------------------------------------------% c | Eigenvalues are returned in the first column | c | of the two dimensional array D and the | c | corresponding eigenvectors are returned in | c | the first NEV columns of the two dimensional | c | array V if requested. Otherwise, an | c | orthogonal basis for the invariant subspace | c | corresponding to the eigenvalues in D is | c | returned in V. | c %----------------------------------------------% c if ( ierr .ne. 0) then c c %------------------------------------% c | Error condition: | c | Check the documentation of DSEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _seupd, info = ', ierr print *, ' Check the documentation of _seupd. ' print *, ' ' c else c nconv = iparam(5) do 20 j=1, nconv c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c call av(nx, v(1,j), ax) call daxpy(n, -d(j,1), v(1,j), 1, ax, 1) d(j,2) = dnrm2(n, ax, 1) d(j,2) = d(j,2) / abs(d(j,1)) c 20 continue c c %-------------------------------% c | Display computed residuals | c %-------------------------------% c call dmout(6, nconv, 2, d, maxncv, -6, & 'Ritz values and relative residuals') end if c c %------------------------------------------% c | Print additional convergence information | c %------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, ' _SDRV1 ' print *, ' ====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program dsdrv1. | c %---------------------------% c 9000 continue c end c c ------------------------------------------------------------------ c matrix vector subroutine c c The matrix used is the 2 dimensional discrete Laplacian on unit c square with zero Dirichlet boundary condition. c c Computes w <--- OP*v, where OP is the nx*nx by nx*nx block c tridiagonal matrix c c | T -I | c |-I T -I | c OP = | -I T | c | ... -I| c | -I T| c c The subroutine TV is called to computed y<---T*x. c subroutine av (nx, v, w) integer nx, j, lo, n2 Double precision & v(nx*nx), w(nx*nx), one, h2 parameter ( one = 1.0D+0 ) c call tv(nx,v(1),w(1)) call daxpy(nx, -one, v(nx+1), 1, w(1), 1) c do 10 j = 2, nx-1 lo = (j-1)*nx call tv(nx, v(lo+1), w(lo+1)) call daxpy(nx, -one, v(lo-nx+1), 1, w(lo+1), 1) call daxpy(nx, -one, v(lo+nx+1), 1, w(lo+1), 1) 10 continue c lo = (nx-1)*nx call tv(nx, v(lo+1), w(lo+1)) call daxpy(nx, -one, v(lo-nx+1), 1, w(lo+1), 1) c c Scale the vector w by (1/h^2), where h is the mesh size c n2 = nx*nx h2 = one / dble((nx+1)*(nx+1)) call dscal(n2, one/h2, w, 1) return end c c------------------------------------------------------------------- subroutine tv (nx, x, y) c integer nx, j Double precision & x(nx), y(nx), dd, dl, du c Double precision & one parameter (one = 1.0D+0 ) c c Compute the matrix vector multiplication y<---T*x c where T is a nx by nx tridiagonal matrix with DD on the c diagonal, DL on the subdiagonal, and DU on the superdiagonal. c c dd = 4.0D+0 dl = -one du = -one c y(1) = dd*x(1) + du*x(2) do 10 j = 2,nx-1 y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1) 10 continue y(nx) = dl*x(nx-1) + dd*x(nx) return end arpack-0.92.1/EXAMPLES/NONSYM/0000755000175000017500000000000010776001577012320 500000000000000arpack-0.92.1/EXAMPLES/NONSYM/dndrv4.f0000644000175000017500000004644010776001577013620 00000000000000 program dndrv4 c c Simple program to illustrate the idea of reverse communication c in shift-invert mode for a generalized nonsymmetric eigenvalue c problem. c c We implement example four of ex-nonsym.doc in DOCUMENTS directory c c\Example-4 c ... Suppose we want to solve A*x = lambda*B*x in inverse mode, c where A and B are derived from the finite element discretization c of the 1-dimensional convection-diffusion operator c (d^2u / dx^2) + rho*(du/dx) c on the interval [0,1] with zero Dirichlet boundary condition c using linear elements. c c ... The shift sigma is a real number. c c ... OP = inv[A-SIGMA*M]*M and B = M. c c ... Use mode 3 of DNAUPD. c c\BeginLib c c\Routines called: c dnaupd ARPACK reverse communication interface routine. c dneupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c dgttrf LAPACK tridiagonal factorization routine. c dgttrs LAPACK tridiagonal linear system solve routine. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c daxpy Level 1 BLAS that computes y <- alpha*x+y. c dcopy Level 1 BLAS that copies one vector to another. c ddot Level 1 BLAS that computes the dot product of two vectors. c dnrm2 Level 1 BLAS that computes the norm of a vector. c av Matrix vector multiplication routine that computes A*x. c mv Matrix vector multiplication routine that computes M*x. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: ndrv4.F SID: 2.5 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c----------------------------------------------------------------------- c c %-----------------------------% c | Define leading dimensions | c | for all arrays. | c | MAXN: Maximum dimension | c | of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %-----------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=10, maxncv=25, & ldv=maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), ipntr(14), ipiv(maxn) logical select(maxncv) Double precision & ax(maxn), mx(maxn), d(maxncv,3), resid(maxn), & v(ldv,maxncv), workd(3*maxn), workev(3*maxncv), & workl(3*maxncv*maxncv+6*maxncv), & dd(maxn), dl(maxn), du(maxn), & du2(maxn) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nev, ncv, lworkl, info, ierr, j, & nconv, maxitr, ishfts, mode Double precision & tol, h, s, & sigmar, sigmai, s1, s2, s3 logical first, rvec c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & ddot, dnrm2, dlapy2 external ddot, dnrm2, dlapy2, dgttrf, dgttrs c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %------------% c | Parameters | c %------------% c Double precision & one, zero, two, six, rho common /convct/ rho parameter (one = 1.0D+0, zero = 0.0D+0, & two = 2.0D+0, six = 6.0D+0) c c %-----------------------% c | Executable statements | c %-----------------------% c c %----------------------------------------------------% c | The number N is the dimension of the matrix. A | c | generalized eigenvalue problem is solved (BMAT = | c | 'G'). NEV is the number of eigenvalues (closest | c | to SIGMAR) to be approximated. Since the | c | shift-invert mode is used, WHICH is set to 'LM'. | c | The user can modify NEV, NCV, SIGMAR to solve | c | problems of different sizes, and to get different | c | parts of the spectrum. However, The following | c | conditions must be satisfied: | c | N <= MAXN, | c | NEV <= MAXNEV, | c | NEV + 2 <= NCV <= MAXNCV | c %----------------------------------------------------% c n = 100 nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _NDRV4: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NDRV4: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NDRV4: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' sigmar = one sigmai = zero c c %--------------------------------------------------% c | Construct C = A - SIGMA*M in real arithmetic, | c | and factor C in real arithmetic (using LAPACK | c | subroutine dgttrf). The matrix A is chosen to be | c | the tridiagonal matrix derived from the standard | c | central difference discretization of the 1-d | c | convection-diffusion operator u" + rho*u' on the | c | interval [0, 1] with zero Dirichlet boundary | c | condition. The matrix M is the mass matrix | c | formed by using piecewise linear elements on | c | [0,1]. | c %--------------------------------------------------% c rho = 1.0D+1 h = one / dble(n+1) s = rho / two c s1 = -one/h - s - sigmar*h/six s2 = two/h - 4.0D+0*sigmar*h/six s3 = -one/h + s - sigmar*h/six c do 10 j = 1, n-1 dl(j) = s1 dd(j) = s2 du(j) = s3 10 continue dd(n) = s2 c call dgttrf(n, dl, dd, du, du2, ipiv, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrf in _NDRV4.' print*, ' ' go to 9000 end if c c %-----------------------------------------------------% c | The work array WORKL is used in DNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in DNAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = 3*ncv**2+6*ncv tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | This program uses exact shifts with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 3 of DNAUPD is used | c | (IPARAM(7) = 3). All these options can be | c | changed by the user. For details, see the | c | documentation in DNAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 3 c iparam(1) = ishfts iparam(3) = maxitr iparam(7) = mode c c %------------------------------------------% c | M A I N L O O P(Reverse communication) | c %------------------------------------------% c 20 continue c c %---------------------------------------------% c | Repeatedly call the routine DNAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call dnaupd ( ido, bmat, n, which, nev, tol, resid, & ncv, v, ldv, iparam, ipntr, workd, & workl, lworkl, info ) c if (ido .eq. -1) then c c %-------------------------------------------% c | Perform y <--- OP*x = inv[A-SIGMA*M]*M*x | c | to force starting vector into the range | c | of OP. The user should supply his/her | c | own matrix vector multiplication routine | c | and a linear system solver. The matrix | c | vector multiplication routine should take | c | workd(ipntr(1)) as the input. The final | c | result should be returned to | c | workd(ipntr(2)). | c %-------------------------------------------% c call mv (n, workd(ipntr(1)), workd(ipntr(2))) call dgttrs('N', n, 1, dl, dd, du, du2, ipiv, & workd(ipntr(2)), n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrs in _NDRV4.' print*, ' ' go to 9000 end if c c %-----------------------------------------% c | L O O P B A C K to call DNAUPD again. | c %-----------------------------------------% c go to 20 c else if ( ido .eq. 1) then c c %-----------------------------------------% c | Perform y <-- OP*x = inv[A-sigma*M]*M*x | c | M*x has been saved in workd(ipntr(3)). | c | The user only need the linear system | c | solver here that takes workd(ipntr(3)) | c | as input, and returns the result to | c | workd(ipntr(2)). | c %-----------------------------------------% c call dcopy( n, workd(ipntr(3)), 1, workd(ipntr(2)), 1) call dgttrs ('N', n, 1, dl, dd, du, du2, ipiv, & workd(ipntr(2)), n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrs in _NDRV4.' print*, ' ' go to 9000 end if c c %-----------------------------------------% c | L O O P B A C K to call DNAUPD again. | c %-----------------------------------------% c go to 20 c else if ( ido .eq. 2) then c c %---------------------------------------------% c | Perform y <--- M*x | c | Need matrix vector multiplication routine | c | here that takes workd(ipntr(1)) as input | c | and returns the result to workd(ipntr(2)). | c %---------------------------------------------% c call mv (n, workd(ipntr(1)), workd(ipntr(2))) c c %-----------------------------------------% c | L O O P B A C K to call DNAUPD again. | c %-----------------------------------------% c go to 20 c end if c c c %-----------------------------------------% c | Either we have convergence, or there is | c | an error. | c %-----------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message, check the | c | documentation in DNAUPD. | c %--------------------------% c print *, ' ' print *, ' Error with _naupd, info = ', info print *, ' Check the documentation in _naupd.' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using DNEUPD. | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may also be computed now if | c | desired. (indicated by rvec = .true.) | c %-------------------------------------------% c rvec = .true. call dneupd ( rvec, 'A', select, d, d(1,2), v, ldv, & sigmar, sigmai, workev, bmat, n, which, nev, tol, & resid, ncv, v, ldv, iparam, ipntr, workd, & workl, lworkl, ierr ) c c %-----------------------------------------------% c | The real part of the eigenvalue is returned | c | in the first column of the two dimensional | c | array D, and the IMAGINARY part is returned | c | in the second column of D. The corresponding | c | eigenvectors are returned in the first NEV | c | columns of the two dimensional array V if | c | requested. Otherwise, an orthogonal basis | c | for the invariant subspace corresponding to | c | the eigenvalues in D is returned in V. | c %-----------------------------------------------% c if ( ierr .ne. 0) then c c %------------------------------------% c | Error condition: | c | Check the documentation of DNEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _neupd, info = ', ierr print *, ' Check the documentation of _neupd. ' print *, ' ' c else c first = .true. nconv = iparam(5) do 30 j=1, nconv c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c if (d(j,2) .eq. zero) then c c %--------------------% c | Ritz value is real | c %--------------------% c call av(n, v(1,j), ax) call mv(n, v(1,j), mx) call daxpy(n, -d(j,1), mx, 1, ax, 1) d(j,3) = dnrm2(n, ax, 1) d(j,3) = d(j,3) / abs(d(j,1)) c else if (first) then c c %------------------------% c | Ritz value is complex. | c | Residual of one Ritz | c | value of the conjugate | c | pair is computed. | c %------------------------% c call av(n, v(1,j), ax) call mv(n, v(1,j), mx) call daxpy(n, -d(j,1), mx, 1, ax, 1) call mv(n, v(1,j+1), mx) call daxpy(n, d(j,2), mx, 1, ax, 1) d(j,3) = dnrm2(n, ax, 1) call av(n, v(1,j+1), ax) call mv(n, v(1,j+1), mx) call daxpy(n, -d(j,1), mx, 1, ax, 1) call mv(n, v(1,j), mx) call daxpy(n, -d(j,2), mx, 1, ax, 1) d(j,3) = dlapy2( d(j,3), dnrm2(n, ax, 1) ) d(j,3) = d(j,3) / dlapy2(d(j,1),d(j,2)) d(j+1,3) = d(j,3) first = .false. else first = .true. end if c 30 continue c c %-----------------------------% c | Display computed residuals. | c %-----------------------------% c call dmout(6, nconv, 3, d, maxncv, -6, & 'Ritz values (Real,Imag) and relative residuals') c end if c c %-------------------------------------------% c | Print additional convergence information. | c %-------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, ' _NDRV4 ' print *, ' ====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program dndrv4. | c %---------------------------% c 9000 continue c end c c========================================================================== c c matrix vector multiplication subroutine c subroutine mv (n, v, w) integer n, j Double precision & v(n), w(n), one, four, six, h parameter (one = 1.0D+0, four = 4.0D+0, six = 6.0D+0) c c Compute the matrix vector multiplication y<---M*x c where M is mass matrix formed by using piecewise linear elements c on [0,1]. c w(1) = ( four*v(1) + one*v(2) ) / six do 10 j = 2,n-1 w(j) = ( one*v(j-1) + four*v(j) + one*v(j+1) ) / six 10 continue w(n) = ( one*v(n-1) + four*v(n) ) / six c h = one / dble(n+1) call dscal(n, h, w, 1) return end c------------------------------------------------------------------ subroutine av (n, v, w) integer n, j Double precision & v(n), w(n), one, two, dd, dl, du, s, h, rho common /convct/ rho parameter (one = 1.0D+0, two = 2.0D+0) c c Compute the matrix vector multiplication y<---A*x c where A is obtained from the finite element discretization of the c 1-dimensional convection diffusion operator c d^u/dx^2 + rho*(du/dx) c on the interval [0,1] with zero Dirichlet boundary condition c using linear elements. c This routine is only used in residual calculation. c h = one / dble(n+1) s = rho / two dd = two / h dl = -one/h - s du = -one/h + s c w(1) = dd*v(1) + du*v(2) do 10 j = 2,n-1 w(j) = dl*v(j-1) + dd*v(j) + du*v(j+1) 10 continue w(n) = dl*v(n-1) + dd*v(n) return end arpack-0.92.1/EXAMPLES/NONSYM/makefile0000644000175000017500000000373110776001577013744 00000000000000# # makefile to run simple examples of the reverse communication # protocol. # # Modify if ARPACK library was built somewhere else. # # If ALIBS (defined in ../../ARmake.inc) contains the BLAS and LAPACK # libraries installed on your system, you DO NOT need to change this # makefile. OTHERWISE, you may need to modify the Makefile in the top level # ARPACK directory tree to include sdrv and/or ddrv in the # definition of the PRECISION variable, and issue 'make lib' from there. # For example: # # PRECISION = single double sdrv ddrv # #\SCCS Information: @(#) # FILE: makefile SID: 2.2 DATE OF SID: 9/24/96 RELEASE: 2 # include ../../ARmake.inc # # Issue "make nonsym" to make all 12 nonsymmetric drivers. # Issue "make sndrv" to make 6 single precision nonsymmetric drivers. # Issue "make dndrv" to make 6 double precision nonsymmetric drivers. # nonsym: sndrv dndrv # #----------------------------------------------------------------------- # Simple nonsymmetric problem using single precision # sndrv: sndrv1 sndrv2 sndrv3 sndrv4 sndrv5 sndrv6 sndrv1: sndrv1.o $(FC) $(FFLAGS) sndrv1.o $(ALIBS) -o sndrv1 # sndrv2: sndrv2.o $(FC) $(FFLAGS) sndrv2.o $(ALIBS) -o sndrv2 # sndrv3: sndrv3.o $(FC) $(FFLAGS) sndrv3.o $(ALIBS) -o sndrv3 # sndrv4: sndrv4.o $(FC) $(FFLAGS) sndrv4.o $(ALIBS) -o sndrv4 # sndrv5: sndrv5.o $(FC) $(FFLAGS) sndrv5.o $(ALIBS) -o sndrv5 # sndrv6: sndrv6.o $(FC) $(FFLAGS) sndrv6.o $(ALIBS) -o sndrv6 # #------------------------------------------------------ # Simple nonsymmetric problem using double precision # dndrv: dndrv1 dndrv2 dndrv3 dndrv4 dndrv5 dndrv6 dndrv1: dndrv1.o $(FC) $(FFLAGS) dndrv1.o $(ALIBS) -o dndrv1 # dndrv2: dndrv2.o $(FC) $(FFLAGS) dndrv2.o $(ALIBS) -o dndrv2 # dndrv3: dndrv3.o $(FC) $(FFLAGS) dndrv3.o $(ALIBS) -o dndrv3 # dndrv4: dndrv4.o $(FC) $(FFLAGS) dndrv4.o $(ALIBS) -o dndrv4 # dndrv5: dndrv5.o $(FC) $(FFLAGS) dndrv5.o $(ALIBS) -o dndrv5 # dndrv6: dndrv6.o $(FC) $(FFLAGS) dndrv6.o $(ALIBS) -o dndrv6 arpack-0.92.1/EXAMPLES/NONSYM/README0000644000175000017500000000421710776001577013124 000000000000001. Purpose ------- This directory contains example drivers that call ARPACK subroutines [s,d]naupd.f and [s,d]neupd.f to solve real NONSYMMETRIC eigenvalue problems using regular, inverse or shift-invert modes. These drivers illustrate how to set various ARPACK parameters to solve different problems in different modes. They provide a guideline on how to use ARPACK's reverse communication interface. The user may modify any one of these drivers, and provide his/her own matrix vector multiplication routine to solve the problem of his/her own interest. 2. Naming convention ----------------- The name for each driver has the form 'XndrvN.f', where X - is 's' (single precision) or 'd' (double precision) N - is a number between 1 and 6. If N = 1, the driver solves a STANDARD eigenvalue problem in REGULAR mode. N = 2, the driver solves a STANDARD eigenvalue problem in SHIFT-INVERT mode with a REAL shift. N = 3, the driver solves a GENERALIZED eigenvalue problem in INVERSE mode. N = 4, the driver solves a GENERALIZED eigenvalue problem in SHIFT-INVERT mode with a REAL shift. These are 4 commonly used drivers. For shift-invert (N=2,4) mode the user needs to supply a linear system solver to perform y=inv[A-sigma*B]*x. If N > 4, shift-invert is used with a complex shift whose imaginary part is nonzero. If N = 5, the driver solves a GENERALIZED eigenvalue problem using mode 3 of [s,d]naupd. N = 6. the driver solves a GENERALIZED eigenvalue problem using mode 4 of [s,d]naupd. These two drivers require the user to provide COMPLEX arithmetic linear system solver. For more information on the use of complex shift, see the following reference: B.N. Parlett & Y. Saad, "Complex Shift and Invert Strategies for Real Matrices", Linear Algebra and its Applications, vol 88/89, pp 575-595, (1987). 3. Usage ----- To run these drivers, you may use the makefile in this directory and issue, for example, "make sndrv1". Then execute using "sndrv1". arpack-0.92.1/EXAMPLES/NONSYM/dndrv5.f0000644000175000017500000005330510776001577013617 00000000000000 program dndrv5 c c Simple program to illustrate the idea of reverse communication c in shift-invert mode for a generalized nonsymmetric eigenvalue problem. c c We implement example five of ex-nonsym.doc in DOCUMENTS directory c c\Example-5 c c ... Suppose we want to solve A*x = lambda*B*x in shift-invert mode c The matrix A is the tridiagonal matrix with 2 on the diagonal, c -2 on the subdiagonal and 3 on the superdiagonal. The matrix M c is the tridiagonal matrix with 4 on the diagonal and 1 on the c off-diagonals. c ... The shift sigma is a complex number (sigmar, sigmai). c ... OP = Real_Part{inv[A-(SIGMAR,SIGMAI)*M]*M and B = M. c ... Use mode 3 of DNAUPD. c c\BeginLib c c\Routines called: c dnaupd ARPACK reverse communication interface routine. c dneupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c zgttrf LAPACK complex matrix factorization routine. c zgttrs LAPACK complex linear system solve routine. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c daxpy Level 1 BLAS that computes y <- alpha*x+y. c ddot Level 1 BLAS that computes the dot product of two vectors. c dnrm2 Level 1 BLAS that computes the norm of a vector c av Matrix vector subroutine that computes A*x. c mv Matrix vector subroutine that computes M*x. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: ndrv5.F SID: 2.5 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c------------------------------------------------------------------------- c c %-----------------------------% c | Define leading dimensions | c | for all arrays. | c | MAXN: Maximum dimension | c | of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %-----------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=10, maxncv=25, & ldv=maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), ipntr(14), ipiv(maxn) logical select(maxncv) Double precision & ax(maxn), mx(maxn), d(maxncv,3), resid(maxn), & v(ldv,maxncv), workd(3*maxn), & workev(3*maxncv), & workl(3*maxncv*maxncv+6*maxncv) Complex*16 & cdd(maxn), cdl(maxn), cdu(maxn), & cdu2(maxn), ctemp(maxn) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nev, ncv, lworkl, info, ierr, j, & nconv, maxitr, ishfts, mode Double precision & tol, numr, numi, denr, deni, sigmar, sigmai Complex*16 & c1, c2, c3 logical first, rvec c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c external zgttrf, zgttrs Double precision & ddot, dnrm2, dlapy2 external ddot, dnrm2, dlapy2 c c c %------------% c | Parameters | c %------------% c Double precision & zero parameter (zero = 0.0D+0) c c %--------------------% c | Intrinsic Function | c %--------------------% c intrinsic dble, dcmplx, abs c c %-----------------------% c | Executable statements | c %-----------------------% c c %----------------------------------------------------% c | The number N is the dimension of the matrix. A | c | generalized eigenvalue problem is solved (BMAT = | c | 'G'). NEV is the number of eigenvalues (closest | c | to the shift (SIGMAR,SIGMAI)) to be approximated. | c | Since the shift-invert mode is used, WHICH is set | c | to 'LM'. The user can modify NEV, NCV, SIGMAR, | c | SIGMAI to solve problems of different sizes, and | c | to get different parts of the spectrum. However, | c | The following conditions must be satisfied: | c | N <= MAXN, | c | NEV <= MAXNEV, | c | NEV + 2 <= NCV <= MAXNCV | c %----------------------------------------------------% c n = 100 nev = 4 ncv = 20 if ( n .gt. maxn ) then print *, ' ERROR with _NDRV5: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NDRV5: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NDRV5: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' sigmar = 4.0D-1 sigmai = 6.0D-1 c c %---------------------------------------------------% c | Construct C = A - (SIGMAR,SIGMAI)*M in complex | c | arithmetic, and factor C in complex arithmetic | c | (using LAPACK subroutine zgttrf). The matrix A is | c | chosen to be the tridiagonal matrix with -2 on | c | the subdiagonal, 2 on the diagonal and 3 on the | c | superdiagonal. The matrix M is chosen to the | c | symmetric tridiagonal matrix with 4 on the | c | diagonal and 1 on the off-diagonals. | c %---------------------------------------------------% c c1 = dcmplx(-2.0D+0-sigmar, -sigmai) c2 = dcmplx( 2.0D+0-4.0D+0*sigmar, -4.0D+0*sigmai) c3 = dcmplx( 3.0D+0-sigmar, -sigmai) c do 10 j = 1, n-1 cdl(j) = c1 cdd(j) = c2 cdu(j) = c3 10 continue cdd(n) = c2 c call zgttrf(n, cdl, cdd, cdu, cdu2, ipiv, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrf in _NDRV5.' print*, ' ' go to 9000 end if c c %-----------------------------------------------------% c | The work array WORKL is used in DNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in DNAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = 3*ncv**2+6*ncv tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | This program uses exact shift with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 3 of DNAUPD is used | c | (IPARAM(7) = 3). All these options can be | c | changed by the user. For details, see the | c | documentation in DNAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 3 c iparam(1) = ishfts iparam(3) = maxitr iparam(7) = mode c c %------------------------------------------% c | M A I N L O O P(Reverse communication) | c %------------------------------------------% c 20 continue c c %---------------------------------------------% c | Repeatedly call the routine DNAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call dnaupd ( ido, bmat, n, which, nev, tol, resid, & ncv, v, ldv, iparam, ipntr, workd, & workl, lworkl, info ) c if (ido .eq. -1) then c c %-------------------------------------------------------% c | Perform | c | y <--- OP*x = Real_Part{inv[A-(SIGMAR,SIGMAI)*M]*M*x} | c | to force starting vector into the range of OP. The | c | user should supply his/her own matrix vector | c | multiplication routine and a complex linear system | c | solver. The matrix vector multiplication routine | c | should take workd(ipntr(1)) as the input. The final | c | result (a real vector) should be returned to | c | workd(ipntr(2)). | c %-------------------------------------------------------% c call mv (n, workd(ipntr(1)), workd(ipntr(2))) do 30 j = 1, n ctemp(j) = dcmplx(workd(ipntr(2)+j-1)) 30 continue c call zgttrs('N', n, 1, cdl, cdd, cdu, cdu2, ipiv, & ctemp, n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrs in _NDRV5.' print*, ' ' go to 9000 end if do 40 j = 1, n workd(ipntr(2)+j-1) = dble(ctemp(j)) 40 continue c c %-----------------------------------------% c | L O O P B A C K to call DNAUPD again. | c %-----------------------------------------% c go to 20 c else if ( ido .eq. 1) then c c %-------------------------------------------------------% c | Perform | c | y <--- OP*x = Real_Part{inv[A-(SIGMAR,SIGMAI)*M]*M*x} | c | M*x has been saved in workd(ipntr(3)). The user only | c | needs the complex linear system solver here that | c | takes complex[workd(ipntr(3))] as input, and returns | c | the result to workd(ipntr(2)). | c %-------------------------------------------------------% c do 50 j = 1,n ctemp(j) = dcmplx(workd(ipntr(3)+j-1)) 50 continue call zgttrs ('N', n, 1, cdl, cdd, cdu, cdu2, ipiv, & ctemp, n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrs in _NDRV5.' print*, ' ' go to 9000 end if do 60 j = 1, n workd(ipntr(2)+j-1) = dble(ctemp(j)) 60 continue c c %-----------------------------------------% c | L O O P B A C K to call DNAUPD again. | c %-----------------------------------------% c go to 20 c else if ( ido .eq. 2) then c c %---------------------------------------------% c | Perform y <--- M*x | c | Need matrix vector multiplication routine | c | here that takes workd(ipntr(1)) as input | c | and returns the result to workd(ipntr(2)). | c %---------------------------------------------% c call mv (n, workd(ipntr(1)), workd(ipntr(2))) c c %-----------------------------------------% c | L O O P B A C K to call DNAUPD again. | c %-----------------------------------------% c go to 20 c end if c c c %------------------------------------------% c | Either we have convergence, or there is | c | an error. | c %------------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message, check the | c | documentation in DNAUPD. | c %--------------------------% c print *, ' ' print *, ' Error with _naupd info = ',info print *, ' Check the documentation of _naupd.' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using DNEUPD. | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may also be computed now if | c | desired. (indicated by rvec = .true.) | c %-------------------------------------------% c rvec = .true. call dneupd ( rvec, 'A', select, d, d(1,2), v, ldv, & sigmar, sigmai, workev, bmat, n, which, nev, tol, & resid, ncv, v, ldv, iparam, ipntr, workd, & workl, lworkl, ierr ) c c %-----------------------------------------------% c | The real part of the eigenvalue is returned | c | in the first column of the two dimensional | c | array D, and the IMAGINARY part is returned | c | in the second column of D. The corresponding | c | eigenvectors are returned in the first NEV | c | columns of the two dimensional array V if | c | requested. Otherwise, an orthogonal basis | c | for the invariant subspace corresponding to | c | the eigenvalues in D is returned in V. | c %-----------------------------------------------% c if ( ierr .ne. 0) then c c %------------------------------------% c | Error condition: | c | Check the documentation of DNEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _neupd = ', ierr print *, ' Check the documentation of _neupd. ' print *, ' ' c else c first = .true. nconv = iparam(5) do 70 j=1,nconv c c %-------------------------------------% c | Use Rayleigh Quotient to recover | c | eigenvalues of the original problem.| c %-------------------------------------% c if ( d(j,2) .eq. zero ) then c c %---------------------------% c | Eigenvalue is real. | c | Compute d = x'(Ax)/x'(Mx).| c %---------------------------% c call av(n, v(1,j), ax ) numr = ddot(n, v(1,j), 1, ax, 1) call mv(n, v(1,j), ax ) denr = ddot(n, v(1,j), 1, ax, 1) d(j,1) = numr / denr c else if (first) then c c %------------------------% c | Eigenvalue is complex. | c | Compute the first one | c | of the conjugate pair. | c %------------------------% c c %----------------% c | Compute x'(Ax) | c %----------------% call av(n, v(1,j), ax ) numr = ddot(n, v(1,j), 1, ax, 1) numi = ddot(n, v(1,j+1), 1, ax, 1) call av(n, v(1,j+1), ax) numr = numr + ddot(n,v(1,j+1),1,ax,1) numi = -numi + ddot(n,v(1,j),1,ax,1) c c %----------------% c | Compute x'(Mx) | c %----------------% c call mv(n, v(1,j), ax ) denr = ddot(n, v(1,j), 1, ax, 1) deni = ddot(n, v(1,j+1), 1, ax, 1) call mv(n, v(1,j+1), ax) denr = denr + ddot(n,v(1,j+1),1,ax,1) deni = -deni + ddot(n,v(1,j),1, ax,1) c c %----------------% c | d=x'(Ax)/x'(Mx)| c %----------------% c d(j,1) = (numr*denr+numi*deni) / & dlapy2(denr, deni) d(j,2) = (numi*denr-numr*deni) / & dlapy2(denr, deni) first = .false. c else c c %------------------------------% c | Get the second eigenvalue of | c | the conjugate pair by taking | c | the conjugate of the last | c | eigenvalue computed. | c %------------------------------% c d(j,1) = d(j-1,1) d(j,2) = -d(j-1,2) first = .true. c end if c 70 continue c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c first = .true. do 80 j=1, nconv c if (d(j,2) .eq. zero) then c c %--------------------% c | Ritz value is real | c %--------------------% c call av(n, v(1,j), ax) call mv(n, v(1,j), mx) call daxpy(n, -d(j,1), mx, 1, ax, 1) d(j,3) = dnrm2(n, ax, 1) d(j,3) = d(j,3) / abs(d(j,1)) c else if (first) then c c %------------------------% c | Ritz value is complex | c | Residual of one Ritz | c | value of the conjugate | c | pair is computed. | c %------------------------% c call av(n, v(1,j), ax) call mv(n, v(1,j), mx) call daxpy(n, -d(j,1), mx, 1, ax, 1) call mv(n, v(1,j+1), mx) call daxpy(n, d(j,2), mx, 1, ax, 1) d(j,3) = dnrm2(n, ax, 1) call av(n, v(1,j+1), ax) call mv(n, v(1,j+1), mx) call daxpy(n, -d(j,1), mx, 1, ax, 1) call mv(n, v(1,j), mx) call daxpy(n, -d(j,2), mx, 1, ax, 1) d(j,3) = dlapy2( d(j,3), dnrm2(n, ax, 1) ) d(j,3) = d(j,3) / dlapy2(d(j,1),d(j,2)) d(j+1,3) = d(j,3) first = .false. else first = .true. end if c 80 continue c c c %-----------------------------% c | Display computed residuals. | c %-----------------------------% c call dmout(6, nconv, 3, d, maxncv, -6, & 'Ritz values (Real,Imag) and relative residuals') c end if c c %-------------------------------------------% c | Print additional convergence information. | c %-------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, ' _NDRV5 ' print *, ' ====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program dndrv5. | c %---------------------------% c 9000 continue c end c c========================================================================== c c matrix vector multiplication subroutine c subroutine mv (n, v, w) integer n, j Double precision & v(n), w(n), one, four parameter (one = 1.0D+0, four = 4.0D+0) c c Compute the matrix vector multiplication y<---M*x c where M is a n by n symmetric tridiagonal matrix with 4 on the c diagonal, 1 on the subdiagonal and superdiagonal. c w(1) = four*v(1) + one*v(2) do 10 j = 2,n-1 w(j) = one*v(j-1) + four*v(j) + one*v(j+1) 10 continue w(n) = one*v(n-1) + four*v(n) return end c------------------------------------------------------------------ subroutine av (n, v, w) integer n, j Double precision & v(n), w(n), three, two parameter (three = 3.0D+0, two = 2.0D+0) c c Compute the matrix vector multiplication y<---A*x c where M is a n by n symmetric tridiagonal matrix with 2 on the c diagonal, -2 on the subdiagonal and 3 on the superdiagonal. c w(1) = two*v(1) + three*v(2) do 10 j = 2,n-1 w(j) = -two*v(j-1) + two*v(j) + three*v(j+1) 10 continue w(n) = -two*v(n-1) + two*v(n) return end arpack-0.92.1/EXAMPLES/NONSYM/dndrv2.f0000644000175000017500000003756110776001577013622 00000000000000 program dndrv2 c c Simple program to illustrate the idea of reverse communication c in shift-invert mode for a standard nonsymmetric eigenvalue problem. c c We implement example two of ex-nonsym.doc in DOCUMENTS directory c c\Example-2 c ... Suppose we want to solve A*x = lambda*x in shift-invert mode, c where A is derived from the centered difference discretization c of the 1-dimensional convection-diffusion operator c (d^2u / dx^2) + rho*(du/dx) c on the interval [0,1] with zero Dirichlet boundary condition. c c ... The shift sigma is a real number. c c ... OP = inv[A-sigma*I] and B = I. c c ... Use mode 3 of DNAUPD. c c\BeginLib c c\Routines called: c dnaupd ARPACK reverse communication interface routine. c dneupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c dgttrf LAPACK tridiagonal factorization routine. c dgttrs LAPACK tridiagonal solve routine. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c daxpy Level 1 BLAS that computes y <- alpha*x+y. c dcopy Level 1 BLAS that copies one vector to another. c ddot Level 1 BLAS that computes the dot product of two vectors. c dnrm2 Level 1 BLAS that computes the norm of a vector. c av Matrix vector multiplication routine that computes A*x. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: ndrv2.F SID: 2.5 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c-------------------------------------------------------------------------- c c %-----------------------------% c | Define leading dimensions | c | for all arrays. | c | MAXN: Maximum dimension | c | of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %-----------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=10, maxncv=25, & ldv=maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), ipntr(14), ipiv(maxn) logical select(maxncv) Double precision & ax(maxn), d(maxncv,3), resid(maxn), & v(ldv, maxncv), workd(3*maxn), & workev(3*maxncv), & workl(3*maxncv*maxncv+6*maxncv), & dd(maxn), dl(maxn), du(maxn), & du2(maxn) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nev, ncv, lworkl, info, j, & ierr, nconv, maxitr, ishfts, mode Double precision & tol, h, s, & sigmar, sigmai, s1, s2, s3 logical first, rvec c c %------------% c | Parameters | c %------------% c Double precision & one, zero, two, rho common /convct/ rho parameter (one = 1.0D+0, zero = 0.0D+0, & two = 2.0D+0) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & ddot, dnrm2, dlapy2 external dgttrf, dgttrs, ddot, dnrm2, dlapy2 c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable statements | c %-----------------------% c c %--------------------------------------------------% c | The number N is the dimension of the matrix. A | c | standard eigenvalue problem is solved (BMAT = | c | 'I'). NEV is the number of eigenvalues (closest | c | to the shift SIGMAR) to be approximated. Since | c | the shift-invert mode is used, WHICH is set to | c | 'LM'. The user can modify NEV, NCV, SIGMAR to | c | solve problems of different sizes, and to get | c | different parts of the spectrum. However, The | c | following conditions must be satisfied: | c | N <= MAXN, | c | NEV <= MAXNEV, | c | NEV + 2 <= NCV <= MAXNCV | c %--------------------------------------------------% c n = 100 nev = 4 ncv = 20 if ( n .gt. maxn ) then print *, ' ERROR with _NDRV2: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NDRV2: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NDRV2: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'I' which = 'LM' sigmar = 1.0D+0 sigmai = 0.0D+0 c c %----------------------------------------------------% c | Construct C = A - SIGMA*I in real arithmetic, and | c | factor C in real arithmetic using LAPACK | c | subroutine dgttrf. The matrix A is chosen to be | c | the tridiagonal matrix derived from standard | c | central difference of the 1-d convection diffusion | c | operator u" + rho*u' on the interval [0, 1] with | c | zero Dirichlet boundary condition. | c %----------------------------------------------------% c rho = 1.0D+1 h = one / dble(n+1) s = rho*h / two c s1 = -one-s s2 = two - sigmar s3 = -one+s c do 10 j = 1, n-1 dl(j) = s1 dd(j) = s2 du(j) = s3 10 continue dd(n) = s2 c call dgttrf(n, dl, dd, du, du2, ipiv, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrf in _NDRV2.' print*, ' ' go to 9000 end if c c %-----------------------------------------------------% c | The work array WORKL is used in DNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in DNAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = 3*ncv**2+6*ncv tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | This program uses exact shifts with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 3 of DNAUPD is used | c | (IPARAM(7) = 3). All these options can be | c | changed by the user. For details see the | c | documentation in DNAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 3 iparam(1) = ishfts iparam(3) = maxitr iparam(7) = mode c c %-------------------------------------------% c | M A I N L O O P (Reverse communication) | c %-------------------------------------------% c 20 continue c c %---------------------------------------------% c | Repeatedly call the routine DNAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call dnaupd ( ido, bmat, n, which, nev, tol, resid, & ncv, v, ldv, iparam, ipntr, workd, workl, lworkl, & info ) c if ( ido .eq. -1 .or. ido .eq. 1) then c c %-------------------------------------------% c | Perform y <--- OP*x = inv[A-SIGMA*I]*x | c | The user should supply his/her own linear | c | system solver here that takes | c | workd(ipntr(1)) as the input, and returns | c | the result to workd(ipntr(2)). | c %-------------------------------------------% c call dcopy( n, workd(ipntr(1)), 1, workd(ipntr(2)), 1) c call dgttrs('N', n, 1, dl, dd, du, du2, ipiv, & workd(ipntr(2)), n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrs in _NDRV2.' print*, ' ' go to 9000 end if c c %-----------------------------------------% c | L O O P B A C K to call DNAUPD again. | c %-----------------------------------------% c go to 20 c end if c c %-----------------------------------------% c | Either we have convergence, or there is | c | an error. | c %-----------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message, check the | c | documentation in DNAUPD. | c %--------------------------% c print *, ' ' print *, ' Error with _naupd, info = ', info print *, ' Check the documentation in _naupd.' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using DNEUPD. | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may also be computed now if | c | desired. (indicated by rvec = .true.) | c %-------------------------------------------% c rvec = .true. c call dneupd ( rvec, 'A', select, d, d(1,2), v, ldv, & sigmar, sigmai, workev, bmat, n, which, nev, tol, & resid, ncv, v, ldv, iparam, ipntr, workd, & workl, lworkl, ierr ) c c %-----------------------------------------------% c | The real part of the eigenvalue is returned | c | in the first column of the two dimensional | c | array D, and the imaginary part is returned | c | in the second column of D. The corresponding | c | eigenvectors are returned in the first NEV | c | columns of the two dimensional array V if | c | requested. Otherwise, an orthogonal basis | c | for the invariant subspace corresponding to | c | the eigenvalues in D is returned in V. | c %-----------------------------------------------% c if ( ierr .ne. 0 ) then c c %------------------------------------% c | Error condition: | c | Check the documentation of DNEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _neupd, info = ', ierr print *, ' Check the documentation of _neupd. ' print *, ' ' c else c first = .true. nconv = iparam(5) do 30 j=1, nconv c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c if (d(j,2) .eq. zero) then c c %--------------------% c | Ritz value is real | c %--------------------% c call av(n, v(1,j), ax) call daxpy(n, -d(j,1), v(1,j), 1, ax, 1) d(j,3) = dnrm2(n, ax, 1) d(j,3) = d(j,3) / abs(d(j,1)) c else if (first) then c c %------------------------% c | Ritz value is complex | c | Residual of one Ritz | c | value of the conjugate | c | pair is computed. | c %------------------------% c call av(n, v(1,j), ax) call daxpy(n, -d(j,1), v(1,j), 1, ax, 1) call daxpy(n, d(j,2), v(1,j+1), 1, ax, 1) d(j,3) = dnrm2(n, ax, 1) call av(n, v(1,j+1), ax) call daxpy(n, -d(j,2), v(1,j), 1, ax, 1) call daxpy(n, -d(j,1), v(1,j+1), 1, ax, 1) d(j,3) = dlapy2( d(j,3), dnrm2(n, ax, 1) ) d(j+1,3) = d(j,3) first = .false. else first = .true. end if c 30 continue c c %-----------------------------% c | Display computed residuals. | c %-----------------------------% c call dmout(6, nconv, 3, d, maxncv, -6, & 'Ritz values (Real,Imag) and relative residuals') c end if c c %-------------------------------------------% c | Print additional convergence information. | c %-------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, ' _NDRV2 ' print *, ' ====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program dndrv2. | c %---------------------------% c 9000 continue c end c c------------------------------------------------------------------- c c matrix vector multiplication subroutine c subroutine av (n, v, w) integer n, j Double precision & v(n), w(n), rho, two, one, dd, dl, du, s, h common /convct/ rho parameter (one = 1.0D+0, two = 2.0D+0 ) c c Compute the matrix vector multiplication y<---A*x c where A is a n by n nonsymmetric tridiagonal matrix derived from c the central difference discretization of the 1-dimensional c convection diffusion operator on the interval [0,1] with c zero Dirichlet boundary condition. c c h = one / dble(n+1) s = rho *h / two dd = two dl = -one - s du = -one + s c w(1) = dd*v(1) + du*v(2) do 10 j = 2,n-1 w(j) = dl*v(j-1) + dd*v(j) + du*v(j+1) 10 continue w(n) = dl*v(n-1) + dd*v(n) return end arpack-0.92.1/EXAMPLES/NONSYM/sndrv2.f0000644000175000017500000003746510776001577013644 00000000000000 program sndrv2 c c Simple program to illustrate the idea of reverse communication c in shift-invert mode for a standard nonsymmetric eigenvalue problem. c c We implement example two of ex-nonsym.doc in DOCUMENTS directory c c\Example-2 c ... Suppose we want to solve A*x = lambda*x in shift-invert mode, c where A is derived from the centered difference discretization c of the 1-dimensional convection-diffusion operator c (d^2u / dx^2) + rho*(du/dx) c on the interval [0,1] with zero Dirichlet boundary condition. c c ... The shift sigma is a real number. c c ... OP = inv[A-sigma*I] and B = I. c c ... Use mode 3 of SNAUPD. c c\BeginLib c c\Routines called: c snaupd ARPACK reverse communication interface routine. c sneupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c sgttrf LAPACK tridiagonal factorization routine. c sgttrs LAPACK tridiagonal solve routine. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c saxpy Level 1 BLAS that computes y <- alpha*x+y. c scopy Level 1 BLAS that copies one vector to another. c sdot Level 1 BLAS that computes the dot product of two vectors. c snrm2 Level 1 BLAS that computes the norm of a vector. c av Matrix vector multiplication routine that computes A*x. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: ndrv2.F SID: 2.5 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c-------------------------------------------------------------------------- c c %-----------------------------% c | Define leading dimensions | c | for all arrays. | c | MAXN: Maximum dimension | c | of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %-----------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=10, maxncv=25, & ldv=maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), ipntr(14), ipiv(maxn) logical select(maxncv) Real & ax(maxn), d(maxncv,3), resid(maxn), & v(ldv, maxncv), workd(3*maxn), & workev(3*maxncv), & workl(3*maxncv*maxncv+6*maxncv), & dd(maxn), dl(maxn), du(maxn), & du2(maxn) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nev, ncv, lworkl, info, j, & ierr, nconv, maxitr, ishfts, mode Real & tol, h, s, & sigmar, sigmai, s1, s2, s3 logical first, rvec c c %------------% c | Parameters | c %------------% c Real & one, zero, two, rho common /convct/ rho parameter (one = 1.0E+0, zero = 0.0E+0, & two = 2.0E+0) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & sdot, snrm2, slapy2 external sgttrf, sgttrs, sdot, snrm2, slapy2 c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable statements | c %-----------------------% c c %--------------------------------------------------% c | The number N is the dimension of the matrix. A | c | standard eigenvalue problem is solved (BMAT = | c | 'I'). NEV is the number of eigenvalues (closest | c | to the shift SIGMAR) to be approximated. Since | c | the shift-invert mode is used, WHICH is set to | c | 'LM'. The user can modify NEV, NCV, SIGMAR to | c | solve problems of different sizes, and to get | c | different parts of the spectrum. However, The | c | following conditions must be satisfied: | c | N <= MAXN, | c | NEV <= MAXNEV, | c | NEV + 2 <= NCV <= MAXNCV | c %--------------------------------------------------% c n = 100 nev = 4 ncv = 20 if ( n .gt. maxn ) then print *, ' ERROR with _NDRV2: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NDRV2: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NDRV2: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'I' which = 'LM' sigmar = 1.0E+0 sigmai = 0.0E+0 c c %----------------------------------------------------% c | Construct C = A - SIGMA*I in real arithmetic, and | c | factor C in real arithmetic using LAPACK | c | subroutine sgttrf. The matrix A is chosen to be | c | the tridiagonal matrix derived from standard | c | central difference of the 1-d convection diffusion | c | operator u" + rho*u' on the interval [0, 1] with | c | zero Dirichlet boundary condition. | c %----------------------------------------------------% c rho = 1.0E+1 h = one / real(n+1) s = rho*h / two c s1 = -one-s s2 = two - sigmar s3 = -one+s c do 10 j = 1, n-1 dl(j) = s1 dd(j) = s2 du(j) = s3 10 continue dd(n) = s2 c call sgttrf(n, dl, dd, du, du2, ipiv, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrf in _NDRV2.' print*, ' ' go to 9000 end if c c %-----------------------------------------------------% c | The work array WORKL is used in SNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in SNAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = 3*ncv**2+6*ncv tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | This program uses exact shifts with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 3 of SNAUPD is used | c | (IPARAM(7) = 3). All these options can be | c | changed by the user. For details see the | c | documentation in SNAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 3 iparam(1) = ishfts iparam(3) = maxitr iparam(7) = mode c c %-------------------------------------------% c | M A I N L O O P (Reverse communication) | c %-------------------------------------------% c 20 continue c c %---------------------------------------------% c | Repeatedly call the routine SNAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call snaupd ( ido, bmat, n, which, nev, tol, resid, & ncv, v, ldv, iparam, ipntr, workd, workl, lworkl, & info ) c if ( ido .eq. -1 .or. ido .eq. 1) then c c %-------------------------------------------% c | Perform y <--- OP*x = inv[A-SIGMA*I]*x | c | The user should supply his/her own linear | c | system solver here that takes | c | workd(ipntr(1)) as the input, and returns | c | the result to workd(ipntr(2)). | c %-------------------------------------------% c call scopy( n, workd(ipntr(1)), 1, workd(ipntr(2)), 1) c call sgttrs('N', n, 1, dl, dd, du, du2, ipiv, & workd(ipntr(2)), n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrs in _NDRV2.' print*, ' ' go to 9000 end if c c %-----------------------------------------% c | L O O P B A C K to call SNAUPD again. | c %-----------------------------------------% c go to 20 c end if c c %-----------------------------------------% c | Either we have convergence, or there is | c | an error. | c %-----------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message, check the | c | documentation in SNAUPD. | c %--------------------------% c print *, ' ' print *, ' Error with _naupd, info = ', info print *, ' Check the documentation in _naupd.' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using SNEUPD. | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may also be computed now if | c | desired. (indicated by rvec = .true.) | c %-------------------------------------------% c rvec = .true. c call sneupd ( rvec, 'A', select, d, d(1,2), v, ldv, & sigmar, sigmai, workev, bmat, n, which, nev, tol, & resid, ncv, v, ldv, iparam, ipntr, workd, & workl, lworkl, ierr ) c c %-----------------------------------------------% c | The real part of the eigenvalue is returned | c | in the first column of the two dimensional | c | array D, and the imaginary part is returned | c | in the second column of D. The corresponding | c | eigenvectors are returned in the first NEV | c | columns of the two dimensional array V if | c | requested. Otherwise, an orthogonal basis | c | for the invariant subspace corresponding to | c | the eigenvalues in D is returned in V. | c %-----------------------------------------------% c if ( ierr .ne. 0 ) then c c %------------------------------------% c | Error condition: | c | Check the documentation of SNEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _neupd, info = ', ierr print *, ' Check the documentation of _neupd. ' print *, ' ' c else c first = .true. nconv = iparam(5) do 30 j=1, nconv c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c if (d(j,2) .eq. zero) then c c %--------------------% c | Ritz value is real | c %--------------------% c call av(n, v(1,j), ax) call saxpy(n, -d(j,1), v(1,j), 1, ax, 1) d(j,3) = snrm2(n, ax, 1) d(j,3) = d(j,3) / abs(d(j,1)) c else if (first) then c c %------------------------% c | Ritz value is complex | c | Residual of one Ritz | c | value of the conjugate | c | pair is computed. | c %------------------------% c call av(n, v(1,j), ax) call saxpy(n, -d(j,1), v(1,j), 1, ax, 1) call saxpy(n, d(j,2), v(1,j+1), 1, ax, 1) d(j,3) = snrm2(n, ax, 1) call av(n, v(1,j+1), ax) call saxpy(n, -d(j,2), v(1,j), 1, ax, 1) call saxpy(n, -d(j,1), v(1,j+1), 1, ax, 1) d(j,3) = slapy2( d(j,3), snrm2(n, ax, 1) ) d(j+1,3) = d(j,3) first = .false. else first = .true. end if c 30 continue c c %-----------------------------% c | Display computed residuals. | c %-----------------------------% c call smout(6, nconv, 3, d, maxncv, -6, & 'Ritz values (Real,Imag) and relative residuals') c end if c c %-------------------------------------------% c | Print additional convergence information. | c %-------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, ' _NDRV2 ' print *, ' ====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program sndrv2. | c %---------------------------% c 9000 continue c end c c------------------------------------------------------------------- c c matrix vector multiplication subroutine c subroutine av (n, v, w) integer n, j Real & v(n), w(n), rho, two, one, dd, dl, du, s, h common /convct/ rho parameter (one = 1.0E+0, two = 2.0E+0 ) c c Compute the matrix vector multiplication y<---A*x c where A is a n by n nonsymmetric tridiagonal matrix derived from c the central difference discretization of the 1-dimensional c convection diffusion operator on the interval [0,1] with c zero Dirichlet boundary condition. c c h = one / real(n+1) s = rho *h / two dd = two dl = -one - s du = -one + s c w(1) = dd*v(1) + du*v(2) do 10 j = 2,n-1 w(j) = dl*v(j-1) + dd*v(j) + du*v(j+1) 10 continue w(n) = dl*v(n-1) + dd*v(n) return end arpack-0.92.1/EXAMPLES/NONSYM/sndrv6.f0000644000175000017500000005335510776001577013644 00000000000000 program sndrv6 c c Simple program to illustrate the idea of reverse communication c in shift-invert mode for a generalized nonsymmetric eigenvalue problem. c c We implement example six of ex-nonsym.doc in DOCUMENTS directory c c\Example-6 c c ... Suppose we want to solve A*x = lambda*B*x in shift-invert mode c The matrix A is the tridiagonal matrix with 2 on the diagonal, c -2 on the subdiagonal and 3 on the superdiagonal. The matrix M c is the tridiagonal matrix with 4 on the diagonal and 1 on the c off-diagonals. c ... The shift sigma is a complex number (sigmar, sigmai). c ... OP = Imaginary_Part{inv[A-(SIGMAR,SIGMAI)*M]*M and B = M. c ... Use mode 4 of SNAUPD. c c\BeginLib c c\Routines called: c snaupd ARPACK reverse communication interface routine. c sneupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c cgttrf LAPACK complex matrix factorization routine. c cgttrs LAPACK complex linear system solve routine. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c saxpy Level 1 BLAS that computes y <- alpha*x+y. c sdot Level 1 BLAS that computes the dot product of two vectors. c snrm2 Level 1 BLAS that computes the norm of a vector. c av Matrix vector subroutine that computes A*x. c mv Matrix vector subroutine that computes M*x. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: ndrv6.F SID: 2.5 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c------------------------------------------------------------------------- c c %-----------------------------% c | Define leading dimensions | c | for all arrays. | c | MAXN: Maximum dimension | c | of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %-----------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=10, maxncv=25, & ldv=maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), ipntr(14), ipiv(maxn) logical select(maxncv) Real & ax(maxn), mx(maxn), d(maxncv,3), resid(maxn), & v(ldv,maxncv), workd(3*maxn), & workev(3*maxncv), & workl(3*maxncv*maxncv+6*maxncv) Complex & cdd(maxn), cdl(maxn), cdu(maxn), & cdu2(maxn), ctemp(maxn) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nev, ncv, lworkl, info, ierr, j, & nconv, maxitr, ishfts, mode Real & tol, numr, numi, denr, deni, sigmar, sigmai Complex & c1, c2, c3 logical first, rvec c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c external cgttrf, cgttrs Real & sdot, snrm2, slapy2 external sdot, snrm2, slapy2 c c %------------% c | Parameters | c %------------% c Real & zero parameter (zero = 0.0E+0) c c %--------------------% c | Intrinsic Function | c %--------------------% c intrinsic aimag, cmplx, abs c c %-----------------------% c | Executable statements | c %-----------------------% c c %----------------------------------------------------% c | The number N is the dimension of the matrix. A | c | generalized eigenvalue problem is solved (BMAT = | c | 'G'). NEV is the number of eigenvalues (closest | c | to the shift (SIGMAR,SIGMAI)) to be approximated. | c | Since the shift-invert mode is used, WHICH is set | c | to 'LM'. The user can modify NEV, NCV, SIGMA to | c | solve problems of different sizes, and to get | c | different parts of the spectrum. However, The | c | following conditions must be satisfied: | c | N <= MAXN, | c | NEV <= MAXNEV, | c | NEV + 2 <= NCV <= MAXNCV | c %----------------------------------------------------% c n = 100 nev = 4 ncv = 20 if ( n .gt. maxn ) then print *, ' ERROR with _NDRV6: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NDRV6: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NDRV6: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' sigmar = 4.0E-1 sigmai = 6.0E-1 c c %----------------------------------------------------% c | Construct C = A - (SIGMAR,SIGMAI)*M in complex | c | arithmetic, and factor C in complex arithmetic | c | (using LAPACK subroutine cgttrf). The matrix A is | c | chosen to be the tridiagonal matrix with -2 on the | c | subdiagonal, 2 on the diagonal and 3 on the | c | superdiagonal. The matrix M is chosen to be the | c | symmetric tridiagonal matrix with 4 on the | c | diagonal and 1 on the off-diagonals. | c %----------------------------------------------------% c c1 = cmplx(-2.0E+0-sigmar, -sigmai) c2 = cmplx( 2.0E+0-4.0E+0*sigmar, -4.0E+0*sigmai) c3 = cmplx( 3.0E+0-sigmar, -sigmai) c do 10 j = 1, n-1 cdl(j) = c1 cdd(j) = c2 cdu(j) = c3 10 continue cdd(n) = c2 c call cgttrf(n, cdl, cdd, cdu, cdu2, ipiv, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrf in _NDRV6.' print*, ' ' go to 9000 end if c c %-----------------------------------------------------% c | The work array WORKL is used in SNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in SNAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = 3*ncv**2+6*ncv tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | This program uses exact shift with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 3 of SNAUPD is used | c | (IPARAM(7) = 3). All these options can be | c | changed by the user. For details, see the | c | documentation in SNAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 3 c iparam(1) = ishfts iparam(3) = maxitr iparam(7) = mode c c %------------------------------------------% c | M A I N L O O P(Reverse communication) | c %------------------------------------------% c 20 continue c c %---------------------------------------------% c | Repeatedly call the routine SNAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call snaupd ( ido, bmat, n, which, nev, tol, resid, & ncv, v, ldv, iparam, ipntr, workd, & workl, lworkl, info ) c if (ido .eq. -1) then c c %------------------------------------------------------------% c | Perform | c | y <--- OP*x = Imaginary_Part{inv[A-(SIGMAR,SIGMAI)*M]*M*x} | c | to force starting vector into the range of OP. The user | c | should supply his/her own matrix vector multiplication | c | routine and a complex linear system solver. The matrix | c | vector multiplication routine should take workd(ipntr(1)) | c | as the input. The final result (a real vector) should be | c | returned to workd(ipntr(2)). | c %------------------------------------------------------------% c call mv (n, workd(ipntr(1)), workd(ipntr(2))) do 30 j = 1, n ctemp(j) = cmplx(workd(ipntr(2)+j-1)) 30 continue c call cgttrs('N', n, 1, cdl, cdd, cdu, cdu2, ipiv, & ctemp, maxn, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrs in _NDRV6.' print*, ' ' go to 9000 end if do 40 j = 1, n workd(ipntr(2)+j-1) = aimag(ctemp(j)) 40 continue c c %-----------------------------------------% c | L O O P B A C K to call SNAUPD again. | c %-----------------------------------------% c go to 20 c else if ( ido .eq. 1) then c c %------------------------------------------------------------% c | Perform | c | y <--- OP*x = Imaginary_Part{inv[A-(SIGMAR,SIGMAI)*M]*M*x} | c | M*x has been saved in workd(ipntr(3)). The user only need | c | the complex linear system solver here that takes | c | complex[workd(ipntr(3))] as input, and returns the result | c | to workd(ipntr(2)). | c %------------------------------------------------------------% c do 50 j = 1,n ctemp(j) = cmplx(workd(ipntr(3)+j-1)) 50 continue call cgttrs ('N', n, 1, cdl, cdd, cdu, cdu2, ipiv, & ctemp, maxn, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrs in _NDRV6.' print*, ' ' go to 9000 end if do 60 j = 1, n workd(ipntr(2)+j-1) = aimag(ctemp(j)) 60 continue c c %-----------------------------------------% c | L O O P B A C K to call SNAUPD again. | c %-----------------------------------------% c go to 20 c else if ( ido .eq. 2) then c c %---------------------------------------------% c | Perform y <--- M*x | c | Need matrix vector multiplication routine | c | here that takes workd(ipntr(1)) as input | c | and returns the result to workd(ipntr(2)). | c %---------------------------------------------% c call mv (n, workd(ipntr(1)), workd(ipntr(2))) c c %-----------------------------------------% c | L O O P B A C K to call SNAUPD again. | c %-----------------------------------------% c go to 20 c end if c c %-----------------------------------------% c | Either we have convergence, or there is | c | an error. | c %-----------------------------------------% c c if ( info .lt. 0 ) then c c %--------------------------% c | Error message, check the | c | documentation in SNAUPD. | c %--------------------------% c print *, ' ' print *, ' Error with _naupd, info = ',info print *, ' Check the documentation of _naupd.' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using SNEUPD. | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may also be computed now if | c | desired. (indicated by rvec = .true.) | c %-------------------------------------------% c rvec = .true. call sneupd ( rvec, 'A', select, d, d(1,2), v, ldv, & sigmar, sigmai, workev, bmat, n, which, nev, tol, & resid, ncv, v, ldv, iparam, ipntr, workd, & workl, lworkl, ierr ) c c %-----------------------------------------------% c | The real part of the eigenvalue is returned | c | in the first column of the two dimensional | c | array D, and the IMAGINARY part is returned | c | in the second column of D. The corresponding | c | eigenvectors are returned in the first NEV | c | columns of the two dimensional array V if | c | requested. Otherwise, an orthogonal basis | c | for the invariant subspace corresponding to | c | the eigenvalues in D is returned in V. | c %-----------------------------------------------% c if ( ierr .ne. 0) then c c %------------------------------------% c | Error condition: | c | Check the documentation of SNEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _neupd, info = ', ierr print *, ' Check the documentation of _neupd. ' print *, ' ' c else c first = .true. nconv = iparam(5) do 70 j=1, nconv c c %-------------------------------------% c | Use Rayleigh Quotient to recover | c | eigenvalues of the original problem.| c %-------------------------------------% c if ( d(j,2) .eq. zero) then c c %----------------------------% c | Eigenvalue is real. | c | Compute d = x'(Ax)/x'(Mx). | c %----------------------------% c call av(n, v(1,j), ax ) numr = sdot(n, v(1,j), 1, ax, 1) call mv(n, v(1,j), ax ) denr = sdot(n, v(1,j), 1, ax, 1) d(j,1) = numr / denr c else if (first) then c c %------------------------% c | Eigenvalue is complex. | c | Compute the first one | c | of the conjugate pair. | c %------------------------% c c %----------------% c | Compute x'(Ax) | c %----------------% c call av(n, v(1,j), ax ) numr = sdot(n, v(1,j), 1, ax, 1) numi = sdot(n, v(1,j+1), 1, ax, 1) call av(n, v(1,j+1), ax) numr = numr + sdot(n,v(1,j+1),1,ax,1) numi = -numi + sdot(n,v(1,j),1,ax,1) c c %----------------% c | Compute x'(Mx) | c %----------------% c call mv(n, v(1,j), ax ) denr = sdot(n, v(1,j), 1, ax, 1) deni = sdot(n, v(1,j+1), 1, ax, 1) call mv(n, v(1,j+1), ax) denr = denr + sdot(n,v(1,j+1),1,ax,1) deni = -deni + sdot(n,v(1,j),1, ax,1) c c %----------------% c | d=x'(Ax)/x'(Mx)| c %----------------% c d(j,1) = (numr*denr+numi*deni) / & slapy2(denr, deni) d(j,2) = (numi*denr-numr*deni) / & slapy2(denr, deni) first = .false. c else c c %------------------------------% c | Get the second eigenvalue of | c | the conjugate pair by taking | c | the conjugate of the last | c | eigenvalue computed. | c %------------------------------% c d(j,1) = d(j-1,1) d(j,2) = -d(j-1,2) first = .true. c end if c 70 continue c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c first = .true. nconv = iparam(5) do 80 j=1, nconv c if (d(j,2) .eq. zero) then c c %--------------------% c | Ritz value is real | c %--------------------% c call av(n, v(1,j), ax) call mv(n, v(1,j), mx) call saxpy(n, -d(j,1), mx, 1, ax, 1) d(j,3) = snrm2(n, ax, 1) d(j,3) = d(j,3) / abs(d(j,1)) c else if (first) then c c %------------------------% c | Ritz value is complex | c | Residual of one Ritz | c | value of the conjugate | c | pair is computed. | c %------------------------% c call av(n, v(1,j), ax) call mv(n, v(1,j), mx) call saxpy(n, -d(j,1), mx, 1, ax, 1) call mv(n, v(1,j+1), mx) call saxpy(n, d(j,2), mx, 1, ax, 1) d(j,3) = snrm2(n, ax, 1) call av(n, v(1,j+1), ax) call mv(n, v(1,j+1), mx) call saxpy(n, -d(j,1), mx, 1, ax, 1) call mv(n, v(1,j), mx) call saxpy(n, -d(j,2), mx, 1, ax, 1) d(j,3) = slapy2( d(j,3), snrm2(n, ax, 1) ) d(j,3) = d(j,3) / slapy2(d(j,1),d(j,2)) d(j+1,3) = d(j,3) first = .false. else first = .true. end if c 80 continue c c %-----------------------------% c | Display computed residuals. | c %-----------------------------% c call smout(6, nconv, 3, d, maxncv, -6, & 'Ritz values (Real,Imag) and relative residuals') c end if c c %-------------------------------------------% c | Print additional convergence information. | c %-------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, ' _NDRV6 ' print *, ' ====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program sndrv6. | c %---------------------------% c 9000 continue c end c c========================================================================== c c matrix vector multiplication subroutine c subroutine mv (n, v, w) integer n, j Real & v(n), w(n), one, four parameter (one = 1.0E+0, four = 4.0E+0) c c Compute the matrix vector multiplication y<---M*x c where M is a n by n symmetric tridiagonal matrix with 4 on the c diagonal, 1 on the subdiagonal and superdiagonal. c w(1) = four*v(1) + one*v(2) do 10 j = 2,n-1 w(j) = one*v(j-1) + four*v(j) + one*v(j+1) 10 continue w(n) = one*v(n-1) + four*v(n) return end c------------------------------------------------------------------ subroutine av (n, v, w) integer n, j Real & v(n), w(n), three, two parameter (three = 3.0E+0, two = 2.0E+0) c c Compute the matrix vector multiplication y<---A*x c where M is a n by n symmetric tridiagonal matrix with 2 on the c diagonal, -2 on the subdiagonal and 3 on the superdiagonal. c w(1) = two*v(1) + three*v(2) do 10 j = 2,n-1 w(j) = -two*v(j-1) + two*v(j) + three*v(j+1) 10 continue w(n) = -two*v(n-1) + two*v(n) return end arpack-0.92.1/EXAMPLES/NONSYM/sndrv4.f0000644000175000017500000004633010776001577013635 00000000000000 program sndrv4 c c Simple program to illustrate the idea of reverse communication c in shift-invert mode for a generalized nonsymmetric eigenvalue c problem. c c We implement example four of ex-nonsym.doc in DOCUMENTS directory c c\Example-4 c ... Suppose we want to solve A*x = lambda*B*x in inverse mode, c where A and B are derived from the finite element discretization c of the 1-dimensional convection-diffusion operator c (d^2u / dx^2) + rho*(du/dx) c on the interval [0,1] with zero Dirichlet boundary condition c using linear elements. c c ... The shift sigma is a real number. c c ... OP = inv[A-SIGMA*M]*M and B = M. c c ... Use mode 3 of SNAUPD. c c\BeginLib c c\Routines called: c snaupd ARPACK reverse communication interface routine. c sneupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c sgttrf LAPACK tridiagonal factorization routine. c sgttrs LAPACK tridiagonal linear system solve routine. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c saxpy Level 1 BLAS that computes y <- alpha*x+y. c scopy Level 1 BLAS that copies one vector to another. c sdot Level 1 BLAS that computes the dot product of two vectors. c snrm2 Level 1 BLAS that computes the norm of a vector. c av Matrix vector multiplication routine that computes A*x. c mv Matrix vector multiplication routine that computes M*x. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: ndrv4.F SID: 2.5 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c----------------------------------------------------------------------- c c %-----------------------------% c | Define leading dimensions | c | for all arrays. | c | MAXN: Maximum dimension | c | of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %-----------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=10, maxncv=25, & ldv=maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), ipntr(14), ipiv(maxn) logical select(maxncv) Real & ax(maxn), mx(maxn), d(maxncv,3), resid(maxn), & v(ldv,maxncv), workd(3*maxn), workev(3*maxncv), & workl(3*maxncv*maxncv+6*maxncv), & dd(maxn), dl(maxn), du(maxn), & du2(maxn) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nev, ncv, lworkl, info, ierr, j, & nconv, maxitr, ishfts, mode Real & tol, h, s, & sigmar, sigmai, s1, s2, s3 logical first, rvec c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & sdot, snrm2, slapy2 external sdot, snrm2, slapy2, sgttrf, sgttrs c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %------------% c | Parameters | c %------------% c Real & one, zero, two, six, rho common /convct/ rho parameter (one = 1.0E+0, zero = 0.0E+0, & two = 2.0E+0, six = 6.0E+0) c c %-----------------------% c | Executable statements | c %-----------------------% c c %----------------------------------------------------% c | The number N is the dimension of the matrix. A | c | generalized eigenvalue problem is solved (BMAT = | c | 'G'). NEV is the number of eigenvalues (closest | c | to SIGMAR) to be approximated. Since the | c | shift-invert mode is used, WHICH is set to 'LM'. | c | The user can modify NEV, NCV, SIGMAR to solve | c | problems of different sizes, and to get different | c | parts of the spectrum. However, The following | c | conditions must be satisfied: | c | N <= MAXN, | c | NEV <= MAXNEV, | c | NEV + 2 <= NCV <= MAXNCV | c %----------------------------------------------------% c n = 100 nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _NDRV4: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NDRV4: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NDRV4: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' sigmar = one sigmai = zero c c %--------------------------------------------------% c | Construct C = A - SIGMA*M in real arithmetic, | c | and factor C in real arithmetic (using LAPACK | c | subroutine sgttrf). The matrix A is chosen to be | c | the tridiagonal matrix derived from the standard | c | central difference discretization of the 1-d | c | convection-diffusion operator u" + rho*u' on the | c | interval [0, 1] with zero Dirichlet boundary | c | condition. The matrix M is the mass matrix | c | formed by using piecewise linear elements on | c | [0,1]. | c %--------------------------------------------------% c rho = 1.0E+1 h = one / real(n+1) s = rho / two c s1 = -one/h - s - sigmar*h/six s2 = two/h - 4.0E+0*sigmar*h/six s3 = -one/h + s - sigmar*h/six c do 10 j = 1, n-1 dl(j) = s1 dd(j) = s2 du(j) = s3 10 continue dd(n) = s2 c call sgttrf(n, dl, dd, du, du2, ipiv, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrf in _NDRV4.' print*, ' ' go to 9000 end if c c %-----------------------------------------------------% c | The work array WORKL is used in SNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in SNAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = 3*ncv**2+6*ncv tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | This program uses exact shifts with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 3 of SNAUPD is used | c | (IPARAM(7) = 3). All these options can be | c | changed by the user. For details, see the | c | documentation in SNAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 3 c iparam(1) = ishfts iparam(3) = maxitr iparam(7) = mode c c %------------------------------------------% c | M A I N L O O P(Reverse communication) | c %------------------------------------------% c 20 continue c c %---------------------------------------------% c | Repeatedly call the routine SNAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call snaupd ( ido, bmat, n, which, nev, tol, resid, & ncv, v, ldv, iparam, ipntr, workd, & workl, lworkl, info ) c if (ido .eq. -1) then c c %-------------------------------------------% c | Perform y <--- OP*x = inv[A-SIGMA*M]*M*x | c | to force starting vector into the range | c | of OP. The user should supply his/her | c | own matrix vector multiplication routine | c | and a linear system solver. The matrix | c | vector multiplication routine should take | c | workd(ipntr(1)) as the input. The final | c | result should be returned to | c | workd(ipntr(2)). | c %-------------------------------------------% c call mv (n, workd(ipntr(1)), workd(ipntr(2))) call sgttrs('N', n, 1, dl, dd, du, du2, ipiv, & workd(ipntr(2)), n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrs in _NDRV4.' print*, ' ' go to 9000 end if c c %-----------------------------------------% c | L O O P B A C K to call SNAUPD again. | c %-----------------------------------------% c go to 20 c else if ( ido .eq. 1) then c c %-----------------------------------------% c | Perform y <-- OP*x = inv[A-sigma*M]*M*x | c | M*x has been saved in workd(ipntr(3)). | c | The user only need the linear system | c | solver here that takes workd(ipntr(3)) | c | as input, and returns the result to | c | workd(ipntr(2)). | c %-----------------------------------------% c call scopy( n, workd(ipntr(3)), 1, workd(ipntr(2)), 1) call sgttrs ('N', n, 1, dl, dd, du, du2, ipiv, & workd(ipntr(2)), n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrs in _NDRV4.' print*, ' ' go to 9000 end if c c %-----------------------------------------% c | L O O P B A C K to call SNAUPD again. | c %-----------------------------------------% c go to 20 c else if ( ido .eq. 2) then c c %---------------------------------------------% c | Perform y <--- M*x | c | Need matrix vector multiplication routine | c | here that takes workd(ipntr(1)) as input | c | and returns the result to workd(ipntr(2)). | c %---------------------------------------------% c call mv (n, workd(ipntr(1)), workd(ipntr(2))) c c %-----------------------------------------% c | L O O P B A C K to call SNAUPD again. | c %-----------------------------------------% c go to 20 c end if c c c %-----------------------------------------% c | Either we have convergence, or there is | c | an error. | c %-----------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message, check the | c | documentation in SNAUPD. | c %--------------------------% c print *, ' ' print *, ' Error with _naupd, info = ', info print *, ' Check the documentation in _naupd.' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using SNEUPD. | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may also be computed now if | c | desired. (indicated by rvec = .true.) | c %-------------------------------------------% c rvec = .true. call sneupd ( rvec, 'A', select, d, d(1,2), v, ldv, & sigmar, sigmai, workev, bmat, n, which, nev, tol, & resid, ncv, v, ldv, iparam, ipntr, workd, & workl, lworkl, ierr ) c c %-----------------------------------------------% c | The real part of the eigenvalue is returned | c | in the first column of the two dimensional | c | array D, and the IMAGINARY part is returned | c | in the second column of D. The corresponding | c | eigenvectors are returned in the first NEV | c | columns of the two dimensional array V if | c | requested. Otherwise, an orthogonal basis | c | for the invariant subspace corresponding to | c | the eigenvalues in D is returned in V. | c %-----------------------------------------------% c if ( ierr .ne. 0) then c c %------------------------------------% c | Error condition: | c | Check the documentation of SNEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _neupd, info = ', ierr print *, ' Check the documentation of _neupd. ' print *, ' ' c else c first = .true. nconv = iparam(5) do 30 j=1, nconv c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c if (d(j,2) .eq. zero) then c c %--------------------% c | Ritz value is real | c %--------------------% c call av(n, v(1,j), ax) call mv(n, v(1,j), mx) call saxpy(n, -d(j,1), mx, 1, ax, 1) d(j,3) = snrm2(n, ax, 1) d(j,3) = d(j,3) / abs(d(j,1)) c else if (first) then c c %------------------------% c | Ritz value is complex. | c | Residual of one Ritz | c | value of the conjugate | c | pair is computed. | c %------------------------% c call av(n, v(1,j), ax) call mv(n, v(1,j), mx) call saxpy(n, -d(j,1), mx, 1, ax, 1) call mv(n, v(1,j+1), mx) call saxpy(n, d(j,2), mx, 1, ax, 1) d(j,3) = snrm2(n, ax, 1) call av(n, v(1,j+1), ax) call mv(n, v(1,j+1), mx) call saxpy(n, -d(j,1), mx, 1, ax, 1) call mv(n, v(1,j), mx) call saxpy(n, -d(j,2), mx, 1, ax, 1) d(j,3) = slapy2( d(j,3), snrm2(n, ax, 1) ) d(j,3) = d(j,3) / slapy2(d(j,1),d(j,2)) d(j+1,3) = d(j,3) first = .false. else first = .true. end if c 30 continue c c %-----------------------------% c | Display computed residuals. | c %-----------------------------% c call smout(6, nconv, 3, d, maxncv, -6, & 'Ritz values (Real,Imag) and relative residuals') c end if c c %-------------------------------------------% c | Print additional convergence information. | c %-------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, ' _NDRV4 ' print *, ' ====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program sndrv4. | c %---------------------------% c 9000 continue c end c c========================================================================== c c matrix vector multiplication subroutine c subroutine mv (n, v, w) integer n, j Real & v(n), w(n), one, four, six, h parameter (one = 1.0E+0, four = 4.0E+0, six = 6.0E+0) c c Compute the matrix vector multiplication y<---M*x c where M is mass matrix formed by using piecewise linear elements c on [0,1]. c w(1) = ( four*v(1) + one*v(2) ) / six do 10 j = 2,n-1 w(j) = ( one*v(j-1) + four*v(j) + one*v(j+1) ) / six 10 continue w(n) = ( one*v(n-1) + four*v(n) ) / six c h = one / real(n+1) call sscal(n, h, w, 1) return end c------------------------------------------------------------------ subroutine av (n, v, w) integer n, j Real & v(n), w(n), one, two, dd, dl, du, s, h, rho common /convct/ rho parameter (one = 1.0E+0, two = 2.0E+0) c c Compute the matrix vector multiplication y<---A*x c where A is obtained from the finite element discretization of the c 1-dimensional convection diffusion operator c d^u/dx^2 + rho*(du/dx) c on the interval [0,1] with zero Dirichlet boundary condition c using linear elements. c This routine is only used in residual calculation. c h = one / real(n+1) s = rho / two dd = two / h dl = -one/h - s du = -one/h + s c w(1) = dd*v(1) + du*v(2) do 10 j = 2,n-1 w(j) = dl*v(j-1) + dd*v(j) + du*v(j+1) 10 continue w(n) = dl*v(n-1) + dd*v(n) return end arpack-0.92.1/EXAMPLES/NONSYM/dndrv1.f0000644000175000017500000004037510776001577013616 00000000000000 program dndrv1 c c c Example program to illustrate the idea of reverse communication c for a standard nonsymmetric eigenvalue problem. c c We implement example one of ex-nonsym.doc in DOCUMENTS directory c c\Example-1 c ... Suppose we want to solve A*x = lambda*x in regular mode, c where A is obtained from the standard central difference c discretization of the convection-diffusion operator c (Laplacian u) + rho*(du / dx) c on the unit square [0,1]x[0,1] with zero Dirichlet boundary c condition. c c ... OP = A and B = I. c c ... Assume "call av (nx,x,y)" computes y = A*x.c c c ... Use mode 1 of DNAUPD. c c\BeginLib c c\Routines called: c dnaupd ARPACK reverse communication interface routine. c dneupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c daxpy Level 1 BLAS that computes y <- alpha*x+y. c dnrm2 Level 1 BLAS that computes the norm of a vector. c av Matrix vector multiplication routine that computes A*x. c tv Matrix vector multiplication routine that computes T*x, c where T is a tridiagonal matrix. It is used in routine c av. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: ndrv1.F SID: 2.5 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c--------------------------------------------------------------------------- c c %-----------------------------% c | Define maximum dimensions | c | for all arrays. | c | MAXN: Maximum dimension | c | of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %-----------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=12, maxncv=30, ldv=maxn) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), ipntr(14) logical select(maxncv) Double precision & ax(maxn), d(maxncv,3), resid(maxn), & v(ldv,maxncv), workd(3*maxn), & workev(3*maxncv), & workl(3*maxncv*maxncv+6*maxncv) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nx, nev, ncv, lworkl, info, j, & ierr, nconv, maxitr, ishfts, mode Double precision & tol, sigmar, sigmai logical first, rvec c c %------------% c | Parameters | c %------------% c Double precision & zero parameter (zero = 0.0D+0) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & dlapy2, dnrm2 external dlapy2, dnrm2, daxpy c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c %--------------------------------------------------% c | The number NX is the number of interior points | c | in the discretization of the 2-dimensional | c | convection-diffusion operator on the unit | c | square with zero Dirichlet boundary condition. | c | The number N(=NX*NX) is the dimension of the | c | matrix. A standard eigenvalue problem is | c | solved (BMAT = 'I'). NEV is the number of | c | eigenvalues to be approximated. The user can | c | modify NX, NEV, NCV, WHICH to solve problems of | c | different sizes, and to get different parts of | c | the spectrum. However, The following | c | conditions must be satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 2 <= NCV <= MAXNCV | c %--------------------------------------------------% c nx = 10 n = nx*nx nev = 4 ncv = 20 if ( n .gt. maxn ) then print *, ' ERROR with _NDRV1: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NDRV1: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NDRV1: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'I' which = 'SM' c c %-----------------------------------------------------% c | The work array WORKL is used in DNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in DNAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = 3*ncv**2+6*ncv tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | This program uses exact shifts with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 1 of DNAUPD is used | c | (IPARAM(7) = 1). All these options can be changed | c | by the user. For details see the documentation in | c | DNAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 1 c iparam(1) = ishfts iparam(3) = maxitr iparam(7) = mode c c %-------------------------------------------% c | M A I N L O O P (Reverse communication) | c %-------------------------------------------% c 10 continue c c %---------------------------------------------% c | Repeatedly call the routine DNAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call dnaupd ( ido, bmat, n, which, nev, tol, resid, & ncv, v, ldv, iparam, ipntr, workd, workl, lworkl, & info ) c if (ido .eq. -1 .or. ido .eq. 1) then c c %-------------------------------------------% c | Perform matrix vector multiplication | c | y <--- OP*x | c | The user should supply his/her own | c | matrix vector multiplication routine here | c | that takes workd(ipntr(1)) as the input | c | vector, and return the matrix vector | c | product to workd(ipntr(2)). | c %-------------------------------------------% c call av (nx, workd(ipntr(1)), workd(ipntr(2))) c c %-----------------------------------------% c | L O O P B A C K to call DNAUPD again. | c %-----------------------------------------% c go to 10 c end if c c %----------------------------------------% c | Either we have convergence or there is | c | an error. | c %----------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message, check the | c | documentation in DNAUPD. | c %--------------------------% c print *, ' ' print *, ' Error with _naupd, info = ', info print *, ' Check the documentation of _naupd' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using DNEUPD. | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may also be computed now if | c | desired. (indicated by rvec = .true.) | c %-------------------------------------------% c rvec = .true. c call dneupd ( rvec, 'A', select, d, d(1,2), v, ldv, & sigmar, sigmai, workev, bmat, n, which, nev, tol, & resid, ncv, v, ldv, iparam, ipntr, workd, workl, & lworkl, ierr ) c c %-----------------------------------------------% c | The real part of the eigenvalue is returned | c | in the first column of the two dimensional | c | array D, and the imaginary part is returned | c | in the second column of D. The corresponding | c | eigenvectors are returned in the first NEV | c | columns of the two dimensional array V if | c | requested. Otherwise, an orthogonal basis | c | for the invariant subspace corresponding to | c | the eigenvalues in D is returned in V. | c %-----------------------------------------------% c if ( ierr .ne. 0) then c c %------------------------------------% c | Error condition: | c | Check the documentation of DNEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _neupd, info = ', ierr print *, ' Check the documentation of _neupd. ' print *, ' ' c else c first = .true. nconv = iparam(5) do 20 j=1, nconv c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c if (d(j,2) .eq. zero) then c c %--------------------% c | Ritz value is real | c %--------------------% c call av(nx, v(1,j), ax) call daxpy(n, -d(j,1), v(1,j), 1, ax, 1) d(j,3) = dnrm2(n, ax, 1) d(j,3) = d(j,3) / abs(d(j,1)) c else if (first) then c c %------------------------% c | Ritz value is complex. | c | Residual of one Ritz | c | value of the conjugate | c | pair is computed. | c %------------------------% c call av(nx, v(1,j), ax) call daxpy(n, -d(j,1), v(1,j), 1, ax, 1) call daxpy(n, d(j,2), v(1,j+1), 1, ax, 1) d(j,3) = dnrm2(n, ax, 1) call av(nx, v(1,j+1), ax) call daxpy(n, -d(j,2), v(1,j), 1, ax, 1) call daxpy(n, -d(j,1), v(1,j+1), 1, ax, 1) d(j,3) = dlapy2( d(j,3), dnrm2(n, ax, 1) ) d(j,3) = d(j,3) / dlapy2(d(j,1),d(j,2)) d(j+1,3) = d(j,3) first = .false. else first = .true. end if c 20 continue c c %-----------------------------% c | Display computed residuals. | c %-----------------------------% c call dmout(6, nconv, 3, d, maxncv, -6, & 'Ritz values (Real,Imag) and relative residuals') end if c c %-------------------------------------------% c | Print additional convergence information. | c %-------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, ' _NDRV1 ' print *, ' ====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program dndrv1. | c %---------------------------% c 9000 continue c end c c========================================================================== c c matrix vector subroutine c c The matrix used is the 2 dimensional convection-diffusion c operator discretized using central difference. c subroutine av (nx, v, w) integer nx, j, lo Double precision & v(nx*nx), w(nx*nx), one, h2 parameter (one = 1.0D+0) external daxpy c c Computes w <--- OP*v, where OP is the nx*nx by nx*nx block c tridiagonal matrix c c | T -I | c |-I T -I | c OP = | -I T | c | ... -I| c | -I T| c c derived from the standard central difference discretization c of the 2 dimensional convection-diffusion operator c (Laplacian u) + rho*(du/dx) on a unit square with zero boundary c condition. c c When rho*h/2 <= 1, the discrete convection-diffusion operator c has real eigenvalues. When rho*h/2 > 1, it has COMPLEX c eigenvalues. c c The subroutine TV is called to compute y<---T*x. c c h2 = one / dble((nx+1)*(nx+1)) c call tv(nx,v(1),w(1)) call daxpy(nx, -one/h2, v(nx+1), 1, w(1), 1) c do 10 j = 2, nx-1 lo = (j-1)*nx call tv(nx, v(lo+1), w(lo+1)) call daxpy(nx, -one/h2, v(lo-nx+1), 1, w(lo+1), 1) call daxpy(nx, -one/h2, v(lo+nx+1), 1, w(lo+1), 1) 10 continue c lo = (nx-1)*nx call tv(nx, v(lo+1), w(lo+1)) call daxpy(nx, -one/h2, v(lo-nx+1), 1, w(lo+1), 1) c return end c========================================================================= subroutine tv (nx, x, y) c integer nx, j Double precision & x(nx), y(nx), h, h2, dd, dl, du c Double precision & one, zero, rho parameter (one = 1.0D+0, zero = 0.0D+0, & rho = 0.0D+0) c c Compute the matrix vector multiplication y<---T*x c where T is a nx by nx tridiagonal matrix with DD on the c diagonal, DL on the subdiagonal, and DU on the superdiagonal. c c When rho*h/2 <= 1, the discrete convection-diffusion operator c has real eigenvalues. When rho*h/2 > 1, it has COMPLEX c eigenvalues. c h = one / dble(nx+1) h2 = h*h dd = 4.0D+0 / h2 dl = -one / h2 - 5.0D-1*rho / h du = -one / h2 + 5.0D-1*rho / h c y(1) = dd*x(1) + du*x(2) do 10 j = 2,nx-1 y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1) 10 continue y(nx) = dl*x(nx-1) + dd*x(nx) return end arpack-0.92.1/EXAMPLES/NONSYM/dndrv6.f0000644000175000017500000005350110776001577013616 00000000000000 program dndrv6 c c Simple program to illustrate the idea of reverse communication c in shift-invert mode for a generalized nonsymmetric eigenvalue problem. c c We implement example six of ex-nonsym.doc in DOCUMENTS directory c c\Example-6 c c ... Suppose we want to solve A*x = lambda*B*x in shift-invert mode c The matrix A is the tridiagonal matrix with 2 on the diagonal, c -2 on the subdiagonal and 3 on the superdiagonal. The matrix M c is the tridiagonal matrix with 4 on the diagonal and 1 on the c off-diagonals. c ... The shift sigma is a complex number (sigmar, sigmai). c ... OP = Imaginary_Part{inv[A-(SIGMAR,SIGMAI)*M]*M and B = M. c ... Use mode 4 of DNAUPD. c c\BeginLib c c\Routines called: c dnaupd ARPACK reverse communication interface routine. c dneupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c zgttrf LAPACK complex matrix factorization routine. c zgttrs LAPACK complex linear system solve routine. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c daxpy Level 1 BLAS that computes y <- alpha*x+y. c ddot Level 1 BLAS that computes the dot product of two vectors. c dnrm2 Level 1 BLAS that computes the norm of a vector. c av Matrix vector subroutine that computes A*x. c mv Matrix vector subroutine that computes M*x. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: ndrv6.F SID: 2.5 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c------------------------------------------------------------------------- c c %-----------------------------% c | Define leading dimensions | c | for all arrays. | c | MAXN: Maximum dimension | c | of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %-----------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=10, maxncv=25, & ldv=maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), ipntr(14), ipiv(maxn) logical select(maxncv) Double precision & ax(maxn), mx(maxn), d(maxncv,3), resid(maxn), & v(ldv,maxncv), workd(3*maxn), & workev(3*maxncv), & workl(3*maxncv*maxncv+6*maxncv) Complex*16 & cdd(maxn), cdl(maxn), cdu(maxn), & cdu2(maxn), ctemp(maxn) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nev, ncv, lworkl, info, ierr, j, & nconv, maxitr, ishfts, mode Double precision & tol, numr, numi, denr, deni, sigmar, sigmai Complex*16 & c1, c2, c3 logical first, rvec c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c external zgttrf, zgttrs Double precision & ddot, dnrm2, dlapy2 external ddot, dnrm2, dlapy2 c c %------------% c | Parameters | c %------------% c Double precision & zero parameter (zero = 0.0D+0) c c %--------------------% c | Intrinsic Function | c %--------------------% c intrinsic dimag, dcmplx, abs c c %-----------------------% c | Executable statements | c %-----------------------% c c %----------------------------------------------------% c | The number N is the dimension of the matrix. A | c | generalized eigenvalue problem is solved (BMAT = | c | 'G'). NEV is the number of eigenvalues (closest | c | to the shift (SIGMAR,SIGMAI)) to be approximated. | c | Since the shift-invert mode is used, WHICH is set | c | to 'LM'. The user can modify NEV, NCV, SIGMA to | c | solve problems of different sizes, and to get | c | different parts of the spectrum. However, The | c | following conditions must be satisfied: | c | N <= MAXN, | c | NEV <= MAXNEV, | c | NEV + 2 <= NCV <= MAXNCV | c %----------------------------------------------------% c n = 100 nev = 4 ncv = 20 if ( n .gt. maxn ) then print *, ' ERROR with _NDRV6: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NDRV6: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NDRV6: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' sigmar = 4.0D-1 sigmai = 6.0D-1 c c %----------------------------------------------------% c | Construct C = A - (SIGMAR,SIGMAI)*M in complex | c | arithmetic, and factor C in complex arithmetic | c | (using LAPACK subroutine zgttrf). The matrix A is | c | chosen to be the tridiagonal matrix with -2 on the | c | subdiagonal, 2 on the diagonal and 3 on the | c | superdiagonal. The matrix M is chosen to be the | c | symmetric tridiagonal matrix with 4 on the | c | diagonal and 1 on the off-diagonals. | c %----------------------------------------------------% c c1 = dcmplx(-2.0D+0-sigmar, -sigmai) c2 = dcmplx( 2.0D+0-4.0D+0*sigmar, -4.0D+0*sigmai) c3 = dcmplx( 3.0D+0-sigmar, -sigmai) c do 10 j = 1, n-1 cdl(j) = c1 cdd(j) = c2 cdu(j) = c3 10 continue cdd(n) = c2 c call zgttrf(n, cdl, cdd, cdu, cdu2, ipiv, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrf in _NDRV6.' print*, ' ' go to 9000 end if c c %-----------------------------------------------------% c | The work array WORKL is used in DNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in DNAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = 3*ncv**2+6*ncv tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | This program uses exact shift with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 3 of DNAUPD is used | c | (IPARAM(7) = 3). All these options can be | c | changed by the user. For details, see the | c | documentation in DNAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 3 c iparam(1) = ishfts iparam(3) = maxitr iparam(7) = mode c c %------------------------------------------% c | M A I N L O O P(Reverse communication) | c %------------------------------------------% c 20 continue c c %---------------------------------------------% c | Repeatedly call the routine DNAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call dnaupd ( ido, bmat, n, which, nev, tol, resid, & ncv, v, ldv, iparam, ipntr, workd, & workl, lworkl, info ) c if (ido .eq. -1) then c c %------------------------------------------------------------% c | Perform | c | y <--- OP*x = Imaginary_Part{inv[A-(SIGMAR,SIGMAI)*M]*M*x} | c | to force starting vector into the range of OP. The user | c | should supply his/her own matrix vector multiplication | c | routine and a complex linear system solver. The matrix | c | vector multiplication routine should take workd(ipntr(1)) | c | as the input. The final result (a real vector) should be | c | returned to workd(ipntr(2)). | c %------------------------------------------------------------% c call mv (n, workd(ipntr(1)), workd(ipntr(2))) do 30 j = 1, n ctemp(j) = dcmplx(workd(ipntr(2)+j-1)) 30 continue c call zgttrs('N', n, 1, cdl, cdd, cdu, cdu2, ipiv, & ctemp, maxn, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrs in _NDRV6.' print*, ' ' go to 9000 end if do 40 j = 1, n workd(ipntr(2)+j-1) = dimag(ctemp(j)) 40 continue c c %-----------------------------------------% c | L O O P B A C K to call DNAUPD again. | c %-----------------------------------------% c go to 20 c else if ( ido .eq. 1) then c c %------------------------------------------------------------% c | Perform | c | y <--- OP*x = Imaginary_Part{inv[A-(SIGMAR,SIGMAI)*M]*M*x} | c | M*x has been saved in workd(ipntr(3)). The user only need | c | the complex linear system solver here that takes | c | complex[workd(ipntr(3))] as input, and returns the result | c | to workd(ipntr(2)). | c %------------------------------------------------------------% c do 50 j = 1,n ctemp(j) = dcmplx(workd(ipntr(3)+j-1)) 50 continue call zgttrs ('N', n, 1, cdl, cdd, cdu, cdu2, ipiv, & ctemp, maxn, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrs in _NDRV6.' print*, ' ' go to 9000 end if do 60 j = 1, n workd(ipntr(2)+j-1) = dimag(ctemp(j)) 60 continue c c %-----------------------------------------% c | L O O P B A C K to call DNAUPD again. | c %-----------------------------------------% c go to 20 c else if ( ido .eq. 2) then c c %---------------------------------------------% c | Perform y <--- M*x | c | Need matrix vector multiplication routine | c | here that takes workd(ipntr(1)) as input | c | and returns the result to workd(ipntr(2)). | c %---------------------------------------------% c call mv (n, workd(ipntr(1)), workd(ipntr(2))) c c %-----------------------------------------% c | L O O P B A C K to call DNAUPD again. | c %-----------------------------------------% c go to 20 c end if c c %-----------------------------------------% c | Either we have convergence, or there is | c | an error. | c %-----------------------------------------% c c if ( info .lt. 0 ) then c c %--------------------------% c | Error message, check the | c | documentation in DNAUPD. | c %--------------------------% c print *, ' ' print *, ' Error with _naupd, info = ',info print *, ' Check the documentation of _naupd.' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using DNEUPD. | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may also be computed now if | c | desired. (indicated by rvec = .true.) | c %-------------------------------------------% c rvec = .true. call dneupd ( rvec, 'A', select, d, d(1,2), v, ldv, & sigmar, sigmai, workev, bmat, n, which, nev, tol, & resid, ncv, v, ldv, iparam, ipntr, workd, & workl, lworkl, ierr ) c c %-----------------------------------------------% c | The real part of the eigenvalue is returned | c | in the first column of the two dimensional | c | array D, and the IMAGINARY part is returned | c | in the second column of D. The corresponding | c | eigenvectors are returned in the first NEV | c | columns of the two dimensional array V if | c | requested. Otherwise, an orthogonal basis | c | for the invariant subspace corresponding to | c | the eigenvalues in D is returned in V. | c %-----------------------------------------------% c if ( ierr .ne. 0) then c c %------------------------------------% c | Error condition: | c | Check the documentation of DNEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _neupd, info = ', ierr print *, ' Check the documentation of _neupd. ' print *, ' ' c else c first = .true. nconv = iparam(5) do 70 j=1, nconv c c %-------------------------------------% c | Use Rayleigh Quotient to recover | c | eigenvalues of the original problem.| c %-------------------------------------% c if ( d(j,2) .eq. zero) then c c %----------------------------% c | Eigenvalue is real. | c | Compute d = x'(Ax)/x'(Mx). | c %----------------------------% c call av(n, v(1,j), ax ) numr = ddot(n, v(1,j), 1, ax, 1) call mv(n, v(1,j), ax ) denr = ddot(n, v(1,j), 1, ax, 1) d(j,1) = numr / denr c else if (first) then c c %------------------------% c | Eigenvalue is complex. | c | Compute the first one | c | of the conjugate pair. | c %------------------------% c c %----------------% c | Compute x'(Ax) | c %----------------% c call av(n, v(1,j), ax ) numr = ddot(n, v(1,j), 1, ax, 1) numi = ddot(n, v(1,j+1), 1, ax, 1) call av(n, v(1,j+1), ax) numr = numr + ddot(n,v(1,j+1),1,ax,1) numi = -numi + ddot(n,v(1,j),1,ax,1) c c %----------------% c | Compute x'(Mx) | c %----------------% c call mv(n, v(1,j), ax ) denr = ddot(n, v(1,j), 1, ax, 1) deni = ddot(n, v(1,j+1), 1, ax, 1) call mv(n, v(1,j+1), ax) denr = denr + ddot(n,v(1,j+1),1,ax,1) deni = -deni + ddot(n,v(1,j),1, ax,1) c c %----------------% c | d=x'(Ax)/x'(Mx)| c %----------------% c d(j,1) = (numr*denr+numi*deni) / & dlapy2(denr, deni) d(j,2) = (numi*denr-numr*deni) / & dlapy2(denr, deni) first = .false. c else c c %------------------------------% c | Get the second eigenvalue of | c | the conjugate pair by taking | c | the conjugate of the last | c | eigenvalue computed. | c %------------------------------% c d(j,1) = d(j-1,1) d(j,2) = -d(j-1,2) first = .true. c end if c 70 continue c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c first = .true. nconv = iparam(5) do 80 j=1, nconv c if (d(j,2) .eq. zero) then c c %--------------------% c | Ritz value is real | c %--------------------% c call av(n, v(1,j), ax) call mv(n, v(1,j), mx) call daxpy(n, -d(j,1), mx, 1, ax, 1) d(j,3) = dnrm2(n, ax, 1) d(j,3) = d(j,3) / abs(d(j,1)) c else if (first) then c c %------------------------% c | Ritz value is complex | c | Residual of one Ritz | c | value of the conjugate | c | pair is computed. | c %------------------------% c call av(n, v(1,j), ax) call mv(n, v(1,j), mx) call daxpy(n, -d(j,1), mx, 1, ax, 1) call mv(n, v(1,j+1), mx) call daxpy(n, d(j,2), mx, 1, ax, 1) d(j,3) = dnrm2(n, ax, 1) call av(n, v(1,j+1), ax) call mv(n, v(1,j+1), mx) call daxpy(n, -d(j,1), mx, 1, ax, 1) call mv(n, v(1,j), mx) call daxpy(n, -d(j,2), mx, 1, ax, 1) d(j,3) = dlapy2( d(j,3), dnrm2(n, ax, 1) ) d(j,3) = d(j,3) / dlapy2(d(j,1),d(j,2)) d(j+1,3) = d(j,3) first = .false. else first = .true. end if c 80 continue c c %-----------------------------% c | Display computed residuals. | c %-----------------------------% c call dmout(6, nconv, 3, d, maxncv, -6, & 'Ritz values (Real,Imag) and relative residuals') c end if c c %-------------------------------------------% c | Print additional convergence information. | c %-------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, ' _NDRV6 ' print *, ' ====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program dndrv6. | c %---------------------------% c 9000 continue c end c c========================================================================== c c matrix vector multiplication subroutine c subroutine mv (n, v, w) integer n, j Double precision & v(n), w(n), one, four parameter (one = 1.0D+0, four = 4.0D+0) c c Compute the matrix vector multiplication y<---M*x c where M is a n by n symmetric tridiagonal matrix with 4 on the c diagonal, 1 on the subdiagonal and superdiagonal. c w(1) = four*v(1) + one*v(2) do 10 j = 2,n-1 w(j) = one*v(j-1) + four*v(j) + one*v(j+1) 10 continue w(n) = one*v(n-1) + four*v(n) return end c------------------------------------------------------------------ subroutine av (n, v, w) integer n, j Double precision & v(n), w(n), three, two parameter (three = 3.0D+0, two = 2.0D+0) c c Compute the matrix vector multiplication y<---A*x c where M is a n by n symmetric tridiagonal matrix with 2 on the c diagonal, -2 on the subdiagonal and 3 on the superdiagonal. c w(1) = two*v(1) + three*v(2) do 10 j = 2,n-1 w(j) = -two*v(j-1) + two*v(j) + three*v(j+1) 10 continue w(n) = -two*v(n-1) + two*v(n) return end arpack-0.92.1/EXAMPLES/NONSYM/sndrv1.f0000644000175000017500000004025110776001577013626 00000000000000 program sndrv1 c c c Example program to illustrate the idea of reverse communication c for a standard nonsymmetric eigenvalue problem. c c We implement example one of ex-nonsym.doc in DOCUMENTS directory c c\Example-1 c ... Suppose we want to solve A*x = lambda*x in regular mode, c where A is obtained from the standard central difference c discretization of the convection-diffusion operator c (Laplacian u) + rho*(du / dx) c on the unit square [0,1]x[0,1] with zero Dirichlet boundary c condition. c c ... OP = A and B = I. c c ... Assume "call av (nx,x,y)" computes y = A*x.c c c ... Use mode 1 of SNAUPD. c c\BeginLib c c\Routines called: c snaupd ARPACK reverse communication interface routine. c sneupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c saxpy Level 1 BLAS that computes y <- alpha*x+y. c snrm2 Level 1 BLAS that computes the norm of a vector. c av Matrix vector multiplication routine that computes A*x. c tv Matrix vector multiplication routine that computes T*x, c where T is a tridiagonal matrix. It is used in routine c av. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: ndrv1.F SID: 2.5 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c--------------------------------------------------------------------------- c c %-----------------------------% c | Define maximum dimensions | c | for all arrays. | c | MAXN: Maximum dimension | c | of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %-----------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=12, maxncv=30, ldv=maxn) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), ipntr(14) logical select(maxncv) Real & ax(maxn), d(maxncv,3), resid(maxn), & v(ldv,maxncv), workd(3*maxn), & workev(3*maxncv), & workl(3*maxncv*maxncv+6*maxncv) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nx, nev, ncv, lworkl, info, j, & ierr, nconv, maxitr, ishfts, mode Real & tol, sigmar, sigmai logical first, rvec c c %------------% c | Parameters | c %------------% c Real & zero parameter (zero = 0.0E+0) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & slapy2, snrm2 external slapy2, snrm2, saxpy c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c %--------------------------------------------------% c | The number NX is the number of interior points | c | in the discretization of the 2-dimensional | c | convection-diffusion operator on the unit | c | square with zero Dirichlet boundary condition. | c | The number N(=NX*NX) is the dimension of the | c | matrix. A standard eigenvalue problem is | c | solved (BMAT = 'I'). NEV is the number of | c | eigenvalues to be approximated. The user can | c | modify NX, NEV, NCV, WHICH to solve problems of | c | different sizes, and to get different parts of | c | the spectrum. However, The following | c | conditions must be satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 2 <= NCV <= MAXNCV | c %--------------------------------------------------% c nx = 10 n = nx*nx nev = 4 ncv = 20 if ( n .gt. maxn ) then print *, ' ERROR with _NDRV1: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NDRV1: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NDRV1: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'I' which = 'SM' c c %-----------------------------------------------------% c | The work array WORKL is used in SNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in SNAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = 3*ncv**2+6*ncv tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | This program uses exact shifts with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 1 of SNAUPD is used | c | (IPARAM(7) = 1). All these options can be changed | c | by the user. For details see the documentation in | c | SNAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 1 c iparam(1) = ishfts iparam(3) = maxitr iparam(7) = mode c c %-------------------------------------------% c | M A I N L O O P (Reverse communication) | c %-------------------------------------------% c 10 continue c c %---------------------------------------------% c | Repeatedly call the routine SNAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call snaupd ( ido, bmat, n, which, nev, tol, resid, & ncv, v, ldv, iparam, ipntr, workd, workl, lworkl, & info ) c if (ido .eq. -1 .or. ido .eq. 1) then c c %-------------------------------------------% c | Perform matrix vector multiplication | c | y <--- OP*x | c | The user should supply his/her own | c | matrix vector multiplication routine here | c | that takes workd(ipntr(1)) as the input | c | vector, and return the matrix vector | c | product to workd(ipntr(2)). | c %-------------------------------------------% c call av (nx, workd(ipntr(1)), workd(ipntr(2))) c c %-----------------------------------------% c | L O O P B A C K to call SNAUPD again. | c %-----------------------------------------% c go to 10 c end if c c %----------------------------------------% c | Either we have convergence or there is | c | an error. | c %----------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message, check the | c | documentation in SNAUPD. | c %--------------------------% c print *, ' ' print *, ' Error with _naupd, info = ', info print *, ' Check the documentation of _naupd' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using SNEUPD. | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may also be computed now if | c | desired. (indicated by rvec = .true.) | c %-------------------------------------------% c rvec = .true. c call sneupd ( rvec, 'A', select, d, d(1,2), v, ldv, & sigmar, sigmai, workev, bmat, n, which, nev, tol, & resid, ncv, v, ldv, iparam, ipntr, workd, workl, & lworkl, ierr ) c c %-----------------------------------------------% c | The real part of the eigenvalue is returned | c | in the first column of the two dimensional | c | array D, and the imaginary part is returned | c | in the second column of D. The corresponding | c | eigenvectors are returned in the first NEV | c | columns of the two dimensional array V if | c | requested. Otherwise, an orthogonal basis | c | for the invariant subspace corresponding to | c | the eigenvalues in D is returned in V. | c %-----------------------------------------------% c if ( ierr .ne. 0) then c c %------------------------------------% c | Error condition: | c | Check the documentation of SNEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _neupd, info = ', ierr print *, ' Check the documentation of _neupd. ' print *, ' ' c else c first = .true. nconv = iparam(5) do 20 j=1, nconv c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c if (d(j,2) .eq. zero) then c c %--------------------% c | Ritz value is real | c %--------------------% c call av(nx, v(1,j), ax) call saxpy(n, -d(j,1), v(1,j), 1, ax, 1) d(j,3) = snrm2(n, ax, 1) d(j,3) = d(j,3) / abs(d(j,1)) c else if (first) then c c %------------------------% c | Ritz value is complex. | c | Residual of one Ritz | c | value of the conjugate | c | pair is computed. | c %------------------------% c call av(nx, v(1,j), ax) call saxpy(n, -d(j,1), v(1,j), 1, ax, 1) call saxpy(n, d(j,2), v(1,j+1), 1, ax, 1) d(j,3) = snrm2(n, ax, 1) call av(nx, v(1,j+1), ax) call saxpy(n, -d(j,2), v(1,j), 1, ax, 1) call saxpy(n, -d(j,1), v(1,j+1), 1, ax, 1) d(j,3) = slapy2( d(j,3), snrm2(n, ax, 1) ) d(j,3) = d(j,3) / slapy2(d(j,1),d(j,2)) d(j+1,3) = d(j,3) first = .false. else first = .true. end if c 20 continue c c %-----------------------------% c | Display computed residuals. | c %-----------------------------% c call smout(6, nconv, 3, d, maxncv, -6, & 'Ritz values (Real,Imag) and relative residuals') end if c c %-------------------------------------------% c | Print additional convergence information. | c %-------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, ' _NDRV1 ' print *, ' ====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program sndrv1. | c %---------------------------% c 9000 continue c end c c========================================================================== c c matrix vector subroutine c c The matrix used is the 2 dimensional convection-diffusion c operator discretized using central difference. c subroutine av (nx, v, w) integer nx, j, lo Real & v(nx*nx), w(nx*nx), one, h2 parameter (one = 1.0E+0) external saxpy c c Computes w <--- OP*v, where OP is the nx*nx by nx*nx block c tridiagonal matrix c c | T -I | c |-I T -I | c OP = | -I T | c | ... -I| c | -I T| c c derived from the standard central difference discretization c of the 2 dimensional convection-diffusion operator c (Laplacian u) + rho*(du/dx) on a unit square with zero boundary c condition. c c When rho*h/2 <= 1, the discrete convection-diffusion operator c has real eigenvalues. When rho*h/2 > 1, it has COMPLEX c eigenvalues. c c The subroutine TV is called to compute y<---T*x. c c h2 = one / real((nx+1)*(nx+1)) c call tv(nx,v(1),w(1)) call saxpy(nx, -one/h2, v(nx+1), 1, w(1), 1) c do 10 j = 2, nx-1 lo = (j-1)*nx call tv(nx, v(lo+1), w(lo+1)) call saxpy(nx, -one/h2, v(lo-nx+1), 1, w(lo+1), 1) call saxpy(nx, -one/h2, v(lo+nx+1), 1, w(lo+1), 1) 10 continue c lo = (nx-1)*nx call tv(nx, v(lo+1), w(lo+1)) call saxpy(nx, -one/h2, v(lo-nx+1), 1, w(lo+1), 1) c return end c========================================================================= subroutine tv (nx, x, y) c integer nx, j Real & x(nx), y(nx), h, h2, dd, dl, du c Real & one, zero, rho parameter (one = 1.0E+0, zero = 0.0E+0, & rho = 0.0E+0) c c Compute the matrix vector multiplication y<---T*x c where T is a nx by nx tridiagonal matrix with DD on the c diagonal, DL on the subdiagonal, and DU on the superdiagonal. c c When rho*h/2 <= 1, the discrete convection-diffusion operator c has real eigenvalues. When rho*h/2 > 1, it has COMPLEX c eigenvalues. c h = one / real(nx+1) h2 = h*h dd = 4.0E+0 / h2 dl = -one / h2 - 5.0E-1*rho / h du = -one / h2 + 5.0E-1*rho / h c y(1) = dd*x(1) + du*x(2) do 10 j = 2,nx-1 y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1) 10 continue y(nx) = dl*x(nx-1) + dd*x(nx) return end arpack-0.92.1/EXAMPLES/NONSYM/sndrv3.f0000644000175000017500000004124610776001577013635 00000000000000 program sndrv3 c c Simple program to illustrate the idea of reverse communication c in inverse mode for a generalized nonsymmetric eigenvalue problem. c c We implement example three of ex-nonsym.doc in DOCUMENTS directory c c\Example-3 c ... Suppose we want to solve A*x = lambda*B*x in inverse mode, c where A and B are derived from the finite element discretization c of the 1-dimensional convection-diffusion operator c (d^2u / dx^2) + rho*(du/dx) c on the interval [0,1] with zero Dirichlet boundary condition c using linear elements. c c ... So OP = inv[M]*A and B = M. c c ... Use mode 2 of SNAUPD. c c\BeginLib c c\Routines called: c snaupd ARPACK reverse communication interface routine. c sneupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c spttrf LAPACK symmetric positive definite tridiagonal factorization c routine. c spttrs LAPACK symmetric positive definite tridiagonal solve routine. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c saxpy Level 1 BLAS that computes y <- alpha*x+y. c snrm2 Level 1 BLAS that computes the norm of a vector. c av Matrix vector multiplication routine that computes A*x. c mv Matrix vector multiplication routine that computes M*x. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: ndrv3.F SID: 2.5 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c-------------------------------------------------------------------------- c c %-----------------------------% c | Define leading dimensions | c | for all arrays. | c | MAXN: Maximum dimension | c | of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %-----------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=10, maxncv=25, & ldv=maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), ipntr(14) logical select(maxncv) Real & ax(maxn), mx(maxn), d(maxncv, 3), resid(maxn), & v(ldv,maxncv), workd(3*maxn), & workev(3*maxncv), & workl(3*maxncv*maxncv+6*maxncv), & md(maxn), me(maxn-1) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nev, ncv, lworkl, info, ierr, j, & nconv, maxitr, ishfts, mode Real & tol, sigmar, sigmai, h logical first, rvec c c %------------% c | Parameters | c %------------% c Real & zero, one parameter (zero = 0.0E+0, one = 1.0E+0) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% Real & snrm2, slapy2 external saxpy, snrm2, spttrf, spttrs, slapy2 c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c %----------------------------------------------------% c | The number N is the dimension of the matrix. A | c | generalized eigenvalue problem is solved (BMAT = | c | 'G'). NEV is the number of eigenvalues to be | c | approximated. The user can modify NEV, NCV, WHICH | c | to solve problems of different sizes, and to get | c | different parts of the spectrum. However, The | c | following conditions must be satisfied: | c | N <= MAXN, | c | NEV <= MAXNEV, | c | NEV + 2 <= NCV <= MAXNCV | c %----------------------------------------------------% c n = 100 nev = 4 ncv = 20 if ( n .gt. maxn ) then print *, ' ERROR with _NDRV3: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NDRV3: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NDRV3: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' c c %------------------------------------------------% c | M is the mass matrix formed by using piecewise | c | linear elements on [0,1]. | c %------------------------------------------------% c h = one / real(n+1) do 20 j = 1, n-1 md(j) = 4.0E+0*h me(j) = one*h 20 continue md(n) = 4.0E+0*h c call spttrf(n, md, me, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _pttrf. ' print*, ' ' go to 9000 end if c c %-----------------------------------------------------% c | The work array WORKL is used in SNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in SNAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = 3*ncv**2+6*ncv tol = 0.0 ido = 0 info = 0 c c %---------------------------------------------------% c | This program uses exact shifts with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 2 of SNAUPD is used | c | (IPARAM(7) = 2). All these options can be | c | changed by the user. For details, see the | c | documentation in SNAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 2 c iparam(1) = ishfts iparam(3) = maxitr iparam(7) = mode c c %-------------------------------------------% c | M A I N L O O P (Reverse communication) | c %-------------------------------------------% c 10 continue c c %---------------------------------------------% c | Repeatedly call the routine SNAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call snaupd ( ido, bmat, n, which, nev, tol, resid, & ncv, v, ldv, iparam, ipntr, workd, & workl, lworkl, info ) c if (ido .eq. -1 .or. ido .eq. 1) then c c %----------------------------------------% c | Perform y <--- OP*x = inv[M]*A*x | c | The user should supply his/her own | c | matrix vector routine and a linear | c | system solver. The matrix-vector | c | subroutine should take workd(ipntr(1)) | c | as input, and the final result should | c | be returned to workd(ipntr(2)). | c %----------------------------------------% c call av (n, workd(ipntr(1)), workd(ipntr(2))) call spttrs(n, 1, md, me, workd(ipntr(2)), n, & ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _pttrs. ' print*, ' ' go to 9000 end if c c %-----------------------------------------% c | L O O P B A C K to call SNAUPD again. | c %-----------------------------------------% c go to 10 c else if ( ido .eq. 2) then c c %-------------------------------------% c | Perform y <--- M*x | c | The matrix vector multiplication | c | routine should take workd(ipntr(1)) | c | as input and return the result to | c | workd(ipntr(2)). | c %-------------------------------------% c call mv (n, workd(ipntr(1)), workd(ipntr(2))) c c %-----------------------------------------% c | L O O P B A C K to call SNAUPD again. | c %-----------------------------------------% c go to 10 c end if c c c %-----------------------------------------% c | Either we have convergence, or there is | c | an error. | c %-----------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message. Check the | c | documentation in SNAUPD. | c %--------------------------% c print *, ' ' print *, ' Error with _naupd, info = ', info print *, ' Check the documentation of _naupd.' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using SNEUPD. | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may also be computed now if | c | desired. (indicated by rvec = .true.) | c %-------------------------------------------% c rvec = .true. call sneupd ( rvec, 'A', select, d, d(1,2), v, ldv, & sigmar, sigmai, workev, bmat, n, which, nev, tol, & resid, ncv, v, ldv, iparam, ipntr, workd, & workl, lworkl, ierr ) c c %-----------------------------------------------% c | The real part of the eigenvalue is returned | c | in the first column of the two dimensional | c | array D, and the IMAGINARY part is returned | c | in the second column of D. The corresponding | c | eigenvectors are returned in the first NEV | c | columns of the two dimensional array V if | c | requested. Otherwise, an orthogonal basis | c | for the invariant subspace corresponding to | c | the eigenvalues in D is returned in V. | c %-----------------------------------------------% c if ( ierr .ne. 0 ) then c c %------------------------------------% c | Error condition: | c | Check the documentation of SNEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _neupd, info = ', ierr print *, ' Check the documentation of _neupd' print *, ' ' c else c first = .true. nconv = iparam(5) do 30 j=1, iparam(5) c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*M*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c if (d(j,2) .eq. zero) then c c %--------------------% c | Ritz value is real | c %--------------------% c call av(n, v(1,j), ax) call mv(n, v(1,j), mx) call saxpy(n, -d(j,1), mx, 1, ax, 1) d(j,3) = snrm2(n, ax, 1) d(j,3) = d(j,3) / abs(d(j,1)) c else if (first) then c c %------------------------% c | Ritz value is complex | c | Residual of one Ritz | c | value of the conjugate | c | pair is computed. | c %------------------------% c call av(n, v(1,j), ax) call mv(n, v(1,j), mx) call saxpy(n, -d(j,1), mx, 1, ax, 1) call mv(n, v(1,j+1), mx) call saxpy(n, d(j,2), mx, 1, ax, 1) d(j,3) = snrm2(n, ax, 1)**2 call av(n, v(1,j+1), ax) call mv(n, v(1,j+1), mx) call saxpy(n, -d(j,1), mx, 1, ax, 1) call mv(n, v(1,j), mx) call saxpy(n, -d(j,2), mx, 1, ax, 1) d(j,3) = slapy2( d(j,3), snrm2(n, ax, 1) ) d(j,3) = d(j,3) / slapy2(d(j,1),d(j,2)) d(j+1,3) = d(j,3) first = .false. else first = .true. end if c 30 continue c c %-----------------------------% c | Display computed residuals. | c %-----------------------------% c call smout(6, nconv, 3, d, maxncv, -6, & 'Ritz values (Real,Imag) and relative residuals') c end if c c %------------------------------------------% c | Print additional convergence information | c %------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, ' _NDRV3 ' print *, ' ====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program sndrv3. | c %---------------------------% c 9000 continue c end c c========================================================================== c c matrix vector multiplication subroutine c subroutine av (n, v, w) integer n, j Real & v(n), w(n), one, two, dd, dl, du, s, h, rho parameter ( rho = 1.0E+1, one = 1.0E+0, & two = 2.0E+0) c c Compute the matrix vector multiplication y<---A*x c where A is stiffness matrix obtained from the finite element c discretization of the 1-dimensional convection diffusion operator c d^2u/dx^2 + rho*(du/dx) c on the interval [0,1] with zero Dirichlet boundary condition using c linear elements. c h = one / real(n+1) s = rho / two dd = two / h dl = -one/h - s du = -one/h + s c w(1) = dd*v(1) + du*v(2) do 10 j = 2,n-1 w(j) = dl*v(j-1) + dd*v(j) + du*v(j+1) 10 continue w(n) = dl*v(n-1) + dd*v(n) return end c------------------------------------------------------------------------ subroutine mv (n, v, w) integer n, j Real & v(n), w(n), one, four, h parameter ( one = 1.0E+0, four = 4.0E+0) c c Compute the matrix vector multiplication y<---M*x c where M is the mass matrix formed by using piecewise linear c elements on [0,1]. c w(1) = four*v(1) + one*v(2) do 10 j = 2,n-1 w(j) = one*v(j-1) + four*v(j) + one*v(j+1) 10 continue w(n) = one*v(n-1) + four*v(n) c h = one / real(n+1) call sscal(n, h, w, 1) return end arpack-0.92.1/EXAMPLES/NONSYM/sndrv5.f0000644000175000017500000005316110776001577013636 00000000000000 program sndrv5 c c Simple program to illustrate the idea of reverse communication c in shift-invert mode for a generalized nonsymmetric eigenvalue problem. c c We implement example five of ex-nonsym.doc in DOCUMENTS directory c c\Example-5 c c ... Suppose we want to solve A*x = lambda*B*x in shift-invert mode c The matrix A is the tridiagonal matrix with 2 on the diagonal, c -2 on the subdiagonal and 3 on the superdiagonal. The matrix M c is the tridiagonal matrix with 4 on the diagonal and 1 on the c off-diagonals. c ... The shift sigma is a complex number (sigmar, sigmai). c ... OP = Real_Part{inv[A-(SIGMAR,SIGMAI)*M]*M and B = M. c ... Use mode 3 of SNAUPD. c c\BeginLib c c\Routines called: c snaupd ARPACK reverse communication interface routine. c sneupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c cgttrf LAPACK complex matrix factorization routine. c cgttrs LAPACK complex linear system solve routine. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c saxpy Level 1 BLAS that computes y <- alpha*x+y. c sdot Level 1 BLAS that computes the dot product of two vectors. c snrm2 Level 1 BLAS that computes the norm of a vector c av Matrix vector subroutine that computes A*x. c mv Matrix vector subroutine that computes M*x. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: ndrv5.F SID: 2.5 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c------------------------------------------------------------------------- c c %-----------------------------% c | Define leading dimensions | c | for all arrays. | c | MAXN: Maximum dimension | c | of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %-----------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=10, maxncv=25, & ldv=maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), ipntr(14), ipiv(maxn) logical select(maxncv) Real & ax(maxn), mx(maxn), d(maxncv,3), resid(maxn), & v(ldv,maxncv), workd(3*maxn), & workev(3*maxncv), & workl(3*maxncv*maxncv+6*maxncv) Complex & cdd(maxn), cdl(maxn), cdu(maxn), & cdu2(maxn), ctemp(maxn) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nev, ncv, lworkl, info, ierr, j, & nconv, maxitr, ishfts, mode Real & tol, numr, numi, denr, deni, sigmar, sigmai Complex & c1, c2, c3 logical first, rvec c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c external cgttrf, cgttrs Real & sdot, snrm2, slapy2 external sdot, snrm2, slapy2 c c c %------------% c | Parameters | c %------------% c Real & zero parameter (zero = 0.0E+0) c c %--------------------% c | Intrinsic Function | c %--------------------% c intrinsic real, cmplx, abs c c %-----------------------% c | Executable statements | c %-----------------------% c c %----------------------------------------------------% c | The number N is the dimension of the matrix. A | c | generalized eigenvalue problem is solved (BMAT = | c | 'G'). NEV is the number of eigenvalues (closest | c | to the shift (SIGMAR,SIGMAI)) to be approximated. | c | Since the shift-invert mode is used, WHICH is set | c | to 'LM'. The user can modify NEV, NCV, SIGMAR, | c | SIGMAI to solve problems of different sizes, and | c | to get different parts of the spectrum. However, | c | The following conditions must be satisfied: | c | N <= MAXN, | c | NEV <= MAXNEV, | c | NEV + 2 <= NCV <= MAXNCV | c %----------------------------------------------------% c n = 100 nev = 4 ncv = 20 if ( n .gt. maxn ) then print *, ' ERROR with _NDRV5: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NDRV5: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NDRV5: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' sigmar = 4.0E-1 sigmai = 6.0E-1 c c %---------------------------------------------------% c | Construct C = A - (SIGMAR,SIGMAI)*M in complex | c | arithmetic, and factor C in complex arithmetic | c | (using LAPACK subroutine cgttrf). The matrix A is | c | chosen to be the tridiagonal matrix with -2 on | c | the subdiagonal, 2 on the diagonal and 3 on the | c | superdiagonal. The matrix M is chosen to the | c | symmetric tridiagonal matrix with 4 on the | c | diagonal and 1 on the off-diagonals. | c %---------------------------------------------------% c c1 = cmplx(-2.0E+0-sigmar, -sigmai) c2 = cmplx( 2.0E+0-4.0E+0*sigmar, -4.0E+0*sigmai) c3 = cmplx( 3.0E+0-sigmar, -sigmai) c do 10 j = 1, n-1 cdl(j) = c1 cdd(j) = c2 cdu(j) = c3 10 continue cdd(n) = c2 c call cgttrf(n, cdl, cdd, cdu, cdu2, ipiv, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrf in _NDRV5.' print*, ' ' go to 9000 end if c c %-----------------------------------------------------% c | The work array WORKL is used in SNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in SNAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = 3*ncv**2+6*ncv tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | This program uses exact shift with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 3 of SNAUPD is used | c | (IPARAM(7) = 3). All these options can be | c | changed by the user. For details, see the | c | documentation in SNAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 3 c iparam(1) = ishfts iparam(3) = maxitr iparam(7) = mode c c %------------------------------------------% c | M A I N L O O P(Reverse communication) | c %------------------------------------------% c 20 continue c c %---------------------------------------------% c | Repeatedly call the routine SNAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call snaupd ( ido, bmat, n, which, nev, tol, resid, & ncv, v, ldv, iparam, ipntr, workd, & workl, lworkl, info ) c if (ido .eq. -1) then c c %-------------------------------------------------------% c | Perform | c | y <--- OP*x = Real_Part{inv[A-(SIGMAR,SIGMAI)*M]*M*x} | c | to force starting vector into the range of OP. The | c | user should supply his/her own matrix vector | c | multiplication routine and a complex linear system | c | solver. The matrix vector multiplication routine | c | should take workd(ipntr(1)) as the input. The final | c | result (a real vector) should be returned to | c | workd(ipntr(2)). | c %-------------------------------------------------------% c call mv (n, workd(ipntr(1)), workd(ipntr(2))) do 30 j = 1, n ctemp(j) = cmplx(workd(ipntr(2)+j-1)) 30 continue c call cgttrs('N', n, 1, cdl, cdd, cdu, cdu2, ipiv, & ctemp, n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrs in _NDRV5.' print*, ' ' go to 9000 end if do 40 j = 1, n workd(ipntr(2)+j-1) = real(ctemp(j)) 40 continue c c %-----------------------------------------% c | L O O P B A C K to call SNAUPD again. | c %-----------------------------------------% c go to 20 c else if ( ido .eq. 1) then c c %-------------------------------------------------------% c | Perform | c | y <--- OP*x = Real_Part{inv[A-(SIGMAR,SIGMAI)*M]*M*x} | c | M*x has been saved in workd(ipntr(3)). The user only | c | needs the complex linear system solver here that | c | takes complex[workd(ipntr(3))] as input, and returns | c | the result to workd(ipntr(2)). | c %-------------------------------------------------------% c do 50 j = 1,n ctemp(j) = cmplx(workd(ipntr(3)+j-1)) 50 continue call cgttrs ('N', n, 1, cdl, cdd, cdu, cdu2, ipiv, & ctemp, n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrs in _NDRV5.' print*, ' ' go to 9000 end if do 60 j = 1, n workd(ipntr(2)+j-1) = real(ctemp(j)) 60 continue c c %-----------------------------------------% c | L O O P B A C K to call SNAUPD again. | c %-----------------------------------------% c go to 20 c else if ( ido .eq. 2) then c c %---------------------------------------------% c | Perform y <--- M*x | c | Need matrix vector multiplication routine | c | here that takes workd(ipntr(1)) as input | c | and returns the result to workd(ipntr(2)). | c %---------------------------------------------% c call mv (n, workd(ipntr(1)), workd(ipntr(2))) c c %-----------------------------------------% c | L O O P B A C K to call SNAUPD again. | c %-----------------------------------------% c go to 20 c end if c c c %------------------------------------------% c | Either we have convergence, or there is | c | an error. | c %------------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message, check the | c | documentation in SNAUPD. | c %--------------------------% c print *, ' ' print *, ' Error with _naupd info = ',info print *, ' Check the documentation of _naupd.' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using SNEUPD. | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may also be computed now if | c | desired. (indicated by rvec = .true.) | c %-------------------------------------------% c rvec = .true. call sneupd ( rvec, 'A', select, d, d(1,2), v, ldv, & sigmar, sigmai, workev, bmat, n, which, nev, tol, & resid, ncv, v, ldv, iparam, ipntr, workd, & workl, lworkl, ierr ) c c %-----------------------------------------------% c | The real part of the eigenvalue is returned | c | in the first column of the two dimensional | c | array D, and the IMAGINARY part is returned | c | in the second column of D. The corresponding | c | eigenvectors are returned in the first NEV | c | columns of the two dimensional array V if | c | requested. Otherwise, an orthogonal basis | c | for the invariant subspace corresponding to | c | the eigenvalues in D is returned in V. | c %-----------------------------------------------% c if ( ierr .ne. 0) then c c %------------------------------------% c | Error condition: | c | Check the documentation of SNEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _neupd = ', ierr print *, ' Check the documentation of _neupd. ' print *, ' ' c else c first = .true. nconv = iparam(5) do 70 j=1,nconv c c %-------------------------------------% c | Use Rayleigh Quotient to recover | c | eigenvalues of the original problem.| c %-------------------------------------% c if ( d(j,2) .eq. zero ) then c c %---------------------------% c | Eigenvalue is real. | c | Compute d = x'(Ax)/x'(Mx).| c %---------------------------% c call av(n, v(1,j), ax ) numr = sdot(n, v(1,j), 1, ax, 1) call mv(n, v(1,j), ax ) denr = sdot(n, v(1,j), 1, ax, 1) d(j,1) = numr / denr c else if (first) then c c %------------------------% c | Eigenvalue is complex. | c | Compute the first one | c | of the conjugate pair. | c %------------------------% c c %----------------% c | Compute x'(Ax) | c %----------------% call av(n, v(1,j), ax ) numr = sdot(n, v(1,j), 1, ax, 1) numi = sdot(n, v(1,j+1), 1, ax, 1) call av(n, v(1,j+1), ax) numr = numr + sdot(n,v(1,j+1),1,ax,1) numi = -numi + sdot(n,v(1,j),1,ax,1) c c %----------------% c | Compute x'(Mx) | c %----------------% c call mv(n, v(1,j), ax ) denr = sdot(n, v(1,j), 1, ax, 1) deni = sdot(n, v(1,j+1), 1, ax, 1) call mv(n, v(1,j+1), ax) denr = denr + sdot(n,v(1,j+1),1,ax,1) deni = -deni + sdot(n,v(1,j),1, ax,1) c c %----------------% c | d=x'(Ax)/x'(Mx)| c %----------------% c d(j,1) = (numr*denr+numi*deni) / & slapy2(denr, deni) d(j,2) = (numi*denr-numr*deni) / & slapy2(denr, deni) first = .false. c else c c %------------------------------% c | Get the second eigenvalue of | c | the conjugate pair by taking | c | the conjugate of the last | c | eigenvalue computed. | c %------------------------------% c d(j,1) = d(j-1,1) d(j,2) = -d(j-1,2) first = .true. c end if c 70 continue c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c first = .true. do 80 j=1, nconv c if (d(j,2) .eq. zero) then c c %--------------------% c | Ritz value is real | c %--------------------% c call av(n, v(1,j), ax) call mv(n, v(1,j), mx) call saxpy(n, -d(j,1), mx, 1, ax, 1) d(j,3) = snrm2(n, ax, 1) d(j,3) = d(j,3) / abs(d(j,1)) c else if (first) then c c %------------------------% c | Ritz value is complex | c | Residual of one Ritz | c | value of the conjugate | c | pair is computed. | c %------------------------% c call av(n, v(1,j), ax) call mv(n, v(1,j), mx) call saxpy(n, -d(j,1), mx, 1, ax, 1) call mv(n, v(1,j+1), mx) call saxpy(n, d(j,2), mx, 1, ax, 1) d(j,3) = snrm2(n, ax, 1) call av(n, v(1,j+1), ax) call mv(n, v(1,j+1), mx) call saxpy(n, -d(j,1), mx, 1, ax, 1) call mv(n, v(1,j), mx) call saxpy(n, -d(j,2), mx, 1, ax, 1) d(j,3) = slapy2( d(j,3), snrm2(n, ax, 1) ) d(j,3) = d(j,3) / slapy2(d(j,1),d(j,2)) d(j+1,3) = d(j,3) first = .false. else first = .true. end if c 80 continue c c c %-----------------------------% c | Display computed residuals. | c %-----------------------------% c call smout(6, nconv, 3, d, maxncv, -6, & 'Ritz values (Real,Imag) and relative residuals') c end if c c %-------------------------------------------% c | Print additional convergence information. | c %-------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, ' _NDRV5 ' print *, ' ====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program sndrv5. | c %---------------------------% c 9000 continue c end c c========================================================================== c c matrix vector multiplication subroutine c subroutine mv (n, v, w) integer n, j Real & v(n), w(n), one, four parameter (one = 1.0E+0, four = 4.0E+0) c c Compute the matrix vector multiplication y<---M*x c where M is a n by n symmetric tridiagonal matrix with 4 on the c diagonal, 1 on the subdiagonal and superdiagonal. c w(1) = four*v(1) + one*v(2) do 10 j = 2,n-1 w(j) = one*v(j-1) + four*v(j) + one*v(j+1) 10 continue w(n) = one*v(n-1) + four*v(n) return end c------------------------------------------------------------------ subroutine av (n, v, w) integer n, j Real & v(n), w(n), three, two parameter (three = 3.0E+0, two = 2.0E+0) c c Compute the matrix vector multiplication y<---A*x c where M is a n by n symmetric tridiagonal matrix with 2 on the c diagonal, -2 on the subdiagonal and 3 on the superdiagonal. c w(1) = two*v(1) + three*v(2) do 10 j = 2,n-1 w(j) = -two*v(j-1) + two*v(j) + three*v(j+1) 10 continue w(n) = -two*v(n-1) + two*v(n) return end arpack-0.92.1/EXAMPLES/NONSYM/dndrv3.f0000644000175000017500000004135610776001577013620 00000000000000 program dndrv3 c c Simple program to illustrate the idea of reverse communication c in inverse mode for a generalized nonsymmetric eigenvalue problem. c c We implement example three of ex-nonsym.doc in DOCUMENTS directory c c\Example-3 c ... Suppose we want to solve A*x = lambda*B*x in inverse mode, c where A and B are derived from the finite element discretization c of the 1-dimensional convection-diffusion operator c (d^2u / dx^2) + rho*(du/dx) c on the interval [0,1] with zero Dirichlet boundary condition c using linear elements. c c ... So OP = inv[M]*A and B = M. c c ... Use mode 2 of DNAUPD. c c\BeginLib c c\Routines called: c dnaupd ARPACK reverse communication interface routine. c dneupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c dpttrf LAPACK symmetric positive definite tridiagonal factorization c routine. c dpttrs LAPACK symmetric positive definite tridiagonal solve routine. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c daxpy Level 1 BLAS that computes y <- alpha*x+y. c dnrm2 Level 1 BLAS that computes the norm of a vector. c av Matrix vector multiplication routine that computes A*x. c mv Matrix vector multiplication routine that computes M*x. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: ndrv3.F SID: 2.5 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c-------------------------------------------------------------------------- c c %-----------------------------% c | Define leading dimensions | c | for all arrays. | c | MAXN: Maximum dimension | c | of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %-----------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=10, maxncv=25, & ldv=maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), ipntr(14) logical select(maxncv) Double precision & ax(maxn), mx(maxn), d(maxncv, 3), resid(maxn), & v(ldv,maxncv), workd(3*maxn), & workev(3*maxncv), & workl(3*maxncv*maxncv+6*maxncv), & md(maxn), me(maxn-1) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nev, ncv, lworkl, info, ierr, j, & nconv, maxitr, ishfts, mode Double precision & tol, sigmar, sigmai, h logical first, rvec c c %------------% c | Parameters | c %------------% c Double precision & zero, one parameter (zero = 0.0D+0, one = 1.0D+0) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% Double precision & dnrm2, dlapy2 external daxpy, dnrm2, dpttrf, dpttrs, dlapy2 c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c %----------------------------------------------------% c | The number N is the dimension of the matrix. A | c | generalized eigenvalue problem is solved (BMAT = | c | 'G'). NEV is the number of eigenvalues to be | c | approximated. The user can modify NEV, NCV, WHICH | c | to solve problems of different sizes, and to get | c | different parts of the spectrum. However, The | c | following conditions must be satisfied: | c | N <= MAXN, | c | NEV <= MAXNEV, | c | NEV + 2 <= NCV <= MAXNCV | c %----------------------------------------------------% c n = 100 nev = 4 ncv = 20 if ( n .gt. maxn ) then print *, ' ERROR with _NDRV3: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NDRV3: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NDRV3: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' c c %------------------------------------------------% c | M is the mass matrix formed by using piecewise | c | linear elements on [0,1]. | c %------------------------------------------------% c h = one / dble(n+1) do 20 j = 1, n-1 md(j) = 4.0D+0*h me(j) = one*h 20 continue md(n) = 4.0D+0*h c call dpttrf(n, md, me, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _pttrf. ' print*, ' ' go to 9000 end if c c %-----------------------------------------------------% c | The work array WORKL is used in DNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in DNAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = 3*ncv**2+6*ncv tol = 0.0 ido = 0 info = 0 c c %---------------------------------------------------% c | This program uses exact shifts with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 2 of DNAUPD is used | c | (IPARAM(7) = 2). All these options can be | c | changed by the user. For details, see the | c | documentation in DNAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 2 c iparam(1) = ishfts iparam(3) = maxitr iparam(7) = mode c c %-------------------------------------------% c | M A I N L O O P (Reverse communication) | c %-------------------------------------------% c 10 continue c c %---------------------------------------------% c | Repeatedly call the routine DNAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call dnaupd ( ido, bmat, n, which, nev, tol, resid, & ncv, v, ldv, iparam, ipntr, workd, & workl, lworkl, info ) c if (ido .eq. -1 .or. ido .eq. 1) then c c %----------------------------------------% c | Perform y <--- OP*x = inv[M]*A*x | c | The user should supply his/her own | c | matrix vector routine and a linear | c | system solver. The matrix-vector | c | subroutine should take workd(ipntr(1)) | c | as input, and the final result should | c | be returned to workd(ipntr(2)). | c %----------------------------------------% c call av (n, workd(ipntr(1)), workd(ipntr(2))) call dpttrs(n, 1, md, me, workd(ipntr(2)), n, & ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _pttrs. ' print*, ' ' go to 9000 end if c c %-----------------------------------------% c | L O O P B A C K to call DNAUPD again. | c %-----------------------------------------% c go to 10 c else if ( ido .eq. 2) then c c %-------------------------------------% c | Perform y <--- M*x | c | The matrix vector multiplication | c | routine should take workd(ipntr(1)) | c | as input and return the result to | c | workd(ipntr(2)). | c %-------------------------------------% c call mv (n, workd(ipntr(1)), workd(ipntr(2))) c c %-----------------------------------------% c | L O O P B A C K to call DNAUPD again. | c %-----------------------------------------% c go to 10 c end if c c c %-----------------------------------------% c | Either we have convergence, or there is | c | an error. | c %-----------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message. Check the | c | documentation in DNAUPD. | c %--------------------------% c print *, ' ' print *, ' Error with _naupd, info = ', info print *, ' Check the documentation of _naupd.' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using DNEUPD. | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may also be computed now if | c | desired. (indicated by rvec = .true.) | c %-------------------------------------------% c rvec = .true. call dneupd ( rvec, 'A', select, d, d(1,2), v, ldv, & sigmar, sigmai, workev, bmat, n, which, nev, tol, & resid, ncv, v, ldv, iparam, ipntr, workd, & workl, lworkl, ierr ) c c %-----------------------------------------------% c | The real part of the eigenvalue is returned | c | in the first column of the two dimensional | c | array D, and the IMAGINARY part is returned | c | in the second column of D. The corresponding | c | eigenvectors are returned in the first NEV | c | columns of the two dimensional array V if | c | requested. Otherwise, an orthogonal basis | c | for the invariant subspace corresponding to | c | the eigenvalues in D is returned in V. | c %-----------------------------------------------% c if ( ierr .ne. 0 ) then c c %------------------------------------% c | Error condition: | c | Check the documentation of DNEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _neupd, info = ', ierr print *, ' Check the documentation of _neupd' print *, ' ' c else c first = .true. nconv = iparam(5) do 30 j=1, iparam(5) c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*M*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c if (d(j,2) .eq. zero) then c c %--------------------% c | Ritz value is real | c %--------------------% c call av(n, v(1,j), ax) call mv(n, v(1,j), mx) call daxpy(n, -d(j,1), mx, 1, ax, 1) d(j,3) = dnrm2(n, ax, 1) d(j,3) = d(j,3) / abs(d(j,1)) c else if (first) then c c %------------------------% c | Ritz value is complex | c | Residual of one Ritz | c | value of the conjugate | c | pair is computed. | c %------------------------% c call av(n, v(1,j), ax) call mv(n, v(1,j), mx) call daxpy(n, -d(j,1), mx, 1, ax, 1) call mv(n, v(1,j+1), mx) call daxpy(n, d(j,2), mx, 1, ax, 1) d(j,3) = dnrm2(n, ax, 1)**2 call av(n, v(1,j+1), ax) call mv(n, v(1,j+1), mx) call daxpy(n, -d(j,1), mx, 1, ax, 1) call mv(n, v(1,j), mx) call daxpy(n, -d(j,2), mx, 1, ax, 1) d(j,3) = dlapy2( d(j,3), dnrm2(n, ax, 1) ) d(j,3) = d(j,3) / dlapy2(d(j,1),d(j,2)) d(j+1,3) = d(j,3) first = .false. else first = .true. end if c 30 continue c c %-----------------------------% c | Display computed residuals. | c %-----------------------------% c call dmout(6, nconv, 3, d, maxncv, -6, & 'Ritz values (Real,Imag) and relative residuals') c end if c c %------------------------------------------% c | Print additional convergence information | c %------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, ' _NDRV3 ' print *, ' ====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program dndrv3. | c %---------------------------% c 9000 continue c end c c========================================================================== c c matrix vector multiplication subroutine c subroutine av (n, v, w) integer n, j Double precision & v(n), w(n), one, two, dd, dl, du, s, h, rho parameter ( rho = 1.0D+1, one = 1.0D+0, & two = 2.0D+0) c c Compute the matrix vector multiplication y<---A*x c where A is stiffness matrix obtained from the finite element c discretization of the 1-dimensional convection diffusion operator c d^2u/dx^2 + rho*(du/dx) c on the interval [0,1] with zero Dirichlet boundary condition using c linear elements. c h = one / dble(n+1) s = rho / two dd = two / h dl = -one/h - s du = -one/h + s c w(1) = dd*v(1) + du*v(2) do 10 j = 2,n-1 w(j) = dl*v(j-1) + dd*v(j) + du*v(j+1) 10 continue w(n) = dl*v(n-1) + dd*v(n) return end c------------------------------------------------------------------------ subroutine mv (n, v, w) integer n, j Double precision & v(n), w(n), one, four, h parameter ( one = 1.0D+0, four = 4.0D+0) c c Compute the matrix vector multiplication y<---M*x c where M is the mass matrix formed by using piecewise linear c elements on [0,1]. c w(1) = four*v(1) + one*v(2) do 10 j = 2,n-1 w(j) = one*v(j-1) + four*v(j) + one*v(j+1) 10 continue w(n) = one*v(n-1) + four*v(n) c h = one / dble(n+1) call dscal(n, h, w, 1) return end arpack-0.92.1/EXAMPLES/SIMPLE/0000755000175000017500000000000010776001577012266 500000000000000arpack-0.92.1/EXAMPLES/SIMPLE/makefile0000644000175000017500000000127310776001577013711 00000000000000# # makefile to run simple examples of the reverse communication # protocol. # # Modify if ARPACK library was built somewhere else. # #\SCCS Information: @(#) # FILE: makefile SID: 2.2 DATE OF SID: 9/24/96 RELEASE: 2 # include ../../ARmake.inc # # simple drivers # simple: sssimp dssimp snsimp dnsimp cnsimp znsimp # sssimp: sssimp.o $(FC) $(FFLAGS) sssimp.o $(ALIBS) -o sssimp dssimp: dssimp.o $(FC) $(FFLAGS) dssimp.o $(ALIBS) -o dssimp snsimp: snsimp.o $(FC) $(FFLAGS) snsimp.o $(ALIBS) -o snsimp dnsimp: dnsimp.o $(FC) $(FFLAGS) dnsimp.o $(ALIBS) -o dnsimp cnsimp: cnsimp.o $(FC) $(FFLAGS) cnsimp.o $(ALIBS) -o cnsimp znsimp: znsimp.o $(FC) $(FFLAGS) znsimp.o $(ALIBS) -o znsimp arpack-0.92.1/EXAMPLES/SIMPLE/README0000644000175000017500000000151710776001577013072 000000000000001. Purpose ------- This directory contains simple example drivers that call ARPACK subroutine __aupd.f and __eupd.f to solve various eigenvalue problems using regular mode. These drivers illustrate how to use ARPACK in considerable detail. If you have never used ARPACK before, this is the place to start. 2. Naming Convention ----------------- The name for each driver has the form 'XYsimp.f', where X - is 's' (single precision) or 'd' (double precision) or 'c' (single complex) or 'z' (double complex) Y - is 's' (symmetric) or 'n' (nonsymmetric) Note: there is no simple driver specifically for hermitian complex. 3. Usage ----- To run these drivers, you may use the makefile in this directory and issue, for example, "make sssimp". Then execute using "sssimp". arpack-0.92.1/EXAMPLES/SIMPLE/debug.h0000644000175000017500000000135110776001577013445 00000000000000c c\SCCS Information: @(#) c FILE: debug.h SID: 2.3 DATE OF SID: 11/16/95 RELEASE: 2 c c %---------------------------------% c | See debug.doc for documentation | c %---------------------------------% integer logfil, ndigit, mgetv0, & msaupd, msaup2, msaitr, mseigt, msapps, msgets, mseupd, & mnaupd, mnaup2, mnaitr, mneigh, mnapps, mngets, mneupd, & mcaupd, mcaup2, mcaitr, mceigh, mcapps, mcgets, mceupd common /debug/ & logfil, ndigit, mgetv0, & msaupd, msaup2, msaitr, mseigt, msapps, msgets, mseupd, & mnaupd, mnaup2, mnaitr, mneigh, mnapps, mngets, mneupd, & mcaupd, mcaup2, mcaitr, mceigh, mcapps, mcgets, mceupd arpack-0.92.1/EXAMPLES/SIMPLE/cnsimp.f0000644000175000017500000005060210776001577013651 00000000000000 program cnsimp c c This example program is intended to illustrate the c simplest case of using ARPACK in considerable detail. c This code may be used to understand basic usage of ARPACK c and as a template for creating an interface to ARPACK. c c This code shows how to use ARPACK to find a few eigenvalues c (lambda) and corresponding eigenvectors (x) for the standard c eigenvalue problem: c c A*x = lambda*x c c where A is a general n by n complex matrix. c c The main points illustrated here are c c 1) How to declare sufficient memory to find NEV c eigenvalues of largest magnitude. Other options c are available. c c 2) Illustration of the reverse communication interface c needed to utilize the top level ARPACK routine CNAUPD c that computes the quantities needed to construct c the desired eigenvalues and eigenvectors(if requested). c c 3) How to extract the desired eigenvalues and eigenvectors c using the ARPACK routine CNEUPD. c c The only thing that must be supplied in order to use this c routine on your problem is to change the array dimensions c appropriately, to specify WHICH eigenvalues you want to compute c and to supply a matrix-vector product c c w <- Av c c in place of the call to AV( ) below. c c c Once usage of this routine is understood, you may wish to explore c the other available options to improve convergence, to solve generalized c problems, etc. Look at the file ex-complex.doc in DOCUMENTS directory. c This codes implements c c c\Example-1 c ... Suppose we want to solve A*x = lambda*x in regular mode, c ... OP = A and B = I. c ... Assume "call av (nx,x,y)" computes y = A*x c ... Use mode 1 of CNAUPD. c c\BeginLib c c\Routines called c cnaupd ARPACK reverse communication interface routine. c cneupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c scnrm2 Level 1 BLAS that computes the norm of a complex vector. c caxpy Level 1 BLAS that computes y <- alpha*x+y. c av Matrix vector multiplication routine that computes A*x. c tv Matrix vector multiplication routine that computes T*x, c where T is a tridiagonal matrix. It is used in routine c av. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: nsimp.F SID: 2.4 DATE OF SID: 10/20/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c--------------------------------------------------------------------------- c c %------------------------------------------------------% c | Storage Declarations: | c | | c | The maximum dimensions for all arrays are | c | set here to accommodate a problem size of | c | N .le. MAXN | c | | c | NEV is the number of eigenvalues requested. | c | See specifications for ARPACK usage below. | c | | c | NCV is the largest number of basis vectors that will | c | be used in the Implicitly Restarted Arnoldi | c | Process. Work per major iteration is | c | proportional to N*NCV*NCV. | c | | c | You must set: | c | | c | MAXN: Maximum dimension of the A allowed. | c | MAXNEV: Maximum NEV allowed. | c | MAXNCV: Maximum NCV allowed. | c %------------------------------------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=12, maxncv=30, ldv=maxn) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), ipntr(14) logical select(maxncv) Complex & ax(maxn), d(maxncv), & v(ldv,maxncv), workd(3*maxn), & workev(2*maxncv), resid(maxn), & workl(3*maxncv*maxncv+5*maxncv) Real & rwork(maxncv), rd(maxncv,3) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nx, nev, ncv, lworkl, info, ierr, & j, ishfts, maxitr, mode1, nconv Complex & sigma Real & tol logical rvec c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & scnrm2, slapy2 external scnrm2, caxpy, slapy2 c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------------------------% c | The following include statement and assignments | c | initiate trace output from the internal | c | actions of ARPACK. See debug.doc in the | c | DOCUMENTS directory for usage. Initially, the | c | most useful information will be a breakdown of | c | time spent in the various stages of computation | c | given by setting mcaupd = 1 | c %-------------------------------------------------% c include 'debug.h' ndigit = -3 logfil = 6 mcaitr = 0 mcapps = 0 mcaupd = 1 mcaup2 = 0 mceigh = 0 mceupd = 0 c c %-------------------------------------------------% c | The following sets dimensions for this problem. | c %-------------------------------------------------% c nx = 10 n = nx*nx c c %-----------------------------------------------% c | | c | Specifications for ARPACK usage are set | c | below: | c | | c | 1) NEV = 4 asks for 4 eigenvalues to be | c | computed. | c | | c | 2) NCV = 20 sets the length of the Arnoldi | c | factorization | c | | c | 3) This is a standard problem | c | (indicated by bmat = 'I') | c | | c | 4) Ask for the NEV eigenvalues of | c | largest magnitude | c | (indicated by which = 'LM') | c | See documentation in CNAUPD for the | c | other options SM, LR, SR, LI, SI. | c | | c | Note: NEV and NCV must satisfy the following | c | conditions: | c | NEV <= MAXNEV | c | NEV + 2 <= NCV <= MAXNCV | c | | c %-----------------------------------------------% c nev = 4 ncv = 20 bmat = 'I' which = 'LM' c if ( n .gt. maxn ) then print *, ' ERROR with _NSIMP: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NSIMP: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NSIMP: NCV is greater than MAXNCV ' go to 9000 end if c c %-----------------------------------------------------% c | | c | Specification of stopping rules and initial | c | conditions before calling CNAUPD | c | | c | TOL determines the stopping criterion. | c | | c | Expect | c | abs(lambdaC - lambdaT) < TOL*abs(lambdaC) | c | computed true | c | | c | If TOL .le. 0, then TOL <- macheps | c | (machine precision) is used. | c | | c | IDO is the REVERSE COMMUNICATION parameter | c | used to specify actions to be taken on return | c | from CNAUPD. (see usage below) | c | | c | It MUST initially be set to 0 before the first | c | call to CNAUPD. | c | | c | INFO on entry specifies starting vector information | c | and on return indicates error codes | c | | c | Initially, setting INFO=0 indicates that a | c | random starting vector is requested to | c | start the ARNOLDI iteration. Setting INFO to | c | a nonzero value on the initial call is used | c | if you want to specify your own starting | c | vector (This vector must be placed in RESID). | c | | c | The work array WORKL is used in CNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. | c | | c %-----------------------------------------------------% c lworkl = 3*ncv**2+5*ncv tol = 0.0 ido = 0 info = 0 c c %---------------------------------------------------% c | Specification of Algorithm Mode: | c | | c | This program uses the exact shift strategy | c | (indicated by setting IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 1 of CNAUPD is used | c | (IPARAM(7) = 1). All these options can be changed | c | by the user. For details see the documentation in | c | CNAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode1 = 1 c iparam(1) = ishfts c iparam(3) = maxitr c iparam(7) = mode1 c c %------------------------------------------------% c | M A I N L O O P (Reverse Communication Loop) | c %------------------------------------------------% c 10 continue c c %---------------------------------------------% c | Repeatedly call the routine CNAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% call cnaupd ( ido, bmat, n, which, nev, tol, resid, ncv, & v, ldv, iparam, ipntr, workd, workl, lworkl, & rwork,info ) c if (ido .eq. -1 .or. ido .eq. 1) then c c %-------------------------------------------% c | Perform matrix vector multiplication | c | | c | y <--- A*x | c | | c | The user should supply his/her own | c | matrix vector multiplication routine here | c | that takes workd(ipntr(1)) as the input | c | vector x , and returns the resulting | c | matrix-vector product y = A*x in the | c | array workd(ipntr(2)). | c %-------------------------------------------% c call av (nx, workd(ipntr(1)), workd(ipntr(2))) c c %-----------------------------------------% c | L O O P B A C K to call CNAUPD again. | c %-----------------------------------------% c go to 10 c endif c c %----------------------------------------% c | Either we have convergence or there is | c | an error. | c %----------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message, check the | c | documentation in CNAUPD | c %--------------------------% c print *, ' ' print *, ' Error with _naupd, info = ', info print *, ' Check the documentation of _naupd' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using CNEUPD. | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may be also computed now if | c | desired. (indicated by rvec = .true.) | c | | c | The routine CNEUPD now called to do this | c | post processing (Other modes may require | c | more complicated post processing than | c | mode1.) | c | | c %-------------------------------------------% c rvec = .true. c call cneupd (rvec, 'A', select, D, V, ldv, sigma, & workev, bmat, n, which, nev, tol, resid, ncv, & v, ldv, iparam, ipntr, workd, workl, lworkl, & rwork, ierr) c c %-----------------------------------------------% c | Eigenvalues are returned in the one | c | dimensional array D and the corresponding | c | eigenvectors are returned in the first | c | NCONV (=IPARAM(5)) columns of the two | c | dimensional array V if requested. Otherwise, | c | an orthogonal basis for the invariant | c | subspace corresponding to the eigenvalues in | c | D is returned in V. | c %-----------------------------------------------% c if ( ierr .ne. 0) then c c %------------------------------------% c | Error condition: | c | Check the documentation of CNEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _neupd, info = ', ierr print *, ' Check the documentation of _neupd. ' print *, ' ' c else c nconv = iparam(5) do 20 j=1, nconv c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c call av(nx, v(1,j), ax) call caxpy(n, -d(j), v(1,j), 1, ax, 1) rd(j,1) = real (d(j)) rd(j,2) = aimag(d(j)) rd(j,3) = scnrm2(n, ax, 1) rd(j,3) = rd(j,3) / slapy2(rd(j,1),rd(j,2)) 20 continue c c %-----------------------------% c | Display computed residuals. | c %-----------------------------% c call smout(6, nconv, 3, rd, maxncv, -6, & 'Ritz values (Real, Imag) and relative residuals') end if c c %-------------------------------------------% c | Print additional convergence information. | c %-------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, '_NSIMP ' print *, '====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program cnsimp. | c %---------------------------% c 9000 continue c end c c========================================================================== c c matrix vector subroutine c c The matrix used is the convection-diffusion operator c discretized using centered difference. c subroutine av (nx, v, w) integer nx, j, lo Complex & v(nx*nx), w(nx*nx), one, h2 parameter (one = (1.0E+0, 0.0E+0) ) external caxpy c c Computes w <--- OP*v, where OP is the nx*nx by nx*nx block c tridiagonal matrix c c | T -I | c |-I T -I | c OP = | -I T | c | ... -I| c | -I T| c c derived from the standard central difference discretization c of the 2-dimensional convection-diffusion operator c (Laplacian u) + rho*(du/dx) c on the unit squqre with zero boundary condition. c c The subroutine TV is called to computed y<---T*x. c c h2 = one / cmplx((nx+1)*(nx+1)) c call tv(nx,v(1),w(1)) call caxpy(nx, -one/h2, v(nx+1), 1, w(1), 1) c do 10 j = 2, nx-1 lo = (j-1)*nx call tv(nx, v(lo+1), w(lo+1)) call caxpy(nx, -one/h2, v(lo-nx+1), 1, w(lo+1), 1) call caxpy(nx, -one/h2, v(lo+nx+1), 1, w(lo+1), 1) 10 continue c lo = (nx-1)*nx call tv(nx, v(lo+1), w(lo+1)) call caxpy(nx, -one/h2, v(lo-nx+1), 1, w(lo+1), 1) c return end c========================================================================= subroutine tv (nx, x, y) c integer nx, j Complex & x(nx), y(nx), h, h2, dd, dl, du c Complex & one, rho parameter (one = (1.0E+0, 0.0E+0) , & rho = (1.0E+2, 0.0E+0) ) c c Compute the matrix vector multiplication y<---T*x c where T is a nx by nx tridiagonal matrix with DD on the c diagonal, DL on the subdiagonal, and DU on the superdiagonal c h = one / cmplx(nx+1) h2 = h*h dd = (4.0E+0, 0.0E+0) / h2 dl = -one/h2 - (5.0E-1, 0.0E+0) *rho/h du = -one/h2 + (5.0E-1, 0.0E+0) *rho/h c y(1) = dd*x(1) + du*x(2) do 10 j = 2,nx-1 y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1) 10 continue y(nx) = dl*x(nx-1) + dd*x(nx) return end arpack-0.92.1/EXAMPLES/SIMPLE/znsimp.f0000644000175000017500000005074110776001577013704 00000000000000 program znsimp c c This example program is intended to illustrate the c simplest case of using ARPACK in considerable detail. c This code may be used to understand basic usage of ARPACK c and as a template for creating an interface to ARPACK. c c This code shows how to use ARPACK to find a few eigenvalues c (lambda) and corresponding eigenvectors (x) for the standard c eigenvalue problem: c c A*x = lambda*x c c where A is a general n by n complex matrix. c c The main points illustrated here are c c 1) How to declare sufficient memory to find NEV c eigenvalues of largest magnitude. Other options c are available. c c 2) Illustration of the reverse communication interface c needed to utilize the top level ARPACK routine ZNAUPD c that computes the quantities needed to construct c the desired eigenvalues and eigenvectors(if requested). c c 3) How to extract the desired eigenvalues and eigenvectors c using the ARPACK routine ZNEUPD . c c The only thing that must be supplied in order to use this c routine on your problem is to change the array dimensions c appropriately, to specify WHICH eigenvalues you want to compute c and to supply a matrix-vector product c c w <- Av c c in place of the call to AV( ) below. c c c Once usage of this routine is understood, you may wish to explore c the other available options to improve convergence, to solve generalized c problems, etc. Look at the file ex-complex.doc in DOCUMENTS directory. c This codes implements c c c\Example-1 c ... Suppose we want to solve A*x = lambda*x in regular mode, c ... OP = A and B = I. c ... Assume "call av (nx,x,y)" computes y = A*x c ... Use mode 1 of ZNAUPD . c c\BeginLib c c\Routines called c znaupd ARPACK reverse communication interface routine. c zneupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c dznrm2 Level 1 BLAS that computes the norm of a complex vector. c zaxpy Level 1 BLAS that computes y <- alpha*x+y. c av Matrix vector multiplication routine that computes A*x. c tv Matrix vector multiplication routine that computes T*x, c where T is a tridiagonal matrix. It is used in routine c av. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: nsimp.F SID: 2.4 DATE OF SID: 10/20/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c--------------------------------------------------------------------------- c c %------------------------------------------------------% c | Storage Declarations: | c | | c | The maximum dimensions for all arrays are | c | set here to accommodate a problem size of | c | N .le. MAXN | c | | c | NEV is the number of eigenvalues requested. | c | See specifications for ARPACK usage below. | c | | c | NCV is the largest number of basis vectors that will | c | be used in the Implicitly Restarted Arnoldi | c | Process. Work per major iteration is | c | proportional to N*NCV*NCV. | c | | c | You must set: | c | | c | MAXN: Maximum dimension of the A allowed. | c | MAXNEV: Maximum NEV allowed. | c | MAXNCV: Maximum NCV allowed. | c %------------------------------------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=12, maxncv=30, ldv=maxn) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), ipntr(14) logical select(maxncv) Complex*16 & ax(maxn), d(maxncv), & v(ldv,maxncv), workd(3*maxn), & workev(2*maxncv), resid(maxn), & workl(3*maxncv*maxncv+5*maxncv) Double precision & rwork(maxncv), rd(maxncv,3) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nx, nev, ncv, lworkl, info, ierr, & j, ishfts, maxitr, mode1, nconv Complex*16 & sigma Double precision & tol logical rvec c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & dznrm2 , dlapy2 external dznrm2 , zaxpy , dlapy2 c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------------------------% c | The following include statement and assignments | c | initiate trace output from the internal | c | actions of ARPACK. See debug.doc in the | c | DOCUMENTS directory for usage. Initially, the | c | most useful information will be a breakdown of | c | time spent in the various stages of computation | c | given by setting mcaupd = 1 | c %-------------------------------------------------% c include 'debug.h' ndigit = -3 logfil = 6 mcaitr = 0 mcapps = 0 mcaupd = 1 mcaup2 = 0 mceigh = 0 mceupd = 0 c c %-------------------------------------------------% c | The following sets dimensions for this problem. | c %-------------------------------------------------% c nx = 10 n = nx*nx c c %-----------------------------------------------% c | | c | Specifications for ARPACK usage are set | c | below: | c | | c | 1) NEV = 4 asks for 4 eigenvalues to be | c | computed. | c | | c | 2) NCV = 20 sets the length of the Arnoldi | c | factorization | c | | c | 3) This is a standard problem | c | (indicated by bmat = 'I') | c | | c | 4) Ask for the NEV eigenvalues of | c | largest magnitude | c | (indicated by which = 'LM') | c | See documentation in ZNAUPD for the | c | other options SM, LR, SR, LI, SI. | c | | c | Note: NEV and NCV must satisfy the following | c | conditions: | c | NEV <= MAXNEV | c | NEV + 2 <= NCV <= MAXNCV | c | | c %-----------------------------------------------% c nev = 4 ncv = 20 bmat = 'I' which = 'LM' c if ( n .gt. maxn ) then print *, ' ERROR with _NSIMP: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NSIMP: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NSIMP: NCV is greater than MAXNCV ' go to 9000 end if c c %-----------------------------------------------------% c | | c | Specification of stopping rules and initial | c | conditions before calling ZNAUPD | c | | c | TOL determines the stopping criterion. | c | | c | Expect | c | abs(lambdaC - lambdaT) < TOL*abs(lambdaC) | c | computed true | c | | c | If TOL .le. 0, then TOL <- macheps | c | (machine precision) is used. | c | | c | IDO is the REVERSE COMMUNICATION parameter | c | used to specify actions to be taken on return | c | from ZNAUPD . (see usage below) | c | | c | It MUST initially be set to 0 before the first | c | call to ZNAUPD . | c | | c | INFO on entry specifies starting vector information | c | and on return indicates error codes | c | | c | Initially, setting INFO=0 indicates that a | c | random starting vector is requested to | c | start the ARNOLDI iteration. Setting INFO to | c | a nonzero value on the initial call is used | c | if you want to specify your own starting | c | vector (This vector must be placed in RESID). | c | | c | The work array WORKL is used in ZNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. | c | | c %-----------------------------------------------------% c lworkl = 3*ncv**2+5*ncv tol = 0.0 ido = 0 info = 0 c c %---------------------------------------------------% c | Specification of Algorithm Mode: | c | | c | This program uses the exact shift strategy | c | (indicated by setting IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 1 of ZNAUPD is used | c | (IPARAM(7) = 1). All these options can be changed | c | by the user. For details see the documentation in | c | ZNAUPD . | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode1 = 1 c iparam(1) = ishfts c iparam(3) = maxitr c iparam(7) = mode1 c c %------------------------------------------------% c | M A I N L O O P (Reverse Communication Loop) | c %------------------------------------------------% c 10 continue c c %---------------------------------------------% c | Repeatedly call the routine ZNAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% call znaupd ( ido, bmat, n, which, nev, tol, resid, ncv, & v, ldv, iparam, ipntr, workd, workl, lworkl, & rwork,info ) c if (ido .eq. -1 .or. ido .eq. 1) then c c %-------------------------------------------% c | Perform matrix vector multiplication | c | | c | y <--- A*x | c | | c | The user should supply his/her own | c | matrix vector multiplication routine here | c | that takes workd(ipntr(1)) as the input | c | vector x , and returns the resulting | c | matrix-vector product y = A*x in the | c | array workd(ipntr(2)). | c %-------------------------------------------% c call av (nx, workd(ipntr(1)), workd(ipntr(2))) c c %-----------------------------------------% c | L O O P B A C K to call ZNAUPD again. | c %-----------------------------------------% c go to 10 c endif c c %----------------------------------------% c | Either we have convergence or there is | c | an error. | c %----------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message, check the | c | documentation in ZNAUPD | c %--------------------------% c print *, ' ' print *, ' Error with _naupd, info = ', info print *, ' Check the documentation of _naupd' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using ZNEUPD . | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may be also computed now if | c | desired. (indicated by rvec = .true.) | c | | c | The routine ZNEUPD now called to do this | c | post processing (Other modes may require | c | more complicated post processing than | c | mode1.) | c | | c %-------------------------------------------% c rvec = .true. c call zneupd (rvec, 'A', select, D, V, ldv, sigma, & workev, bmat, n, which, nev, tol, resid, ncv, & v, ldv, iparam, ipntr, workd, workl, lworkl, & rwork, ierr) c c %-----------------------------------------------% c | Eigenvalues are returned in the one | c | dimensional array D and the corresponding | c | eigenvectors are returned in the first | c | NCONV (=IPARAM(5)) columns of the two | c | dimensional array V if requested. Otherwise, | c | an orthogonal basis for the invariant | c | subspace corresponding to the eigenvalues in | c | D is returned in V. | c %-----------------------------------------------% c if ( ierr .ne. 0) then c c %------------------------------------% c | Error condition: | c | Check the documentation of ZNEUPD . | c %------------------------------------% c print *, ' ' print *, ' Error with _neupd, info = ', ierr print *, ' Check the documentation of _neupd. ' print *, ' ' c else c nconv = iparam(5) do 20 j=1, nconv c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c call av(nx, v(1,j), ax) call zaxpy (n, -d(j), v(1,j), 1, ax, 1) rd(j,1) = dble (d(j)) rd(j,2) = dimag (d(j)) rd(j,3) = dznrm2 (n, ax, 1) rd(j,3) = rd(j,3) / dlapy2 (rd(j,1),rd(j,2)) 20 continue c c %-----------------------------% c | Display computed residuals. | c %-----------------------------% c call dmout (6, nconv, 3, rd, maxncv, -6, & 'Ritz values (Real, Imag) and relative residuals') end if c c %-------------------------------------------% c | Print additional convergence information. | c %-------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, '_NSIMP ' print *, '====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program znsimp . | c %---------------------------% c 9000 continue c end c c========================================================================== c c matrix vector subroutine c c The matrix used is the convection-diffusion operator c discretized using centered difference. c subroutine av (nx, v, w) integer nx, j, lo Complex*16 & v(nx*nx), w(nx*nx), one, h2 parameter (one = (1.0D+0, 0.0D+0) ) external zaxpy c c Computes w <--- OP*v, where OP is the nx*nx by nx*nx block c tridiagonal matrix c c | T -I | c |-I T -I | c OP = | -I T | c | ... -I| c | -I T| c c derived from the standard central difference discretization c of the 2-dimensional convection-diffusion operator c (Laplacian u) + rho*(du/dx) c on the unit squqre with zero boundary condition. c c The subroutine TV is called to computed y<---T*x. c c h2 = one / dcmplx ((nx+1)*(nx+1)) c call tv(nx,v(1),w(1)) call zaxpy (nx, -one/h2, v(nx+1), 1, w(1), 1) c do 10 j = 2, nx-1 lo = (j-1)*nx call tv(nx, v(lo+1), w(lo+1)) call zaxpy (nx, -one/h2, v(lo-nx+1), 1, w(lo+1), 1) call zaxpy (nx, -one/h2, v(lo+nx+1), 1, w(lo+1), 1) 10 continue c lo = (nx-1)*nx call tv(nx, v(lo+1), w(lo+1)) call zaxpy (nx, -one/h2, v(lo-nx+1), 1, w(lo+1), 1) c return end c========================================================================= subroutine tv (nx, x, y) c integer nx, j Complex*16 & x(nx), y(nx), h, h2, dd, dl, du c Complex*16 & one, rho parameter (one = (1.0D+0, 0.0D+0) , & rho = (1.0D+2, 0.0D+0) ) c c Compute the matrix vector multiplication y<---T*x c where T is a nx by nx tridiagonal matrix with DD on the c diagonal, DL on the subdiagonal, and DU on the superdiagonal c h = one / dcmplx (nx+1) h2 = h*h dd = (4.0D+0, 0.0D+0) / h2 dl = -one/h2 - (5.0D-1, 0.0D+0) *rho/h du = -one/h2 + (5.0D-1, 0.0D+0) *rho/h c y(1) = dd*x(1) + du*x(2) do 10 j = 2,nx-1 y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1) 10 continue y(nx) = dl*x(nx-1) + dd*x(nx) return end arpack-0.92.1/EXAMPLES/SIMPLE/dssimp.f0000644000175000017500000004732510776001577013667 00000000000000 program dssimp c c This example program is intended to illustrate the c simplest case of using ARPACK in considerable detail. c This code may be used to understand basic usage of ARPACK c and as a template for creating an interface to ARPACK. c c This code shows how to use ARPACK to find a few eigenvalues c (lambda) and corresponding eigenvectors (x) for the standard c eigenvalue problem: c c A*x = lambda*x c c where A is an n by n real symmetric matrix. c c The main points illustrated here are c c 1) How to declare sufficient memory to find NEV c eigenvalues of largest magnitude. Other options c are available. c c 2) Illustration of the reverse communication interface c needed to utilize the top level ARPACK routine DSAUPD c that computes the quantities needed to construct c the desired eigenvalues and eigenvectors(if requested). c c 3) How to extract the desired eigenvalues and eigenvectors c using the ARPACK routine DSEUPD. c c The only thing that must be supplied in order to use this c routine on your problem is to change the array dimensions c appropriately, to specify WHICH eigenvalues you want to compute c and to supply a matrix-vector product c c w <- Av c c in place of the call to AV( ) below. c c Once usage of this routine is understood, you may wish to explore c the other available options to improve convergence, to solve generalized c problems, etc. Look at the file ex-sym.doc in DOCUMENTS directory. c This codes implements c c\Example-1 c ... Suppose we want to solve A*x = lambda*x in regular mode, c where A is derived from the central difference discretization c of the 2-dimensional Laplacian on the unit square with c zero Dirichlet boundary condition. c ... OP = A and B = I. c ... Assume "call av (n,x,y)" computes y = A*x c ... Use mode 1 of DSAUPD. c c\BeginLib c c\Routines called: c dsaupd ARPACK reverse communication interface routine. c dseupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c dnrm2 Level 1 BLAS that computes the norm of a vector. c daxpy Level 1 BLAS that computes y <- alpha*x+y. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: ssimp.F SID: 2.6 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c----------------------------------------------------------------------- c c %------------------------------------------------------% c | Storage Declarations: | c | | c | The maximum dimensions for all arrays are | c | set here to accommodate a problem size of | c | N .le. MAXN | c | | c | NEV is the number of eigenvalues requested. | c | See specifications for ARPACK usage below. | c | | c | NCV is the largest number of basis vectors that will | c | be used in the Implicitly Restarted Arnoldi | c | Process. Work per major iteration is | c | proportional to N*NCV*NCV. | c | | c | You must set: | c | | c | MAXN: Maximum dimension of the A allowed. | c | MAXNEV: Maximum NEV allowed. | c | MAXNCV: Maximum NCV allowed. | c %------------------------------------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=10, maxncv=25, $ ldv=maxn ) c c %--------------% c | Local Arrays | c %--------------% c Double precision & v(ldv,maxncv), workl(maxncv*(maxncv+8)), & workd(3*maxn), d(maxncv,2), resid(maxn), & ax(maxn) logical select(maxncv) integer iparam(11), ipntr(11) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nev, ncv, lworkl, info, ierr, & j, nx, ishfts, maxitr, mode1, nconv logical rvec Double precision & tol, sigma c c %------------% c | Parameters | c %------------% c Double precision & zero parameter (zero = 0.0D+0) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & dnrm2 external dnrm2, daxpy c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------------------------% c | The following include statement and assignments | c | initiate trace output from the internal | c | actions of ARPACK. See debug.doc in the | c | DOCUMENTS directory for usage. Initially, the | c | most useful information will be a breakdown of | c | time spent in the various stages of computation | c | given by setting msaupd = 1. | c %-------------------------------------------------% c include 'debug.h' ndigit = -3 logfil = 6 msgets = 0 msaitr = 0 msapps = 0 msaupd = 1 msaup2 = 0 mseigt = 0 mseupd = 0 c c %-------------------------------------------------% c | The following sets dimensions for this problem. | c %-------------------------------------------------% c nx = 10 n = nx*nx c c %-----------------------------------------------% c | | c | Specifications for ARPACK usage are set | c | below: | c | | c | 1) NEV = 4 asks for 4 eigenvalues to be | c | computed. | c | | c | 2) NCV = 20 sets the length of the Arnoldi | c | factorization | c | | c | 3) This is a standard problem | c | (indicated by bmat = 'I') | c | | c | 4) Ask for the NEV eigenvalues of | c | largest magnitude | c | (indicated by which = 'LM') | c | See documentation in DSAUPD for the | c | other options SM, LA, SA, LI, SI. | c | | c | Note: NEV and NCV must satisfy the following | c | conditions: | c | NEV <= MAXNEV | c | NEV + 1 <= NCV <= MAXNCV | c %-----------------------------------------------% c nev = 4 ncv = 20 bmat = 'I' which = 'LM' c if ( n .gt. maxn ) then print *, ' ERROR with _SSIMP: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _SSIMP: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _SSIMP: NCV is greater than MAXNCV ' go to 9000 end if c c %-----------------------------------------------------% c | | c | Specification of stopping rules and initial | c | conditions before calling DSAUPD | c | | c | TOL determines the stopping criterion. | c | | c | Expect | c | abs(lambdaC - lambdaT) < TOL*abs(lambdaC) | c | computed true | c | | c | If TOL .le. 0, then TOL <- macheps | c | (machine precision) is used. | c | | c | IDO is the REVERSE COMMUNICATION parameter | c | used to specify actions to be taken on return | c | from DSAUPD. (See usage below.) | c | | c | It MUST initially be set to 0 before the first | c | call to DSAUPD. | c | | c | INFO on entry specifies starting vector information | c | and on return indicates error codes | c | | c | Initially, setting INFO=0 indicates that a | c | random starting vector is requested to | c | start the ARNOLDI iteration. Setting INFO to | c | a nonzero value on the initial call is used | c | if you want to specify your own starting | c | vector (This vector must be placed in RESID.) | c | | c | The work array WORKL is used in DSAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. | c | | c %-----------------------------------------------------% c lworkl = ncv*(ncv+8) tol = zero info = 0 ido = 0 c c %---------------------------------------------------% c | Specification of Algorithm Mode: | c | | c | This program uses the exact shift strategy | c | (indicated by setting PARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 1 of DSAUPD is used | c | (IPARAM(7) = 1). All these options can be changed | c | by the user. For details see the documentation in | c | DSAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode1 = 1 c iparam(1) = ishfts c iparam(3) = maxitr c iparam(7) = mode1 c c %------------------------------------------------% c | M A I N L O O P (Reverse communication loop) | c %------------------------------------------------% c 10 continue c c %---------------------------------------------% c | Repeatedly call the routine DSAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call dsaupd ( ido, bmat, n, which, nev, tol, resid, & ncv, v, ldv, iparam, ipntr, workd, workl, & lworkl, info ) c if (ido .eq. -1 .or. ido .eq. 1) then c c %--------------------------------------% c | Perform matrix vector multiplication | c | y <--- OP*x | c | The user should supply his/her own | c | matrix vector multiplication routine | c | here that takes workd(ipntr(1)) as | c | the input, and return the result to | c | workd(ipntr(2)). | c %--------------------------------------% c call av (nx, workd(ipntr(1)), workd(ipntr(2))) c c %-----------------------------------------% c | L O O P B A C K to call DSAUPD again. | c %-----------------------------------------% c go to 10 c end if c c %----------------------------------------% c | Either we have convergence or there is | c | an error. | c %----------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message. Check the | c | documentation in DSAUPD. | c %--------------------------% c print *, ' ' print *, ' Error with _saupd, info = ', info print *, ' Check documentation in _saupd ' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using DSEUPD. | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may be also computed now if | c | desired. (indicated by rvec = .true.) | c | | c | The routine DSEUPD now called to do this | c | post processing (Other modes may require | c | more complicated post processing than | c | mode1.) | c | | c %-------------------------------------------% c rvec = .true. c call dseupd ( rvec, 'All', select, d, v, ldv, sigma, & bmat, n, which, nev, tol, resid, ncv, v, ldv, & iparam, ipntr, workd, workl, lworkl, ierr ) c c %----------------------------------------------% c | Eigenvalues are returned in the first column | c | of the two dimensional array D and the | c | corresponding eigenvectors are returned in | c | the first NCONV (=IPARAM(5)) columns of the | c | two dimensional array V if requested. | c | Otherwise, an orthogonal basis for the | c | invariant subspace corresponding to the | c | eigenvalues in D is returned in V. | c %----------------------------------------------% c if ( ierr .ne. 0) then c c %------------------------------------% c | Error condition: | c | Check the documentation of DSEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _seupd, info = ', ierr print *, ' Check the documentation of _seupd. ' print *, ' ' c else c nconv = iparam(5) do 20 j=1, nconv c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c call av(nx, v(1,j), ax) call daxpy(n, -d(j,1), v(1,j), 1, ax, 1) d(j,2) = dnrm2(n, ax, 1) d(j,2) = d(j,2) / abs(d(j,1)) c 20 continue c c %-----------------------------% c | Display computed residuals. | c %-----------------------------% c call dmout(6, nconv, 2, d, maxncv, -6, & 'Ritz values and relative residuals') end if c c %-------------------------------------------% c | Print additional convergence information. | c %-------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, ' _SSIMP ' print *, ' ====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program dssimp. | c %---------------------------% c 9000 continue c end c c ------------------------------------------------------------------ c matrix vector subroutine c c The matrix used is the 2 dimensional discrete Laplacian on unit c square with zero Dirichlet boundary condition. c c Computes w <--- OP*v, where OP is the nx*nx by nx*nx block c tridiagonal matrix c c | T -I | c |-I T -I | c OP = | -I T | c | ... -I| c | -I T| c c The subroutine TV is called to computed y<---T*x. c subroutine av (nx, v, w) integer nx, j, lo, n2 Double precision & v(nx*nx), w(nx*nx), one, h2 parameter ( one = 1.0D+0 ) c call tv(nx,v(1),w(1)) call daxpy(nx, -one, v(nx+1), 1, w(1), 1) c do 10 j = 2, nx-1 lo = (j-1)*nx call tv(nx, v(lo+1), w(lo+1)) call daxpy(nx, -one, v(lo-nx+1), 1, w(lo+1), 1) call daxpy(nx, -one, v(lo+nx+1), 1, w(lo+1), 1) 10 continue c lo = (nx-1)*nx call tv(nx, v(lo+1), w(lo+1)) call daxpy(nx, -one, v(lo-nx+1), 1, w(lo+1), 1) c c Scale the vector w by (1/h^2), where h is the mesh size c n2 = nx*nx h2 = one / dble((nx+1)*(nx+1)) call dscal(n2, one/h2, w, 1) return end c c------------------------------------------------------------------- subroutine tv (nx, x, y) c integer nx, j Double precision & x(nx), y(nx), dd, dl, du c Double precision & one, four parameter (one = 1.0D+0, four = 4.0D+0) c c Compute the matrix vector multiplication y<---T*x c where T is a nx by nx tridiagonal matrix with DD on the c diagonal, DL on the subdiagonal, and DU on the superdiagonal. c c dd = four dl = -one du = -one c y(1) = dd*x(1) + du*x(2) do 10 j = 2,nx-1 y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1) 10 continue y(nx) = dl*x(nx-1) + dd*x(nx) return end arpack-0.92.1/EXAMPLES/SIMPLE/snsimp.f0000644000175000017500000005351610776001577013700 00000000000000 program snsimp c c c This example program is intended to illustrate the c simplest case of using ARPACK in considerable detail. c This code may be used to understand basic usage of ARPACK c and as a template for creating an interface to ARPACK. c c This code shows how to use ARPACK to find a few eigenvalues c (lambda) and corresponding eigenvectors (x) for the standard c eigenvalue problem: c c A*x = lambda*x c c where A is a n by n real nonsymmetric matrix. c c The main points illustrated here are c c 1) How to declare sufficient memory to find NEV c eigenvalues of largest magnitude. Other options c are available. c c 2) Illustration of the reverse communication interface c needed to utilize the top level ARPACK routine SNAUPD c that computes the quantities needed to construct c the desired eigenvalues and eigenvectors(if requested). c c 3) How to extract the desired eigenvalues and eigenvectors c using the ARPACK routine SNEUPD. c c The only thing that must be supplied in order to use this c routine on your problem is to change the array dimensions c appropriately, to specify WHICH eigenvalues you want to compute c and to supply a matrix-vector product c c w <- Av c c in place of the call to AV( ) below. c c Once usage of this routine is understood, you may wish to explore c the other available options to improve convergence, to solve generalized c problems, etc. Look at the file ex-nonsym.doc in DOCUMENTS directory. c This codes implements c c\Example-1 c ... Suppose we want to solve A*x = lambda*x in regular mode, c where A is obtained from the standard central difference c discretization of the convection-diffusion operator c (Laplacian u) + rho*(du / dx) c on the unit square, with zero Dirichlet boundary condition. c c ... OP = A and B = I. c ... Assume "call av (nx,x,y)" computes y = A*x c ... Use mode 1 of SNAUPD. c c\BeginLib c c\Routines called: c snaupd ARPACK reverse communication interface routine. c sneupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c saxpy Level 1 BLAS that computes y <- alpha*x+y. c snrm2 Level 1 BLAS that computes the norm of a vector. c av Matrix vector multiplication routine that computes A*x. c tv Matrix vector multiplication routine that computes T*x, c where T is a tridiagonal matrix. It is used in routine c av. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: nsimp.F SID: 2.5 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c--------------------------------------------------------------------------- c c %------------------------------------------------------% c | Storage Declarations: | c | | c | The maximum dimensions for all arrays are | c | set here to accommodate a problem size of | c | N .le. MAXN | c | | c | NEV is the number of eigenvalues requested. | c | See specifications for ARPACK usage below. | c | | c | NCV is the largest number of basis vectors that will | c | be used in the Implicitly Restarted Arnoldi | c | Process. Work per major iteration is | c | proportional to N*NCV*NCV. | c | | c | You must set: | c | | c | MAXN: Maximum dimension of the A allowed. | c | MAXNEV: Maximum NEV allowed. | c | MAXNCV: Maximum NCV allowed. | c %------------------------------------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=12, maxncv=30, ldv=maxn) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), ipntr(14) logical select(maxncv) Real & ax(maxn), d(maxncv,3), resid(maxn), & v(ldv,maxncv), workd(3*maxn), & workev(3*maxncv), & workl(3*maxncv*maxncv+6*maxncv) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nx, nev, ncv, lworkl, info, ierr, & j, ishfts, maxitr, mode1, nconv Real & tol, sigmar, sigmai logical first, rvec c c %------------% c | Parameters | c %------------% c Real & zero parameter (zero = 0.0E+0) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & slapy2, snrm2 external slapy2, snrm2, saxpy c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------------------------% c | The following include statement and assignments | c | initiate trace output from the internal | c | actions of ARPACK. See debug.doc in the | c | DOCUMENTS directory for usage. Initially, the | c | most useful information will be a breakdown of | c | time spent in the various stages of computation | c | given by setting mnaupd = 1. | c %-------------------------------------------------% c include 'debug.h' ndigit = -3 logfil = 6 mnaitr = 0 mnapps = 0 mnaupd = 1 mnaup2 = 0 mneigh = 0 mneupd = 0 c c %-------------------------------------------------% c | The following sets dimensions for this problem. | c %-------------------------------------------------% c nx = 10 n = nx*nx c c %-----------------------------------------------% c | | c | Specifications for ARPACK usage are set | c | below: | c | | c | 1) NEV = 4 asks for 4 eigenvalues to be | c | computed. | c | | c | 2) NCV = 20 sets the length of the Arnoldi | c | factorization. | c | | c | 3) This is a standard problem. | c | (indicated by bmat = 'I') | c | | c | 4) Ask for the NEV eigenvalues of | c | largest magnitude. | c | (indicated by which = 'LM') | c | See documentation in SNAUPD for the | c | other options SM, LR, SR, LI, SI. | c | | c | Note: NEV and NCV must satisfy the following | c | conditions: | c | NEV <= MAXNEV | c | NEV + 2 <= NCV <= MAXNCV | c | | c %-----------------------------------------------% c nev = 4 ncv = 20 bmat = 'I' which = 'LM' c if ( n .gt. maxn ) then print *, ' ERROR with _NSIMP: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NSIMP: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NSIMP: NCV is greater than MAXNCV ' go to 9000 end if c c %-----------------------------------------------------% c | | c | Specification of stopping rules and initial | c | conditions before calling SNAUPD | c | | c | TOL determines the stopping criterion. | c | | c | Expect | c | abs(lambdaC - lambdaT) < TOL*abs(lambdaC) | c | computed true | c | | c | If TOL .le. 0, then TOL <- macheps | c | (machine precision) is used. | c | | c | IDO is the REVERSE COMMUNICATION parameter | c | used to specify actions to be taken on return | c | from SNAUPD. (see usage below) | c | | c | It MUST initially be set to 0 before the first | c | call to SNAUPD. | c | | c | INFO on entry specifies starting vector information | c | and on return indicates error codes | c | | c | Initially, setting INFO=0 indicates that a | c | random starting vector is requested to | c | start the ARNOLDI iteration. Setting INFO to | c | a nonzero value on the initial call is used | c | if you want to specify your own starting | c | vector (This vector must be placed in RESID). | c | | c | The work array WORKL is used in SNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. | c | | c %-----------------------------------------------------% c lworkl = 3*ncv**2+6*ncv tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | Specification of Algorithm Mode: | c | | c | This program uses the exact shift strategy | c | (indicated by setting IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 1 of SNAUPD is used | c | (IPARAM(7) = 1). All these options can be changed | c | by the user. For details see the documentation in | c | SNAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode1 = 1 c iparam(1) = ishfts c iparam(3) = maxitr c iparam(7) = mode1 c c %-------------------------------------------% c | M A I N L O O P (Reverse communication) | c %-------------------------------------------% c 10 continue c c %---------------------------------------------% c | Repeatedly call the routine SNAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call snaupd ( ido, bmat, n, which, nev, tol, resid, ncv, & v, ldv, iparam, ipntr, workd, workl, lworkl, & info ) c if (ido .eq. -1 .or. ido .eq. 1) then c c %-------------------------------------------% c | Perform matrix vector multiplication | c | y <--- Op*x | c | The user should supply his/her own | c | matrix vector multiplication routine here | c | that takes workd(ipntr(1)) as the input | c | vector, and return the matrix vector | c | product to workd(ipntr(2)). | c %-------------------------------------------% c call av (nx, workd(ipntr(1)), workd(ipntr(2))) c c %-----------------------------------------% c | L O O P B A C K to call SNAUPD again. | c %-----------------------------------------% c go to 10 c endif c c %----------------------------------------% c | Either we have convergence or there is | c | an error. | c %----------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message, check the | c | documentation in SNAUPD. | c %--------------------------% c print *, ' ' print *, ' Error with _naupd, info = ',info print *, ' Check the documentation of _naupd' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using SNEUPD. | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may be also computed now if | c | desired. (indicated by rvec = .true.) | c | | c | The routine SNEUPD now called to do this | c | post processing (Other modes may require | c | more complicated post processing than | c | mode1,) | c | | c %-------------------------------------------% c rvec = .true. c call sneupd ( rvec, 'A', select, d, d(1,2), v, ldv, & sigmar, sigmai, workev, bmat, n, which, nev, tol, & resid, ncv, v, ldv, iparam, ipntr, workd, workl, & lworkl, ierr ) c c %------------------------------------------------% c | The real parts of the eigenvalues are returned | c | in the first column of the two dimensional | c | array D, and the IMAGINARY part are returned | c | in the second column of D. The corresponding | c | eigenvectors are returned in the first | c | NCONV (= IPARAM(5)) columns of the two | c | dimensional array V if requested. Otherwise, | c | an orthogonal basis for the invariant subspace | c | corresponding to the eigenvalues in D is | c | returned in V. | c %------------------------------------------------% c if ( ierr .ne. 0) then c c %------------------------------------% c | Error condition: | c | Check the documentation of SNEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _neupd, info = ', ierr print *, ' Check the documentation of _neupd. ' print *, ' ' c else c first = .true. nconv = iparam(5) do 20 j=1, nconv c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (IPARAM(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c if (d(j,2) .eq. zero) then c c %--------------------% c | Ritz value is real | c %--------------------% c call av(nx, v(1,j), ax) call saxpy(n, -d(j,1), v(1,j), 1, ax, 1) d(j,3) = snrm2(n, ax, 1) d(j,3) = d(j,3) / abs(d(j,1)) c else if (first) then c c %------------------------% c | Ritz value is complex. | c | Residual of one Ritz | c | value of the conjugate | c | pair is computed. | c %------------------------% c call av(nx, v(1,j), ax) call saxpy(n, -d(j,1), v(1,j), 1, ax, 1) call saxpy(n, d(j,2), v(1,j+1), 1, ax, 1) d(j,3) = snrm2(n, ax, 1) call av(nx, v(1,j+1), ax) call saxpy(n, -d(j,2), v(1,j), 1, ax, 1) call saxpy(n, -d(j,1), v(1,j+1), 1, ax, 1) d(j,3) = slapy2( d(j,3), snrm2(n, ax, 1) ) d(j,3) = d(j,3) / slapy2(d(j,1),d(j,2)) d(j+1,3) = d(j,3) first = .false. else first = .true. end if c 20 continue c c %-----------------------------% c | Display computed residuals. | c %-----------------------------% c call smout(6, nconv, 3, d, maxncv, -6, & 'Ritz values (Real, Imag) and residual residuals') end if c c %-------------------------------------------% c | Print additional convergence information. | c %-------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, ' _NSIMP ' print *, ' ====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program snsimp. | c %---------------------------% c 9000 continue c end c c========================================================================== c c matrix vector subroutine c c The matrix used is the 2 dimensional convection-diffusion c operator discretized using central difference. c subroutine av (nx, v, w) integer nx, j, lo Real & v(nx*nx), w(nx*nx), one, h2 parameter (one = 1.0E+0) external saxpy, tv c c Computes w <--- OP*v, where OP is the nx*nx by nx*nx block c tridiagonal matrix c c | T -I | c |-I T -I | c OP = | -I T | c | ... -I| c | -I T| c c derived from the standard central difference discretization c of the 2 dimensional convection-diffusion operator c (Laplacian u) + rho*(du/dx) on a unit square with zero boundary c condition. c c When rho*h/2 <= 1, the discrete convection-diffusion operator c has real eigenvalues. When rho*h/2 > 1, it has complex c eigenvalues. c c The subroutine TV is called to computed y<---T*x. c c h2 = one / real((nx+1)*(nx+1)) c call tv(nx,v(1),w(1)) call saxpy(nx, -one/h2, v(nx+1), 1, w(1), 1) c do 10 j = 2, nx-1 lo = (j-1)*nx call tv(nx, v(lo+1), w(lo+1)) call saxpy(nx, -one/h2, v(lo-nx+1), 1, w(lo+1), 1) call saxpy(nx, -one/h2, v(lo+nx+1), 1, w(lo+1), 1) 10 continue c lo = (nx-1)*nx call tv(nx, v(lo+1), w(lo+1)) call saxpy(nx, -one/h2, v(lo-nx+1), 1, w(lo+1), 1) c return end c========================================================================= subroutine tv (nx, x, y) c integer nx, j Real & x(nx), y(nx), h, dd, dl, du, h2 c Real & one, rho parameter (one = 1.0E+0, rho = 1.0E+2) c c Compute the matrix vector multiplication y<---T*x c where T is a nx by nx tridiagonal matrix with DD on the c diagonal, DL on the subdiagonal, and DU on the superdiagonal. c c When rho*h/2 <= 1, the discrete convection-diffusion operator c has real eigenvalues. When rho*h/2 > 1, it has complex c eigenvalues. c h = one / real(nx+1) h2 = h*h dd = 4.0E+0 / h2 dl = -one/h2 - 5.0E-1*rho/h du = -one/h2 + 5.0E-1*rho/h c y(1) = dd*x(1) + du*x(2) do 10 j = 2,nx-1 y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1) 10 continue y(nx) = dl*x(nx-1) + dd*x(nx) return end arpack-0.92.1/EXAMPLES/SIMPLE/dnsimp.f0000644000175000017500000005364210776001577013661 00000000000000 program dnsimp c c c This example program is intended to illustrate the c simplest case of using ARPACK in considerable detail. c This code may be used to understand basic usage of ARPACK c and as a template for creating an interface to ARPACK. c c This code shows how to use ARPACK to find a few eigenvalues c (lambda) and corresponding eigenvectors (x) for the standard c eigenvalue problem: c c A*x = lambda*x c c where A is a n by n real nonsymmetric matrix. c c The main points illustrated here are c c 1) How to declare sufficient memory to find NEV c eigenvalues of largest magnitude. Other options c are available. c c 2) Illustration of the reverse communication interface c needed to utilize the top level ARPACK routine DNAUPD c that computes the quantities needed to construct c the desired eigenvalues and eigenvectors(if requested). c c 3) How to extract the desired eigenvalues and eigenvectors c using the ARPACK routine DNEUPD. c c The only thing that must be supplied in order to use this c routine on your problem is to change the array dimensions c appropriately, to specify WHICH eigenvalues you want to compute c and to supply a matrix-vector product c c w <- Av c c in place of the call to AV( ) below. c c Once usage of this routine is understood, you may wish to explore c the other available options to improve convergence, to solve generalized c problems, etc. Look at the file ex-nonsym.doc in DOCUMENTS directory. c This codes implements c c\Example-1 c ... Suppose we want to solve A*x = lambda*x in regular mode, c where A is obtained from the standard central difference c discretization of the convection-diffusion operator c (Laplacian u) + rho*(du / dx) c on the unit square, with zero Dirichlet boundary condition. c c ... OP = A and B = I. c ... Assume "call av (nx,x,y)" computes y = A*x c ... Use mode 1 of DNAUPD. c c\BeginLib c c\Routines called: c dnaupd ARPACK reverse communication interface routine. c dneupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c daxpy Level 1 BLAS that computes y <- alpha*x+y. c dnrm2 Level 1 BLAS that computes the norm of a vector. c av Matrix vector multiplication routine that computes A*x. c tv Matrix vector multiplication routine that computes T*x, c where T is a tridiagonal matrix. It is used in routine c av. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: nsimp.F SID: 2.5 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c--------------------------------------------------------------------------- c c %------------------------------------------------------% c | Storage Declarations: | c | | c | The maximum dimensions for all arrays are | c | set here to accommodate a problem size of | c | N .le. MAXN | c | | c | NEV is the number of eigenvalues requested. | c | See specifications for ARPACK usage below. | c | | c | NCV is the largest number of basis vectors that will | c | be used in the Implicitly Restarted Arnoldi | c | Process. Work per major iteration is | c | proportional to N*NCV*NCV. | c | | c | You must set: | c | | c | MAXN: Maximum dimension of the A allowed. | c | MAXNEV: Maximum NEV allowed. | c | MAXNCV: Maximum NCV allowed. | c %------------------------------------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=12, maxncv=30, ldv=maxn) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), ipntr(14) logical select(maxncv) Double precision & ax(maxn), d(maxncv,3), resid(maxn), & v(ldv,maxncv), workd(3*maxn), & workev(3*maxncv), & workl(3*maxncv*maxncv+6*maxncv) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nx, nev, ncv, lworkl, info, ierr, & j, ishfts, maxitr, mode1, nconv Double precision & tol, sigmar, sigmai logical first, rvec c c %------------% c | Parameters | c %------------% c Double precision & zero parameter (zero = 0.0D+0) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & dlapy2, dnrm2 external dlapy2, dnrm2, daxpy c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------------------------% c | The following include statement and assignments | c | initiate trace output from the internal | c | actions of ARPACK. See debug.doc in the | c | DOCUMENTS directory for usage. Initially, the | c | most useful information will be a breakdown of | c | time spent in the various stages of computation | c | given by setting mnaupd = 1. | c %-------------------------------------------------% c include 'debug.h' ndigit = -3 logfil = 6 mnaitr = 0 mnapps = 0 mnaupd = 1 mnaup2 = 0 mneigh = 0 mneupd = 0 c c %-------------------------------------------------% c | The following sets dimensions for this problem. | c %-------------------------------------------------% c nx = 10 n = nx*nx c c %-----------------------------------------------% c | | c | Specifications for ARPACK usage are set | c | below: | c | | c | 1) NEV = 4 asks for 4 eigenvalues to be | c | computed. | c | | c | 2) NCV = 20 sets the length of the Arnoldi | c | factorization. | c | | c | 3) This is a standard problem. | c | (indicated by bmat = 'I') | c | | c | 4) Ask for the NEV eigenvalues of | c | largest magnitude. | c | (indicated by which = 'LM') | c | See documentation in DNAUPD for the | c | other options SM, LR, SR, LI, SI. | c | | c | Note: NEV and NCV must satisfy the following | c | conditions: | c | NEV <= MAXNEV | c | NEV + 2 <= NCV <= MAXNCV | c | | c %-----------------------------------------------% c nev = 4 ncv = 20 bmat = 'I' which = 'LM' c if ( n .gt. maxn ) then print *, ' ERROR with _NSIMP: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NSIMP: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NSIMP: NCV is greater than MAXNCV ' go to 9000 end if c c %-----------------------------------------------------% c | | c | Specification of stopping rules and initial | c | conditions before calling DNAUPD | c | | c | TOL determines the stopping criterion. | c | | c | Expect | c | abs(lambdaC - lambdaT) < TOL*abs(lambdaC) | c | computed true | c | | c | If TOL .le. 0, then TOL <- macheps | c | (machine precision) is used. | c | | c | IDO is the REVERSE COMMUNICATION parameter | c | used to specify actions to be taken on return | c | from DNAUPD. (see usage below) | c | | c | It MUST initially be set to 0 before the first | c | call to DNAUPD. | c | | c | INFO on entry specifies starting vector information | c | and on return indicates error codes | c | | c | Initially, setting INFO=0 indicates that a | c | random starting vector is requested to | c | start the ARNOLDI iteration. Setting INFO to | c | a nonzero value on the initial call is used | c | if you want to specify your own starting | c | vector (This vector must be placed in RESID). | c | | c | The work array WORKL is used in DNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. | c | | c %-----------------------------------------------------% c lworkl = 3*ncv**2+6*ncv tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | Specification of Algorithm Mode: | c | | c | This program uses the exact shift strategy | c | (indicated by setting IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 1 of DNAUPD is used | c | (IPARAM(7) = 1). All these options can be changed | c | by the user. For details see the documentation in | c | DNAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode1 = 1 c iparam(1) = ishfts c iparam(3) = maxitr c iparam(7) = mode1 c c %-------------------------------------------% c | M A I N L O O P (Reverse communication) | c %-------------------------------------------% c 10 continue c c %---------------------------------------------% c | Repeatedly call the routine DNAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call dnaupd ( ido, bmat, n, which, nev, tol, resid, ncv, & v, ldv, iparam, ipntr, workd, workl, lworkl, & info ) c if (ido .eq. -1 .or. ido .eq. 1) then c c %-------------------------------------------% c | Perform matrix vector multiplication | c | y <--- Op*x | c | The user should supply his/her own | c | matrix vector multiplication routine here | c | that takes workd(ipntr(1)) as the input | c | vector, and return the matrix vector | c | product to workd(ipntr(2)). | c %-------------------------------------------% c call av (nx, workd(ipntr(1)), workd(ipntr(2))) c c %-----------------------------------------% c | L O O P B A C K to call DNAUPD again. | c %-----------------------------------------% c go to 10 c endif c c %----------------------------------------% c | Either we have convergence or there is | c | an error. | c %----------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message, check the | c | documentation in DNAUPD. | c %--------------------------% c print *, ' ' print *, ' Error with _naupd, info = ',info print *, ' Check the documentation of _naupd' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using DNEUPD. | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may be also computed now if | c | desired. (indicated by rvec = .true.) | c | | c | The routine DNEUPD now called to do this | c | post processing (Other modes may require | c | more complicated post processing than | c | mode1,) | c | | c %-------------------------------------------% c rvec = .true. c call dneupd ( rvec, 'A', select, d, d(1,2), v, ldv, & sigmar, sigmai, workev, bmat, n, which, nev, tol, & resid, ncv, v, ldv, iparam, ipntr, workd, workl, & lworkl, ierr ) c c %------------------------------------------------% c | The real parts of the eigenvalues are returned | c | in the first column of the two dimensional | c | array D, and the IMAGINARY part are returned | c | in the second column of D. The corresponding | c | eigenvectors are returned in the first | c | NCONV (= IPARAM(5)) columns of the two | c | dimensional array V if requested. Otherwise, | c | an orthogonal basis for the invariant subspace | c | corresponding to the eigenvalues in D is | c | returned in V. | c %------------------------------------------------% c if ( ierr .ne. 0) then c c %------------------------------------% c | Error condition: | c | Check the documentation of DNEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _neupd, info = ', ierr print *, ' Check the documentation of _neupd. ' print *, ' ' c else c first = .true. nconv = iparam(5) do 20 j=1, nconv c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (IPARAM(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c if (d(j,2) .eq. zero) then c c %--------------------% c | Ritz value is real | c %--------------------% c call av(nx, v(1,j), ax) call daxpy(n, -d(j,1), v(1,j), 1, ax, 1) d(j,3) = dnrm2(n, ax, 1) d(j,3) = d(j,3) / abs(d(j,1)) c else if (first) then c c %------------------------% c | Ritz value is complex. | c | Residual of one Ritz | c | value of the conjugate | c | pair is computed. | c %------------------------% c call av(nx, v(1,j), ax) call daxpy(n, -d(j,1), v(1,j), 1, ax, 1) call daxpy(n, d(j,2), v(1,j+1), 1, ax, 1) d(j,3) = dnrm2(n, ax, 1) call av(nx, v(1,j+1), ax) call daxpy(n, -d(j,2), v(1,j), 1, ax, 1) call daxpy(n, -d(j,1), v(1,j+1), 1, ax, 1) d(j,3) = dlapy2( d(j,3), dnrm2(n, ax, 1) ) d(j,3) = d(j,3) / dlapy2(d(j,1),d(j,2)) d(j+1,3) = d(j,3) first = .false. else first = .true. end if c 20 continue c c %-----------------------------% c | Display computed residuals. | c %-----------------------------% c call dmout(6, nconv, 3, d, maxncv, -6, & 'Ritz values (Real, Imag) and residual residuals') end if c c %-------------------------------------------% c | Print additional convergence information. | c %-------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, ' _NSIMP ' print *, ' ====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program dnsimp. | c %---------------------------% c 9000 continue c end c c========================================================================== c c matrix vector subroutine c c The matrix used is the 2 dimensional convection-diffusion c operator discretized using central difference. c subroutine av (nx, v, w) integer nx, j, lo Double precision & v(nx*nx), w(nx*nx), one, h2 parameter (one = 1.0D+0) external daxpy, tv c c Computes w <--- OP*v, where OP is the nx*nx by nx*nx block c tridiagonal matrix c c | T -I | c |-I T -I | c OP = | -I T | c | ... -I| c | -I T| c c derived from the standard central difference discretization c of the 2 dimensional convection-diffusion operator c (Laplacian u) + rho*(du/dx) on a unit square with zero boundary c condition. c c When rho*h/2 <= 1, the discrete convection-diffusion operator c has real eigenvalues. When rho*h/2 > 1, it has complex c eigenvalues. c c The subroutine TV is called to computed y<---T*x. c c h2 = one / dble((nx+1)*(nx+1)) c call tv(nx,v(1),w(1)) call daxpy(nx, -one/h2, v(nx+1), 1, w(1), 1) c do 10 j = 2, nx-1 lo = (j-1)*nx call tv(nx, v(lo+1), w(lo+1)) call daxpy(nx, -one/h2, v(lo-nx+1), 1, w(lo+1), 1) call daxpy(nx, -one/h2, v(lo+nx+1), 1, w(lo+1), 1) 10 continue c lo = (nx-1)*nx call tv(nx, v(lo+1), w(lo+1)) call daxpy(nx, -one/h2, v(lo-nx+1), 1, w(lo+1), 1) c return end c========================================================================= subroutine tv (nx, x, y) c integer nx, j Double precision & x(nx), y(nx), h, dd, dl, du, h2 c Double precision & one, rho parameter (one = 1.0D+0, rho = 1.0D+2) c c Compute the matrix vector multiplication y<---T*x c where T is a nx by nx tridiagonal matrix with DD on the c diagonal, DL on the subdiagonal, and DU on the superdiagonal. c c When rho*h/2 <= 1, the discrete convection-diffusion operator c has real eigenvalues. When rho*h/2 > 1, it has complex c eigenvalues. c h = one / dble(nx+1) h2 = h*h dd = 4.0D+0 / h2 dl = -one/h2 - 5.0D-1*rho/h du = -one/h2 + 5.0D-1*rho/h c y(1) = dd*x(1) + du*x(2) do 10 j = 2,nx-1 y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1) 10 continue y(nx) = dl*x(nx-1) + dd*x(nx) return end arpack-0.92.1/EXAMPLES/SIMPLE/sssimp.f0000644000175000017500000004720110776001577013677 00000000000000 program sssimp c c This example program is intended to illustrate the c simplest case of using ARPACK in considerable detail. c This code may be used to understand basic usage of ARPACK c and as a template for creating an interface to ARPACK. c c This code shows how to use ARPACK to find a few eigenvalues c (lambda) and corresponding eigenvectors (x) for the standard c eigenvalue problem: c c A*x = lambda*x c c where A is an n by n real symmetric matrix. c c The main points illustrated here are c c 1) How to declare sufficient memory to find NEV c eigenvalues of largest magnitude. Other options c are available. c c 2) Illustration of the reverse communication interface c needed to utilize the top level ARPACK routine SSAUPD c that computes the quantities needed to construct c the desired eigenvalues and eigenvectors(if requested). c c 3) How to extract the desired eigenvalues and eigenvectors c using the ARPACK routine SSEUPD. c c The only thing that must be supplied in order to use this c routine on your problem is to change the array dimensions c appropriately, to specify WHICH eigenvalues you want to compute c and to supply a matrix-vector product c c w <- Av c c in place of the call to AV( ) below. c c Once usage of this routine is understood, you may wish to explore c the other available options to improve convergence, to solve generalized c problems, etc. Look at the file ex-sym.doc in DOCUMENTS directory. c This codes implements c c\Example-1 c ... Suppose we want to solve A*x = lambda*x in regular mode, c where A is derived from the central difference discretization c of the 2-dimensional Laplacian on the unit square with c zero Dirichlet boundary condition. c ... OP = A and B = I. c ... Assume "call av (n,x,y)" computes y = A*x c ... Use mode 1 of SSAUPD. c c\BeginLib c c\Routines called: c ssaupd ARPACK reverse communication interface routine. c sseupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c snrm2 Level 1 BLAS that computes the norm of a vector. c saxpy Level 1 BLAS that computes y <- alpha*x+y. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: ssimp.F SID: 2.6 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c----------------------------------------------------------------------- c c %------------------------------------------------------% c | Storage Declarations: | c | | c | The maximum dimensions for all arrays are | c | set here to accommodate a problem size of | c | N .le. MAXN | c | | c | NEV is the number of eigenvalues requested. | c | See specifications for ARPACK usage below. | c | | c | NCV is the largest number of basis vectors that will | c | be used in the Implicitly Restarted Arnoldi | c | Process. Work per major iteration is | c | proportional to N*NCV*NCV. | c | | c | You must set: | c | | c | MAXN: Maximum dimension of the A allowed. | c | MAXNEV: Maximum NEV allowed. | c | MAXNCV: Maximum NCV allowed. | c %------------------------------------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=10, maxncv=25, $ ldv=maxn ) c c %--------------% c | Local Arrays | c %--------------% c Real & v(ldv,maxncv), workl(maxncv*(maxncv+8)), & workd(3*maxn), d(maxncv,2), resid(maxn), & ax(maxn) logical select(maxncv) integer iparam(11), ipntr(11) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nev, ncv, lworkl, info, ierr, & j, nx, ishfts, maxitr, mode1, nconv logical rvec Real & tol, sigma c c %------------% c | Parameters | c %------------% c Real & zero parameter (zero = 0.0E+0) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & snrm2 external snrm2, saxpy c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------------------------% c | The following include statement and assignments | c | initiate trace output from the internal | c | actions of ARPACK. See debug.doc in the | c | DOCUMENTS directory for usage. Initially, the | c | most useful information will be a breakdown of | c | time spent in the various stages of computation | c | given by setting msaupd = 1. | c %-------------------------------------------------% c include 'debug.h' ndigit = -3 logfil = 6 msgets = 0 msaitr = 0 msapps = 0 msaupd = 1 msaup2 = 0 mseigt = 0 mseupd = 0 c c %-------------------------------------------------% c | The following sets dimensions for this problem. | c %-------------------------------------------------% c nx = 10 n = nx*nx c c %-----------------------------------------------% c | | c | Specifications for ARPACK usage are set | c | below: | c | | c | 1) NEV = 4 asks for 4 eigenvalues to be | c | computed. | c | | c | 2) NCV = 20 sets the length of the Arnoldi | c | factorization | c | | c | 3) This is a standard problem | c | (indicated by bmat = 'I') | c | | c | 4) Ask for the NEV eigenvalues of | c | largest magnitude | c | (indicated by which = 'LM') | c | See documentation in SSAUPD for the | c | other options SM, LA, SA, LI, SI. | c | | c | Note: NEV and NCV must satisfy the following | c | conditions: | c | NEV <= MAXNEV | c | NEV + 1 <= NCV <= MAXNCV | c %-----------------------------------------------% c nev = 4 ncv = 20 bmat = 'I' which = 'LM' c if ( n .gt. maxn ) then print *, ' ERROR with _SSIMP: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _SSIMP: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _SSIMP: NCV is greater than MAXNCV ' go to 9000 end if c c %-----------------------------------------------------% c | | c | Specification of stopping rules and initial | c | conditions before calling SSAUPD | c | | c | TOL determines the stopping criterion. | c | | c | Expect | c | abs(lambdaC - lambdaT) < TOL*abs(lambdaC) | c | computed true | c | | c | If TOL .le. 0, then TOL <- macheps | c | (machine precision) is used. | c | | c | IDO is the REVERSE COMMUNICATION parameter | c | used to specify actions to be taken on return | c | from SSAUPD. (See usage below.) | c | | c | It MUST initially be set to 0 before the first | c | call to SSAUPD. | c | | c | INFO on entry specifies starting vector information | c | and on return indicates error codes | c | | c | Initially, setting INFO=0 indicates that a | c | random starting vector is requested to | c | start the ARNOLDI iteration. Setting INFO to | c | a nonzero value on the initial call is used | c | if you want to specify your own starting | c | vector (This vector must be placed in RESID.) | c | | c | The work array WORKL is used in SSAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. | c | | c %-----------------------------------------------------% c lworkl = ncv*(ncv+8) tol = zero info = 0 ido = 0 c c %---------------------------------------------------% c | Specification of Algorithm Mode: | c | | c | This program uses the exact shift strategy | c | (indicated by setting PARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 1 of SSAUPD is used | c | (IPARAM(7) = 1). All these options can be changed | c | by the user. For details see the documentation in | c | SSAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode1 = 1 c iparam(1) = ishfts c iparam(3) = maxitr c iparam(7) = mode1 c c %------------------------------------------------% c | M A I N L O O P (Reverse communication loop) | c %------------------------------------------------% c 10 continue c c %---------------------------------------------% c | Repeatedly call the routine SSAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call ssaupd ( ido, bmat, n, which, nev, tol, resid, & ncv, v, ldv, iparam, ipntr, workd, workl, & lworkl, info ) c if (ido .eq. -1 .or. ido .eq. 1) then c c %--------------------------------------% c | Perform matrix vector multiplication | c | y <--- OP*x | c | The user should supply his/her own | c | matrix vector multiplication routine | c | here that takes workd(ipntr(1)) as | c | the input, and return the result to | c | workd(ipntr(2)). | c %--------------------------------------% c call av (nx, workd(ipntr(1)), workd(ipntr(2))) c c %-----------------------------------------% c | L O O P B A C K to call SSAUPD again. | c %-----------------------------------------% c go to 10 c end if c c %----------------------------------------% c | Either we have convergence or there is | c | an error. | c %----------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message. Check the | c | documentation in SSAUPD. | c %--------------------------% c print *, ' ' print *, ' Error with _saupd, info = ', info print *, ' Check documentation in _saupd ' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using SSEUPD. | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may be also computed now if | c | desired. (indicated by rvec = .true.) | c | | c | The routine SSEUPD now called to do this | c | post processing (Other modes may require | c | more complicated post processing than | c | mode1.) | c | | c %-------------------------------------------% c rvec = .true. c call sseupd ( rvec, 'All', select, d, v, ldv, sigma, & bmat, n, which, nev, tol, resid, ncv, v, ldv, & iparam, ipntr, workd, workl, lworkl, ierr ) c c %----------------------------------------------% c | Eigenvalues are returned in the first column | c | of the two dimensional array D and the | c | corresponding eigenvectors are returned in | c | the first NCONV (=IPARAM(5)) columns of the | c | two dimensional array V if requested. | c | Otherwise, an orthogonal basis for the | c | invariant subspace corresponding to the | c | eigenvalues in D is returned in V. | c %----------------------------------------------% c if ( ierr .ne. 0) then c c %------------------------------------% c | Error condition: | c | Check the documentation of SSEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _seupd, info = ', ierr print *, ' Check the documentation of _seupd. ' print *, ' ' c else c nconv = iparam(5) do 20 j=1, nconv c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c call av(nx, v(1,j), ax) call saxpy(n, -d(j,1), v(1,j), 1, ax, 1) d(j,2) = snrm2(n, ax, 1) d(j,2) = d(j,2) / abs(d(j,1)) c 20 continue c c %-----------------------------% c | Display computed residuals. | c %-----------------------------% c call smout(6, nconv, 2, d, maxncv, -6, & 'Ritz values and relative residuals') end if c c %-------------------------------------------% c | Print additional convergence information. | c %-------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, ' _SSIMP ' print *, ' ====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program sssimp. | c %---------------------------% c 9000 continue c end c c ------------------------------------------------------------------ c matrix vector subroutine c c The matrix used is the 2 dimensional discrete Laplacian on unit c square with zero Dirichlet boundary condition. c c Computes w <--- OP*v, where OP is the nx*nx by nx*nx block c tridiagonal matrix c c | T -I | c |-I T -I | c OP = | -I T | c | ... -I| c | -I T| c c The subroutine TV is called to computed y<---T*x. c subroutine av (nx, v, w) integer nx, j, lo, n2 Real & v(nx*nx), w(nx*nx), one, h2 parameter ( one = 1.0E+0 ) c call tv(nx,v(1),w(1)) call saxpy(nx, -one, v(nx+1), 1, w(1), 1) c do 10 j = 2, nx-1 lo = (j-1)*nx call tv(nx, v(lo+1), w(lo+1)) call saxpy(nx, -one, v(lo-nx+1), 1, w(lo+1), 1) call saxpy(nx, -one, v(lo+nx+1), 1, w(lo+1), 1) 10 continue c lo = (nx-1)*nx call tv(nx, v(lo+1), w(lo+1)) call saxpy(nx, -one, v(lo-nx+1), 1, w(lo+1), 1) c c Scale the vector w by (1/h^2), where h is the mesh size c n2 = nx*nx h2 = one / real((nx+1)*(nx+1)) call sscal(n2, one/h2, w, 1) return end c c------------------------------------------------------------------- subroutine tv (nx, x, y) c integer nx, j Real & x(nx), y(nx), dd, dl, du c Real & one, four parameter (one = 1.0E+0, four = 4.0E+0) c c Compute the matrix vector multiplication y<---T*x c where T is a nx by nx tridiagonal matrix with DD on the c diagonal, DL on the subdiagonal, and DU on the superdiagonal. c c dd = four dl = -one du = -one c y(1) = dd*x(1) + du*x(2) do 10 j = 2,nx-1 y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1) 10 continue y(nx) = dl*x(nx-1) + dd*x(nx) return end arpack-0.92.1/EXAMPLES/BAND/0000755000175000017500000000000010776001577012001 500000000000000arpack-0.92.1/EXAMPLES/BAND/znbdr1.f0000644000175000017500000002510110776001577013267 00000000000000 program znbdr1 c c ... Construct the matrix A in LAPACK-style band form. c The matrix A is derived from the discretization of c the 2-d convection-diffusion operator c c -Laplacian(u) + rho*partial(u)/partial(x). c c on the unit square with zero Dirichlet boundary condition c using standard central difference. c c ... Call ZNBAND to find eigenvalues LAMBDA such that c A*x = x*LAMBDA. c c ... Use mode 1 of ZNAUPD . c c\BeginLib c c znband ARPACK banded eigenproblem solver. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c zlaset LAPACK routine to initialize a matrix to zero. c zaxpy Level 1 BLAS that computes y <- alpha*x+y. c dznrm2 Level 1 BLAS that computes the norm of a vector. c zgbmv Level 2 BLAS that computes the band matrix vector product c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: nbdr1.F SID: 2.3 DATE OF SID: 08/26/96 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c---------------------------------------------------------------------- c c %-------------------------------------% c | Define leading dimensions for all | c | arrays. | c | MAXN - Maximum size of the matrix | c | MAXNEV - Maximum number of | c | eigenvalues to be computed | c | MAXNCV - Maximum number of Arnoldi | c | vectors stored | c | MAXBDW - Maximum bandwidth | c %-------------------------------------% c integer maxn, maxnev, maxncv, maxbdw, lda, & lworkl, ldv parameter ( maxn = 1000, maxnev = 25, maxncv=50, & maxbdw=50, lda = maxbdw, ldv = maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), iwork(maxn) logical select(maxncv) Complex*16 & a(lda,maxn), m(lda,maxn), fac(lda,maxn), & workl(3*maxncv*maxncv+5*maxncv), workd(3*maxn), & workev(2*maxncv), v(ldv, maxncv), & resid(maxn), d(maxncv), ax(maxn) Double precision & rwork(maxn), rd(maxncv,3) c c %---------------% c | Local Scalars | c %---------------% c character which*2, bmat integer nev, ncv, kl, ku, info, i, j, & n, nx, lo, isub, isup, idiag, maxitr, mode, & nconv logical rvec Double precision & tol Complex*16 & rho, h, h2, sigma c c %------------% c | Parameters | c %------------% c Complex*16 & one, zero, two parameter ( one = (1.0D+0, 0.0D+0) , & zero = (0.0D+0, 0.0D+0) , & two = (2.0D+0, 0.0D+0) ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & dznrm2 , dlapy2 external dznrm2 , zgbmv , zaxpy , dlapy2 , zlaset c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------------------------% c | The number NX is the number of interior points | c | in the discretization of the 2-dimensional | c | convection-diffusion operator on the unit | c | square with zero Dirichlet boundary condition. | c | The number N(=NX*NX) is the dimension of the | c | matrix. A standard eigenvalue problem is | c | solved (BMAT = 'I'). NEV is the number of | c | eigenvalues to be approximated. The user can | c | modify NX, NEV, NCV and WHICH to solve problems | c | of different sizes, and to get different parts | c | the spectrum. However, the following | c | conditions must be satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 2 <= NCV <= MAXNCV | c %-------------------------------------------------% c nx = 10 n = nx*nx nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _NBDR1: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NBDR1: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NBDR1: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'I' which = 'LM' c c %-----------------------------------------------------% c | The work array WORKL is used in ZNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. Setting INFO=0 indicates that a | c | random vector is generated in ZNAUPD to start the | c | Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = 3*ncv**2+5*ncv tol = 0.0 info = 0 c c %---------------------------------------------------% c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 1 of ZNAUPD is used | c | (IPARAM(7) = 1). All these options can be changed | c | by the user. For details, see the documentation | c | in znband . | c %---------------------------------------------------% c maxitr = 300 mode = 1 c iparam(3) = maxitr iparam(7) = mode c c %----------------------------------------% c | Construct the matrix A in LAPACK-style | c | banded form. | c %----------------------------------------% c c %---------------------------------------------% c | Zero out the workspace for banded matrices. | c %---------------------------------------------% c call zlaset ('A', lda, n, zero, zero, a, lda) call zlaset ('A', lda, n, zero, zero, m, lda) call zlaset ('A', lda, n, zero, zero, fac, lda) c c %-------------------------------------% c | KU, KL are number of superdiagonals | c | and subdiagonals within the band of | c | matrices A and M. | c %-------------------------------------% c kl = nx ku = nx c c %---------------% c | Main diagonal | c %---------------% c h = one / dcmplx (nx+1) h2 = h*h c idiag = kl+ku+1 do 30 j = 1, n a(idiag,j) = (4.0D+0, 0.0D+0) / h2 30 continue c c %-------------------------------------% c | First subdiagonal and superdiagonal | c %-------------------------------------% c rho = (1.0D+2, 0.0D+0) isup = kl+ku isub = kl+ku+2 do 50 i = 1, nx lo = (i-1)*nx do 40 j = lo+1, lo+nx-1 a(isup,j+1) = -one/h2 + rho/two/h a(isub,j) = -one/h2 - rho/two/h 40 continue 50 continue c c %------------------------------------% c | KL-th subdiagonal and KU-th super- | c | diagonal. | c %------------------------------------% c isup = kl+1 isub = 2*kl+ku+1 do 80 i = 1, nx-1 lo = (i-1)*nx do 70 j = lo+1, lo+nx a(isup,nx+j) = -one / h2 a(isub,j) = -one / h2 70 continue 80 continue c c %-----------------------------------------------% c | Call ARPACK banded solver to find eigenvalues | c | and eigenvectors. Eigenvalues are returned in | c | the one dimensional array D. Eigenvectors | c | are returned in the first NCONV (=IPARAM(5)) | c | columns of V. | c %-----------------------------------------------% c rvec = .true. call znband (rvec, 'A', select, d, v, ldv, sigma, & workev, n, a, m, lda, fac, kl, ku, which, & bmat, nev, tol, resid, ncv, v, ldv, iparam, & workd, workl, lworkl, rwork, iwork, info) c if ( info .eq. 0) then c nconv = iparam(5) c c %-----------------------------------% c | Print out convergence information | c %-----------------------------------% c print *, ' ' print *, '_NBDR1 ' print *, '====== ' print *, ' ' print *, ' The size of the matrix is ', n print *, ' Number of eigenvalue requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' The number of converged Ritz values is ', & nconv print *, ' What portion of the spectrum ', which print *, ' The number of Implicit Arnoldi ', & ' update taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence tolerance is ', tol print *, ' ' c c %----------------------------% c | Compute the residual norm. | c | || A*x - lambda*x || | c %----------------------------% c do 90 j = 1, nconv c c %---------------------------% c | Compute the residual norm | c | || A*x - lambda*x || | c %---------------------------% c call zgbmv ('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call zaxpy (n, -d(j), v(1,j), 1, ax, 1) rd(j,1) = dble (d(j)) rd(j,2) = dimag (d(j)) rd(j,3) = dznrm2 (n, ax, 1) rd(j,3) = rd(j,3) / dlapy2 (rd(j,1),rd(j,2)) 90 continue call dmout (6, nconv, 3, rd, maxncv, -6, & 'Ritz values (Real,Imag) and relative residuals') else c c %-------------------------------------% c | Either convergence failed, or there | c | is error. Check the documentation | c | for znband . | c %-------------------------------------% c print *, ' ' print *, ' Error with _nband, info= ', info print *, ' Check the documentation of _nband ' print *, ' ' c end if c 9000 end arpack-0.92.1/EXAMPLES/BAND/ssbdr2.f0000644000175000017500000002416410776001577013276 00000000000000 program ssbdr2 c c ... Construct the matrix A in LAPACK-style band form. c The matrix A is derived from the discretization of c the 2-dimensional Laplacian on the unit square c with zero Dirichlet boundary condition using standard c central difference. c c ... Call SSBAND to find eigenvalues LAMBDA closest to c SIGMA such that c A*x = x*LAMBDA. c c ... Use mode 3 of SSAUPD. c c\BeginLib c c\Routines called: c ssband ARPACK banded eigenproblem solver. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c slaset LAPACK routine to initialize a matrix to zero. c saxpy Level 1 BLAS that computes y <- alpha*x+y. c snrm2 Level 1 BLAS that computes the norm of a vector. c sgbmv Level 2 BLAS that computes the band matrix vector product. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: sbdr2.F SID: 2.6 DATE OF SID: 07/21/02 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c---------------------------------------------------------------------- c c %-------------------------------------% c | Define leading dimensions for all | c | arrays. | c | MAXN - Maximum size of the matrix | c | MAXNEV - Maximum number of | c | eigenvalues to be computed | c | MAXNCV - Maximum number of Arnoldi | c | vectors stored | c | MAXBDW - Maximum bandwidth | c %-------------------------------------% c integer maxn, maxnev, maxncv, maxbdw, lda, & lworkl, ldv parameter ( maxn = 1000, maxnev = 25, maxncv=50, & maxbdw=50, lda = maxbdw, ldv = maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), iwork(maxn) logical select(maxncv) Real & a(lda,maxn), m(lda,maxn), rfac(lda,maxn), & workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn), & v(ldv, maxncv), resid(maxn), d(maxncv, 2), & ax(maxn) c c %---------------% c | Local Scalars | c %---------------% c character which*2, bmat integer nev, ncv, ku, kl, info, i, j, ido, & n, nx, lo, isub, isup, idiag, maxitr, mode, & nconv Real & tol, sigma, h2 logical rvec c c %------------% c | Parameters | c %------------% c Real & one, zero, two parameter (one = 1.0E+0, zero = 0.0E+0, two = 2.0E+0) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & slapy2, snrm2 external slapy2, snrm2, saxpy, sgbmv c c %-----------------------% c | Executable Statements | c %-----------------------% c c %--------------------------------------------------% c | The number NX is the number of interior points | c | in the discretization of the 2-dimensional | c | Laplacian operator on the unit square with zero | c | Dirichlet boundary condition. The number | c | N(=NX*NX) is the dimension of the matrix. A | c | standard eigenvalue problem is solved | c | (BMAT = 'I'). NEV is the number of eigenvalues | c | (closest to the shift SIGMA) to be approximated. | c | Since the shift and invert mode is used, WHICH | c | is set to 'LM'. The user can modify NX, NEV, | c | NCV and SIGMA to solve problems of different | c | sizes, and to get different parts the spectrum. | c | However, the following conditions must be | c | satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 1 <= NCV <= MAXNCV | c %--------------------------------------------------% c nx = 10 n = nx*nx nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _SBDR2: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _SBDR2: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _SBDR2: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'I' which = 'LM' sigma = zero c c %-----------------------------------------------------% c | The work array WORKL is used in SSAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in SSAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = ncv*ncv+8*ncv tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 3 of SSAUPD is used | c | (IPARAM(7) = 3). All these options can be changed | c | by the user. For details see the documentation in | c | SSBAND. | c %---------------------------------------------------% c maxitr = 300 mode = 3 c iparam(3) = maxitr iparam(7) = mode c c %----------------------------------------% c | Construct the matrix A in LAPACK-style | c | banded form. | c %----------------------------------------% c c %---------------------------------------------% c | Zero out the workspace for banded matrices. | c %---------------------------------------------% c call slaset('A', lda, n, zero, zero, a, lda) call slaset('A', lda, n, zero, zero, m, lda) call slaset('A', lda, n, zero, zero, rfac, lda) c c %-------------------------------------% c | KU, KL are number of superdiagonals | c | and subdiagonals within the band of | c | matrices A and M. | c %-------------------------------------% c kl = nx ku = nx c c %---------------% c | Main diagonal | c %---------------% c h2 = one / ((nx+1)*(nx+1)) idiag = kl+ku+1 do 30 j = 1, n a(idiag,j) = 4.0E+0 / h2 30 continue c c %-------------------------------------% c | First subdiagonal and superdiagonal | c %-------------------------------------% c isup = kl+ku isub = kl+ku+2 do 50 i = 1, nx lo = (i-1)*nx do 40 j = lo+1, lo+nx-1 a(isup,j+1) = -one / h2 a(isub,j) = -one / h2 40 continue 50 continue c c %------------------------------------% c | KL-th subdiagonal and KU-th super- | c | diagonal. | c %------------------------------------% c isup = kl+1 isub = 2*kl+ku+1 do 80 i = 1, nx-1 lo = (i-1)*nx do 70 j = lo+1, lo+nx a(isup,nx+j) = -one / h2 a(isub,j) = -one / h2 70 continue 80 continue c c %-------------------------------------% c | Call SSBAND to find eigenvalues and | c | eigenvectors. Eigenvalues are | c | returned in the first column of D. | c | Eigenvectors are returned in the | c | first NCONV (=IPARAM(5)) columns of | c | V. | c %-------------------------------------% c rvec = .true. call ssband( rvec,'A', select, d, v, ldv, sigma, n, a, m, & lda, rfac, kl, ku, which, bmat, nev, tol, & resid, ncv, v, ldv, iparam, workd, workl, lworkl, & iwork, info) c if ( info .eq. 0) then c nconv = iparam(5) c c %-----------------------------------% c | Print out convergence information | c %-----------------------------------% c print *, ' ' print *, ' _SBDR2 ' print *, ' ====== ' print *, ' ' print *, ' The size of the matrix is ', n print *, ' Number of eigenvalue requested is ', nev print *, ' The number of Lanczos vectors generated', & ' (NCV) is ', ncv print *, ' The number of converged Ritz values is ', & nconv print *, ' What portion of the spectrum ', which print *, ' The number of Implicit Arnoldi', & ' update taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence tolerance is ', tol print *, ' ' c c %----------------------------% c | Compute the residual norm. | c | || A*x - lambda*x || | c %----------------------------% c do 90 j = 1, nconv call sgbmv('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call saxpy(n, -d(j,1), v(1,j), 1, ax, 1) d(j,2) = snrm2(n, ax, 1) d(j,2) = d(j,2) / abs(d(j,1)) c 90 continue call smout(6, nconv, 2, d, maxncv, -6, & 'Ritz values and relative residuals') else c c %-------------------------------------% c | Either convergence failed, or there | c | is error. Check the documentation | c | for SSBAND. | c %-------------------------------------% c print *, ' ' print *, ' Error with _sband, info= ', info print *, ' Check the documentation of _sband ' print *, ' ' c end if c 9000 end arpack-0.92.1/EXAMPLES/BAND/znbdr2.f0000644000175000017500000002532310776001577013276 00000000000000 program znbdr2 c c ... Construct the matrix A in LAPACK-style band form. c The matrix A is derived from the discretization of c the 2-d convection-diffusion operator c c -Laplacian(u) + rho*partial(u)/partial(x). c c on the unit square with zero Dirichlet boundary condition c using standard central difference. c c ... Call ZNBAND to find eigenvalues LAMBDA such that c A*x = x*LAMBDA. c c ... Use mode 3 of ZNAUPD . c c\BeginLib c c znband ARPACK banded eigenproblem solver. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c zlaset LAPACK routine to initialize a matrix to zero. c zaxpy Level 1 BLAS that computes y <- alpha*x+y. c dznrm2 Level 1 BLAS that computes the norm of a vector. c zgbmv Level 2 BLAS that computes the band matrix vector product c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: nbdr2.F SID: 2.4 DATE OF SID: 10/20/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c---------------------------------------------------------------------- c c %-------------------------------------% c | Define leading dimensions for all | c | arrays. | c | MAXN - Maximum size of the matrix | c | MAXNEV - Maximum number of | c | eigenvalues to be computed | c | MAXNCV - Maximum number of Arnoldi | c | vectors stored | c | MAXBDW - Maximum bandwidth | c %-------------------------------------% c integer maxn, maxnev, maxncv, maxbdw, lda, & lworkl, ldv parameter ( maxn = 1000, maxnev = 25, maxncv=50, & maxbdw=50, lda = maxbdw, ldv = maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), iwork(maxn) logical select(maxncv) Complex*16 & a(lda,maxn), m(lda,maxn), fac(lda,maxn), & workl(3*maxncv*maxncv+5*maxncv), workd(3*maxn), & workev(2*maxncv), v(ldv, maxncv), & resid(maxn), d(maxncv), ax(maxn) Double precision & rwork(maxn), rd(maxncv,3) c c %---------------% c | Local Scalars | c %---------------% c character which*2, bmat integer nev, ncv, kl, ku, info, i, j, & n, nxi, lo, isub, isup, idiag, maxitr, mode, & nconv logical rvec Double precision & tol Complex*16 & rho, h, h2, sigma c c %------------% c | Parameters | c %------------% c Complex*16 & one, zero, two parameter (one = (1.0D+0, 0.0D+0) , & zero = (0.0D+0, 0.0D+0) , & two = (2.0D+0, 0.0D+0) ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & dznrm2 , dlapy2 external dznrm2 , zgbmv , zaxpy , dlapy2 , zlaset c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------------------------% c | The number NX is the number of interior points | c | in the discretization of the 2-dimensional | c | convection-diffusion operator on the unit | c | square with zero Dirichlet boundary condition. | c | The number N(=NX*NX) is the dimension of the | c | matrix. A standard eigenvalue problem is | c | solved (BMAT = 'I'). NEV is the number of | c | eigenvalues (closest to SIGMA) to be | c | approximated. Since the shift and invert mode | c | is used, WHICH is set to 'LM'. The user can | c | modify NX, NEV and NCV to solve problems of | c | different sizes, and to get different parts the | c | spectrum. However, the following conditions | c | must be satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 2 <= NCV <= MAXNCV | c %-------------------------------------------------% c nxi = 10 n = nxi*nxi nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _NBDR2: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NBDR2: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NBDR2: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'I' which = 'LM' sigma = zero c c %-----------------------------------------------------% c | The work array WORKL is used in ZNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. Setting INFO=0 indicates that a | c | random vector is generated in ZNAUPD to start the | c | Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = 3*ncv**2+5*ncv tol = 0.0 info = 0 c c %---------------------------------------------------% c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 3 of ZNAUPD is used | c | (IPARAM(7) = 3). All these options can be changed | c | by the user. For details, see the documentation | c | in znband . | c %---------------------------------------------------% c maxitr = 300 mode = 3 c iparam(3) = maxitr iparam(7) = mode c c %----------------------------------------% c | Construct the matrix A in LAPACK-style | c | banded form. | c %----------------------------------------% c c %---------------------------------------------% c | Zero out the workspace for banded matrices. | c %---------------------------------------------% c call zlaset ('A', lda, n, zero, zero, a, lda) call zlaset ('A', lda, n, zero, zero, m, lda) call zlaset ('A', lda, n, zero, zero, fac, lda) c c %-------------------------------------% c | KU, KL are number of superdiagonals | c | and subdiagonals within the band of | c | matrices A and M. | c %-------------------------------------% c kl = nxi ku = nxi c c %---------------% c | Main diagonal | c %---------------% c h = one / dcmplx (nxi+1) h2 = h*h c idiag = kl+ku+1 do 30 j = 1, n a(idiag,j) = (4.0D+0, 0.0D+0) / h2 30 continue c c %-------------------------------------% c | First subdiagonal and superdiagonal | c %-------------------------------------% c rho = (1.0D+2, 0.0D+0) isup = kl+ku isub = kl+ku+2 do 50 i = 1, nxi lo = (i-1)*nxi do 40 j = lo+1, lo+nxi-1 a(isup,j+1) = -one/h2 + rho/two/h a(isub,j) = -one/h2 - rho/two/h 40 continue 50 continue c c %------------------------------------% c | KL-th subdiagonal and KU-th super- | c | diagonal. | c %------------------------------------% c isup = kl+1 isub = 2*kl+ku+1 do 80 i = 1, nxi-1 lo = (i-1)*nxi do 70 j = lo+1, lo+nxi a(isup,nxi+j) = -one / h2 a(isub,j) = -one / h2 70 continue 80 continue c c %-----------------------------------------------% c | Call ARPACK banded solver to find eigenvalues | c | and eigenvectors. Eigenvalues are returned in | c | the one dimensional array D. Eigenvectors | c | are returned in the first NCONV (=IPARAM(5)) | c | columns of V. | c %-----------------------------------------------% c rvec = .true. call znband (rvec, 'A', select, d, v, ldv, sigma, & workev, n, a, m, lda, fac, kl, ku, which, & bmat, nev, tol, resid, ncv, v, ldv, iparam, & workd, workl, lworkl, rwork, iwork, info) c if ( info .eq. 0) then c nconv = iparam(5) c c %-----------------------------------% c | Print out convergence information | c %-----------------------------------% c print *, ' ' print *, '_NBDR2 ' print *, '====== ' print *, ' ' print *, ' The size of the matrix is ', n print *, ' Number of eigenvalue requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' The number of converged Ritz values is ', & nconv print *, ' What portion of the spectrum ', which print *, ' The number of Implicit Arnoldi ', & ' update taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence tolerance is ', tol print *, ' ' c c %----------------------------% c | Compute the residual norm. | c | || A*x - lambda*x || | c %----------------------------% c do 90 j = 1, nconv c c %---------------------------% c | Compute the residual norm | c | || A*x - lambda*x || | c %---------------------------% c call zgbmv ('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call zaxpy (n, -d(j), v(1,j), 1, ax, 1) rd(j,1) = dble (d(j)) rd(j,2) = dimag (d(j)) rd(j,3) = dznrm2 (n, ax, 1) rd(j,3) = rd(j,3) / dlapy2 (rd(j,1),rd(j,2)) 90 continue call dmout (6, nconv, 3, rd, maxncv, -6, & 'Ritz values (Real,Imag) and relative residuals') else c c %-------------------------------------% c | Either convergence failed, or there | c | is error. Check the documentation | c | for znband . | c %-------------------------------------% c print *, ' ' print *, ' Error with _nband, info= ', info print *, ' Check the documentation of _nband ' print *, ' ' c end if c 9000 end arpack-0.92.1/EXAMPLES/BAND/cnband.f0000644000175000017500000005507010776001577013324 00000000000000c \BeginDoc c c \Name: cnband c c \Description: c This subroutine returns the converged approximations to eigenvalues c of A*z = lambda*B*z and (optionally): c c (1) The corresponding approximate eigenvectors; c c (2) An orthonormal basis for the associated approximate c invariant subspace; c c (3) Both. c c Matrices A and B are stored in LAPACK-style banded form. c c There is negligible additional cost to obtain eigenvectors. An orthonormal c basis is always computed. There is an additional storage cost of n*nev c if both are requested (in this case a separate array Z must be supplied). c c The approximate eigenvalues and eigenvectors of A*z = lambda*B*z c are commonly called Ritz values and Ritz vectors respectively. They are c referred to as such in the comments that follow. The computed orthonormal c basis for the invariant subspace corresponding to these Ritz values is c referred to as a Schur basis. c c cnband can be called with one of the following modes: c c Mode 1: A*z = lambda*z. c ===> OP = A and B = I. c c Mode 2: A*z = lambda*M*z, M symmetric positive definite c ===> OP = inv[M]*A and B = M. c c Mode 3: A*z = lambda*M*z, M symmetric semi-definite c ===> OP = inv[A - sigma*M]*M and B = M. c ===> shift-and-invert mode. c c Choice of different modes can be specified in IPARAM(7) defined below. c c \Usage c call cnband c ( RVEC, HOWMNY, SELECT, D , Z, LDZ, SIGMA, WORKEV, N, AB, c MB, LDA, FAC, KL, KU, WHICH, BMAT, NEV, TOL, RESID, NCV, c V, LDV, IPARAM, WORKD, WORKL, LWORKL, RWORK, IWORK, INFO ) c c \Arguments c RVEC LOGICAL (INPUT) c Specifies whether a basis for the invariant subspace corresponding c to the converged Ritz value approximations for the eigenproblem c A*z = lambda*B*z is computed. c c RVEC = .FALSE. Compute Ritz values only. c c RVEC = .TRUE. Compute Ritz vectors or Schur vectors. c See Remarks below. c c HOWMNY Character*1 (INPUT) c Specifies the form of the invariant subspace to be computed c corresponding to the converged Ritz values. c = 'A': Compute NEV Ritz vectors; c = 'P': Compute NEV Schur vectors; c = 'S': compute some of the Ritz vectors, specified c by the logical array SELECT. c c SELECT Logical array of dimension NCV. (INPUT) c If HOWMNY = 'S', SELECT specifies the Ritz vectors to be c computed. To select the real Ritz vector corresponding to a c Ritz value D(j), SELECT(j) must be set to .TRUE.. c If HOWMNY = 'A' or 'P', SELECT need not be initialized c but it is used as internal workspace. c c D Complex array of dimension NEV+1. (OUTPUT) c On exit, D contains the Ritz approximations c to the eigenvalues lambda for A*z = lambda*B*z. c c Z Complex N by NEV array (OUTPUT) c On exit, if RVEC = .TRUE. and HOWMNY = 'A', then the columns of c Z represents approximate eigenvectors (Ritz vectors) corresponding c to the NCONV=IPARAM(5) Ritz values for eigensystem c A*z = lambda*B*z. c c If RVEC = .FALSE. or HOWMNY = 'P', then Z is NOT REFERENCED. c c NOTE: If if RVEC = .TRUE. and a Schur basis is not required, c the array Z may be set equal to first NEV columns of the c array V. c c LDZ Integer. (INPUT) c The leading dimension of the array Z. If Ritz vectors are c desired, then LDZ .ge. max( 1, N ) is required. c In any case, LDZ .ge. 1 is required. c c SIGMA Complex (INPUT) c If IPARAM(7) = 3 then SIGMA represents the shift. c Not referenced if IPARAM(7) = 1 or 2. c c WORKEV Complex work array of dimension NCV. (WORKSPACE) c c N Integer. (INPUT) c Dimension of the eigenproblem. c c AB Complex array of dimension LDA by N. (INPUT) c The matrix A in band storage, in rows KL+1 to c 2*KL+KU+1; rows 1 to KL of the array need not be set. c The j-th column of A is stored in the j-th column of the c array AB as follows: c AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) c c MB Complex array of dimension LDA by N. (INPUT) c The matrix M in band storage, in rows KL+1 to c 2*KL+KU+1; rows 1 to KL of the array need not be set. c The j-th column of M is stored in the j-th column of the c array MB as follows: c MB(kl+ku+1+i-j,j) = M(i,j) for max(1,j-ku)<=i<=min(m,j+kl) c Not referenced if IPARAM(7)=1. c c LDA Integer. (INPUT) c Leading dimension of AB, MB, FAC. c c FAC Complex array of LDA by N. (WORKSPACE/OUTPUT) c FAC is used to store the LU factors of MB when mode 2 c is invoked. It is used to store the LU factors of c (A-sigma*M) when mode 3 is invoked. c It is not referenced when IPARAM(7)=1. c c KL Integer. (INPUT) c Max(number of subdiagonals of A, number of subdiagonals of M) c c KU Integer. (OUTPUT) c Max(number of superdiagonals of A, number of superdiagonals of M) c c WHICH Character*2. (INPUT) c When mode 1,2 are used, WHICH can be set to any one of c the following. c c 'LM' -> want the NEV eigenvalues of largest magnitude. c 'SM' -> want the NEV eigenvalues of smallest magnitude. c 'LR' -> want the NEV eigenvalues of largest real part. c 'SR' -> want the NEV eigenvalues of smallest real part. c 'LI' -> want the NEV eigenvalues of largest imaginary part. c 'SI' -> want the NEV eigenvalues of smallest imaginary part. c c When mode 3 is used, WHICH should be set to 'LM' only. c c BMAT Character*1. (INPUT) c BMAT specifies the type of the matrix B that defines the c semi-inner product for the operator OP. c BMAT = 'I' -> standard eigenvalue problem A*x = lambda*x c BMAT = 'G' -> generalized eigenvalue problem A*x = lambda*M*x c NEV Integer. (INPUT) c Number of eigenvalues of to be computed. c c TOL Real scalar. (INPUT) c Stopping criteria: the relative accuracy of the Ritz value c is considered acceptable if BOUNDS(I) .LE. TOL*ABS(RITZ(I)) c where ABS(RITZ(I)) is the magnitude when RITZ(I) is complex. c DEFAULT = slamch('EPS') (machine precision as computed c by the LAPACK auxilliary subroutine slamch). c c RESID Complex array of length N. (INPUT/OUTPUT) c On INPUT: c If INFO .EQ. 0, a random initial residual vector is used. c If INFO .NE. 0, RESID contains the initial residual vector, c possibly from a previous run. c On OUTPUT: c RESID contains the final residual vector. c c NCV Integer. (INPUT) c Number of columns of the matrix V. NCV must satisfy the two c inequalities 2 <= NCV-NEV and NCV <= N. c This will indicate how many Arnoldi vectors are generated c at each iteration. After the startup phase in which NEV c Arnoldi vectors are generated, the algorithm generates c approximately NCV-NEV Arnoldi vectors at each subsequent update c iteration. Most of the cost in generating each Arnoldi vector is c in the matrix-vector operation OP*x. c c V Complex array N by NCV. (OUTPUT) c Upon OUTPUT: If RVEC = .TRUE. the first NCONV=IPARAM(5) columns c contain approximate Schur vectors that span the c desired invariant subspace. c c NOTE: If the array Z has been set equal to first NEV+1 columns c of the array V and RVEC=.TRUE. and HOWMNY= 'A', then c the first NCONV=IPARAM(5) columns of V will contain Ritz vectors c of the eigensystem A*z = lambda*B*z. c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling c program. LDV must be great than or equal to N. c c IPARAM Integer array of length 11. (INPUT/OUTPUT) c IPARAM(1) = ISHIFT: c The shifts selected at each iteration are used to restart c the Arnoldi iteration in an implicit fashion. c It is set to 1 in this subroutine. The user do not need c to set this parameter. c ---------------------------------------------------------- c ISHIFT = 1: exact shift with respect to the current c Hessenberg matrix H. This is equivalent to c restarting the iteration from the beginning c after updating the starting vector with a linear c combination of Ritz vectors associated with the c "wanted" eigenvalues. c ------------------------------------------------------------- c c IPARAM(2) = Not referenced. c c IPARAM(3) = MXITER c On INPUT: max number of Arnoldi update iterations allowed. c On OUTPUT: actual number of Arnoldi update iterations taken. c c IPARAM(4) = NB: blocksize to be used in the recurrence. c The code currently works only for NB = 1. c c IPARAM(5) = NCONV: number of "converged" eigenvalues. c c IPARAM(6) = IUPD c Not referenced. Implicit restarting is ALWAYS used. c c IPARAM(7) = MODE c On INPUT determines what type of eigenproblem is being solved. c Must be 1,2 or 3; See under \Description of cnband for the c three modes available. c c WORKD Complex work array of length at least 3*n. (WORKSPACE) c c WORKL Complex work array of length LWORKL. (WORKSPACE) c c LWORKL Integer. (INPUT) c LWORKL must be at least 3*NCV**2 + 5*NCV. c c RWORK Real array of length N (WORKSPACE) c Workspace used in cnaupd. c c IWORK Integer array of dimension at least N. (WORKSPACE) c Used to mode 2,3. Store the pivot information in the c factorization of M or (A-SIGMA*M). c c INFO Integer. (INPUT/OUTPUT) c Error flag on output. c = 0: Normal exit. c = -1: N must be positive. c = -2: NEV must be positive. c = -3: NCV-NEV >= 2 and less than or equal to N. c = -5: WHICH must be one of 'LM', 'SM', 'LR', 'SR', 'LI', 'SI' c = -6: BMAT must be one of 'I' or 'G'. c = -7: Length of private work WORKL array is not sufficient. c = -8: Error return from LAPACK eigenvalue calculation. c This should never happened. c = -10: IPARAM(7) must be 1,2,3. c = -11: IPARAM(7) = 1 and BMAT = 'G' are incompatible. c = -12: HOWMNY = 'S' not yet implemented c = -13: HOWMNY must be one of 'A' or 'P' if RVEC = .true. c = -14: CNAUPD did not find any eigenvalues to sufficient c accuracy. c c \EndDoc c c------------------------------------------------------------------------ c c\BeginLib c c\Routines called c cnaupd ARPACK reverse communication interface routine. c cneupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c cgbtrf LAPACK band matrix factorization routine. c cgbtrs LAPACK band linear system solve routine. c clacpy LAPACK matrix copy routine. c ccopy Level 1 BLAS that copies one vector to another. c scnrm2 Level 1 BLAS that computes the norm of a vector. c cgbmv Level 2 BLAS that computes the band matrix vector product. c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly c Restarted Arnoldi Iteration", Ph.D thesis, TR95-13, Rice Univ, c May 1995. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: nband.F SID: 2.3 DATE OF SID: 10/17/00 RELEASE: 2 c c\EndLib c c----------------------------------------------------------------------- c subroutine cnband(rvec, howmny, select, d , z, ldz, sigma, & workev, n, ab, mb, lda, fac, kl, ku, which, & bmat, nev, tol, resid, ncv, v, ldv, iparam, & workd, workl, lworkl, rwork, iwork, info ) c c %------------------% c | Scalar Arguments | c %------------------% c Character which*2, bmat, howmny Logical rvec Integer n, lda, kl, ku, nev, ncv, ldv, & ldz, lworkl, info Complex & sigma Real & tol c c %-----------------% c | Array Arguments | c %-----------------% c Integer iparam(*), iwork(*) Logical select(*) Complex & d(*), resid(*), v(ldv,*), z(ldz,*), & ab(lda,*), mb(lda,*), fac(lda,*), & workd(*), workl(*), workev(*) Real & rwork(*) c c %--------------% c | Local Arrays | c %--------------% c integer ipntr(14) c c %---------------% c | Local Scalars | c %---------------% c integer ido, i, j, mode, ierr, itop, imid, ibot c c %------------% c | Parameters | c %------------% c Complex & one, zero parameter (one = (1.0E+0, 0.0E+0) , & zero = (0.0E+0, 0.0E+0) ) c c %-----------------------------% c | LAPACK & BLAS routines used | c %-----------------------------% c Real & scnrm2 external ccopy, cgbmv, cgbtrf, cgbtrs, scnrm2, clacpy c c %-----------------------% c | Executable Statements | c %-----------------------% c mode = iparam(7) c c %------------------------% c | Initialize the reverse | c | communication flag. | c %------------------------% c ido = 0 c c %----------------% c | Exact shift is | c | used. | c %----------------% c iparam(1) = 1 c c %-----------------------------------% c | Both matrices A and M are stored | c | between rows itop and ibot. Imid | c | is the index of the row that | c | stores the diagonal elements. | c %-----------------------------------% c itop = kl + 1 imid = kl + ku + 1 ibot = 2*kl + ku + 1 c if ( mode .eq. 2 ) then c c %-----------------------------------------------% c | Copy M to fac and Call LAPACK routine cgbtrf | c | to factor M. | c %-----------------------------------------------% c call clacpy ('A', ibot, n, mb, lda, fac, lda ) call cgbtrf(n, n, kl, ku, fac, lda, iwork, ierr) if (ierr .ne. 0) then print*, ' ' print*,'_band: error in _gbtrf' print*, ' ' go to 9000 end if c else if ( mode .eq. 3 ) then c if (bmat .eq. 'I') then c c %-------------------------% c | Construct (A - sigma*I) | c %-------------------------% c call clacpy ('A', ibot, n, ab, lda, fac, lda ) do 10 j = 1,n fac(imid,j) = ab(imid,j) - sigma 10 continue c else c c %---------------------------% c | Construct (A - sigma*M) | c %---------------------------% c do 30 j = 1,n do 20 i = itop, ibot fac(i,j) = ab(i,j) - sigma*mb(i,j) 20 continue 30 continue c end if c c %------------------------% c | Factor (A - sigma*M) | c %------------------------% c call cgbtrf(n, n, kl, ku, fac, lda, iwork, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, '_band: error in _gbtrf.' print*, ' ' go to 9000 end if c end if c c %--------------------------------------------% c | M A I N L O O P (reverse communication) | c %--------------------------------------------% c 40 continue c call cnaupd ( ido, bmat, n, which, nev, tol, resid, ncv, & v, ldv, iparam, ipntr, workd, workl, lworkl, & rwork,info ) c if (ido .eq. -1) then c if ( mode .eq. 1) then c c %----------------------------% c | Perform y <--- OP*x = A*x | c %----------------------------% c call cgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) c else if ( mode .eq. 2 ) then c c %-----------------------------------% c | Perform y <--- OP*x = inv[M]*A*x | c %-----------------------------------% c call cgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) c call cgbtrs ('Notranspose', n, kl, ku, 1, fac, lda, & iwork, workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_band: error in sbgtrs.' print*, ' ' go to 9000 end if c else if ( mode .eq. 3 ) then c c %-----------------------------------------% c | Perform y <-- OP*x | c | = inv[A-SIGMA*M]*M* x c | to force the starting vector into the | c | range of OP. | c %-----------------------------------------% c call cgbmv('Notranspose', n, n, kl, ku, one, mb(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) c call cgbtrs ('Notranspose', n, kl, ku, 1, fac, lda, & iwork, workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_band: error in _gbtrs.' print*, ' ' go to 9000 end if c end if c else if (ido .eq. 1) then c if ( mode .eq. 1) then c c %----------------------------% c | Perform y <--- OP*x = A*x | c %----------------------------% c call cgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) c else if ( mode .eq. 2 ) then c c %-----------------------------------% c | Perform y <--- OP*x = inv[M]*A*x | c %-----------------------------------% c call cgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) c call cgbtrs ('Notranspose', n, kl, ku, 1, fac, lda, & iwork, workd(ipntr(2)), ldv, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_band: error in sbgtrs.' print*, ' ' go to 9000 end if c else if ( mode .eq. 3 ) then c if ( bmat .eq. 'I' ) then c c %----------------------------------% c | Perform y <-- inv(A-sigma*I)*x. | c %----------------------------------% c call ccopy(n, workd(ipntr(1)), 1, workd(ipntr(2)), 1) call cgbtrs ('Notranspose', n, kl, ku, 1, fac, lda, & iwork, workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_band: error in _gbtrs.' print*, ' ' go to 9000 end if c else c c %--------------------------------------% c | Perform y <-- inv(A-sigma*M)*(M*x). | c | (M*x) has been computed and stored | c | in workd(ipntr(3)). | c %--------------------------------------% c call ccopy(n, workd(ipntr(3)), 1, workd(ipntr(2)), 1) call cgbtrs ('Notranspose', n, kl, ku, 1, fac, lda, & iwork, workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_band: error in _gbtrs.' print*, ' ' go to 9000 end if c end if c endif c else if (ido .eq. 2) then c c %--------------------% c | Perform y <-- M*x | c %--------------------% c call cgbmv('Notranspose', n, n, kl, ku, one, mb(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) c else c c %-------------------------------------------% c | Either we have convergence, or there is | c | error. | c %-------------------------------------------% c if ( info .ne. 0) then c c %--------------------------% c | Error message, check the | c | documentation in dnaupd | c %--------------------------% c print *, ' ' print *, ' Error with _naupd info = ',info print *, ' Check the documentation of _naupd ' print *, ' ' c else c call cneupd (rvec, howmny , select, d, z, ldz, sigma, & workev, bmat, n, which, nev, tol, & resid, ncv, v, ldv, iparam, ipntr, workd, & workl, lworkl, rwork, info) c if ( info .ne. 0) then c c %------------------------------------% c | Check the documentation of cneupd. | c %------------------------------------% c print *, ' ' print *, ' Error with _neupd = ', info print *, ' Check the documentation of _neupd ' print *, ' ' c endif c end if c go to 9000 c end if c c %----------------------------------------% c | L O O P B A C K to call cnaupd again. | c %----------------------------------------% c go to 40 c 9000 continue c end arpack-0.92.1/EXAMPLES/BAND/znbdr4.f0000644000175000017500000002462710776001577013306 00000000000000 program zndrv4 c c ... Construct matrices A and M in LAPACK-style band form. c Matries A and M are derived from the finite c element discretization of the 1-dimensional c convection-diffusion operator c (d^2u/dx^2) + rho*(du/dx) c on the interval [0,1] with zero boundary condition using c piecewise linear elements. c c ... Call ZNBAND to find eigenvalues LAMBDA such that c A*x = M*x*LAMBDA. c c ... Use mode 3 of ZNAUPD . c c\BeginLib c c\Routines called: c znband ARPACK banded eigenproblem solver. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c zlaset LAPACK routine to initialize a matrix to zero. c zaxpy Level 1 BLAS that computes y <- alpha*x+y. c dznrm2 Level 1 BLAS that computes the norm of a vector. c zgbmv Level 2 BLAS that computes the band matrix vector product. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: nbdr4.F SID: 2.5 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c------------------------------------------------------------------------- c c %-------------------------------------% c | Define leading dimensions for all | c | arrays. | c | MAXN - Maximum size of the matrix | c | MAXNEV - Maximum number of | c | eigenvalues to be computed | c | MAXNCV - Maximum number of Arnoldi | c | vectors stored | c | MAXBDW - Maximum bandwidth | c %-------------------------------------% c integer maxn, maxnev, maxncv, maxbdw, lda, & lworkl, ldv parameter ( maxn = 1000, maxnev = 25, maxncv=50, & maxbdw=50, lda = maxbdw, ldv = maxn) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), iwork(maxn) logical select(maxncv) Complex*16 & a(lda,maxn), m(lda,maxn), fac(lda,maxn), & workl(3*maxncv*maxncv+5*maxncv), workd(3*maxn), & workev(2*maxncv), v(ldv, maxncv), & resid(maxn), d(maxncv), ax(maxn), mx(maxn) Double precision & rwork(maxn), rd(maxncv,3) c c %---------------% c | Local Scalars | c %---------------% c character which*2, bmat integer nev, ncv, ku, kl, info, j, & n, idiag, isup, isub, maxitr, mode, & nconv logical rvec Double precision & tol Complex*16 & rho, h, sigma c c %------------% c | Parameters | c %------------% c Complex*16 & one, zero, two, four, six parameter (one = (1.0D+0, 0.0D+0) , & zero = (0.0D+0, 0.0D+0) , & two = (2.0D+0, 0.0D+0) , & four = (4.0D+0, 0.0D+0) , & six = (6.0D+0, 0.0D+0) ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & dznrm2 , dlapy2 external dznrm2 , zgbmv , zaxpy , dlapy2 , zlaset c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------------------------% c | The number NX is the number of interior points | c | in the discretization of the 2-dimensional | c | convection-diffusion operator on the unit | c | square with zero Dirichlet boundary condition. | c | The number N(=NX*NX) is the dimension of the | c | matrix. A generalized eigenvalue problem is | c | solved (BMAT = 'G'). NEV is the number of | c | eigenvalues (closest to the shift SIGMA) to be | c | approximated. Since the shift and invert mode | c | is used, WHICH is set to 'LM'. The user can | c | modify NX, NEV and NCV to solve problems of | c | different sizes, and to get different parts the | c | spectrum. However, the following conditions | c | must be satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 2 <= NCV <= MAXNCV | c %-------------------------------------------------% c n = 100 nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _NBDR4: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NBDR4: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NBDR4: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' sigma = (1.0D+1, 0.0D+0) c c %----------------------------------------------------% c | The work array WORKL is used in ZNAUPD as | c | workspace. Its dimension LWORKL has to be set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine machine | c | precision is used. Setting INFO=0 indicates that | c | we using a randomly generated vector to start the | c | the ARNOLDI process. | c %----------------------------------------------------% c lworkl = 3*ncv**2+5*ncv info = 0 tol = 0.0 c c %---------------------------------------------------% c | IPARAm(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 3 of ZNAUPD is used | c | (IPARAm(7) = 3). All these options can be changed | c | by the user. For details, see the documentation | c | in znband . | c %---------------------------------------------------% c maxitr = 300 mode = 3 c iparam(3) = maxitr iparam(7) = mode c c %--------------------------------------------% c | Construct matrices A and M in LAPACK-style | c | banded form. | c %--------------------------------------------% c c %---------------------------------------------% c | Zero out the workspace for banded matrices. | c %---------------------------------------------% c call zlaset ('A', lda, n, zero, zero, a, lda) call zlaset ('A', lda, n, zero, zero, m, lda) call zlaset ('A', lda, n, zero, zero, fac, lda) c c %-------------------------------------% c | KU, KL are number of superdiagonals | c | and subdiagonals within the band of | c | matrices A and M. | c %-------------------------------------% c kl = 1 ku = 1 c c %---------------% c | Main diagonal | c %---------------% c h = one / dcmplx (n+1) idiag = kl+ku+1 do 30 j = 1, n a(idiag,j) = two / h m(idiag,j) = four * h / six 30 continue c c %-------------------------------------% c | First subdiagonal and superdiagonal | c %-------------------------------------% c isup = kl+ku isub = kl+ku+2 rho = (1.0D+1, 0.0D+0) do 40 j = 1, n-1 a(isup,j+1) = -one/h + rho/two a(isub,j) = -one/h - rho/two m(isup,j+1) = one*h / six m(isub,j) = one*h / six 40 continue c c %-----------------------------------------------% c | Call ARPACK banded solver to find eigenvalues | c | and eigenvectors. Eigenvalues are returned in | c | the one dimensional array D. Eigenvectors | c | are returned in the first NCONV (=IPARAM(5)) | c | columns of V. | c %-----------------------------------------------% c rvec = .true. call znband (rvec, 'A', select, d, v, ldv, sigma, & workev, n, a, m, lda, fac, kl, ku, which, & bmat, nev, tol, resid, ncv, v, ldv, iparam, & workd, workl, lworkl, rwork, iwork, info) c if ( info .eq. 0) then c nconv = iparam(5) c c %-----------------------------------% c | Print out convergence information | c %-----------------------------------% c print *, ' ' print *, '_NBDR4 ' print *, '====== ' print *, ' ' print *, ' The size of the matrix is ', n print *, ' Number of eigenvalue requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' The number of converged Ritz values is ', & nconv print *, ' What portion of the spectrum ', which print *, ' The number of Implicit Arnoldi ', & ' update taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence tolerance is ', tol print *, ' ' c do 90 j = 1, nconv c c %----------------------------% c | Compute the residual norm. | c | || A*x - lambda*x || | c %----------------------------% c call zgbmv ('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call zgbmv ('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j), 1, zero, & mx, 1) call zaxpy (n, -d(j), mx, 1, ax, 1) rd(j,1) = dble (d(j)) rd(j,2) = dimag (d(j)) rd(j,3) = dznrm2 (n, ax, 1) rd(j,3) = rd(j,3) / dlapy2 (rd(j,1), rd(j,2)) 90 continue call dmout (6, nconv, 3, rd, maxncv, -6, & 'Ritz values (Real,Imag) and relative residuals') else c c %-------------------------------------% c | Either convergence failed, or there | c | is error. Check the documentation | c | for znband . | c %-------------------------------------% c print *, ' ' print *, ' Error with _band, info= ', info print *, ' Check the documentation of _band ' print *, ' ' c end if c 9000 end arpack-0.92.1/EXAMPLES/BAND/snbdr5.f0000644000175000017500000002763610776001577013303 00000000000000 program snbdr5 c c ... Construct matrices A and M in LAPACK-style band form. c The matrix A is a block tridiagonal matrix. Each c diagonal block is a tridiagonal matrix with c 4 on the diagonal, 1-rho*h/2 on the subdiagonal and c 1+rho*h/2 on the superdiagonal. Each off-diagonal block c of A is an identity matrices. c c ... Define COMPLEX shift SIGMA = (SIGMAR,SIGMAI), SIGMAI .ne. 0. c c ... Call SNBAND to find eigenvalues LAMBDA closest to SIGMA c such that c A*x = LAMBDA*x. c c ... Use mode 4 of SNAUPD. c c\BeginLib c c\Routines called: c snband ARPACK banded eigenproblem solver. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c slaset LAPACK routine to initialize a matrix to zero. c saxpy Level 1 BLAS that computes y <- alpha*x+y. c snrm2 Level 1 BLAS that computes the norm of a vector. c sgbmv Level 2 BLAS that computes the band matrix vector product. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: nbdr5.F SID: 2.5 DATE OF SID: 08/26/96 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c------------------------------------------------------------------------- c c %-------------------------------------% c | Define leading dimensions for all | c | arrays. | c | MAXN - Maximum size of the matrix | c | MAXNEV - Maximum number of | c | eigenvalues to be computed | c | MAXNCV - Maximum number of Arnoldi | c | vectors stored | c | MAXBDW - Maximum bandwidth | c %-------------------------------------% c integer maxn, maxnev, maxncv, maxbdw, lda, & lworkl, ldv parameter ( maxn = 1000, maxnev = 25, maxncv=50, & maxbdw=50, lda = maxbdw, ldv = maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), iwork(maxn) logical select(maxncv) Real & a(lda,maxn), m(lda,maxn), rfac(lda,maxn), & workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn), & workev(3*maxncv), v(ldv, maxncv), & resid(maxn), d(maxncv, 3), ax(maxn) Complex & cfac(lda, maxn), workc(maxn) c c %---------------% c | Local Scalars | c %---------------% c character which*2, bmat integer nev, ncv, ku, kl, info, i, j, ido, & n, nx, lo, idiag, isup, isub, mode, maxitr, & nconv logical rvec, first Real & tol, rho, h, sigmar, sigmai c c %------------% c | Parameters | c %------------% c Real & one, zero, two parameter (one = 1.0E+0 , zero = 0.0E+0 , & two = 2.0E+0 ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & slapy2, snrm2 external slapy2, snrm2, sgbmv, saxpy c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c %--------------------------------------------------% c | The number NX is the size of each block diagonal | c | of A. The number N(=NX*NX) is the dimension of | c | the matrix. A standard eigenvalue problem is | c | solved (BMAT = 'I'). NEV is the number of | c | eigenvalues (closest to (SIGMAR,SIGMAI)) to be | c | approximated. Since the shift-invert moded is | c | used, WHICH is set to 'LM'. The user can modify | c | NX, NEV, NCV, SIGMAR, SIGMAI to solve problems | c | of different sizes, and to get different parts | c | the spectrum. However, The following conditions | c | must be satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 2 <= NCV <= MAXNCV | c %--------------------------------------------------% c nx = 10 n = nx*nx nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _NBDR5: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NBDR5: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NBDR5: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'I' which = 'LM' sigmar = 4.0E-1 sigmai = 6.0E-1 c c %-----------------------------------------------------% c | The work array WORKL is used in SNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in SNAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = 3*ncv**2+6*ncv tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 4 of SNAUPD is used | c | (IPARAM(7) = 4). All these options can be changed | c | by the user. For details, see the documentation | c | in SNBAND. | c %---------------------------------------------------% c maxitr = 300 mode = 4 c iparam(3) = maxitr iparam(7) = mode c c %--------------------------------------------% c | Construct matrices A and M in LAPACK-style | c | banded form. | c %--------------------------------------------% c c %---------------------------------------------% c | Zero out the workspace for banded matrices. | c %---------------------------------------------% c call slaset('A', lda, n, zero, zero, a, lda) call slaset('A', lda, n, zero, zero, m, lda) call slaset('A', lda, n, zero, zero, rfac, lda) c c %-------------------------------------% c | KU, KL are number of superdiagonals | c | and subdiagonals within the band of | c | matrices A and M. | c %-------------------------------------% c kl = nx ku = nx c c %---------------% c | Main diagonal | c %---------------% c idiag = kl+ku+1 do 30 j = 1, n a(idiag,j) = 4.0E+0 m(idiag,j) = 4.0E+0 30 continue c c %-------------------------------------% c | First subdiagonal and superdiagonal | c %-------------------------------------% c isup = kl+ku isub = kl+kl+2 h = one / real (nx+1) rho = 1.0E+2 do 50 i = 1, nx lo = (i-1)*nx do 40 j = lo+1, lo+nx-1 a(isup,j+1) = -one+h*rho/two a(isub,j) = -one-h*rho/two 40 continue 50 continue c do 60 j = 1, n-1 m(isup,j+1) = one m(isub,j) = one 60 continue c c %------------------------------------% c | KL-th subdiagonal and KU-th super- | c | diagonal. | c %------------------------------------% c isup = kl+1 isub = 2*kl+ku+1 do 80 i = 1, nx-1 lo = (i-1)*nx do 70 j = lo+1, lo+nx a(isup,nx+j) = -one a(isub,j) = -one 70 continue 80 continue c c %------------------------------------------------% c | Call ARPACK banded solver to find eigenvalues | c | and eigenvectors. The real parts of the | c | eigenvalues are returned in the first column | c | of D, the imaginary parts are returned in the | c | second column of D. Eigenvectors are returned | c | in the first NCONV (=IPARAM(5)) columns of V. | c %------------------------------------------------% c rvec = .true. call snband(rvec, 'A', select, d, d(1,2), v, ldv, sigmar, & sigmai, workev, n, a, m, lda, rfac, cfac, ku, kl, & which, bmat, nev, tol, resid, ncv, v, ldv, iparam, & workd, workl, lworkl, workc, iwork, info) c if ( info .eq. 0) then c c %-----------------------------------% c | Print out convergence information | c %-----------------------------------% c nconv = iparam(5) c print *, ' ' print *, ' _NBDR5 ' print *, ' ====== ' print *, ' ' print *, ' The size of the matrix is ', n print *, ' Number of eigenvalue requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' The number of converged Ritz values is ', & nconv print *, ' What portion of the spectrum ', which print *, ' The number of Implicit Arnoldi ', & ' update taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence tolerance is ', tol print *, ' ' c c %----------------------------% c | Compute the residual norm. | c | || A*x - lambda*x || | c %----------------------------% c first = .true. do 90 j = 1, nconv c if ( d(j,2) .eq. zero ) then c c %--------------------% c | Ritz value is real | c %--------------------% c call sgbmv('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call saxpy(n, -d(j,1), v(1,j), 1, ax, 1) d(j,3) = snrm2(n, ax, 1) d(j,3) = d(j,3) / abs(d(j,1)) c else if ( first ) then c c %------------------------% c | Ritz value is complex | c | Residual of one Ritz | c | value of the conjugate | c | pair is computed. | c %------------------------% c call sgbmv('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call saxpy(n, -d(j,1), v(1,j), 1, ax, 1) call saxpy(n, d(j,2), v(1,j+1), 1, ax, 1) d(j,3) = snrm2(n, ax, 1) call sgbmv('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j+1), 1, zero, & ax, 1) call saxpy(n, -d(j,1), v(1,j+1), 1, ax, 1) call saxpy(n, -d(j,2), v(1,j), 1, ax, 1) d(j,3) = slapy2( d(j,3), snrm2(n, ax, 1) ) d(j,3) = d(j,3) / slapy2(d(j,1),d(j,2)) d(j+1,3) = d(j,3) first = .false. else first = .true. end if c 90 continue call smout(6, nconv, 3, d, maxncv, -6, & 'Ritz values (Real,Imag) and relative residuals') else c c %-------------------------------------% c | Either convergence failed, or there | c | is error. Check the documentation | c | for SNBAND. | c %-------------------------------------% c print *, ' ' print *, ' Error with _nband, info= ', info print *, ' Check the documentation of _nband ' print *, ' ' c end if c 9000 end arpack-0.92.1/EXAMPLES/BAND/dsbdr4.f0000644000175000017500000002343210776001577013256 00000000000000 program dsbdr4 c c ... Construct the matrix A in LAPACK-style band form. c The matrix A is the 1-dimensional discrete Laplacian on [0,1] c with zero Dirichlet boundary condition, M is the mass c formed by using piecewise linear elements on [0,1]. c c ... Call DSBAND with shift-invert mode to find eigenvalues LAMBDA c closest to SIGMA such that c A*x = LAMBDA*M*x. c c ... Use mode 3 of DSAUPD . c c\BeginLib c c\Routines called: c dsband ARPACK banded eigenproblem solver. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c dlaset LAPACK routine to initialize a matrix to zero. c daxpy Level 1 BLAS that computes y <- alpha*x+y. c dnrm2 Level 1 BLAS that computes the norm of a vector. c dgbmv Level 2 BLAS that computes the band matrix vector product c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: sbdr4.F SID: 2.5 DATE OF SID: 08/26/96 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c---------------------------------------------------------------------- c c %-------------------------------------% c | Define leading dimensions for all | c | arrays. | c | MAXN - Maximum size of the matrix | c | MAXNEV - Maximum number of | c | eigenvalues to be computed | c | MAXNCV - Maximum number of Arnoldi | c | vectors stored | c | MAXBDW - Maximum bandwidth | c %-------------------------------------% c integer maxn, maxnev, maxncv, maxbdw, lda, & lworkl, ldv parameter ( maxn = 1000, maxnev = 25, maxncv=50, & maxbdw=50, lda = maxbdw, ldv = maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), iwork(maxn) logical select(maxncv) Double precision & a(lda,maxn), m(lda,maxn), rfac(lda,maxn), & workl(maxncv*maxncv+8*maxncv), workd(3*maxn), & v(ldv, maxncv), resid(maxn), d(maxncv, 2), & ax(maxn), mx(maxn) c c %---------------% c | Local Scalars | c %---------------% c character which*2, bmat integer nev, ncv, ku, kl, info, j, ido, & n, isub, isup, idiag, maxitr, mode, nconv Double precision & tol, h, sigma, r1, r2 logical rvec c c %------------% c | Parameters | c %------------% c Double precision & one, zero, two, four, six parameter (one = 1.0D+0 , zero = 0.0D+0 , two = 2.0D+0 , & four = 4.0D+0 , six = 6.0D+0 ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & dlapy2 , dnrm2 external dlapy2 , dnrm2 , daxpy , dgbmv c c %-----------------------% c | Executable Statements | c %-----------------------% c c %--------------------------------------------------% c | The number N is the dimension of the matrix. A | c | generalized eigenvalue problem is solved | c | (BMAT = 'G'). NEV is the number of eigenvalues | c | (closest to the shift SIGMA) to be approximated. | c | Since the shift and invert mode is used, WHICH | c | is set to 'LM'. The user can modify N, NEV, NCV | c | and SIGMA to solve problems of different sizes, | c | and to get different parts the spectrum. | c | However, the following conditions must be | c | satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 1 <= NCV <= MAXNCV | c %--------------------------------------------------% c n = 100 nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _SBDR4: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _SBDR4: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _SBDR4: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' sigma = zero c c %-----------------------------------------------------% c | The work array WORKL is used in DSAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in DSAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = ncv**2+8*ncv tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 3 of DSAUPD is used | c | (IPARAM(7) = 3). All these options can be changed | c | by the user. For details, see the documentation | c | in DSBAND . | c %---------------------------------------------------% c maxitr = 300 mode = 3 c iparam(3) = maxitr iparam(7) = mode c c %----------------------------------------% c | Construct the matrix A in LAPACK-style | c | banded form. | c %----------------------------------------% c c %---------------------------------------------% c | Zero out the workspace for banded matrices. | c %---------------------------------------------% c call dlaset ('A', lda, n, zero, zero, a, lda) call dlaset ('A', lda, n, zero, zero, m, lda) call dlaset ('A', lda, n, zero, zero, rfac, lda) c c %-------------------------------------% c | KU, KL are number of superdiagonals | c | and subdiagonals within the band of | c | matrices A and M. | c %-------------------------------------% c kl = 1 ku = 1 c c %---------------% c | Main diagonal | c %---------------% c h = one / dble (n+1) r1 = four / six idiag = kl+ku+1 do 30 j = 1, n a(idiag,j) = two / h m(idiag,j) = r1 * h 30 continue c c %-------------------------------------% c | First subdiagonal and superdiagonal | c %-------------------------------------% c r2 = one / six isup = kl+ku isub = kl+ku+2 do 60 j = 1, n-1 a(isup,j+1) = -one / h a(isub,j) = -one / h m(isup,j+1) = r2 * h m(isub,j) = r2 * h 60 continue c c %-------------------------------------% c | Call DSBAND to find eigenvalues and | c | eigenvectors. Eigenvalues are | c | returned in the first column of D. | c | Eigenvectors are returned in the | c | first NCONV (=IPARAM(5)) columns of | c | V. | c %-------------------------------------% c rvec = .true. call dsband ( rvec, 'A', select, d, v, ldv, sigma, n, a, m, & lda, rfac, kl, ku, which, bmat, nev, tol, & resid, ncv, v, ldv, iparam, workd, workl, lworkl, & iwork, info) c if ( info .eq. 0) then c nconv = iparam(5) c c %-----------------------------------% c | Print out convergence information | c %-----------------------------------% c print *, ' ' print *, ' _SBDR4 ' print *, ' ====== ' print *, ' ' print *, ' The size of the matrix is ', n print *, ' Number of eigenvalue requested is ', nev print *, ' The number of Lanczos vectors generated', & ' (NCV) is ', ncv print *, ' The number of converged Ritz values is ', & nconv print *, ' What portion of the spectrum ', which print *, ' The number of Implicit Arnoldi', & ' update taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence tolerance is ', tol print *, ' ' c c %----------------------------% c | Compute the residual norm. | c | || A*x - lambda*x || | c %----------------------------% c do 90 j = 1, nconv call dgbmv ('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call dgbmv ('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j), 1, zero, & mx, 1) call daxpy (n, -d(j,1), mx, 1, ax, 1) d(j,2) = dnrm2 (n, ax, 1) d(j,2) = d(j,2) / abs(d(j,1)) c 90 continue call dmout (6, nconv, 2, d, maxncv, -6, & 'Ritz values and relative residuals') else c c %-------------------------------------% c | Either convergence failed, or there | c | is error. Check the documentation | c | for DSBAND . | c %-------------------------------------% c print *, ' ' print *, ' Error with _sband, info= ', info print *, ' Check the documentation of _sband ' print *, ' ' c end if c 9000 end arpack-0.92.1/EXAMPLES/BAND/ssbdr3.f0000644000175000017500000002322510776001577013274 00000000000000 program ssbdr3 c c ... Construct the matrix A in LAPACK-style band form. c The matrix A is the 1-dimensional discrete Laplacian on [0,1] c with zero Dirichlet boundary condition, M is the mass c formed by using piecewise linear elements on [0,1]. c c ... Call SSBAND with regular mode to find eigenvalues LAMBDA c such that c A*x = LAMBDA*M*x. c c ... Use mode 2 of SSAUPD. c c\BeginLib c c\Routines called: c ssband ARPACK banded eigenproblem solver. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c slaset LAPACK routine to initialize a matrix to zero. c saxpy Level 1 BLAS that computes y <- alpha*x+y. c snrm2 Level 1 BLAS that computes the norm of a vector. c sgbmv Level 2 BLAS that computes the band matrix vector product c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: sbdr3.F SID: 2.5 DATE OF SID: 08/26/96 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c---------------------------------------------------------------------- c c %-------------------------------------% c | Define leading dimensions for all | c | arrays. | c | MAXN - Maximum size of the matrix | c | MAXNEV - Maximum number of | c | eigenvalues to be computed | c | MAXNCV - Maximum number of Arnoldi | c | vectors stored | c | MAXBDW - Maximum bandwidth | c %-------------------------------------% c integer maxn, maxnev, maxncv, maxbdw, lda, & lworkl, ldv parameter ( maxn = 1000, maxnev = 25, maxncv=50, & maxbdw=50, lda = maxbdw, ldv = maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), iwork(maxn) logical select(maxncv) Real & a(lda,maxn), m(lda,maxn), rfac(lda,maxn), & workl(maxncv*maxncv+8*maxncv), workd(3*maxn), & v(ldv, maxncv), resid(maxn), d(maxncv, 2), & ax(maxn), mx(maxn) c c %---------------% c | Local Scalars | c %---------------% c character which*2, bmat integer nev, ncv, ku, kl, info, j, ido, & n, isub, isup, idiag, maxitr, mode, nconv Real & tol, h, sigma, r1, r2 logical rvec c c %------------% c | Parameters | c %------------% c Real & one, zero, two, four, six parameter (one = 1.0E+0 , zero = 0.0E+0 , two = 2.0E+0 , & four = 4.0E+0 , six = 6.0E+0 ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & slapy2, snrm2 external slapy2, snrm2, saxpy, sgbmv c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------------------------% c | The number N is the dimension of the matrix. A | c | generalized eigenvalue problem is solved | c | (BMAT = 'G'). NEV is the number of eigenvalues | c | to be approximated. The user can modify N, NEV, | c | NCV and WHICH to solve problems of different | c | sizes, and to get different parts the spectrum. | c | However, the following conditions must be | c | satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 1 <= NCV <= MAXNCV | c %-------------------------------------------------% c n = 100 nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _SBDR3: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _SBDR3: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _SBDR3: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' c c %-----------------------------------------------------% c | The work array WORKL is used in SSAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in SSAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = ncv**2+8*ncv tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 2 of SSAUPD is used | c | (IPARAM(7) = 2). All these options can be changed | c | by the user. For details see the documentation in | c | SSBAND. | c %---------------------------------------------------% c maxitr = 300 mode = 2 c iparam(3) = maxitr iparam(7) = mode c c %----------------------------------------% c | Construct the matrix A in LAPACK-style | c | banded form. | c %----------------------------------------% c c %---------------------------------------------% c | Zero out the workspace for banded matrices. | c %---------------------------------------------% c call slaset('A', lda, n, zero, zero, a, lda) call slaset('A', lda, n, zero, zero, m, lda) call slaset('A', lda, n, zero, zero, rfac, lda) c c %-------------------------------------% c | KU, KL are number of superdiagonals | c | and subdiagonals within the band of | c | matrices A and M. | c %-------------------------------------% c kl = 1 ku = 1 c c %---------------% c | Main diagonal | c %---------------% c h = one / real (n+1) r1 = four / six idiag = kl+ku+1 do 30 j = 1, n a(idiag,j) = two / h m(idiag,j) = r1 * h 30 continue c c %-------------------------------------% c | First subdiagonal and superdiagonal | c %-------------------------------------% c r2 = one / six isup = kl+ku isub = kl+ku+2 do 60 j = 1, n-1 a(isup,j+1) = -one / h a(isub,j) = -one / h m(isup,j+1) = r2 * h m(isub,j) = r2 * h 60 continue c c %-------------------------------------% c | Call SSBAND to find eigenvalues and | c | eigenvectors. Eigenvalues are | c | returned in the first column of D. | c | Eigenvectors are returned in the | c | first NCONV (=IPARAM(5)) columns of | c | V. | c %-------------------------------------% c rvec = .true. call ssband( rvec, 'A', select, d, v, ldv, sigma, n, a, m, lda, & rfac, kl, ku, which, bmat, nev, tol, & resid, ncv, v, ldv, iparam, workd, workl, lworkl, & iwork, info) c if ( info .eq. 0) then c nconv = iparam(5) c c %-----------------------------------% c | Print out convergence information | c %-----------------------------------% c print *, ' ' print *, ' _SBDR3 ' print *, ' ====== ' print *, ' ' print *, ' The size of the matrix is ', n print *, ' Number of eigenvalue requested is ', nev print *, ' The number of Lanczos vectors generated', & ' (NCV) is ', ncv print *, ' The number of converged Ritz values is ', & nconv print *, ' What portion of the spectrum ', which print *, ' The number of Implicit Arnoldi', & ' update taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence tolerance is ', tol print *, ' ' c c %----------------------------% c | Compute the residual norm. | c | || A*x - lambda*x || | c %----------------------------% c do 90 j = 1, nconv call sgbmv('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call sgbmv('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j), 1, zero, & mx, 1) call saxpy(n, -d(j,1), mx, 1, ax, 1) d(j,2) = snrm2(n, ax, 1) d(j,2) = d(j,2) / abs(d(j,1)) c 90 continue call smout(6, nconv, 2, d, maxncv, -6, & 'Ritz values and relative residuals') else c c %-------------------------------------% c | Either convergence failed, or there | c | is error. Check the documentation | c | for SSBAND. | c %-------------------------------------% c print *, ' ' print *, ' Error with _sband, info= ', info print *, ' Check the documentation of _sband ' print *, ' ' c end if c 9000 end arpack-0.92.1/EXAMPLES/BAND/dsbdr1.f0000644000175000017500000002422010776001577013247 00000000000000 program dsbdr1 c c ... Construct the matrix A in LAPACK-style band form. c The matrix A is derived from the discretization of c the 2-dimensional Laplacian on the unit square with c zero Dirichlet boundary condition using standard c central difference. c c ... Call DSBAND to find eigenvalues LAMBDA such that c A*x = x*LAMBDA. c c ... Use mode 1 of DSAUPD . c c\BeginLib c c\Routines called: c dsband ARPACK banded eigenproblem solver. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c dlaset LAPACK routine to initialize a matrix to zero. c daxpy Level 1 BLAS that computes y <- alpha*x+y. c dnrm2 Level 1 BLAS that computes the norm of a vector. c dgbmv Level 2 BLAS that computes the band matrix vector product c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: sbdr1.F SID: 2.5 DATE OF SID: 08/26/96 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c---------------------------------------------------------------------- c c %-------------------------------------% c | Define leading dimensions for all | c | arrays. | c | MAXN - Maximum size of the matrix | c | MAXNEV - Maximum number of | c | eigenvalues to be computed | c | MAXNCV - Maximum number of Arnoldi | c | vectors stored | c | MAXBDW - Maximum bandwidth | c %-------------------------------------% c integer maxn, maxnev, maxncv, maxbdw, lda, & lworkl, ldv parameter ( maxn = 1000, maxnev = 25, maxncv=50, & maxbdw=50, lda = maxbdw, ldv = maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), iwork(maxn) logical select(maxncv) Double precision & a(lda,maxn), m(lda,maxn), rfac(lda,maxn), & workl(maxncv*maxncv+8*maxncv), workd(3*maxn), & v(ldv, maxncv), resid(maxn), d(maxncv, 2), & ax(maxn) c c %---------------% c | Local Scalars | c %---------------% c character which*2, bmat integer nev, ncv, ku, kl, info, i, j, ido, & n, nx, lo, isub, isup, idiag, maxitr, mode, & nconv Double precision & tol, sigma, h2 logical rvec c c %------------% c | Parameters | c %------------% c Double precision & one, zero, two parameter (one = 1.0D+0 , zero = 0.0D+0 , two = 2.0D+0 ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & dlapy2 , dnrm2 external dlapy2 , dnrm2 , dgbmv , daxpy c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------------------------% c | The number NX is the number of interior points | c | in the discretization of the 2-dimensional | c | Laplacian operator on the unit square with zero | c | Dirichlet boundary condition. The number | c | N(=NX*NX) is the dimension of the matrix. A | c | standard eigenvalue problem is solved | c | (BMAT = 'I'). NEV is the number of eigenvalues | c | to be approximated. The user can modify NX,NEV, | c | NCV and WHICH to solve problems of different | c | sizes, and to get different parts the spectrum. | c | However, the following conditions must be | c | satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 1 <= NCV <= MAXNCV | c %-------------------------------------------------% c nx = 10 n = nx*nx nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _SBDR1: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _SBDR1: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _SBDR1: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'I' which = 'LM' c c %-----------------------------------------------------% c | The work array WORKL is used in DSAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in DSAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = ncv**2+8*ncv tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 1 of DSAUPD is used | c | (IPARAM(7) = 1). All these options can be changed | c | by the user. For details see the documentation in | c | DSBAND . | c %---------------------------------------------------% c maxitr = 300 mode = 1 c iparam(3) = maxitr iparam(7) = mode c c %----------------------------------------% c | Construct the matrix A in LAPACK-style | c | banded form. | c %----------------------------------------% c c %---------------------------------------------% c | Zero out the workspace for banded matrices. | c %---------------------------------------------% c call dlaset ('A', lda, n, zero, zero, a, lda) call dlaset ('A', lda, n, zero, zero, m, lda) call dlaset ('A', lda, n, zero, zero, rfac, lda) c c %-------------------------------------% c | KU, KL are number of superdiagonals | c | and subdiagonals within the band of | c | matrices A and M. | c %-------------------------------------% c kl = nx ku = nx c c %---------------% c | Main diagonal | c %---------------% c h2 = one / ((nx+1)*(nx+1)) idiag = kl+ku+1 do 30 j = 1, n a(idiag,j) = 4.0D+0 / h2 30 continue c c %-------------------------------------% c | First subdiagonal and superdiagonal | c %-------------------------------------% c isup = kl+ku isub = kl+ku+2 do 50 i = 1, nx lo = (i-1)*nx do 40 j = lo+1, lo+nx-1 a(isup,j+1) = -one / h2 a(isub,j) = -one / h2 40 continue 50 continue c c %------------------------------------% c | KL-th subdiagonal and KU-th super- | c | diagonal. | c %------------------------------------% c isup = kl+1 isub = 2*kl+ku+1 do 80 i = 1, nx-1 lo = (i-1)*nx do 70 j = lo+1, lo+nx a(isup,nx+j) = -one / h2 a(isub,j) = -one / h2 70 continue 80 continue c c %-------------------------------------% c | Call DSBAND to find eigenvalues and | c | eigenvectors. Eigenvalues are | c | returned in the first column of D. | c | Eigenvectors are returned in the | c | first NCONV (=IPARAM(5)) columns of | c | V. | c %-------------------------------------% c rvec = .true. call dsband ( rvec, 'A', select, d, v, ldv, sigma, n, a, m, lda, & rfac, kl, ku, which, bmat, nev, tol, & resid, ncv, v, ldv, iparam, workd, workl, lworkl, & iwork, info) c if ( info .eq. 0) then c nconv = iparam(5) c c %-----------------------------------% c | Print out convergence information | c %-----------------------------------% c print *, ' ' print *, ' _SBDR1 ' print *, ' ====== ' print *, ' ' print *, ' The size of the matrix is ', n print *, ' Number of eigenvalue requested is ', nev print *, ' The number of Lanczos vectors generated', & ' (NCV) is ', ncv print *, ' The number of converged Ritz values is ', & nconv print *, ' What portion of the spectrum ', which print *, ' The number of Implicit Arnoldi', & ' update taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence tolerance is ', tol print *, ' ' c c %----------------------------% c | Compute the residual norm. | c | || A*x - lambda*x || | c %----------------------------% c do 90 j = 1, nconv call dgbmv ('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call daxpy (n, -d(j,1), v(1,j), 1, ax, 1) d(j,2) = dnrm2 (n, ax, 1) d(j,2) = d(j,2) / abs(d(j,1)) c 90 continue call dmout (6, nconv, 2, d, maxncv, -6, & 'Ritz values and relative residuals') else c c %-------------------------------------% c | Either convergence failed, or there | c | is error. Check the documentation | c | for DSBAND . | c %-------------------------------------% c print *, ' ' print *, ' Error with _sband, info= ', info print *, ' Check the documentation of _sband ' print *, ' ' c end if c 9000 end arpack-0.92.1/EXAMPLES/BAND/makefile0000644000175000017500000001151510776001577013424 00000000000000# # makefile to run simple examples of the reverse communication # protocol. # # Modify if ARPACK library was built somewhere else. # # If ALIBS (defined in ../../ARmake.inc) contains the BLAS and LAPACK # libraries installed on your system, you DO NOT need to change this # makefile. OTHERWISE, you may need to modify the Makefile in the top level # ARPACK directory tree to include sdrv, ddrv, cdrv, or zdrv in the # definition of the PRECISION variable, and issue 'make lib' there. # For example: # # PRECISION = single double sdrv ddrv # #\SCCS Information: @(#) # FILE: makefile SID: 2.2 DATE OF SID: 9/24/96 RELEASE: 2 # include ../../ARmake.inc # Issue "make band" to make all 32 band drivers. # Issue "make ssbdr" to make 6 single precision symmetric band drivers. # Issue "make dsbdr" to make 6 double precision symmetric band drivers. # Issue "make snbdr" to make 6 single precision nonsymmetric band drivers. # Issue "make dnbdr" to make 6 double precision nonsymmetric band drivers. # Issue "make cnbdr" to make 4 single precision complex band drivers. # Issue "make znbdr" to make 4 double precision complex band drivers. # band: ssbdr dsbdr snbdr dnbdr cnbdr znbdr # #--------------------------------------------------------------------- # Simple symetric problem using BAND solver (single precision) # ssbdr: ssbdr1 ssbdr2 ssbdr3 ssbdr4 ssbdr5 ssbdr6 ssbdr1: ssbdr1.o ssband.o $(FC) $(FFLAGS) ssbdr1.o ssband.o $(ALIBS) -o ssbdr1 # ssbdr2: ssbdr2.o ssband.o $(FC) $(FFLAGS) ssbdr2.o ssband.o $(ALIBS) -o ssbdr2 # ssbdr3: ssbdr3.o ssband.o $(FC) $(FFLAGS) ssbdr3.o ssband.o $(ALIBS) -o ssbdr3 # ssbdr4: ssbdr4.o ssband.o $(FC) $(FFLAGS) ssbdr4.o ssband.o $(ALIBS) -o ssbdr4 # ssbdr5: ssbdr5.o ssband.o $(FC) $(FFLAGS) ssbdr5.o ssband.o $(ALIBS) -o ssbdr5 # ssbdr6: ssbdr6.o ssband.o $(FC) $(FFLAGS) ssbdr6.o ssband.o $(ALIBS) -o ssbdr6 # #------------------------------------------------------------- # # Simple symmetric problem using BAND solver (double precision) # dsbdr: dsbdr1 dsbdr2 dsbdr3 dsbdr4 dsbdr5 dsbdr6 dsbdr1: dsbdr1.o dsband.o $(FC) $(FFLAGS) dsbdr1.o dsband.o $(ALIBS) -o dsbdr1 # dsbdr2: dsbdr2.o dsband.o $(FC) $(FFLAGS) dsbdr2.o dsband.o $(ALIBS) -o dsbdr2 # dsbdr3: dsbdr3.o dsband.o $(FC) $(FFLAGS) dsbdr3.o dsband.o $(ALIBS) -o dsbdr3 # dsbdr4: dsbdr4.o dsband.o $(FC) $(FFLAGS) dsbdr4.o dsband.o $(ALIBS) -o dsbdr4 # dsbdr5: dsbdr5.o dsband.o $(FC) $(FFLAGS) dsbdr5.o dsband.o $(ALIBS) -o dsbdr5 # dsbdr6: dsbdr6.o dsband.o $(FC) $(FFLAGS) dsbdr6.o dsband.o $(ALIBS) -o dsbdr6 # #---------------------------------------------------------------------- # Simple nonsymmetric problem using BAND solver (single precision) # snbdr: snbdr1 snbdr2 snbdr3 snbdr4 snbdr5 snbdr6 snbdr1: snbdr1.o snband.o $(FC) $(FFLAGS) snbdr1.o snband.o $(ALIBS) -o snbdr1 # snbdr2: snbdr2.o snband.o $(FC) $(FFLAGS) snbdr2.o snband.o $(ALIBS) -o snbdr2 # snbdr3: snbdr3.o snband.o $(FC) $(FFLAGS) snbdr3.o snband.o $(ALIBS) -o snbdr3 # snbdr4: snbdr4.o snband.o $(FC) $(FFLAGS) snbdr4.o snband.o $(ALIBS) -o snbdr4 # snbdr5: snbdr5.o snband.o $(FC) $(FFLAGS) snbdr5.o snband.o $(ALIBS) -o snbdr5 # snbdr6: snbdr6.o snband.o $(FC) $(FFLAGS) snbdr6.o snband.o $(ALIBS) -o snbdr6 # #------------------------------------------------------------------------- # Simple nonsymmetric problem using BAND solver (double precision) # dnbdr: dnbdr1 dnbdr2 dnbdr3 dnbdr4 dnbdr5 dnbdr6 dnbdr1: dnbdr1.o dnband.o $(FC) $(FFLAGS) dnbdr1.o dnband.o $(ALIBS) -o dnbdr1 # dnbdr2: dnbdr2.o dnband.o $(FC) $(FFLAGS) dnbdr2.o dnband.o $(ALIBS) -o dnbdr2 # dnbdr3: dnbdr3.o dnband.o $(FC) $(FFLAGS) dnbdr3.o dnband.o $(ALIBS) -o dnbdr3 # dnbdr4: dnbdr4.o dnband.o $(FC) $(FFLAGS) dnbdr4.o dnband.o $(ALIBS) -o dnbdr4 # dnbdr5: dnbdr5.o dnband.o $(FC) $(FFLAGS) dnbdr5.o dnband.o $(ALIBS) -o dnbdr5 # dnbdr6: dnbdr6.o dnband.o $(FC) $(FFLAGS) dnbdr6.o dnband.o $(ALIBS) -o dnbdr6 # #------------------------------------------------------------------------- # Complex problem using BAND solver (single precision complex) # cnbdr: cnbdr1 cnbdr2 cnbdr3 cnbdr4 cnbdr1: cnbdr1.o cnband.o $(FC) $(FFLAGS) cnbdr1.o cnband.o $(ALIBS) -o cnbdr1 # cnbdr2: cnbdr2.o cnband.o $(FC) $(FFLAGS) cnbdr2.o cnband.o $(ALIBS) -o cnbdr2 # cnbdr3: cnbdr3.o cnband.o $(FC) $(FFLAGS) cnbdr3.o cnband.o $(ALIBS) -o cnbdr3 # cnbdr4: cnbdr4.o cnband.o $(FC) $(FFLAGS) cnbdr4.o cnband.o $(ALIBS) -o cnbdr4 # #------------------------------------------------------------------------- # Complex problem using BAND solver (double precision complex) # znbdr: znbdr1 znbdr2 znbdr3 znbdr4 znbdr1: znbdr1.o znband.o $(FC) $(FFLAGS) znbdr1.o znband.o $(ALIBS) -o znbdr1 # znbdr2: znbdr2.o znband.o $(FC) $(FFLAGS) znbdr2.o znband.o $(ALIBS) -o znbdr2 # znbdr3: znbdr3.o znband.o $(FC) $(FFLAGS) znbdr3.o znband.o $(ALIBS) -o znbdr3 # znbdr4: znbdr4.o znband.o $(FC) $(FFLAGS) znbdr4.o znband.o $(ALIBS) -o znbdr4 arpack-0.92.1/EXAMPLES/BAND/README0000644000175000017500000000457410776001577012613 000000000000001. Purpose ------- This directory contains example drivers that call subroutines [s,d]sband.f, [s,d]nband.f or [c,z]nband.f to solve various eigenvalue problems in which matrices have BANDED structure. These drivers illustrate how to construct LAPACK-style banded matrices, and how to set various ARPACK parameters to solve different problems in different modes. The user may modify any one of these drivers, and construct his/her own matrix to solve the problem of his/her own interest. 2. Naming convention ----------------- The name for each banded solver has the form 'XYband.f', where X - is 's' (single precision) or 'd' (double precision) or 'c' (single precision complex) or 'z' (double precision complex) Y - is 's' (symmetric) or 'n' (nonsymmetric) The name for each driver has the form 'XYbdrN.f', where X - is 's' (single precision) or 'd' (double precision) or 'c' (single precision complex) or 'z' (double precision complex) Y - is 's' (symmetric) or 'n' (nonsymmetric) N - is a number between 1 and 6. If N = 1, the driver solves a STANDARD eigenvalue problem in REGULAR mode. N = 2, the driver solves a STANDARD eigenvalue problem in SHIFT-INVERT mode. N = 3, the driver solves a GENERALIZED eigenvalue problem in INVERSE mode. N = 4, the driver solves a GENERALIZED eigenvalue problem in SHIFT-INVERT mode (using mode 3 of __aupd.) These are four commonly used drivers. When N > 4 (only for real matrices), a special mode is used. For symmetric problem, if N = 5, the driver solves a GENERALIZED eigenvalue problem in BUCKLING mode. N = 6, the driver solves a GENERALIZED eigenvalue problem in CAYLEY mode. For nonsymmetric problem, if N = 5, the driver solves a STANDARD eigenvalue problem in SHIFT-INVERT mode using mode 4 of [d,s]naupd.f. N = 6. the driver solves a GENERALIZED eigenvalue problem SHIFT-INVERT mode using mode 4 of [d,s]naupd.f. Note: the imaginary part of the shift MUST be nonzero when these two drivers are used. 3. Usage ----- To run these drivers, you may use the makefile in this directory and issue, for example, "make snbdr1". Then execute using "snbdr1". arpack-0.92.1/EXAMPLES/BAND/ssbdr6.f0000644000175000017500000002334410776001577013301 00000000000000 program ssbdr6 c c ... Construct the matrix A in LAPACK-style band form. c The matrix A is the 1-dimensional discrete Laplacian on [0,1] c with zero Dirichlet boundary condition, M is the mass c formed by using piecewise linear elements on [0,1]. c c ... Call SSBAND with Cayley mode to find eigenvalues LAMBDA such that c A*x = LAMBDA*M*x. c c ... Use mode 5 of SSAUPD. c c\BeginLib c c\Routines called: c ssband ARPACK banded eigenproblem solver. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c slaset LAPACK routine to initialize a matrix to zero. c saxpy Level 1 BLAS that computes y <- alpha*x+y. c snrm2 Level 1 BLAS that computes the norm of a vector. c sgbmv Level 2 BLAS that computes the band matrix vector product c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: sbdr6.F SID: 2.5 DATE OF SID: 08/26/96 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c---------------------------------------------------------------------- c c %-------------------------------------% c | Define leading dimensions for all | c | arrays. | c | MAXN - Maximum size of the matrix | c | MAXNEV - Maximum number of | c | eigenvalues to be computed | c | MAXNCV - Maximum number of Arnoldi | c | vectors stored | c | MAXBDW - Maximum bandwidth | c %-------------------------------------% c integer maxn, maxnev, maxncv, maxbdw, lda, & lworkl, ldv parameter ( maxn = 1000, maxnev = 25, maxncv=50, & maxbdw=50, lda = maxbdw, ldv = maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), iwork(maxn) logical select(maxncv) Real & a(lda,maxn), m(lda,maxn), rfac(lda,maxn), & workl(maxncv*maxncv+8*maxncv), workd(3*maxn), & v(ldv, maxncv), resid(maxn), d(maxncv, 2), & ax(maxn), mx(maxn) c c %---------------% c | Local Scalars | c %---------------% c character which*2, bmat integer nev, ncv, ku, kl, info, j, ido, & n, isub, isup, idiag, maxitr, mode, nconv Real & tol, h, sigma, r1, r2 logical rvec c c %------------% c | Parameters | c %------------% c Real & one, zero, two, four, six parameter (one = 1.0E+0 , zero = 0.0E+0 , two = 2.0E+0 , & four = 4.0E+0 , six = 6.0E+0 ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & slapy2, snrm2 external slapy2, snrm2, saxpy, sgbmv c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c %--------------------------------------------------% c | The number N is the dimension of the matrix. A | c | generalized eigenvalue problem is solved | c | (BMAT = 'G'). NEV is the number of eigenvalues | c | to be approximated. Since the Cayley mode is | c | used, WHICH is set to 'LM'. The user can | c | modify N, NEV, NCV and SIGMA to solve problems | c | of different sizes, and to get different parts | c | the spectrum. However, the following conditions | c | must be satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 1 <= NCV <= MAXNCV | c %--------------------------------------------------% c n = 100 nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _SBDR6: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _SBDR6: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _SBDR6: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' sigma = 150.0 c c %-----------------------------------------------------% c | The work array WORKL is used in SSAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in SSAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = ncv**2+8*ncv tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 5 of SSAUPD is used | c | (IPARAM(7) = 5). All these options can be changed | c | by the user. For details, see the documentation | c | in SBAND. | c %---------------------------------------------------% c maxitr = 300 mode = 5 c iparam(3) = maxitr iparam(7) = mode c c %----------------------------------------% c | Construct the matrix A in LAPACK-style | c | banded form. | c %----------------------------------------% c c %---------------------------------------------% c | Zero out the workspace for banded matrices. | c %---------------------------------------------% c call slaset('A', lda, n, zero, zero, a, lda) call slaset('A', lda, n, zero, zero, m, lda) call slaset('A', lda, n, zero, zero, rfac, lda) c c %-------------------------------------% c | KU, KL are number of superdiagonals | c | and subdiagonals within the band of | c | matrices A and M. | c %-------------------------------------% c kl = 1 ku = 1 c c %---------------% c | Main diagonal | c %---------------% c h = one / real (n+1) r1 = four / six idiag = kl+ku+1 do 30 j = 1, n a(idiag,j) = two / h m(idiag,j) = r1 * h 30 continue c c %-------------------------------------% c | First subdiagonal and superdiagonal | c %-------------------------------------% c r2 = one / six isup = kl+ku isub = kl+ku+2 do 60 j = 1, n-1 a(isup,j+1) = -one / h a(isub,j) = -one / h m(isup,j+1) = r2 * h m(isub,j) = r2 * h 60 continue c c %-------------------------------------% c | Call SSBAND to find eigenvalues and | c | eigenvectors. Eigenvalues are | c | returned in the first column of D. | c | Eigenvectors are returned in the | c | first NCONV (=IPARAM(5)) columns of | c | V. | c %-------------------------------------% c rvec = .true. call ssband( rvec, 'A', select, d, v, ldv, sigma, n, a, m, lda, & rfac, kl, ku, which, bmat, nev, tol, & resid, ncv, v, ldv, iparam, workd, workl, lworkl, & iwork, info) c if ( info .eq. 0) then c nconv = iparam(5) c c %-----------------------------------% c | Print out convergence information | c %-----------------------------------% c print *, ' ' print *, ' _SBDR6 ' print *, ' ====== ' print *, ' ' print *, ' The size of the matrix is ', n print *, ' Number of eigenvalue requested is ', nev print *, ' The number of Lanczos vectors generated', & ' (NCV) is ', ncv print *, ' The number of converged Ritz values is ', & nconv print *, ' What portion of the spectrum ', which print *, ' The number of Implicit Arnoldi', & ' update taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence tolerance is ', tol print *, ' ' c c %----------------------------% c | Compute the residual norm. | c | || A*x - lambda*x || | c %----------------------------% c do 90 j = 1, nconv call sgbmv('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call sgbmv('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j), 1, zero, & mx, 1) call saxpy(n, -d(j,1), mx, 1, ax, 1) d(j,2) = snrm2(n, ax, 1) d(j,2) = d(j,2) / abs(d(j,1)) c 90 continue call smout(6, nconv, 2, d, maxncv, -6, & 'Ritz values and relative residuals') else c c %-------------------------------------% c | Either convergence failed, or there | c | is error. Check the documentation | c | for SSBAND. | c %-------------------------------------% c print *, ' ' print *, ' Error with _band, info= ', info print *, ' Check the documentation of _band ' print *, ' ' c end if c 9000 end arpack-0.92.1/EXAMPLES/BAND/dnbdr2.f0000644000175000017500000003003210776001577013241 00000000000000 program dnbdr2 c c ... Construct matrices A in LAPACK-style band form. c The matrix A is derived from the discretization of c the 2-d convection-diffusion operator c c -Laplacian(u) + rho*partial(u)/partial(x). c c on the unit square with zero Dirichlet boundary condition c using standard central difference. c c ... Define the shift SIGMA = (SIGMAR, SIGMAI). c c ... Call DNBAND to find eigenvalues LAMBDA closest to SIGMA c such that c A*x = LAMBDA*x. c c ... Use mode 3 of DNAUPD . c c\BeginLib c c\Routines called: c dnband ARPACK banded eigenproblem solver. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c dlaset LAPACK routine to initialize a matrix to zero. c daxpy Level 1 BLAS that computes y <- alpha*x+y. c dnrm2 Level 1 BLAS that computes the norm of a vector. c dgbmv Level 2 BLAS that computes the band matrix vector product c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: nbdr2.F SID: 2.5 DATE OF SID: 08/26/96 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c--------------------------------------------------------------------- c c %-------------------------------------% c | Define leading dimensions for all | c | arrays. | c | MAXN - Maximum size of the matrix | c | MAXNEV - Maximum number of | c | eigenvalues to be computed | c | MAXNCV - Maximum number of Arnoldi | c | vectors stored | c | MAXBDW - Maximum bandwidth | c %-------------------------------------% c integer maxn, maxnev, maxncv, maxbdw, lda, & lworkl, ldv parameter ( maxn = 1000, maxnev = 25, maxncv=50, & maxbdw=50, lda = maxbdw, ldv = maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), iwork(maxn) logical select(maxncv) Double precision & a(lda,maxn), m(lda,maxn), rfac(lda,maxn), & workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn), & workev(3*maxncv), v(ldv, maxncv), & resid(maxn), d(maxncv, 3), ax(maxn) Complex*16 & cfac(lda, maxn), workc(maxn) c c %---------------% c | Local Scalars | c %---------------% c character which*2, bmat integer nev, ncv, ku, kl, info, i, j, ido, & n, nx, lo, idiag, isub, isup, mode, maxitr, & nconv logical rvec, first Double precision & tol, rho, h2, h, sigmar, sigmai c c %------------% c | Parameters | c %------------% c Double precision & one, zero, two parameter (one = 1.0D+0 , zero = 0.0D+0 , & two = 2.0D+0 ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & dlapy2 , dnrm2 external dlapy2 , dnrm2 , daxpy , dgbmv c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------------------------% c | The number NX is the number of interior points | c | in the discretization of the 2-dimensional | c | convection-diffusion operator on the unit | c | square with zero Dirichlet boundary condition. | c | The number N(=NX*NX) is the dimension of the | c | matrix. A standard eigenvalue problem is | c | solved (BMAT = 'I'). NEV is the number of | c | eigenvalues (closest to (SIGMAR,SIGMAI)) to be | c | approximated. Since the shift-invert moded is | c | used, WHICH is set to 'LM'. The user can modify | c | NX, NEV, NCV, SIGMAR, SIGMAI to solve problems | c | of different sizes, and to get different parts | c | the spectrum. However, The following conditions | c | must be satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 2 <= NCV <= MAXNCV | c %-------------------------------------------------% c nx = 10 n = nx*nx nev = 4 ncv = 20 if ( n .gt. maxn ) then print *, ' ERROR with _NBDR2: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NBDR2: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NBDR2: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'I' which = 'LM' sigmar = 1.0D+4 sigmai = 0.0D+0 c c %-----------------------------------------------------% c | The work array WORKL is used in DNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in DNAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = 3*ncv**2+6*ncv tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 3 of DNAUPD is used | c | (IPARAM(7) = 3). All these options can be changed | c | by the user. For details, see the documentation | c | in DNBAND . | c %---------------------------------------------------% c maxitr = 300 mode = 3 c iparam(3) = maxitr iparam(7) = mode c c %----------------------------------------% c | Construct the matrix A in LAPACK-style | c | banded form. | c %----------------------------------------% c c %---------------------------------------------% c | Zero out the workspace for banded matrices. | c %---------------------------------------------% c call dlaset ('A', lda, n, zero, zero, a, lda) call dlaset ('A', lda, n, zero, zero, m, lda) call dlaset ('A', lda, n, zero, zero, rfac, lda) c c %-------------------------------------% c | KU, KL are number of superdiagonals | c | and subdiagonals within the band of | c | matrices A. | c %-------------------------------------% c kl = nx ku = nx c c %---------------% c | Main diagonal | c %---------------% c h = one / dble (nx+1) h2 = h*h c idiag = kl+ku+1 do 30 j = 1, n a(idiag,j) = 4.0D+0 / h2 30 continue c c %-------------------------------------% c | First subdiagonal and superdiagonal | c %-------------------------------------% c isup = kl+ku isub = kl+ku+2 rho = 1.0D+1 do 50 i = 1, nx lo = (i-1)*nx do 40 j = lo+1, lo+nx-1 a(isub,j+1) = -one/h2 + rho/two/h a(isup,j) = -one/h2 - rho/two/h 40 continue 50 continue c c %------------------------------------% c | KL-th subdiagonal and KU-th super- | c | diagonal. | c %------------------------------------% c isup = kl+1 isub = 2*kl+ku+1 do 80 i = 1, nx-1 lo = (i-1)*nx do 70 j = lo+1, lo+nx a(isup,nx+j) = -one / h2 a(isub,j) = -one / h2 70 continue 80 continue c c %------------------------------------------------% c | Call ARPACK banded solver to find eigenvalues | c | and eigenvectors. The real parts of the | c | eigenvalues are returned in the first column | c | of D, the imaginary parts are returned in the | c | second column of D. Eigenvectors are returned | c | in the first NCONV (=IPARAM(5)) columns of V. | c %------------------------------------------------% c rvec = .true. call dnband (rvec, 'A', select, d, d(1,2), v, ldv, sigmar, & sigmai, workev, n, a, m, lda, rfac, cfac, kl, ku, & which, bmat, nev, tol, resid, ncv, v, ldv, iparam, & workd, workl, lworkl, workc, iwork, info) c if ( info .eq. 0) then c c %-----------------------------------% c | Print out convergence information | c %-----------------------------------% c nconv = iparam(5) c print *, ' ' print *, ' _NBDR2 ' print *, ' ====== ' print *, ' ' print *, ' The size of the matrix is ', n print *, ' Number of eigenvalue requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' The number of converged Ritz values is ', & nconv print *, ' What portion of the spectrum ', which print *, ' The number of Implicit Arnoldi ', & ' update taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence tolerance is ', tol print *, ' ' c c %----------------------------% c | Compute the residual norm. | c | || A*x - lambda*x || | c %----------------------------% c first = .true. do 90 j = 1, nconv c if ( d(j,2) .eq. zero ) then c c %--------------------% c | Ritz value is real | c %--------------------% c call dgbmv ('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call daxpy (n, -d(j,1), v(1,j), 1, ax, 1) d(j,3) = dnrm2 (n, ax, 1) d(j,3) = d(j,3) / abs(d(j,1)) c else if ( first ) then c c %------------------------% c | Ritz value is complex | c | Residual of one Ritz | c | value of the conjugate | c | pair is computed. | c %------------------------% c call dgbmv ('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call daxpy (n, -d(j,1), v(1,j), 1, ax, 1) call daxpy (n, d(j,2), v(1,j+1), 1, ax, 1) d(j,3) = dnrm2 (n, ax, 1) call dgbmv ('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j+1), 1, zero, & ax, 1) call daxpy (n, -d(j,1), v(1,j+1), 1, ax, 1) call daxpy (n, -d(j,2), v(1,j), 1, ax, 1) d(j,3) = dlapy2 ( d(j,3), dnrm2 (n, ax, 1) ) d(j,3) = d(j,3) / dlapy2 (d(j,1),d(j,2)) d(j+1,3) = d(j,3) first = .false. else first = .true. end if c 90 continue call dmout (6, nconv, 3, d, maxncv, -6, & 'Ritz values (Real,Imag) and relative residuals') else c c %-------------------------------------% c | Either convergence failed, or there | c | is error. Check the documentation | c | for DNBAND . | c %-------------------------------------% c print *, ' ' print *, ' Error with _nband, info= ', info print *, ' Check the documentation of _nband ' print *, ' ' c end if c 9000 end arpack-0.92.1/EXAMPLES/BAND/snbdr2.f0000644000175000017500000002770110776001577013271 00000000000000 program snbdr2 c c ... Construct matrices A in LAPACK-style band form. c The matrix A is derived from the discretization of c the 2-d convection-diffusion operator c c -Laplacian(u) + rho*partial(u)/partial(x). c c on the unit square with zero Dirichlet boundary condition c using standard central difference. c c ... Define the shift SIGMA = (SIGMAR, SIGMAI). c c ... Call SNBAND to find eigenvalues LAMBDA closest to SIGMA c such that c A*x = LAMBDA*x. c c ... Use mode 3 of SNAUPD. c c\BeginLib c c\Routines called: c snband ARPACK banded eigenproblem solver. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c slaset LAPACK routine to initialize a matrix to zero. c saxpy Level 1 BLAS that computes y <- alpha*x+y. c snrm2 Level 1 BLAS that computes the norm of a vector. c sgbmv Level 2 BLAS that computes the band matrix vector product c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: nbdr2.F SID: 2.5 DATE OF SID: 08/26/96 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c--------------------------------------------------------------------- c c %-------------------------------------% c | Define leading dimensions for all | c | arrays. | c | MAXN - Maximum size of the matrix | c | MAXNEV - Maximum number of | c | eigenvalues to be computed | c | MAXNCV - Maximum number of Arnoldi | c | vectors stored | c | MAXBDW - Maximum bandwidth | c %-------------------------------------% c integer maxn, maxnev, maxncv, maxbdw, lda, & lworkl, ldv parameter ( maxn = 1000, maxnev = 25, maxncv=50, & maxbdw=50, lda = maxbdw, ldv = maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), iwork(maxn) logical select(maxncv) Real & a(lda,maxn), m(lda,maxn), rfac(lda,maxn), & workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn), & workev(3*maxncv), v(ldv, maxncv), & resid(maxn), d(maxncv, 3), ax(maxn) Complex & cfac(lda, maxn), workc(maxn) c c %---------------% c | Local Scalars | c %---------------% c character which*2, bmat integer nev, ncv, ku, kl, info, i, j, ido, & n, nx, lo, idiag, isub, isup, mode, maxitr, & nconv logical rvec, first Real & tol, rho, h2, h, sigmar, sigmai c c %------------% c | Parameters | c %------------% c Real & one, zero, two parameter (one = 1.0E+0 , zero = 0.0E+0 , & two = 2.0E+0 ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & slapy2, snrm2 external slapy2, snrm2, saxpy, sgbmv c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------------------------% c | The number NX is the number of interior points | c | in the discretization of the 2-dimensional | c | convection-diffusion operator on the unit | c | square with zero Dirichlet boundary condition. | c | The number N(=NX*NX) is the dimension of the | c | matrix. A standard eigenvalue problem is | c | solved (BMAT = 'I'). NEV is the number of | c | eigenvalues (closest to (SIGMAR,SIGMAI)) to be | c | approximated. Since the shift-invert moded is | c | used, WHICH is set to 'LM'. The user can modify | c | NX, NEV, NCV, SIGMAR, SIGMAI to solve problems | c | of different sizes, and to get different parts | c | the spectrum. However, The following conditions | c | must be satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 2 <= NCV <= MAXNCV | c %-------------------------------------------------% c nx = 10 n = nx*nx nev = 4 ncv = 20 if ( n .gt. maxn ) then print *, ' ERROR with _NBDR2: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NBDR2: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NBDR2: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'I' which = 'LM' sigmar = 1.0E+4 sigmai = 0.0E+0 c c %-----------------------------------------------------% c | The work array WORKL is used in SNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in SNAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = 3*ncv**2+6*ncv tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 3 of SNAUPD is used | c | (IPARAM(7) = 3). All these options can be changed | c | by the user. For details, see the documentation | c | in SNBAND. | c %---------------------------------------------------% c maxitr = 300 mode = 3 c iparam(3) = maxitr iparam(7) = mode c c %----------------------------------------% c | Construct the matrix A in LAPACK-style | c | banded form. | c %----------------------------------------% c c %---------------------------------------------% c | Zero out the workspace for banded matrices. | c %---------------------------------------------% c call slaset('A', lda, n, zero, zero, a, lda) call slaset('A', lda, n, zero, zero, m, lda) call slaset('A', lda, n, zero, zero, rfac, lda) c c %-------------------------------------% c | KU, KL are number of superdiagonals | c | and subdiagonals within the band of | c | matrices A. | c %-------------------------------------% c kl = nx ku = nx c c %---------------% c | Main diagonal | c %---------------% c h = one / real (nx+1) h2 = h*h c idiag = kl+ku+1 do 30 j = 1, n a(idiag,j) = 4.0E+0 / h2 30 continue c c %-------------------------------------% c | First subdiagonal and superdiagonal | c %-------------------------------------% c isup = kl+ku isub = kl+ku+2 rho = 1.0E+1 do 50 i = 1, nx lo = (i-1)*nx do 40 j = lo+1, lo+nx-1 a(isub,j+1) = -one/h2 + rho/two/h a(isup,j) = -one/h2 - rho/two/h 40 continue 50 continue c c %------------------------------------% c | KL-th subdiagonal and KU-th super- | c | diagonal. | c %------------------------------------% c isup = kl+1 isub = 2*kl+ku+1 do 80 i = 1, nx-1 lo = (i-1)*nx do 70 j = lo+1, lo+nx a(isup,nx+j) = -one / h2 a(isub,j) = -one / h2 70 continue 80 continue c c %------------------------------------------------% c | Call ARPACK banded solver to find eigenvalues | c | and eigenvectors. The real parts of the | c | eigenvalues are returned in the first column | c | of D, the imaginary parts are returned in the | c | second column of D. Eigenvectors are returned | c | in the first NCONV (=IPARAM(5)) columns of V. | c %------------------------------------------------% c rvec = .true. call snband(rvec, 'A', select, d, d(1,2), v, ldv, sigmar, & sigmai, workev, n, a, m, lda, rfac, cfac, kl, ku, & which, bmat, nev, tol, resid, ncv, v, ldv, iparam, & workd, workl, lworkl, workc, iwork, info) c if ( info .eq. 0) then c c %-----------------------------------% c | Print out convergence information | c %-----------------------------------% c nconv = iparam(5) c print *, ' ' print *, ' _NBDR2 ' print *, ' ====== ' print *, ' ' print *, ' The size of the matrix is ', n print *, ' Number of eigenvalue requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' The number of converged Ritz values is ', & nconv print *, ' What portion of the spectrum ', which print *, ' The number of Implicit Arnoldi ', & ' update taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence tolerance is ', tol print *, ' ' c c %----------------------------% c | Compute the residual norm. | c | || A*x - lambda*x || | c %----------------------------% c first = .true. do 90 j = 1, nconv c if ( d(j,2) .eq. zero ) then c c %--------------------% c | Ritz value is real | c %--------------------% c call sgbmv('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call saxpy(n, -d(j,1), v(1,j), 1, ax, 1) d(j,3) = snrm2(n, ax, 1) d(j,3) = d(j,3) / abs(d(j,1)) c else if ( first ) then c c %------------------------% c | Ritz value is complex | c | Residual of one Ritz | c | value of the conjugate | c | pair is computed. | c %------------------------% c call sgbmv('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call saxpy(n, -d(j,1), v(1,j), 1, ax, 1) call saxpy(n, d(j,2), v(1,j+1), 1, ax, 1) d(j,3) = snrm2(n, ax, 1) call sgbmv('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j+1), 1, zero, & ax, 1) call saxpy(n, -d(j,1), v(1,j+1), 1, ax, 1) call saxpy(n, -d(j,2), v(1,j), 1, ax, 1) d(j,3) = slapy2( d(j,3), snrm2(n, ax, 1) ) d(j,3) = d(j,3) / slapy2(d(j,1),d(j,2)) d(j+1,3) = d(j,3) first = .false. else first = .true. end if c 90 continue call smout(6, nconv, 3, d, maxncv, -6, & 'Ritz values (Real,Imag) and relative residuals') else c c %-------------------------------------% c | Either convergence failed, or there | c | is error. Check the documentation | c | for SNBAND. | c %-------------------------------------% c print *, ' ' print *, ' Error with _nband, info= ', info print *, ' Check the documentation of _nband ' print *, ' ' c end if c 9000 end arpack-0.92.1/EXAMPLES/BAND/dnbdr5.f0000644000175000017500000002776710776001577013271 00000000000000 program dnbdr5 c c ... Construct matrices A and M in LAPACK-style band form. c The matrix A is a block tridiagonal matrix. Each c diagonal block is a tridiagonal matrix with c 4 on the diagonal, 1-rho*h/2 on the subdiagonal and c 1+rho*h/2 on the superdiagonal. Each off-diagonal block c of A is an identity matrices. c c ... Define COMPLEX shift SIGMA = (SIGMAR,SIGMAI), SIGMAI .ne. 0. c c ... Call DNBAND to find eigenvalues LAMBDA closest to SIGMA c such that c A*x = LAMBDA*x. c c ... Use mode 4 of DNAUPD . c c\BeginLib c c\Routines called: c dnband ARPACK banded eigenproblem solver. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c dlaset LAPACK routine to initialize a matrix to zero. c daxpy Level 1 BLAS that computes y <- alpha*x+y. c dnrm2 Level 1 BLAS that computes the norm of a vector. c dgbmv Level 2 BLAS that computes the band matrix vector product. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: nbdr5.F SID: 2.5 DATE OF SID: 08/26/96 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c------------------------------------------------------------------------- c c %-------------------------------------% c | Define leading dimensions for all | c | arrays. | c | MAXN - Maximum size of the matrix | c | MAXNEV - Maximum number of | c | eigenvalues to be computed | c | MAXNCV - Maximum number of Arnoldi | c | vectors stored | c | MAXBDW - Maximum bandwidth | c %-------------------------------------% c integer maxn, maxnev, maxncv, maxbdw, lda, & lworkl, ldv parameter ( maxn = 1000, maxnev = 25, maxncv=50, & maxbdw=50, lda = maxbdw, ldv = maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), iwork(maxn) logical select(maxncv) Double precision & a(lda,maxn), m(lda,maxn), rfac(lda,maxn), & workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn), & workev(3*maxncv), v(ldv, maxncv), & resid(maxn), d(maxncv, 3), ax(maxn) Complex*16 & cfac(lda, maxn), workc(maxn) c c %---------------% c | Local Scalars | c %---------------% c character which*2, bmat integer nev, ncv, ku, kl, info, i, j, ido, & n, nx, lo, idiag, isup, isub, mode, maxitr, & nconv logical rvec, first Double precision & tol, rho, h, sigmar, sigmai c c %------------% c | Parameters | c %------------% c Double precision & one, zero, two parameter (one = 1.0D+0 , zero = 0.0D+0 , & two = 2.0D+0 ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & dlapy2 , dnrm2 external dlapy2 , dnrm2 , dgbmv , daxpy c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c %--------------------------------------------------% c | The number NX is the size of each block diagonal | c | of A. The number N(=NX*NX) is the dimension of | c | the matrix. A standard eigenvalue problem is | c | solved (BMAT = 'I'). NEV is the number of | c | eigenvalues (closest to (SIGMAR,SIGMAI)) to be | c | approximated. Since the shift-invert moded is | c | used, WHICH is set to 'LM'. The user can modify | c | NX, NEV, NCV, SIGMAR, SIGMAI to solve problems | c | of different sizes, and to get different parts | c | the spectrum. However, The following conditions | c | must be satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 2 <= NCV <= MAXNCV | c %--------------------------------------------------% c nx = 10 n = nx*nx nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _NBDR5: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NBDR5: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NBDR5: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'I' which = 'LM' sigmar = 4.0D-1 sigmai = 6.0D-1 c c %-----------------------------------------------------% c | The work array WORKL is used in DNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in DNAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = 3*ncv**2+6*ncv tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 4 of DNAUPD is used | c | (IPARAM(7) = 4). All these options can be changed | c | by the user. For details, see the documentation | c | in DNBAND . | c %---------------------------------------------------% c maxitr = 300 mode = 4 c iparam(3) = maxitr iparam(7) = mode c c %--------------------------------------------% c | Construct matrices A and M in LAPACK-style | c | banded form. | c %--------------------------------------------% c c %---------------------------------------------% c | Zero out the workspace for banded matrices. | c %---------------------------------------------% c call dlaset ('A', lda, n, zero, zero, a, lda) call dlaset ('A', lda, n, zero, zero, m, lda) call dlaset ('A', lda, n, zero, zero, rfac, lda) c c %-------------------------------------% c | KU, KL are number of superdiagonals | c | and subdiagonals within the band of | c | matrices A and M. | c %-------------------------------------% c kl = nx ku = nx c c %---------------% c | Main diagonal | c %---------------% c idiag = kl+ku+1 do 30 j = 1, n a(idiag,j) = 4.0D+0 m(idiag,j) = 4.0D+0 30 continue c c %-------------------------------------% c | First subdiagonal and superdiagonal | c %-------------------------------------% c isup = kl+ku isub = kl+kl+2 h = one / dble (nx+1) rho = 1.0D+2 do 50 i = 1, nx lo = (i-1)*nx do 40 j = lo+1, lo+nx-1 a(isup,j+1) = -one+h*rho/two a(isub,j) = -one-h*rho/two 40 continue 50 continue c do 60 j = 1, n-1 m(isup,j+1) = one m(isub,j) = one 60 continue c c %------------------------------------% c | KL-th subdiagonal and KU-th super- | c | diagonal. | c %------------------------------------% c isup = kl+1 isub = 2*kl+ku+1 do 80 i = 1, nx-1 lo = (i-1)*nx do 70 j = lo+1, lo+nx a(isup,nx+j) = -one a(isub,j) = -one 70 continue 80 continue c c %------------------------------------------------% c | Call ARPACK banded solver to find eigenvalues | c | and eigenvectors. The real parts of the | c | eigenvalues are returned in the first column | c | of D, the imaginary parts are returned in the | c | second column of D. Eigenvectors are returned | c | in the first NCONV (=IPARAM(5)) columns of V. | c %------------------------------------------------% c rvec = .true. call dnband (rvec, 'A', select, d, d(1,2), v, ldv, sigmar, & sigmai, workev, n, a, m, lda, rfac, cfac, ku, kl, & which, bmat, nev, tol, resid, ncv, v, ldv, iparam, & workd, workl, lworkl, workc, iwork, info) c if ( info .eq. 0) then c c %-----------------------------------% c | Print out convergence information | c %-----------------------------------% c nconv = iparam(5) c print *, ' ' print *, ' _NBDR5 ' print *, ' ====== ' print *, ' ' print *, ' The size of the matrix is ', n print *, ' Number of eigenvalue requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' The number of converged Ritz values is ', & nconv print *, ' What portion of the spectrum ', which print *, ' The number of Implicit Arnoldi ', & ' update taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence tolerance is ', tol print *, ' ' c c %----------------------------% c | Compute the residual norm. | c | || A*x - lambda*x || | c %----------------------------% c first = .true. do 90 j = 1, nconv c if ( d(j,2) .eq. zero ) then c c %--------------------% c | Ritz value is real | c %--------------------% c call dgbmv ('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call daxpy (n, -d(j,1), v(1,j), 1, ax, 1) d(j,3) = dnrm2 (n, ax, 1) d(j,3) = d(j,3) / abs(d(j,1)) c else if ( first ) then c c %------------------------% c | Ritz value is complex | c | Residual of one Ritz | c | value of the conjugate | c | pair is computed. | c %------------------------% c call dgbmv ('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call daxpy (n, -d(j,1), v(1,j), 1, ax, 1) call daxpy (n, d(j,2), v(1,j+1), 1, ax, 1) d(j,3) = dnrm2 (n, ax, 1) call dgbmv ('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j+1), 1, zero, & ax, 1) call daxpy (n, -d(j,1), v(1,j+1), 1, ax, 1) call daxpy (n, -d(j,2), v(1,j), 1, ax, 1) d(j,3) = dlapy2 ( d(j,3), dnrm2 (n, ax, 1) ) d(j,3) = d(j,3) / dlapy2 (d(j,1),d(j,2)) d(j+1,3) = d(j,3) first = .false. else first = .true. end if c 90 continue call dmout (6, nconv, 3, d, maxncv, -6, & 'Ritz values (Real,Imag) and relative residuals') else c c %-------------------------------------% c | Either convergence failed, or there | c | is error. Check the documentation | c | for DNBAND . | c %-------------------------------------% c print *, ' ' print *, ' Error with _nband, info= ', info print *, ' Check the documentation of _nband ' print *, ' ' c end if c 9000 end arpack-0.92.1/EXAMPLES/BAND/ssbdr5.f0000644000175000017500000002336310776001577013301 00000000000000 program ssbdr5 c c ... Construct the matrix A in LAPACK-style band form. c The matrix A is the 1-dimensional discrete Laplacian on [0,1] c with zero Dirichlet boundary condition, KG is the mass c formed by using piecewise linear elements on [0,1]. c c ... Call SSBAND with Buckling mode to find eigenvalues LAMBDA c such that c A*x = M*x*LAMBDA. c c ... Use mode 4 of SSAUPD. c c\BeginLib c c\Routines called: c ssband ARPACK banded eigenproblem solver. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c slaset LAPACK routine to initialize a matrix to zero. c saxpy Level 1 BLAS that computes y <- alpha*x+y. c snrm2 Level 1 BLAS that computes the norm of a vector. c sgbmv Level 2 BLAS that computes the band matrix vector product c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: sbdr5.F SID: 2.5 DATE OF SID: 08/26/96 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c---------------------------------------------------------------------- c c %-------------------------------------% c | Define leading dimensions for all | c | arrays. | c | MAXN - Maximum size of the matrix | c | MAXNEV - Maximum number of | c | eigenvalues to be computed | c | MAXNCV - Maximum number of Arnoldi | c | vectors stored | c | MAXBDW - Maximum bandwidth | c %-------------------------------------% c integer maxn, maxnev, maxncv, maxbdw, lda, & lworkl, ldv parameter ( maxn = 1000, maxnev = 25, maxncv=50, & maxbdw=50, lda = maxbdw, ldv = maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), iwork(maxn) logical select(maxncv) Real & a(lda,maxn), m(lda,maxn), rfac(lda,maxn), & workl(maxncv*maxncv+8*maxncv), workd(3*maxn), & v(ldv, maxncv), resid(maxn), d(maxncv, 2), & ax(maxn), mx(maxn) c c %---------------% c | Local Scalars | c %---------------% c character which*2, bmat integer nev, ncv, kl, ku, info, j, ido, & n, isub, isup, idiag, maxitr, mode, nconv Real & tol, h, sigma, r1, r2 logical rvec c c %------------% c | Parameters | c %------------% c Real & one, zero, two, four, six parameter (one = 1.0E+0 , zero = 0.0E+0 , two = 2.0E+0 , & four = 4.0E+0 , six = 6.0E+0 ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & slapy2, snrm2 external slapy2, snrm2, sgbmv, saxpy c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c %--------------------------------------------------% c | The number N is the dimension of the matrix. A | c | generalized eigenvalue problem is solved | c | (BMAT = 'G'). NEV is the number of eigenvalues | c | to be approximated. Since the Buckling mode is | c | is used, WHICH is set to 'LM'. The user can | c | modify N, NEV, NCV and SIGMA to solve problems | c | of different sizes, and to get different parts | c | the spectrum. However, the following conditions | c | must be satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 1 <= NCV <= MAXNCV | c %--------------------------------------------------% c n = 100 nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _SBDR5: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _SBDR5: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _SBDR5: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' sigma = 1.0 c c %-----------------------------------------------------% c | The work array WORKL is used in SSAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in SSAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = ncv**2+8*ncv tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 4 of SSAUPD is used | c | (IPARAM(7) = 4). All these options can be changed | c | by the user. For details see the documentation in | c | SSBAND. | c %---------------------------------------------------% c maxitr = 300 mode = 4 c iparam(3) = maxitr iparam(7) = mode c c %----------------------------------------% c | Construct the matrix A in LAPACK-style | c | banded form. | c %----------------------------------------% c c %---------------------------------------------% c | Zero out the workspace for banded matrices. | c %---------------------------------------------% c call slaset('A', lda, n, zero, zero, a, lda) call slaset('A', lda, n, zero, zero, m, lda) call slaset('A', lda, n, zero, zero, rfac, lda) c c %-------------------------------------% c | KU, KL are number of superdiagonals | c | and subdiagonals within the band of | c | matrices A and M. | c %-------------------------------------% c kl = 1 ku = 1 c c %---------------% c | Main diagonal | c %---------------% c h = one / real (n+1) r1 = four / six idiag = kl+ku+1 do 30 j = 1, n a(idiag,j) = two / h m(idiag,j) = r1 * h 30 continue c c %-------------------------------------% c | First subdiagonal and superdiagonal | c %-------------------------------------% c r2 = one / six isup = kl+ku isub = kl+ku+2 do 60 j = 1, n-1 a(isup,j+1) = -one / h a(isub,j) = -one / h m(isup,j+1) = r2 * h m(isub,j) = r2 * h 60 continue c c %-------------------------------------% c | Call SSBAND to find eigenvalues and | c | eigenvectors. Eigenvalues are | c | returned in the first column of D. | c | Eigenvectors are returned in the | c | first NCONV (=IPARAM(5)) columns of | c | V. | c %-------------------------------------% c rvec = .true. call ssband( rvec, 'A', select, d, v, ldv, sigma, n, a, m, lda, & rfac, kl, ku, which, bmat, nev, tol, & resid, ncv, v, ldv, iparam, workd, workl, lworkl, & iwork, info) c if ( info .eq. 0) then c nconv = iparam(5) c c %-----------------------------------% c | Print out convergence information | c %-----------------------------------% c print *, ' ' print *, ' _SBDR5 ' print *, ' ====== ' print *, ' ' print *, ' The size of the matrix is ', n print *, ' Number of eigenvalue requested is ', nev print *, ' The number of Lanczos vectors generated', & ' (NCV) is ', ncv print *, ' The number of converged Ritz values is ', & nconv print *, ' What portion of the spectrum ', which print *, ' The number of Implicit Arnoldi', & ' update taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence tolerance is ', tol print *, ' ' c c %----------------------------% c | Compute the residual norm. | c | || A*x - lambda*x || | c %----------------------------% c do 90 j = 1, nconv call sgbmv('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call sgbmv('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j), 1, zero, & mx, 1) call saxpy(n, -d(j,1), mx, 1, ax, 1) d(j,2) = snrm2(n, ax, 1) d(j,2) = d(j,2) / abs(d(j,1)) c 90 continue call smout(6, nconv, 2, d, maxncv, -6, & 'Ritz values and relative residuals') else c c %-------------------------------------% c | Either convergence failed, or there | c | is error. Check the documentation | c | for SSBAND. | c %-------------------------------------% c print *, ' ' print *, ' Error with _sband, info= ', info print *, ' Check the documentation of _sband ' print *, ' ' c end if c 9000 end arpack-0.92.1/EXAMPLES/BAND/dnbdr3.f0000644000175000017500000002773710776001577013264 00000000000000 program dnbdr3 c c ... Construct matrices A and M in LAPACK-style band form. c The matrix A and M are derived from the finite element c discretization of the 1-dimensional convection-diffusion operator c (d^2u/dx^2) + rho*(du/dx) c on the interval [0,1] with zero boundary condition, c ... Call DNBAND to find eigenvalues LAMBDA such that c A*x = LAMBDA*M*x. c c ... Eigenvalues with largest real parts are sought. c c ... Use mode 2 of DNAUPD . c c\BeginLib c c\Routines called: c dnband ARPACK banded eigenproblem solver. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c dlaset LAPACK routine to initialize a matrix to zero. c daxpy Level 1 BLAS that computes y <- alpha*x+y. c dnrm2 Level 1 BLAS that computes the norm of a vector. c dgbmv Level 2 BLAS that computes the band matrix vector product. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: nbdr3.F SID: 2.5 DATE OF SID: 08/26/96 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c------------------------------------------------------------------------- c c %-------------------------------------% c | Define leading dimensions for all | c | arrays. | c | MAXN - Maximum size of the matrix | c | MAXNEV - Maximum number of | c | eigenvalues to be computed | c | MAXNCV - Maximum number of Arnoldi | c | vectors stored | c | MAXBDW - Maximum bandwidth | c %-------------------------------------% c integer maxn, maxnev, maxncv, maxbdw, lda, & lworkl, ldv parameter ( maxn = 1000, maxnev = 25, maxncv=50, & maxbdw=50, lda = maxbdw, ldv = maxn) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), iwork(maxn) logical select(maxncv) Double precision & a(lda,maxn), m(lda,maxn), rfac(lda,maxn), & workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn), & workev(3*maxncv), v(ldv, maxncv), & resid(maxn), d(maxncv, 3), ax(maxn), mx(maxn) Complex*16 & cfac(lda, maxn), workc(maxn) c c %---------------% c | Local Scalars | c %---------------% c character which*2, bmat integer nev, ncv, ku, kl, info, j, ido, & n, idiag, isup, isub, mode, maxitr, & nconv logical rvec, first Double precision & tol, rho, h, sigmar, sigmai c c %------------% c | Parameters | c %------------% c Double precision & one, zero, two parameter (one = 1.0D+0 , zero = 0.0D+0 , & two = 2.0D+0 ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & dlapy2 , dnrm2 external dlapy2 , dnrm2 , dgbmv , daxpy c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------------------------% c | The number N is the dimension of the matrix. A | c | generalized eigenvalue problem is solved | c | (BMAT = 'G'). NEV is the number of eigenvalues | c | to be approximated. The user can modify N, NEV, | c | NCV and WHICH to solve problems of different | c | sizes, and to get different parts the spectrum. | c | However, the following conditions must be | c | satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 2 <= NCV <= MAXNCV | c %-------------------------------------------------% c n = 100 nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _NBDR3: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NBDR3: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NBDR3: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' c c %----------------------------------------------------% c | The work array WORKL is used in DNAUPD as | c | workspace. Its dimension LWORKL has to be set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine machine | c | precision is used. The number IDO is used for | c | reverse communication and has to be set to 0 at | c | the beginning. Setting INFO=0 indicates that we | c | using a randomly generated vector to start the | c | the ARNOLDI process. | c %----------------------------------------------------% c lworkl = 3*ncv**2+6*ncv info = 0 tol = zero ido = 0 c c %---------------------------------------------------% c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 2 of DNAUPD is used | c | (IPARAM(7) = 2). All these options can be changed | c | by the user. For details, see the documentation | c | in DNBAND . | c %---------------------------------------------------% c mode = 2 maxitr = 300 c iparam(3) = maxitr iparam(7) = mode c c %--------------------------------------------% c | Construct matrices A and M in LAPACK-style | c | banded form. | c %--------------------------------------------% c c %---------------------------------------------% c | Zero out the workspace for banded matrices. | c %---------------------------------------------% c call dlaset ('A', lda, n, zero, zero, a, lda) call dlaset ('A', lda, n, zero, zero, m, lda) call dlaset ('A', lda, n, zero, zero, rfac, lda) c c %-------------------------------------% c | KU, KL are number of superdiagonals | c | and subdiagonals within the band of | c | matrices A and M. | c %-------------------------------------% c kl = 1 ku = 1 c c %---------------% c | Main diagonal | c %---------------% c h = one / dble (n+1) c idiag = kl+ku+1 do 30 j = 1, n a(idiag,j) = 2.0D+0 / h m(idiag,j) = 4.0D+0 * h 30 continue c c %-------------------------------------% c | First subdiagonal and superdiagonal | c %-------------------------------------% c isup = kl+ku isub = kl+ku+2 rho = 1.0D+1 do 50 j = 1, n a(isup,j+1) = -one/h + rho/two a(isub,j) = -one/h - rho/two m(isup,j+1) = one*h m(isub,j) = one*h 50 continue c c %------------------------------------------------% c | Call ARPACK banded solver to find eigenvalues | c | and eigenvectors. The real parts of the | c | eigenvalues are returned in the first column | c | of D, the imaginary parts are returned in the | c | second column of D. Eigenvectors are returned | c | in the first NCONV (=IPARAM(5)) columns of V. | c %------------------------------------------------% c rvec = .true. call dnband ( rvec, 'A', select, d, d(1,2), v, ldv, sigmar, & sigmai, workev, n, A, M, lda, rfac, cfac, kl, ku, & which, bmat, nev, tol, resid, ncv, v, ldv, iparam, & workd, workl, lworkl, workc, iwork, info) c if ( info .eq. 0) then c c %-----------------------------------% c | Print out convergence information | c %-----------------------------------% c nconv = iparam(5) c print *, ' ' print *, ' _NBDR3 ' print *, ' ====== ' print *, ' ' print *, ' The size of the matrix is ', n print *, ' Number of eigenvalue requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' The number of converged Ritz values is ', & nconv print *, ' What portion of the spectrum ', which print *, ' The number of Implicit Arnoldi ', & ' update taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence tolerance is ', tol print *, ' ' c c %----------------------------% c | Compute the residual norm. | c | || A*x - lambda*x || | c %----------------------------% c first = .true. do 90 j = 1, nconv c if ( d(j,2) .eq. zero ) then c c %--------------------% c | Ritz value is real | c %--------------------% c call dgbmv ('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call dgbmv ('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j), 1, zero, & mx, 1) call daxpy (n, -d(j,1), mx, 1, ax, 1) d(j,3) = dnrm2 (n, ax, 1) d(j,3) = d(j,3) / abs(d(j,1)) c else if ( first ) then c c %------------------------% c | Ritz value is complex | c | Residual of one Ritz | c | value of the conjugate | c | pair is computed. | c %------------------------% c call dgbmv ('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call dgbmv ('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j), 1, zero, & mx, 1) call daxpy (n, -d(j,1), mx, 1, ax, 1) call dgbmv ('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j+1), 1, zero, & mx, 1) call daxpy (n, d(j,2), mx, 1, ax, 1) d(j,3) = dnrm2 (n, ax, 1) call dgbmv ('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j+1), 1, zero, & ax, 1) call dgbmv ('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j+1), 1, zero, & mx, 1) call daxpy (n, -d(j,1), mx, 1, ax, 1) call dgbmv ('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j), 1, zero, & mx, 1) call daxpy (n, -d(j,2), mx, 1, ax, 1) d(j,3) = dlapy2 ( d(j,3), dnrm2 (n, ax, 1) ) d(j,3) = d(j,3) / dlapy2 (d(j,1),d(j,2)) d(j+1,3) = d(j,3) first = .false. else first = .true. end if c 90 continue call dmout (6, nconv, 3, d, maxncv, -6, & 'Ritz values (Real,Imag) and relative residuals') else c c %-------------------------------------% c | Either convergence failed, or there | c | is error. Check the documentation | c | for DNBAND . | c %-------------------------------------% c print *, ' ' print *, ' Error with _nband, info= ', info print *, ' Check the documentation of _nband ' print *, ' ' c end if c 9000 end arpack-0.92.1/EXAMPLES/BAND/dsbdr5.f0000644000175000017500000002350110776001577013254 00000000000000 program dsbdr5 c c ... Construct the matrix A in LAPACK-style band form. c The matrix A is the 1-dimensional discrete Laplacian on [0,1] c with zero Dirichlet boundary condition, KG is the mass c formed by using piecewise linear elements on [0,1]. c c ... Call DSBAND with Buckling mode to find eigenvalues LAMBDA c such that c A*x = M*x*LAMBDA. c c ... Use mode 4 of DSAUPD . c c\BeginLib c c\Routines called: c dsband ARPACK banded eigenproblem solver. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c dlaset LAPACK routine to initialize a matrix to zero. c daxpy Level 1 BLAS that computes y <- alpha*x+y. c dnrm2 Level 1 BLAS that computes the norm of a vector. c dgbmv Level 2 BLAS that computes the band matrix vector product c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: sbdr5.F SID: 2.5 DATE OF SID: 08/26/96 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c---------------------------------------------------------------------- c c %-------------------------------------% c | Define leading dimensions for all | c | arrays. | c | MAXN - Maximum size of the matrix | c | MAXNEV - Maximum number of | c | eigenvalues to be computed | c | MAXNCV - Maximum number of Arnoldi | c | vectors stored | c | MAXBDW - Maximum bandwidth | c %-------------------------------------% c integer maxn, maxnev, maxncv, maxbdw, lda, & lworkl, ldv parameter ( maxn = 1000, maxnev = 25, maxncv=50, & maxbdw=50, lda = maxbdw, ldv = maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), iwork(maxn) logical select(maxncv) Double precision & a(lda,maxn), m(lda,maxn), rfac(lda,maxn), & workl(maxncv*maxncv+8*maxncv), workd(3*maxn), & v(ldv, maxncv), resid(maxn), d(maxncv, 2), & ax(maxn), mx(maxn) c c %---------------% c | Local Scalars | c %---------------% c character which*2, bmat integer nev, ncv, kl, ku, info, j, ido, & n, isub, isup, idiag, maxitr, mode, nconv Double precision & tol, h, sigma, r1, r2 logical rvec c c %------------% c | Parameters | c %------------% c Double precision & one, zero, two, four, six parameter (one = 1.0D+0 , zero = 0.0D+0 , two = 2.0D+0 , & four = 4.0D+0 , six = 6.0D+0 ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & dlapy2 , dnrm2 external dlapy2 , dnrm2 , dgbmv , daxpy c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c %--------------------------------------------------% c | The number N is the dimension of the matrix. A | c | generalized eigenvalue problem is solved | c | (BMAT = 'G'). NEV is the number of eigenvalues | c | to be approximated. Since the Buckling mode is | c | is used, WHICH is set to 'LM'. The user can | c | modify N, NEV, NCV and SIGMA to solve problems | c | of different sizes, and to get different parts | c | the spectrum. However, the following conditions | c | must be satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 1 <= NCV <= MAXNCV | c %--------------------------------------------------% c n = 100 nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _SBDR5: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _SBDR5: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _SBDR5: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' sigma = 1.0 c c %-----------------------------------------------------% c | The work array WORKL is used in DSAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in DSAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = ncv**2+8*ncv tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 4 of DSAUPD is used | c | (IPARAM(7) = 4). All these options can be changed | c | by the user. For details see the documentation in | c | DSBAND . | c %---------------------------------------------------% c maxitr = 300 mode = 4 c iparam(3) = maxitr iparam(7) = mode c c %----------------------------------------% c | Construct the matrix A in LAPACK-style | c | banded form. | c %----------------------------------------% c c %---------------------------------------------% c | Zero out the workspace for banded matrices. | c %---------------------------------------------% c call dlaset ('A', lda, n, zero, zero, a, lda) call dlaset ('A', lda, n, zero, zero, m, lda) call dlaset ('A', lda, n, zero, zero, rfac, lda) c c %-------------------------------------% c | KU, KL are number of superdiagonals | c | and subdiagonals within the band of | c | matrices A and M. | c %-------------------------------------% c kl = 1 ku = 1 c c %---------------% c | Main diagonal | c %---------------% c h = one / dble (n+1) r1 = four / six idiag = kl+ku+1 do 30 j = 1, n a(idiag,j) = two / h m(idiag,j) = r1 * h 30 continue c c %-------------------------------------% c | First subdiagonal and superdiagonal | c %-------------------------------------% c r2 = one / six isup = kl+ku isub = kl+ku+2 do 60 j = 1, n-1 a(isup,j+1) = -one / h a(isub,j) = -one / h m(isup,j+1) = r2 * h m(isub,j) = r2 * h 60 continue c c %-------------------------------------% c | Call DSBAND to find eigenvalues and | c | eigenvectors. Eigenvalues are | c | returned in the first column of D. | c | Eigenvectors are returned in the | c | first NCONV (=IPARAM(5)) columns of | c | V. | c %-------------------------------------% c rvec = .true. call dsband ( rvec, 'A', select, d, v, ldv, sigma, n, a, m, lda, & rfac, kl, ku, which, bmat, nev, tol, & resid, ncv, v, ldv, iparam, workd, workl, lworkl, & iwork, info) c if ( info .eq. 0) then c nconv = iparam(5) c c %-----------------------------------% c | Print out convergence information | c %-----------------------------------% c print *, ' ' print *, ' _SBDR5 ' print *, ' ====== ' print *, ' ' print *, ' The size of the matrix is ', n print *, ' Number of eigenvalue requested is ', nev print *, ' The number of Lanczos vectors generated', & ' (NCV) is ', ncv print *, ' The number of converged Ritz values is ', & nconv print *, ' What portion of the spectrum ', which print *, ' The number of Implicit Arnoldi', & ' update taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence tolerance is ', tol print *, ' ' c c %----------------------------% c | Compute the residual norm. | c | || A*x - lambda*x || | c %----------------------------% c do 90 j = 1, nconv call dgbmv ('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call dgbmv ('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j), 1, zero, & mx, 1) call daxpy (n, -d(j,1), mx, 1, ax, 1) d(j,2) = dnrm2 (n, ax, 1) d(j,2) = d(j,2) / abs(d(j,1)) c 90 continue call dmout (6, nconv, 2, d, maxncv, -6, & 'Ritz values and relative residuals') else c c %-------------------------------------% c | Either convergence failed, or there | c | is error. Check the documentation | c | for DSBAND . | c %-------------------------------------% c print *, ' ' print *, ' Error with _sband, info= ', info print *, ' Check the documentation of _sband ' print *, ' ' c end if c 9000 end arpack-0.92.1/EXAMPLES/BAND/cnbdr4.f0000644000175000017500000002451110776001577013247 00000000000000 program cndrv4 c c ... Construct matrices A and M in LAPACK-style band form. c Matries A and M are derived from the finite c element discretization of the 1-dimensional c convection-diffusion operator c (d^2u/dx^2) + rho*(du/dx) c on the interval [0,1] with zero boundary condition using c piecewise linear elements. c c ... Call CNBAND to find eigenvalues LAMBDA such that c A*x = M*x*LAMBDA. c c ... Use mode 3 of CNAUPD. c c\BeginLib c c\Routines called: c cnband ARPACK banded eigenproblem solver. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c claset LAPACK routine to initialize a matrix to zero. c caxpy Level 1 BLAS that computes y <- alpha*x+y. c scnrm2 Level 1 BLAS that computes the norm of a vector. c cgbmv Level 2 BLAS that computes the band matrix vector product. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: nbdr4.F SID: 2.5 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c------------------------------------------------------------------------- c c %-------------------------------------% c | Define leading dimensions for all | c | arrays. | c | MAXN - Maximum size of the matrix | c | MAXNEV - Maximum number of | c | eigenvalues to be computed | c | MAXNCV - Maximum number of Arnoldi | c | vectors stored | c | MAXBDW - Maximum bandwidth | c %-------------------------------------% c integer maxn, maxnev, maxncv, maxbdw, lda, & lworkl, ldv parameter ( maxn = 1000, maxnev = 25, maxncv=50, & maxbdw=50, lda = maxbdw, ldv = maxn) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), iwork(maxn) logical select(maxncv) Complex & a(lda,maxn), m(lda,maxn), fac(lda,maxn), & workl(3*maxncv*maxncv+5*maxncv), workd(3*maxn), & workev(2*maxncv), v(ldv, maxncv), & resid(maxn), d(maxncv), ax(maxn), mx(maxn) Real & rwork(maxn), rd(maxncv,3) c c %---------------% c | Local Scalars | c %---------------% c character which*2, bmat integer nev, ncv, ku, kl, info, j, & n, idiag, isup, isub, maxitr, mode, & nconv logical rvec Real & tol Complex & rho, h, sigma c c %------------% c | Parameters | c %------------% c Complex & one, zero, two, four, six parameter (one = (1.0E+0, 0.0E+0) , & zero = (0.0E+0, 0.0E+0) , & two = (2.0E+0, 0.0E+0) , & four = (4.0E+0, 0.0E+0) , & six = (6.0E+0, 0.0E+0) ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & scnrm2, slapy2 external scnrm2, cgbmv, caxpy, slapy2, claset c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------------------------% c | The number NX is the number of interior points | c | in the discretization of the 2-dimensional | c | convection-diffusion operator on the unit | c | square with zero Dirichlet boundary condition. | c | The number N(=NX*NX) is the dimension of the | c | matrix. A generalized eigenvalue problem is | c | solved (BMAT = 'G'). NEV is the number of | c | eigenvalues (closest to the shift SIGMA) to be | c | approximated. Since the shift and invert mode | c | is used, WHICH is set to 'LM'. The user can | c | modify NX, NEV and NCV to solve problems of | c | different sizes, and to get different parts the | c | spectrum. However, the following conditions | c | must be satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 2 <= NCV <= MAXNCV | c %-------------------------------------------------% c n = 100 nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _NBDR4: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NBDR4: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NBDR4: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' sigma = (1.0E+1, 0.0E+0) c c %----------------------------------------------------% c | The work array WORKL is used in CNAUPD as | c | workspace. Its dimension LWORKL has to be set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine machine | c | precision is used. Setting INFO=0 indicates that | c | we using a randomly generated vector to start the | c | the ARNOLDI process. | c %----------------------------------------------------% c lworkl = 3*ncv**2+5*ncv info = 0 tol = 0.0 c c %---------------------------------------------------% c | IPARAm(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 3 of CNAUPD is used | c | (IPARAm(7) = 3). All these options can be changed | c | by the user. For details, see the documentation | c | in cnband. | c %---------------------------------------------------% c maxitr = 300 mode = 3 c iparam(3) = maxitr iparam(7) = mode c c %--------------------------------------------% c | Construct matrices A and M in LAPACK-style | c | banded form. | c %--------------------------------------------% c c %---------------------------------------------% c | Zero out the workspace for banded matrices. | c %---------------------------------------------% c call claset('A', lda, n, zero, zero, a, lda) call claset('A', lda, n, zero, zero, m, lda) call claset('A', lda, n, zero, zero, fac, lda) c c %-------------------------------------% c | KU, KL are number of superdiagonals | c | and subdiagonals within the band of | c | matrices A and M. | c %-------------------------------------% c kl = 1 ku = 1 c c %---------------% c | Main diagonal | c %---------------% c h = one / cmplx(n+1) idiag = kl+ku+1 do 30 j = 1, n a(idiag,j) = two / h m(idiag,j) = four * h / six 30 continue c c %-------------------------------------% c | First subdiagonal and superdiagonal | c %-------------------------------------% c isup = kl+ku isub = kl+ku+2 rho = (1.0E+1, 0.0E+0) do 40 j = 1, n-1 a(isup,j+1) = -one/h + rho/two a(isub,j) = -one/h - rho/two m(isup,j+1) = one*h / six m(isub,j) = one*h / six 40 continue c c %-----------------------------------------------% c | Call ARPACK banded solver to find eigenvalues | c | and eigenvectors. Eigenvalues are returned in | c | the one dimensional array D. Eigenvectors | c | are returned in the first NCONV (=IPARAM(5)) | c | columns of V. | c %-----------------------------------------------% c rvec = .true. call cnband(rvec, 'A', select, d, v, ldv, sigma, & workev, n, a, m, lda, fac, kl, ku, which, & bmat, nev, tol, resid, ncv, v, ldv, iparam, & workd, workl, lworkl, rwork, iwork, info) c if ( info .eq. 0) then c nconv = iparam(5) c c %-----------------------------------% c | Print out convergence information | c %-----------------------------------% c print *, ' ' print *, '_NBDR4 ' print *, '====== ' print *, ' ' print *, ' The size of the matrix is ', n print *, ' Number of eigenvalue requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' The number of converged Ritz values is ', & nconv print *, ' What portion of the spectrum ', which print *, ' The number of Implicit Arnoldi ', & ' update taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence tolerance is ', tol print *, ' ' c do 90 j = 1, nconv c c %----------------------------% c | Compute the residual norm. | c | || A*x - lambda*x || | c %----------------------------% c call cgbmv('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call cgbmv('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j), 1, zero, & mx, 1) call caxpy(n, -d(j), mx, 1, ax, 1) rd(j,1) = real (d(j)) rd(j,2) = aimag(d(j)) rd(j,3) = scnrm2(n, ax, 1) rd(j,3) = rd(j,3) / slapy2(rd(j,1), rd(j,2)) 90 continue call smout(6, nconv, 3, rd, maxncv, -6, & 'Ritz values (Real,Imag) and relative residuals') else c c %-------------------------------------% c | Either convergence failed, or there | c | is error. Check the documentation | c | for cnband. | c %-------------------------------------% c print *, ' ' print *, ' Error with _band, info= ', info print *, ' Check the documentation of _band ' print *, ' ' c end if c 9000 end arpack-0.92.1/EXAMPLES/BAND/cnbdr2.f0000644000175000017500000002520510776001577013246 00000000000000 program cnbdr2 c c ... Construct the matrix A in LAPACK-style band form. c The matrix A is derived from the discretization of c the 2-d convection-diffusion operator c c -Laplacian(u) + rho*partial(u)/partial(x). c c on the unit square with zero Dirichlet boundary condition c using standard central difference. c c ... Call CNBAND to find eigenvalues LAMBDA such that c A*x = x*LAMBDA. c c ... Use mode 3 of CNAUPD. c c\BeginLib c c cnband ARPACK banded eigenproblem solver. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c claset LAPACK routine to initialize a matrix to zero. c caxpy Level 1 BLAS that computes y <- alpha*x+y. c scnrm2 Level 1 BLAS that computes the norm of a vector. c cgbmv Level 2 BLAS that computes the band matrix vector product c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: nbdr2.F SID: 2.4 DATE OF SID: 10/20/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c---------------------------------------------------------------------- c c %-------------------------------------% c | Define leading dimensions for all | c | arrays. | c | MAXN - Maximum size of the matrix | c | MAXNEV - Maximum number of | c | eigenvalues to be computed | c | MAXNCV - Maximum number of Arnoldi | c | vectors stored | c | MAXBDW - Maximum bandwidth | c %-------------------------------------% c integer maxn, maxnev, maxncv, maxbdw, lda, & lworkl, ldv parameter ( maxn = 1000, maxnev = 25, maxncv=50, & maxbdw=50, lda = maxbdw, ldv = maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), iwork(maxn) logical select(maxncv) Complex & a(lda,maxn), m(lda,maxn), fac(lda,maxn), & workl(3*maxncv*maxncv+5*maxncv), workd(3*maxn), & workev(2*maxncv), v(ldv, maxncv), & resid(maxn), d(maxncv), ax(maxn) Real & rwork(maxn), rd(maxncv,3) c c %---------------% c | Local Scalars | c %---------------% c character which*2, bmat integer nev, ncv, kl, ku, info, i, j, & n, nxi, lo, isub, isup, idiag, maxitr, mode, & nconv logical rvec Real & tol Complex & rho, h, h2, sigma c c %------------% c | Parameters | c %------------% c Complex & one, zero, two parameter (one = (1.0E+0, 0.0E+0) , & zero = (0.0E+0, 0.0E+0) , & two = (2.0E+0, 0.0E+0) ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & scnrm2, slapy2 external scnrm2, cgbmv, caxpy, slapy2, claset c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------------------------% c | The number NX is the number of interior points | c | in the discretization of the 2-dimensional | c | convection-diffusion operator on the unit | c | square with zero Dirichlet boundary condition. | c | The number N(=NX*NX) is the dimension of the | c | matrix. A standard eigenvalue problem is | c | solved (BMAT = 'I'). NEV is the number of | c | eigenvalues (closest to SIGMA) to be | c | approximated. Since the shift and invert mode | c | is used, WHICH is set to 'LM'. The user can | c | modify NX, NEV and NCV to solve problems of | c | different sizes, and to get different parts the | c | spectrum. However, the following conditions | c | must be satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 2 <= NCV <= MAXNCV | c %-------------------------------------------------% c nxi = 10 n = nxi*nxi nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _NBDR2: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NBDR2: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NBDR2: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'I' which = 'LM' sigma = zero c c %-----------------------------------------------------% c | The work array WORKL is used in CNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. Setting INFO=0 indicates that a | c | random vector is generated in CNAUPD to start the | c | Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = 3*ncv**2+5*ncv tol = 0.0 info = 0 c c %---------------------------------------------------% c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 3 of CNAUPD is used | c | (IPARAM(7) = 3). All these options can be changed | c | by the user. For details, see the documentation | c | in cnband. | c %---------------------------------------------------% c maxitr = 300 mode = 3 c iparam(3) = maxitr iparam(7) = mode c c %----------------------------------------% c | Construct the matrix A in LAPACK-style | c | banded form. | c %----------------------------------------% c c %---------------------------------------------% c | Zero out the workspace for banded matrices. | c %---------------------------------------------% c call claset('A', lda, n, zero, zero, a, lda) call claset('A', lda, n, zero, zero, m, lda) call claset('A', lda, n, zero, zero, fac, lda) c c %-------------------------------------% c | KU, KL are number of superdiagonals | c | and subdiagonals within the band of | c | matrices A and M. | c %-------------------------------------% c kl = nxi ku = nxi c c %---------------% c | Main diagonal | c %---------------% c h = one / cmplx(nxi+1) h2 = h*h c idiag = kl+ku+1 do 30 j = 1, n a(idiag,j) = (4.0E+0, 0.0E+0) / h2 30 continue c c %-------------------------------------% c | First subdiagonal and superdiagonal | c %-------------------------------------% c rho = (1.0E+2, 0.0E+0) isup = kl+ku isub = kl+ku+2 do 50 i = 1, nxi lo = (i-1)*nxi do 40 j = lo+1, lo+nxi-1 a(isup,j+1) = -one/h2 + rho/two/h a(isub,j) = -one/h2 - rho/two/h 40 continue 50 continue c c %------------------------------------% c | KL-th subdiagonal and KU-th super- | c | diagonal. | c %------------------------------------% c isup = kl+1 isub = 2*kl+ku+1 do 80 i = 1, nxi-1 lo = (i-1)*nxi do 70 j = lo+1, lo+nxi a(isup,nxi+j) = -one / h2 a(isub,j) = -one / h2 70 continue 80 continue c c %-----------------------------------------------% c | Call ARPACK banded solver to find eigenvalues | c | and eigenvectors. Eigenvalues are returned in | c | the one dimensional array D. Eigenvectors | c | are returned in the first NCONV (=IPARAM(5)) | c | columns of V. | c %-----------------------------------------------% c rvec = .true. call cnband(rvec, 'A', select, d, v, ldv, sigma, & workev, n, a, m, lda, fac, kl, ku, which, & bmat, nev, tol, resid, ncv, v, ldv, iparam, & workd, workl, lworkl, rwork, iwork, info) c if ( info .eq. 0) then c nconv = iparam(5) c c %-----------------------------------% c | Print out convergence information | c %-----------------------------------% c print *, ' ' print *, '_NBDR2 ' print *, '====== ' print *, ' ' print *, ' The size of the matrix is ', n print *, ' Number of eigenvalue requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' The number of converged Ritz values is ', & nconv print *, ' What portion of the spectrum ', which print *, ' The number of Implicit Arnoldi ', & ' update taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence tolerance is ', tol print *, ' ' c c %----------------------------% c | Compute the residual norm. | c | || A*x - lambda*x || | c %----------------------------% c do 90 j = 1, nconv c c %---------------------------% c | Compute the residual norm | c | || A*x - lambda*x || | c %---------------------------% c call cgbmv('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call caxpy(n, -d(j), v(1,j), 1, ax, 1) rd(j,1) = real (d(j)) rd(j,2) = aimag(d(j)) rd(j,3) = scnrm2(n, ax, 1) rd(j,3) = rd(j,3) / slapy2(rd(j,1),rd(j,2)) 90 continue call smout(6, nconv, 3, rd, maxncv, -6, & 'Ritz values (Real,Imag) and relative residuals') else c c %-------------------------------------% c | Either convergence failed, or there | c | is error. Check the documentation | c | for cnband. | c %-------------------------------------% c print *, ' ' print *, ' Error with _nband, info= ', info print *, ' Check the documentation of _nband ' print *, ' ' c end if c 9000 end arpack-0.92.1/EXAMPLES/BAND/znbdr3.f0000644000175000017500000002441110776001577013274 00000000000000 program znbdr3 c c ... Construct matrices A and M in LAPACK-style band form. c Matrices A and M are derived from the finite c element discretization of the 1-dimensional c convection-diffusion operator c (d^2u/dx^2) + rho*(du/dx) c on the interval [0,1] with zero boundary condition using c piecewise linear elements. c c ... Call ZNBAND to find eigenvalues LAMBDA such that c A*x = M*x*LAMBDA. c c ... Eigenvalues with largest real parts are sought. c c ... Use mode 2 of ZNAUPD . c c\BeginLib c c\Routines called: c znband ARPACK banded eigenproblem solver. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c zlaset LAPACK routine to initialize a matrix to zero. c zaxpy Level 1 BLAS that computes y <- alpha*x+y. c dznrm2 Level 1 BLAS that computes the norm of a vector. c zgbmv Level 2 BLAS that computes the band matrix vector product. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: nbdr3.F SID: 2.4 DATE OF SID: 10/20/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c------------------------------------------------------------------------- c c %-------------------------------------% c | Define leading dimensions for all | c | arrays. | c | MAXN - Maximum size of the matrix | c | MAXNEV - Maximum number of | c | eigenvalues to be computed | c | MAXNCV - Maximum number of Arnoldi | c | vectors stored | c | MAXBDW - Maximum bandwidth | c %-------------------------------------% c integer maxn, maxnev, maxncv, maxbdw, lda, & lworkl, ldv parameter ( maxn = 1000, maxnev = 25, maxncv=50, & maxbdw=50, lda = maxbdw, ldv = maxn) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), iwork(maxn) logical select(maxncv) Complex*16 & a(lda,maxn), m(lda,maxn), fac(lda,maxn), & workl(3*maxncv*maxncv+5*maxncv), workd(3*maxn), & workev(2*maxncv), v(ldv, maxncv), & resid(maxn), d(maxncv), ax(maxn), mx(maxn) Double precision & rwork(maxn), rd(maxncv,3) c c %---------------% c | Local Scalars | c %---------------% c character which*2, bmat integer nev, ncv, ku, kl, info, j, & n, idiag, isup, isub, maxitr, & mode, nconv logical rvec Double precision & tol Complex*16 & rho, h, sigma c c %------------% c | Parameters | c %------------% c Complex*16 & one, zero, two parameter (one = (1.0D+0, 0.0D+0) , & zero = (0.0D+0, 0.0D+0) , & two = (2.0D+0, 0.0D+0) ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & dznrm2 , dlapy2 external dznrm2 , zgbmv , zaxpy , dlapy2 , zlaset c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------------------------% c | The number NX is the number of interior points | c | in the discretization of the 2-dimensional | c | convection-diffusion operator on the unit | c | square with zero Dirichlet boundary condition. | c | The number N(=NX*NX) is the dimension of the | c | matrix. A generalized eigenvalue problem is | c | solved (BMAT = 'G'). NEV is the number of | c | eigenvalues to be approximated. The user can | c | modify NX, NEV, NCV and WHICH to solve problems | c | of different sizes, and to get different parts | c | the spectrum. However, The following | c | conditions must be satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 2 <= NCV <= MAXNCV | c %-------------------------------------------------% c n = 100 nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _NBDR3: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NBDR3: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NBDR3: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' sigma = zero c c %----------------------------------------------------% c | The work array WORKL is used in ZNAUPD as | c | workspace. Its dimension LWORKL has to be set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine machine | c | precision is used. Setting INFO=0 indicates that | c | using a randomly generated vector to start the | c | the ARNOLDI process. | c %----------------------------------------------------% c lworkl = 3*ncv**2+5*ncv info = 0 tol = 0.0 c c %---------------------------------------------------% c | IPARAm(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 2 of ZNAUPD is used | c | (IPARAm(7) = 2). All these options can be changed | c | by the user. For details, see the documentation | c | in znband . | c %---------------------------------------------------% c maxitr = 300 mode = 2 c iparam(3) = maxitr iparam(7) = mode c c %--------------------------------------------% c | Construct matrices A and M in LAPACK-style | c | banded form. | c %--------------------------------------------% c c %---------------------------------------------% c | Zero out the workspace for banded matrices. | c %---------------------------------------------% c call zlaset ('A', lda, n, zero, zero, a, lda) call zlaset ('A', lda, n, zero, zero, m, lda) call zlaset ('A', lda, n, zero, zero, fac, lda) c c %-------------------------------------% c | KU, KL are number of superdiagonals | c | and subdiagonals within the band of | c | matrices A and M. | c %-------------------------------------% c kl = 1 ku = 1 c c %---------------% c | Main diagonal | c %---------------% c h = one / dcmplx (n+1) c idiag = kl+ku+1 do 30 j = 1, n a(idiag,j) = (2.0D+0, 0.0D+0) / h m(idiag,j) = (4.0D+0, 0.0D+0) * h 30 continue c c %-------------------------------------% c | First subdiagonal and superdiagonal | c %-------------------------------------% c isup = kl+ku isub = kl+ku+2 rho = (1.0D+1, 0.0D+0) do 40 j = 1, n-1 a(isup,j+1) = -one/h + rho/two a(isub,j) = -one/h - rho/two m(isup,j+1) = one*h m(isub,j) = one*h 40 continue c c %-----------------------------------------------% c | Call ARPACK banded solver to find eigenvalues | c | and eigenvectors. Eigenvalues are returned in | c | the one dimensional array D. Eigenvectors | c | are returned in the first NCONV (=IPARAM(5)) | c | columns of V. | c %-----------------------------------------------% c rvec = .true. call znband (rvec, 'A', select, d, v, ldv, sigma, & workev, n, a, m, lda, fac, kl, ku, which, & bmat, nev, tol, resid, ncv, v, ldv, iparam, & workd, workl, lworkl, rwork, iwork, info) c if ( info .eq. 0) then c nconv = iparam(5) c c %-----------------------------------% c | Print out convergence information | c %-----------------------------------% c print *, ' ' print *, '_NBDR3 ' print *, '====== ' print *, ' ' print *, ' The size of the matrix is ', n print *, ' Number of eigenvalue requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' The number of converged Ritz values is ', & nconv print *, ' What portion of the spectrum ', which print *, ' The number of Implicit Arnoldi ', & ' update taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence tolerance is ', tol print *, ' ' c do 50 j = 1, nconv c c %----------------------------% c | Compute the residual norm. | c | || A*x - lambda*x || | c %----------------------------% c call zgbmv ('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call zgbmv ('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j), 1, zero, & mx, 1) call zaxpy (n, -d(j), mx, 1, ax, 1) rd(j,1) = dble (d(j)) rd(j,2) = dimag (d(j)) rd(j,3) = dznrm2 (n, ax, 1) rd(j,3) = rd(j,3) / dlapy2 (rd(j,1), rd(j,2)) 50 continue call dmout (6, nconv, 3, rd, maxncv, -6, & 'Ritz values (Real,Imag) and relative residuals') else c c %-------------------------------------% c | Either convergence failed, or there | c | is error. Check the documentation | c | for znband . | c %-------------------------------------% c print *, ' ' print *, ' Error with _band, info= ', info print *, ' Check the documentation of _band ' print *, ' ' c end if c 9000 end arpack-0.92.1/EXAMPLES/BAND/znband.f0000644000175000017500000005531410776001577013354 00000000000000c \BeginDoc c c \Name: znband c c \Description: c This subroutine returns the converged approximations to eigenvalues c of A*z = lambda*B*z and (optionally): c c (1) The corresponding approximate eigenvectors; c c (2) An orthonormal basis for the associated approximate c invariant subspace; c c (3) Both. c c Matrices A and B are stored in LAPACK-style banded form. c c There is negligible additional cost to obtain eigenvectors. An orthonormal c basis is always computed. There is an additional storage cost of n*nev c if both are requested (in this case a separate array Z must be supplied). c c The approximate eigenvalues and eigenvectors of A*z = lambda*B*z c are commonly called Ritz values and Ritz vectors respectively. They are c referred to as such in the comments that follow. The computed orthonormal c basis for the invariant subspace corresponding to these Ritz values is c referred to as a Schur basis. c c znband can be called with one of the following modes: c c Mode 1: A*z = lambda*z. c ===> OP = A and B = I. c c Mode 2: A*z = lambda*M*z, M symmetric positive definite c ===> OP = inv[M]*A and B = M. c c Mode 3: A*z = lambda*M*z, M symmetric semi-definite c ===> OP = inv[A - sigma*M]*M and B = M. c ===> shift-and-invert mode. c c Choice of different modes can be specified in IPARAM(7) defined below. c c \Usage c call znband c ( RVEC, HOWMNY, SELECT, D , Z, LDZ, SIGMA, WORKEV, N, AB, c MB, LDA, FAC, KL, KU, WHICH, BMAT, NEV, TOL, RESID, NCV, c V, LDV, IPARAM, WORKD, WORKL, LWORKL, RWORK, IWORK, INFO ) c c \Arguments c RVEC LOGICAL (INPUT) c Specifies whether a basis for the invariant subspace corresponding c to the converged Ritz value approximations for the eigenproblem c A*z = lambda*B*z is computed. c c RVEC = .FALSE. Compute Ritz values only. c c RVEC = .TRUE. Compute Ritz vectors or Schur vectors. c See Remarks below. c c HOWMNY Character*1 (INPUT) c Specifies the form of the invariant subspace to be computed c corresponding to the converged Ritz values. c = 'A': Compute NEV Ritz vectors; c = 'P': Compute NEV Schur vectors; c = 'S': compute some of the Ritz vectors, specified c by the logical array SELECT. c c SELECT Logical array of dimension NCV. (INPUT) c If HOWMNY = 'S', SELECT specifies the Ritz vectors to be c computed. To select the real Ritz vector corresponding to a c Ritz value D(j), SELECT(j) must be set to .TRUE.. c If HOWMNY = 'A' or 'P', SELECT need not be initialized c but it is used as internal workspace. c c D Complex*16 array of dimension NEV+1. (OUTPUT) c On exit, D contains the Ritz approximations c to the eigenvalues lambda for A*z = lambda*B*z. c c Z Complex*16 N by NEV array (OUTPUT) c On exit, if RVEC = .TRUE. and HOWMNY = 'A', then the columns of c Z represents approximate eigenvectors (Ritz vectors) corresponding c to the NCONV=IPARAM(5) Ritz values for eigensystem c A*z = lambda*B*z. c c If RVEC = .FALSE. or HOWMNY = 'P', then Z is NOT REFERENCED. c c NOTE: If if RVEC = .TRUE. and a Schur basis is not required, c the array Z may be set equal to first NEV columns of the c array V. c c LDZ Integer. (INPUT) c The leading dimension of the array Z. If Ritz vectors are c desired, then LDZ .ge. max( 1, N ) is required. c In any case, LDZ .ge. 1 is required. c c SIGMA Complex*16 (INPUT) c If IPARAM(7) = 3 then SIGMA represents the shift. c Not referenced if IPARAM(7) = 1 or 2. c c WORKEV Complex*16 work array of dimension NCV. (WORKSPACE) c c N Integer. (INPUT) c Dimension of the eigenproblem. c c AB Complex*16 array of dimension LDA by N. (INPUT) c The matrix A in band storage, in rows KL+1 to c 2*KL+KU+1; rows 1 to KL of the array need not be set. c The j-th column of A is stored in the j-th column of the c array AB as follows: c AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) c c MB Complex*16 array of dimension LDA by N. (INPUT) c The matrix M in band storage, in rows KL+1 to c 2*KL+KU+1; rows 1 to KL of the array need not be set. c The j-th column of M is stored in the j-th column of the c array MB as follows: c MB(kl+ku+1+i-j,j) = M(i,j) for max(1,j-ku)<=i<=min(m,j+kl) c Not referenced if IPARAM(7)=1. c c LDA Integer. (INPUT) c Leading dimension of AB, MB, FAC. c c FAC Complex*16 array of LDA by N. (WORKSPACE/OUTPUT) c FAC is used to store the LU factors of MB when mode 2 c is invoked. It is used to store the LU factors of c (A-sigma*M) when mode 3 is invoked. c It is not referenced when IPARAM(7)=1. c c KL Integer. (INPUT) c Max(number of subdiagonals of A, number of subdiagonals of M) c c KU Integer. (OUTPUT) c Max(number of superdiagonals of A, number of superdiagonals of M) c c WHICH Character*2. (INPUT) c When mode 1,2 are used, WHICH can be set to any one of c the following. c c 'LM' -> want the NEV eigenvalues of largest magnitude. c 'SM' -> want the NEV eigenvalues of smallest magnitude. c 'LR' -> want the NEV eigenvalues of largest real part. c 'SR' -> want the NEV eigenvalues of smallest real part. c 'LI' -> want the NEV eigenvalues of largest imaginary part. c 'SI' -> want the NEV eigenvalues of smallest imaginary part. c c When mode 3 is used, WHICH should be set to 'LM' only. c c BMAT Character*1. (INPUT) c BMAT specifies the type of the matrix B that defines the c semi-inner product for the operator OP. c BMAT = 'I' -> standard eigenvalue problem A*x = lambda*x c BMAT = 'G' -> generalized eigenvalue problem A*x = lambda*M*x c NEV Integer. (INPUT) c Number of eigenvalues of to be computed. c c TOL Double precision scalar. (INPUT) c Stopping criteria: the relative accuracy of the Ritz value c is considered acceptable if BOUNDS(I) .LE. TOL*ABS(RITZ(I)) c where ABS(RITZ(I)) is the magnitude when RITZ(I) is complex. c DEFAULT = dlamch ('EPS') (machine precision as computed c by the LAPACK auxilliary subroutine dlamch ). c c RESID Complex*16 array of length N. (INPUT/OUTPUT) c On INPUT: c If INFO .EQ. 0, a random initial residual vector is used. c If INFO .NE. 0, RESID contains the initial residual vector, c possibly from a previous run. c On OUTPUT: c RESID contains the final residual vector. c c NCV Integer. (INPUT) c Number of columns of the matrix V. NCV must satisfy the two c inequalities 2 <= NCV-NEV and NCV <= N. c This will indicate how many Arnoldi vectors are generated c at each iteration. After the startup phase in which NEV c Arnoldi vectors are generated, the algorithm generates c approximately NCV-NEV Arnoldi vectors at each subsequent update c iteration. Most of the cost in generating each Arnoldi vector is c in the matrix-vector operation OP*x. c c V Complex*16 array N by NCV. (OUTPUT) c Upon OUTPUT: If RVEC = .TRUE. the first NCONV=IPARAM(5) columns c contain approximate Schur vectors that span the c desired invariant subspace. c c NOTE: If the array Z has been set equal to first NEV+1 columns c of the array V and RVEC=.TRUE. and HOWMNY= 'A', then c the first NCONV=IPARAM(5) columns of V will contain Ritz vectors c of the eigensystem A*z = lambda*B*z. c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling c program. LDV must be great than or equal to N. c c IPARAM Integer array of length 11. (INPUT/OUTPUT) c IPARAM(1) = ISHIFT: c The shifts selected at each iteration are used to restart c the Arnoldi iteration in an implicit fashion. c It is set to 1 in this subroutine. The user do not need c to set this parameter. c ---------------------------------------------------------- c ISHIFT = 1: exact shift with respect to the current c Hessenberg matrix H. This is equivalent to c restarting the iteration from the beginning c after updating the starting vector with a linear c combination of Ritz vectors associated with the c "wanted" eigenvalues. c ------------------------------------------------------------- c c IPARAM(2) = Not referenced. c c IPARAM(3) = MXITER c On INPUT: max number of Arnoldi update iterations allowed. c On OUTPUT: actual number of Arnoldi update iterations taken. c c IPARAM(4) = NB: blocksize to be used in the recurrence. c The code currently works only for NB = 1. c c IPARAM(5) = NCONV: number of "converged" eigenvalues. c c IPARAM(6) = IUPD c Not referenced. Implicit restarting is ALWAYS used. c c IPARAM(7) = MODE c On INPUT determines what type of eigenproblem is being solved. c Must be 1,2 or 3; See under \Description of znband for the c three modes available. c c WORKD Complex*16 work array of length at least 3*n. (WORKSPACE) c c WORKL Complex*16 work array of length LWORKL. (WORKSPACE) c c LWORKL Integer. (INPUT) c LWORKL must be at least 3*NCV**2 + 5*NCV. c c RWORK Double precision array of length N (WORKSPACE) c Workspace used in znaupd . c c IWORK Integer array of dimension at least N. (WORKSPACE) c Used to mode 2,3. Store the pivot information in the c factorization of M or (A-SIGMA*M). c c INFO Integer. (INPUT/OUTPUT) c Error flag on output. c = 0: Normal exit. c = -1: N must be positive. c = -2: NEV must be positive. c = -3: NCV-NEV >= 2 and less than or equal to N. c = -5: WHICH must be one of 'LM', 'SM', 'LR', 'SR', 'LI', 'SI' c = -6: BMAT must be one of 'I' or 'G'. c = -7: Length of private work WORKL array is not sufficient. c = -8: Error return from LAPACK eigenvalue calculation. c This should never happened. c = -10: IPARAM(7) must be 1,2,3. c = -11: IPARAM(7) = 1 and BMAT = 'G' are incompatible. c = -12: HOWMNY = 'S' not yet implemented c = -13: HOWMNY must be one of 'A' or 'P' if RVEC = .true. c = -14: ZNAUPD did not find any eigenvalues to sufficient c accuracy. c c \EndDoc c c------------------------------------------------------------------------ c c\BeginLib c c\Routines called c znaupd ARPACK reverse communication interface routine. c zneupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c zgbtrf LAPACK band matrix factorization routine. c zgbtrs LAPACK band linear system solve routine. c zlacpy LAPACK matrix copy routine. c zcopy Level 1 BLAS that copies one vector to another. c dznrm2 Level 1 BLAS that computes the norm of a vector. c zgbmv Level 2 BLAS that computes the band matrix vector product. c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly c Restarted Arnoldi Iteration", Ph.D thesis, TR95-13, Rice Univ, c May 1995. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: nband.F SID: 2.3 DATE OF SID: 10/17/00 RELEASE: 2 c c\EndLib c c----------------------------------------------------------------------- c subroutine znband (rvec, howmny, select, d , z, ldz, sigma, & workev, n, ab, mb, lda, fac, kl, ku, which, & bmat, nev, tol, resid, ncv, v, ldv, iparam, & workd, workl, lworkl, rwork, iwork, info ) c c %------------------% c | Scalar Arguments | c %------------------% c Character which*2, bmat, howmny Logical rvec Integer n, lda, kl, ku, nev, ncv, ldv, & ldz, lworkl, info Complex*16 & sigma Double precision & tol c c %-----------------% c | Array Arguments | c %-----------------% c Integer iparam(*), iwork(*) Logical select(*) Complex*16 & d(*), resid(*), v(ldv,*), z(ldz,*), & ab(lda,*), mb(lda,*), fac(lda,*), & workd(*), workl(*), workev(*) Double precision & rwork(*) c c %--------------% c | Local Arrays | c %--------------% c integer ipntr(14) c c %---------------% c | Local Scalars | c %---------------% c integer ido, i, j, mode, ierr, itop, imid, ibot c c %------------% c | Parameters | c %------------% c Complex*16 & one, zero parameter (one = (1.0D+0, 0.0D+0) , & zero = (0.0D+0, 0.0D+0) ) c c %-----------------------------% c | LAPACK & BLAS routines used | c %-----------------------------% c Double precision & dznrm2 external zcopy , zgbmv , zgbtrf , zgbtrs , dznrm2 , zlacpy c c %-----------------------% c | Executable Statements | c %-----------------------% c mode = iparam(7) c c %------------------------% c | Initialize the reverse | c | communication flag. | c %------------------------% c ido = 0 c c %----------------% c | Exact shift is | c | used. | c %----------------% c iparam(1) = 1 c c %-----------------------------------% c | Both matrices A and M are stored | c | between rows itop and ibot. Imid | c | is the index of the row that | c | stores the diagonal elements. | c %-----------------------------------% c itop = kl + 1 imid = kl + ku + 1 ibot = 2*kl + ku + 1 c if ( mode .eq. 2 ) then c c %-----------------------------------------------% c | Copy M to fac and Call LAPACK routine zgbtrf | c | to factor M. | c %-----------------------------------------------% c call zlacpy ('A', ibot, n, mb, lda, fac, lda ) call zgbtrf (n, n, kl, ku, fac, lda, iwork, ierr) if (ierr .ne. 0) then print*, ' ' print*,'_band: error in _gbtrf' print*, ' ' go to 9000 end if c else if ( mode .eq. 3 ) then c if (bmat .eq. 'I') then c c %-------------------------% c | Construct (A - sigma*I) | c %-------------------------% c call zlacpy ('A', ibot, n, ab, lda, fac, lda ) do 10 j = 1,n fac(imid,j) = ab(imid,j) - sigma 10 continue c else c c %---------------------------% c | Construct (A - sigma*M) | c %---------------------------% c do 30 j = 1,n do 20 i = itop, ibot fac(i,j) = ab(i,j) - sigma*mb(i,j) 20 continue 30 continue c end if c c %------------------------% c | Factor (A - sigma*M) | c %------------------------% c call zgbtrf (n, n, kl, ku, fac, lda, iwork, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, '_band: error in _gbtrf.' print*, ' ' go to 9000 end if c end if c c %--------------------------------------------% c | M A I N L O O P (reverse communication) | c %--------------------------------------------% c 40 continue c call znaupd ( ido, bmat, n, which, nev, tol, resid, ncv, & v, ldv, iparam, ipntr, workd, workl, lworkl, & rwork,info ) c if (ido .eq. -1) then c if ( mode .eq. 1) then c c %----------------------------% c | Perform y <--- OP*x = A*x | c %----------------------------% c call zgbmv ('Notranspose', n, n, kl, ku, one, ab(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) c else if ( mode .eq. 2 ) then c c %-----------------------------------% c | Perform y <--- OP*x = inv[M]*A*x | c %-----------------------------------% c call zgbmv ('Notranspose', n, n, kl, ku, one, ab(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) c call zgbtrs ('Notranspose', n, kl, ku, 1, fac, lda, & iwork, workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_band: error in sbgtrs.' print*, ' ' go to 9000 end if c else if ( mode .eq. 3 ) then c c %-----------------------------------------% c | Perform y <-- OP*x | c | = inv[A-SIGMA*M]*M* x c | to force the starting vector into the | c | range of OP. | c %-----------------------------------------% c call zgbmv ('Notranspose', n, n, kl, ku, one, mb(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) c call zgbtrs ('Notranspose', n, kl, ku, 1, fac, lda, & iwork, workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_band: error in _gbtrs.' print*, ' ' go to 9000 end if c end if c else if (ido .eq. 1) then c if ( mode .eq. 1) then c c %----------------------------% c | Perform y <--- OP*x = A*x | c %----------------------------% c call zgbmv ('Notranspose', n, n, kl, ku, one, ab(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) c else if ( mode .eq. 2 ) then c c %-----------------------------------% c | Perform y <--- OP*x = inv[M]*A*x | c %-----------------------------------% c call zgbmv ('Notranspose', n, n, kl, ku, one, ab(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) c call zgbtrs ('Notranspose', n, kl, ku, 1, fac, lda, & iwork, workd(ipntr(2)), ldv, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_band: error in sbgtrs.' print*, ' ' go to 9000 end if c else if ( mode .eq. 3 ) then c if ( bmat .eq. 'I' ) then c c %----------------------------------% c | Perform y <-- inv(A-sigma*I)*x. | c %----------------------------------% c call zcopy (n, workd(ipntr(1)), 1, workd(ipntr(2)), 1) call zgbtrs ('Notranspose', n, kl, ku, 1, fac, lda, & iwork, workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_band: error in _gbtrs.' print*, ' ' go to 9000 end if c else c c %--------------------------------------% c | Perform y <-- inv(A-sigma*M)*(M*x). | c | (M*x) has been computed and stored | c | in workd(ipntr(3)). | c %--------------------------------------% c call zcopy (n, workd(ipntr(3)), 1, workd(ipntr(2)), 1) call zgbtrs ('Notranspose', n, kl, ku, 1, fac, lda, & iwork, workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_band: error in _gbtrs.' print*, ' ' go to 9000 end if c end if c endif c else if (ido .eq. 2) then c c %--------------------% c | Perform y <-- M*x | c %--------------------% c call zgbmv ('Notranspose', n, n, kl, ku, one, mb(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) c else c c %-------------------------------------------% c | Either we have convergence, or there is | c | error. | c %-------------------------------------------% c if ( info .ne. 0) then c c %--------------------------% c | Error message, check the | c | documentation in dnaupd | c %--------------------------% c print *, ' ' print *, ' Error with _naupd info = ',info print *, ' Check the documentation of _naupd ' print *, ' ' c else c call zneupd (rvec, howmny , select, d, z, ldz, sigma, & workev, bmat, n, which, nev, tol, & resid, ncv, v, ldv, iparam, ipntr, workd, & workl, lworkl, rwork, info) c if ( info .ne. 0) then c c %------------------------------------% c | Check the documentation of zneupd . | c %------------------------------------% c print *, ' ' print *, ' Error with _neupd = ', info print *, ' Check the documentation of _neupd ' print *, ' ' c endif c end if c go to 9000 c end if c c %----------------------------------------% c | L O O P B A C K to call znaupd again. | c %----------------------------------------% c go to 40 c 9000 continue c end arpack-0.92.1/EXAMPLES/BAND/dsbdr6.f0000644000175000017500000002346110776001577013262 00000000000000 program dsbdr6 c c ... Construct the matrix A in LAPACK-style band form. c The matrix A is the 1-dimensional discrete Laplacian on [0,1] c with zero Dirichlet boundary condition, M is the mass c formed by using piecewise linear elements on [0,1]. c c ... Call DSBAND with Cayley mode to find eigenvalues LAMBDA such that c A*x = LAMBDA*M*x. c c ... Use mode 5 of DSAUPD . c c\BeginLib c c\Routines called: c dsband ARPACK banded eigenproblem solver. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c dlaset LAPACK routine to initialize a matrix to zero. c daxpy Level 1 BLAS that computes y <- alpha*x+y. c dnrm2 Level 1 BLAS that computes the norm of a vector. c dgbmv Level 2 BLAS that computes the band matrix vector product c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: sbdr6.F SID: 2.5 DATE OF SID: 08/26/96 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c---------------------------------------------------------------------- c c %-------------------------------------% c | Define leading dimensions for all | c | arrays. | c | MAXN - Maximum size of the matrix | c | MAXNEV - Maximum number of | c | eigenvalues to be computed | c | MAXNCV - Maximum number of Arnoldi | c | vectors stored | c | MAXBDW - Maximum bandwidth | c %-------------------------------------% c integer maxn, maxnev, maxncv, maxbdw, lda, & lworkl, ldv parameter ( maxn = 1000, maxnev = 25, maxncv=50, & maxbdw=50, lda = maxbdw, ldv = maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), iwork(maxn) logical select(maxncv) Double precision & a(lda,maxn), m(lda,maxn), rfac(lda,maxn), & workl(maxncv*maxncv+8*maxncv), workd(3*maxn), & v(ldv, maxncv), resid(maxn), d(maxncv, 2), & ax(maxn), mx(maxn) c c %---------------% c | Local Scalars | c %---------------% c character which*2, bmat integer nev, ncv, ku, kl, info, j, ido, & n, isub, isup, idiag, maxitr, mode, nconv Double precision & tol, h, sigma, r1, r2 logical rvec c c %------------% c | Parameters | c %------------% c Double precision & one, zero, two, four, six parameter (one = 1.0D+0 , zero = 0.0D+0 , two = 2.0D+0 , & four = 4.0D+0 , six = 6.0D+0 ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & dlapy2 , dnrm2 external dlapy2 , dnrm2 , daxpy , dgbmv c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c %--------------------------------------------------% c | The number N is the dimension of the matrix. A | c | generalized eigenvalue problem is solved | c | (BMAT = 'G'). NEV is the number of eigenvalues | c | to be approximated. Since the Cayley mode is | c | used, WHICH is set to 'LM'. The user can | c | modify N, NEV, NCV and SIGMA to solve problems | c | of different sizes, and to get different parts | c | the spectrum. However, the following conditions | c | must be satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 1 <= NCV <= MAXNCV | c %--------------------------------------------------% c n = 100 nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _SBDR6: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _SBDR6: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _SBDR6: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' sigma = 150.0 c c %-----------------------------------------------------% c | The work array WORKL is used in DSAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in DSAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = ncv**2+8*ncv tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 5 of DSAUPD is used | c | (IPARAM(7) = 5). All these options can be changed | c | by the user. For details, see the documentation | c | in SBAND. | c %---------------------------------------------------% c maxitr = 300 mode = 5 c iparam(3) = maxitr iparam(7) = mode c c %----------------------------------------% c | Construct the matrix A in LAPACK-style | c | banded form. | c %----------------------------------------% c c %---------------------------------------------% c | Zero out the workspace for banded matrices. | c %---------------------------------------------% c call dlaset ('A', lda, n, zero, zero, a, lda) call dlaset ('A', lda, n, zero, zero, m, lda) call dlaset ('A', lda, n, zero, zero, rfac, lda) c c %-------------------------------------% c | KU, KL are number of superdiagonals | c | and subdiagonals within the band of | c | matrices A and M. | c %-------------------------------------% c kl = 1 ku = 1 c c %---------------% c | Main diagonal | c %---------------% c h = one / dble (n+1) r1 = four / six idiag = kl+ku+1 do 30 j = 1, n a(idiag,j) = two / h m(idiag,j) = r1 * h 30 continue c c %-------------------------------------% c | First subdiagonal and superdiagonal | c %-------------------------------------% c r2 = one / six isup = kl+ku isub = kl+ku+2 do 60 j = 1, n-1 a(isup,j+1) = -one / h a(isub,j) = -one / h m(isup,j+1) = r2 * h m(isub,j) = r2 * h 60 continue c c %-------------------------------------% c | Call DSBAND to find eigenvalues and | c | eigenvectors. Eigenvalues are | c | returned in the first column of D. | c | Eigenvectors are returned in the | c | first NCONV (=IPARAM(5)) columns of | c | V. | c %-------------------------------------% c rvec = .true. call dsband ( rvec, 'A', select, d, v, ldv, sigma, n, a, m, lda, & rfac, kl, ku, which, bmat, nev, tol, & resid, ncv, v, ldv, iparam, workd, workl, lworkl, & iwork, info) c if ( info .eq. 0) then c nconv = iparam(5) c c %-----------------------------------% c | Print out convergence information | c %-----------------------------------% c print *, ' ' print *, ' _SBDR6 ' print *, ' ====== ' print *, ' ' print *, ' The size of the matrix is ', n print *, ' Number of eigenvalue requested is ', nev print *, ' The number of Lanczos vectors generated', & ' (NCV) is ', ncv print *, ' The number of converged Ritz values is ', & nconv print *, ' What portion of the spectrum ', which print *, ' The number of Implicit Arnoldi', & ' update taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence tolerance is ', tol print *, ' ' c c %----------------------------% c | Compute the residual norm. | c | || A*x - lambda*x || | c %----------------------------% c do 90 j = 1, nconv call dgbmv ('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call dgbmv ('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j), 1, zero, & mx, 1) call daxpy (n, -d(j,1), mx, 1, ax, 1) d(j,2) = dnrm2 (n, ax, 1) d(j,2) = d(j,2) / abs(d(j,1)) c 90 continue call dmout (6, nconv, 2, d, maxncv, -6, & 'Ritz values and relative residuals') else c c %-------------------------------------% c | Either convergence failed, or there | c | is error. Check the documentation | c | for DSBAND . | c %-------------------------------------% c print *, ' ' print *, ' Error with _band, info= ', info print *, ' Check the documentation of _band ' print *, ' ' c end if c 9000 end arpack-0.92.1/EXAMPLES/BAND/cnbdr3.f0000644000175000017500000002427310776001577013253 00000000000000 program cnbdr3 c c ... Construct matrices A and M in LAPACK-style band form. c Matrices A and M are derived from the finite c element discretization of the 1-dimensional c convection-diffusion operator c (d^2u/dx^2) + rho*(du/dx) c on the interval [0,1] with zero boundary condition using c piecewise linear elements. c c ... Call CNBAND to find eigenvalues LAMBDA such that c A*x = M*x*LAMBDA. c c ... Eigenvalues with largest real parts are sought. c c ... Use mode 2 of CNAUPD. c c\BeginLib c c\Routines called: c cnband ARPACK banded eigenproblem solver. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c claset LAPACK routine to initialize a matrix to zero. c caxpy Level 1 BLAS that computes y <- alpha*x+y. c scnrm2 Level 1 BLAS that computes the norm of a vector. c cgbmv Level 2 BLAS that computes the band matrix vector product. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: nbdr3.F SID: 2.4 DATE OF SID: 10/20/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c------------------------------------------------------------------------- c c %-------------------------------------% c | Define leading dimensions for all | c | arrays. | c | MAXN - Maximum size of the matrix | c | MAXNEV - Maximum number of | c | eigenvalues to be computed | c | MAXNCV - Maximum number of Arnoldi | c | vectors stored | c | MAXBDW - Maximum bandwidth | c %-------------------------------------% c integer maxn, maxnev, maxncv, maxbdw, lda, & lworkl, ldv parameter ( maxn = 1000, maxnev = 25, maxncv=50, & maxbdw=50, lda = maxbdw, ldv = maxn) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), iwork(maxn) logical select(maxncv) Complex & a(lda,maxn), m(lda,maxn), fac(lda,maxn), & workl(3*maxncv*maxncv+5*maxncv), workd(3*maxn), & workev(2*maxncv), v(ldv, maxncv), & resid(maxn), d(maxncv), ax(maxn), mx(maxn) Real & rwork(maxn), rd(maxncv,3) c c %---------------% c | Local Scalars | c %---------------% c character which*2, bmat integer nev, ncv, ku, kl, info, j, & n, idiag, isup, isub, maxitr, & mode, nconv logical rvec Real & tol Complex & rho, h, sigma c c %------------% c | Parameters | c %------------% c Complex & one, zero, two parameter (one = (1.0E+0, 0.0E+0) , & zero = (0.0E+0, 0.0E+0) , & two = (2.0E+0, 0.0E+0) ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & scnrm2, slapy2 external scnrm2, cgbmv, caxpy, slapy2, claset c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------------------------% c | The number NX is the number of interior points | c | in the discretization of the 2-dimensional | c | convection-diffusion operator on the unit | c | square with zero Dirichlet boundary condition. | c | The number N(=NX*NX) is the dimension of the | c | matrix. A generalized eigenvalue problem is | c | solved (BMAT = 'G'). NEV is the number of | c | eigenvalues to be approximated. The user can | c | modify NX, NEV, NCV and WHICH to solve problems | c | of different sizes, and to get different parts | c | the spectrum. However, The following | c | conditions must be satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 2 <= NCV <= MAXNCV | c %-------------------------------------------------% c n = 100 nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _NBDR3: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NBDR3: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NBDR3: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' sigma = zero c c %----------------------------------------------------% c | The work array WORKL is used in CNAUPD as | c | workspace. Its dimension LWORKL has to be set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine machine | c | precision is used. Setting INFO=0 indicates that | c | using a randomly generated vector to start the | c | the ARNOLDI process. | c %----------------------------------------------------% c lworkl = 3*ncv**2+5*ncv info = 0 tol = 0.0 c c %---------------------------------------------------% c | IPARAm(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 2 of CNAUPD is used | c | (IPARAm(7) = 2). All these options can be changed | c | by the user. For details, see the documentation | c | in cnband. | c %---------------------------------------------------% c maxitr = 300 mode = 2 c iparam(3) = maxitr iparam(7) = mode c c %--------------------------------------------% c | Construct matrices A and M in LAPACK-style | c | banded form. | c %--------------------------------------------% c c %---------------------------------------------% c | Zero out the workspace for banded matrices. | c %---------------------------------------------% c call claset('A', lda, n, zero, zero, a, lda) call claset('A', lda, n, zero, zero, m, lda) call claset('A', lda, n, zero, zero, fac, lda) c c %-------------------------------------% c | KU, KL are number of superdiagonals | c | and subdiagonals within the band of | c | matrices A and M. | c %-------------------------------------% c kl = 1 ku = 1 c c %---------------% c | Main diagonal | c %---------------% c h = one / cmplx(n+1) c idiag = kl+ku+1 do 30 j = 1, n a(idiag,j) = (2.0E+0, 0.0E+0) / h m(idiag,j) = (4.0E+0, 0.0E+0) * h 30 continue c c %-------------------------------------% c | First subdiagonal and superdiagonal | c %-------------------------------------% c isup = kl+ku isub = kl+ku+2 rho = (1.0E+1, 0.0E+0) do 40 j = 1, n-1 a(isup,j+1) = -one/h + rho/two a(isub,j) = -one/h - rho/two m(isup,j+1) = one*h m(isub,j) = one*h 40 continue c c %-----------------------------------------------% c | Call ARPACK banded solver to find eigenvalues | c | and eigenvectors. Eigenvalues are returned in | c | the one dimensional array D. Eigenvectors | c | are returned in the first NCONV (=IPARAM(5)) | c | columns of V. | c %-----------------------------------------------% c rvec = .true. call cnband(rvec, 'A', select, d, v, ldv, sigma, & workev, n, a, m, lda, fac, kl, ku, which, & bmat, nev, tol, resid, ncv, v, ldv, iparam, & workd, workl, lworkl, rwork, iwork, info) c if ( info .eq. 0) then c nconv = iparam(5) c c %-----------------------------------% c | Print out convergence information | c %-----------------------------------% c print *, ' ' print *, '_NBDR3 ' print *, '====== ' print *, ' ' print *, ' The size of the matrix is ', n print *, ' Number of eigenvalue requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' The number of converged Ritz values is ', & nconv print *, ' What portion of the spectrum ', which print *, ' The number of Implicit Arnoldi ', & ' update taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence tolerance is ', tol print *, ' ' c do 50 j = 1, nconv c c %----------------------------% c | Compute the residual norm. | c | || A*x - lambda*x || | c %----------------------------% c call cgbmv('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call cgbmv('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j), 1, zero, & mx, 1) call caxpy(n, -d(j), mx, 1, ax, 1) rd(j,1) = real (d(j)) rd(j,2) = aimag(d(j)) rd(j,3) = scnrm2(n, ax, 1) rd(j,3) = rd(j,3) / slapy2(rd(j,1), rd(j,2)) 50 continue call smout(6, nconv, 3, rd, maxncv, -6, & 'Ritz values (Real,Imag) and relative residuals') else c c %-------------------------------------% c | Either convergence failed, or there | c | is error. Check the documentation | c | for cnband. | c %-------------------------------------% c print *, ' ' print *, ' Error with _band, info= ', info print *, ' Check the documentation of _band ' print *, ' ' c end if c 9000 end arpack-0.92.1/EXAMPLES/BAND/cnbdr1.f0000644000175000017500000002476310776001577013255 00000000000000 program cnbdr1 c c ... Construct the matrix A in LAPACK-style band form. c The matrix A is derived from the discretization of c the 2-d convection-diffusion operator c c -Laplacian(u) + rho*partial(u)/partial(x). c c on the unit square with zero Dirichlet boundary condition c using standard central difference. c c ... Call CNBAND to find eigenvalues LAMBDA such that c A*x = x*LAMBDA. c c ... Use mode 1 of CNAUPD. c c\BeginLib c c cnband ARPACK banded eigenproblem solver. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c claset LAPACK routine to initialize a matrix to zero. c caxpy Level 1 BLAS that computes y <- alpha*x+y. c scnrm2 Level 1 BLAS that computes the norm of a vector. c cgbmv Level 2 BLAS that computes the band matrix vector product c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: nbdr1.F SID: 2.3 DATE OF SID: 08/26/96 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c---------------------------------------------------------------------- c c %-------------------------------------% c | Define leading dimensions for all | c | arrays. | c | MAXN - Maximum size of the matrix | c | MAXNEV - Maximum number of | c | eigenvalues to be computed | c | MAXNCV - Maximum number of Arnoldi | c | vectors stored | c | MAXBDW - Maximum bandwidth | c %-------------------------------------% c integer maxn, maxnev, maxncv, maxbdw, lda, & lworkl, ldv parameter ( maxn = 1000, maxnev = 25, maxncv=50, & maxbdw=50, lda = maxbdw, ldv = maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), iwork(maxn) logical select(maxncv) Complex & a(lda,maxn), m(lda,maxn), fac(lda,maxn), & workl(3*maxncv*maxncv+5*maxncv), workd(3*maxn), & workev(2*maxncv), v(ldv, maxncv), & resid(maxn), d(maxncv), ax(maxn) Real & rwork(maxn), rd(maxncv,3) c c %---------------% c | Local Scalars | c %---------------% c character which*2, bmat integer nev, ncv, kl, ku, info, i, j, & n, nx, lo, isub, isup, idiag, maxitr, mode, & nconv logical rvec Real & tol Complex & rho, h, h2, sigma c c %------------% c | Parameters | c %------------% c Complex & one, zero, two parameter ( one = (1.0E+0, 0.0E+0) , & zero = (0.0E+0, 0.0E+0) , & two = (2.0E+0, 0.0E+0) ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & scnrm2, slapy2 external scnrm2, cgbmv, caxpy, slapy2, claset c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------------------------% c | The number NX is the number of interior points | c | in the discretization of the 2-dimensional | c | convection-diffusion operator on the unit | c | square with zero Dirichlet boundary condition. | c | The number N(=NX*NX) is the dimension of the | c | matrix. A standard eigenvalue problem is | c | solved (BMAT = 'I'). NEV is the number of | c | eigenvalues to be approximated. The user can | c | modify NX, NEV, NCV and WHICH to solve problems | c | of different sizes, and to get different parts | c | the spectrum. However, the following | c | conditions must be satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 2 <= NCV <= MAXNCV | c %-------------------------------------------------% c nx = 10 n = nx*nx nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _NBDR1: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NBDR1: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NBDR1: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'I' which = 'LM' c c %-----------------------------------------------------% c | The work array WORKL is used in CNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. Setting INFO=0 indicates that a | c | random vector is generated in CNAUPD to start the | c | Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = 3*ncv**2+5*ncv tol = 0.0 info = 0 c c %---------------------------------------------------% c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 1 of CNAUPD is used | c | (IPARAM(7) = 1). All these options can be changed | c | by the user. For details, see the documentation | c | in cnband. | c %---------------------------------------------------% c maxitr = 300 mode = 1 c iparam(3) = maxitr iparam(7) = mode c c %----------------------------------------% c | Construct the matrix A in LAPACK-style | c | banded form. | c %----------------------------------------% c c %---------------------------------------------% c | Zero out the workspace for banded matrices. | c %---------------------------------------------% c call claset('A', lda, n, zero, zero, a, lda) call claset('A', lda, n, zero, zero, m, lda) call claset('A', lda, n, zero, zero, fac, lda) c c %-------------------------------------% c | KU, KL are number of superdiagonals | c | and subdiagonals within the band of | c | matrices A and M. | c %-------------------------------------% c kl = nx ku = nx c c %---------------% c | Main diagonal | c %---------------% c h = one / cmplx(nx+1) h2 = h*h c idiag = kl+ku+1 do 30 j = 1, n a(idiag,j) = (4.0E+0, 0.0E+0) / h2 30 continue c c %-------------------------------------% c | First subdiagonal and superdiagonal | c %-------------------------------------% c rho = (1.0E+2, 0.0E+0) isup = kl+ku isub = kl+ku+2 do 50 i = 1, nx lo = (i-1)*nx do 40 j = lo+1, lo+nx-1 a(isup,j+1) = -one/h2 + rho/two/h a(isub,j) = -one/h2 - rho/two/h 40 continue 50 continue c c %------------------------------------% c | KL-th subdiagonal and KU-th super- | c | diagonal. | c %------------------------------------% c isup = kl+1 isub = 2*kl+ku+1 do 80 i = 1, nx-1 lo = (i-1)*nx do 70 j = lo+1, lo+nx a(isup,nx+j) = -one / h2 a(isub,j) = -one / h2 70 continue 80 continue c c %-----------------------------------------------% c | Call ARPACK banded solver to find eigenvalues | c | and eigenvectors. Eigenvalues are returned in | c | the one dimensional array D. Eigenvectors | c | are returned in the first NCONV (=IPARAM(5)) | c | columns of V. | c %-----------------------------------------------% c rvec = .true. call cnband(rvec, 'A', select, d, v, ldv, sigma, & workev, n, a, m, lda, fac, kl, ku, which, & bmat, nev, tol, resid, ncv, v, ldv, iparam, & workd, workl, lworkl, rwork, iwork, info) c if ( info .eq. 0) then c nconv = iparam(5) c c %-----------------------------------% c | Print out convergence information | c %-----------------------------------% c print *, ' ' print *, '_NBDR1 ' print *, '====== ' print *, ' ' print *, ' The size of the matrix is ', n print *, ' Number of eigenvalue requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' The number of converged Ritz values is ', & nconv print *, ' What portion of the spectrum ', which print *, ' The number of Implicit Arnoldi ', & ' update taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence tolerance is ', tol print *, ' ' c c %----------------------------% c | Compute the residual norm. | c | || A*x - lambda*x || | c %----------------------------% c do 90 j = 1, nconv c c %---------------------------% c | Compute the residual norm | c | || A*x - lambda*x || | c %---------------------------% c call cgbmv('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call caxpy(n, -d(j), v(1,j), 1, ax, 1) rd(j,1) = real (d(j)) rd(j,2) = aimag(d(j)) rd(j,3) = scnrm2(n, ax, 1) rd(j,3) = rd(j,3) / slapy2(rd(j,1),rd(j,2)) 90 continue call smout(6, nconv, 3, rd, maxncv, -6, & 'Ritz values (Real,Imag) and relative residuals') else c c %-------------------------------------% c | Either convergence failed, or there | c | is error. Check the documentation | c | for cnband. | c %-------------------------------------% c print *, ' ' print *, ' Error with _nband, info= ', info print *, ' Check the documentation of _nband ' print *, ' ' c end if c 9000 end arpack-0.92.1/EXAMPLES/BAND/dsbdr2.f0000644000175000017500000002424410776001577013256 00000000000000 program dsbdr2 c c ... Construct the matrix A in LAPACK-style band form. c The matrix A is derived from the discretization of c the 2-dimensional Laplacian on the unit square c with zero Dirichlet boundary condition using standard c central difference. c c ... Call DSBAND to find eigenvalues LAMBDA closest to c SIGMA such that c A*x = x*LAMBDA. c c ... Use mode 3 of DSAUPD. c c\BeginLib c c\Routines called: c dsband ARPACK banded eigenproblem solver. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c dlaset LAPACK routine to initialize a matrix to zero. c daxpy Level 1 BLAS that computes y <- alpha*x+y. c dnrm2 Level 1 BLAS that computes the norm of a vector. c dgbmv Level 2 BLAS that computes the band matrix vector product. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: sbdr2.F SID: 2.6 DATE OF SID: 07/21/02 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c---------------------------------------------------------------------- c c %-------------------------------------% c | Define leading dimensions for all | c | arrays. | c | MAXN - Maximum size of the matrix | c | MAXNEV - Maximum number of | c | eigenvalues to be computed | c | MAXNCV - Maximum number of Arnoldi | c | vectors stored | c | MAXBDW - Maximum bandwidth | c %-------------------------------------% c integer maxn, maxnev, maxncv, maxbdw, lda, & lworkl, ldv parameter ( maxn = 1000, maxnev = 25, maxncv=50, & maxbdw=50, lda = maxbdw, ldv = maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), iwork(maxn) logical select(maxncv) Double precision & a(lda,maxn), m(lda,maxn), rfac(lda,maxn), & workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn), & v(ldv, maxncv), resid(maxn), d(maxncv, 2), & ax(maxn) c c %---------------% c | Local Scalars | c %---------------% c character which*2, bmat integer nev, ncv, ku, kl, info, i, j, ido, & n, nx, lo, isub, isup, idiag, maxitr, mode, & nconv Double precision & tol, sigma, h2 logical rvec c c %------------% c | Parameters | c %------------% c Double precision & one, zero, two parameter (one = 1.0D+0, zero = 0.0D+0, two = 2.0D+0) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & dlapy2, dnrm2 external dlapy2, dnrm2, daxpy, dgbmv c c %-----------------------% c | Executable Statements | c %-----------------------% c c %--------------------------------------------------% c | The number NX is the number of interior points | c | in the discretization of the 2-dimensional | c | Laplacian operator on the unit square with zero | c | Dirichlet boundary condition. The number | c | N(=NX*NX) is the dimension of the matrix. A | c | standard eigenvalue problem is solved | c | (BMAT = 'I'). NEV is the number of eigenvalues | c | (closest to the shift SIGMA) to be approximated. | c | Since the shift and invert mode is used, WHICH | c | is set to 'LM'. The user can modify NX, NEV, | c | NCV and SIGMA to solve problems of different | c | sizes, and to get different parts the spectrum. | c | However, the following conditions must be | c | satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 1 <= NCV <= MAXNCV | c %--------------------------------------------------% c nx = 10 n = nx*nx nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _SBDR2: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _SBDR2: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _SBDR2: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'I' which = 'LM' sigma = zero c c %-----------------------------------------------------% c | The work array WORKL is used in DSAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in DSAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = ncv*ncv+8*ncv tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 3 of DSAUPD is used | c | (IPARAM(7) = 3). All these options can be changed | c | by the user. For details see the documentation in | c | DSBAND. | c %---------------------------------------------------% c maxitr = 300 mode = 3 c iparam(3) = maxitr iparam(7) = mode c c %----------------------------------------% c | Construct the matrix A in LAPACK-style | c | banded form. | c %----------------------------------------% c c %---------------------------------------------% c | Zero out the workspace for banded matrices. | c %---------------------------------------------% c call dlaset('A', lda, n, zero, zero, a, lda) call dlaset('A', lda, n, zero, zero, m, lda) call dlaset('A', lda, n, zero, zero, rfac, lda) c c %-------------------------------------% c | KU, KL are number of superdiagonals | c | and subdiagonals within the band of | c | matrices A and M. | c %-------------------------------------% c kl = nx ku = nx c c %---------------% c | Main diagonal | c %---------------% c h2 = one / ((nx+1)*(nx+1)) idiag = kl+ku+1 do 30 j = 1, n a(idiag,j) = 4.0D+0 / h2 30 continue c c %-------------------------------------% c | First subdiagonal and superdiagonal | c %-------------------------------------% c isup = kl+ku isub = kl+ku+2 do 50 i = 1, nx lo = (i-1)*nx do 40 j = lo+1, lo+nx-1 a(isup,j+1) = -one / h2 a(isub,j) = -one / h2 40 continue 50 continue c c %------------------------------------% c | KL-th subdiagonal and KU-th super- | c | diagonal. | c %------------------------------------% c isup = kl+1 isub = 2*kl+ku+1 do 80 i = 1, nx-1 lo = (i-1)*nx do 70 j = lo+1, lo+nx a(isup,nx+j) = -one / h2 a(isub,j) = -one / h2 70 continue 80 continue c c %-------------------------------------% c | Call DSBAND to find eigenvalues and | c | eigenvectors. Eigenvalues are | c | returned in the first column of D. | c | Eigenvectors are returned in the | c | first NCONV (=IPARAM(5)) columns of | c | V. | c %-------------------------------------% c rvec = .true. call dsband( rvec,'A', select, d, v, ldv, sigma, n, a, m, & lda, rfac, kl, ku, which, bmat, nev, tol, & resid, ncv, v, ldv, iparam, workd, workl, lworkl, & iwork, info) c if ( info .eq. 0) then c nconv = iparam(5) c c %-----------------------------------% c | Print out convergence information | c %-----------------------------------% c print *, ' ' print *, ' _SBDR2 ' print *, ' ====== ' print *, ' ' print *, ' The size of the matrix is ', n print *, ' Number of eigenvalue requested is ', nev print *, ' The number of Lanczos vectors generated', & ' (NCV) is ', ncv print *, ' The number of converged Ritz values is ', & nconv print *, ' What portion of the spectrum ', which print *, ' The number of Implicit Arnoldi', & ' update taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence tolerance is ', tol print *, ' ' c c %----------------------------% c | Compute the residual norm. | c | || A*x - lambda*x || | c %----------------------------% c do 90 j = 1, nconv call dgbmv('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call daxpy(n, -d(j,1), v(1,j), 1, ax, 1) d(j,2) = dnrm2(n, ax, 1) d(j,2) = d(j,2) / abs(d(j,1)) c 90 continue call dmout(6, nconv, 2, d, maxncv, -6, & 'Ritz values and relative residuals') else c c %-------------------------------------% c | Either convergence failed, or there | c | is error. Check the documentation | c | for DSBAND. | c %-------------------------------------% c print *, ' ' print *, ' Error with _sband, info= ', info print *, ' Check the documentation of _sband ' print *, ' ' c end if c 9000 end arpack-0.92.1/EXAMPLES/BAND/dnbdr4.f0000644000175000017500000002772710776001577013264 00000000000000 program dnbdr4 c c ... Construct matrices A and M in LAPACK-style band form. c The matrix A and M are derived from the finite element c discretization of the 1-dimensional convection-diffusion operator c (d^2u/dx^2) + rho*(du/dx) c on the interval [0,1] with zero boundary condition. c c ... Define the shift SIGMA = (SIGMAR, SIGMAI). c c ... Call DNBAND to find eigenvalues LAMBDA closest to SIGMA c such that c A*x = LAMBDA*M*x. c c ... Use mode 3 of DNAUPD. c c\BeginLib c c\Routines called: c dnband ARPACK banded eigenproblem solver. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c dlaset LAPACK routine to initialize a matrix to zero. c daxpy Level 1 BLAS that computes y <- alpha*x+y. c dnrm2 Level 1 BLAS that computes the norm of a vector. c dgbmv Level 2 BLAS that computes the band matrix vector product. c c\Author c Danny Sorensen c Richard Lehoucq c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: nbdr4.F SID: 2.6 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c---------------------------------------------------------------------- c c %-------------------------------------% c | Define leading dimensions for all | c | arrays. | c | MAXN - Maximum size of the matrix | c | MAXNEV - Maximum number of | c | eigenvalues to be computed | c | MAXNCV - Maximum number of Arnoldi | c | vectors stored | c | MAXBDW - Maximum bandwidth | c %-------------------------------------% c integer maxn, maxnev, maxncv, maxbdw, lda, & lworkl, ldv parameter ( maxn = 1000, maxnev = 25, maxncv=50, & maxbdw=50, lda = maxbdw, ldv = maxn) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), iwork(maxn) logical select(maxncv) Double precision & a(lda,maxn), m(lda,maxn), rfac(lda,maxn), & workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn), & workev(3*maxncv), v(ldv, maxncv), & resid(maxn), d(maxncv, 3), ax(maxn), mx(maxn) Complex*16 & cfac(lda, maxn), workc(maxn) c c %---------------% c | Local Scalars | c %---------------% c character which*2, bmat integer nev, ncv, ku, kl, info, j, ido, & n, idiag, isup, isub, mode, maxitr, & nconv logical rvec, first Double precision & tol, rho, h, sigmar, sigmai c c %------------% c | Parameters | c %------------% c Double precision & one, zero, two, six parameter (one = 1.0D+0, zero = 0.0D+0, & two = 2.0D+0, six = 6.0D+0) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & dlapy2, dnrm2 external dlapy2, dnrm2, dgbmv, daxpy c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------------------------% c | The number N is the dimension of the matrix. A | c | generalized eigenvalue problem is solved | c | (BMAT = 'G'). NEV is the number of eigenvalues | c | to be approximated. The user can modify N, NEV, | c | NCV and WHICH to solve problems of different | c | sizes, and to get different parts the spectrum. | c | However, the following conditions must be | c | satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 2 <= NCV <= MAXNCV | c %-------------------------------------------------% c n = 100 nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _NBDR4: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NBDR4: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NBDR4: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' sigmar = 1.0D+1 sigmai = 0.0D+0 c c %-----------------------------------------------------% c | The work array WORKL is used in DNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in DNAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = 3*ncv**2+6*ncv info = 0 tol = zero ido = 0 c c %---------------------------------------------------% c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 3 of dnaupd is used | c | (IPARAM(7) = 3). All these options can be changed | c | by the user. For details, see the documentation | c | in dnaupd. | c %---------------------------------------------------% c maxitr = 300 mode = 3 c iparam(3) = n iparam(7) = 3 c c %--------------------------------------------% c | Construct matrices A and M in LAPACK-style | c | banded form. | c %--------------------------------------------% c c %---------------------------------------------% c | Zero out the workspace for banded matrices. | c %---------------------------------------------% c call dlaset('A', lda, n, zero, zero, a, lda) call dlaset('A', lda, n, zero, zero, m, lda) call dlaset('A', lda, n, zero, zero, rfac, lda) c c %-------------------------------------% c | KU, KL are number of superdiagonals | c | and subdiagonals within the band of | c | matrices A and M. | c %-------------------------------------% c kl = 1 ku = 1 c c %---------------% c | Main diagonal | c %---------------% c h = one / dble(n+1) idiag = kl+ku+1 do 30 j = 1, n a(idiag,j) = 2.0D+0 / h m(idiag,j) = 4.0D+0 * h / six 30 continue c c %-------------------------------------% c | First subdiagonal and superdiagonal | c %-------------------------------------% c isup = kl+ku isub = kl+ku+2 rho = 1.0D+1 do 40 j = 1, n-1 a(isup,j+1) = -one/h + rho/two a(isub,j) = -one/h - rho/two m(isup,j+1) = one*h/six m(isub,j) = one*h/six 40 continue c c %------------------------------------------------% c | Call ARPACK banded solver to find eigenvalues | c | and eigenvectors. The real parts of the | c | eigenvalues are returned in the first column | c | of D, the imaginary parts are returned in the | c | second column of D. Eigenvectors are returned | c | in the first NCONV (=IPARAM(5)) columns of V. | c %------------------------------------------------% c rvec = .true. call dnband(rvec, 'A', select, d, d(1,2), v, ldv, sigmar, & sigmai, workev, n, A, M, lda, rfac, cfac, kl, ku, & which, bmat, nev, tol, resid, ncv, v, ldv, iparam, & workd, workl, lworkl, workc, iwork, info) c if ( info .eq. 0) then c c %-----------------------------------% c | Print out convergence information | c %-----------------------------------% c nconv = iparam(5) c print *, ' ' print *, ' _NBDR4 ' print *, ' ====== ' print *, ' ' print *, ' The size of the matrix is ', n print *, ' Number of eigenvalue requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' The number of converged Ritz values is ', & nconv print *, ' What portion of the spectrum ', which print *, ' The number of Implicit Arnoldi ', & ' update taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence tolerance is ', tol print *, ' ' c c %----------------------------% c | Compute the residual norm. | c | || A*x - lambda*x || | c %----------------------------% c first = .true. do 50 j = 1, nconv c if ( d(j,2) .eq. zero ) then c c %--------------------% c | Ritz value is real | c %--------------------% c call dgbmv('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call dgbmv('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j), 1, zero, & mx, 1) call daxpy(n, -d(j,1), mx, 1, ax, 1) d(j,3) = dnrm2(n, ax, 1) d(j,3) = d(j,3) / abs(d(j,1)) c else if ( first ) then c c %------------------------% c | Ritz value is complex | c | Residual of one Ritz | c | value of the conjugate | c | pair is computed. | c %------------------------% c call dgbmv('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call dgbmv('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j), 1, zero, & mx, 1) call daxpy(n, -d(j,1), mx, 1, ax, 1) call dgbmv('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j+1), 1, zero, & mx, 1) call daxpy(n, d(j,2), mx, 1, ax, 1) d(j,3) = dnrm2(n, ax, 1) call dgbmv('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j+1), 1, zero, & ax, 1) call dgbmv('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j+1), 1, zero, & mx, 1) call daxpy(n, -d(j,1), mx, 1, ax, 1) call dgbmv('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j), 1, zero, & mx, 1) call daxpy(n, -d(j,2), mx, 1, ax, 1) d(j,3) = dlapy2( d(j,3), dnrm2(n, ax, 1) ) d(j,3) = d(j,3) / dlapy2(d(j,1),d(j,2)) d(j+1,3) = d(j,3) first = .false. else first = .true. end if c 50 continue call dmout(6, nconv, 3, d, maxncv, -6, & 'Ritz values (Real,Imag) and relatve residuals') else c c %-------------------------------------% c | Either convergence failed, or there | c | is error. Check the documentation | c | for DNBAND. | c %-------------------------------------% c print *, ' ' print *, ' Error with _nband, info= ', info print *, ' Check the documentation of _nband ' print *, ' ' c end if c 9000 end arpack-0.92.1/EXAMPLES/BAND/ssbdr1.f0000644000175000017500000002410310776001577013266 00000000000000 program ssbdr1 c c ... Construct the matrix A in LAPACK-style band form. c The matrix A is derived from the discretization of c the 2-dimensional Laplacian on the unit square with c zero Dirichlet boundary condition using standard c central difference. c c ... Call SSBAND to find eigenvalues LAMBDA such that c A*x = x*LAMBDA. c c ... Use mode 1 of SSAUPD. c c\BeginLib c c\Routines called: c ssband ARPACK banded eigenproblem solver. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c slaset LAPACK routine to initialize a matrix to zero. c saxpy Level 1 BLAS that computes y <- alpha*x+y. c snrm2 Level 1 BLAS that computes the norm of a vector. c sgbmv Level 2 BLAS that computes the band matrix vector product c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: sbdr1.F SID: 2.5 DATE OF SID: 08/26/96 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c---------------------------------------------------------------------- c c %-------------------------------------% c | Define leading dimensions for all | c | arrays. | c | MAXN - Maximum size of the matrix | c | MAXNEV - Maximum number of | c | eigenvalues to be computed | c | MAXNCV - Maximum number of Arnoldi | c | vectors stored | c | MAXBDW - Maximum bandwidth | c %-------------------------------------% c integer maxn, maxnev, maxncv, maxbdw, lda, & lworkl, ldv parameter ( maxn = 1000, maxnev = 25, maxncv=50, & maxbdw=50, lda = maxbdw, ldv = maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), iwork(maxn) logical select(maxncv) Real & a(lda,maxn), m(lda,maxn), rfac(lda,maxn), & workl(maxncv*maxncv+8*maxncv), workd(3*maxn), & v(ldv, maxncv), resid(maxn), d(maxncv, 2), & ax(maxn) c c %---------------% c | Local Scalars | c %---------------% c character which*2, bmat integer nev, ncv, ku, kl, info, i, j, ido, & n, nx, lo, isub, isup, idiag, maxitr, mode, & nconv Real & tol, sigma, h2 logical rvec c c %------------% c | Parameters | c %------------% c Real & one, zero, two parameter (one = 1.0E+0 , zero = 0.0E+0 , two = 2.0E+0 ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & slapy2, snrm2 external slapy2, snrm2, sgbmv, saxpy c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------------------------% c | The number NX is the number of interior points | c | in the discretization of the 2-dimensional | c | Laplacian operator on the unit square with zero | c | Dirichlet boundary condition. The number | c | N(=NX*NX) is the dimension of the matrix. A | c | standard eigenvalue problem is solved | c | (BMAT = 'I'). NEV is the number of eigenvalues | c | to be approximated. The user can modify NX,NEV, | c | NCV and WHICH to solve problems of different | c | sizes, and to get different parts the spectrum. | c | However, the following conditions must be | c | satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 1 <= NCV <= MAXNCV | c %-------------------------------------------------% c nx = 10 n = nx*nx nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _SBDR1: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _SBDR1: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _SBDR1: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'I' which = 'LM' c c %-----------------------------------------------------% c | The work array WORKL is used in SSAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in SSAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = ncv**2+8*ncv tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 1 of SSAUPD is used | c | (IPARAM(7) = 1). All these options can be changed | c | by the user. For details see the documentation in | c | SSBAND. | c %---------------------------------------------------% c maxitr = 300 mode = 1 c iparam(3) = maxitr iparam(7) = mode c c %----------------------------------------% c | Construct the matrix A in LAPACK-style | c | banded form. | c %----------------------------------------% c c %---------------------------------------------% c | Zero out the workspace for banded matrices. | c %---------------------------------------------% c call slaset('A', lda, n, zero, zero, a, lda) call slaset('A', lda, n, zero, zero, m, lda) call slaset('A', lda, n, zero, zero, rfac, lda) c c %-------------------------------------% c | KU, KL are number of superdiagonals | c | and subdiagonals within the band of | c | matrices A and M. | c %-------------------------------------% c kl = nx ku = nx c c %---------------% c | Main diagonal | c %---------------% c h2 = one / ((nx+1)*(nx+1)) idiag = kl+ku+1 do 30 j = 1, n a(idiag,j) = 4.0E+0 / h2 30 continue c c %-------------------------------------% c | First subdiagonal and superdiagonal | c %-------------------------------------% c isup = kl+ku isub = kl+ku+2 do 50 i = 1, nx lo = (i-1)*nx do 40 j = lo+1, lo+nx-1 a(isup,j+1) = -one / h2 a(isub,j) = -one / h2 40 continue 50 continue c c %------------------------------------% c | KL-th subdiagonal and KU-th super- | c | diagonal. | c %------------------------------------% c isup = kl+1 isub = 2*kl+ku+1 do 80 i = 1, nx-1 lo = (i-1)*nx do 70 j = lo+1, lo+nx a(isup,nx+j) = -one / h2 a(isub,j) = -one / h2 70 continue 80 continue c c %-------------------------------------% c | Call SSBAND to find eigenvalues and | c | eigenvectors. Eigenvalues are | c | returned in the first column of D. | c | Eigenvectors are returned in the | c | first NCONV (=IPARAM(5)) columns of | c | V. | c %-------------------------------------% c rvec = .true. call ssband( rvec, 'A', select, d, v, ldv, sigma, n, a, m, lda, & rfac, kl, ku, which, bmat, nev, tol, & resid, ncv, v, ldv, iparam, workd, workl, lworkl, & iwork, info) c if ( info .eq. 0) then c nconv = iparam(5) c c %-----------------------------------% c | Print out convergence information | c %-----------------------------------% c print *, ' ' print *, ' _SBDR1 ' print *, ' ====== ' print *, ' ' print *, ' The size of the matrix is ', n print *, ' Number of eigenvalue requested is ', nev print *, ' The number of Lanczos vectors generated', & ' (NCV) is ', ncv print *, ' The number of converged Ritz values is ', & nconv print *, ' What portion of the spectrum ', which print *, ' The number of Implicit Arnoldi', & ' update taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence tolerance is ', tol print *, ' ' c c %----------------------------% c | Compute the residual norm. | c | || A*x - lambda*x || | c %----------------------------% c do 90 j = 1, nconv call sgbmv('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call saxpy(n, -d(j,1), v(1,j), 1, ax, 1) d(j,2) = snrm2(n, ax, 1) d(j,2) = d(j,2) / abs(d(j,1)) c 90 continue call smout(6, nconv, 2, d, maxncv, -6, & 'Ritz values and relative residuals') else c c %-------------------------------------% c | Either convergence failed, or there | c | is error. Check the documentation | c | for SSBAND. | c %-------------------------------------% c print *, ' ' print *, ' Error with _sband, info= ', info print *, ' Check the documentation of _sband ' print *, ' ' c end if c 9000 end arpack-0.92.1/EXAMPLES/BAND/dnbdr1.f0000644000175000017500000002746710776001577013262 00000000000000 program dnbdr1 c c ... Construct the matrix A in LAPACK-style band form. c The matrix A is derived from the discretization of c the 2-d convection-diffusion operator c c -Laplacian(u) + rho*partial(u)/partial(x). c c on the unit square with zero Dirichlet boundary condition c using standard central difference. c c ... Call DNBAND to find eigenvalues LAMBDA such that c A*x = LAMBDA*x. c c ... Use mode 1 of DNAUPD . c c\BeginLib c c dnband ARPACK banded eigenproblem solver. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c dlaset LAPACK routine to initialize a matrix to zero. c daxpy Level 1 BLAS that computes y <- alpha*x+y. c dnrm2 Level 1 BLAS that computes the norm of a vector. c dgbmv Level 2 BLAS that computes the band matrix vector product c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: nbdr1.F SID: 2.5 DATE OF SID: 08/26/96 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c---------------------------------------------------------------------- c c %-------------------------------------% c | Define leading dimensions for all | c | arrays. | c | MAXN - Maximum size of the matrix | c | MAXNEV - Maximum number of | c | eigenvalues to be computed | c | MAXNCV - Maximum number of Arnoldi | c | vectors stored | c | MAXBDW - Maximum bandwidth | c %-------------------------------------% c integer maxn, maxnev, maxncv, maxbdw, lda, & lworkl, ldv parameter ( maxn = 1000, maxnev = 25, maxncv=50, & maxbdw=50, lda = maxbdw, ldv = maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), iwork(maxn) logical select(maxncv) Double precision & a(lda,maxn), m(lda,maxn), rfac(lda,maxn), & workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn), & workev(3*maxncv), v(ldv, maxncv), & resid(maxn), d(maxncv, 3), ax(maxn) Complex*16 & cfac(lda, maxn), workc(maxn) c c %---------------% c | Local Scalars | c %---------------% c character which*2, bmat integer nev, ncv, ku, kl, info, i, j, ido, & n, nx, lo, isub, isup, idiag, mode, maxitr, & nconv logical rvec, first Double precision & tol, rho, h, h2, sigmar, sigmai c c %------------% c | Parameters | c %------------% c Double precision & one, zero, two parameter (one = 1.0D+0 , zero = 0.0D+0 , & two = 2.0D+0 ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & dlapy2 , dnrm2 external dlapy2 , dnrm2 , dgbmv , daxpy c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------------------------% c | The number NX is the number of interior points | c | in the discretization of the 2-dimensional | c | convection-diffusion operator on the unit | c | square with zero Dirichlet boundary condition. | c | The number N(=NX*NX) is the dimension of the | c | matrix. A standard eigenvalue problem is | c | solved (BMAT = 'I'). NEV is the number of | c | eigenvalues to be approximated. The user can | c | modify NX, NEV, NCV, WHICH to solve problems of | c | different sizes, and to get different parts the | c | spectrum. However, The following conditions | c | must be satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 2 <= NCV <= MAXNCV | c %-------------------------------------------------% c nx = 10 n = nx*nx nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _NBDR1: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NBDR1: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NBDR1: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'I' which = 'SM' c c %-----------------------------------------------------% c | The work array WORKL is used in DNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in DNAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = 3*ncv**2+6*ncv tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 1 of DNAUPD is used | c | (IPARAM(7) = 1). All these options can be changed | c | by the user. For details, see the documentation | c | in DNBAND . | c %---------------------------------------------------% c maxitr = 300 mode = 1 c iparam(3) = maxitr iparam(7) = mode c c %----------------------------------------% c | Construct the matrix A in LAPACK-style | c | banded form. | c %----------------------------------------% c c %---------------------------------------------% c | Zero out the workspace for banded matrices. | c %---------------------------------------------% c call dlaset ('A', lda, n, zero, zero, a, lda) call dlaset ('A', lda, n, zero, zero, m, lda) call dlaset ('A', lda, n, zero, zero, rfac, lda) c c %-------------------------------------% c | KU, KL are number of superdiagonals | c | and subdiagonals within the band of | c | matrices A and M. | c %-------------------------------------% c kl = nx ku = nx c c %---------------% c | Main diagonal | c %---------------% c h = one / dble (nx+1) h2 = h*h c idiag = kl+ku+1 do 30 j = 1, n a(idiag,j) = 4.0D+0 / h2 30 continue c c %-------------------------------------% c | First subdiagonal and superdiagonal | c %-------------------------------------% c rho = 1.0D+2 isup = kl+ku isub = kl+ku+2 do 50 i = 1, nx lo = (i-1)*nx do 40 j = lo+1, lo+nx-1 a(isup,j+1) = -one/h2 + rho/two/h a(isub,j) = -one/h2 - rho/two/h 40 continue 50 continue c c %------------------------------------% c | KL-th subdiagonal and KU-th super- | c | diagonal. | c %------------------------------------% c isup = kl+1 isub = 2*kl+ku+1 do 80 i = 1, nx-1 lo = (i-1)*nx do 70 j = lo+1, lo+nx a(isup,nx+j) = -one / h2 a(isub,j) = -one / h2 70 continue 80 continue c c %------------------------------------------------% c | Call ARPACK banded solver to find eigenvalues | c | and eigenvectors. The real parts of the | c | eigenvalues are returned in the first column | c | of D, the imaginary parts are returned in the | c | second column of D. Eigenvectors are returned | c | in the first NCONV (=IPARAM(5)) columns of V. | c %------------------------------------------------% c rvec = .true. call dnband (rvec, 'A', select, d, d(1,2), v, ldv, sigmar, sigmai, & workev, n, a, m, lda, rfac, cfac, kl, ku, which, & bmat, nev, tol, resid, ncv, v, ldv, iparam, workd, & workl, lworkl, workc, iwork, info) c if ( info .eq. 0) then c c %-----------------------------------% c | Print out convergence information | c %-----------------------------------% c nconv = iparam(5) c print *, ' ' print *, ' _NBDR1 ' print *, ' ====== ' print *, ' ' print *, ' The size of the matrix is ', n print *, ' Number of eigenvalue requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' The number of converged Ritz values is ', & nconv print *, ' What portion of the spectrum ', which print *, ' The number of Implicit Arnoldi ', & ' update taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence tolerance is ', tol print *, ' ' c c %----------------------------% c | Compute the residual norm. | c | || A*x - lambda*x || | c %----------------------------% c first = .true. do 90 j = 1, nconv c if ( d(j,2) .eq. zero ) then c c %--------------------% c | Ritz value is real | c %--------------------% c call dgbmv ('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call daxpy (n, -d(j,1), v(1,j), 1, ax, 1) d(j,3) = dnrm2 (n, ax, 1) d(j,3) = d(j,3) / abs(d(j,1)) c else if ( first ) then c c %------------------------% c | Ritz value is complex | c | Residual of one Ritz | c | value of the conjugate | c | pair is computed. | c %------------------------% c call dgbmv ('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call daxpy (n, -d(j,1), v(1,j), 1, ax, 1) call daxpy (n, d(j,2), v(1,j+1), 1, ax, 1) d(j,3) = dnrm2 (n, ax, 1) call dgbmv ('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j+1), 1, zero, & ax, 1) call daxpy (n, -d(j,2), v(1,j), 1, ax, 1) call daxpy (n, -d(j,1), v(1,j+1), 1, ax, 1) d(j,3) = dlapy2 ( d(j,3), dnrm2 (n, ax, 1) ) d(j,3) = d(j,3) / dlapy2 (d(j,1),d(j,2)) d(j+1,3) = d(j,3) first = .false. else first = .true. end if c 90 continue call dmout (6, nconv, 3, d, maxncv, -6, & 'Ritz values (Real,Imag) and relative residuals') else c c %-------------------------------------% c | Either convergence failed, or there | c | is error. Check the documentation | c | for DNBAND . | c %-------------------------------------% c print *, ' ' print *, ' Error with _nband, info= ', info print *, ' Check the documentation of _nband ' print *, ' ' c end if c 9000 end arpack-0.92.1/EXAMPLES/BAND/snbdr4.f0000644000175000017500000002764410776001577013301 00000000000000 program snbdr4 c c ... Construct matrices A and M in LAPACK-style band form. c The matrix A and M are derived from the finite element c discretization of the 1-dimensional convection-diffusion operator c (d^2u/dx^2) + rho*(du/dx) c on the interval [0,1] with zero boundary condition. c c ... Define the shift SIGMA = (SIGMAR, SIGMAI). c c ... Call SNBAND to find eigenvalues LAMBDA closest to SIGMA c such that c A*x = LAMBDA*M*x. c c ... Use mode 3 of SNAUPD. c c\BeginLib c c\Routines called: c snband ARPACK banded eigenproblem solver. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c slaset LAPACK routine to initialize a matrix to zero. c saxpy Level 1 BLAS that computes y <- alpha*x+y. c snrm2 Level 1 BLAS that computes the norm of a vector. c sgbmv Level 2 BLAS that computes the band matrix vector product. c c\Author c Danny Sorensen c Richard Lehoucq c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: nbdr4.F SID: 2.6 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c---------------------------------------------------------------------- c c %-------------------------------------% c | Define leading dimensions for all | c | arrays. | c | MAXN - Maximum size of the matrix | c | MAXNEV - Maximum number of | c | eigenvalues to be computed | c | MAXNCV - Maximum number of Arnoldi | c | vectors stored | c | MAXBDW - Maximum bandwidth | c %-------------------------------------% c integer maxn, maxnev, maxncv, maxbdw, lda, & lworkl, ldv parameter ( maxn = 1000, maxnev = 25, maxncv=50, & maxbdw=50, lda = maxbdw, ldv = maxn) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), iwork(maxn) logical select(maxncv) Real & a(lda,maxn), m(lda,maxn), rfac(lda,maxn), & workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn), & workev(3*maxncv), v(ldv, maxncv), & resid(maxn), d(maxncv, 3), ax(maxn), mx(maxn) Complex & cfac(lda, maxn), workc(maxn) c c %---------------% c | Local Scalars | c %---------------% c character which*2, bmat integer nev, ncv, ku, kl, info, j, ido, & n, idiag, isup, isub, mode, maxitr, & nconv logical rvec, first Real & tol, rho, h, sigmar, sigmai c c %------------% c | Parameters | c %------------% c Real & one, zero, two, six parameter (one = 1.0E+0, zero = 0.0E+0, & two = 2.0E+0, six = 6.0E+0) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & slapy2, snrm2 external slapy2, snrm2, sgbmv, saxpy c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------------------------% c | The number N is the dimension of the matrix. A | c | generalized eigenvalue problem is solved | c | (BMAT = 'G'). NEV is the number of eigenvalues | c | to be approximated. The user can modify N, NEV, | c | NCV and WHICH to solve problems of different | c | sizes, and to get different parts the spectrum. | c | However, the following conditions must be | c | satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 2 <= NCV <= MAXNCV | c %-------------------------------------------------% c n = 100 nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _NBDR4: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NBDR4: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NBDR4: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' sigmar = 1.0E+1 sigmai = 0.0E+0 c c %-----------------------------------------------------% c | The work array WORKL is used in SNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in SNAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = 3*ncv**2+6*ncv info = 0 tol = zero ido = 0 c c %---------------------------------------------------% c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 3 of snaupd is used | c | (IPARAM(7) = 3). All these options can be changed | c | by the user. For details, see the documentation | c | in snaupd. | c %---------------------------------------------------% c maxitr = 300 mode = 3 c iparam(3) = n iparam(7) = 3 c c %--------------------------------------------% c | Construct matrices A and M in LAPACK-style | c | banded form. | c %--------------------------------------------% c c %---------------------------------------------% c | Zero out the workspace for banded matrices. | c %---------------------------------------------% c call slaset('A', lda, n, zero, zero, a, lda) call slaset('A', lda, n, zero, zero, m, lda) call slaset('A', lda, n, zero, zero, rfac, lda) c c %-------------------------------------% c | KU, KL are number of superdiagonals | c | and subdiagonals within the band of | c | matrices A and M. | c %-------------------------------------% c kl = 1 ku = 1 c c %---------------% c | Main diagonal | c %---------------% c h = one / real(n+1) idiag = kl+ku+1 do 30 j = 1, n a(idiag,j) = 2.0E+0 / h m(idiag,j) = 4.0E+0 * h / six 30 continue c c %-------------------------------------% c | First subdiagonal and superdiagonal | c %-------------------------------------% c isup = kl+ku isub = kl+ku+2 rho = 1.0E+1 do 40 j = 1, n-1 a(isup,j+1) = -one/h + rho/two a(isub,j) = -one/h - rho/two m(isup,j+1) = one*h/six m(isub,j) = one*h/six 40 continue c c %------------------------------------------------% c | Call ARPACK banded solver to find eigenvalues | c | and eigenvectors. The real parts of the | c | eigenvalues are returned in the first column | c | of D, the imaginary parts are returned in the | c | second column of D. Eigenvectors are returned | c | in the first NCONV (=IPARAM(5)) columns of V. | c %------------------------------------------------% c rvec = .true. call snband(rvec, 'A', select, d, d(1,2), v, ldv, sigmar, & sigmai, workev, n, A, M, lda, rfac, cfac, kl, ku, & which, bmat, nev, tol, resid, ncv, v, ldv, iparam, & workd, workl, lworkl, workc, iwork, info) c if ( info .eq. 0) then c c %-----------------------------------% c | Print out convergence information | c %-----------------------------------% c nconv = iparam(5) c print *, ' ' print *, ' _NBDR4 ' print *, ' ====== ' print *, ' ' print *, ' The size of the matrix is ', n print *, ' Number of eigenvalue requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' The number of converged Ritz values is ', & nconv print *, ' What portion of the spectrum ', which print *, ' The number of Implicit Arnoldi ', & ' update taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence tolerance is ', tol print *, ' ' c c %----------------------------% c | Compute the residual norm. | c | || A*x - lambda*x || | c %----------------------------% c first = .true. do 50 j = 1, nconv c if ( d(j,2) .eq. zero ) then c c %--------------------% c | Ritz value is real | c %--------------------% c call sgbmv('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call sgbmv('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j), 1, zero, & mx, 1) call saxpy(n, -d(j,1), mx, 1, ax, 1) d(j,3) = snrm2(n, ax, 1) d(j,3) = d(j,3) / abs(d(j,1)) c else if ( first ) then c c %------------------------% c | Ritz value is complex | c | Residual of one Ritz | c | value of the conjugate | c | pair is computed. | c %------------------------% c call sgbmv('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call sgbmv('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j), 1, zero, & mx, 1) call saxpy(n, -d(j,1), mx, 1, ax, 1) call sgbmv('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j+1), 1, zero, & mx, 1) call saxpy(n, d(j,2), mx, 1, ax, 1) d(j,3) = snrm2(n, ax, 1) call sgbmv('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j+1), 1, zero, & ax, 1) call sgbmv('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j+1), 1, zero, & mx, 1) call saxpy(n, -d(j,1), mx, 1, ax, 1) call sgbmv('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j), 1, zero, & mx, 1) call saxpy(n, -d(j,2), mx, 1, ax, 1) d(j,3) = slapy2( d(j,3), snrm2(n, ax, 1) ) d(j,3) = d(j,3) / slapy2(d(j,1),d(j,2)) d(j+1,3) = d(j,3) first = .false. else first = .true. end if c 50 continue call smout(6, nconv, 3, d, maxncv, -6, & 'Ritz values (Real,Imag) and relatve residuals') else c c %-------------------------------------% c | Either convergence failed, or there | c | is error. Check the documentation | c | for SNBAND. | c %-------------------------------------% c print *, ' ' print *, ' Error with _nband, info= ', info print *, ' Check the documentation of _nband ' print *, ' ' c end if c 9000 end arpack-0.92.1/EXAMPLES/BAND/dsband.f0000644000175000017500000007716210776001577013340 00000000000000c \BeginDoc c c \Name: dsband c c \Description: c c This subroutine returns the converged approximations to eigenvalues c of A*z = lambda*B*z and (optionally): c c (1) The corresponding approximate eigenvectors; c c (2) An orthonormal (Lanczos) basis for the associated approximate c invariant subspace; c c (3) Both. c c Matrices A and B are stored in LAPACK-style band form. c c There is negligible additional cost to obtain eigenvectors. An orthonormal c (Lanczos) basis is always computed. There is an additional storage cost c of n*nev if both are requested (in this case a separate array Z must be c supplied). c c The approximate eigenvalues and eigenvectors of A*z = lambda*B*z c are called Ritz values and Ritz vectors respectively. They are referred c to as such in the comments that follow. The computed orthonormal basis c for the invariant subspace corresponding to these Ritz values is referred c to as a Lanczos basis. c c dsband can be called with one of the following modes: c c Mode 1: A*x = lambda*x, A symmetric c ===> OP = A and B = I. c c Mode 2: A*x = lambda*M*x, A symmetric, M symmetric positive definite c ===> OP = inv[M]*A and B = M. c ===> (If M can be factored see remark 3 in DSAUPD) c c Mode 3: K*x = lambda*M*x, K symmetric, M symmetric positive semi-definite c ===> OP = (inv[K - sigma*M])*M and B = M. c ===> Shift-and-Invert mode c c Mode 4: K*x = lambda*KG*x, K symmetric positive semi-definite, c KG symmetric indefinite c ===> OP = (inv[K - sigma*KG])*K and B = K. c ===> Buckling mode c c Mode 5: A*x = lambda*M*x, A symmetric, M symmetric positive semi-definite c ===> OP = inv[A - sigma*M]*[A + sigma*M] and B = M. c ===> Cayley transformed mode c c The choice of mode must be specified in IPARAM(7) defined below. c c \Usage c call dsband c ( RVEC, HOWMNY, SELECT, D, Z, LDZ, SIGMA, N, AB, MB, LDA, c RFAC, KL, KU, WHICH, BMAT, NEV, TOL, RESID, NCV, V, c LDV, IPARAM, WORKD, WORKL, LWORKL, IWORK, INFO ) c c \Arguments c c RVEC Logical (INPUT) c Specifies whether Ritz vectors corresponding to the Ritz value c approximations to the eigenproblem A*z = lambda*B*z are computed. c c RVEC = .FALSE. Compute Ritz values only. c c RVEC = .TRUE. Compute the associated Ritz vectors. c c HOWMNY Character*1 (INPUT) c Specifies how many Ritz vectors are wanted and the form of Z c the matrix of Ritz vectors. See remark 1 below. c = 'A': compute all Ritz vectors; c = 'S': compute some of the Ritz vectors, specified c by the logical array SELECT. c c SELECT Logical array of dimension NCV. (INPUT) c If HOWMNY = 'S', SELECT specifies the Ritz vectors to be c computed. To select the Ritz vector corresponding to a c Ritz value D(j), SELECT(j) must be set to .TRUE.. c If HOWMNY = 'A' , SELECT is not referenced. c c D Double precision array of dimension NEV. (OUTPUT) c On exit, D contains the Ritz value approximations to the c eigenvalues of A*z = lambda*B*z. The values are returned c in ascending order. If IPARAM(7) = 3,4,5 then D represents c the Ritz values of OP computed by dsaupd transformed to c those of the original eigensystem A*z = lambda*B*z. If c IPARAM(7) = 1,2 then the Ritz values of OP are the same c as the those of A*z = lambda*B*z. c c Z Double precision N by NEV array if HOWMNY = 'A'. (OUTPUT) c On exit, Z contains the B-orthonormal Ritz vectors of the c eigensystem A*z = lambda*B*z corresponding to the Ritz c value approximations. c c If RVEC = .FALSE. then Z is not referenced. c NOTE: The array Z may be set equal to first NEV columns of the c Lanczos basis array V computed by DSAUPD. c c LDZ Integer. (INPUT) c The leading dimension of the array Z. If Ritz vectors are c desired, then LDZ .ge. max( 1, N ). In any case, LDZ .ge. 1. c c SIGMA Double precision (INPUT) c If IPARAM(7) = 3,4,5 represents the shift. Not referenced if c IPARAM(7) = 1 or 2. c c N Integer. (INPUT) c Dimension of the eigenproblem. c c AB Double precision array of dimension LDA by N. (INPUT) c The matrix A in band storage, in rows KL+1 to c 2*KL+KU+1; rows 1 to KL of the array need not be set. c The j-th column of A is stored in the j-th column of the c array AB as follows: c AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) c c MB Double precision array of dimension LDA by N. (INPUT) c The matrix M in band storage, in rows KL+1 to c 2*KL+KU+1; rows 1 to KL of the array need not be set. c The j-th column of M is stored in the j-th column of the c array AB as follows: c MB(kl+ku+1+i-j,j) = M(i,j) for max(1,j-ku)<=i<=min(m,j+kl) c Not referenced if IPARAM(7) = 1 c c LDA Integer. (INPUT) c Leading dimension of AB, MB, RFAC. c c RFAC Double precision array of LDA by N. (WORKSPACE/OUTPUT) c RFAC is used to store the LU factors of MB when IPARAM(7) = 2 c is invoked. It is used to store the LU factors of c (A-sigma*M) when IPARAM(7) = 3,4,5 is invoked. c It is not referenced when IPARAM(7) = 1. c c KL Integer. (INPUT) c Max(number of subdiagonals of A, number of subdiagonals of M) c c KU Integer. (OUTPUT) c Max(number of superdiagonals of A, number of superdiagonals of M) c c WHICH Character*2. (INPUT) c When IPARAM(7)= 1 or 2, WHICH can be set to any one of c the following. c c 'LM' -> want the NEV eigenvalues of largest magnitude. c 'SM' -> want the NEV eigenvalues of smallest magnitude. c 'LA' -> want the NEV eigenvalues of largest REAL part. c 'SA' -> want the NEV eigenvalues of smallest REAL part. c 'BE' -> Compute NEV eigenvalues, half from each end of the c spectrum. When NEV is odd, compute one more from c the high end than from the low end. c c When IPARAM(7) = 3, 4, or 5, WHICH should be set to 'LM' only. c c BMAT Character*1. (INPUT) c BMAT specifies the type of the matrix B that defines the c semi-inner product for the operator OP. c BMAT = 'I' -> standard eigenvalue problem A*x = lambda*x c BMAT = 'G' -> generalized eigenvalue problem A*x = lambda*M*x c NEV Integer. (INPUT) c Number of eigenvalues of OP to be computed. c c TOL Double precision scalar. (INPUT) c Stopping criterion: the relative accuracy of the Ritz value c is considered acceptable if BOUNDS(I) .LE. TOL*ABS(RITZ(I)). c If TOL .LE. 0. is passed a default is set: c DEFAULT = DLAMCH('EPS') (machine precision as computed c by the LAPACK auxiliary subroutine DLAMCH). c c RESID Double precision array of length N. (INPUT/OUTPUT) c On INPUT: c If INFO .EQ. 0, a random initial residual vector is used. c If INFO .NE. 0, RESID contains the initial residual vector, c possibly from a previous run. c On OUTPUT: c RESID contains the final residual vector. c c NCV Integer. (INPUT) c Number of columns of the matrix V (less than or equal to N). c Represents the dimension of the Lanczos basis constructed c by dsaupd for OP. c c V Double precision array N by NCV. (OUTPUT) c Upon INPUT: the NCV columns of V contain the Lanczos basis c vectors as constructed by dsaupd for OP. c Upon OUTPUT: If RVEC = .TRUE. the first NCONV=IPARAM(5) columns c represent the Ritz vectors that span the desired c invariant subspace. c NOTE: The array Z may be set equal to first NEV columns of the c Lanczos basis vector array V computed by dsaupd. In this case c if RVEC=.TRUE., the first NCONV=IPARAM(5) columns of V contain c the desired Ritz vectors. c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling c program. c c IPARAM Integer array of length 11. (INPUT/OUTPUT) c IPARAM(1) = ISHIFT: c The shifts selected at each iteration are used to restart c the Arnoldi iteration in an implicit fashion. c It is set to 1 in this subroutine. The user do not need c to set this parameter. c ------------------------------------------------------------ c ISHIFT = 1: exact shifts with respect to the reduced c tridiagonal matrix T. This is equivalent to c restarting the iteration with a starting vector c that is a linear combination of Ritz vectors c associated with the "wanted" Ritz values. c ------------------------------------------------------------- c c IPARAM(2) = No longer referenced. c c IPARAM(3) = MXITER c On INPUT: max number of Arnoldi update iterations allowed. c On OUTPUT: actual number of Arnoldi update iterations taken. c c IPARAM(4) = NB: blocksize to be used in the recurrence. c The code currently works only for NB = 1. c c IPARAM(5) = NCONV: number of "converged" eigenvalues. c This represents the number of Ritz values that satisfy c the convergence criterion. c c IPARAM(6) = IUPD c No longer referenced. Implicit restarting is ALWAYS used. c c IPARAM(7) = MODE c On INPUT determines what type of eigenproblem is being solved. c Must be 1,2,3,4,5; See under \Description of dsband for the c five modes available. c c IPARAM(8) = NP c Not referenced. c c IPARAM(9) = NUMOP, IPARAM(10) = NUMOPB, IPARAM(11) = NUMREO, c OUTPUT: NUMOP = total number of OP*x operations, c NUMOPB = total number of B*x operations if BMAT='G', c NUMREO = total number of steps of re-orthogonalization. c c WORKD Double precision work array of length at least 3*n. (WORKSPACE) c c WORKL Double precision work array of length LWORKL. (WORKSPACE) c c LWORKL Integer. (INPUT) c LWORKL must be at least NCV**2 + 8*NCV. c c IWORK Integer array of dimension at least N. (WORKSPACE) c Used when IPARAM(7)=2,3,4,5 to store the pivot information in the c factorization of M or (A-SIGMA*M). c c INFO Integer. (INPUT/OUTPUT) c Error flag on output. c = 0: Normal exit. c = 1: Maximum number of iterations taken. c All possible eigenvalues of OP has been found. IPARAM(5) c returns the number of wanted converged Ritz values. c = 3: No shifts could be applied during a cycle of the c Implicitly restarted Arnoldi iteration. One possibility c is to increase the size of NCV relative to NEV. c See remark 4 in DSAUPD. c c = -1: N must be positive. c = -2: NEV must be positive. c = -3: NCV-NEV >= 2 and less than or equal to N. c = -5: WHICH must be one of 'LM', 'SM', 'LR', 'SR', 'LI', 'SI' c = -6: BMAT must be one of 'I' or 'G'. c = -7: Length of private work WORKL array is not sufficient. c = -8: Error return from trid. eigenvalue calculation; c Informational error from LAPACK routine dsteqr. c = -9: Starting vector is zero. c = -10: IPARAM(7) must be 1,2,3,4,5. c = -11: IPARAM(7) = 1 and BMAT = 'G' are incompatible. c = -12: NEV and WHICH = 'BE' are incompatible. c = -13: HOWMNY must be one of 'A' or 'P' c = -14: DSAUPD did not find any eigenvalues to sufficient c accuracy. c = -9999: Could not build an Arnoldi factorization. c IPARAM(5) returns the size of the current c Arnoldi factorization. c c \EndDoc c c------------------------------------------------------------------------ c c\BeginLib c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly c Restarted Arnoldi Iteration", Ph.D thesis, TR95-13, Rice Univ, c May 1995. c c\Routines called: c dsaupd ARPACK reverse communication interface routine. c dseupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c dgbtrf LAPACK band matrix factorization routine. c dgbtrs LAPACK band linear system solve routine. c dlacpy LAPACK matrix copy routine. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c dcopy Level 1 BLAS that copies one vector to another. c ddot Level 1 BLAS that computes the dot product of two vectors. c dnrm2 Level 1 BLAS that computes the norm of a vector. c dgbmv Level 2 BLAS that computes the band matrix vector product. c c\Remarks c 1. The converged Ritz values are always returned in increasing c (algebraic) order. c c 2. Currently only HOWMNY = 'A' is implemented. It is included at this c stage for the user who wants to incorporate it. c c\Author c Danny Sorensen c Richard Lehoucq c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: sband.F SID: 2.3 DATE OF SID: 10/17/00 RELEASE: 2 c c\EndLib c c--------------------------------------------------------------------- c subroutine dsband( rvec, howmny, select, d, z, ldz, sigma, & n, ab, mb, lda, rfac, kl, ku, which, bmat, nev, & tol, resid, ncv, v, ldv, iparam, workd, workl, & lworkl, iwork, info) c c %------------------% c | Scalar Arguments | c %------------------% c character which*2, bmat, howmny integer n, lda, kl, ku, nev, ncv, ldv, & ldz, lworkl, info Double precision & tol, sigma logical rvec c c %-----------------% c | Array Arguments | c %-----------------% c integer iparam(*), iwork(*) logical select(*) Double precision & d(*), resid(*), v(ldv,*), z(ldz,*), & ab(lda,*), mb(lda,*), rfac(lda,*), & workd(*), workl(*) c c %--------------% c | Local Arrays | c %--------------% c integer ipntr(14) c c %---------------% c | Local Scalars | c %---------------% c integer ido, i, j, type, imid, itop, ibot, ierr c c %------------% c | Parameters | c %------------% c Double precision & one, zero parameter (one = 1.0, zero = 0.0) c c c %-----------------------------% c | LAPACK & BLAS routines used | c %-----------------------------% c Double precision & ddot, dnrm2, dlapy2 external ddot, dcopy, dgbmv, dgbtrf, & dgbtrs, dnrm2, dlapy2, dlacpy c c %-----------------------% c | Executable Statements | c %-----------------------% c c %----------------------------------------------------------------% c | Set type of the problem to be solved. Check consistency | c | between BMAT and IPARAM(7). | c | type = 1 --> Solving standard problem in regular mode. | c | type = 2 --> Solving standard problem in shift-invert mode. | c | type = 3 --> Solving generalized problem in regular mode. | c | type = 4 --> Solving generalized problem in shift-invert mode. | c | type = 5 --> Solving generalized problem in Buckling mode. | c | type = 6 --> Solving generalized problem in Cayley mode. | c %----------------------------------------------------------------% c if ( iparam(7) .eq. 1 ) then type = 1 else if ( iparam(7) .eq. 3 .and. bmat .eq. 'I') then type = 2 else if ( iparam(7) .eq. 2 ) then type = 3 else if ( iparam(7) .eq. 3 .and. bmat .eq. 'G') then type = 4 else if ( iparam(7) .eq. 4 ) then type = 5 else if ( iparam(7) .eq. 5 ) then type = 6 else print*, ' ' print*, 'BMAT is inconsistent with IPARAM(7).' print*, ' ' go to 9000 end if c c %------------------------% c | Initialize the reverse | c | communication flag. | c %------------------------% c ido = 0 c c %----------------% c | Exact shift is | c | used. | c %----------------% c iparam(1) = 1 c c %-----------------------------------% c | Both matrices A and M are stored | c | between rows itop and ibot. Imid | c | is the index of the row that | c | stores the diagonal elements. | c %-----------------------------------% c itop = kl + 1 imid = kl + ku + 1 ibot = 2*kl + ku + 1 c if ( type .eq. 2 .or. type .eq. 6 .and. bmat .eq. 'I' ) then c c %----------------------------------% c | Solving a standard eigenvalue | c | problem in shift-invert or | c | Cayley mode. Factor (A-sigma*I). | c %----------------------------------% c call dlacpy ('A', ibot, n, ab, lda, rfac, lda ) do 10 j = 1, n rfac(imid,j) = ab(imid,j) - sigma 10 continue call dgbtrf(n, n, kl, ku, rfac, lda, iwork, ierr ) if (ierr .ne. 0) then print*, ' ' print*, ' _SBAND: Error with _gbtrf. ' print*, ' ' go to 9000 end if c else if ( type .eq. 3 ) then c c %----------------------------------------------% c | Solving generalized eigenvalue problem in | c | regular mode. Copy M to rfac and Call LAPACK | c | routine dgbtrf to factor M. | c %----------------------------------------------% c call dlacpy ('A', ibot, n, mb, lda, rfac, lda ) call dgbtrf(n, n, kl, ku, rfac, lda, iwork, ierr) if (ierr .ne. 0) then print*, ' ' print*,'_SBAND: Error with _gbtrf.' print*, ' ' go to 9000 end if c else if ( type .eq. 4 .or. type .eq. 5 .or. type .eq. 6 & .and. bmat .eq. 'G' ) then c c %-------------------------------------------% c | Solving generalized eigenvalue problem in | c | shift-invert, Buckling, or Cayley mode. | c %-------------------------------------------% c c %-------------------------------------% c | Construct and factor (A - sigma*M). | c %-------------------------------------% c do 60 j = 1,n do 50 i = itop, ibot rfac(i,j) = ab(i,j) - sigma*mb(i,j) 50 continue 60 continue c call dgbtrf(n, n, kl, ku, rfac, lda, iwork, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, '_SBAND: Error with _gbtrf.' print*, ' ' go to 9000 end if c end if c c %--------------------------------------------% c | M A I N L O O P (reverse communication) | c %--------------------------------------------% c 90 continue c call dsaupd ( ido, bmat, n, which, nev, tol, resid, ncv, & v, ldv, iparam, ipntr, workd, workl, lworkl, & info ) c if (ido .eq. -1) then c if ( type .eq. 1) then c c %----------------------------% c | Perform y <--- OP*x = A*x | c %----------------------------% c call dgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) c else if ( type .eq. 2 ) then c c %----------------------------------% c | Perform | c | y <--- OP*x = inv[A-sigma*I]*x | c | to force the starting vector | c | into the range of OP. | c %----------------------------------% c call dcopy (n, workd(ipntr(1)), 1, workd(ipntr(2)), 1) call dgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, & iwork, workd(ipntr(2)), n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' _SBAND: Error with _bgtrs. ' print*, ' ' go to 9000 end if c else if ( type .eq. 3 ) then c c %-----------------------------------% c | Perform y <--- OP*x = inv[M]*A*x | c | to force the starting vector into | c | the range of OP. | c %-----------------------------------% c call dgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) call dcopy(n, workd(ipntr(2)), 1, workd(ipntr(1)), 1) call dgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, & iwork, workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_SBAND: Error with sbgtrs.' print*, ' ' go to 9000 end if c else if ( type .eq. 4 ) then c c %-----------------------------------------% c | Perform y <-- OP*x | c | = inv[A-SIGMA*M]*M | c | to force the starting vector into the | c | range of OP. | c %-----------------------------------------% c call dgbmv('Notranspose', n, n, kl, ku, one, mb(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) call dgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, & iwork, workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_SBAND: Error with _gbtrs.' print*, ' ' go to 9000 end if c else if ( type .eq. 5) then c c %---------------------------------------% c | Perform y <-- OP*x | c | = inv[A-SIGMA*M]*A | c | to force the starting vector into the | c | range of OP. | c %---------------------------------------% c call dgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) call dgbtrs('Notranspose', n, kl, ku, 1, rfac, lda, & iwork, workd(ipntr(2)), n, ierr) c if ( ierr .ne. 0 ) then print*, ' ' print*, ' _SBAND: Error with _gbtrs. ' print*, ' ' go to 9000 end if c else if ( type .eq. 6 ) then c c %---------------------------------------% c | Perform y <-- OP*x | c | = (inv[A-SIGMA*M])*(A+SIGMA*M)*x | c | to force the starting vector into the | c | range of OP. | c %---------------------------------------% c if ( bmat .eq. 'G' ) then call dgbmv('Notranspose', n, n, kl, ku, one, & ab(itop,1), lda, workd(ipntr(1)), 1, & zero, workd(ipntr(2)), 1) call dgbmv('Notranspose', n, n, kl, ku, sigma, & mb(itop,1), lda, workd(ipntr(1)), 1, & one, workd(ipntr(2)), 1) else call dcopy(n, workd(ipntr(1)), 1, workd(ipntr(2)), 1) call dgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), & lda, workd(ipntr(1)), 1, sigma, & workd(ipntr(2)), 1) end if c call dgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, & iwork, workd(ipntr(2)), n, ierr) c if (ierr .ne. 0) then print*, ' ' print*, '_SBAND: Error with _gbtrs.' print*, ' ' go to 9000 end if c end if c else if (ido .eq. 1) then c if ( type .eq. 1) then c c %----------------------------% c | Perform y <--- OP*x = A*x | c %----------------------------% c call dgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) c else if ( type .eq. 2) then c c %----------------------------------% c | Perform | c | y <--- OP*x = inv[A-sigma*I]*x. | c %----------------------------------% c call dcopy (n, workd(ipntr(1)), 1, workd(ipntr(2)), 1) call dgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, & iwork, workd(ipntr(2)), n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, '_SBAND: Error with _gbtrs.' print*, ' ' go to 9000 end if c else if ( type .eq. 3 ) then c c %-----------------------------------% c | Perform y <--- OP*x = inv[M]*A*x | c %-----------------------------------% c call dgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) call dcopy(n, workd(ipntr(2)), 1, workd(ipntr(1)), 1) call dgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, & iwork, workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_SBAND: error with _bgtrs.' print*, ' ' go to 9000 end if c else if ( type .eq. 4 ) then c c %-------------------------------------% c | Perform y <-- inv(A-sigma*M)*(M*x). | c | (M*x) has been computed and stored | c | in workd(ipntr(3)). | c %-------------------------------------% c call dcopy(n, workd(ipntr(3)), 1, workd(ipntr(2)), 1) call dgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, & iwork, workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_SBAND: Error with _gbtrs.' print*, ' ' go to 9000 end if c else if ( type .eq. 5 ) then c c %-------------------------------% c | Perform y <-- OP*x | c | = inv[A-SIGMA*M]*A*x | c | B*x = A*x has been computed | c | and saved in workd(ipntr(3)). | c %-------------------------------% c call dcopy (n, workd(ipntr(3)), 1, workd(ipntr(2)), 1) call dgbtrs('Notranspose', n, kl, ku, 1, rfac, lda, & iwork, workd(ipntr(2)), n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' _SBAND: Error with _gbtrs. ' print*, ' ' go to 9000 end if c else if ( type .eq. 6) then c c %---------------------------------% c | Perform y <-- OP*x | c | = inv[A-SIGMA*M]*(A+SIGMA*M)*x. | c | (M*x) has been saved in | c | workd(ipntr(3)). | c %---------------------------------% c if ( bmat .eq. 'G' ) then call dgbmv('Notranspose', n, n, kl, ku, one, & ab(itop,1), lda, workd(ipntr(1)), 1, & zero, workd(ipntr(2)), 1) call daxpy( n, sigma, workd(ipntr(3)), 1, & workd(ipntr(2)), 1 ) else call dcopy (n, workd(ipntr(1)), 1, workd(ipntr(2)), 1) call dgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), & lda, workd(ipntr(1)), 1, sigma, & workd(ipntr(2)), 1) end if call dgbtrs('Notranspose', n, kl, ku, 1, rfac, lda, & iwork, workd(ipntr(2)), n, ierr) c end if c else if (ido .eq. 2) then c c %----------------------------------% c | Perform y <-- B*x | c | Note when Buckling mode is used, | c | B = A, otherwise B=M. | c %----------------------------------% c if (type .eq. 5) then c c %---------------------% c | Buckling Mode, B=A. | c %---------------------% c call dgbmv('Notranspose', n, n, kl, ku, one, & ab(itop,1), lda, workd(ipntr(1)), 1, & zero, workd(ipntr(2)), 1) else call dgbmv('Notranspose', n, n, kl, ku, one, & mb(itop,1), lda, workd(ipntr(1)), 1, & zero, workd(ipntr(2)), 1) end if c else c c %-----------------------------------------% c | Either we have convergence, or there is | c | error. | c %-----------------------------------------% c if ( info .lt. 0) then c c %--------------------------% c | Error message, check the | c | documentation in DSAUPD | c %--------------------------% c print *, ' ' print *, ' Error with _saupd info = ',info print *, ' Check the documentation of _saupd ' print *, ' ' go to 9000 c else c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c if (iparam(5) .gt. 0) then c call dseupd ( rvec, 'A', select, d, z, ldz, sigma, & bmat, n, which, nev, tol, resid, ncv, v, ldv, & iparam, ipntr, workd, workl, lworkl, info ) c if ( info .ne. 0) then c c %------------------------------------% c | Check the documentation of dneupd. | c %------------------------------------% c print *, ' ' print *, ' Error with _neupd = ', info print *, ' Check the documentation of _neupd ' print *, ' ' go to 9000 c end if c end if c end if c go to 9000 c end if c c %----------------------------------------% c | L O O P B A C K to call DSAUPD again. | c %----------------------------------------% c go to 90 c 9000 continue c end arpack-0.92.1/EXAMPLES/BAND/snbdr6.f0000644000175000017500000003147410776001577013277 00000000000000 program snbdr6 c c ... Construct matrices A and M in LAPACK-style band form. c The matrix A is a block tridiagonal matrix. Each c diagonal block is a tridiagonal matrix with c 4 on the diagonal, 1-rho*h/2 on the subdiagonal and c 1+rho*h/2 on the superdiagonal. Each subdiagonal block c of A is an identity matrix. The matrix M is the c tridiagonal matrix with 4 on the diagonal and 1 on the c subdiagonal and superdiagonal. c c ... Define COMPLEX shift SIGMA=(SIGMAR,SIGMAI), SIGMAI .ne. zero. c c ... Call snband to find eigenvalues LAMBDA closest to SIGMA c such that c A*x = LAMBDA*M*x. c c ... Use mode 4 of SNAUPD. c c\BeginLib c c\Routines called: c snband ARPACK banded eigenproblem solver. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c slaset LAPACK routine to initialize a matrix to zero. c saxpy Level 1 BLAS that computes y <- alpha*x+y. c snrm2 Level 1 BLAS that computes the norm of a vector. c sgbmv Level 2 BLAS that computes the band matrix vector product. c c\Author c Danny Sorensen c Richard Lehoucq c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: nbdr6.F SID: 2.5 DATE OF SID: 08/26/96 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c--------------------------------------------------------------------- c c %-------------------------------------% c | Define leading dimensions for all | c | arrays. | c | MAXN - Maximum size of the matrix | c | MAXNEV - Maximum number of | c | eigenvalues to be computed | c | MAXNCV - Maximum number of Arnoldi | c | vectors stored | c | MAXBDW - Maximum bandwidth | c %-------------------------------------% c integer maxn, maxnev, maxncv, maxbdw, lda, & lworkl, ldv parameter ( maxn = 1000, maxnev = 25, maxncv=50, & maxbdw=50, lda = maxbdw, ldv = maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), iwork(maxn) logical select(maxncv) Real & a(lda,maxn), m(lda,maxn), rfac(lda,maxn), & workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn), & workev(3*maxncv), v(ldv, maxncv), & resid(maxn), d(maxncv, 3), ax(maxn), mx(maxn) Complex & cfac(lda, maxn), workc(maxn) c c %---------------% c | Local Scalars | c %---------------% c character which*2, bmat integer nev, ncv, ku, kl, info, i, j, ido, & n, nx, lo, idiag, isup, isub, mode, maxitr, & nconv logical rvec, first Real & tol, rho, h, sigmar, sigmai c c %------------% c | Parameters | c %------------% c Real & one, zero, two parameter (one = 1.0E+0 , zero = 0.0E+0 , & two = 2.0E+0 ) c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & slapy2, snrm2 external slapy2, snrm2, sgbmv, saxpy c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-----------------------------------------------------% c | The number NX is the size of each diagonal block of | c | A. The number N(=NX*NX) is the dimension of the | c | matrix. The number N(=NX*NX) is the dimension of | c | the matrix. A generalized eigenvalue problem is | c | solved (BMAT = 'G'). NEV numbers of eigenvalues | c | closest to the COMPLEX shift (SIGMAR,SIGMAI) | c | (WHICH='LM') and their corresponding eigenvectors | c | are computed. The user can modify NX, NEV, NCV, | c | WHICH to solve problems of different sizes, and | c | to get different parts the spectrum. However, the | c | following rules must be satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 2 <= NCV <= MAXNCV | c %-----------------------------------------------------% c nx = 10 n = nx*nx nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _NBDR6: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NBDR6: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NBDR6: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' sigmar = 4.0E-1 sigmai = 6.0E-1 c c %-----------------------------------------------------% c | The work array WORKL is used in SNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in SNAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = 3*ncv**2+6*ncv tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 4 of SNAUPD is used | c | (IPARAm(7) = 4). All these options can be changed | c | by the user. For details, see the documentation | c | in snband. | c %---------------------------------------------------% c maxitr = 300 mode = 4 c iparam(3) = maxitr iparam(7) = mode c c %--------------------------------------------% c | Construct matrices A and M in LAPACK-style | c | banded form. | c %--------------------------------------------% c c %---------------------------------------------% c | Zero out the workspace for banded matrices. | c %---------------------------------------------% c call slaset('A', lda, n, zero, zero, a, lda) call slaset('A', lda, n, zero, zero, m, lda) call slaset('A', lda, n, zero, zero, rfac, lda) c c %-------------------------------------% c | KU, KL are number of superdiagonals | c | and subdiagonals within the band of | c | matrices A and M. | c %-------------------------------------% c kl = nx ku = nx c c %---------------% c | Main diagonal | c %---------------% c idiag = kl+ku+1 do 30 j = 1, n a(idiag,j) = 4.0E+0 m(idiag,j) = 4.0E+0 30 continue c c %-------------------------------------% c | First subdiagonal and superdiagonal | c %-------------------------------------% c isup = kl+ku isub = kl+ku+2 h = one / real (nx+1) rho = 1.0E+2 do 50 i = 1, nx lo = (i-1)*nx do 40 j = lo+1, lo+nx-1 a(isub,j+1) = -one+h*rho/two a(isup,j) = -one-h*rho/two 40 continue 50 continue c do 60 j = 1, n-1 m(isub,j+1) = one m(isup,j) = one 60 continue c c %------------------------------------% c | KL-th subdiagonal and KU-th super- | c | diagonal. | c %------------------------------------% c isup = kl+1 isub = 2*kl+ku+1 do 80 i = 1, nx-1 lo = (i-1)*nx do 70 j = lo+1, lo+nx a(isup,nx+j) = -one a(isub,j) = -one 70 continue 80 continue c c %------------------------------------------------% c | Call ARPACK banded solver to find eigenvalues | c | and eigenvectors. The real parts of the | c | eigenvalues are returned in the first column | c | of D, the imaginary parts are returned in the | c | second column of D. Eigenvectors are returned | c | in the first NCONV (=IPARAM(5)) columns of V. | c %------------------------------------------------% c rvec = .true. call snband(rvec, 'A', select, d, d(1,2), v, ldv, sigmar, & sigmai, workev, n, a, m, lda, rfac, cfac, ku, kl, & which, bmat, nev, tol, resid, ncv, v, ldv, iparam, & workd, workl, lworkl, workc, iwork, info) c if ( info .eq. 0) then c c %-----------------------------------% c | Print out convergence information | c %-----------------------------------% c nconv = iparam(5) c print *, ' ' print *, ' _NBDR6 ' print *, ' ====== ' print *, ' ' print *, ' The size of the matrix is ', n print *, ' Number of eigenvalue requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' The number of converged Ritz values is ', & nconv print *, ' What portion of the spectrum ', which print *, ' The number of Implicit Arnoldi ', & ' update taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence tolerance is ', tol print *, ' ' c c %----------------------------% c | Compute the residual norm. | c | || A*x - lambda*x || | c %----------------------------% c first = .true. do 90 j = 1, nconv c if ( d(j,2) .eq. zero ) then c c %--------------------% c | Ritz value is real | c %--------------------% c call sgbmv('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call sgbmv('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j), 1, zero, & mx, 1) call saxpy(n, -d(j,1), mx, 1, ax, 1) d(j,3) = snrm2(n, ax, 1) d(j,3) = d(j,3) / abs(d(j,1)) c else if ( first ) then c c %------------------------% c | Ritz value is complex | c | Residual of one Ritz | c | value of the conjugate | c | pair is computed. | c %------------------------% c call sgbmv('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call sgbmv('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j), 1, zero, & mx, 1) call saxpy(n, -d(j,1), mx, 1, ax, 1) call sgbmv('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j+1), 1, zero, & mx, 1) call saxpy(n, d(j,2), mx, 1, ax, 1) d(j,3) = snrm2(n, ax, 1) call sgbmv('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j+1), 1, zero, & ax, 1) call sgbmv('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j+1), 1, zero, & mx, 1) call saxpy(n, -d(j,1), mx, 1, ax, 1) call sgbmv('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j), 1, zero, & mx, 1) call saxpy(n, -d(j,2), mx, 1, ax, 1) d(j,3) = slapy2( d(j,3), snrm2(n, ax, 1) ) d(j,3) = d(j,3) / slapy2(d(j,1),d(j,2)) d(j+1,3) = d(j,3) first = .false. else first = .true. end if c 90 continue call smout(6, nconv, 3, d, maxncv, -6, & 'Ritz values (Real,Imag) and relative residuals') else c c %-------------------------------------% c | Either convergence failed, or there | c | is error. Check the documentation | c | for snband. | c %-------------------------------------% c print *, ' ' print *, ' Error with _nband, info= ', info print *, ' Check the documentation of _nband ' print *, ' ' c end if c 9000 end arpack-0.92.1/EXAMPLES/BAND/snbdr3.f0000644000175000017500000002760210776001577013272 00000000000000 program snbdr3 c c ... Construct matrices A and M in LAPACK-style band form. c The matrix A and M are derived from the finite element c discretization of the 1-dimensional convection-diffusion operator c (d^2u/dx^2) + rho*(du/dx) c on the interval [0,1] with zero boundary condition, c ... Call SNBAND to find eigenvalues LAMBDA such that c A*x = LAMBDA*M*x. c c ... Eigenvalues with largest real parts are sought. c c ... Use mode 2 of SNAUPD. c c\BeginLib c c\Routines called: c snband ARPACK banded eigenproblem solver. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c slaset LAPACK routine to initialize a matrix to zero. c saxpy Level 1 BLAS that computes y <- alpha*x+y. c snrm2 Level 1 BLAS that computes the norm of a vector. c sgbmv Level 2 BLAS that computes the band matrix vector product. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: nbdr3.F SID: 2.5 DATE OF SID: 08/26/96 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c------------------------------------------------------------------------- c c %-------------------------------------% c | Define leading dimensions for all | c | arrays. | c | MAXN - Maximum size of the matrix | c | MAXNEV - Maximum number of | c | eigenvalues to be computed | c | MAXNCV - Maximum number of Arnoldi | c | vectors stored | c | MAXBDW - Maximum bandwidth | c %-------------------------------------% c integer maxn, maxnev, maxncv, maxbdw, lda, & lworkl, ldv parameter ( maxn = 1000, maxnev = 25, maxncv=50, & maxbdw=50, lda = maxbdw, ldv = maxn) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), iwork(maxn) logical select(maxncv) Real & a(lda,maxn), m(lda,maxn), rfac(lda,maxn), & workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn), & workev(3*maxncv), v(ldv, maxncv), & resid(maxn), d(maxncv, 3), ax(maxn), mx(maxn) Complex & cfac(lda, maxn), workc(maxn) c c %---------------% c | Local Scalars | c %---------------% c character which*2, bmat integer nev, ncv, ku, kl, info, j, ido, & n, idiag, isup, isub, mode, maxitr, & nconv logical rvec, first Real & tol, rho, h, sigmar, sigmai c c %------------% c | Parameters | c %------------% c Real & one, zero, two parameter (one = 1.0E+0 , zero = 0.0E+0 , & two = 2.0E+0 ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & slapy2, snrm2 external slapy2, snrm2, sgbmv, saxpy c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------------------------% c | The number N is the dimension of the matrix. A | c | generalized eigenvalue problem is solved | c | (BMAT = 'G'). NEV is the number of eigenvalues | c | to be approximated. The user can modify N, NEV, | c | NCV and WHICH to solve problems of different | c | sizes, and to get different parts the spectrum. | c | However, the following conditions must be | c | satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 2 <= NCV <= MAXNCV | c %-------------------------------------------------% c n = 100 nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _NBDR3: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NBDR3: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NBDR3: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' c c %----------------------------------------------------% c | The work array WORKL is used in SNAUPD as | c | workspace. Its dimension LWORKL has to be set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine machine | c | precision is used. The number IDO is used for | c | reverse communication and has to be set to 0 at | c | the beginning. Setting INFO=0 indicates that we | c | using a randomly generated vector to start the | c | the ARNOLDI process. | c %----------------------------------------------------% c lworkl = 3*ncv**2+6*ncv info = 0 tol = zero ido = 0 c c %---------------------------------------------------% c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 2 of SNAUPD is used | c | (IPARAM(7) = 2). All these options can be changed | c | by the user. For details, see the documentation | c | in SNBAND. | c %---------------------------------------------------% c mode = 2 maxitr = 300 c iparam(3) = maxitr iparam(7) = mode c c %--------------------------------------------% c | Construct matrices A and M in LAPACK-style | c | banded form. | c %--------------------------------------------% c c %---------------------------------------------% c | Zero out the workspace for banded matrices. | c %---------------------------------------------% c call slaset('A', lda, n, zero, zero, a, lda) call slaset('A', lda, n, zero, zero, m, lda) call slaset('A', lda, n, zero, zero, rfac, lda) c c %-------------------------------------% c | KU, KL are number of superdiagonals | c | and subdiagonals within the band of | c | matrices A and M. | c %-------------------------------------% c kl = 1 ku = 1 c c %---------------% c | Main diagonal | c %---------------% c h = one / real (n+1) c idiag = kl+ku+1 do 30 j = 1, n a(idiag,j) = 2.0E+0 / h m(idiag,j) = 4.0E+0 * h 30 continue c c %-------------------------------------% c | First subdiagonal and superdiagonal | c %-------------------------------------% c isup = kl+ku isub = kl+ku+2 rho = 1.0E+1 do 50 j = 1, n a(isup,j+1) = -one/h + rho/two a(isub,j) = -one/h - rho/two m(isup,j+1) = one*h m(isub,j) = one*h 50 continue c c %------------------------------------------------% c | Call ARPACK banded solver to find eigenvalues | c | and eigenvectors. The real parts of the | c | eigenvalues are returned in the first column | c | of D, the imaginary parts are returned in the | c | second column of D. Eigenvectors are returned | c | in the first NCONV (=IPARAM(5)) columns of V. | c %------------------------------------------------% c rvec = .true. call snband( rvec, 'A', select, d, d(1,2), v, ldv, sigmar, & sigmai, workev, n, A, M, lda, rfac, cfac, kl, ku, & which, bmat, nev, tol, resid, ncv, v, ldv, iparam, & workd, workl, lworkl, workc, iwork, info) c if ( info .eq. 0) then c c %-----------------------------------% c | Print out convergence information | c %-----------------------------------% c nconv = iparam(5) c print *, ' ' print *, ' _NBDR3 ' print *, ' ====== ' print *, ' ' print *, ' The size of the matrix is ', n print *, ' Number of eigenvalue requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' The number of converged Ritz values is ', & nconv print *, ' What portion of the spectrum ', which print *, ' The number of Implicit Arnoldi ', & ' update taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence tolerance is ', tol print *, ' ' c c %----------------------------% c | Compute the residual norm. | c | || A*x - lambda*x || | c %----------------------------% c first = .true. do 90 j = 1, nconv c if ( d(j,2) .eq. zero ) then c c %--------------------% c | Ritz value is real | c %--------------------% c call sgbmv('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call sgbmv('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j), 1, zero, & mx, 1) call saxpy(n, -d(j,1), mx, 1, ax, 1) d(j,3) = snrm2(n, ax, 1) d(j,3) = d(j,3) / abs(d(j,1)) c else if ( first ) then c c %------------------------% c | Ritz value is complex | c | Residual of one Ritz | c | value of the conjugate | c | pair is computed. | c %------------------------% c call sgbmv('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call sgbmv('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j), 1, zero, & mx, 1) call saxpy(n, -d(j,1), mx, 1, ax, 1) call sgbmv('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j+1), 1, zero, & mx, 1) call saxpy(n, d(j,2), mx, 1, ax, 1) d(j,3) = snrm2(n, ax, 1) call sgbmv('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j+1), 1, zero, & ax, 1) call sgbmv('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j+1), 1, zero, & mx, 1) call saxpy(n, -d(j,1), mx, 1, ax, 1) call sgbmv('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j), 1, zero, & mx, 1) call saxpy(n, -d(j,2), mx, 1, ax, 1) d(j,3) = slapy2( d(j,3), snrm2(n, ax, 1) ) d(j,3) = d(j,3) / slapy2(d(j,1),d(j,2)) d(j+1,3) = d(j,3) first = .false. else first = .true. end if c 90 continue call smout(6, nconv, 3, d, maxncv, -6, & 'Ritz values (Real,Imag) and relative residuals') else c c %-------------------------------------% c | Either convergence failed, or there | c | is error. Check the documentation | c | for SNBAND. | c %-------------------------------------% c print *, ' ' print *, ' Error with _nband, info= ', info print *, ' Check the documentation of _nband ' print *, ' ' c end if c 9000 end arpack-0.92.1/EXAMPLES/BAND/snband.f0000644000175000017500000014511010776001577013337 00000000000000c \BeginDoc c c \Name: snband c c \Description: c c This subroutine returns the converged approximations to eigenvalues c of A*z = lambda*B*z and (optionally): c c (1) The corresponding approximate eigenvectors; c c (2) An orthonormal basis for the associated approximate c invariant subspace; c c (3) Both. c c Matrices A and B are stored in LAPACK-style banded form. c c There is negligible additional cost to obtain eigenvectors. An orthonormal c basis is always computed. There is an additional storage cost of n*nev c if both are requested (in this case a separate array Z must be supplied). c c The approximate eigenvalues and vectors are commonly called Ritz c values and Ritz vectors respectively. They are referred to as such c in the comments that follow. The computed orthonormal basis for the c invariant subspace corresponding to these Ritz values is referred to as a c Schur basis. c c snband can be called with one of the following modes: c c Mode 1: A*z = lambda*z. c ===> OP = A and B = I. c c Mode 2: A*z = lambda*M*z, M symmetric positive definite c ===> OP = inv[M]*A and B = M. c c Mode 3: A*z = lambda*M*z, M symmetric semi-definite c ===> OP = Real_Part{ inv[A - sigma*M]*M } and B = M. c ===> shift-and-invert mode (in real arithmetic) c If OP*z = amu*z, then c amu = 1/2 * [ 1/(lambda-sigma) + 1/(lambda-conjg(sigma)) ]. c Note: If sigma is real, i.e. imaginary part of sigma is zero; c Real_Part{ inv[A - sigma*M]*M } == inv[A - sigma*M]*M c amu == 1/(lambda-sigma). c c Mode 4: A*z = lambda*M*z, M symmetric semi-definite c ===> OP = Imaginary_Part{ inv[A - sigma*M]*M } and B = M. c ===> shift-and-invert mode (in real arithmetic) c If OP*z = amu*z, then c amu = 1/2i * [ 1/(lambda-sigma) - 1/(lambda-conjg(sigma)) ]. c c c The choice of mode must be specified in IPARAM(7) defined below. c c \Usage c call snband c ( RVEC, HOWMNY, SELECT, DR, DI, Z, LDZ, SIGMAR, SIGMAI, c WORKEV, V, N, AB, MB, LDA, RFAC, CFAC, KL, KU, WHICH, c BMAT, NEV, TOL, RESID, NCV, V, LDV, IPARAM, WORKD, c WORKL, LWORKL, WORKC, IWORK, INFO ) c c \Arguments c c RVEC LOGICAL (INPUT) c Specifies whether a basis for the invariant subspace corresponding c to the converged Ritz value approximations for the eigenproblem c A*z = lambda*B*z is computed. c c RVEC = .FALSE. Compute Ritz values only. c c RVEC = .TRUE. Compute the Ritz vectors or Schur vectors. c See Remarks below. c c HOWMNY Character*1 (INPUT) c Specifies the form of the basis for the invariant subspace c corresponding to the converged Ritz values that is to be computed. c c = 'A': Compute NEV Ritz vectors; c = 'P': Compute NEV Schur vectors; c = 'S': compute some of the Ritz vectors, specified c by the logical array SELECT. c c SELECT Logical array of dimension NCV. (INPUT) c If HOWMNY = 'S', SELECT specifies the Ritz vectors to be c computed. To select the Ritz vector corresponding to a c Ritz value (DR(j), DI(j)), SELECT(j) must be set to .TRUE.. c If HOWMNY = 'A' or 'P', SELECT is used as internal workspace. c c DR Real array of dimension NEV+1. (OUTPUT) c On exit, DR contains the real part of the Ritz value approximations c to the eigenvalues of A*z = lambda*B*z. c c DI Real array of dimension NEV+1. (OUTPUT) c On exit, DI contains the imaginary part of the Ritz value c approximations to the eigenvalues of A*z = lambda*B*z associated c with DR. c c NOTE: When Ritz values are complex, they will come in complex c conjugate pairs. If eigenvectors are requested, the c corresponding Ritz vectors will also come in conjugate c pairs and the real and imaginary parts of these are c represented in two consecutive columns of the array Z c (see below). c c Z Real N by NEV+1 array if RVEC = .TRUE. and HOWMNY = 'A'. (OUTPUT) c On exit, c if RVEC = .TRUE. and HOWMNY = 'A', then the columns of c Z represent approximate eigenvectors (Ritz vectors) corresponding c to the NCONV=IPARAM(5) Ritz values for eigensystem c A*z = lambda*B*z computed by SNAUPD. c c The complex Ritz vector associated with the Ritz value c with positive imaginary part is stored in two consecutive c columns. The first column holds the real part of the Ritz c vector and the second column holds the imaginary part. The c Ritz vector associated with the Ritz value with negative c imaginary part is simply the complex conjugate of the Ritz vector c associated with the positive imaginary part. c c If RVEC = .FALSE. or HOWMNY = 'P', then Z is not referenced. c c NOTE: If if RVEC = .TRUE. and a Schur basis is not required, c the array Z may be set equal to first NEV+1 columns of the Arnoldi c basis array V computed by SNAUPD. In this case the Arnoldi basis c will be destroyed and overwritten with the eigenvector basis. c c LDZ Integer. (INPUT) c The leading dimension of the array Z. If Ritz vectors are c desired, then LDZ >= max( 1, N ). In any case, LDZ >= 1. c c SIGMAR Real (INPUT) c If IPARAM(7) = 3 or 4, represents the real part of the shift. c Not referenced if IPARAM(7) = 1 or 2. c c SIGMAI Real (INPUT) c If IPARAM(7) = 3 or 4, represents the imaginary part of the c shift. c Not referenced if IPARAM(7) = 1 or 2. c c WORKEV Real work array of dimension 3*NCV. (WORKSPACE) c c N Integer. (INPUT) c Dimension of the eigenproblem. c c AB Real array of dimension LDA by N. (INPUT) c The matrix A in band storage, in rows KL+1 to c 2*KL+KU+1; rows 1 to KL of the array need not be set. c The j-th column of A is stored in the j-th column of the c array AB as follows: c AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) c c MB Real array of dimension LDA by N. (INPUT) c The matrix M in band storage, in rows KL+1 to c 2*KL+KU+1; rows 1 to KL of the array need not be set. c The j-th column of M is stored in the j-th column of the c array AB as follows: c MB(kl+ku+1+i-j,j) = M(i,j) for max(1,j-ku)<=i<=min(m,j+kl) c Not referenced if IPARAM(7) = 1 c c LDA Integer. (INPUT) c Leading dimension of AB, MB, RFAC and CFAC. c c RFAC Real array of LDA by N. (WORKSPACE/OUTPUT) c RFAC is used to store the LU factors of MB when IPARAM(7) = 2 c is invoked. It is used to store the LU factors of c (A-sigma*M) when IPARAM(7) = 3 is invoked with a real shift. c It is not referenced when IPARAM(7) = 1 or 4. c c CFAC Complex array of LDA by N. (WORKSPACE/OUTPUT) c CFAC is used to store (A-SIGMA*M) and its LU factors c when IPARAM(7) = 3 or 4 are used with a complex shift SIGMA. c On exit, it contains the LU factors of (A-SIGMA*M). c It is not referenced when IPARAM(7) = 1 or 2. c c KL Integer. (INPUT) c Max(number of subdiagonals of A, number of subdiagonals of M) c c KU Integer. (OUTPUT) c Max(number of superdiagonals of A, number of superdiagonals of M) c c WHICH Character*2. (INPUT) c When IPARAM(7)= 1 or 2, WHICH can be set to any one of c the following. c c 'LM' -> want the NEV eigenvalues of largest magnitude. c 'SM' -> want the NEV eigenvalues of smallest magnitude. c 'LR' -> want the NEV eigenvalues of largest real part. c 'SR' -> want the NEV eigenvalues of smallest real part. c 'LI' -> want the NEV eigenvalues of largest imaginary part. c 'SI' -> want the NEV eigenvalues of smallest imaginary part. c c When IPARAM(7) = 3 or 4, WHICH should be set to 'LM' only. c c BMAT Character*1. (INPUT) c BMAT specifies the type of the matrix B that defines the c semi-inner product for the operator OP. c BMAT = 'I' -> standard eigenvalue problem A*z = lambda*z c BMAT = 'G' -> generalized eigenvalue problem A*z = lambda*M*z c NEV Integer. (INPUT) c Number of eigenvalues to be computed. c c TOL Real scalar. (INPUT) c Stopping criteria: the relative accuracy of the Ritz value c is considered acceptable if BOUNDS(I) .LE. TOL*ABS(RITZ(I)). c If TOL .LE. 0. is passed a default is set: c DEFAULT = SLAMCH('EPS') (machine precision as computed c by the LAPACK auxiliary subroutine SLAMCH). c c RESID Real array of length N. (INPUT/OUTPUT) c On INPUT: c If INFO .EQ. 0, a random initial residual vector is used. c If INFO .NE. 0, RESID contains the initial residual vector, c possibly from a previous run. c On OUTPUT: c RESID contains the final residual vector. c c NCV Integer. (INPUT) c Number of columns of the matrix V (less than or equal to N). c Represents the dimension of the Arnoldi basis constructed c by snaupd for OP. c c V Real array N by NCV+1. (OUTPUT) c Upon OUTPUT: If RVEC = .TRUE. the first NCONV=IPARAM(5) columns c represent approximate Schur vectors that span the c desired invariant subspace. c NOTE: The array Z may be set equal to first NEV+1 columns of the c Arnoldi basis vector array V computed by SNAUPD. In this case c if RVEC = .TRUE. and HOWMNY='A', then the first NCONV=IPARAM(5) c are the desired Ritz vectors. c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling c program. c c IPARAM Integer array of length 11. (INPUT/OUTPUT) c IPARAM(1) = ISHIFT: c The shifts selected at each iteration are used to restart c the Arnoldi iteration in an implicit fashion. c It is set to 1 in this subroutine. The user do not need c to set this parameter. c ---------------------------------------------------------- c ISHIFT = 1: exact shift with respect to the current c Hessenberg matrix H. This is equivalent to c restarting the iteration from the beginning c after updating the starting vector with a linear c combination of Ritz vectors associated with the c "wanted" eigenvalues. c ------------------------------------------------------------- c c IPARAM(2) = No longer referenced. c c IPARAM(3) = MXITER c On INPUT: max number of Arnoldi update iterations allowed. c On OUTPUT: actual number of Arnoldi update iterations taken. c c IPARAM(4) = NB: blocksize to be used in the recurrence. c The code currently works only for NB = 1. c c IPARAM(5) = NCONV: number of "converged" eigenvalues. c c IPARAM(6) = IUPD c Not referenced. Implicit restarting is ALWAYS used. c c IPARAM(7) = IPARAM(7): c On INPUT determines what type of eigenproblem is being solved. c Must be 1,2,3,4; See under \Description of snband for the c four modes available. c c IPARAM(9) = NUMOP, IPARAM(10) = NUMOPB, IPARAM(11) = NUMREO, c OUTPUT: NUMOP = total number of OP*z operations, c NUMOPB = total number of B*z operations if BMAT='G', c NUMREO = total number of steps of re-orthogonalization. c c WORKD Real work array of length at least 3*n. (WORKSPACE) c c WORKL Real work array of length LWORKL. (WORKSPACE) c c LWORKL Integer. (INPUT) c LWORKL must be at least 3*NCV**2 + 6*NCV. c c WORKC Complex array of length N. (WORKSPACE) c Workspace used when IPARAM(7) = 3 or 4 for storing a temporary c complex vector. c c IWORK Integer array of dimension at least N. (WORKSPACE) c Used when IPARAM(7)=2,3,4 to store the pivot information in the c factorization of M or (A-SIGMA*M). c c INFO Integer. (INPUT/OUTPUT) c Error flag on output. c = 0: Normal exit. c = 1: The Schur form computed by LAPACK routine slahqr c could not be reordered by LAPACK routine strsen. c Re-enter subroutine SNEUPD with IPARAM(5)=NCV and c increase the size of the arrays DR and DI to have c dimension at least NCV and allocate at least NCV c columns for Z. NOTE: Not necessary if Z and V share c the same space. Please notify the authors. c c = -1: N must be positive. c = -2: NEV must be positive. c = -3: NCV-NEV >= 2 and less than or equal to N. c = -5: WHICH must be one of 'LM', 'SM', 'LR', 'SR', 'LI', 'SI' c = -6: BMAT must be one of 'I' or 'G'. c = -7: Length of private work WORKL array is not sufficient. c = -8: Error return from calculation of a real Schur form. c Informational error from LAPACK routine slahqr. c = -9: Error return from calculation of eigenvectors. c Informational error from LAPACK routine strevc. c = -10: IPARAM(7) must be 1,2,3,4. c = -11: IPARAM(7) = 1 and BMAT = 'G' are incompatible. c = -12: HOWMNY = 'S' not yet implemented c = -13: HOWMNY must be one of 'A' or 'P' c = -14: SNAUPD did not find any eigenvalues to sufficient c accuracy. c = -15: Overflow occurs when we try to transform the Ritz c values returned from SNAUPD to those of the original c problem using Rayleigh Quotient. c = -9999: Could not build an Arnoldi factorization. c IPARAM(5) returns the size of the current c Arnoldi factorization. c c \EndDoc c c------------------------------------------------------------------------ c c\BeginLib c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly c Restarted Arnoldi Iteration", Ph.D thesis, TR95-13, Rice Univ, c May 1995. c c\Routines called: c snaupd ARPACK reverse communication interface routine. c sneupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c sgbtrf LAPACK band matrix factorization routine. c sgbtrs LAPACK band linear system solve routine. c cgbtrf LAPACK complex band matrix factorization routine. c cgbtrs LAPACK complex linear system solve routine. c slacpy LAPACK matrix copy routine. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c slamch LAPACK routine to compute the underflow threshold. c scopy Level 1 BLAS that copies one vector to another. c sdot Level 1 BLAS that computes the dot product of two vectors. c snrm2 Level 1 BLAS that computes the norm of a vector. c sgbmv Level 2 BLAS that computes the band matrix vector product. c c\Remarks c c 1. Currently only HOWMNY = 'A' and 'P' are implemented. c c Let X' denote the transpose of X. c c 2. Schur vectors are an orthogonal representation for the basis of c Ritz vectors. Thus, their numerical properties are often superior. c If RVEC = .TRUE. then the relationship c A * V(:,1:IPARAM(5)) = V(:,1:IPARAM(5)) * T, and c V(:,1:IPARAM(5))' * V(:,1:IPARAM(5)) = I are approximately satisfied. c Here T is the leading submatrix of order IPARAM(5) of the real c upper quasi-triangular matrix stored workl(ipntr(12)). That is, c T is block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; c each 2-by-2 diagonal block has its diagonal elements equal and its c off-diagonal elements of opposite sign. Corresponding to each 2-by-2 c diagonal block is a complex conjugate pair of Ritz values. The real c Ritz values are stored on the diagonal of T. c c\Author c Danny Sorensen c Richard Lehoucq c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: nband.F SID: 2.3 DATE OF SID: 10/17/00 RELEASE: 2 c c\EndLib c c--------------------------------------------------------------------- c subroutine snband( rvec, howmny, select, dr, di, z, ldz, sigmar, & sigmai, workev, n, ab, mb, lda, rfac, cfac, kl, ku, & which, bmat, nev, tol, resid, ncv, v, ldv, & iparam, workd, workl, lworkl, workc, iwork, info) c c %------------------% c | Scalar Arguments | c %------------------% c character which*2, bmat, howmny integer n, lda, kl, ku, nev, ncv, ldv, & ldz, lworkl, info Real & tol, sigmar, sigmai c c %-----------------% c | Array Arguments | c %-----------------% c integer iparam(*), iwork(*) logical select(*) Real & dr(*), di(*), resid(*), v(ldv,*), z(ldz,*), & ab(lda,*), mb(lda,*), rfac(lda,*), & workd(*), workl(*), workev(*) Complex & cfac(lda,*), workc(*) c c %--------------% c | Local Arrays | c %--------------% c integer ipntr(14) c c %---------------% c | Local Scalars | c %---------------% c integer ido, i, j, type, imid, itop, ibot, ierr Real & numr, denr, deni, dmdul, safmin logical rvec, first c c %------------% c | Parameters | c %------------% c Real & one, zero parameter (one = 1.0E+0, zero = 0.0E+0) c c c %-----------------------------% c | LAPACK & BLAS routines used | c %-----------------------------% c Real & sdot, snrm2, slapy2, slamch external sdot, scopy, sgbmv, cgbtrf, cgbtrs, sgbtrf, & sgbtrs, snrm2, slapy2, slacpy, slamch c c %---------------------% c | Intrinsic Functions | c %---------------------% c Intrinsic real, aimag, cmplx c c %-----------------------% c | Executable Statements | c %-----------------------% c c %--------------------------------% c | safmin = safe minimum is such | c | that 1/sfmin does not overflow | c %--------------------------------% c safmin = slamch('safmin') c c %----------------------------------------------------------------% c | Set type of the problem to be solved. Check consistency | c | between BMAT and IPARAM(7). | c | type = 1 --> Solving standard problem in regular mode. | c | type = 2 --> Solving standard problem in shift-invert mode. | c | type = 3 --> Solving generalized problem in regular mode. | c | type = 4 --> Solving generalized problem in shift-invert mode. | c | type = 5 --> Solving standard problem in shift-invert mode | c | using iparam(7) = 4 in SNAUPD. | c | type = 6 --> Solving generalized problem in shift-invert mode. | c | using iparam(7) = 4 in SNAUPD. | c %----------------------------------------------------------------% c if ( iparam(7) .eq. 1 ) then type = 1 else if ( iparam(7) .eq. 3 .and. bmat .eq. 'I') then type = 2 else if ( iparam(7) .eq. 2 ) then type = 3 else if ( iparam(7) .eq. 3 .and. bmat .eq. 'G') then type = 4 else if ( iparam(7) .eq. 4 .and. bmat .eq. 'I') then type = 5 else if ( iparam(7) .eq. 4 .and. bmat .eq. 'G') then type = 6 else print*, ' ' print*, 'BMAT is inconsistent with IPARAM(7).' print*, ' ' go to 9000 end if c c %----------------------------------% c | When type = 5,6 are used, sigmai | c | must be nonzero. | c %----------------------------------% c if ( type .eq. 5 .or. type .eq. 6 ) then if ( sigmai .eq. zero ) then print*, ' ' print*, '_NBAND: sigmai must be nonzero when type 5 or 6 & is used. ' print*, ' ' go to 9000 end if end if c c %------------------------% c | Initialize the reverse | c | communication flag. | c %------------------------% c ido = 0 c c %----------------% c | Exact shift is | c | used. | c %----------------% c iparam(1) = 1 c c %-----------------------------------% c | Both matrices A and M are stored | c | between rows itop and ibot. Imid | c | is the index of the row that | c | stores the diagonal elements. | c %-----------------------------------% c itop = kl + 1 imid = kl + ku + 1 ibot = 2*kl + ku + 1 c if ( type .eq. 2 .or. type .eq. 5 ) then c c %-------------------------------% c | Solving a standard eigenvalue | c | problem in shift-invert mode. | c | Factor (A-sigma*I). | c %-------------------------------% c if (sigmai .eq. zero) then c c %-----------------------------------% c | Construct (A-sigmar*I) and factor | c | in real arithmetic. | c %-----------------------------------% c call slacpy ('A', ibot, n, ab, lda, rfac, lda ) do 10 j = 1, n rfac(imid,j) = ab(imid,j) - sigmar 10 continue call sgbtrf(n, n, kl, ku, rfac, lda, iwork, ierr ) if (ierr .ne. 0) then print*, ' ' print*, ' _NBAND: Error with _gbtrf. ' print*, ' ' go to 9000 end if c else c c %-----------------------------------% c | Construct (A-sigmar*I) and factor | c | in COMPLEX arithmetic. | c %-----------------------------------% c do 30 j = 1, n do 20 i = itop, ibot cfac(i,j) = cmplx(ab(i,j)) 20 continue 30 continue c do 40 j = 1, n cfac(imid,j) = cfac(imid,j) $ - cmplx(sigmar, sigmai) 40 continue c call cgbtrf(n, n, kl, ku, cfac, lda, iwork, ierr ) if ( ierr .ne. 0) then print*, ' ' print*, ' _NBAND: Error with _gbtrf. ' print*, ' ' go to 9000 end if c end if else if ( type .eq. 3 ) then c c %-----------------------------------------------% c | Solving generalized eigenvalue problem in | c | regular mode. Copy M to rfac, and call LAPACK | c | routine sgbtrf to factor M. | c %-----------------------------------------------% c call slacpy ('A', ibot, n, mb, lda, rfac, lda ) call sgbtrf(n, n, kl, ku, rfac, lda, iwork, ierr) if (ierr .ne. 0) then print*, ' ' print*,'_NBAND: Error with _gbtrf.' print*, ' ' go to 9000 end if c else if ( type .eq. 4 .or. type .eq. 6 ) then c c %-------------------------------------------% c | Solving generalized eigenvalue problem in | c | shift-invert mode. | c %-------------------------------------------% c if ( sigmai .eq. zero ) then c c %--------------------------------------------% c | Construct (A - sigma*M) and factor in real | c | arithmetic. | c %--------------------------------------------% c do 60 j = 1,n do 50 i = itop, ibot rfac(i,j) = ab(i,j) - sigmar*mb(i,j) 50 continue 60 continue c call sgbtrf(n, n, kl, ku, rfac, lda, iwork, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, '_NBAND: Error with _gbtrf.' print*, ' ' go to 9000 end if c else c c %-----------------------------------------------% c | Construct (A - sigma*M) and factor in complex | c | arithmetic. | c %-----------------------------------------------% c do 80 j = 1,n do 70 i = itop, ibot cfac(i,j) = cmplx( ab(i,j)-sigmar*mb(i,j), & -sigmai*mb(i,j) ) 70 continue 80 continue c call cgbtrf(n, n, kl, ku, cfac, lda, iwork, ierr) if ( ierr .NE. 0 ) then print*, ' ' print*, '_NBAND: Error with _gbtrf.' print*, ' ' go to 9000 end if c end if c end if c c %--------------------------------------------% c | M A I N L O O P (reverse communication) | c %--------------------------------------------% c 90 continue c call snaupd ( ido, bmat, n, which, nev, tol, resid, ncv, & v, ldv, iparam, ipntr, workd, workl, lworkl, & info ) c if (ido .eq. -1) then c if ( type .eq. 1) then c c %----------------------------% c | Perform y <--- OP*x = A*x | c %----------------------------% c call sgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) c else if ( type .eq. 2 ) then c if (sigmai .eq. zero) then c c %----------------------------------% c | Shift is real. Perform | c | y <--- OP*x = inv[A-sigmar*I]*x | c | to force the starting vector | c | into the range of OP. | c %----------------------------------% c call scopy (n, workd(ipntr(1)), 1, workd(ipntr(2)), 1) call sgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, & iwork, workd(ipntr(2)), n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' _NBAND: Error with _bgtrs. ' print*, ' ' go to 9000 end if c else c c %--------------------------------------------% c | Shift is COMPLEX. Perform | c | y <--- OP*x = Real_Part{inv[A-sigma*I]*x} | c | to force the starting vector into the | c | range of OP. | c %--------------------------------------------% c do 100 j = 1, n workc(j) = cmplx(workd(ipntr(1)+j-1)) 100 continue c call cgbtrs ('Notranspose', n, kl, ku, 1, cfac, lda, & iwork, workc, n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' _NBAND: Error with _gbtrs. ' print*, ' ' go to 9000 end if c do 110 j = 1, n workd(ipntr(2)+j-1) = real(workc(j)) 110 continue c end if c else if ( type .eq. 3 ) then c c %-----------------------------------% c | Perform y <--- OP*x = inv[M]*A*x | c | to force the starting vector into | c | the range of OP. | c %-----------------------------------% c call sgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) c call sgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, & iwork, workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_NBAND: Error with _bgtrs.' print*, ' ' go to 9000 end if c else if ( type .eq. 4 ) then c c %-----------------------------------------% c | Perform y <-- OP*x | c | = Real_part{inv[A-SIGMA*M]*M}*x | c | to force the starting vector into the | c | range of OP. | c %-----------------------------------------% c call sgbmv('Notranspose', n, n, kl, ku, one, mb(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) c if ( sigmai .eq. zero ) then c c %---------------------% c | Shift is real, stay | c | in real arithmetic. | c %---------------------% c call sgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, & iwork, workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_NBAND: Error with _gbtrs.' print*, ' ' go to 9000 end if c else c c %--------------------------% c | Goto complex arithmetic. | c %--------------------------% c do 120 i = 1,n workc(i) = cmplx(workd(ipntr(2)+i-1)) 120 continue c call cgbtrs ('Notranspose', n, kl, ku, 1, cfac, lda, & iwork, workc, n, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_NBAND: Error with _gbtrs.' print*, ' ' go to 9000 end if c do 130 i = 1, n workd(ipntr(2)+i-1) = real(workc(i)) 130 continue c end if c else if ( type .eq. 5) then c c %---------------------------------------% c | Perform y <-- OP*x | c | = Imaginary_part{inv[A-SIGMA*I]}*x | c | to force the starting vector into the | c | range of OP. | c %---------------------------------------% c do 140 j = 1, n workc(j) = cmplx(workd(ipntr(1)+j-1)) 140 continue c call cgbtrs ('Notranspose', n, kl, ku, 1, cfac, lda, & iwork, workc, n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' _NBAND: Error with _gbtrs. ' print*, ' ' go to 9000 end if c do 150 j = 1, n workd(ipntr(2)+j-1) = aimag(workc(j)) 150 continue c else if ( type .eq. 6 ) then c c %----------------------------------------% c | Perform y <-- OP*x | c | Imaginary_part{inv[A-SIGMA*M]*M} | c | to force the starting vector into the | c | range of OP. | c %----------------------------------------% c call sgbmv('Notranspose', n, n, kl, ku, one, mb(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) c do 160 i = 1,n workc(i) = cmplx(workd(ipntr(2)+i-1)) 160 continue c call cgbtrs ('Notranspose', n, kl, ku, 1, cfac, lda, & iwork, workc, n, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_NBAND: Error with _gbtrs.' print*, ' ' go to 9000 end if c do 170 i = 1, n workd(ipntr(2)+i-1) = aimag(workc(i)) 170 continue c end if c else if (ido .eq. 1) then c if ( type .eq. 1) then c c %----------------------------% c | Perform y <--- OP*x = A*x | c %----------------------------% c call sgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) c else if ( type .eq. 2) then c if ( sigmai .eq. zero) then c c %----------------------------------% c | Shift is real. Perform | c | y <--- OP*x = inv[A-sigmar*I]*x. | c %----------------------------------% c call scopy (n, workd(ipntr(1)), 1, workd(ipntr(2)), 1) call sgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, & iwork, workd(ipntr(2)), n, ierr) else c c %------------------------------------------% c | Shift is COMPLEX. Perform | c | y <-- OP*x = Real_Part{inv[A-sigma*I]*x} | c | in COMPLEX arithmetic. | c %------------------------------------------% c do 180 j = 1, n workc(j) = cmplx(workd(ipntr(1)+j-1)) 180 continue c call cgbtrs ('Notranspose', n, kl, ku, 1, cfac, lda, & iwork, workc, n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, '_NBAND: Error with _gbtrs.' print*, ' ' go to 9000 end if c do 190 j = 1, n workd(ipntr(2)+j-1) = real(workc(j)) 190 continue c end if c else if ( type .eq. 3 ) then c c %-----------------------------------% c | Perform y <--- OP*x = inv[M]*A*x | c %-----------------------------------% c call sgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) c call sgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, & iwork, workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_NBAND: Error with _bgtrs.' print*, ' ' go to 9000 end if c else if ( type .eq. 4 ) then c c %--------------------------------------% c | Perform y <-- inv(A-sigma*M)*(M*x). | c | (M*x) has been computed and stored | c | in workd(ipntr(3)). | c %--------------------------------------% c if ( sigmai .eq. zero ) then c c %------------------------% c | Shift is real, stay in | c | real arithmetic. | c %------------------------% c call scopy(n, workd(ipntr(3)), 1, workd(ipntr(2)), 1) call sgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, & iwork, workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_NBAND: Error with _gbtrs.' print*, ' ' go to 9000 end if c else c c %---------------------------% c | Go to COMPLEX arithmetic. | c %---------------------------% c do 200 i = 1,n workc(i) = cmplx(workd(ipntr(3)+i-1)) 200 continue c call cgbtrs ('Notranspose', n, kl, ku, 1, cfac, lda, & iwork, workc, n, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_NBAND: Error in _gbtrs.' print*, ' ' go to 9000 end if c do 210 i = 1,n workd(ipntr(2)+i-1) = real(workc(i)) 210 continue c end if c else if ( type .eq. 5 ) then c c %---------------------------------------% c | Perform y <-- OP*x | c | = Imaginary_part{inv[A-SIGMA*I]*x} | c %---------------------------------------% c do 220 j = 1, n workc(j) = cmplx(workd(ipntr(1)+j-1)) 220 continue c call cgbtrs ('Notranspose', n, kl, ku, 1, cfac, lda, & iwork, workc, n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' _NBAND: Error with _gbtrs. ' print*, ' ' go to 9000 end if c do 230 j = 1, n workd(ipntr(2)+j-1) = aimag(workc(j)) 230 continue c else if ( type .eq. 6) then c c %-----------------------------------------% c | Perform y <-- OP*x | c | = Imaginary_part{inv[A-SIGMA*M]*M}*x. | c %-----------------------------------------% c do 240 i = 1,n workc(i) = cmplx(workd(ipntr(3)+i-1)) 240 continue c call cgbtrs ('Notranspose', n, kl, ku, 1, cfac, lda, & iwork, workc, n, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_NBAND: Error with _gbtrs.' print*, ' ' go to 9000 end if c do 250 i = 1, n workd(ipntr(2)+i-1) = aimag(workc(i)) 250 continue c end if c else if (ido .eq. 2) then c c %--------------------% c | Perform y <-- M*x | c | Not used when | c | type = 1,2. | c %--------------------% c call sgbmv('Notranspose', n, n, kl, ku, one, mb(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) c else c c %-----------------------------------------% c | Either we have convergence, or there is | c | error. | c %-----------------------------------------% c if ( info .lt. 0) then c c %--------------------------% c | Error message, check the | c | documentation in SNAUPD | c %--------------------------% c print *, ' ' print *, ' Error with _naupd info = ',info print *, ' Check the documentation of _naupd ' print *, ' ' go to 9000 c else c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c if (iparam(5) .gt. 0) then c call sneupd ( rvec, 'A', select, dr, di, z, ldz, & sigmar, sigmai, workev, bmat, n, which, & nev, tol, resid, ncv, v, ldv, iparam, & ipntr, workd, workl, lworkl, info ) c if ( info .ne. 0) then c c %------------------------------------% c | Check the documentation of SNEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _neupd = ', info print *, ' Check the documentation of _neupd ' print *, ' ' go to 9000 c else if ( sigmai .ne. zero ) then c if ( type .eq. 4 .or. type .eq. 6 ) then c first = .true. do 270 j = 1, iparam(5) c c %----------------------------------% c | Use Rayleigh Quotient to recover | c | eigenvalues of the original | c | generalized eigenvalue problem. | c %----------------------------------% c if ( di(j) .eq. zero ) then c c %--------------------------------------% c | Eigenvalue is real. Compute | c | d = (x'*inv[A-sigma*M]*M*x) / (x'*x) | c %--------------------------------------% c call sgbmv('Nontranspose', n, n, kl, ku, one, $ mb(itop,1), lda, z(1,j), 1, zero, $ workd, 1) do i = 1, n workc(i) = cmplx(workd(i)) end do call cgbtrs ('Notranspose', n, kl, ku, 1, $ cfac, lda, iwork, workc, n, info) do i = 1, n workd(i) = real(workc(i)) workd(i+n) = aimag(workc(i)) end do denr = sdot(n, z(1,j), 1, workd, 1) deni = sdot(n, z(1,j), 1, workd(n+1), 1) numr = snrm2(n, z(1,j), 1)**2 dmdul = slapy2(denr,deni)**2 if ( dmdul .ge. safmin ) then dr(j) = sigmar + numr*denr / dmdul else c c %---------------------% c | dmdul is too small. | c | Exit to avoid | c | overflow. | c %---------------------% c info = -15 go to 9000 end if c else if (first) then c c %------------------------% c | Eigenvalue is complex. | c | Compute the first one | c | of the conjugate pair. | c %------------------------% c c %-------------% c | Compute M*x | c %-------------% c call sgbmv('Nontranspose', n, n, kl, ku, $ one, mb(itop,1), lda, z(1,j), 1, zero, $ workd, 1) call sgbmv('Nontranspose', n, n, kl, ku, $ one, mb(itop,1), lda, z(1,j+1), 1, $ zero, workd(n+1), 1) do i = 1, n workc(i) = cmplx(workd(i),workd(i+n)) end do c c %----------------------------% c | Compute inv(A-sigma*M)*M*x | c %----------------------------% c call cgbtrs('Notranspose',n,kl,ku,1,cfac, $ lda, iwork, workc, n, info) c c %-------------------------------% c | Compute x'*inv(A-sigma*M)*M*x | c %-------------------------------% c do i = 1, n workd(i) = real(workc(i)) workd(i+n) = aimag(workc(i)) end do denr = sdot(n,z(1,j),1,workd,1) denr = denr+sdot(n,z(1,j+1),1,workd(n+1),1) deni = sdot(n,z(1,j),1,workd(n+1),1) deni = deni - sdot(n,z(1,j+1),1,workd,1) c c %----------------% c | Compute (x'*x) | c %----------------% c numr = slapy2( snrm2(n, z(1,j), 1), & snrm2(n, z(1, j+1), 1) )**2 c c %----------------------------------------% c | Compute (x'x) / (x'*inv(A-sigma*M)*Mx) | c %----------------------------------------% c dmdul = slapy2(denr,deni)**2 if ( dmdul .ge. safmin ) then dr(j) = sigmar+numr*denr / dmdul di(j) = sigmai-numr*deni / dmdul first = .false. else c c %---------------------% c | dmdul is too small. | c | Exit to avoid | c | overflow. | c %---------------------% c info = -15 go to 9000 c end if c else c c %---------------------------% c | Get the second eigenvalue | c | of the conjugate pair by | c | taking the conjugate of | c | previous one. | c %---------------------------% c dr(j) = dr(j-1) di(j) = -di(j-1) first = .true. c end if c 270 continue c else if ( type .eq. 2 .or. type .eq. 5) then c first = .true. do 280 j = 1, iparam(5) c c %----------------------------------% c | Use Rayleigh Quotient to recover | c | eigenvalues of the original | c | standard eigenvalue problem. | c %----------------------------------% c if ( di(j) .eq. zero ) then c c %-------------------------------------% c | Eigenvalue is real. Compute | c | d = (x'*inv[A-sigma*I]*x) / (x'*x). | c %-------------------------------------% c do i = 1, n workc(i) = cmplx(z(i,j)) end do call cgbtrs ('Notranspose', n, kl, ku, 1, $ cfac, lda, iwork, workc, n, info) do i = 1, n workd(i) = real(workc(i)) workd(i+n) = aimag(workc(i)) end do denr = sdot(n,z(1,j),1,workd,1) deni = sdot(n,z(1,j),1,workd(n+1),1) numr = snrm2(n, z(1,j), 1)**2 dmdul = slapy2(denr,deni)**2 if ( dmdul .ge. safmin ) then dr(j) = sigmar + numr*denr / dmdul else c c %---------------------% c | dmdul is too small. | c | Exit to avoid | c | overflow. | c %---------------------% c info = -15 go to 9000 c end if c else if (first) then c c %------------------------% c | Eigenvalue is complex. | c | Compute the first one | c | of the conjugate pair. | c %------------------------% c do i = 1, n workc(i) = cmplx( z(i,j), z(i,j+1) ) end do c c %---------------------------% c | Compute inv[A-sigma*I]*x. | c %---------------------------% c call cgbtrs('Notranspose',n,kl,ku,1,cfac, $ lda, iwork, workc, n, info) c c %-----------------------------% c | Compute x'*inv(A-sigma*I)*x | c %-----------------------------% c do i = 1, n workd(i) = real(workc(i)) workd(i+n) = aimag(workc(i)) end do denr = sdot(n,z(1,j),1,workd,1) denr = denr+sdot(n,z(1,j+1),1,workd(n+1),1) deni = sdot(n,z(1,j),1,workd(n+1),1) deni = deni - sdot(n,z(1,j+1),1,workd,1) c c %----------------% c | Compute (x'*x) | c %----------------% c numr = slapy2( snrm2(n, z(1,j), 1), & snrm2(n, z(1,j+1), 1))**2 c c %----------------------------------------% c | Compute (x'x) / (x'*inv(A-sigma*I)*x). | c %----------------------------------------% c dmdul = slapy2(denr,deni)**2 if (dmdul .ge. safmin) then dr(j) = sigmar+numr*denr / dmdul di(j) = sigmai-numr*deni / dmdul first = .false. else c c %---------------------% c | dmdul is too small. | c | Exit to avoid | c | overflow. | c %---------------------% c info = -15 go to 9000 end if c else c c %---------------------------% c | Get the second eigenvalue | c | of the conjugate pair by | c | taking the conjugate of | c | previous one. | c %---------------------------% c dr(j) = dr(j-1) di(j) = -di(j-1) first = .true. c end if c 280 continue c end if c end if c end if c end if c go to 9000 c end if c c %----------------------------------------% c | L O O P B A C K to call SNAUPD again. | c %----------------------------------------% c go to 90 c 9000 continue c end arpack-0.92.1/EXAMPLES/BAND/dsbdr3.f0000644000175000017500000002334310776001577013256 00000000000000 program dsbdr3 c c ... Construct the matrix A in LAPACK-style band form. c The matrix A is the 1-dimensional discrete Laplacian on [0,1] c with zero Dirichlet boundary condition, M is the mass c formed by using piecewise linear elements on [0,1]. c c ... Call DSBAND with regular mode to find eigenvalues LAMBDA c such that c A*x = LAMBDA*M*x. c c ... Use mode 2 of DSAUPD . c c\BeginLib c c\Routines called: c dsband ARPACK banded eigenproblem solver. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c dlaset LAPACK routine to initialize a matrix to zero. c daxpy Level 1 BLAS that computes y <- alpha*x+y. c dnrm2 Level 1 BLAS that computes the norm of a vector. c dgbmv Level 2 BLAS that computes the band matrix vector product c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: sbdr3.F SID: 2.5 DATE OF SID: 08/26/96 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c---------------------------------------------------------------------- c c %-------------------------------------% c | Define leading dimensions for all | c | arrays. | c | MAXN - Maximum size of the matrix | c | MAXNEV - Maximum number of | c | eigenvalues to be computed | c | MAXNCV - Maximum number of Arnoldi | c | vectors stored | c | MAXBDW - Maximum bandwidth | c %-------------------------------------% c integer maxn, maxnev, maxncv, maxbdw, lda, & lworkl, ldv parameter ( maxn = 1000, maxnev = 25, maxncv=50, & maxbdw=50, lda = maxbdw, ldv = maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), iwork(maxn) logical select(maxncv) Double precision & a(lda,maxn), m(lda,maxn), rfac(lda,maxn), & workl(maxncv*maxncv+8*maxncv), workd(3*maxn), & v(ldv, maxncv), resid(maxn), d(maxncv, 2), & ax(maxn), mx(maxn) c c %---------------% c | Local Scalars | c %---------------% c character which*2, bmat integer nev, ncv, ku, kl, info, j, ido, & n, isub, isup, idiag, maxitr, mode, nconv Double precision & tol, h, sigma, r1, r2 logical rvec c c %------------% c | Parameters | c %------------% c Double precision & one, zero, two, four, six parameter (one = 1.0D+0 , zero = 0.0D+0 , two = 2.0D+0 , & four = 4.0D+0 , six = 6.0D+0 ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & dlapy2 , dnrm2 external dlapy2 , dnrm2 , daxpy , dgbmv c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------------------------% c | The number N is the dimension of the matrix. A | c | generalized eigenvalue problem is solved | c | (BMAT = 'G'). NEV is the number of eigenvalues | c | to be approximated. The user can modify N, NEV, | c | NCV and WHICH to solve problems of different | c | sizes, and to get different parts the spectrum. | c | However, the following conditions must be | c | satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 1 <= NCV <= MAXNCV | c %-------------------------------------------------% c n = 100 nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _SBDR3: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _SBDR3: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _SBDR3: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' c c %-----------------------------------------------------% c | The work array WORKL is used in DSAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in DSAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = ncv**2+8*ncv tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 2 of DSAUPD is used | c | (IPARAM(7) = 2). All these options can be changed | c | by the user. For details see the documentation in | c | DSBAND . | c %---------------------------------------------------% c maxitr = 300 mode = 2 c iparam(3) = maxitr iparam(7) = mode c c %----------------------------------------% c | Construct the matrix A in LAPACK-style | c | banded form. | c %----------------------------------------% c c %---------------------------------------------% c | Zero out the workspace for banded matrices. | c %---------------------------------------------% c call dlaset ('A', lda, n, zero, zero, a, lda) call dlaset ('A', lda, n, zero, zero, m, lda) call dlaset ('A', lda, n, zero, zero, rfac, lda) c c %-------------------------------------% c | KU, KL are number of superdiagonals | c | and subdiagonals within the band of | c | matrices A and M. | c %-------------------------------------% c kl = 1 ku = 1 c c %---------------% c | Main diagonal | c %---------------% c h = one / dble (n+1) r1 = four / six idiag = kl+ku+1 do 30 j = 1, n a(idiag,j) = two / h m(idiag,j) = r1 * h 30 continue c c %-------------------------------------% c | First subdiagonal and superdiagonal | c %-------------------------------------% c r2 = one / six isup = kl+ku isub = kl+ku+2 do 60 j = 1, n-1 a(isup,j+1) = -one / h a(isub,j) = -one / h m(isup,j+1) = r2 * h m(isub,j) = r2 * h 60 continue c c %-------------------------------------% c | Call DSBAND to find eigenvalues and | c | eigenvectors. Eigenvalues are | c | returned in the first column of D. | c | Eigenvectors are returned in the | c | first NCONV (=IPARAM(5)) columns of | c | V. | c %-------------------------------------% c rvec = .true. call dsband ( rvec, 'A', select, d, v, ldv, sigma, n, a, m, lda, & rfac, kl, ku, which, bmat, nev, tol, & resid, ncv, v, ldv, iparam, workd, workl, lworkl, & iwork, info) c if ( info .eq. 0) then c nconv = iparam(5) c c %-----------------------------------% c | Print out convergence information | c %-----------------------------------% c print *, ' ' print *, ' _SBDR3 ' print *, ' ====== ' print *, ' ' print *, ' The size of the matrix is ', n print *, ' Number of eigenvalue requested is ', nev print *, ' The number of Lanczos vectors generated', & ' (NCV) is ', ncv print *, ' The number of converged Ritz values is ', & nconv print *, ' What portion of the spectrum ', which print *, ' The number of Implicit Arnoldi', & ' update taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence tolerance is ', tol print *, ' ' c c %----------------------------% c | Compute the residual norm. | c | || A*x - lambda*x || | c %----------------------------% c do 90 j = 1, nconv call dgbmv ('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call dgbmv ('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j), 1, zero, & mx, 1) call daxpy (n, -d(j,1), mx, 1, ax, 1) d(j,2) = dnrm2 (n, ax, 1) d(j,2) = d(j,2) / abs(d(j,1)) c 90 continue call dmout (6, nconv, 2, d, maxncv, -6, & 'Ritz values and relative residuals') else c c %-------------------------------------% c | Either convergence failed, or there | c | is error. Check the documentation | c | for DSBAND . | c %-------------------------------------% c print *, ' ' print *, ' Error with _sband, info= ', info print *, ' Check the documentation of _sband ' print *, ' ' c end if c 9000 end arpack-0.92.1/EXAMPLES/BAND/dnbdr6.f0000644000175000017500000003163210776001577013254 00000000000000 program dnbdr6 c c ... Construct matrices A and M in LAPACK-style band form. c The matrix A is a block tridiagonal matrix. Each c diagonal block is a tridiagonal matrix with c 4 on the diagonal, 1-rho*h/2 on the subdiagonal and c 1+rho*h/2 on the superdiagonal. Each subdiagonal block c of A is an identity matrix. The matrix M is the c tridiagonal matrix with 4 on the diagonal and 1 on the c subdiagonal and superdiagonal. c c ... Define COMPLEX shift SIGMA=(SIGMAR,SIGMAI), SIGMAI .ne. zero. c c ... Call dnband to find eigenvalues LAMBDA closest to SIGMA c such that c A*x = LAMBDA*M*x. c c ... Use mode 4 of DNAUPD . c c\BeginLib c c\Routines called: c dnband ARPACK banded eigenproblem solver. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c dlaset LAPACK routine to initialize a matrix to zero. c daxpy Level 1 BLAS that computes y <- alpha*x+y. c dnrm2 Level 1 BLAS that computes the norm of a vector. c dgbmv Level 2 BLAS that computes the band matrix vector product. c c\Author c Danny Sorensen c Richard Lehoucq c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: nbdr6.F SID: 2.5 DATE OF SID: 08/26/96 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c--------------------------------------------------------------------- c c %-------------------------------------% c | Define leading dimensions for all | c | arrays. | c | MAXN - Maximum size of the matrix | c | MAXNEV - Maximum number of | c | eigenvalues to be computed | c | MAXNCV - Maximum number of Arnoldi | c | vectors stored | c | MAXBDW - Maximum bandwidth | c %-------------------------------------% c integer maxn, maxnev, maxncv, maxbdw, lda, & lworkl, ldv parameter ( maxn = 1000, maxnev = 25, maxncv=50, & maxbdw=50, lda = maxbdw, ldv = maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), iwork(maxn) logical select(maxncv) Double precision & a(lda,maxn), m(lda,maxn), rfac(lda,maxn), & workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn), & workev(3*maxncv), v(ldv, maxncv), & resid(maxn), d(maxncv, 3), ax(maxn), mx(maxn) Complex*16 & cfac(lda, maxn), workc(maxn) c c %---------------% c | Local Scalars | c %---------------% c character which*2, bmat integer nev, ncv, ku, kl, info, i, j, ido, & n, nx, lo, idiag, isup, isub, mode, maxitr, & nconv logical rvec, first Double precision & tol, rho, h, sigmar, sigmai c c %------------% c | Parameters | c %------------% c Double precision & one, zero, two parameter (one = 1.0D+0 , zero = 0.0D+0 , & two = 2.0D+0 ) c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & dlapy2 , dnrm2 external dlapy2 , dnrm2 , dgbmv , daxpy c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-----------------------------------------------------% c | The number NX is the size of each diagonal block of | c | A. The number N(=NX*NX) is the dimension of the | c | matrix. The number N(=NX*NX) is the dimension of | c | the matrix. A generalized eigenvalue problem is | c | solved (BMAT = 'G'). NEV numbers of eigenvalues | c | closest to the COMPLEX shift (SIGMAR,SIGMAI) | c | (WHICH='LM') and their corresponding eigenvectors | c | are computed. The user can modify NX, NEV, NCV, | c | WHICH to solve problems of different sizes, and | c | to get different parts the spectrum. However, the | c | following rules must be satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 2 <= NCV <= MAXNCV | c %-----------------------------------------------------% c nx = 10 n = nx*nx nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _NBDR6: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NBDR6: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NBDR6: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' sigmar = 4.0D-1 sigmai = 6.0D-1 c c %-----------------------------------------------------% c | The work array WORKL is used in DNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in DNAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = 3*ncv**2+6*ncv tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 4 of DNAUPD is used | c | (IPARAm(7) = 4). All these options can be changed | c | by the user. For details, see the documentation | c | in dnband . | c %---------------------------------------------------% c maxitr = 300 mode = 4 c iparam(3) = maxitr iparam(7) = mode c c %--------------------------------------------% c | Construct matrices A and M in LAPACK-style | c | banded form. | c %--------------------------------------------% c c %---------------------------------------------% c | Zero out the workspace for banded matrices. | c %---------------------------------------------% c call dlaset ('A', lda, n, zero, zero, a, lda) call dlaset ('A', lda, n, zero, zero, m, lda) call dlaset ('A', lda, n, zero, zero, rfac, lda) c c %-------------------------------------% c | KU, KL are number of superdiagonals | c | and subdiagonals within the band of | c | matrices A and M. | c %-------------------------------------% c kl = nx ku = nx c c %---------------% c | Main diagonal | c %---------------% c idiag = kl+ku+1 do 30 j = 1, n a(idiag,j) = 4.0D+0 m(idiag,j) = 4.0D+0 30 continue c c %-------------------------------------% c | First subdiagonal and superdiagonal | c %-------------------------------------% c isup = kl+ku isub = kl+ku+2 h = one / dble (nx+1) rho = 1.0D+2 do 50 i = 1, nx lo = (i-1)*nx do 40 j = lo+1, lo+nx-1 a(isub,j+1) = -one+h*rho/two a(isup,j) = -one-h*rho/two 40 continue 50 continue c do 60 j = 1, n-1 m(isub,j+1) = one m(isup,j) = one 60 continue c c %------------------------------------% c | KL-th subdiagonal and KU-th super- | c | diagonal. | c %------------------------------------% c isup = kl+1 isub = 2*kl+ku+1 do 80 i = 1, nx-1 lo = (i-1)*nx do 70 j = lo+1, lo+nx a(isup,nx+j) = -one a(isub,j) = -one 70 continue 80 continue c c %------------------------------------------------% c | Call ARPACK banded solver to find eigenvalues | c | and eigenvectors. The real parts of the | c | eigenvalues are returned in the first column | c | of D, the imaginary parts are returned in the | c | second column of D. Eigenvectors are returned | c | in the first NCONV (=IPARAM(5)) columns of V. | c %------------------------------------------------% c rvec = .true. call dnband (rvec, 'A', select, d, d(1,2), v, ldv, sigmar, & sigmai, workev, n, a, m, lda, rfac, cfac, ku, kl, & which, bmat, nev, tol, resid, ncv, v, ldv, iparam, & workd, workl, lworkl, workc, iwork, info) c if ( info .eq. 0) then c c %-----------------------------------% c | Print out convergence information | c %-----------------------------------% c nconv = iparam(5) c print *, ' ' print *, ' _NBDR6 ' print *, ' ====== ' print *, ' ' print *, ' The size of the matrix is ', n print *, ' Number of eigenvalue requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' The number of converged Ritz values is ', & nconv print *, ' What portion of the spectrum ', which print *, ' The number of Implicit Arnoldi ', & ' update taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence tolerance is ', tol print *, ' ' c c %----------------------------% c | Compute the residual norm. | c | || A*x - lambda*x || | c %----------------------------% c first = .true. do 90 j = 1, nconv c if ( d(j,2) .eq. zero ) then c c %--------------------% c | Ritz value is real | c %--------------------% c call dgbmv ('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call dgbmv ('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j), 1, zero, & mx, 1) call daxpy (n, -d(j,1), mx, 1, ax, 1) d(j,3) = dnrm2 (n, ax, 1) d(j,3) = d(j,3) / abs(d(j,1)) c else if ( first ) then c c %------------------------% c | Ritz value is complex | c | Residual of one Ritz | c | value of the conjugate | c | pair is computed. | c %------------------------% c call dgbmv ('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call dgbmv ('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j), 1, zero, & mx, 1) call daxpy (n, -d(j,1), mx, 1, ax, 1) call dgbmv ('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j+1), 1, zero, & mx, 1) call daxpy (n, d(j,2), mx, 1, ax, 1) d(j,3) = dnrm2 (n, ax, 1) call dgbmv ('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j+1), 1, zero, & ax, 1) call dgbmv ('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j+1), 1, zero, & mx, 1) call daxpy (n, -d(j,1), mx, 1, ax, 1) call dgbmv ('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j), 1, zero, & mx, 1) call daxpy (n, -d(j,2), mx, 1, ax, 1) d(j,3) = dlapy2 ( d(j,3), dnrm2 (n, ax, 1) ) d(j,3) = d(j,3) / dlapy2 (d(j,1),d(j,2)) d(j+1,3) = d(j,3) first = .false. else first = .true. end if c 90 continue call dmout (6, nconv, 3, d, maxncv, -6, & 'Ritz values (Real,Imag) and relative residuals') else c c %-------------------------------------% c | Either convergence failed, or there | c | is error. Check the documentation | c | for dnband . | c %-------------------------------------% c print *, ' ' print *, ' Error with _nband, info= ', info print *, ' Check the documentation of _nband ' print *, ' ' c end if c 9000 end arpack-0.92.1/EXAMPLES/BAND/ssband.f0000644000175000017500000007667610776001577013370 00000000000000c \BeginDoc c c \Name: ssband c c \Description: c c This subroutine returns the converged approximations to eigenvalues c of A*z = lambda*B*z and (optionally): c c (1) The corresponding approximate eigenvectors; c c (2) An orthonormal (Lanczos) basis for the associated approximate c invariant subspace; c c (3) Both. c c Matrices A and B are stored in LAPACK-style band form. c c There is negligible additional cost to obtain eigenvectors. An orthonormal c (Lanczos) basis is always computed. There is an additional storage cost c of n*nev if both are requested (in this case a separate array Z must be c supplied). c c The approximate eigenvalues and eigenvectors of A*z = lambda*B*z c are called Ritz values and Ritz vectors respectively. They are referred c to as such in the comments that follow. The computed orthonormal basis c for the invariant subspace corresponding to these Ritz values is referred c to as a Lanczos basis. c c ssband can be called with one of the following modes: c c Mode 1: A*x = lambda*x, A symmetric c ===> OP = A and B = I. c c Mode 2: A*x = lambda*M*x, A symmetric, M symmetric positive definite c ===> OP = inv[M]*A and B = M. c ===> (If M can be factored see remark 3 in SSAUPD) c c Mode 3: K*x = lambda*M*x, K symmetric, M symmetric positive semi-definite c ===> OP = (inv[K - sigma*M])*M and B = M. c ===> Shift-and-Invert mode c c Mode 4: K*x = lambda*KG*x, K symmetric positive semi-definite, c KG symmetric indefinite c ===> OP = (inv[K - sigma*KG])*K and B = K. c ===> Buckling mode c c Mode 5: A*x = lambda*M*x, A symmetric, M symmetric positive semi-definite c ===> OP = inv[A - sigma*M]*[A + sigma*M] and B = M. c ===> Cayley transformed mode c c The choice of mode must be specified in IPARAM(7) defined below. c c \Usage c call ssband c ( RVEC, HOWMNY, SELECT, D, Z, LDZ, SIGMA, N, AB, MB, LDA, c RFAC, KL, KU, WHICH, BMAT, NEV, TOL, RESID, NCV, V, c LDV, IPARAM, WORKD, WORKL, LWORKL, IWORK, INFO ) c c \Arguments c c RVEC Logical (INPUT) c Specifies whether Ritz vectors corresponding to the Ritz value c approximations to the eigenproblem A*z = lambda*B*z are computed. c c RVEC = .FALSE. Compute Ritz values only. c c RVEC = .TRUE. Compute the associated Ritz vectors. c c HOWMNY Character*1 (INPUT) c Specifies how many Ritz vectors are wanted and the form of Z c the matrix of Ritz vectors. See remark 1 below. c = 'A': compute all Ritz vectors; c = 'S': compute some of the Ritz vectors, specified c by the logical array SELECT. c c SELECT Logical array of dimension NCV. (INPUT) c If HOWMNY = 'S', SELECT specifies the Ritz vectors to be c computed. To select the Ritz vector corresponding to a c Ritz value D(j), SELECT(j) must be set to .TRUE.. c If HOWMNY = 'A' , SELECT is not referenced. c c D Real array of dimension NEV. (OUTPUT) c On exit, D contains the Ritz value approximations to the c eigenvalues of A*z = lambda*B*z. The values are returned c in ascending order. If IPARAM(7) = 3,4,5 then D represents c the Ritz values of OP computed by ssaupd transformed to c those of the original eigensystem A*z = lambda*B*z. If c IPARAM(7) = 1,2 then the Ritz values of OP are the same c as the those of A*z = lambda*B*z. c c Z Real N by NEV array if HOWMNY = 'A'. (OUTPUT) c On exit, Z contains the B-orthonormal Ritz vectors of the c eigensystem A*z = lambda*B*z corresponding to the Ritz c value approximations. c c If RVEC = .FALSE. then Z is not referenced. c NOTE: The array Z may be set equal to first NEV columns of the c Lanczos basis array V computed by SSAUPD. c c LDZ Integer. (INPUT) c The leading dimension of the array Z. If Ritz vectors are c desired, then LDZ .ge. max( 1, N ). In any case, LDZ .ge. 1. c c SIGMA Real (INPUT) c If IPARAM(7) = 3,4,5 represents the shift. Not referenced if c IPARAM(7) = 1 or 2. c c N Integer. (INPUT) c Dimension of the eigenproblem. c c AB Real array of dimension LDA by N. (INPUT) c The matrix A in band storage, in rows KL+1 to c 2*KL+KU+1; rows 1 to KL of the array need not be set. c The j-th column of A is stored in the j-th column of the c array AB as follows: c AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) c c MB Real array of dimension LDA by N. (INPUT) c The matrix M in band storage, in rows KL+1 to c 2*KL+KU+1; rows 1 to KL of the array need not be set. c The j-th column of M is stored in the j-th column of the c array AB as follows: c MB(kl+ku+1+i-j,j) = M(i,j) for max(1,j-ku)<=i<=min(m,j+kl) c Not referenced if IPARAM(7) = 1 c c LDA Integer. (INPUT) c Leading dimension of AB, MB, RFAC. c c RFAC Real array of LDA by N. (WORKSPACE/OUTPUT) c RFAC is used to store the LU factors of MB when IPARAM(7) = 2 c is invoked. It is used to store the LU factors of c (A-sigma*M) when IPARAM(7) = 3,4,5 is invoked. c It is not referenced when IPARAM(7) = 1. c c KL Integer. (INPUT) c Max(number of subdiagonals of A, number of subdiagonals of M) c c KU Integer. (OUTPUT) c Max(number of superdiagonals of A, number of superdiagonals of M) c c WHICH Character*2. (INPUT) c When IPARAM(7)= 1 or 2, WHICH can be set to any one of c the following. c c 'LM' -> want the NEV eigenvalues of largest magnitude. c 'SM' -> want the NEV eigenvalues of smallest magnitude. c 'LA' -> want the NEV eigenvalues of largest REAL part. c 'SA' -> want the NEV eigenvalues of smallest REAL part. c 'BE' -> Compute NEV eigenvalues, half from each end of the c spectrum. When NEV is odd, compute one more from c the high end than from the low end. c c When IPARAM(7) = 3, 4, or 5, WHICH should be set to 'LM' only. c c BMAT Character*1. (INPUT) c BMAT specifies the type of the matrix B that defines the c semi-inner product for the operator OP. c BMAT = 'I' -> standard eigenvalue problem A*x = lambda*x c BMAT = 'G' -> generalized eigenvalue problem A*x = lambda*M*x c NEV Integer. (INPUT) c Number of eigenvalues of OP to be computed. c c TOL Real scalar. (INPUT) c Stopping criterion: the relative accuracy of the Ritz value c is considered acceptable if BOUNDS(I) .LE. TOL*ABS(RITZ(I)). c If TOL .LE. 0. is passed a default is set: c DEFAULT = SLAMCH('EPS') (machine precision as computed c by the LAPACK auxiliary subroutine SLAMCH). c c RESID Real array of length N. (INPUT/OUTPUT) c On INPUT: c If INFO .EQ. 0, a random initial residual vector is used. c If INFO .NE. 0, RESID contains the initial residual vector, c possibly from a previous run. c On OUTPUT: c RESID contains the final residual vector. c c NCV Integer. (INPUT) c Number of columns of the matrix V (less than or equal to N). c Represents the dimension of the Lanczos basis constructed c by ssaupd for OP. c c V Real array N by NCV. (OUTPUT) c Upon INPUT: the NCV columns of V contain the Lanczos basis c vectors as constructed by ssaupd for OP. c Upon OUTPUT: If RVEC = .TRUE. the first NCONV=IPARAM(5) columns c represent the Ritz vectors that span the desired c invariant subspace. c NOTE: The array Z may be set equal to first NEV columns of the c Lanczos basis vector array V computed by ssaupd. In this case c if RVEC=.TRUE., the first NCONV=IPARAM(5) columns of V contain c the desired Ritz vectors. c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling c program. c c IPARAM Integer array of length 11. (INPUT/OUTPUT) c IPARAM(1) = ISHIFT: c The shifts selected at each iteration are used to restart c the Arnoldi iteration in an implicit fashion. c It is set to 1 in this subroutine. The user do not need c to set this parameter. c ------------------------------------------------------------ c ISHIFT = 1: exact shifts with respect to the reduced c tridiagonal matrix T. This is equivalent to c restarting the iteration with a starting vector c that is a linear combination of Ritz vectors c associated with the "wanted" Ritz values. c ------------------------------------------------------------- c c IPARAM(2) = No longer referenced. c c IPARAM(3) = MXITER c On INPUT: max number of Arnoldi update iterations allowed. c On OUTPUT: actual number of Arnoldi update iterations taken. c c IPARAM(4) = NB: blocksize to be used in the recurrence. c The code currently works only for NB = 1. c c IPARAM(5) = NCONV: number of "converged" eigenvalues. c This represents the number of Ritz values that satisfy c the convergence criterion. c c IPARAM(6) = IUPD c No longer referenced. Implicit restarting is ALWAYS used. c c IPARAM(7) = MODE c On INPUT determines what type of eigenproblem is being solved. c Must be 1,2,3,4,5; See under \Description of ssband for the c five modes available. c c IPARAM(8) = NP c Not referenced. c c IPARAM(9) = NUMOP, IPARAM(10) = NUMOPB, IPARAM(11) = NUMREO, c OUTPUT: NUMOP = total number of OP*x operations, c NUMOPB = total number of B*x operations if BMAT='G', c NUMREO = total number of steps of re-orthogonalization. c c WORKD Real work array of length at least 3*n. (WORKSPACE) c c WORKL Real work array of length LWORKL. (WORKSPACE) c c LWORKL Integer. (INPUT) c LWORKL must be at least NCV**2 + 8*NCV. c c IWORK Integer array of dimension at least N. (WORKSPACE) c Used when IPARAM(7)=2,3,4,5 to store the pivot information in the c factorization of M or (A-SIGMA*M). c c INFO Integer. (INPUT/OUTPUT) c Error flag on output. c = 0: Normal exit. c = 1: Maximum number of iterations taken. c All possible eigenvalues of OP has been found. IPARAM(5) c returns the number of wanted converged Ritz values. c = 3: No shifts could be applied during a cycle of the c Implicitly restarted Arnoldi iteration. One possibility c is to increase the size of NCV relative to NEV. c See remark 4 in SSAUPD. c c = -1: N must be positive. c = -2: NEV must be positive. c = -3: NCV-NEV >= 2 and less than or equal to N. c = -5: WHICH must be one of 'LM', 'SM', 'LR', 'SR', 'LI', 'SI' c = -6: BMAT must be one of 'I' or 'G'. c = -7: Length of private work WORKL array is not sufficient. c = -8: Error return from trid. eigenvalue calculation; c Informational error from LAPACK routine ssteqr. c = -9: Starting vector is zero. c = -10: IPARAM(7) must be 1,2,3,4,5. c = -11: IPARAM(7) = 1 and BMAT = 'G' are incompatible. c = -12: NEV and WHICH = 'BE' are incompatible. c = -13: HOWMNY must be one of 'A' or 'P' c = -14: SSAUPD did not find any eigenvalues to sufficient c accuracy. c = -9999: Could not build an Arnoldi factorization. c IPARAM(5) returns the size of the current c Arnoldi factorization. c c \EndDoc c c------------------------------------------------------------------------ c c\BeginLib c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly c Restarted Arnoldi Iteration", Ph.D thesis, TR95-13, Rice Univ, c May 1995. c c\Routines called: c ssaupd ARPACK reverse communication interface routine. c sseupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c sgbtrf LAPACK band matrix factorization routine. c sgbtrs LAPACK band linear system solve routine. c slacpy LAPACK matrix copy routine. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c scopy Level 1 BLAS that copies one vector to another. c sdot Level 1 BLAS that computes the dot product of two vectors. c snrm2 Level 1 BLAS that computes the norm of a vector. c sgbmv Level 2 BLAS that computes the band matrix vector product. c c\Remarks c 1. The converged Ritz values are always returned in increasing c (algebraic) order. c c 2. Currently only HOWMNY = 'A' is implemented. It is included at this c stage for the user who wants to incorporate it. c c\Author c Danny Sorensen c Richard Lehoucq c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: sband.F SID: 2.3 DATE OF SID: 10/17/00 RELEASE: 2 c c\EndLib c c--------------------------------------------------------------------- c subroutine ssband( rvec, howmny, select, d, z, ldz, sigma, & n, ab, mb, lda, rfac, kl, ku, which, bmat, nev, & tol, resid, ncv, v, ldv, iparam, workd, workl, & lworkl, iwork, info) c c %------------------% c | Scalar Arguments | c %------------------% c character which*2, bmat, howmny integer n, lda, kl, ku, nev, ncv, ldv, & ldz, lworkl, info Real & tol, sigma logical rvec c c %-----------------% c | Array Arguments | c %-----------------% c integer iparam(*), iwork(*) logical select(*) Real & d(*), resid(*), v(ldv,*), z(ldz,*), & ab(lda,*), mb(lda,*), rfac(lda,*), & workd(*), workl(*) c c %--------------% c | Local Arrays | c %--------------% c integer ipntr(14) c c %---------------% c | Local Scalars | c %---------------% c integer ido, i, j, type, imid, itop, ibot, ierr c c %------------% c | Parameters | c %------------% c Real & one, zero parameter (one = 1.0, zero = 0.0) c c c %-----------------------------% c | LAPACK & BLAS routines used | c %-----------------------------% c Real & sdot, snrm2, slapy2 external sdot, scopy, sgbmv, sgbtrf, & sgbtrs, snrm2, slapy2, slacpy c c %-----------------------% c | Executable Statements | c %-----------------------% c c %----------------------------------------------------------------% c | Set type of the problem to be solved. Check consistency | c | between BMAT and IPARAM(7). | c | type = 1 --> Solving standard problem in regular mode. | c | type = 2 --> Solving standard problem in shift-invert mode. | c | type = 3 --> Solving generalized problem in regular mode. | c | type = 4 --> Solving generalized problem in shift-invert mode. | c | type = 5 --> Solving generalized problem in Buckling mode. | c | type = 6 --> Solving generalized problem in Cayley mode. | c %----------------------------------------------------------------% c if ( iparam(7) .eq. 1 ) then type = 1 else if ( iparam(7) .eq. 3 .and. bmat .eq. 'I') then type = 2 else if ( iparam(7) .eq. 2 ) then type = 3 else if ( iparam(7) .eq. 3 .and. bmat .eq. 'G') then type = 4 else if ( iparam(7) .eq. 4 ) then type = 5 else if ( iparam(7) .eq. 5 ) then type = 6 else print*, ' ' print*, 'BMAT is inconsistent with IPARAM(7).' print*, ' ' go to 9000 end if c c %------------------------% c | Initialize the reverse | c | communication flag. | c %------------------------% c ido = 0 c c %----------------% c | Exact shift is | c | used. | c %----------------% c iparam(1) = 1 c c %-----------------------------------% c | Both matrices A and M are stored | c | between rows itop and ibot. Imid | c | is the index of the row that | c | stores the diagonal elements. | c %-----------------------------------% c itop = kl + 1 imid = kl + ku + 1 ibot = 2*kl + ku + 1 c if ( type .eq. 2 .or. type .eq. 6 .and. bmat .eq. 'I' ) then c c %----------------------------------% c | Solving a standard eigenvalue | c | problem in shift-invert or | c | Cayley mode. Factor (A-sigma*I). | c %----------------------------------% c call slacpy ('A', ibot, n, ab, lda, rfac, lda ) do 10 j = 1, n rfac(imid,j) = ab(imid,j) - sigma 10 continue call sgbtrf(n, n, kl, ku, rfac, lda, iwork, ierr ) if (ierr .ne. 0) then print*, ' ' print*, ' _SBAND: Error with _gbtrf. ' print*, ' ' go to 9000 end if c else if ( type .eq. 3 ) then c c %----------------------------------------------% c | Solving generalized eigenvalue problem in | c | regular mode. Copy M to rfac and Call LAPACK | c | routine sgbtrf to factor M. | c %----------------------------------------------% c call slacpy ('A', ibot, n, mb, lda, rfac, lda ) call sgbtrf(n, n, kl, ku, rfac, lda, iwork, ierr) if (ierr .ne. 0) then print*, ' ' print*,'_SBAND: Error with _gbtrf.' print*, ' ' go to 9000 end if c else if ( type .eq. 4 .or. type .eq. 5 .or. type .eq. 6 & .and. bmat .eq. 'G' ) then c c %-------------------------------------------% c | Solving generalized eigenvalue problem in | c | shift-invert, Buckling, or Cayley mode. | c %-------------------------------------------% c c %-------------------------------------% c | Construct and factor (A - sigma*M). | c %-------------------------------------% c do 60 j = 1,n do 50 i = itop, ibot rfac(i,j) = ab(i,j) - sigma*mb(i,j) 50 continue 60 continue c call sgbtrf(n, n, kl, ku, rfac, lda, iwork, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, '_SBAND: Error with _gbtrf.' print*, ' ' go to 9000 end if c end if c c %--------------------------------------------% c | M A I N L O O P (reverse communication) | c %--------------------------------------------% c 90 continue c call ssaupd ( ido, bmat, n, which, nev, tol, resid, ncv, & v, ldv, iparam, ipntr, workd, workl, lworkl, & info ) c if (ido .eq. -1) then c if ( type .eq. 1) then c c %----------------------------% c | Perform y <--- OP*x = A*x | c %----------------------------% c call sgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) c else if ( type .eq. 2 ) then c c %----------------------------------% c | Perform | c | y <--- OP*x = inv[A-sigma*I]*x | c | to force the starting vector | c | into the range of OP. | c %----------------------------------% c call scopy (n, workd(ipntr(1)), 1, workd(ipntr(2)), 1) call sgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, & iwork, workd(ipntr(2)), n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' _SBAND: Error with _bgtrs. ' print*, ' ' go to 9000 end if c else if ( type .eq. 3 ) then c c %-----------------------------------% c | Perform y <--- OP*x = inv[M]*A*x | c | to force the starting vector into | c | the range of OP. | c %-----------------------------------% c call sgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) call scopy(n, workd(ipntr(2)), 1, workd(ipntr(1)), 1) call sgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, & iwork, workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_SBAND: Error with sbgtrs.' print*, ' ' go to 9000 end if c else if ( type .eq. 4 ) then c c %-----------------------------------------% c | Perform y <-- OP*x | c | = inv[A-SIGMA*M]*M | c | to force the starting vector into the | c | range of OP. | c %-----------------------------------------% c call sgbmv('Notranspose', n, n, kl, ku, one, mb(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) call sgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, & iwork, workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_SBAND: Error with _gbtrs.' print*, ' ' go to 9000 end if c else if ( type .eq. 5) then c c %---------------------------------------% c | Perform y <-- OP*x | c | = inv[A-SIGMA*M]*A | c | to force the starting vector into the | c | range of OP. | c %---------------------------------------% c call sgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) call sgbtrs('Notranspose', n, kl, ku, 1, rfac, lda, & iwork, workd(ipntr(2)), n, ierr) c if ( ierr .ne. 0 ) then print*, ' ' print*, ' _SBAND: Error with _gbtrs. ' print*, ' ' go to 9000 end if c else if ( type .eq. 6 ) then c c %---------------------------------------% c | Perform y <-- OP*x | c | = (inv[A-SIGMA*M])*(A+SIGMA*M)*x | c | to force the starting vector into the | c | range of OP. | c %---------------------------------------% c if ( bmat .eq. 'G' ) then call sgbmv('Notranspose', n, n, kl, ku, one, & ab(itop,1), lda, workd(ipntr(1)), 1, & zero, workd(ipntr(2)), 1) call sgbmv('Notranspose', n, n, kl, ku, sigma, & mb(itop,1), lda, workd(ipntr(1)), 1, & one, workd(ipntr(2)), 1) else call scopy(n, workd(ipntr(1)), 1, workd(ipntr(2)), 1) call sgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), & lda, workd(ipntr(1)), 1, sigma, & workd(ipntr(2)), 1) end if c call sgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, & iwork, workd(ipntr(2)), n, ierr) c if (ierr .ne. 0) then print*, ' ' print*, '_SBAND: Error with _gbtrs.' print*, ' ' go to 9000 end if c end if c else if (ido .eq. 1) then c if ( type .eq. 1) then c c %----------------------------% c | Perform y <--- OP*x = A*x | c %----------------------------% c call sgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) c else if ( type .eq. 2) then c c %----------------------------------% c | Perform | c | y <--- OP*x = inv[A-sigma*I]*x. | c %----------------------------------% c call scopy (n, workd(ipntr(1)), 1, workd(ipntr(2)), 1) call sgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, & iwork, workd(ipntr(2)), n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, '_SBAND: Error with _gbtrs.' print*, ' ' go to 9000 end if c else if ( type .eq. 3 ) then c c %-----------------------------------% c | Perform y <--- OP*x = inv[M]*A*x | c %-----------------------------------% c call sgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) call scopy(n, workd(ipntr(2)), 1, workd(ipntr(1)), 1) call sgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, & iwork, workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_SBAND: error with _bgtrs.' print*, ' ' go to 9000 end if c else if ( type .eq. 4 ) then c c %-------------------------------------% c | Perform y <-- inv(A-sigma*M)*(M*x). | c | (M*x) has been computed and stored | c | in workd(ipntr(3)). | c %-------------------------------------% c call scopy(n, workd(ipntr(3)), 1, workd(ipntr(2)), 1) call sgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, & iwork, workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_SBAND: Error with _gbtrs.' print*, ' ' go to 9000 end if c else if ( type .eq. 5 ) then c c %-------------------------------% c | Perform y <-- OP*x | c | = inv[A-SIGMA*M]*A*x | c | B*x = A*x has been computed | c | and saved in workd(ipntr(3)). | c %-------------------------------% c call scopy (n, workd(ipntr(3)), 1, workd(ipntr(2)), 1) call sgbtrs('Notranspose', n, kl, ku, 1, rfac, lda, & iwork, workd(ipntr(2)), n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' _SBAND: Error with _gbtrs. ' print*, ' ' go to 9000 end if c else if ( type .eq. 6) then c c %---------------------------------% c | Perform y <-- OP*x | c | = inv[A-SIGMA*M]*(A+SIGMA*M)*x. | c | (M*x) has been saved in | c | workd(ipntr(3)). | c %---------------------------------% c if ( bmat .eq. 'G' ) then call sgbmv('Notranspose', n, n, kl, ku, one, & ab(itop,1), lda, workd(ipntr(1)), 1, & zero, workd(ipntr(2)), 1) call saxpy( n, sigma, workd(ipntr(3)), 1, & workd(ipntr(2)), 1 ) else call scopy (n, workd(ipntr(1)), 1, workd(ipntr(2)), 1) call sgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), & lda, workd(ipntr(1)), 1, sigma, & workd(ipntr(2)), 1) end if call sgbtrs('Notranspose', n, kl, ku, 1, rfac, lda, & iwork, workd(ipntr(2)), n, ierr) c end if c else if (ido .eq. 2) then c c %----------------------------------% c | Perform y <-- B*x | c | Note when Buckling mode is used, | c | B = A, otherwise B=M. | c %----------------------------------% c if (type .eq. 5) then c c %---------------------% c | Buckling Mode, B=A. | c %---------------------% c call sgbmv('Notranspose', n, n, kl, ku, one, & ab(itop,1), lda, workd(ipntr(1)), 1, & zero, workd(ipntr(2)), 1) else call sgbmv('Notranspose', n, n, kl, ku, one, & mb(itop,1), lda, workd(ipntr(1)), 1, & zero, workd(ipntr(2)), 1) end if c else c c %-----------------------------------------% c | Either we have convergence, or there is | c | error. | c %-----------------------------------------% c if ( info .lt. 0) then c c %--------------------------% c | Error message, check the | c | documentation in SSAUPD | c %--------------------------% c print *, ' ' print *, ' Error with _saupd info = ',info print *, ' Check the documentation of _saupd ' print *, ' ' go to 9000 c else c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c if (iparam(5) .gt. 0) then c call sseupd ( rvec, 'A', select, d, z, ldz, sigma, & bmat, n, which, nev, tol, resid, ncv, v, ldv, & iparam, ipntr, workd, workl, lworkl, info ) c if ( info .ne. 0) then c c %------------------------------------% c | Check the documentation of sneupd. | c %------------------------------------% c print *, ' ' print *, ' Error with _neupd = ', info print *, ' Check the documentation of _neupd ' print *, ' ' go to 9000 c end if c end if c end if c go to 9000 c end if c c %----------------------------------------% c | L O O P B A C K to call SSAUPD again. | c %----------------------------------------% c go to 90 c 9000 continue c end arpack-0.92.1/EXAMPLES/BAND/dnband.f0000644000175000017500000014547110776001577013332 00000000000000c \BeginDoc c c \Name: dnband c c \Description: c c This subroutine returns the converged approximations to eigenvalues c of A*z = lambda*B*z and (optionally): c c (1) The corresponding approximate eigenvectors; c c (2) An orthonormal basis for the associated approximate c invariant subspace; c c (3) Both. c c Matrices A and B are stored in LAPACK-style banded form. c c There is negligible additional cost to obtain eigenvectors. An orthonormal c basis is always computed. There is an additional storage cost of n*nev c if both are requested (in this case a separate array Z must be supplied). c c The approximate eigenvalues and vectors are commonly called Ritz c values and Ritz vectors respectively. They are referred to as such c in the comments that follow. The computed orthonormal basis for the c invariant subspace corresponding to these Ritz values is referred to as a c Schur basis. c c dnband can be called with one of the following modes: c c Mode 1: A*z = lambda*z. c ===> OP = A and B = I. c c Mode 2: A*z = lambda*M*z, M symmetric positive definite c ===> OP = inv[M]*A and B = M. c c Mode 3: A*z = lambda*M*z, M symmetric semi-definite c ===> OP = Real_Part{ inv[A - sigma*M]*M } and B = M. c ===> shift-and-invert mode (in real arithmetic) c If OP*z = amu*z, then c amu = 1/2 * [ 1/(lambda-sigma) + 1/(lambda-conjg(sigma)) ]. c Note: If sigma is real, i.e. imaginary part of sigma is zero; c Real_Part{ inv[A - sigma*M]*M } == inv[A - sigma*M]*M c amu == 1/(lambda-sigma). c c Mode 4: A*z = lambda*M*z, M symmetric semi-definite c ===> OP = Imaginary_Part{ inv[A - sigma*M]*M } and B = M. c ===> shift-and-invert mode (in real arithmetic) c If OP*z = amu*z, then c amu = 1/2i * [ 1/(lambda-sigma) - 1/(lambda-conjg(sigma)) ]. c c c The choice of mode must be specified in IPARAM(7) defined below. c c \Usage c call dnband c ( RVEC, HOWMNY, SELECT, DR, DI, Z, LDZ, SIGMAR, SIGMAI, c WORKEV, V, N, AB, MB, LDA, RFAC, CFAC, KL, KU, WHICH, c BMAT, NEV, TOL, RESID, NCV, V, LDV, IPARAM, WORKD, c WORKL, LWORKL, WORKC, IWORK, INFO ) c c \Arguments c c RVEC LOGICAL (INPUT) c Specifies whether a basis for the invariant subspace corresponding c to the converged Ritz value approximations for the eigenproblem c A*z = lambda*B*z is computed. c c RVEC = .FALSE. Compute Ritz values only. c c RVEC = .TRUE. Compute the Ritz vectors or Schur vectors. c See Remarks below. c c HOWMNY Character*1 (INPUT) c Specifies the form of the basis for the invariant subspace c corresponding to the converged Ritz values that is to be computed. c c = 'A': Compute NEV Ritz vectors; c = 'P': Compute NEV Schur vectors; c = 'S': compute some of the Ritz vectors, specified c by the logical array SELECT. c c SELECT Logical array of dimension NCV. (INPUT) c If HOWMNY = 'S', SELECT specifies the Ritz vectors to be c computed. To select the Ritz vector corresponding to a c Ritz value (DR(j), DI(j)), SELECT(j) must be set to .TRUE.. c If HOWMNY = 'A' or 'P', SELECT is used as internal workspace. c c DR Double precision array of dimension NEV+1. (OUTPUT) c On exit, DR contains the real part of the Ritz value approximations c to the eigenvalues of A*z = lambda*B*z. c c DI Double precision array of dimension NEV+1. (OUTPUT) c On exit, DI contains the imaginary part of the Ritz value c approximations to the eigenvalues of A*z = lambda*B*z associated c with DR. c c NOTE: When Ritz values are complex, they will come in complex c conjugate pairs. If eigenvectors are requested, the c corresponding Ritz vectors will also come in conjugate c pairs and the real and imaginary parts of these are c represented in two consecutive columns of the array Z c (see below). c c Z Real N by NEV+1 array if RVEC = .TRUE. and HOWMNY = 'A'. (OUTPUT) c On exit, c if RVEC = .TRUE. and HOWMNY = 'A', then the columns of c Z represent approximate eigenvectors (Ritz vectors) corresponding c to the NCONV=IPARAM(5) Ritz values for eigensystem c A*z = lambda*B*z computed by DNAUPD. c c The complex Ritz vector associated with the Ritz value c with positive imaginary part is stored in two consecutive c columns. The first column holds the real part of the Ritz c vector and the second column holds the imaginary part. The c Ritz vector associated with the Ritz value with negative c imaginary part is simply the complex conjugate of the Ritz vector c associated with the positive imaginary part. c c If RVEC = .FALSE. or HOWMNY = 'P', then Z is not referenced. c c NOTE: If if RVEC = .TRUE. and a Schur basis is not required, c the array Z may be set equal to first NEV+1 columns of the Arnoldi c basis array V computed by DNAUPD. In this case the Arnoldi basis c will be destroyed and overwritten with the eigenvector basis. c c LDZ Integer. (INPUT) c The leading dimension of the array Z. If Ritz vectors are c desired, then LDZ >= max( 1, N ). In any case, LDZ >= 1. c c SIGMAR Double precision (INPUT) c If IPARAM(7) = 3 or 4, represents the real part of the shift. c Not referenced if IPARAM(7) = 1 or 2. c c SIGMAI Double precision (INPUT) c If IPARAM(7) = 3 or 4, represents the imaginary part of the c shift. c Not referenced if IPARAM(7) = 1 or 2. c c WORKEV Double precision work array of dimension 3*NCV. (WORKSPACE) c c N Integer. (INPUT) c Dimension of the eigenproblem. c c AB Double precision array of dimension LDA by N. (INPUT) c The matrix A in band storage, in rows KL+1 to c 2*KL+KU+1; rows 1 to KL of the array need not be set. c The j-th column of A is stored in the j-th column of the c array AB as follows: c AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) c c MB Double precision array of dimension LDA by N. (INPUT) c The matrix M in band storage, in rows KL+1 to c 2*KL+KU+1; rows 1 to KL of the array need not be set. c The j-th column of M is stored in the j-th column of the c array AB as follows: c MB(kl+ku+1+i-j,j) = M(i,j) for max(1,j-ku)<=i<=min(m,j+kl) c Not referenced if IPARAM(7) = 1 c c LDA Integer. (INPUT) c Leading dimension of AB, MB, RFAC and CFAC. c c RFAC Double precision array of LDA by N. (WORKSPACE/OUTPUT) c RFAC is used to store the LU factors of MB when IPARAM(7) = 2 c is invoked. It is used to store the LU factors of c (A-sigma*M) when IPARAM(7) = 3 is invoked with a real shift. c It is not referenced when IPARAM(7) = 1 or 4. c c CFAC Complex*16 array of LDA by N. (WORKSPACE/OUTPUT) c CFAC is used to store (A-SIGMA*M) and its LU factors c when IPARAM(7) = 3 or 4 are used with a complex shift SIGMA. c On exit, it contains the LU factors of (A-SIGMA*M). c It is not referenced when IPARAM(7) = 1 or 2. c c KL Integer. (INPUT) c Max(number of subdiagonals of A, number of subdiagonals of M) c c KU Integer. (OUTPUT) c Max(number of superdiagonals of A, number of superdiagonals of M) c c WHICH Character*2. (INPUT) c When IPARAM(7)= 1 or 2, WHICH can be set to any one of c the following. c c 'LM' -> want the NEV eigenvalues of largest magnitude. c 'SM' -> want the NEV eigenvalues of smallest magnitude. c 'LR' -> want the NEV eigenvalues of largest real part. c 'SR' -> want the NEV eigenvalues of smallest real part. c 'LI' -> want the NEV eigenvalues of largest imaginary part. c 'SI' -> want the NEV eigenvalues of smallest imaginary part. c c When IPARAM(7) = 3 or 4, WHICH should be set to 'LM' only. c c BMAT Character*1. (INPUT) c BMAT specifies the type of the matrix B that defines the c semi-inner product for the operator OP. c BMAT = 'I' -> standard eigenvalue problem A*z = lambda*z c BMAT = 'G' -> generalized eigenvalue problem A*z = lambda*M*z c NEV Integer. (INPUT) c Number of eigenvalues to be computed. c c TOL Double precision scalar. (INPUT) c Stopping criteria: the relative accuracy of the Ritz value c is considered acceptable if BOUNDS(I) .LE. TOL*ABS(RITZ(I)). c If TOL .LE. 0. is passed a default is set: c DEFAULT = DLAMCH('EPS') (machine precision as computed c by the LAPACK auxiliary subroutine DLAMCH). c c RESID Double precision array of length N. (INPUT/OUTPUT) c On INPUT: c If INFO .EQ. 0, a random initial residual vector is used. c If INFO .NE. 0, RESID contains the initial residual vector, c possibly from a previous run. c On OUTPUT: c RESID contains the final residual vector. c c NCV Integer. (INPUT) c Number of columns of the matrix V (less than or equal to N). c Represents the dimension of the Arnoldi basis constructed c by dnaupd for OP. c c V Double precision array N by NCV+1. (OUTPUT) c Upon OUTPUT: If RVEC = .TRUE. the first NCONV=IPARAM(5) columns c represent approximate Schur vectors that span the c desired invariant subspace. c NOTE: The array Z may be set equal to first NEV+1 columns of the c Arnoldi basis vector array V computed by DNAUPD. In this case c if RVEC = .TRUE. and HOWMNY='A', then the first NCONV=IPARAM(5) c are the desired Ritz vectors. c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling c program. c c IPARAM Integer array of length 11. (INPUT/OUTPUT) c IPARAM(1) = ISHIFT: c The shifts selected at each iteration are used to restart c the Arnoldi iteration in an implicit fashion. c It is set to 1 in this subroutine. The user do not need c to set this parameter. c ---------------------------------------------------------- c ISHIFT = 1: exact shift with respect to the current c Hessenberg matrix H. This is equivalent to c restarting the iteration from the beginning c after updating the starting vector with a linear c combination of Ritz vectors associated with the c "wanted" eigenvalues. c ------------------------------------------------------------- c c IPARAM(2) = No longer referenced. c c IPARAM(3) = MXITER c On INPUT: max number of Arnoldi update iterations allowed. c On OUTPUT: actual number of Arnoldi update iterations taken. c c IPARAM(4) = NB: blocksize to be used in the recurrence. c The code currently works only for NB = 1. c c IPARAM(5) = NCONV: number of "converged" eigenvalues. c c IPARAM(6) = IUPD c Not referenced. Implicit restarting is ALWAYS used. c c IPARAM(7) = IPARAM(7): c On INPUT determines what type of eigenproblem is being solved. c Must be 1,2,3,4; See under \Description of dnband for the c four modes available. c c IPARAM(9) = NUMOP, IPARAM(10) = NUMOPB, IPARAM(11) = NUMREO, c OUTPUT: NUMOP = total number of OP*z operations, c NUMOPB = total number of B*z operations if BMAT='G', c NUMREO = total number of steps of re-orthogonalization. c c WORKD Double precision work array of length at least 3*n. (WORKSPACE) c c WORKL Double precision work array of length LWORKL. (WORKSPACE) c c LWORKL Integer. (INPUT) c LWORKL must be at least 3*NCV**2 + 6*NCV. c c WORKC Complex*16 array of length N. (WORKSPACE) c Workspace used when IPARAM(7) = 3 or 4 for storing a temporary c complex vector. c c IWORK Integer array of dimension at least N. (WORKSPACE) c Used when IPARAM(7)=2,3,4 to store the pivot information in the c factorization of M or (A-SIGMA*M). c c INFO Integer. (INPUT/OUTPUT) c Error flag on output. c = 0: Normal exit. c = 1: The Schur form computed by LAPACK routine dlahqr c could not be reordered by LAPACK routine dtrsen. c Re-enter subroutine DNEUPD with IPARAM(5)=NCV and c increase the size of the arrays DR and DI to have c dimension at least NCV and allocate at least NCV c columns for Z. NOTE: Not necessary if Z and V share c the same space. Please notify the authors. c c = -1: N must be positive. c = -2: NEV must be positive. c = -3: NCV-NEV >= 2 and less than or equal to N. c = -5: WHICH must be one of 'LM', 'SM', 'LR', 'SR', 'LI', 'SI' c = -6: BMAT must be one of 'I' or 'G'. c = -7: Length of private work WORKL array is not sufficient. c = -8: Error return from calculation of a real Schur form. c Informational error from LAPACK routine dlahqr. c = -9: Error return from calculation of eigenvectors. c Informational error from LAPACK routine dtrevc. c = -10: IPARAM(7) must be 1,2,3,4. c = -11: IPARAM(7) = 1 and BMAT = 'G' are incompatible. c = -12: HOWMNY = 'S' not yet implemented c = -13: HOWMNY must be one of 'A' or 'P' c = -14: DNAUPD did not find any eigenvalues to sufficient c accuracy. c = -15: Overflow occurs when we try to transform the Ritz c values returned from DNAUPD to those of the original c problem using Rayleigh Quotient. c = -9999: Could not build an Arnoldi factorization. c IPARAM(5) returns the size of the current c Arnoldi factorization. c c \EndDoc c c------------------------------------------------------------------------ c c\BeginLib c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly c Restarted Arnoldi Iteration", Ph.D thesis, TR95-13, Rice Univ, c May 1995. c c\Routines called: c dnaupd ARPACK reverse communication interface routine. c dneupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c dgbtrf LAPACK band matrix factorization routine. c dgbtrs LAPACK band linear system solve routine. c zgbtrf LAPACK complex band matrix factorization routine. c zgbtrs LAPACK complex linear system solve routine. c dlacpy LAPACK matrix copy routine. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c dlamch LAPACK routine to compute the underflow threshold. c dcopy Level 1 BLAS that copies one vector to another. c ddot Level 1 BLAS that computes the dot product of two vectors. c dnrm2 Level 1 BLAS that computes the norm of a vector. c dgbmv Level 2 BLAS that computes the band matrix vector product. c c\Remarks c c 1. Currently only HOWMNY = 'A' and 'P' are implemented. c c Let X' denote the transpose of X. c c 2. Schur vectors are an orthogonal representation for the basis of c Ritz vectors. Thus, their numerical properties are often superior. c If RVEC = .TRUE. then the relationship c A * V(:,1:IPARAM(5)) = V(:,1:IPARAM(5)) * T, and c V(:,1:IPARAM(5))' * V(:,1:IPARAM(5)) = I are approximately satisfied. c Here T is the leading submatrix of order IPARAM(5) of the real c upper quasi-triangular matrix stored workl(ipntr(12)). That is, c T is block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; c each 2-by-2 diagonal block has its diagonal elements equal and its c off-diagonal elements of opposite sign. Corresponding to each 2-by-2 c diagonal block is a complex conjugate pair of Ritz values. The real c Ritz values are stored on the diagonal of T. c c\Author c Danny Sorensen c Richard Lehoucq c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: nband.F SID: 2.3 DATE OF SID: 10/17/00 RELEASE: 2 c c\EndLib c c--------------------------------------------------------------------- c subroutine dnband( rvec, howmny, select, dr, di, z, ldz, sigmar, & sigmai, workev, n, ab, mb, lda, rfac, cfac, kl, ku, & which, bmat, nev, tol, resid, ncv, v, ldv, & iparam, workd, workl, lworkl, workc, iwork, info) c c %------------------% c | Scalar Arguments | c %------------------% c character which*2, bmat, howmny integer n, lda, kl, ku, nev, ncv, ldv, & ldz, lworkl, info Double precision & tol, sigmar, sigmai c c %-----------------% c | Array Arguments | c %-----------------% c integer iparam(*), iwork(*) logical select(*) Double precision & dr(*), di(*), resid(*), v(ldv,*), z(ldz,*), & ab(lda,*), mb(lda,*), rfac(lda,*), & workd(*), workl(*), workev(*) Complex*16 & cfac(lda,*), workc(*) c c %--------------% c | Local Arrays | c %--------------% c integer ipntr(14) c c %---------------% c | Local Scalars | c %---------------% c integer ido, i, j, type, imid, itop, ibot, ierr Double precision & numr, denr, deni, dmdul, safmin logical rvec, first c c %------------% c | Parameters | c %------------% c Double precision & one, zero parameter (one = 1.0D+0, zero = 0.0D+0) c c c %-----------------------------% c | LAPACK & BLAS routines used | c %-----------------------------% c Double precision & ddot, dnrm2, dlapy2, dlamch external ddot, dcopy, dgbmv, zgbtrf, zgbtrs, dgbtrf, & dgbtrs, dnrm2, dlapy2, dlacpy, dlamch c c %---------------------% c | Intrinsic Functions | c %---------------------% c Intrinsic dble, dimag, dcmplx c c %-----------------------% c | Executable Statements | c %-----------------------% c c %--------------------------------% c | safmin = safe minimum is such | c | that 1/sfmin does not overflow | c %--------------------------------% c safmin = dlamch('safmin') c c %----------------------------------------------------------------% c | Set type of the problem to be solved. Check consistency | c | between BMAT and IPARAM(7). | c | type = 1 --> Solving standard problem in regular mode. | c | type = 2 --> Solving standard problem in shift-invert mode. | c | type = 3 --> Solving generalized problem in regular mode. | c | type = 4 --> Solving generalized problem in shift-invert mode. | c | type = 5 --> Solving standard problem in shift-invert mode | c | using iparam(7) = 4 in DNAUPD. | c | type = 6 --> Solving generalized problem in shift-invert mode. | c | using iparam(7) = 4 in DNAUPD. | c %----------------------------------------------------------------% c if ( iparam(7) .eq. 1 ) then type = 1 else if ( iparam(7) .eq. 3 .and. bmat .eq. 'I') then type = 2 else if ( iparam(7) .eq. 2 ) then type = 3 else if ( iparam(7) .eq. 3 .and. bmat .eq. 'G') then type = 4 else if ( iparam(7) .eq. 4 .and. bmat .eq. 'I') then type = 5 else if ( iparam(7) .eq. 4 .and. bmat .eq. 'G') then type = 6 else print*, ' ' print*, 'BMAT is inconsistent with IPARAM(7).' print*, ' ' go to 9000 end if c c %----------------------------------% c | When type = 5,6 are used, sigmai | c | must be nonzero. | c %----------------------------------% c if ( type .eq. 5 .or. type .eq. 6 ) then if ( sigmai .eq. zero ) then print*, ' ' print*, '_NBAND: sigmai must be nonzero when type 5 or 6 & is used. ' print*, ' ' go to 9000 end if end if c c %------------------------% c | Initialize the reverse | c | communication flag. | c %------------------------% c ido = 0 c c %----------------% c | Exact shift is | c | used. | c %----------------% c iparam(1) = 1 c c %-----------------------------------% c | Both matrices A and M are stored | c | between rows itop and ibot. Imid | c | is the index of the row that | c | stores the diagonal elements. | c %-----------------------------------% c itop = kl + 1 imid = kl + ku + 1 ibot = 2*kl + ku + 1 c if ( type .eq. 2 .or. type .eq. 5 ) then c c %-------------------------------% c | Solving a standard eigenvalue | c | problem in shift-invert mode. | c | Factor (A-sigma*I). | c %-------------------------------% c if (sigmai .eq. zero) then c c %-----------------------------------% c | Construct (A-sigmar*I) and factor | c | in real arithmetic. | c %-----------------------------------% c call dlacpy ('A', ibot, n, ab, lda, rfac, lda ) do 10 j = 1, n rfac(imid,j) = ab(imid,j) - sigmar 10 continue call dgbtrf(n, n, kl, ku, rfac, lda, iwork, ierr ) if (ierr .ne. 0) then print*, ' ' print*, ' _NBAND: Error with _gbtrf. ' print*, ' ' go to 9000 end if c else c c %-----------------------------------% c | Construct (A-sigmar*I) and factor | c | in COMPLEX arithmetic. | c %-----------------------------------% c do 30 j = 1, n do 20 i = itop, ibot cfac(i,j) = dcmplx(ab(i,j)) 20 continue 30 continue c do 40 j = 1, n cfac(imid,j) = cfac(imid,j) $ - dcmplx(sigmar, sigmai) 40 continue c call zgbtrf(n, n, kl, ku, cfac, lda, iwork, ierr ) if ( ierr .ne. 0) then print*, ' ' print*, ' _NBAND: Error with _gbtrf. ' print*, ' ' go to 9000 end if c end if else if ( type .eq. 3 ) then c c %-----------------------------------------------% c | Solving generalized eigenvalue problem in | c | regular mode. Copy M to rfac, and call LAPACK | c | routine dgbtrf to factor M. | c %-----------------------------------------------% c call dlacpy ('A', ibot, n, mb, lda, rfac, lda ) call dgbtrf(n, n, kl, ku, rfac, lda, iwork, ierr) if (ierr .ne. 0) then print*, ' ' print*,'_NBAND: Error with _gbtrf.' print*, ' ' go to 9000 end if c else if ( type .eq. 4 .or. type .eq. 6 ) then c c %-------------------------------------------% c | Solving generalized eigenvalue problem in | c | shift-invert mode. | c %-------------------------------------------% c if ( sigmai .eq. zero ) then c c %--------------------------------------------% c | Construct (A - sigma*M) and factor in real | c | arithmetic. | c %--------------------------------------------% c do 60 j = 1,n do 50 i = itop, ibot rfac(i,j) = ab(i,j) - sigmar*mb(i,j) 50 continue 60 continue c call dgbtrf(n, n, kl, ku, rfac, lda, iwork, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, '_NBAND: Error with _gbtrf.' print*, ' ' go to 9000 end if c else c c %-----------------------------------------------% c | Construct (A - sigma*M) and factor in complex | c | arithmetic. | c %-----------------------------------------------% c do 80 j = 1,n do 70 i = itop, ibot cfac(i,j) = dcmplx( ab(i,j)-sigmar*mb(i,j), & -sigmai*mb(i,j) ) 70 continue 80 continue c call zgbtrf(n, n, kl, ku, cfac, lda, iwork, ierr) if ( ierr .NE. 0 ) then print*, ' ' print*, '_NBAND: Error with _gbtrf.' print*, ' ' go to 9000 end if c end if c end if c c %--------------------------------------------% c | M A I N L O O P (reverse communication) | c %--------------------------------------------% c 90 continue c call dnaupd ( ido, bmat, n, which, nev, tol, resid, ncv, & v, ldv, iparam, ipntr, workd, workl, lworkl, & info ) c if (ido .eq. -1) then c if ( type .eq. 1) then c c %----------------------------% c | Perform y <--- OP*x = A*x | c %----------------------------% c call dgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) c else if ( type .eq. 2 ) then c if (sigmai .eq. zero) then c c %----------------------------------% c | Shift is real. Perform | c | y <--- OP*x = inv[A-sigmar*I]*x | c | to force the starting vector | c | into the range of OP. | c %----------------------------------% c call dcopy (n, workd(ipntr(1)), 1, workd(ipntr(2)), 1) call dgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, & iwork, workd(ipntr(2)), n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' _NBAND: Error with _bgtrs. ' print*, ' ' go to 9000 end if c else c c %--------------------------------------------% c | Shift is COMPLEX. Perform | c | y <--- OP*x = Real_Part{inv[A-sigma*I]*x} | c | to force the starting vector into the | c | range of OP. | c %--------------------------------------------% c do 100 j = 1, n workc(j) = dcmplx(workd(ipntr(1)+j-1)) 100 continue c call zgbtrs ('Notranspose', n, kl, ku, 1, cfac, lda, & iwork, workc, n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' _NBAND: Error with _gbtrs. ' print*, ' ' go to 9000 end if c do 110 j = 1, n workd(ipntr(2)+j-1) = dble(workc(j)) 110 continue c end if c else if ( type .eq. 3 ) then c c %-----------------------------------% c | Perform y <--- OP*x = inv[M]*A*x | c | to force the starting vector into | c | the range of OP. | c %-----------------------------------% c call dgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) c call dgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, & iwork, workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_NBAND: Error with _bgtrs.' print*, ' ' go to 9000 end if c else if ( type .eq. 4 ) then c c %-----------------------------------------% c | Perform y <-- OP*x | c | = Real_part{inv[A-SIGMA*M]*M}*x | c | to force the starting vector into the | c | range of OP. | c %-----------------------------------------% c call dgbmv('Notranspose', n, n, kl, ku, one, mb(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) c if ( sigmai .eq. zero ) then c c %---------------------% c | Shift is real, stay | c | in real arithmetic. | c %---------------------% c call dgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, & iwork, workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_NBAND: Error with _gbtrs.' print*, ' ' go to 9000 end if c else c c %--------------------------% c | Goto complex arithmetic. | c %--------------------------% c do 120 i = 1,n workc(i) = dcmplx(workd(ipntr(2)+i-1)) 120 continue c call zgbtrs ('Notranspose', n, kl, ku, 1, cfac, lda, & iwork, workc, n, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_NBAND: Error with _gbtrs.' print*, ' ' go to 9000 end if c do 130 i = 1, n workd(ipntr(2)+i-1) = dble(workc(i)) 130 continue c end if c else if ( type .eq. 5) then c c %---------------------------------------% c | Perform y <-- OP*x | c | = Imaginary_part{inv[A-SIGMA*I]}*x | c | to force the starting vector into the | c | range of OP. | c %---------------------------------------% c do 140 j = 1, n workc(j) = dcmplx(workd(ipntr(1)+j-1)) 140 continue c call zgbtrs ('Notranspose', n, kl, ku, 1, cfac, lda, & iwork, workc, n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' _NBAND: Error with _gbtrs. ' print*, ' ' go to 9000 end if c do 150 j = 1, n workd(ipntr(2)+j-1) = dimag(workc(j)) 150 continue c else if ( type .eq. 6 ) then c c %----------------------------------------% c | Perform y <-- OP*x | c | Imaginary_part{inv[A-SIGMA*M]*M} | c | to force the starting vector into the | c | range of OP. | c %----------------------------------------% c call dgbmv('Notranspose', n, n, kl, ku, one, mb(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) c do 160 i = 1,n workc(i) = dcmplx(workd(ipntr(2)+i-1)) 160 continue c call zgbtrs ('Notranspose', n, kl, ku, 1, cfac, lda, & iwork, workc, n, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_NBAND: Error with _gbtrs.' print*, ' ' go to 9000 end if c do 170 i = 1, n workd(ipntr(2)+i-1) = dimag(workc(i)) 170 continue c end if c else if (ido .eq. 1) then c if ( type .eq. 1) then c c %----------------------------% c | Perform y <--- OP*x = A*x | c %----------------------------% c call dgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) c else if ( type .eq. 2) then c if ( sigmai .eq. zero) then c c %----------------------------------% c | Shift is real. Perform | c | y <--- OP*x = inv[A-sigmar*I]*x. | c %----------------------------------% c call dcopy (n, workd(ipntr(1)), 1, workd(ipntr(2)), 1) call dgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, & iwork, workd(ipntr(2)), n, ierr) else c c %------------------------------------------% c | Shift is COMPLEX. Perform | c | y <-- OP*x = Real_Part{inv[A-sigma*I]*x} | c | in COMPLEX arithmetic. | c %------------------------------------------% c do 180 j = 1, n workc(j) = dcmplx(workd(ipntr(1)+j-1)) 180 continue c call zgbtrs ('Notranspose', n, kl, ku, 1, cfac, lda, & iwork, workc, n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, '_NBAND: Error with _gbtrs.' print*, ' ' go to 9000 end if c do 190 j = 1, n workd(ipntr(2)+j-1) = dble(workc(j)) 190 continue c end if c else if ( type .eq. 3 ) then c c %-----------------------------------% c | Perform y <--- OP*x = inv[M]*A*x | c %-----------------------------------% c call dgbmv('Notranspose', n, n, kl, ku, one, ab(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) c call dgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, & iwork, workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_NBAND: Error with _bgtrs.' print*, ' ' go to 9000 end if c else if ( type .eq. 4 ) then c c %--------------------------------------% c | Perform y <-- inv(A-sigma*M)*(M*x). | c | (M*x) has been computed and stored | c | in workd(ipntr(3)). | c %--------------------------------------% c if ( sigmai .eq. zero ) then c c %------------------------% c | Shift is real, stay in | c | real arithmetic. | c %------------------------% c call dcopy(n, workd(ipntr(3)), 1, workd(ipntr(2)), 1) call dgbtrs ('Notranspose', n, kl, ku, 1, rfac, lda, & iwork, workd(ipntr(2)), n, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_NBAND: Error with _gbtrs.' print*, ' ' go to 9000 end if c else c c %---------------------------% c | Go to COMPLEX arithmetic. | c %---------------------------% c do 200 i = 1,n workc(i) = dcmplx(workd(ipntr(3)+i-1)) 200 continue c call zgbtrs ('Notranspose', n, kl, ku, 1, cfac, lda, & iwork, workc, n, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_NBAND: Error in _gbtrs.' print*, ' ' go to 9000 end if c do 210 i = 1,n workd(ipntr(2)+i-1) = dble(workc(i)) 210 continue c end if c else if ( type .eq. 5 ) then c c %---------------------------------------% c | Perform y <-- OP*x | c | = Imaginary_part{inv[A-SIGMA*I]*x} | c %---------------------------------------% c do 220 j = 1, n workc(j) = dcmplx(workd(ipntr(1)+j-1)) 220 continue c call zgbtrs ('Notranspose', n, kl, ku, 1, cfac, lda, & iwork, workc, n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' _NBAND: Error with _gbtrs. ' print*, ' ' go to 9000 end if c do 230 j = 1, n workd(ipntr(2)+j-1) = dimag(workc(j)) 230 continue c else if ( type .eq. 6) then c c %-----------------------------------------% c | Perform y <-- OP*x | c | = Imaginary_part{inv[A-SIGMA*M]*M}*x. | c %-----------------------------------------% c do 240 i = 1,n workc(i) = dcmplx(workd(ipntr(3)+i-1)) 240 continue c call zgbtrs ('Notranspose', n, kl, ku, 1, cfac, lda, & iwork, workc, n, ierr) if (ierr .ne. 0) then print*, ' ' print*, '_NBAND: Error with _gbtrs.' print*, ' ' go to 9000 end if c do 250 i = 1, n workd(ipntr(2)+i-1) = dimag(workc(i)) 250 continue c end if c else if (ido .eq. 2) then c c %--------------------% c | Perform y <-- M*x | c | Not used when | c | type = 1,2. | c %--------------------% c call dgbmv('Notranspose', n, n, kl, ku, one, mb(itop,1), & lda, workd(ipntr(1)), 1, zero, & workd(ipntr(2)), 1) c else c c %-----------------------------------------% c | Either we have convergence, or there is | c | error. | c %-----------------------------------------% c if ( info .lt. 0) then c c %--------------------------% c | Error message, check the | c | documentation in DNAUPD | c %--------------------------% c print *, ' ' print *, ' Error with _naupd info = ',info print *, ' Check the documentation of _naupd ' print *, ' ' go to 9000 c else c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c if (iparam(5) .gt. 0) then c call dneupd ( rvec, 'A', select, dr, di, z, ldz, & sigmar, sigmai, workev, bmat, n, which, & nev, tol, resid, ncv, v, ldv, iparam, & ipntr, workd, workl, lworkl, info ) c if ( info .ne. 0) then c c %------------------------------------% c | Check the documentation of DNEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _neupd = ', info print *, ' Check the documentation of _neupd ' print *, ' ' go to 9000 c else if ( sigmai .ne. zero ) then c if ( type .eq. 4 .or. type .eq. 6 ) then c first = .true. do 270 j = 1, iparam(5) c c %----------------------------------% c | Use Rayleigh Quotient to recover | c | eigenvalues of the original | c | generalized eigenvalue problem. | c %----------------------------------% c if ( di(j) .eq. zero ) then c c %--------------------------------------% c | Eigenvalue is real. Compute | c | d = (x'*inv[A-sigma*M]*M*x) / (x'*x) | c %--------------------------------------% c call dgbmv('Nontranspose', n, n, kl, ku, one, $ mb(itop,1), lda, z(1,j), 1, zero, $ workd, 1) do i = 1, n workc(i) = dcmplx(workd(i)) end do call zgbtrs ('Notranspose', n, kl, ku, 1, $ cfac, lda, iwork, workc, n, info) do i = 1, n workd(i) = dble(workc(i)) workd(i+n) = dimag(workc(i)) end do denr = ddot(n, z(1,j), 1, workd, 1) deni = ddot(n, z(1,j), 1, workd(n+1), 1) numr = dnrm2(n, z(1,j), 1)**2 dmdul = dlapy2(denr,deni)**2 if ( dmdul .ge. safmin ) then dr(j) = sigmar + numr*denr / dmdul else c c %---------------------% c | dmdul is too small. | c | Exit to avoid | c | overflow. | c %---------------------% c info = -15 go to 9000 end if c else if (first) then c c %------------------------% c | Eigenvalue is complex. | c | Compute the first one | c | of the conjugate pair. | c %------------------------% c c %-------------% c | Compute M*x | c %-------------% c call dgbmv('Nontranspose', n, n, kl, ku, $ one, mb(itop,1), lda, z(1,j), 1, zero, $ workd, 1) call dgbmv('Nontranspose', n, n, kl, ku, $ one, mb(itop,1), lda, z(1,j+1), 1, $ zero, workd(n+1), 1) do i = 1, n workc(i) = dcmplx(workd(i),workd(i+n)) end do c c %----------------------------% c | Compute inv(A-sigma*M)*M*x | c %----------------------------% c call zgbtrs('Notranspose',n,kl,ku,1,cfac, $ lda, iwork, workc, n, info) c c %-------------------------------% c | Compute x'*inv(A-sigma*M)*M*x | c %-------------------------------% c do i = 1, n workd(i) = dble(workc(i)) workd(i+n) = dimag(workc(i)) end do denr = ddot(n,z(1,j),1,workd,1) denr = denr+ddot(n,z(1,j+1),1,workd(n+1),1) deni = ddot(n,z(1,j),1,workd(n+1),1) deni = deni - ddot(n,z(1,j+1),1,workd,1) c c %----------------% c | Compute (x'*x) | c %----------------% c numr = dlapy2( dnrm2(n, z(1,j), 1), & dnrm2(n, z(1, j+1), 1) )**2 c c %----------------------------------------% c | Compute (x'x) / (x'*inv(A-sigma*M)*Mx) | c %----------------------------------------% c dmdul = dlapy2(denr,deni)**2 if ( dmdul .ge. safmin ) then dr(j) = sigmar+numr*denr / dmdul di(j) = sigmai-numr*deni / dmdul first = .false. else c c %---------------------% c | dmdul is too small. | c | Exit to avoid | c | overflow. | c %---------------------% c info = -15 go to 9000 c end if c else c c %---------------------------% c | Get the second eigenvalue | c | of the conjugate pair by | c | taking the conjugate of | c | previous one. | c %---------------------------% c dr(j) = dr(j-1) di(j) = -di(j-1) first = .true. c end if c 270 continue c else if ( type .eq. 2 .or. type .eq. 5) then c first = .true. do 280 j = 1, iparam(5) c c %----------------------------------% c | Use Rayleigh Quotient to recover | c | eigenvalues of the original | c | standard eigenvalue problem. | c %----------------------------------% c if ( di(j) .eq. zero ) then c c %-------------------------------------% c | Eigenvalue is real. Compute | c | d = (x'*inv[A-sigma*I]*x) / (x'*x). | c %-------------------------------------% c do i = 1, n workc(i) = dcmplx(z(i,j)) end do call zgbtrs ('Notranspose', n, kl, ku, 1, $ cfac, lda, iwork, workc, n, info) do i = 1, n workd(i) = dble(workc(i)) workd(i+n) = dimag(workc(i)) end do denr = ddot(n,z(1,j),1,workd,1) deni = ddot(n,z(1,j),1,workd(n+1),1) numr = dnrm2(n, z(1,j), 1)**2 dmdul = dlapy2(denr,deni)**2 if ( dmdul .ge. safmin ) then dr(j) = sigmar + numr*denr / dmdul else c c %---------------------% c | dmdul is too small. | c | Exit to avoid | c | overflow. | c %---------------------% c info = -15 go to 9000 c end if c else if (first) then c c %------------------------% c | Eigenvalue is complex. | c | Compute the first one | c | of the conjugate pair. | c %------------------------% c do i = 1, n workc(i) = dcmplx( z(i,j), z(i,j+1) ) end do c c %---------------------------% c | Compute inv[A-sigma*I]*x. | c %---------------------------% c call zgbtrs('Notranspose',n,kl,ku,1,cfac, $ lda, iwork, workc, n, info) c c %-----------------------------% c | Compute x'*inv(A-sigma*I)*x | c %-----------------------------% c do i = 1, n workd(i) = dble(workc(i)) workd(i+n) = dimag(workc(i)) end do denr = ddot(n,z(1,j),1,workd,1) denr = denr+ddot(n,z(1,j+1),1,workd(n+1),1) deni = ddot(n,z(1,j),1,workd(n+1),1) deni = deni - ddot(n,z(1,j+1),1,workd,1) c c %----------------% c | Compute (x'*x) | c %----------------% c numr = dlapy2( dnrm2(n, z(1,j), 1), & dnrm2(n, z(1,j+1), 1))**2 c c %----------------------------------------% c | Compute (x'x) / (x'*inv(A-sigma*I)*x). | c %----------------------------------------% c dmdul = dlapy2(denr,deni)**2 if (dmdul .ge. safmin) then dr(j) = sigmar+numr*denr / dmdul di(j) = sigmai-numr*deni / dmdul first = .false. else c c %---------------------% c | dmdul is too small. | c | Exit to avoid | c | overflow. | c %---------------------% c info = -15 go to 9000 end if c else c c %---------------------------% c | Get the second eigenvalue | c | of the conjugate pair by | c | taking the conjugate of | c | previous one. | c %---------------------------% c dr(j) = dr(j-1) di(j) = -di(j-1) first = .true. c end if c 280 continue c end if c end if c end if c end if c go to 9000 c end if c c %----------------------------------------% c | L O O P B A C K to call DNAUPD again. | c %----------------------------------------% c go to 90 c 9000 continue c end arpack-0.92.1/EXAMPLES/BAND/snbdr1.f0000644000175000017500000002733610776001577013274 00000000000000 program snbdr1 c c ... Construct the matrix A in LAPACK-style band form. c The matrix A is derived from the discretization of c the 2-d convection-diffusion operator c c -Laplacian(u) + rho*partial(u)/partial(x). c c on the unit square with zero Dirichlet boundary condition c using standard central difference. c c ... Call SNBAND to find eigenvalues LAMBDA such that c A*x = LAMBDA*x. c c ... Use mode 1 of SNAUPD. c c\BeginLib c c snband ARPACK banded eigenproblem solver. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c slaset LAPACK routine to initialize a matrix to zero. c saxpy Level 1 BLAS that computes y <- alpha*x+y. c snrm2 Level 1 BLAS that computes the norm of a vector. c sgbmv Level 2 BLAS that computes the band matrix vector product c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: nbdr1.F SID: 2.5 DATE OF SID: 08/26/96 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c---------------------------------------------------------------------- c c %-------------------------------------% c | Define leading dimensions for all | c | arrays. | c | MAXN - Maximum size of the matrix | c | MAXNEV - Maximum number of | c | eigenvalues to be computed | c | MAXNCV - Maximum number of Arnoldi | c | vectors stored | c | MAXBDW - Maximum bandwidth | c %-------------------------------------% c integer maxn, maxnev, maxncv, maxbdw, lda, & lworkl, ldv parameter ( maxn = 1000, maxnev = 25, maxncv=50, & maxbdw=50, lda = maxbdw, ldv = maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), iwork(maxn) logical select(maxncv) Real & a(lda,maxn), m(lda,maxn), rfac(lda,maxn), & workl(3*maxncv*maxncv+6*maxncv), workd(3*maxn), & workev(3*maxncv), v(ldv, maxncv), & resid(maxn), d(maxncv, 3), ax(maxn) Complex & cfac(lda, maxn), workc(maxn) c c %---------------% c | Local Scalars | c %---------------% c character which*2, bmat integer nev, ncv, ku, kl, info, i, j, ido, & n, nx, lo, isub, isup, idiag, mode, maxitr, & nconv logical rvec, first Real & tol, rho, h, h2, sigmar, sigmai c c %------------% c | Parameters | c %------------% c Real & one, zero, two parameter (one = 1.0E+0 , zero = 0.0E+0 , & two = 2.0E+0 ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & slapy2, snrm2 external slapy2, snrm2, sgbmv, saxpy c c %--------------------% c | Intrinsic function | c %--------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------------------------% c | The number NX is the number of interior points | c | in the discretization of the 2-dimensional | c | convection-diffusion operator on the unit | c | square with zero Dirichlet boundary condition. | c | The number N(=NX*NX) is the dimension of the | c | matrix. A standard eigenvalue problem is | c | solved (BMAT = 'I'). NEV is the number of | c | eigenvalues to be approximated. The user can | c | modify NX, NEV, NCV, WHICH to solve problems of | c | different sizes, and to get different parts the | c | spectrum. However, The following conditions | c | must be satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 2 <= NCV <= MAXNCV | c %-------------------------------------------------% c nx = 10 n = nx*nx nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _NBDR1: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NBDR1: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NBDR1: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'I' which = 'SM' c c %-----------------------------------------------------% c | The work array WORKL is used in SNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in SNAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = 3*ncv**2+6*ncv tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 1 of SNAUPD is used | c | (IPARAM(7) = 1). All these options can be changed | c | by the user. For details, see the documentation | c | in SNBAND. | c %---------------------------------------------------% c maxitr = 300 mode = 1 c iparam(3) = maxitr iparam(7) = mode c c %----------------------------------------% c | Construct the matrix A in LAPACK-style | c | banded form. | c %----------------------------------------% c c %---------------------------------------------% c | Zero out the workspace for banded matrices. | c %---------------------------------------------% c call slaset('A', lda, n, zero, zero, a, lda) call slaset('A', lda, n, zero, zero, m, lda) call slaset('A', lda, n, zero, zero, rfac, lda) c c %-------------------------------------% c | KU, KL are number of superdiagonals | c | and subdiagonals within the band of | c | matrices A and M. | c %-------------------------------------% c kl = nx ku = nx c c %---------------% c | Main diagonal | c %---------------% c h = one / real (nx+1) h2 = h*h c idiag = kl+ku+1 do 30 j = 1, n a(idiag,j) = 4.0E+0 / h2 30 continue c c %-------------------------------------% c | First subdiagonal and superdiagonal | c %-------------------------------------% c rho = 1.0E+2 isup = kl+ku isub = kl+ku+2 do 50 i = 1, nx lo = (i-1)*nx do 40 j = lo+1, lo+nx-1 a(isup,j+1) = -one/h2 + rho/two/h a(isub,j) = -one/h2 - rho/two/h 40 continue 50 continue c c %------------------------------------% c | KL-th subdiagonal and KU-th super- | c | diagonal. | c %------------------------------------% c isup = kl+1 isub = 2*kl+ku+1 do 80 i = 1, nx-1 lo = (i-1)*nx do 70 j = lo+1, lo+nx a(isup,nx+j) = -one / h2 a(isub,j) = -one / h2 70 continue 80 continue c c %------------------------------------------------% c | Call ARPACK banded solver to find eigenvalues | c | and eigenvectors. The real parts of the | c | eigenvalues are returned in the first column | c | of D, the imaginary parts are returned in the | c | second column of D. Eigenvectors are returned | c | in the first NCONV (=IPARAM(5)) columns of V. | c %------------------------------------------------% c rvec = .true. call snband(rvec, 'A', select, d, d(1,2), v, ldv, sigmar, sigmai, & workev, n, a, m, lda, rfac, cfac, kl, ku, which, & bmat, nev, tol, resid, ncv, v, ldv, iparam, workd, & workl, lworkl, workc, iwork, info) c if ( info .eq. 0) then c c %-----------------------------------% c | Print out convergence information | c %-----------------------------------% c nconv = iparam(5) c print *, ' ' print *, ' _NBDR1 ' print *, ' ====== ' print *, ' ' print *, ' The size of the matrix is ', n print *, ' Number of eigenvalue requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' The number of converged Ritz values is ', & nconv print *, ' What portion of the spectrum ', which print *, ' The number of Implicit Arnoldi ', & ' update taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence tolerance is ', tol print *, ' ' c c %----------------------------% c | Compute the residual norm. | c | || A*x - lambda*x || | c %----------------------------% c first = .true. do 90 j = 1, nconv c if ( d(j,2) .eq. zero ) then c c %--------------------% c | Ritz value is real | c %--------------------% c call sgbmv('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call saxpy(n, -d(j,1), v(1,j), 1, ax, 1) d(j,3) = snrm2(n, ax, 1) d(j,3) = d(j,3) / abs(d(j,1)) c else if ( first ) then c c %------------------------% c | Ritz value is complex | c | Residual of one Ritz | c | value of the conjugate | c | pair is computed. | c %------------------------% c call sgbmv('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call saxpy(n, -d(j,1), v(1,j), 1, ax, 1) call saxpy(n, d(j,2), v(1,j+1), 1, ax, 1) d(j,3) = snrm2(n, ax, 1) call sgbmv('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j+1), 1, zero, & ax, 1) call saxpy(n, -d(j,2), v(1,j), 1, ax, 1) call saxpy(n, -d(j,1), v(1,j+1), 1, ax, 1) d(j,3) = slapy2( d(j,3), snrm2(n, ax, 1) ) d(j,3) = d(j,3) / slapy2(d(j,1),d(j,2)) d(j+1,3) = d(j,3) first = .false. else first = .true. end if c 90 continue call smout(6, nconv, 3, d, maxncv, -6, & 'Ritz values (Real,Imag) and relative residuals') else c c %-------------------------------------% c | Either convergence failed, or there | c | is error. Check the documentation | c | for SNBAND. | c %-------------------------------------% c print *, ' ' print *, ' Error with _nband, info= ', info print *, ' Check the documentation of _nband ' print *, ' ' c end if c 9000 end arpack-0.92.1/EXAMPLES/BAND/ssbdr4.f0000644000175000017500000002331410776001577013274 00000000000000 program ssbdr4 c c ... Construct the matrix A in LAPACK-style band form. c The matrix A is the 1-dimensional discrete Laplacian on [0,1] c with zero Dirichlet boundary condition, M is the mass c formed by using piecewise linear elements on [0,1]. c c ... Call SSBAND with shift-invert mode to find eigenvalues LAMBDA c closest to SIGMA such that c A*x = LAMBDA*M*x. c c ... Use mode 3 of SSAUPD. c c\BeginLib c c\Routines called: c ssband ARPACK banded eigenproblem solver. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c slaset LAPACK routine to initialize a matrix to zero. c saxpy Level 1 BLAS that computes y <- alpha*x+y. c snrm2 Level 1 BLAS that computes the norm of a vector. c sgbmv Level 2 BLAS that computes the band matrix vector product c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: sbdr4.F SID: 2.5 DATE OF SID: 08/26/96 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c---------------------------------------------------------------------- c c %-------------------------------------% c | Define leading dimensions for all | c | arrays. | c | MAXN - Maximum size of the matrix | c | MAXNEV - Maximum number of | c | eigenvalues to be computed | c | MAXNCV - Maximum number of Arnoldi | c | vectors stored | c | MAXBDW - Maximum bandwidth | c %-------------------------------------% c integer maxn, maxnev, maxncv, maxbdw, lda, & lworkl, ldv parameter ( maxn = 1000, maxnev = 25, maxncv=50, & maxbdw=50, lda = maxbdw, ldv = maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), iwork(maxn) logical select(maxncv) Real & a(lda,maxn), m(lda,maxn), rfac(lda,maxn), & workl(maxncv*maxncv+8*maxncv), workd(3*maxn), & v(ldv, maxncv), resid(maxn), d(maxncv, 2), & ax(maxn), mx(maxn) c c %---------------% c | Local Scalars | c %---------------% c character which*2, bmat integer nev, ncv, ku, kl, info, j, ido, & n, isub, isup, idiag, maxitr, mode, nconv Real & tol, h, sigma, r1, r2 logical rvec c c %------------% c | Parameters | c %------------% c Real & one, zero, two, four, six parameter (one = 1.0E+0 , zero = 0.0E+0 , two = 2.0E+0 , & four = 4.0E+0 , six = 6.0E+0 ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & slapy2, snrm2 external slapy2, snrm2, saxpy, sgbmv c c %-----------------------% c | Executable Statements | c %-----------------------% c c %--------------------------------------------------% c | The number N is the dimension of the matrix. A | c | generalized eigenvalue problem is solved | c | (BMAT = 'G'). NEV is the number of eigenvalues | c | (closest to the shift SIGMA) to be approximated. | c | Since the shift and invert mode is used, WHICH | c | is set to 'LM'. The user can modify N, NEV, NCV | c | and SIGMA to solve problems of different sizes, | c | and to get different parts the spectrum. | c | However, the following conditions must be | c | satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 1 <= NCV <= MAXNCV | c %--------------------------------------------------% c n = 100 nev = 4 ncv = 10 if ( n .gt. maxn ) then print *, ' ERROR with _SBDR4: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _SBDR4: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _SBDR4: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' sigma = zero c c %-----------------------------------------------------% c | The work array WORKL is used in SSAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in SSAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = ncv**2+8*ncv tol = zero ido = 0 info = 0 c c %---------------------------------------------------% c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 3 of SSAUPD is used | c | (IPARAM(7) = 3). All these options can be changed | c | by the user. For details, see the documentation | c | in SSBAND. | c %---------------------------------------------------% c maxitr = 300 mode = 3 c iparam(3) = maxitr iparam(7) = mode c c %----------------------------------------% c | Construct the matrix A in LAPACK-style | c | banded form. | c %----------------------------------------% c c %---------------------------------------------% c | Zero out the workspace for banded matrices. | c %---------------------------------------------% c call slaset('A', lda, n, zero, zero, a, lda) call slaset('A', lda, n, zero, zero, m, lda) call slaset('A', lda, n, zero, zero, rfac, lda) c c %-------------------------------------% c | KU, KL are number of superdiagonals | c | and subdiagonals within the band of | c | matrices A and M. | c %-------------------------------------% c kl = 1 ku = 1 c c %---------------% c | Main diagonal | c %---------------% c h = one / real (n+1) r1 = four / six idiag = kl+ku+1 do 30 j = 1, n a(idiag,j) = two / h m(idiag,j) = r1 * h 30 continue c c %-------------------------------------% c | First subdiagonal and superdiagonal | c %-------------------------------------% c r2 = one / six isup = kl+ku isub = kl+ku+2 do 60 j = 1, n-1 a(isup,j+1) = -one / h a(isub,j) = -one / h m(isup,j+1) = r2 * h m(isub,j) = r2 * h 60 continue c c %-------------------------------------% c | Call SSBAND to find eigenvalues and | c | eigenvectors. Eigenvalues are | c | returned in the first column of D. | c | Eigenvectors are returned in the | c | first NCONV (=IPARAM(5)) columns of | c | V. | c %-------------------------------------% c rvec = .true. call ssband( rvec, 'A', select, d, v, ldv, sigma, n, a, m, & lda, rfac, kl, ku, which, bmat, nev, tol, & resid, ncv, v, ldv, iparam, workd, workl, lworkl, & iwork, info) c if ( info .eq. 0) then c nconv = iparam(5) c c %-----------------------------------% c | Print out convergence information | c %-----------------------------------% c print *, ' ' print *, ' _SBDR4 ' print *, ' ====== ' print *, ' ' print *, ' The size of the matrix is ', n print *, ' Number of eigenvalue requested is ', nev print *, ' The number of Lanczos vectors generated', & ' (NCV) is ', ncv print *, ' The number of converged Ritz values is ', & nconv print *, ' What portion of the spectrum ', which print *, ' The number of Implicit Arnoldi', & ' update taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence tolerance is ', tol print *, ' ' c c %----------------------------% c | Compute the residual norm. | c | || A*x - lambda*x || | c %----------------------------% c do 90 j = 1, nconv call sgbmv('Notranspose', n, n, kl, ku, one, & a(kl+1,1), lda, v(1,j), 1, zero, & ax, 1) call sgbmv('Notranspose', n, n, kl, ku, one, & m(kl+1,1), lda, v(1,j), 1, zero, & mx, 1) call saxpy(n, -d(j,1), mx, 1, ax, 1) d(j,2) = snrm2(n, ax, 1) d(j,2) = d(j,2) / abs(d(j,1)) c 90 continue call smout(6, nconv, 2, d, maxncv, -6, & 'Ritz values and relative residuals') else c c %-------------------------------------% c | Either convergence failed, or there | c | is error. Check the documentation | c | for SSBAND. | c %-------------------------------------% c print *, ' ' print *, ' Error with _sband, info= ', info print *, ' Check the documentation of _sband ' print *, ' ' c end if c 9000 end arpack-0.92.1/EXAMPLES/COMPLEX/0000755000175000017500000000000010776001577012404 500000000000000arpack-0.92.1/EXAMPLES/COMPLEX/zndrv2.f0000644000175000017500000003520410776001577013724 00000000000000 program zndrv2 c c Simple program to illustrate the idea of reverse communication c in shift-invert mode for a standard complex nonsymmetric eigenvalue c problem. c c We implement example two of ex-complex.doc in DOCUMENTS directory c c\Example-2 c ... Suppose we want to solve A*x = lambda*x in shift-invert mode, c where A is derived from the central difference discretization c of the 1-dimensional convection-diffusion operator c (d^2u/dx^2) + rho*(du/dx) c on the interval [0,1] with zero Dirichlet boundary condition. c ... The shift sigma is a complex number. c c ... OP = inv[A-sigma*I] and B = I. c c ... Use mode 3 of ZNAUPD . c c\BeginLib c c\Routines called: c znaupd ARPACK reverse communication interface routine. c zneupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c zgttrf LAPACK tridiagonal factorization routine. c zgttrs LAPACK tridiagonal solve routine. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c zaxpy Level 1 BLAS that computes y <- alpha*x+y. c zcopy Level 1 BLAS that copies one vector to another. c dznrm2 Level 1 BLAS that computes the norm of a vector. c av Matrix vector multiplication routine that computes A*x. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: ndrv2.F SID: 2.6 DATE OF SID: 10/18/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c-------------------------------------------------------------------------- c c %-----------------------------% c | Define leading dimensions | c | for all arrays. | c | MAXN: Maximum dimension | c | of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %-----------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=10, maxncv=25, & ldv=maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), ipntr(14), ipiv(maxn) logical select(maxncv) Complex*16 & ax(maxn), d(maxncv), resid(maxn), & v(ldv, maxncv), workd(3*maxn), & workev(2*maxncv), & workl(3*maxncv*maxncv+5*maxncv), & dd(maxn), dl(maxn), du(maxn), & du2(maxn) Double precision & rwork(maxn), rd(maxncv,3) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nev, ncv, lworkl, info, j, ierr, & nconv, maxitr, ishfts, mode Complex*16 & h, h2, s, sigma, s1, s2, s3, rho common /convct/ rho c Double precision & tol logical rvec c c %------------% c | Parameters | c %------------% c Complex*16 & one, zero, two parameter (one = (1.0D+0, 0.0D+0) , & zero = (0.0D+0, 0.0D+0) , & two = (2.0D+0, 0.0D+0) ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & dznrm2 , dlapy2 external zgttrf , zgttrs , zaxpy , zcopy , dznrm2 , & dlapy2 c c %-----------------------% c | Executable statements | c %-----------------------% c c %--------------------------------------------------% c | The number N is the dimension of the matrix. A | c | standard eigenvalue problem is solved (BMAT = | c | 'I'). NEV is the number of eigenvalues (closest | c | to the shift SIGMA) to be approximated. Since | c | the shift-invert mode is used, WHICH is set to | c | 'LM'. The user can modify NEV, NCV, SIGMA to | c | solve problems of different sizes, and to get | c | different parts of the spectrum. However, The | c | following conditions must be satisfied: | c | N <= MAXN, | c | NEV <= MAXNEV, | c | NEV + 2 <= NCV <= MAXNCV | c %--------------------------------------------------% c n = 100 nev = 4 ncv = 20 if ( n .gt. maxn ) then print *, ' ERROR with _NDRV2: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NDRV2: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NDRV2: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'I' which = 'LM' sigma = zero c c %----------------------------------------------------% c | Construct C = A - SIGMA*I, factor C in complex | c | arithmetic (using LAPACK subroutine zgttrf ). The | c | matrix A is chosen to be the tridiagonal matrix | c | derived from standard central difference of the | c | 1-d convection diffusion operator - u``+ rho*u` on | c | the interval [0, 1] with zero Dirichlet boundary | c | condition. | c %----------------------------------------------------% c rho = (1.0D+1, 0.0D+0) h = one / dcmplx (n+1) h2 = h*h s = rho / two c s1 = -one/h2 - s/h s2 = two/h2 - sigma s3 = -one/h2 + s/h c do 10 j = 1, n-1 dl(j) = s1 dd(j) = s2 du(j) = s3 10 continue dd(n) = s2 c call zgttrf (n, dl, dd, du, du2, ipiv, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrf in _NDRV2.' print*, ' ' go to 9000 end if c c %-----------------------------------------------------% c | The work array WORKL is used in ZNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in ZNAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = 3*ncv**2+5*ncv tol = 0.0 ido = 0 info = 0 c c %---------------------------------------------------% c | This program uses exact shifts with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 3 of ZNAUPD is used | c | (IPARAM(7) = 3). All these options can be | c | changed by the user. For details see the | c | documentation in ZNAUPD . | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 3 c iparam(1) = ishfts iparam(3) = maxitr iparam(7) = mode c c %-------------------------------------------% c | M A I N L O O P (Reverse communication) | c %-------------------------------------------% c 20 continue c c %---------------------------------------------% c | Repeatedly call the routine ZNAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call znaupd ( ido, bmat, n, which, nev, tol, resid, ncv, & v, ldv, iparam, ipntr, workd, workl, lworkl, & rwork,info ) c if (ido .eq. -1 .or. ido .eq. 1 ) then c c %-------------------------------------------% c | Perform y <--- OP*x = inv[A-SIGMA*I]*x | c | The user should supply his/her own linear | c | system solver here that takes | c | workd(ipntr(1)) as the input, and returns | c | the result to workd(ipntr(2)). | c %-------------------------------------------% c call zcopy ( n, workd(ipntr(1)),1, workd(ipntr(2)), 1) c call zgttrs ('N', n, 1, dl, dd, du, du2, ipiv, & workd(ipntr(2)), n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrs in _NDRV2.' print*, ' ' go to 9000 end if c c %-----------------------------------------% c | L O O P B A C K to call ZNAUPD again. | c %-----------------------------------------% c go to 20 c end if c c %-----------------------------------------% c | Either we have convergence, or there is | c | an error. | c %-----------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message, check the | c | documentation in ZNAUPD | c %--------------------------% c print *, ' ' print *, ' Error with _naupd, info = ',info print *, ' Check the documentation in _naupd.' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using ZNEUPD . | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may also be computed now if | c | desired. (indicated by rvec = .true.) | c %-------------------------------------------% c rvec = .true. c call zneupd (rvec, 'A', select, d, v, ldv, sigma, & workev, bmat, n, which, nev, tol, & resid, ncv, v, ldv, iparam, ipntr, workd, & workl, lworkl, rwork, ierr) c c %----------------------------------------------% c | Eigenvalues are returned in the one | c | dimensional array D. The corresponding | c | eigenvectors are returned in the first NCONV | c | (=IPARAM(5)) columns of the two dimensional | c | array V if requested. Otherwise, an | c | orthogonal basis for the invariant subspace | c | corresponding to the eigenvalues in D is | c | returned in V. | c %----------------------------------------------% c if ( ierr .ne. 0) then c c %------------------------------------% c | Error condition: | c | Check the documentation of ZNEUPD . | c %------------------------------------% c print *, ' ' print *, ' Error with _neupd, info = ', ierr print *, ' Check the documentation of _neupd. ' print *, ' ' else c nconv = iparam(5) do 60 j=1, nconv c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c call av(n, v(1,j), ax) call zaxpy (n, -d(j), v(1,j), 1, ax, 1) rd(j,1) = dble (d(j)) rd(j,2) = dimag (d(j)) rd(j,3) = dznrm2 (n, ax, 1) rd(j,3) = rd(j,3) / dlapy2 (rd(j,1),rd(j,2)) 60 continue c c %-----------------------------% c | Display computed residuals. | c %-----------------------------% c call dmout (6, nconv, 3, rd, maxncv, -6, & 'Ritz values (Real, Imag) and relative residuals') c end if c c %-------------------------------------------% c | Print additional convergence information. | c %-------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, '_NDRV2 ' print *, '====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program zndrv2 . | c %---------------------------% c 9000 continue c end c c------------------------------------------------------------------- c c matrix vector multiplication subroutine c subroutine av (n, v, w) integer n, j Complex*16 & v(n), w(n), rho, two, one, dd, dl, du, s, h, & h2 parameter (one = (1.0D+0, 0.0D+0) , & two = (2.0D+0, 0.0D+0) ) common /convct/ rho c h = one / dcmplx (n+1) h2 = h*h s = rho / two dd = two / h2 dl = -one/h2 - s/h du = -one/h2 + s/h c w(1) = dd*v(1) + du*v(2) do 10 j = 2,n-1 w(j) = dl*v(j-1) + dd*v(j) + du*v(j+1) 10 continue w(n) = dl*v(n-1) + dd*v(n) return end arpack-0.92.1/EXAMPLES/COMPLEX/makefile0000644000175000017500000000321410776001577014024 00000000000000# # makefile to run simple examples of the reverse communication # protocol. # # Modify if ALIBS library was built somewhere else. # # If ALIBS (defined in ../../ARmake.inc) contains the BLAS and LAPACK # libraries installed on your system, you DO NOT need to change this # makefile. OTHERWISE, you may need to modify the Makefile in the top level # ARPACK directory tree to include cdrv and/or zdrv in the # definition of the PRECISION variable, and issue 'make lib' from there. # For example: # # PRECISION = single double sdrv ddrv # #\SCCS Information: @(#) # FILE: makefile SID: 2.2 DATE OF SID: 9/24/96 RELEASE: 2 # include ../../ARmake.inc # # Issue "complex" to make all 8 complex drivers. # Issue "cndrv" to make 4 single precision complex drivers. # Issue "zndrv" to make 4 double precision complex drivers. # complex: cndrv zndrv #----------------------------------------------------------------------- # Complex problem using single complex # cndrv: cndrv1 cndrv2 cndrv3 cndrv4 cndrv1: cndrv1.o $(FC) $(FFLAGS) cndrv1.o $(ALIBS) -o cndrv1 # cndrv2: cndrv2.o $(FC) $(FFLAGS) cndrv2.o $(ALIBS) -o cndrv2 # cndrv3: cndrv3.o $(FC) $(FFLAGS) cndrv3.o $(ALIBS) -o cndrv3 # cndrv4: cndrv4.o $(FC) $(FFLAGS) cndrv4.o $(ALIBS) -o cndrv4 # #---------------------------------------------------------------------- # Complex problem using double complex # zndrv: zndrv1 zndrv2 zndrv3 zndrv4 zndrv1: zndrv1.o $(FC) $(FFLAGS) zndrv1.o $(ALIBS) -o zndrv1 # zndrv2: zndrv2.o $(FC) $(FFLAGS) zndrv2.o $(ALIBS) -o zndrv2 # zndrv3: zndrv3.o $(FC) $(FFLAGS) zndrv3.o $(ALIBS) -o zndrv3 # zndrv4: zndrv4.o $(FC) $(FFLAGS) zndrv4.o $(ALIBS) -o zndrv4 arpack-0.92.1/EXAMPLES/COMPLEX/README0000644000175000017500000000271210776001577013206 000000000000001. Purpose ------- This directory contains example drivers that call ARPACK subroutines [c,z]naupd.f and [c,z]neupd.f to solve COMPLEX eigenvalue problems using regular, inverse or shift-invert modes. These drivers illustrate how to set various ARPACK parameters to solve different problems in different modes. They provide a guideline on how to use ARPACK's reverse communication interface. The user may modify any one of these drivers, and provide his/her own matrix vector multiplication routine to solve the problem of his/her own interest. 2. Naming convention ----------------- The name for each driver has the form 'XndrvN.f', where X - is 'c' (single precision complex) or 'z' (double precision complex) N - is a number between 1 and 4. If N = 1, the driver solves a STANDARD eigenvalue problem in REGULAR mode N = 2, the driver solves a STANDARD eigenvalue problem in SHIFT-INVERT mode. N = 3, the driver solves a GENERALIZED eigenvalue problem in INVERSE mode N = 4, the driver solves a GENERALIZED eigenvalue problem in SHIFT-INVERT mode. For shift-invert modes (N=2,4), the user needs to provide a complex linear system solver to perform y=inv[A-sigma*B]*x. 3. Usage ----- To run these drivers, you may use the makefile in this directory and issue, for example, "make cndrv1". Then execute using "cndrv1". arpack-0.92.1/EXAMPLES/COMPLEX/zndrv4.f0000644000175000017500000004221010776001577013721 00000000000000 program zndrv4 c c Simple program to illustrate the idea of reverse communication c in shift and invert mode for a generalized complex nonsymmetric c eigenvalue problem. c c We implement example four of ex-complex.doc in DOCUMENTS directory c c\Example-4 c ... Suppose we want to solve A*x = lambda*B*x in shift-invert mode, c where A and B are derived from a finite element discretization c of a 1-dimensional convection-diffusion operator c (d^2u/dx^2) + rho*(du/dx) c on the interval [0,1] with zero boundary condition using c piecewise linear elements. c c ... where the shift sigma is a complex number. c c ... OP = inv[A-SIGMA*M]*M and B = M. c c ... Use mode 3 of ZNAUPD . c c\BeginLib c c\Routines called: c znaupd ARPACK reverse communication interface routine. c zneupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c zgttrf LAPACK tridiagonal factorization routine. c zgttrs LAPACK tridiagonal solve routine. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c zaxpy Level 1 BLAS that computes y <- alpha*x+y. c zcopy Level 1 BLAS that copies one vector to another. c dznrm2 Level 1 BLAS that computes the norm of a complex vector. c av Matrix vector multiplication routine that computes A*x. c mv Matrix vector multiplication routine that computes M*x. c c\Author c Danny Sorensen c Richard Lehoucq c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: ndrv4.F SID: 2.4 DATE OF SID: 10/18/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c----------------------------------------------------------------------- c c %-----------------------------% c | Define leading dimensions | c | for all arrays. | c | MAXN: Maximum dimension | c | of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %-----------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=10, maxncv=25, & ldv=maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), ipntr(14), ipiv(maxn) logical select(maxncv) Complex*16 & ax(maxn), mx(maxn), d(maxncv), & v(ldv,maxncv), workd(3*maxn), resid(maxn), & workev(2*maxncv), & workl(3*maxncv*maxncv+5*maxncv), & dd(maxn), dl(maxn), du(maxn), & du2(maxn) Double precision & rwork(maxn), rd(maxncv,3) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nev, ncv, lworkl, info, j, ierr, & nconv, maxitr, ishfts, mode Complex*16 & rho, h, s, & sigma, s1, s2, s3 common /convct/ rho c Double precision & tol logical rvec c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & dznrm2 , dlapy2 external dznrm2 , zaxpy , zcopy , zgttrf , zgttrs , & dlapy2 c c %------------% c | Parameters | c %------------% c Complex*16 & one, zero, two, four, six parameter (one = (1.0D+0, 0.0D+0) , & zero = (0.0D+0, 0.0D+0) , & two = (2.0D+0, 0.0D+0) , & four = (4.0D+0, 0.0D+0) , & six = (6.0D+0, 0.0D+0) ) c c %-----------------------% c | Executable statements | c %-----------------------% c c %----------------------------------------------------% c | The number N is the dimension of the matrix. A | c | generalized eigenvalue problem is solved (BMAT = | c | 'G'). NEV is the number of eigenvalues (closest | c | to SIGMAR) to be approximated. Since the | c | shift-invert mode is used, WHICH is set to 'LM'. | c | The user can modify NEV, NCV, SIGMA to solve | c | problems of different sizes, and to get different | c | parts of the spectrum. However, The following | c | conditions must be satisfied: | c | N <= MAXN, | c | NEV <= MAXNEV, | c | NEV + 2 <= NCV <= MAXNCV | c %----------------------------------------------------% c n = 100 nev = 4 ncv = 20 if ( n .gt. maxn ) then print *, ' ERROR with _NDRV4: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NDRV4: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NDRV4: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' sigma = one c c %--------------------------------------------------% c | Construct C = A - SIGMA*M in COMPLEX arithmetic. | c | Factor C in COMPLEX arithmetic (using LAPACK | c | subroutine zgttrf ). The matrix A is chosen to be | c | the tridiagonal matrix derived from the standard | c | central difference discretization of the 1-d | c | convection-diffusion operator u``+ rho*u` on the | c | interval [0, 1] with zero Dirichlet boundary | c | condition. The matrix M is chosen to be the | c | symmetric tridiagonal matrix with 4.0 on the | c | diagonal and 1.0 on the off-diagonals. | c %--------------------------------------------------% c rho = (1.0D+1, 0.0D+0) h = one / dcmplx (n+1) s = rho / two c s1 = -one/h - s - sigma*h/six s2 = two/h - four*sigma*h/six s3 = -one/h + s - sigma*h/six c do 10 j = 1, n-1 dl(j) = s1 dd(j) = s2 du(j) = s3 10 continue dd(n) = s2 c call zgttrf (n, dl, dd, du, du2, ipiv, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrf in _NDRV4.' print*, ' ' go to 9000 end if c c %-----------------------------------------------------% c | The work array WORKL is used in ZNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in ZNAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = 3*ncv**2+5*ncv tol = 0.0 ido = 0 info = 0 c c %---------------------------------------------------% c | This program uses exact shifts with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 3 of ZNAUPD is used | c | (IPARAM(7) = 3). All these options can be | c | changed by the user. For details see the | c | documentation in ZNAUPD . | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 3 c iparam(1) = ishfts iparam(3) = maxitr iparam(7) = mode c c %------------------------------------------% c | M A I N L O O P(Reverse communication) | c %------------------------------------------% c 20 continue c c %---------------------------------------------% c | Repeatedly call the routine ZNAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call znaupd ( ido, bmat, n, which, nev, tol, resid, ncv, & v, ldv, iparam, ipntr, workd, workl, lworkl, & rwork, info ) c if (ido .eq. -1) then c c %-------------------------------------------% c | Perform y <--- OP*x = inv[A-SIGMA*M]*M*x | c | to force starting vector into the range | c | of OP. The user should supply his/her | c | own matrix vector multiplication routine | c | and a linear system solver. The matrix | c | vector multiplication routine should take | c | workd(ipntr(1)) as the input. The final | c | result should be returned to | c | workd(ipntr(2)). | c %-------------------------------------------% c call mv (n, workd(ipntr(1)), workd(ipntr(2))) call zgttrs ('N', n, 1, dl, dd, du, du2, ipiv, & workd(ipntr(2)), n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrs in _NDRV4.' print*, ' ' go to 9000 end if c c %-----------------------------------------% c | L O O P B A C K to call ZNAUPD again. | c %-----------------------------------------% c go to 20 c else if ( ido .eq. 1) then c c %-----------------------------------------% c | Perform y <-- OP*x = inv[A-sigma*M]*M*x | c | M*x has been saved in workd(ipntr(3)). | c | The user only need the linear system | c | solver here that takes workd(ipntr(3)) | c | as input, and returns the result to | c | workd(ipntr(2)). | c %-----------------------------------------% c call zcopy ( n, workd(ipntr(3)), 1, workd(ipntr(2)), 1) call zgttrs ('N', n, 1, dl, dd, du, du2, ipiv, & workd(ipntr(2)), n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrs in _NDRV4.' print*, ' ' go to 9000 end if c c %-----------------------------------------% c | L O O P B A C K to call ZNAUPD again. | c %-----------------------------------------% c go to 20 c else if ( ido .eq. 2) then c c %---------------------------------------------% c | Perform y <--- M*x | c | Need matrix vector multiplication routine | c | here that takes workd(ipntr(1)) as input | c | and returns the result to workd(ipntr(2)). | c %---------------------------------------------% c call mv (n, workd(ipntr(1)), workd(ipntr(2))) c c %-----------------------------------------% c | L O O P B A C K to call ZNAUPD again. | c %-----------------------------------------% c go to 20 c end if c c %-----------------------------------------% c | Either we have convergence, or there is | c | an error. | c %-----------------------------------------% c if ( info .lt. 0 ) then c c %----------------------------% c | Error message, check the | c | documentation in ZNAUPD | c %----------------------------% c print *, ' ' print *, ' Error with _naupd, info = ', info print *, ' Check the documentation of _naupd.' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using ZNEUPD . | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may also be computed now if | c | desired. (indicated by rvec = .true.) | c %-------------------------------------------% c rvec = .true. c call zneupd (rvec, 'A', select, d, v, ldv, sigma, & workev, bmat, n, which, nev, tol, resid, ncv, v, & ldv, iparam, ipntr, workd, workl, lworkl, rwork, & ierr) c c %----------------------------------------------% c | Eigenvalues are returned in the one | c | dimensional array D. The corresponding | c | eigenvectors are returned in the first NCONV | c | (=IPARAM(5)) columns of the two dimensional | c | array V if requested. Otherwise, an | c | orthogonal basis for the invariant subspace | c | corresponding to the eigenvalues in D is | c | returned in V. | c %----------------------------------------------% c if ( ierr .ne. 0) then c c %------------------------------------% c | Error condition: | c | Check the documentation of ZNEUPD . | c %------------------------------------% c print *, ' ' print *, ' Error with _neupd, info = ', ierr print *, ' Check the documentation of _neupd. ' print *, ' ' c else c nconv = iparam(5) do 80 j=1, nconv c call av(n, v(1,j), ax) call mv(n, v(1,j), mx) call zaxpy (n, -d(j), mx, 1, ax, 1) rd(j,1) = dble (d(j)) rd(j,2) = dimag (d(j)) rd(j,3) = dznrm2 (n, ax, 1) rd(j,3) = rd(j,3) / dlapy2 (rd(j,1),rd(j,2)) 80 continue c c %-----------------------------% c | Display computed residuals. | c %-----------------------------% c call dmout (6, nconv, 3, rd, maxncv, -6, & 'Ritz values (Real, Imag) and direct residuals') c end if c c %-------------------------------------------% c | Print additional convergence information. | c %-------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, '_NDRV4 ' print *, '====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c 9000 continue c end c c========================================================================== c c matrix vector multiplication subroutine c subroutine mv (n, v, w) integer n, j Complex*16 & v(n), w(n), one, four, six, h parameter (one = (1.0D+0, 0.0D+0) , & four = (4.0D+0, 0.0D+0) , & six = (6.0D+0, 0.0D+0) ) c c Compute the matrix vector multiplication y<---M*x c where M is a n by n symmetric tridiagonal matrix with 4 on the c diagonal, 1 on the subdiagonal and superdiagonal. c w(1) = ( four*v(1) + one*v(2) ) / six do 40 j = 2,n-1 w(j) = ( one*v(j-1) + four*v(j) + one*v(j+1) ) / six 40 continue w(n) = ( one*v(n-1) + four*v(n) ) / six c h = one / dcmplx (n+1) call zscal (n, h, w, 1) return end c------------------------------------------------------------------ subroutine av (n, v, w) integer n, j Complex*16 & v(n), w(n), one, two, dd, dl, du, s, h, rho parameter (one = (1.0D+0, 0.0D+0) , & two = (2.0D+0, 0.0D+0) ) common /convct/ rho c h = one / dcmplx (n+1) s = rho / two dd = two / h dl = -one/h - s du = -one/h + s c w(1) = dd*v(1) + du*v(2) do 40 j = 2,n-1 w(j) = dl*v(j-1) + dd*v(j) + du*v(j+1) 40 continue w(n) = dl*v(n-1) + dd*v(n) return end arpack-0.92.1/EXAMPLES/COMPLEX/cndrv3.f0000644000175000017500000003673410776001577013707 00000000000000 program cndrv3 c c Simple program to illustrate the idea of reverse communication c in inverse mode for a generalized complex nonsymmetric eigenvalue c problem. c c We implement example three of ex-complex.doc in DOCUMENTS directory c c\Example-3 c ... Suppose we want to solve A*x = lambda*B*x in regular mode, c where A and B are derived from the finite element discretization c of the 1-dimensional convection-diffusion operator c (d^2u/dx^2) + rho*(du/dx) c on the interval [0,1] with zero boundary condition using c piecewise linear elements. c c ... OP = inv[M]*A and B = M. c c ... Use mode 2 of CNAUPD. c c\BeginLib c c\Routines called: c cnaupd ARPACK reverse communication interface routine. c cneupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c cgttrf LAPACK tridiagonal factorization routine. c cgttrs LAPACK tridiagonal solve routine. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c caxpy Level 1 BLAS that computes y <- alpha*x+y. c scnrm2 Level 1 BLAS that computes the norm of a vector. c av Matrix vector multiplication routine that computes A*x. c mv Matrix vector multiplication routine that computes M*x. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: ndrv3.F SID: 2.4 DATE OF SID: 10/18/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c-------------------------------------------------------------------------- c c %-----------------------------% c | Define leading dimensions | c | for all arrays. | c | MAXN: Maximum dimension | c | of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %-----------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=10, maxncv=25, & ldv=maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), ipntr(14), ipiv(maxn) logical select(maxncv) Complex & ax(maxn), mx(maxn), d(maxncv), resid(maxn), & v(ldv,maxncv), workd(3*maxn), & workev(2*maxncv), & workl(3*maxncv*maxncv+5*maxncv), & dd(maxn), dl(maxn), du(maxn), du2(maxn) Real & rwork(maxn), rd(maxncv,3) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nev, ncv, lworkl, info, ierr, j, & nconv, maxitr, ishfts, mode Complex & sigma, h Real & tol logical rvec c c %------------% c | Parameters | c %------------% c Complex & zero, one parameter (zero = (0.0E+0, 0.0E+0) , & one = (1.0E+0, 0.0E+0) ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & scnrm2, slapy2 external caxpy, ccopy, scnrm2, cgttrf, cgttrs, & slapy2 c c %-----------------------% c | Executable Statements | c %-----------------------% c c %----------------------------------------------------% c | The number N is the dimension of the matrix. A | c | generalized eigenvalue problem is solved (BMAT = | c | 'G'). NEV is the number of eigenvalues to be | c | approximated. The user can modify NEV, NCV, WHICH | c | to solve problems of different sizes, and to get | c | different parts of the spectrum. However, The | c | following conditions must be satisfied: | c | N <= MAXN, | c | NEV <= MAXNEV, | c | NEV + 2 <= NCV <= MAXNCV | c %----------------------------------------------------% c n = 100 nev = 4 ncv = 20 if ( n .gt. maxn ) then print *, ' ERROR with _NDRV3: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NDRV3: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NDRV3: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' sigma = zero c c %-----------------------------------------------------% c | The matrix M is chosen to be the symmetric tri- | c | diagonal matrix with 4 on the diagonal and 1 on the | c | off diagonals. It is factored by LAPACK subroutine | c | cgttrf. | c %-----------------------------------------------------% c h = one / cmplx(n+1) do 20 j = 1, n-1 dl(j) = one*h dd(j) = (4.0E+0, 0.0E+0) *h du(j) = one*h 20 continue dd(n) = (4.0E+0, 0.0E+0) *h c call cgttrf(n, dl, dd, du, du2, ipiv, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrf. ' print*, ' ' go to 9000 end if c c %-----------------------------------------------------% c | The work array WORKL is used in CNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in CNAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = 3*ncv**2+5*ncv tol = 0.0 ido = 0 info = 0 c c %---------------------------------------------------% c | This program uses exact shifts with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 2 of CNAUPD is used | c | (IPARAM(7) = 2). All these options can be | c | changed by the user. For details, see the | c | documentation in CNAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 2 c iparam(1) = ishfts iparam(3) = maxitr iparam(7) = mode c c %-------------------------------------------% c | M A I N L O O P (Reverse communication) | c %-------------------------------------------% c 10 continue c c %---------------------------------------------% c | Repeatedly call the routine CNAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call cnaupd ( ido, bmat, n, which, nev, tol, resid, ncv, & v, ldv, iparam, ipntr, workd, workl, lworkl, & rwork, info ) c if (ido .eq. -1 .or. ido .eq. 1) then c c %----------------------------------------% c | Perform y <--- OP*x = inv[M]*A*x | c | The user should supply his/her own | c | matrix vector routine and a linear | c | system solver. The matrix-vector | c | subroutine should take workd(ipntr(1)) | c | as input, and the final result should | c | be returned to workd(ipntr(2)). | c %----------------------------------------% c call av (n, workd(ipntr(1)), workd(ipntr(2))) call cgttrs('N', n, 1, dl, dd, du, du2, ipiv, & workd(ipntr(2)), n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrs. ' print*, ' ' go to 9000 end if c c %-----------------------------------------% c | L O O P B A C K to call CNAUPD again. | c %-----------------------------------------% c go to 10 c else if ( ido .eq. 2) then c c %-------------------------------------% c | Perform y <--- M*x | c | The matrix vector multiplication | c | routine should take workd(ipntr(1)) | c | as input and return the result to | c | workd(ipntr(2)). | c %-------------------------------------% c call mv (n, workd(ipntr(1)), workd(ipntr(2))) c c %-----------------------------------------% c | L O O P B A C K to call CNAUPD again. | c %-----------------------------------------% c go to 10 c end if c c %-----------------------------------------% c | Either we have convergence, or there is | c | an error. | c %-----------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message. Check the | c | documentation in CNAUPD. | c %--------------------------% c print *, ' ' print *, ' Error with _naupd, info = ',info print *, ' Check the documentation of _naupd.' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using CNEUPD. | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may also be computed now if | c | desired. (indicated by rvec = .true.) | c %-------------------------------------------% c rvec = .true. c call cneupd ( rvec, 'A', select, d, v, ldv, sigma, & workev, bmat, n, which, nev, tol, resid, ncv, v, & ldv, iparam, ipntr, workd, workl, lworkl, rwork, & ierr ) c c %----------------------------------------------% c | Eigenvalues are returned in the one | c | dimensional array D. The corresponding | c | eigenvectors are returned in the first NCONV | c | (=IPARAM(5)) columns of the two dimensional | c | array V if requested. Otherwise, an | c | orthogonal basis for the invariant subspace | c | corresponding to the eigenvalues in D is | c | returned in V. | c %----------------------------------------------% c if ( ierr .ne. 0 ) then c c %------------------------------------% c | Error condition: | c | Check the documentation of CNEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _neupd, info = ', ierr print *, ' Check the documentation of _neupd' print *, ' ' c else c nconv = iparam(5) do 80 j=1, nconv c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*M*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c call av(n, v(1,j), ax) call mv(n, v(1,j), mx) call caxpy(n, -d(j), mx, 1, ax, 1) rd(j,1) = real (d(j)) rd(j,2) = aimag(d(j)) rd(j,3) = scnrm2(n, ax, 1) rd(j,3) = rd(j,3) / slapy2(rd(j,1),rd(j,2)) 80 continue c c %-----------------------------% c | Display computed residuals. | c %-----------------------------% c call smout(6, nconv, 3, rd, maxncv, -6, & 'Ritz values (Real, Imag) and relative residuals') c end if c c %------------------------------------------% c | Print additional convergence information | c %------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, '_NDRV3 ' print *, '====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated ', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c 9000 continue c end c c========================================================================== c c matrix vector multiplication subroutine c subroutine av (n, v, w) integer n, j Complex & v(n), w(n), one, two, dd, dl, du, s, h, rho parameter (one = (1.0E+0, 0.0E+0) , & two = (2.0E+0, 0.0E+0) , & rho = (1.0E+1, 0.0E+0) ) c c Compute the matrix vector multiplication y<---A*x c where A is the stiffness matrix formed by using piecewise linear c elements on [0,1]. c h = one / cmplx(n+1) s = rho / two dd = two / h dl = -one/h - s du = -one/h + s c w(1) = dd*v(1) + du*v(2) do 10 j = 2,n-1 w(j) = dl*v(j-1) + dd*v(j) + du*v(j+1) 10 continue w(n) = dl*v(n-1) + dd*v(n) return end c------------------------------------------------------------------------ subroutine mv (n, v, w) integer n, j Complex & v(n), w(n), one, four, h parameter (one = (1.0E+0, 0.0E+0) , & four = (4.0E+0, 0.0E+0) ) c c Compute the matrix vector multiplication y<---M*x c where M is the mass matrix formed by using piecewise linear elements c on [0,1]. c w(1) = four*v(1) + one*v(2) do 10 j = 2,n-1 w(j) = one*v(j-1) + four*v(j) + one*v(j+1) 10 continue w(n) = one*v(n-1) + four*v(n) c h = one / cmplx(n+1) call cscal(n, h, w, 1) return end arpack-0.92.1/EXAMPLES/COMPLEX/zndrv3.f0000644000175000017500000003707310776001577013733 00000000000000 program zndrv3 c c Simple program to illustrate the idea of reverse communication c in inverse mode for a generalized complex nonsymmetric eigenvalue c problem. c c We implement example three of ex-complex.doc in DOCUMENTS directory c c\Example-3 c ... Suppose we want to solve A*x = lambda*B*x in regular mode, c where A and B are derived from the finite element discretization c of the 1-dimensional convection-diffusion operator c (d^2u/dx^2) + rho*(du/dx) c on the interval [0,1] with zero boundary condition using c piecewise linear elements. c c ... OP = inv[M]*A and B = M. c c ... Use mode 2 of ZNAUPD . c c\BeginLib c c\Routines called: c znaupd ARPACK reverse communication interface routine. c zneupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c zgttrf LAPACK tridiagonal factorization routine. c zgttrs LAPACK tridiagonal solve routine. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c zaxpy Level 1 BLAS that computes y <- alpha*x+y. c dznrm2 Level 1 BLAS that computes the norm of a vector. c av Matrix vector multiplication routine that computes A*x. c mv Matrix vector multiplication routine that computes M*x. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: ndrv3.F SID: 2.4 DATE OF SID: 10/18/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c-------------------------------------------------------------------------- c c %-----------------------------% c | Define leading dimensions | c | for all arrays. | c | MAXN: Maximum dimension | c | of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %-----------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=10, maxncv=25, & ldv=maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), ipntr(14), ipiv(maxn) logical select(maxncv) Complex*16 & ax(maxn), mx(maxn), d(maxncv), resid(maxn), & v(ldv,maxncv), workd(3*maxn), & workev(2*maxncv), & workl(3*maxncv*maxncv+5*maxncv), & dd(maxn), dl(maxn), du(maxn), du2(maxn) Double precision & rwork(maxn), rd(maxncv,3) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nev, ncv, lworkl, info, ierr, j, & nconv, maxitr, ishfts, mode Complex*16 & sigma, h Double precision & tol logical rvec c c %------------% c | Parameters | c %------------% c Complex*16 & zero, one parameter (zero = (0.0D+0, 0.0D+0) , & one = (1.0D+0, 0.0D+0) ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & dznrm2 , dlapy2 external zaxpy , zcopy , dznrm2 , zgttrf , zgttrs , & dlapy2 c c %-----------------------% c | Executable Statements | c %-----------------------% c c %----------------------------------------------------% c | The number N is the dimension of the matrix. A | c | generalized eigenvalue problem is solved (BMAT = | c | 'G'). NEV is the number of eigenvalues to be | c | approximated. The user can modify NEV, NCV, WHICH | c | to solve problems of different sizes, and to get | c | different parts of the spectrum. However, The | c | following conditions must be satisfied: | c | N <= MAXN, | c | NEV <= MAXNEV, | c | NEV + 2 <= NCV <= MAXNCV | c %----------------------------------------------------% c n = 100 nev = 4 ncv = 20 if ( n .gt. maxn ) then print *, ' ERROR with _NDRV3: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NDRV3: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NDRV3: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' sigma = zero c c %-----------------------------------------------------% c | The matrix M is chosen to be the symmetric tri- | c | diagonal matrix with 4 on the diagonal and 1 on the | c | off diagonals. It is factored by LAPACK subroutine | c | zgttrf . | c %-----------------------------------------------------% c h = one / dcmplx (n+1) do 20 j = 1, n-1 dl(j) = one*h dd(j) = (4.0D+0, 0.0D+0) *h du(j) = one*h 20 continue dd(n) = (4.0D+0, 0.0D+0) *h c call zgttrf (n, dl, dd, du, du2, ipiv, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrf. ' print*, ' ' go to 9000 end if c c %-----------------------------------------------------% c | The work array WORKL is used in ZNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in ZNAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = 3*ncv**2+5*ncv tol = 0.0 ido = 0 info = 0 c c %---------------------------------------------------% c | This program uses exact shifts with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 2 of ZNAUPD is used | c | (IPARAM(7) = 2). All these options can be | c | changed by the user. For details, see the | c | documentation in ZNAUPD . | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 2 c iparam(1) = ishfts iparam(3) = maxitr iparam(7) = mode c c %-------------------------------------------% c | M A I N L O O P (Reverse communication) | c %-------------------------------------------% c 10 continue c c %---------------------------------------------% c | Repeatedly call the routine ZNAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call znaupd ( ido, bmat, n, which, nev, tol, resid, ncv, & v, ldv, iparam, ipntr, workd, workl, lworkl, & rwork, info ) c if (ido .eq. -1 .or. ido .eq. 1) then c c %----------------------------------------% c | Perform y <--- OP*x = inv[M]*A*x | c | The user should supply his/her own | c | matrix vector routine and a linear | c | system solver. The matrix-vector | c | subroutine should take workd(ipntr(1)) | c | as input, and the final result should | c | be returned to workd(ipntr(2)). | c %----------------------------------------% c call av (n, workd(ipntr(1)), workd(ipntr(2))) call zgttrs ('N', n, 1, dl, dd, du, du2, ipiv, & workd(ipntr(2)), n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrs. ' print*, ' ' go to 9000 end if c c %-----------------------------------------% c | L O O P B A C K to call ZNAUPD again. | c %-----------------------------------------% c go to 10 c else if ( ido .eq. 2) then c c %-------------------------------------% c | Perform y <--- M*x | c | The matrix vector multiplication | c | routine should take workd(ipntr(1)) | c | as input and return the result to | c | workd(ipntr(2)). | c %-------------------------------------% c call mv (n, workd(ipntr(1)), workd(ipntr(2))) c c %-----------------------------------------% c | L O O P B A C K to call ZNAUPD again. | c %-----------------------------------------% c go to 10 c end if c c %-----------------------------------------% c | Either we have convergence, or there is | c | an error. | c %-----------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message. Check the | c | documentation in ZNAUPD . | c %--------------------------% c print *, ' ' print *, ' Error with _naupd, info = ',info print *, ' Check the documentation of _naupd.' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using ZNEUPD . | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may also be computed now if | c | desired. (indicated by rvec = .true.) | c %-------------------------------------------% c rvec = .true. c call zneupd ( rvec, 'A', select, d, v, ldv, sigma, & workev, bmat, n, which, nev, tol, resid, ncv, v, & ldv, iparam, ipntr, workd, workl, lworkl, rwork, & ierr ) c c %----------------------------------------------% c | Eigenvalues are returned in the one | c | dimensional array D. The corresponding | c | eigenvectors are returned in the first NCONV | c | (=IPARAM(5)) columns of the two dimensional | c | array V if requested. Otherwise, an | c | orthogonal basis for the invariant subspace | c | corresponding to the eigenvalues in D is | c | returned in V. | c %----------------------------------------------% c if ( ierr .ne. 0 ) then c c %------------------------------------% c | Error condition: | c | Check the documentation of ZNEUPD . | c %------------------------------------% c print *, ' ' print *, ' Error with _neupd, info = ', ierr print *, ' Check the documentation of _neupd' print *, ' ' c else c nconv = iparam(5) do 80 j=1, nconv c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*M*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c call av(n, v(1,j), ax) call mv(n, v(1,j), mx) call zaxpy (n, -d(j), mx, 1, ax, 1) rd(j,1) = dble (d(j)) rd(j,2) = dimag (d(j)) rd(j,3) = dznrm2 (n, ax, 1) rd(j,3) = rd(j,3) / dlapy2 (rd(j,1),rd(j,2)) 80 continue c c %-----------------------------% c | Display computed residuals. | c %-----------------------------% c call dmout (6, nconv, 3, rd, maxncv, -6, & 'Ritz values (Real, Imag) and relative residuals') c end if c c %------------------------------------------% c | Print additional convergence information | c %------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, '_NDRV3 ' print *, '====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated ', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c 9000 continue c end c c========================================================================== c c matrix vector multiplication subroutine c subroutine av (n, v, w) integer n, j Complex*16 & v(n), w(n), one, two, dd, dl, du, s, h, rho parameter (one = (1.0D+0, 0.0D+0) , & two = (2.0D+0, 0.0D+0) , & rho = (1.0D+1, 0.0D+0) ) c c Compute the matrix vector multiplication y<---A*x c where A is the stiffness matrix formed by using piecewise linear c elements on [0,1]. c h = one / dcmplx (n+1) s = rho / two dd = two / h dl = -one/h - s du = -one/h + s c w(1) = dd*v(1) + du*v(2) do 10 j = 2,n-1 w(j) = dl*v(j-1) + dd*v(j) + du*v(j+1) 10 continue w(n) = dl*v(n-1) + dd*v(n) return end c------------------------------------------------------------------------ subroutine mv (n, v, w) integer n, j Complex*16 & v(n), w(n), one, four, h parameter (one = (1.0D+0, 0.0D+0) , & four = (4.0D+0, 0.0D+0) ) c c Compute the matrix vector multiplication y<---M*x c where M is the mass matrix formed by using piecewise linear elements c on [0,1]. c w(1) = four*v(1) + one*v(2) do 10 j = 2,n-1 w(j) = one*v(j-1) + four*v(j) + one*v(j+1) 10 continue w(n) = one*v(n-1) + four*v(n) c h = one / dcmplx (n+1) call zscal (n, h, w, 1) return end arpack-0.92.1/EXAMPLES/COMPLEX/zndrv1.f0000644000175000017500000003520510776001577013724 00000000000000 program zndrv1 c c Example program to illustrate the idea of reverse communication c for a standard complex nonsymmetric eigenvalue problem. c c We implement example one of ex-complex.doc in DOCUMENTS directory c c\Example-1 c ... Suppose we want to solve A*x = lambda*x in regular mode, c where A is obtained from the standard central difference c discretization of the convection-diffusion operator c (Laplacian u) + rho*(du / dx) c on the unit squre [0,1]x[0,1] with zero Dirichlet boundary c condition. c c ... OP = A and B = I. c c ... Assume "call av (nx,x,y)" computes y = A*x c c ... Use mode 1 of ZNAUPD . c c\BeginLib c c\Routines called c znaupd ARPACK reverse communication interface routine. c zneupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c dznrm2 Level 1 BLAS that computes the norm of a complex vector. c zaxpy Level 1 BLAS that computes y <- alpha*x+y. c av Matrix vector multiplication routine that computes A*x. c tv Matrix vector multiplication routine that computes T*x, c where T is a tridiagonal matrix. It is used in routine c av. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: ndrv1.F SID: 2.4 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c--------------------------------------------------------------------------- c c %-----------------------------% c | Define maximum dimensions | c | for all arrays. | c | MAXN: Maximum dimension | c | of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %-----------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=12, maxncv=30, ldv=maxn) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), ipntr(14) logical select(maxncv) Complex*16 & ax(maxn), d(maxncv), & v(ldv,maxncv), workd(3*maxn), & workev(3*maxncv), resid(maxn), & workl(3*maxncv*maxncv+5*maxncv) Double precision & rwork(maxncv), rd(maxncv,3) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nx, nev, ncv, lworkl, info, j, & ierr, nconv, maxitr, ishfts, mode Complex*16 & sigma Double precision & tol logical rvec c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Double precision & dznrm2 , dlapy2 external dznrm2 , zaxpy , dlapy2 c c %-----------------------% c | Executable Statements | c %-----------------------% c c %--------------------------------------------------% c | The number NX is the number of interior points | c | in the discretization of the 2-dimensional | c | convection-diffusion operator on the unit | c | square with zero Dirichlet boundary condition. | c | The number N(=NX*NX) is the dimension of the | c | matrix. A standard eigenvalue problem is | c | solved (BMAT = 'I'). NEV is the number of | c | eigenvalues to be approximated. The user can | c | modify NX, NEV, NCV, WHICH to solve problems of | c | different sizes, and to get different parts of | c | the spectrum. However, The following | c | conditions must be satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 2 <= NCV <= MAXNCV | c %--------------------------------------------------% c nx = 10 n = nx*nx nev = 4 ncv = 20 if ( n .gt. maxn ) then print *, ' ERROR with _NDRV1: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NDRV1: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NDRV1: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'I' which = 'LM' c c %---------------------------------------------------% c | The work array WORKL is used in ZNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated to start the ARNOLDI iteration. | c %---------------------------------------------------% c lworkl = 3*ncv**2+5*ncv tol = 0.0 ido = 0 info = 0 c c %---------------------------------------------------% c | This program uses exact shift with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 1 of ZNAUPD is used | c | (IPARAM(7) = 1). All these options can be changed | c | by the user. For details see the documentation in | c | ZNAUPD . | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 1 c iparam(1) = ishfts iparam(3) = maxitr iparam(7) = mode c c %-------------------------------------------% c | M A I N L O O P (Reverse communication) | c %-------------------------------------------% c 10 continue c c %---------------------------------------------% c | Repeatedly call the routine ZNAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call znaupd ( ido, bmat, n, which, nev, tol, resid, ncv, & v, ldv, iparam, ipntr, workd, workl, lworkl, & rwork,info ) c if (ido .eq. -1 .or. ido .eq. 1) then c c %-------------------------------------------% c | Perform matrix vector multiplication | c | y <--- OP*x | c | The user should supply his/her own | c | matrix vector multiplication routine here | c | that takes workd(ipntr(1)) as the input | c | vector, and return the matrix vector | c | product to workd(ipntr(2)). | c %-------------------------------------------% c call av (nx, workd(ipntr(1)), workd(ipntr(2))) c c %-----------------------------------------% c | L O O P B A C K to call ZNAUPD again. | c %-----------------------------------------% c go to 10 end if c c %----------------------------------------% c | Either we have convergence or there is | c | an error. | c %----------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message, check the | c | documentation in ZNAUPD | c %--------------------------% c print *, ' ' print *, ' Error with _naupd, info = ', info print *, ' Check the documentation of _naupd' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using ZNEUPD . | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may also be computed now if | c | desired. (indicated by rvec = .true.) | c %-------------------------------------------% c rvec = .true. c call zneupd (rvec, 'A', select, d, v, ldv, sigma, & workev, bmat, n, which, nev, tol, resid, ncv, & v, ldv, iparam, ipntr, workd, workl, lworkl, & rwork, ierr) c c %----------------------------------------------% c | Eigenvalues are returned in the one | c | dimensional array D. The corresponding | c | eigenvectors are returned in the first NCONV | c | (=IPARAM(5)) columns of the two dimensional | c | array V if requested. Otherwise, an | c | orthogonal basis for the invariant subspace | c | corresponding to the eigenvalues in D is | c | returned in V. | c %----------------------------------------------% c if ( ierr .ne. 0) then c c %------------------------------------% c | Error condition: | c | Check the documentation of ZNEUPD . | c %------------------------------------% c print *, ' ' print *, ' Error with _neupd, info = ', ierr print *, ' Check the documentation of _neupd. ' print *, ' ' c else c nconv = iparam(5) do 20 j=1, nconv c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c call av(nx, v(1,j), ax) call zaxpy (n, -d(j), v(1,j), 1, ax, 1) rd(j,1) = dble (d(j)) rd(j,2) = dimag (d(j)) rd(j,3) = dznrm2 (n, ax, 1) rd(j,3) = rd(j,3) / dlapy2 (rd(j,1),rd(j,2)) 20 continue c c %-----------------------------% c | Display computed residuals. | c %-----------------------------% c call dmout (6, nconv, 3, rd, maxncv, -6, & 'Ritz values (Real, Imag) and relative residuals') end if c c %-------------------------------------------% c | Print additional convergence information. | c %-------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, '_NDRV1' print *, '====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program zndrv1 . | c %---------------------------% c 9000 continue c end c c========================================================================== c c matrix vector subroutine c c The matrix used is the convection-diffusion operator c discretized using centered difference. c subroutine av (nx, v, w) integer nx, j, lo Complex*16 & v(nx*nx), w(nx*nx), one, h2 parameter (one = (1.0D+0, 0.0D+0) ) external zaxpy , tv c c Computes w <--- OP*v, where OP is the nx*nx by nx*nx block c tridiagonal matrix c c | T -I | c |-I T -I | c OP = | -I T | c | ... -I| c | -I T| c c derived from the standard central difference discretization c of the convection-diffusion operator (Laplacian u) + rho*(du/dx) c with zero boundary condition. c c The subroutine TV is called to computed y<---T*x. c c h2 = one / dcmplx ((nx+1)*(nx+1)) c call tv(nx,v(1),w(1)) call zaxpy (nx, -one/h2, v(nx+1), 1, w(1), 1) c do 10 j = 2, nx-1 lo = (j-1)*nx call tv(nx, v(lo+1), w(lo+1)) call zaxpy (nx, -one/h2, v(lo-nx+1), 1, w(lo+1), 1) call zaxpy (nx, -one/h2, v(lo+nx+1), 1, w(lo+1), 1) 10 continue c lo = (nx-1)*nx call tv(nx, v(lo+1), w(lo+1)) call zaxpy (nx, -one/h2, v(lo-nx+1), 1, w(lo+1), 1) c return end c========================================================================= subroutine tv (nx, x, y) c integer nx, j Complex*16 & x(nx), y(nx), h, h2, dd, dl, du c Complex*16 & one, rho parameter (one = (1.0D+0, 0.0D+0) , & rho = (1.0D+2, 0.0D+0) ) c c Compute the matrix vector multiplication y<---T*x c where T is a nx by nx tridiagonal matrix with DD on the c diagonal, DL on the subdiagonal, and DU on the superdiagonal c h = one / dcmplx (nx+1) h2 = h*h dd = (4.0D+0, 0.0D+0) / h2 dl = -one/h2 - (5.0D-1, 0.0D+0) *rho/h du = -one/h2 + (5.0D-1, 0.0D+0) *rho/h c y(1) = dd*x(1) + du*x(2) do 10 j = 2,nx-1 y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1) 10 continue y(nx) = dl*x(nx-1) + dd*x(nx) return end arpack-0.92.1/EXAMPLES/COMPLEX/cndrv2.f0000644000175000017500000003505110776001577013675 00000000000000 program cndrv2 c c Simple program to illustrate the idea of reverse communication c in shift-invert mode for a standard complex nonsymmetric eigenvalue c problem. c c We implement example two of ex-complex.doc in DOCUMENTS directory c c\Example-2 c ... Suppose we want to solve A*x = lambda*x in shift-invert mode, c where A is derived from the central difference discretization c of the 1-dimensional convection-diffusion operator c (d^2u/dx^2) + rho*(du/dx) c on the interval [0,1] with zero Dirichlet boundary condition. c ... The shift sigma is a complex number. c c ... OP = inv[A-sigma*I] and B = I. c c ... Use mode 3 of CNAUPD. c c\BeginLib c c\Routines called: c cnaupd ARPACK reverse communication interface routine. c cneupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c cgttrf LAPACK tridiagonal factorization routine. c cgttrs LAPACK tridiagonal solve routine. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c caxpy Level 1 BLAS that computes y <- alpha*x+y. c ccopy Level 1 BLAS that copies one vector to another. c scnrm2 Level 1 BLAS that computes the norm of a vector. c av Matrix vector multiplication routine that computes A*x. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: ndrv2.F SID: 2.6 DATE OF SID: 10/18/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c-------------------------------------------------------------------------- c c %-----------------------------% c | Define leading dimensions | c | for all arrays. | c | MAXN: Maximum dimension | c | of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %-----------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=10, maxncv=25, & ldv=maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), ipntr(14), ipiv(maxn) logical select(maxncv) Complex & ax(maxn), d(maxncv), resid(maxn), & v(ldv, maxncv), workd(3*maxn), & workev(2*maxncv), & workl(3*maxncv*maxncv+5*maxncv), & dd(maxn), dl(maxn), du(maxn), & du2(maxn) Real & rwork(maxn), rd(maxncv,3) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nev, ncv, lworkl, info, j, ierr, & nconv, maxitr, ishfts, mode Complex & h, h2, s, sigma, s1, s2, s3, rho common /convct/ rho c Real & tol logical rvec c c %------------% c | Parameters | c %------------% c Complex & one, zero, two parameter (one = (1.0E+0, 0.0E+0) , & zero = (0.0E+0, 0.0E+0) , & two = (2.0E+0, 0.0E+0) ) c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & scnrm2, slapy2 external cgttrf, cgttrs, caxpy, ccopy, scnrm2, & slapy2 c c %-----------------------% c | Executable statements | c %-----------------------% c c %--------------------------------------------------% c | The number N is the dimension of the matrix. A | c | standard eigenvalue problem is solved (BMAT = | c | 'I'). NEV is the number of eigenvalues (closest | c | to the shift SIGMA) to be approximated. Since | c | the shift-invert mode is used, WHICH is set to | c | 'LM'. The user can modify NEV, NCV, SIGMA to | c | solve problems of different sizes, and to get | c | different parts of the spectrum. However, The | c | following conditions must be satisfied: | c | N <= MAXN, | c | NEV <= MAXNEV, | c | NEV + 2 <= NCV <= MAXNCV | c %--------------------------------------------------% c n = 100 nev = 4 ncv = 20 if ( n .gt. maxn ) then print *, ' ERROR with _NDRV2: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NDRV2: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NDRV2: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'I' which = 'LM' sigma = zero c c %----------------------------------------------------% c | Construct C = A - SIGMA*I, factor C in complex | c | arithmetic (using LAPACK subroutine cgttrf). The | c | matrix A is chosen to be the tridiagonal matrix | c | derived from standard central difference of the | c | 1-d convection diffusion operator - u``+ rho*u` on | c | the interval [0, 1] with zero Dirichlet boundary | c | condition. | c %----------------------------------------------------% c rho = (1.0E+1, 0.0E+0) h = one / cmplx(n+1) h2 = h*h s = rho / two c s1 = -one/h2 - s/h s2 = two/h2 - sigma s3 = -one/h2 + s/h c do 10 j = 1, n-1 dl(j) = s1 dd(j) = s2 du(j) = s3 10 continue dd(n) = s2 c call cgttrf(n, dl, dd, du, du2, ipiv, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrf in _NDRV2.' print*, ' ' go to 9000 end if c c %-----------------------------------------------------% c | The work array WORKL is used in CNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in CNAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = 3*ncv**2+5*ncv tol = 0.0 ido = 0 info = 0 c c %---------------------------------------------------% c | This program uses exact shifts with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 3 of CNAUPD is used | c | (IPARAM(7) = 3). All these options can be | c | changed by the user. For details see the | c | documentation in CNAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 3 c iparam(1) = ishfts iparam(3) = maxitr iparam(7) = mode c c %-------------------------------------------% c | M A I N L O O P (Reverse communication) | c %-------------------------------------------% c 20 continue c c %---------------------------------------------% c | Repeatedly call the routine CNAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call cnaupd ( ido, bmat, n, which, nev, tol, resid, ncv, & v, ldv, iparam, ipntr, workd, workl, lworkl, & rwork,info ) c if (ido .eq. -1 .or. ido .eq. 1 ) then c c %-------------------------------------------% c | Perform y <--- OP*x = inv[A-SIGMA*I]*x | c | The user should supply his/her own linear | c | system solver here that takes | c | workd(ipntr(1)) as the input, and returns | c | the result to workd(ipntr(2)). | c %-------------------------------------------% c call ccopy( n, workd(ipntr(1)),1, workd(ipntr(2)), 1) c call cgttrs('N', n, 1, dl, dd, du, du2, ipiv, & workd(ipntr(2)), n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrs in _NDRV2.' print*, ' ' go to 9000 end if c c %-----------------------------------------% c | L O O P B A C K to call CNAUPD again. | c %-----------------------------------------% c go to 20 c end if c c %-----------------------------------------% c | Either we have convergence, or there is | c | an error. | c %-----------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message, check the | c | documentation in CNAUPD | c %--------------------------% c print *, ' ' print *, ' Error with _naupd, info = ',info print *, ' Check the documentation in _naupd.' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using CNEUPD. | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may also be computed now if | c | desired. (indicated by rvec = .true.) | c %-------------------------------------------% c rvec = .true. c call cneupd (rvec, 'A', select, d, v, ldv, sigma, & workev, bmat, n, which, nev, tol, & resid, ncv, v, ldv, iparam, ipntr, workd, & workl, lworkl, rwork, ierr) c c %----------------------------------------------% c | Eigenvalues are returned in the one | c | dimensional array D. The corresponding | c | eigenvectors are returned in the first NCONV | c | (=IPARAM(5)) columns of the two dimensional | c | array V if requested. Otherwise, an | c | orthogonal basis for the invariant subspace | c | corresponding to the eigenvalues in D is | c | returned in V. | c %----------------------------------------------% c if ( ierr .ne. 0) then c c %------------------------------------% c | Error condition: | c | Check the documentation of CNEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _neupd, info = ', ierr print *, ' Check the documentation of _neupd. ' print *, ' ' else c nconv = iparam(5) do 60 j=1, nconv c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c call av(n, v(1,j), ax) call caxpy(n, -d(j), v(1,j), 1, ax, 1) rd(j,1) = real (d(j)) rd(j,2) = aimag(d(j)) rd(j,3) = scnrm2(n, ax, 1) rd(j,3) = rd(j,3) / slapy2(rd(j,1),rd(j,2)) 60 continue c c %-----------------------------% c | Display computed residuals. | c %-----------------------------% c call smout(6, nconv, 3, rd, maxncv, -6, & 'Ritz values (Real, Imag) and relative residuals') c end if c c %-------------------------------------------% c | Print additional convergence information. | c %-------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, '_NDRV2 ' print *, '====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program cndrv2. | c %---------------------------% c 9000 continue c end c c------------------------------------------------------------------- c c matrix vector multiplication subroutine c subroutine av (n, v, w) integer n, j Complex & v(n), w(n), rho, two, one, dd, dl, du, s, h, & h2 parameter (one = (1.0E+0, 0.0E+0) , & two = (2.0E+0, 0.0E+0) ) common /convct/ rho c h = one / cmplx(n+1) h2 = h*h s = rho / two dd = two / h2 dl = -one/h2 - s/h du = -one/h2 + s/h c w(1) = dd*v(1) + du*v(2) do 10 j = 2,n-1 w(j) = dl*v(j-1) + dd*v(j) + du*v(j+1) 10 continue w(n) = dl*v(n-1) + dd*v(n) return end arpack-0.92.1/EXAMPLES/COMPLEX/cndrv1.f0000644000175000017500000003505510776001577013700 00000000000000 program cndrv1 c c Example program to illustrate the idea of reverse communication c for a standard complex nonsymmetric eigenvalue problem. c c We implement example one of ex-complex.doc in DOCUMENTS directory c c\Example-1 c ... Suppose we want to solve A*x = lambda*x in regular mode, c where A is obtained from the standard central difference c discretization of the convection-diffusion operator c (Laplacian u) + rho*(du / dx) c on the unit squre [0,1]x[0,1] with zero Dirichlet boundary c condition. c c ... OP = A and B = I. c c ... Assume "call av (nx,x,y)" computes y = A*x c c ... Use mode 1 of CNAUPD. c c\BeginLib c c\Routines called c cnaupd ARPACK reverse communication interface routine. c cneupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c scnrm2 Level 1 BLAS that computes the norm of a complex vector. c caxpy Level 1 BLAS that computes y <- alpha*x+y. c av Matrix vector multiplication routine that computes A*x. c tv Matrix vector multiplication routine that computes T*x, c where T is a tridiagonal matrix. It is used in routine c av. c c\Author c Richard Lehoucq c Danny Sorensen c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: ndrv1.F SID: 2.4 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c--------------------------------------------------------------------------- c c %-----------------------------% c | Define maximum dimensions | c | for all arrays. | c | MAXN: Maximum dimension | c | of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %-----------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=12, maxncv=30, ldv=maxn) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), ipntr(14) logical select(maxncv) Complex & ax(maxn), d(maxncv), & v(ldv,maxncv), workd(3*maxn), & workev(3*maxncv), resid(maxn), & workl(3*maxncv*maxncv+5*maxncv) Real & rwork(maxncv), rd(maxncv,3) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nx, nev, ncv, lworkl, info, j, & ierr, nconv, maxitr, ishfts, mode Complex & sigma Real & tol logical rvec c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & scnrm2, slapy2 external scnrm2, caxpy, slapy2 c c %-----------------------% c | Executable Statements | c %-----------------------% c c %--------------------------------------------------% c | The number NX is the number of interior points | c | in the discretization of the 2-dimensional | c | convection-diffusion operator on the unit | c | square with zero Dirichlet boundary condition. | c | The number N(=NX*NX) is the dimension of the | c | matrix. A standard eigenvalue problem is | c | solved (BMAT = 'I'). NEV is the number of | c | eigenvalues to be approximated. The user can | c | modify NX, NEV, NCV, WHICH to solve problems of | c | different sizes, and to get different parts of | c | the spectrum. However, The following | c | conditions must be satisfied: | c | N <= MAXN | c | NEV <= MAXNEV | c | NEV + 2 <= NCV <= MAXNCV | c %--------------------------------------------------% c nx = 10 n = nx*nx nev = 4 ncv = 20 if ( n .gt. maxn ) then print *, ' ERROR with _NDRV1: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NDRV1: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NDRV1: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'I' which = 'LM' c c %---------------------------------------------------% c | The work array WORKL is used in CNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated to start the ARNOLDI iteration. | c %---------------------------------------------------% c lworkl = 3*ncv**2+5*ncv tol = 0.0 ido = 0 info = 0 c c %---------------------------------------------------% c | This program uses exact shift with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 1 of CNAUPD is used | c | (IPARAM(7) = 1). All these options can be changed | c | by the user. For details see the documentation in | c | CNAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 1 c iparam(1) = ishfts iparam(3) = maxitr iparam(7) = mode c c %-------------------------------------------% c | M A I N L O O P (Reverse communication) | c %-------------------------------------------% c 10 continue c c %---------------------------------------------% c | Repeatedly call the routine CNAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call cnaupd ( ido, bmat, n, which, nev, tol, resid, ncv, & v, ldv, iparam, ipntr, workd, workl, lworkl, & rwork,info ) c if (ido .eq. -1 .or. ido .eq. 1) then c c %-------------------------------------------% c | Perform matrix vector multiplication | c | y <--- OP*x | c | The user should supply his/her own | c | matrix vector multiplication routine here | c | that takes workd(ipntr(1)) as the input | c | vector, and return the matrix vector | c | product to workd(ipntr(2)). | c %-------------------------------------------% c call av (nx, workd(ipntr(1)), workd(ipntr(2))) c c %-----------------------------------------% c | L O O P B A C K to call CNAUPD again. | c %-----------------------------------------% c go to 10 end if c c %----------------------------------------% c | Either we have convergence or there is | c | an error. | c %----------------------------------------% c if ( info .lt. 0 ) then c c %--------------------------% c | Error message, check the | c | documentation in CNAUPD | c %--------------------------% c print *, ' ' print *, ' Error with _naupd, info = ', info print *, ' Check the documentation of _naupd' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using CNEUPD. | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may also be computed now if | c | desired. (indicated by rvec = .true.) | c %-------------------------------------------% c rvec = .true. c call cneupd (rvec, 'A', select, d, v, ldv, sigma, & workev, bmat, n, which, nev, tol, resid, ncv, & v, ldv, iparam, ipntr, workd, workl, lworkl, & rwork, ierr) c c %----------------------------------------------% c | Eigenvalues are returned in the one | c | dimensional array D. The corresponding | c | eigenvectors are returned in the first NCONV | c | (=IPARAM(5)) columns of the two dimensional | c | array V if requested. Otherwise, an | c | orthogonal basis for the invariant subspace | c | corresponding to the eigenvalues in D is | c | returned in V. | c %----------------------------------------------% c if ( ierr .ne. 0) then c c %------------------------------------% c | Error condition: | c | Check the documentation of CNEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _neupd, info = ', ierr print *, ' Check the documentation of _neupd. ' print *, ' ' c else c nconv = iparam(5) do 20 j=1, nconv c c %---------------------------% c | Compute the residual norm | c | | c | || A*x - lambda*x || | c | | c | for the NCONV accurately | c | computed eigenvalues and | c | eigenvectors. (iparam(5) | c | indicates how many are | c | accurate to the requested | c | tolerance) | c %---------------------------% c call av(nx, v(1,j), ax) call caxpy(n, -d(j), v(1,j), 1, ax, 1) rd(j,1) = real (d(j)) rd(j,2) = aimag(d(j)) rd(j,3) = scnrm2(n, ax, 1) rd(j,3) = rd(j,3) / slapy2(rd(j,1),rd(j,2)) 20 continue c c %-----------------------------% c | Display computed residuals. | c %-----------------------------% c call smout(6, nconv, 3, rd, maxncv, -6, & 'Ritz values (Real, Imag) and relative residuals') end if c c %-------------------------------------------% c | Print additional convergence information. | c %-------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, '_NDRV1' print *, '====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c c %---------------------------% c | Done with program cndrv1. | c %---------------------------% c 9000 continue c end c c========================================================================== c c matrix vector subroutine c c The matrix used is the convection-diffusion operator c discretized using centered difference. c subroutine av (nx, v, w) integer nx, j, lo Complex & v(nx*nx), w(nx*nx), one, h2 parameter (one = (1.0E+0, 0.0E+0) ) external caxpy, tv c c Computes w <--- OP*v, where OP is the nx*nx by nx*nx block c tridiagonal matrix c c | T -I | c |-I T -I | c OP = | -I T | c | ... -I| c | -I T| c c derived from the standard central difference discretization c of the convection-diffusion operator (Laplacian u) + rho*(du/dx) c with zero boundary condition. c c The subroutine TV is called to computed y<---T*x. c c h2 = one / cmplx((nx+1)*(nx+1)) c call tv(nx,v(1),w(1)) call caxpy(nx, -one/h2, v(nx+1), 1, w(1), 1) c do 10 j = 2, nx-1 lo = (j-1)*nx call tv(nx, v(lo+1), w(lo+1)) call caxpy(nx, -one/h2, v(lo-nx+1), 1, w(lo+1), 1) call caxpy(nx, -one/h2, v(lo+nx+1), 1, w(lo+1), 1) 10 continue c lo = (nx-1)*nx call tv(nx, v(lo+1), w(lo+1)) call caxpy(nx, -one/h2, v(lo-nx+1), 1, w(lo+1), 1) c return end c========================================================================= subroutine tv (nx, x, y) c integer nx, j Complex & x(nx), y(nx), h, h2, dd, dl, du c Complex & one, rho parameter (one = (1.0E+0, 0.0E+0) , & rho = (1.0E+2, 0.0E+0) ) c c Compute the matrix vector multiplication y<---T*x c where T is a nx by nx tridiagonal matrix with DD on the c diagonal, DL on the subdiagonal, and DU on the superdiagonal c h = one / cmplx(nx+1) h2 = h*h dd = (4.0E+0, 0.0E+0) / h2 dl = -one/h2 - (5.0E-1, 0.0E+0) *rho/h du = -one/h2 + (5.0E-1, 0.0E+0) *rho/h c y(1) = dd*x(1) + du*x(2) do 10 j = 2,nx-1 y(j) = dl*x(j-1) + dd*x(j) + du*x(j+1) 10 continue y(nx) = dl*x(nx-1) + dd*x(nx) return end arpack-0.92.1/EXAMPLES/COMPLEX/cndrv4.f0000644000175000017500000004204510776001577013700 00000000000000 program cndrv4 c c Simple program to illustrate the idea of reverse communication c in shift and invert mode for a generalized complex nonsymmetric c eigenvalue problem. c c We implement example four of ex-complex.doc in DOCUMENTS directory c c\Example-4 c ... Suppose we want to solve A*x = lambda*B*x in shift-invert mode, c where A and B are derived from a finite element discretization c of a 1-dimensional convection-diffusion operator c (d^2u/dx^2) + rho*(du/dx) c on the interval [0,1] with zero boundary condition using c piecewise linear elements. c c ... where the shift sigma is a complex number. c c ... OP = inv[A-SIGMA*M]*M and B = M. c c ... Use mode 3 of CNAUPD. c c\BeginLib c c\Routines called: c cnaupd ARPACK reverse communication interface routine. c cneupd ARPACK routine that returns Ritz values and (optionally) c Ritz vectors. c cgttrf LAPACK tridiagonal factorization routine. c cgttrs LAPACK tridiagonal solve routine. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c caxpy Level 1 BLAS that computes y <- alpha*x+y. c ccopy Level 1 BLAS that copies one vector to another. c scnrm2 Level 1 BLAS that computes the norm of a complex vector. c av Matrix vector multiplication routine that computes A*x. c mv Matrix vector multiplication routine that computes M*x. c c\Author c Danny Sorensen c Richard Lehoucq c Chao Yang c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: ndrv4.F SID: 2.4 DATE OF SID: 10/18/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c----------------------------------------------------------------------- c c %-----------------------------% c | Define leading dimensions | c | for all arrays. | c | MAXN: Maximum dimension | c | of the A allowed. | c | MAXNEV: Maximum NEV allowed | c | MAXNCV: Maximum NCV allowed | c %-----------------------------% c integer maxn, maxnev, maxncv, ldv parameter (maxn=256, maxnev=10, maxncv=25, & ldv=maxn ) c c %--------------% c | Local Arrays | c %--------------% c integer iparam(11), ipntr(14), ipiv(maxn) logical select(maxncv) Complex & ax(maxn), mx(maxn), d(maxncv), & v(ldv,maxncv), workd(3*maxn), resid(maxn), & workev(2*maxncv), & workl(3*maxncv*maxncv+5*maxncv), & dd(maxn), dl(maxn), du(maxn), & du2(maxn) Real & rwork(maxn), rd(maxncv,3) c c %---------------% c | Local Scalars | c %---------------% c character bmat*1, which*2 integer ido, n, nev, ncv, lworkl, info, j, ierr, & nconv, maxitr, ishfts, mode Complex & rho, h, s, & sigma, s1, s2, s3 common /convct/ rho c Real & tol logical rvec c c %-----------------------------% c | BLAS & LAPACK routines used | c %-----------------------------% c Real & scnrm2, slapy2 external scnrm2, caxpy, ccopy, cgttrf, cgttrs, & slapy2 c c %------------% c | Parameters | c %------------% c Complex & one, zero, two, four, six parameter (one = (1.0E+0, 0.0E+0) , & zero = (0.0E+0, 0.0E+0) , & two = (2.0E+0, 0.0E+0) , & four = (4.0E+0, 0.0E+0) , & six = (6.0E+0, 0.0E+0) ) c c %-----------------------% c | Executable statements | c %-----------------------% c c %----------------------------------------------------% c | The number N is the dimension of the matrix. A | c | generalized eigenvalue problem is solved (BMAT = | c | 'G'). NEV is the number of eigenvalues (closest | c | to SIGMAR) to be approximated. Since the | c | shift-invert mode is used, WHICH is set to 'LM'. | c | The user can modify NEV, NCV, SIGMA to solve | c | problems of different sizes, and to get different | c | parts of the spectrum. However, The following | c | conditions must be satisfied: | c | N <= MAXN, | c | NEV <= MAXNEV, | c | NEV + 2 <= NCV <= MAXNCV | c %----------------------------------------------------% c n = 100 nev = 4 ncv = 20 if ( n .gt. maxn ) then print *, ' ERROR with _NDRV4: N is greater than MAXN ' go to 9000 else if ( nev .gt. maxnev ) then print *, ' ERROR with _NDRV4: NEV is greater than MAXNEV ' go to 9000 else if ( ncv .gt. maxncv ) then print *, ' ERROR with _NDRV4: NCV is greater than MAXNCV ' go to 9000 end if bmat = 'G' which = 'LM' sigma = one c c %--------------------------------------------------% c | Construct C = A - SIGMA*M in COMPLEX arithmetic. | c | Factor C in COMPLEX arithmetic (using LAPACK | c | subroutine cgttrf). The matrix A is chosen to be | c | the tridiagonal matrix derived from the standard | c | central difference discretization of the 1-d | c | convection-diffusion operator u``+ rho*u` on the | c | interval [0, 1] with zero Dirichlet boundary | c | condition. The matrix M is chosen to be the | c | symmetric tridiagonal matrix with 4.0 on the | c | diagonal and 1.0 on the off-diagonals. | c %--------------------------------------------------% c rho = (1.0E+1, 0.0E+0) h = one / cmplx(n+1) s = rho / two c s1 = -one/h - s - sigma*h/six s2 = two/h - four*sigma*h/six s3 = -one/h + s - sigma*h/six c do 10 j = 1, n-1 dl(j) = s1 dd(j) = s2 du(j) = s3 10 continue dd(n) = s2 c call cgttrf(n, dl, dd, du, du2, ipiv, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrf in _NDRV4.' print*, ' ' go to 9000 end if c c %-----------------------------------------------------% c | The work array WORKL is used in CNAUPD as | c | workspace. Its dimension LWORKL is set as | c | illustrated below. The parameter TOL determines | c | the stopping criterion. If TOL<=0, machine | c | precision is used. The variable IDO is used for | c | reverse communication, and is initially set to 0. | c | Setting INFO=0 indicates that a random vector is | c | generated in CNAUPD to start the Arnoldi iteration. | c %-----------------------------------------------------% c lworkl = 3*ncv**2+5*ncv tol = 0.0 ido = 0 info = 0 c c %---------------------------------------------------% c | This program uses exact shifts with respect to | c | the current Hessenberg matrix (IPARAM(1) = 1). | c | IPARAM(3) specifies the maximum number of Arnoldi | c | iterations allowed. Mode 3 of CNAUPD is used | c | (IPARAM(7) = 3). All these options can be | c | changed by the user. For details see the | c | documentation in CNAUPD. | c %---------------------------------------------------% c ishfts = 1 maxitr = 300 mode = 3 c iparam(1) = ishfts iparam(3) = maxitr iparam(7) = mode c c %------------------------------------------% c | M A I N L O O P(Reverse communication) | c %------------------------------------------% c 20 continue c c %---------------------------------------------% c | Repeatedly call the routine CNAUPD and take | c | actions indicated by parameter IDO until | c | either convergence is indicated or maxitr | c | has been exceeded. | c %---------------------------------------------% c call cnaupd ( ido, bmat, n, which, nev, tol, resid, ncv, & v, ldv, iparam, ipntr, workd, workl, lworkl, & rwork, info ) c if (ido .eq. -1) then c c %-------------------------------------------% c | Perform y <--- OP*x = inv[A-SIGMA*M]*M*x | c | to force starting vector into the range | c | of OP. The user should supply his/her | c | own matrix vector multiplication routine | c | and a linear system solver. The matrix | c | vector multiplication routine should take | c | workd(ipntr(1)) as the input. The final | c | result should be returned to | c | workd(ipntr(2)). | c %-------------------------------------------% c call mv (n, workd(ipntr(1)), workd(ipntr(2))) call cgttrs('N', n, 1, dl, dd, du, du2, ipiv, & workd(ipntr(2)), n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrs in _NDRV4.' print*, ' ' go to 9000 end if c c %-----------------------------------------% c | L O O P B A C K to call CNAUPD again. | c %-----------------------------------------% c go to 20 c else if ( ido .eq. 1) then c c %-----------------------------------------% c | Perform y <-- OP*x = inv[A-sigma*M]*M*x | c | M*x has been saved in workd(ipntr(3)). | c | The user only need the linear system | c | solver here that takes workd(ipntr(3)) | c | as input, and returns the result to | c | workd(ipntr(2)). | c %-----------------------------------------% c call ccopy( n, workd(ipntr(3)), 1, workd(ipntr(2)), 1) call cgttrs ('N', n, 1, dl, dd, du, du2, ipiv, & workd(ipntr(2)), n, ierr) if ( ierr .ne. 0 ) then print*, ' ' print*, ' ERROR with _gttrs in _NDRV4.' print*, ' ' go to 9000 end if c c %-----------------------------------------% c | L O O P B A C K to call CNAUPD again. | c %-----------------------------------------% c go to 20 c else if ( ido .eq. 2) then c c %---------------------------------------------% c | Perform y <--- M*x | c | Need matrix vector multiplication routine | c | here that takes workd(ipntr(1)) as input | c | and returns the result to workd(ipntr(2)). | c %---------------------------------------------% c call mv (n, workd(ipntr(1)), workd(ipntr(2))) c c %-----------------------------------------% c | L O O P B A C K to call CNAUPD again. | c %-----------------------------------------% c go to 20 c end if c c %-----------------------------------------% c | Either we have convergence, or there is | c | an error. | c %-----------------------------------------% c if ( info .lt. 0 ) then c c %----------------------------% c | Error message, check the | c | documentation in CNAUPD | c %----------------------------% c print *, ' ' print *, ' Error with _naupd, info = ', info print *, ' Check the documentation of _naupd.' print *, ' ' c else c c %-------------------------------------------% c | No fatal errors occurred. | c | Post-Process using CNEUPD. | c | | c | Computed eigenvalues may be extracted. | c | | c | Eigenvectors may also be computed now if | c | desired. (indicated by rvec = .true.) | c %-------------------------------------------% c rvec = .true. c call cneupd (rvec, 'A', select, d, v, ldv, sigma, & workev, bmat, n, which, nev, tol, resid, ncv, v, & ldv, iparam, ipntr, workd, workl, lworkl, rwork, & ierr) c c %----------------------------------------------% c | Eigenvalues are returned in the one | c | dimensional array D. The corresponding | c | eigenvectors are returned in the first NCONV | c | (=IPARAM(5)) columns of the two dimensional | c | array V if requested. Otherwise, an | c | orthogonal basis for the invariant subspace | c | corresponding to the eigenvalues in D is | c | returned in V. | c %----------------------------------------------% c if ( ierr .ne. 0) then c c %------------------------------------% c | Error condition: | c | Check the documentation of CNEUPD. | c %------------------------------------% c print *, ' ' print *, ' Error with _neupd, info = ', ierr print *, ' Check the documentation of _neupd. ' print *, ' ' c else c nconv = iparam(5) do 80 j=1, nconv c call av(n, v(1,j), ax) call mv(n, v(1,j), mx) call caxpy(n, -d(j), mx, 1, ax, 1) rd(j,1) = real (d(j)) rd(j,2) = aimag(d(j)) rd(j,3) = scnrm2(n, ax, 1) rd(j,3) = rd(j,3) / slapy2(rd(j,1),rd(j,2)) 80 continue c c %-----------------------------% c | Display computed residuals. | c %-----------------------------% c call smout(6, nconv, 3, rd, maxncv, -6, & 'Ritz values (Real, Imag) and direct residuals') c end if c c %-------------------------------------------% c | Print additional convergence information. | c %-------------------------------------------% c if ( info .eq. 1) then print *, ' ' print *, ' Maximum number of iterations reached.' print *, ' ' else if ( info .eq. 3) then print *, ' ' print *, ' No shifts could be applied during implicit', & ' Arnoldi update, try increasing NCV.' print *, ' ' end if c print *, ' ' print *, '_NDRV4 ' print *, '====== ' print *, ' ' print *, ' Size of the matrix is ', n print *, ' The number of Ritz values requested is ', nev print *, ' The number of Arnoldi vectors generated', & ' (NCV) is ', ncv print *, ' What portion of the spectrum: ', which print *, ' The number of converged Ritz values is ', & nconv print *, ' The number of Implicit Arnoldi update', & ' iterations taken is ', iparam(3) print *, ' The number of OP*x is ', iparam(9) print *, ' The convergence criterion is ', tol print *, ' ' c end if c 9000 continue c end c c========================================================================== c c matrix vector multiplication subroutine c subroutine mv (n, v, w) integer n, j Complex & v(n), w(n), one, four, six, h parameter (one = (1.0E+0, 0.0E+0) , & four = (4.0E+0, 0.0E+0) , & six = (6.0E+0, 0.0E+0) ) c c Compute the matrix vector multiplication y<---M*x c where M is a n by n symmetric tridiagonal matrix with 4 on the c diagonal, 1 on the subdiagonal and superdiagonal. c w(1) = ( four*v(1) + one*v(2) ) / six do 40 j = 2,n-1 w(j) = ( one*v(j-1) + four*v(j) + one*v(j+1) ) / six 40 continue w(n) = ( one*v(n-1) + four*v(n) ) / six c h = one / cmplx(n+1) call cscal(n, h, w, 1) return end c------------------------------------------------------------------ subroutine av (n, v, w) integer n, j Complex & v(n), w(n), one, two, dd, dl, du, s, h, rho parameter (one = (1.0E+0, 0.0E+0) , & two = (2.0E+0, 0.0E+0) ) common /convct/ rho c h = one / cmplx(n+1) s = rho / two dd = two / h dl = -one/h - s du = -one/h + s c w(1) = dd*v(1) + du*v(2) do 40 j = 2,n-1 w(j) = dl*v(j-1) + dd*v(j) + du*v(j+1) 40 continue w(n) = dl*v(n-1) + dd*v(n) return end arpack-0.92.1/README0000644000175000017500000001004210776001577010654 000000000000001. You have successfully unbundled ARPACK and are now in the ARPACK directory that was created for you. 2. Recent bug fixes are included in patch.tar.gz and ppatch.tar.gz (only needed if you are using PARPACK also.) If you have not retrieved these files, please do so and place them in the directory right above the current directory. (They should be in the same directory where arpack96.tar reside). Use uncompress or gunzip to unzip the tar files, and use 'tar -xvf ' to unbundle these patches. The source codes in these patches will overwrite those contained in arpack96.tar and parpack96.tar. 3. Upon executing the 'ls | more ' command you should see BLAS DOCUMENTS EXAMPLES LAPACK README SRC UTIL Makefile ARmake.inc ARMAKES The following entries are directories: ARMAKES, BLAS, DOCUMENTS, EXAMPLES, LAPACK, SRC, UTIL The directory SRC contains the top level routines including the highest level reverse communication interface routines ssaupd, dsaupd - symmetric single and double precision snaupd, dnaupd - non-symmetric single and double precision cnaupd, cnaupd - complex non-symmetric single and double precision The headers of these routines contain full documentation of calling sequence and usage. Additional information is in the DOCUMENTS directory. 4. Example driver programs that illustrate all the computational modes, data types and precisions may be found in the EXAMPLES directory. Upon executing the 'ls EXAMPLES | more ' command you should see BAND COMPLEX NONSYM README SIMPLE SVD SYM Example programs for banded, complex, nonsymmetric, symmetric, and singular value decomposition may be found in the directories BAND, COMPLEX, NONSYM, SYM, SVD respectively. Look at the README file for further information. To get started, get into the SIMPLE directory to see example programs that illustrate the use of ARPACK in the simplest modes of operation for the most commonly posed standard eigenvalue problems. The following instructions explain how to make the ARPACK library. 5. Before you can compile anything, you must first edit and correct the file ARmake.inc. Sample ARmake.inc's can be found in the ARMAKES directory. Edit "ARmake.inc" and change the definition "home" to the root of the source tree (Top level of ARPACK directory) The makefile is set up to build a self-contained library which includes the needed BLAS 1/2/3 and LAPACK routines. If you already have the BLAS and LAPACK libraries installed on your system you might want to change the definition of DIRS as indicated in the ARmake.inc file. *** NOTE *** Unless the LAPACK library on your system is version 2.0, we strongly recommend that you install the LAPACK routines provided with ARPACK. Note that the current LAPACK release is version 3.0; if you are not sure which version of LAPACK is installed, pleaase compile and link to the subset of LAPACK included with ARPACK. 6. You will also need to change the file "second.f" in the UTIL directory to whatever is appropriate for timing on your system. The "second" routine provided works on most workstations. If you are running on a Cray, you can just edit the makefile in UTIL and take out the reference to "second.o" to use the system second routine. 7. Do "make lib" in the current directory to build the standard library "libarpack_$(PLAT).a" 8. Within DOCUMENTS directory there are three files ex-sym.doc ex-nonsym.doc and ex-complex.doc for templates on how to invoke the computational modes of ARPACK. Also look in the README file for explanations concerning the other documents. Danny Sorensen at sorensen@caam.rice.edu Richard Lehoucq at rblehou@sandia.gov Chao Yang at cyang@lbl.gov Kristi Maschhoff at kristyn@tera.com If you have questions regarding using ARPACK, please send email to arpack@caam.rice.edu. Good luck and enjoy. arpack-0.92.1/CPLUSPLUS/0000755000175000017500000000000011540551365011444 500000000000000arpack-0.92.1/CPLUSPLUS/matrix_operator.hpp0000644000175000017500000002351011540551354015313 00000000000000// // Copyright (c) 2004-2008 // Andreas Kloeckner // // Permission to use, copy, modify, distribute and sell this software // and its documentation for any purpose is hereby granted without fee, // provided that the above copyright notice appear in all copies and // that both that copyright notice and this permission notice appear // in supporting documentation. The authors make no representations // about the suitability of this software for any purpose. // It is provided "as is" without express or implied warranty. // #ifndef HEADER_SEEN_MATRIX_OPERATOR_HPP #define HEADER_SEEN_MATRIX_OPERATOR_HPP #include #include #include namespace pyublasext { template class matrix_operator { public: // types typedef typename OperandType::size_type size_type; typedef OperandType operand_type; typedef typename boost::remove_reference::type result_type; typedef ResultType complete_result_type; // interface virtual ~matrix_operator() { } virtual unsigned size1() const = 0; virtual unsigned size2() const = 0; /** Before using apply, operand and result must have the correct size. */ virtual void apply(const OperandType &operand, ResultType result) const { if (size2() != operand.size() || size1() != result.size()) throw std::runtime_error("invalid vector sizes in matrix_operator::apply"); } // matrix_expression compatibility const matrix_operator &operator()() const { return *this; } }; template class algorithm_matrix_operator : public matrix_operator { protected: unsigned m_lastIterationCount; unsigned m_debugLevel; public: algorithm_matrix_operator() : m_lastIterationCount(0), m_debugLevel(0) { } unsigned get_debug_level() const { return m_debugLevel; } void set_debug_level(unsigned dl) { m_debugLevel = dl; } unsigned get_last_iteration_count() const { return m_lastIterationCount; } }; template class iterative_solver_matrix_operator : public algorithm_matrix_operator { protected: unsigned m_maxIterations; double m_tolerance; public: iterative_solver_matrix_operator(unsigned maxit = 0, double tol = 0) : m_maxIterations(maxit), m_tolerance(tol) { } unsigned get_max_iterations() const { return m_maxIterations; } void set_max_iterations(unsigned maxit) { m_maxIterations = maxit; } double get_tolerance() const { return m_tolerance; } void set_tolerance(double tol) { m_tolerance = tol; } }; template class ublas_matrix_operator : public matrix_operator { private: MatrixHolder m_matrix; typedef matrix_operator super; public: ublas_matrix_operator(const MatrixType &m) : m_matrix(m) { } unsigned size1() const { return m_matrix.size1(); } unsigned size2() const { return m_matrix.size2(); } void apply(const OperandType &operand, ResultType result) const { super::apply(operand, result); using namespace boost::numeric::ublas; axpy_prod(m_matrix, operand, result, /* init */ true); } }; template class identity_matrix_operator : public matrix_operator { private: typedef matrix_operator super; unsigned m_size; public: identity_matrix_operator(unsigned size) : m_size(size) { } unsigned size2() const { return m_size; } unsigned size1() const { return m_size; } void apply(const OperandType &operand, ResultType result) const { super::apply(operand, result); result.assign(operand); } }; template class composite_matrix_operator : public matrix_operator { private: typedef matrix_operator super; const super &m_outer, &m_inner; public: composite_matrix_operator(const super &outer, const super &inner) : m_outer(outer), m_inner(inner) { if (m_inner.size1() != m_outer.size2()) throw std::runtime_error("composite_matrix_operator: sizes do not match"); } unsigned size1() const { return m_outer.size1(); } unsigned size2() const { return m_inner.size2(); } void apply(const OperandType &operand, ResultType result) const { super::apply(operand, result); OperandType temp(m_inner.size1()); temp.clear(); m_inner.apply(operand, temp); m_outer.apply(temp, result); } }; template class sum_of_matrix_operators : public matrix_operator { private: typedef matrix_operator super; const super &m_op1, &m_op2; public: sum_of_matrix_operators (const super &op1, const super &op2) : m_op1(op1), m_op2(op2) { if (m_op1.size1() != m_op2.size1()) throw std::runtime_error("sum_of_matrix_operators: sizes do not match"); if (m_op1.size2() != m_op2.size2()) throw std::runtime_error("sum_of_matrix_operators: sizes do not match"); } unsigned size1() const { return m_op1.size1(); } unsigned size2() const { return m_op1.size2(); } void apply(const OperandType &operand, ResultType result) const { super::apply(operand, result); ResultType temp(result); m_op1.apply(operand, temp); m_op2.apply(operand, result); result += temp; } }; template class complex_matrix_operator_adaptor : public matrix_operator { private: typedef matrix_operator super; public: typedef RealOp real_operator; private: const real_operator &m_real, &m_imaginary; public: complex_matrix_operator_adaptor( const real_operator &real_part, const real_operator &imaginary_part) : m_real(real_part), m_imaginary(imaginary_part) { if (m_real.size1() != m_imaginary.size1()) throw std::runtime_error("complex_matrix_operator_adaptor: sizes do not match"); if (m_real.size2() != m_imaginary.size2()) throw std::runtime_error("complex_matrix_operator_adaptor: sizes do not match"); } unsigned size1() const { return m_real.size1(); } unsigned size2() const { return m_real.size2(); } void apply(const OperandType &operand, ResultType result) const { super::apply(operand, result); typedef typename real_operator::result_type::value_type real_t; typedef std::complex complex_t; typename real_operator::operand_type operand_real(real(operand)), operand_imag(imag(operand)); typename real_operator::result_type result_real_1(real(result)), result_imag_1(imag(result)), result_real_2(real(result)), result_imag_2(imag(result)); m_real.apply(operand_real, result_real_1); m_imaginary.apply(operand_imag, result_real_2); result_real_2 *= -1; m_imaginary.apply(operand_real, result_imag_1); m_real.apply(operand_imag, result_imag_2); OperandType result_imag_12 = result_imag_1 + result_imag_2; result.assign(result_real_1 + result_real_2 + complex_t(0,1) * result_imag_12); } }; template class scalar_multiplication_matrix_operator : public matrix_operator { private: typedef matrix_operator super; ScalarType m_factor; unsigned m_size; public: scalar_multiplication_matrix_operator(const ScalarType &factor, unsigned size) : m_factor(factor), m_size(size) { } unsigned size1() const { return m_size; } unsigned size2() const { return m_size; } void apply(const OperandType &operand, ResultType result) const { super::apply(operand, result); result.assign(m_factor * operand); } }; // generic prod() interface --------------------------------------------------- template ResultType prod( const matrix_operator &mo, const OperandType &vec, bool clear_result = false) { ResultType result(mo.size1()); if (clear_result) result.clear(); mo.apply(vec, result); return result; } } #endif arpack-0.92.1/CPLUSPLUS/arpack_proto.hpp0000644000175000017500000002277211540551365014573 00000000000000/* ARPACK++ v1.0 8/1/1997 c++ interface to ARPACK code. MODULE arpackf.h ARPACK FORTRAN routines. ARPACK Authors Richard Lehoucq Danny Sorensen Chao Yang Dept. of Computational & Applied Mathematics Rice University Houston, Texas Slightly modified for PyLinear by Andreas Kloeckner 2003. */ #ifndef ARPACKF_H #define ARPACKF_H #include #include typedef int integer; typedef int logical; #define ARPACK_F77NAME(x) x##_ extern "C" { // double precision symmetric routines. void ARPACK_F77NAME(dsaupd)(integer *ido, char *bmat, integer *n, char *which, integer *nev, double *tol, double *resid, integer *ncv, double *V, integer *ldv, integer *iparam, integer *ipntr, double *workd, double *workl, integer *lworkl, integer *info); void ARPACK_F77NAME(dseupd)(logical *rvec, char *HowMny, logical *select, double *d, double *Z, integer *ldz, double *sigma, char *bmat, integer *n, char *which, integer *nev, double *tol, double *resid, integer *ncv, double *V, integer *ldv, integer *iparam, integer *ipntr, double *workd, double *workl, integer *lworkl, integer *info); // double precision nonsymmetric routines. void ARPACK_F77NAME(dnaupd)(integer *ido, char *bmat, integer *n, char *which, integer *nev, double *tol, double *resid, integer *ncv, double *V, integer *ldv, integer *iparam, integer *ipntr, double *workd, double *workl, integer *lworkl, integer *info); void ARPACK_F77NAME(dneupd)(logical *rvec, char *HowMny, logical *select, double *dr, double *di, double *Z, integer *ldz, double *sigmar, double *sigmai, double *workev, char *bmat, integer *n, char *which, integer *nev, double *tol, double *resid, integer *ncv, double *V, integer *ldv, integer *iparam, integer *ipntr, double *workd, double *workl, integer *lworkl, integer *info); // single precision symmetric routines. void ARPACK_F77NAME(ssaupd)(integer *ido, char *bmat, integer *n, char *which, integer *nev, float *tol, float *resid, integer *ncv, float *V, integer *ldv, integer *iparam, integer *ipntr, float *workd, float *workl, integer *lworkl, integer *info); void ARPACK_F77NAME(sseupd)(logical *rvec, char *HowMny, logical *select, float *d, float *Z, integer *ldz, float *sigma, char *bmat, integer *n, char *which, integer *nev, float *tol, float *resid, integer *ncv, float *V, integer *ldv, integer *iparam, integer *ipntr, float *workd, float *workl, integer *lworkl, integer *info); // single precision nonsymmetric routines. void ARPACK_F77NAME(snaupd)(integer *ido, char *bmat, integer *n, char *which, integer *nev, float *tol, float *resid, integer *ncv, float *V, integer *ldv, integer *iparam, integer *ipntr, float *workd, float *workl, integer *lworkl, integer *info); void ARPACK_F77NAME(sneupd)(logical *rvec, char *HowMny, logical *select, float *dr, float *di, float *Z, integer *ldz, float *sigmar, float *sigmai, float *workev, char *bmat, integer *n, char *which, integer *nev, float *tol, float *resid, integer *ncv, float *V, integer *ldv, integer *iparam, integer *ipntr, float *workd, float *workl, integer *lworkl, integer *info); // single precision complex routines. void ARPACK_F77NAME(cnaupd)(integer *ido, char *bmat, integer *n, char *which, integer *nev, float *tol, std::complex *resid, integer *ncv, std::complex *V, integer *ldv, integer *iparam, integer *ipntr, std::complex *workd, std::complex *workl, integer *lworkl, float *rwork, integer *info); void ARPACK_F77NAME(cneupd)(logical *rvec, char *HowMny, logical *select, std::complex *d, std::complex *Z, integer *ldz, std::complex *sigma, std::complex *workev, char *bmat, integer *n, char *which, integer *nev, float *tol, std::complex *resid, integer *ncv, std::complex *V, integer *ldv, integer *iparam, integer *ipntr, std::complex *workd, std::complex *workl, integer *lworkl, float *rwork, integer *info); // double precision complex routines. void ARPACK_F77NAME(znaupd)(integer *ido, char *bmat, integer *n, char *which, integer *nev, double *tol, std::complex *resid, integer *ncv, std::complex *V, integer *ldv, integer *iparam, integer *ipntr, std::complex *workd, std::complex *workl, integer *lworkl, double *rwork, integer *info); void ARPACK_F77NAME(zneupd)(logical *rvec, char *HowMny, logical *select, std::complex *d, std::complex *Z, integer *ldz, std::complex *sigma, std::complex *workev, char *bmat, integer *n, char *which, integer *nev, double *tol, std::complex *resid, integer *ncv, std::complex *V, integer *ldv, integer *iparam, integer *ipntr, std::complex *workd, std::complex *workl, integer *lworkl, double *rwork, integer *info); } namespace boost { namespace numeric { namespace bindings { namespace arpack { namespace detail { #define DECLARE_NAUPD(TYPE, BASETYPE) \ inline void naupd(integer *ido, char *bmat, integer *n, char *which, \ /*5*/integer *nev, BASETYPE *tol, TYPE *resid, \ /*9*/integer *ncv, TYPE *V, integer *ldv, \ /*12*/integer *iparam, integer *ipntr, TYPE *workd, \ /*15*/TYPE *workl, integer *lworkl, \ BASETYPE *rwork, integer *info) #define DEFINE_REAL_NAUPD(BASETYPE, LETTER) \ DECLARE_NAUPD(BASETYPE, BASETYPE) \ { \ ARPACK_F77NAME(LETTER##naupd)(ido, bmat, n, which, nev, tol, resid, ncv, V, ldv, iparam, ipntr, workd, workl, \ lworkl, info); \ } #define DEFINE_COMPLEX_NAUPD(BASETYPE, LETTER) \ DECLARE_NAUPD(std::complex, BASETYPE) \ { \ ARPACK_F77NAME(LETTER##naupd)(ido, bmat, n, which, nev, tol, resid, ncv, V, ldv, iparam, ipntr, workd, workl, \ lworkl, rwork, info); \ } #define DECLARE_NEUPD(TYPE, BASETYPE) \ inline void neupd(logical *rvec, char *HowMny, logical *select, \ /*4*/std::complex *d, TYPE *Z, integer *ldz, \ /*7*/std::complex *sigma, TYPE *workev, \ /*9*/char *bmat, integer *n, char *which, integer *nev, \ /*13*/BASETYPE *tol, TYPE *resid, integer *ncv, \ TYPE *V, integer *ldv, integer *iparam, \ integer *ipntr, TYPE *workd, \ TYPE *workl, integer *lworkl, \ BASETYPE *rwork, integer *info) \ #define DEFINE_REAL_NEUPD(BASETYPE, LETTER) \ DECLARE_NEUPD(BASETYPE, BASETYPE) \ { \ int nev_copy = *nev; /* BEWARE: neupd changes nev! */ \ boost::scoped_array d_real(new BASETYPE[nev_copy + 1]); \ boost::scoped_array d_imag(new BASETYPE[nev_copy + 1]); \ for (int i = 0; i < nev_copy+1; i++) /* This silences valgrind. */ \ { \ d_real[i] = 0; \ d_imag[i] = 0; \ } \ BASETYPE sigma_real = std::real(*sigma); \ BASETYPE sigma_imag = std::imag(*sigma); \ ARPACK_F77NAME(LETTER##neupd)(rvec, HowMny, select, d_real.get(), d_imag.get(), Z, ldz, \ &sigma_real, &sigma_imag, workev, bmat, n, which, nev, \ tol, resid, ncv, V, ldv, iparam, ipntr, workd, workl, lworkl, \ info); \ for (int i = 0; i < nev_copy+1; i++) \ d[i] = std::complex(d_real[i], d_imag[i]); \ } #define DEFINE_COMPLEX_NEUPD(BASETYPE, LETTER) \ DECLARE_NEUPD(std::complex, BASETYPE) \ { \ ARPACK_F77NAME(LETTER##neupd)(rvec, HowMny, select, d, Z, ldz, sigma, workev, bmat, n, which, nev, \ tol, resid, ncv, V, ldv, iparam, ipntr, workd, workl, lworkl, rwork, \ info); \ } DEFINE_REAL_NAUPD(float, s); DEFINE_REAL_NAUPD(double, d); DEFINE_COMPLEX_NAUPD(float, c); DEFINE_COMPLEX_NAUPD(double, z); DEFINE_REAL_NEUPD(float, s); DEFINE_REAL_NEUPD(double, d); DEFINE_COMPLEX_NEUPD(float, c); DEFINE_COMPLEX_NEUPD(double, z); }}}}} #endif // ARPACKF_H arpack-0.92.1/CPLUSPLUS/arpack.hpp0000644000175000017500000003360111540551342013334 00000000000000// // Boost C++ ARPACK bindings. // // Copyright (c) 2004-2006 // Andreas Kloeckner // // Permission to use, copy, modify, distribute and sell this software // and its documentation for any purpose is hereby granted without fee, // provided that the above copyright notice appear in all copies and // that both that copyright notice and this permission notice appear // in supporting documentation. The authors make no representations // about the suitability of this software for any purpose. // It is provided "as is" without express or implied warranty. // /* * For ARPACK Copyright, License and Availability see * detail/arpack_proto.hpp */ #ifndef HEADER_SEEN_ARPACK_HPP #define HEADER_SEEN_ARPACK_HPP #include #include #include #include #include #include #include //#include extern "C" { void dlarnv_(int *idist, int *iseed, int *n, double *x); } namespace boost { namespace numeric { namespace bindings { namespace arpack { enum which_eigenvalues { LARGEST_MAGNITUDE, SMALLEST_MAGNITUDE, LARGEST_REAL_PART, SMALLEST_REAL_PART, LARGEST_IMAGINARY_PART, SMALLEST_IMAGINARY_PART }; namespace detail { const char *map_which_to_string(which_eigenvalues we) { switch (we) { case LARGEST_MAGNITUDE: return "LM"; case SMALLEST_MAGNITUDE: return "SM"; case LARGEST_REAL_PART: return "LR"; case SMALLEST_REAL_PART: return "SR"; case LARGEST_IMAGINARY_PART: return "LI"; case SMALLEST_IMAGINARY_PART: return "SI"; default: throw std::runtime_error("arpack: invalid eigenvalue selector"); } } } enum arpack_mode { REGULAR_NON_GENERALIZED = 1, REGULAR_GENERALIZED = 2, SHIFT_AND_INVERT_GENERALIZED = 3 }; /* VectorType needs to be complex-valued. */ template struct results { typedef typename boost::numeric::bindings::traits::type_traits< typename boost::numeric::bindings::traits::vector_traits::value_type >::real_type real_type; typedef std::complex complex_type; typedef std::vector value_container; typedef std::vector vector_container; value_container m_ritz_values; vector_container m_ritz_vectors; }; namespace detail { template void make_results(unsigned nconv, unsigned n, typename results::real_type *z, std::complex::real_type> *d, results &my_results) { // result generation for real types // slightly more complicated: take care of complex conjugate pairs typedef typename results::real_type real_type; typedef std::complex complex_type; unsigned i = 0; my_results.m_ritz_values.clear(); my_results.m_ritz_vectors.clear(); while (i < nconv) { if (imag(d[i]) != 0) { // complex-conjugate pair if (i + 1 >= nconv) throw std::runtime_error("arpack: complex pair split up"); my_results.m_ritz_values.push_back(d[i]); my_results.m_ritz_values.push_back(d[i+1]); VectorType ritz_vector(n); // un-conjugate ritz vector for (unsigned j = 0; j < n; j++) ritz_vector[j] = complex_type(z[i*n + j], z[(i+1)*n +j]); my_results.m_ritz_vectors.push_back(ritz_vector); VectorType ritz_vector_2(n); // conjugate ritz vector for (unsigned j = 0; j < n; j++) ritz_vector_2[j] = complex_type(z[i*n + j], -z[(i+1)*n +j]); my_results.m_ritz_vectors.push_back(ritz_vector_2); i += 2; } else { // real eigenvalue, single eigenvector my_results.m_ritz_values.push_back(d[i]); VectorType ritz_vector(n); for (unsigned j = 0; j < n; j++) ritz_vector[j] = z[i*n + j]; my_results.m_ritz_vectors.push_back(ritz_vector); i++; } } } template void make_results(unsigned nconv, unsigned n, std::complex::real_type> *z, std::complex::real_type> *d, results &my_results) { // result generation for complex types my_results.m_ritz_values.clear(); my_results.m_ritz_vectors.clear(); // simple: just copy everything over. for (unsigned i = 0; i < nconv; i++) { my_results.m_ritz_values.push_back(d[i]); VectorType ritz_vector(n); for (unsigned j = 0; j < n; j++) ritz_vector[j] = z[i*n + j]; my_results.m_ritz_vectors.push_back(ritz_vector); } } template inline bool is_complex(const T &) { return false; } template inline bool is_complex(const std::complex &) { return true; } } template inline void perform_reverse_communication( const MatrixOrOperator &op, const MatrixOrOperator *m, arpack_mode mode, std::complex::real_type> spectral_shift, int number_of_eigenvalues, int number_of_arnoldi_vectors, results &res, const IterationVectorType &starting_vector, which_eigenvalues which_e = LARGEST_MAGNITUDE, typename boost::numeric::bindings::traits::type_traits< typename MatrixOrOperator::operand_type::value_type >::real_type tolerance = 1e-8, int max_iterations = 0 ) { typedef typename MatrixOrOperator::operand_type::value_type value_type; typedef typename boost::numeric::bindings::traits::type_traits::real_type real_type; typedef std::complex complex_type; int ido = 0; char bmat = m == 0 ? 'I' : 'G'; int n = op.size1(); if ((unsigned) n != op.size2()) throw std::runtime_error("arpack: matrix sizes don't match."); if ((m != 0) && ((unsigned) n != m->size1() || (unsigned) n != m->size2())) throw std::runtime_error("arpack: matrix sizes don't match."); char *which = const_cast(detail::map_which_to_string(which_e)); boost::scoped_array residual(new value_type[n]); for (int i = 0; i < n; i++) residual[i] = starting_vector[i]; boost::scoped_array v(new value_type[number_of_arnoldi_vectors * n]); int ldv = n; int iparam[11]; iparam[1-1] = 1; // exact shifts iparam[2-1] = 0; // unused iparam[3-1] = max_iterations != 0 ? max_iterations : 10000 * n; iparam[4-1] = 1; // block size iparam[5-1] = 0; // NCONV iparam[6-1] = 0; // IUPD, unused iparam[7-1] = mode; iparam[8-1] = 0; // NP, something to do with user-provided shifts iparam[9-1] = 0; // NUMOP iparam[10-1] = 0; // NUMOPB iparam[11-1] = 0; // NUMREO int info = 1; // we are specifying a previous residual int ipntr[14]; boost::scoped_array workd(new value_type[3*n]); int lworkl; lworkl = 3 * number_of_arnoldi_vectors * number_of_arnoldi_vectors + 6 * number_of_arnoldi_vectors; boost::scoped_array workl(new value_type[lworkl]); boost::scoped_array rwork(new double[number_of_arnoldi_vectors]); do { detail::naupd( &ido, &bmat, &n, which, &number_of_eigenvalues, &tolerance, residual.get(), &number_of_arnoldi_vectors, v.get(), &ldv, iparam, ipntr, workd.get(), workl.get(), &lworkl, rwork.get(), &info ); switch (info) { case 0: break; case 1: throw std::runtime_error("arpack, naupd: performed max. number of iterations (1)"); case 3: throw std::runtime_error("arpack, naupd: could not apply shifts (3)"); case -1: throw std::runtime_error("arpack, naupd: n not positive (-1)"); case -2: throw std::runtime_error("arpack, naupd: nev not positive (-2)"); case -3: throw std::runtime_error("arpack, naupd: ncv <= nev or ncv > n (-3)"); case -4: throw std::runtime_error("arpack, naupd: max_iterations must be bigger than zero (-4)"); case -5: throw std::runtime_error("arpack, naupd: invalid WHICH (-5)"); case -6: throw std::runtime_error("arpack, naupd: invalid BMAT (-6)"); case -7: throw std::runtime_error("arpack, naupd: work array too short (-7)"); case -8: throw std::runtime_error("arpack, naupd: LAPACK error (-8)"); case -9: throw std::runtime_error("arpack, naupd: starting vector is zero (-9)"); case -10: throw std::runtime_error("arpack, naupd: invalid MODE (-10)"); case -11: throw std::runtime_error("arpack, naupd: MODE and BMAT don't agree (-11)"); case -12: throw std::runtime_error("arpack, naupd: ISHIFT invalid (-12)"); case -9999: throw std::runtime_error("arpack, naupd: failed to build an Arnoldi factorization (-9999)"); default: throw std::runtime_error("arpack, naupd: invalid naupd error code: " + boost::lexical_cast(info)); } if (ido == -1 || ido == 1 || ido == 2) { value_type *x = workd.get() + ipntr[1-1] - 1; value_type *y = workd.get() + ipntr[2-1] - 1; IterationVectorType operand; operand.resize(n); std::copy(x, x+n, operand.begin()); IterationVectorType result; if (ido == 2) { if (m == 0) throw std::runtime_error("arpack, rci: multiplication by m requested, but m not supplied"); else result = prod(*m, operand); } else result = prod(op, operand); std::copy(result.begin(), result.end(), y); } else if (ido == 99) /*nothing*/; else throw std::runtime_error("arpack: reverse communication failure"); } while (ido != 99); if (max_iterations != 0) { if (max_iterations <= iparam[2]) throw std::runtime_error("arpack: hit iteration count limit"); max_iterations -= iparam[2]; } { // prepare for call to neupd int rvec = 1; char howmny = 'A'; boost::scoped_array select(new int[number_of_arnoldi_vectors]); // no-op boost::scoped_array d(new complex_type[number_of_eigenvalues+1]); unsigned z_size; unsigned workev_size; if (detail::is_complex(value_type())) { z_size = number_of_eigenvalues; workev_size = 2*number_of_arnoldi_vectors; } else { z_size = number_of_eigenvalues+1; workev_size = 3*number_of_arnoldi_vectors; } boost::scoped_array z(new value_type[z_size*n]); int ldz = n; boost::scoped_array workev(new value_type[workev_size]); detail::neupd( &rvec, &howmny, select.get(), d.get(), z.get(), &ldz, &spectral_shift, workev.get(), // naupd parameters follow &bmat, &n, which, &number_of_eigenvalues, &tolerance, residual.get(), &number_of_arnoldi_vectors, v.get(), &ldv, iparam, ipntr, workd.get(), workl.get(), &lworkl, rwork.get(), &info ); switch (info) { case 0: break; case 1: throw std::runtime_error("arpack, neupd: schur form could not be reordered (1)"); case -1: throw std::runtime_error("arpack, neupd: n not positive (-1)"); case -2: throw std::runtime_error("arpack, neupd: nev not positive (-2)"); case -3: throw std::runtime_error("arpack, neupd: ncv <= nev or ncv > n (-3)"); case -5: throw std::runtime_error("arpack, neupd: invalid WHICH (-5)"); case -6: throw std::runtime_error("arpack, neupd: invalid BMAT (-6)"); case -7: throw std::runtime_error("arpack, neupd: work array too short (-7)"); case -8: throw std::runtime_error("arpack, neupd: LAPACK error (-8)"); case -9: throw std::runtime_error("arpack, neupd: LAPACK _trevc failed (-9)"); case -10: throw std::runtime_error("arpack, neupd: invalid MODE (-10)"); case -11: throw std::runtime_error("arpack, neupd: MODE and BMAT don't agree (-11)"); case -12: throw std::runtime_error("arpack, neupd: HOWNY = S invalid (-12)"); case -13: throw std::runtime_error("arpack, neupd: HOWNY and RVEC don't agree (-13)"); case -14: throw std::runtime_error("arpack, neupd: no eigenvalues found (-14)"); default: throw std::runtime_error("arpack, neupd: invalid neupd error code: " + boost::lexical_cast(info)); } unsigned nconv = iparam[5-1]; detail::make_results(nconv, n, z.get(), d.get(), res); } } }}}} #endif arpack-0.92.1/COPYING0000644000175000017500000000374710776002551011036 00000000000000Rice BSD Software License Permits source and binary redistribution of the software ARPACK and P_ARPACK for both non-commercial and commercial use. Copyright (©) 2001, Rice University Developed by D.C. Sorensen, R.B. Lehoucq, C. Yang, and K. Maschhoff. All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. * If you modify the source for these routines we ask that you change the name of the routine and comment the changes made to the original. * Written notification is provided to the developers of intent to use this software. Also, we ask that use of ARPACK is properly cited in any resulting publications or software documentation. * Neither the name of Rice University (RICE) nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY RICE AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL RICE OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. arpack-0.92.1/config.guess0000755000175000017500000012763711344453613012331 00000000000000#! /bin/sh # Attempt to guess a canonical system name. # Copyright (C) 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, # 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 # Free Software Foundation, Inc. timestamp='2009-12-30' # This file is free software; you can redistribute it and/or modify it # under the terms of the GNU General Public License as published by # the Free Software Foundation; either version 2 of the License, or # (at your option) any later version. # # This program is distributed in the hope that it will be useful, but # WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU # General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program; if not, write to the Free Software # Foundation, Inc., 51 Franklin Street - Fifth Floor, Boston, MA # 02110-1301, USA. # # As a special exception to the GNU General Public License, if you # distribute this file as part of a program that contains a # configuration script generated by Autoconf, you may include it under # the same distribution terms that you use for the rest of that program. # Originally written by Per Bothner. Please send patches (context # diff format) to and include a ChangeLog # entry. # # This script attempts to guess a canonical system name similar to # config.sub. If it succeeds, it prints the system name on stdout, and # exits with 0. Otherwise, it exits with 1. # # You can get the latest version of this script from: # http://git.savannah.gnu.org/gitweb/?p=config.git;a=blob_plain;f=config.guess;hb=HEAD me=`echo "$0" | sed -e 's,.*/,,'` usage="\ Usage: $0 [OPTION] Output the configuration name of the system \`$me' is run on. Operation modes: -h, --help print this help, then exit -t, --time-stamp print date of last modification, then exit -v, --version print version number, then exit Report bugs and patches to ." version="\ GNU config.guess ($timestamp) Originally written by Per Bothner. Copyright (C) 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 Free Software Foundation, Inc. This is free software; see the source for copying conditions. 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) HP_ARCH=m68000 ;; 9000/[34]?? ) HP_ARCH=m68k ;; 9000/[678][0-9][0-9]) if [ -x /usr/bin/getconf ]; then sc_cpu_version=`/usr/bin/getconf SC_CPU_VERSION 2>/dev/null` sc_kernel_bits=`/usr/bin/getconf SC_KERNEL_BITS 2>/dev/null` case "${sc_cpu_version}" in 523) HP_ARCH="hppa1.0" ;; # CPU_PA_RISC1_0 528) HP_ARCH="hppa1.1" ;; # CPU_PA_RISC1_1 532) # CPU_PA_RISC2_0 case "${sc_kernel_bits}" in 32) HP_ARCH="hppa2.0n" ;; 64) HP_ARCH="hppa2.0w" ;; '') HP_ARCH="hppa2.0" ;; # HP-UX 10.20 esac ;; esac fi if [ "${HP_ARCH}" = "" ]; then eval $set_cc_for_build sed 's/^ //' << EOF >$dummy.c #define _HPUX_SOURCE #include #include int main () { #if defined(_SC_KERNEL_BITS) long bits = sysconf(_SC_KERNEL_BITS); #endif long cpu = sysconf (_SC_CPU_VERSION); switch (cpu) { case CPU_PA_RISC1_0: puts ("hppa1.0"); break; case CPU_PA_RISC1_1: puts ("hppa1.1"); break; case CPU_PA_RISC2_0: #if defined(_SC_KERNEL_BITS) switch (bits) { case 64: puts ("hppa2.0w"); break; case 32: puts ("hppa2.0n"); break; default: puts ("hppa2.0"); break; } break; #else /* !defined(_SC_KERNEL_BITS) */ puts ("hppa2.0"); break; #endif default: puts ("hppa1.0"); break; } exit (0); } EOF (CCOPTS= $CC_FOR_BUILD -o $dummy $dummy.c 2>/dev/null) && HP_ARCH=`$dummy` test -z "$HP_ARCH" && HP_ARCH=hppa fi ;; esac if [ ${HP_ARCH} = "hppa2.0w" ] then eval $set_cc_for_build # hppa2.0w-hp-hpux* has a 64-bit kernel and a compiler generating # 32-bit code. hppa64-hp-hpux* has the same kernel and a compiler # generating 64-bit code. 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CPU_IS_PA_RISC returns correct results, however. */ if (CPU_IS_PA_RISC (cpu)) { switch (cpu) { case CPU_PA_RISC1_0: puts ("hppa1.0-hitachi-hiuxwe2"); break; case CPU_PA_RISC1_1: puts ("hppa1.1-hitachi-hiuxwe2"); break; case CPU_PA_RISC2_0: puts ("hppa2.0-hitachi-hiuxwe2"); break; default: puts ("hppa-hitachi-hiuxwe2"); break; } } else if (CPU_IS_HP_MC68K (cpu)) puts ("m68k-hitachi-hiuxwe2"); else puts ("unknown-hitachi-hiuxwe2"); exit (0); } EOF $CC_FOR_BUILD -o $dummy $dummy.c && SYSTEM_NAME=`$dummy` && { echo "$SYSTEM_NAME"; exit; } echo unknown-hitachi-hiuxwe2 exit ;; 9000/7??:4.3bsd:*:* | 9000/8?[79]:4.3bsd:*:* ) echo hppa1.1-hp-bsd exit ;; 9000/8??:4.3bsd:*:*) echo hppa1.0-hp-bsd exit ;; *9??*:MPE/iX:*:* | *3000*:MPE/iX:*:*) echo hppa1.0-hp-mpeix exit ;; hp7??:OSF1:*:* | hp8?[79]:OSF1:*:* ) echo hppa1.1-hp-osf exit ;; hp8??:OSF1:*:*) echo hppa1.0-hp-osf exit ;; i*86:OSF1:*:*) if [ -x /usr/sbin/sysversion ] ; then echo ${UNAME_MACHINE}-unknown-osf1mk else echo ${UNAME_MACHINE}-unknown-osf1 fi exit ;; parisc*:Lites*:*:*) echo hppa1.1-hp-lites exit ;; C1*:ConvexOS:*:* | convex:ConvexOS:C1*:*) echo c1-convex-bsd exit ;; C2*:ConvexOS:*:* | convex:ConvexOS:C2*:*) if getsysinfo -f scalar_acc then echo c32-convex-bsd else echo c2-convex-bsd fi exit ;; C34*:ConvexOS:*:* | convex:ConvexOS:C34*:*) echo c34-convex-bsd exit ;; C38*:ConvexOS:*:* | convex:ConvexOS:C38*:*) echo c38-convex-bsd exit ;; C4*:ConvexOS:*:* | convex:ConvexOS:C4*:*) echo c4-convex-bsd exit ;; CRAY*Y-MP:*:*:*) echo ymp-cray-unicos${UNAME_RELEASE} | sed -e 's/\.[^.]*$/.X/' exit ;; CRAY*[A-Z]90:*:*:*) echo ${UNAME_MACHINE}-cray-unicos${UNAME_RELEASE} \ | sed -e 's/CRAY.*\([A-Z]90\)/\1/' \ -e y/ABCDEFGHIJKLMNOPQRSTUVWXYZ/abcdefghijklmnopqrstuvwxyz/ \ -e 's/\.[^.]*$/.X/' exit ;; CRAY*TS:*:*:*) echo t90-cray-unicos${UNAME_RELEASE} | sed -e 's/\.[^.]*$/.X/' exit ;; CRAY*T3E:*:*:*) echo alphaev5-cray-unicosmk${UNAME_RELEASE} | sed -e 's/\.[^.]*$/.X/' exit ;; CRAY*SV1:*:*:*) echo sv1-cray-unicos${UNAME_RELEASE} | sed -e 's/\.[^.]*$/.X/' exit ;; *:UNICOS/mp:*:*) echo craynv-cray-unicosmp${UNAME_RELEASE} | sed -e 's/\.[^.]*$/.X/' exit ;; F30[01]:UNIX_System_V:*:* | F700:UNIX_System_V:*:*) FUJITSU_PROC=`uname -m | tr 'ABCDEFGHIJKLMNOPQRSTUVWXYZ' 'abcdefghijklmnopqrstuvwxyz'` FUJITSU_SYS=`uname -p | tr 'ABCDEFGHIJKLMNOPQRSTUVWXYZ' 'abcdefghijklmnopqrstuvwxyz' | sed -e 's/\///'` FUJITSU_REL=`echo ${UNAME_RELEASE} | sed -e 's/ /_/'` echo "${FUJITSU_PROC}-fujitsu-${FUJITSU_SYS}${FUJITSU_REL}" exit ;; 5000:UNIX_System_V:4.*:*) FUJITSU_SYS=`uname -p | tr 'ABCDEFGHIJKLMNOPQRSTUVWXYZ' 'abcdefghijklmnopqrstuvwxyz' | sed -e 's/\///'` FUJITSU_REL=`echo ${UNAME_RELEASE} | tr 'ABCDEFGHIJKLMNOPQRSTUVWXYZ' 'abcdefghijklmnopqrstuvwxyz' | sed -e 's/ /_/'` echo "sparc-fujitsu-${FUJITSU_SYS}${FUJITSU_REL}" exit ;; i*86:BSD/386:*:* | i*86:BSD/OS:*:* | *:Ascend\ Embedded/OS:*:*) echo ${UNAME_MACHINE}-pc-bsdi${UNAME_RELEASE} exit ;; sparc*:BSD/OS:*:*) echo sparc-unknown-bsdi${UNAME_RELEASE} exit ;; *:BSD/OS:*:*) echo ${UNAME_MACHINE}-unknown-bsdi${UNAME_RELEASE} exit ;; *:FreeBSD:*:*) case ${UNAME_MACHINE} in pc98) echo i386-unknown-freebsd`echo ${UNAME_RELEASE}|sed -e 's/[-(].*//'` ;; amd64) echo x86_64-unknown-freebsd`echo ${UNAME_RELEASE}|sed -e 's/[-(].*//'` ;; *) echo ${UNAME_MACHINE}-unknown-freebsd`echo ${UNAME_RELEASE}|sed -e 's/[-(].*//'` ;; esac exit ;; i*:CYGWIN*:*) echo ${UNAME_MACHINE}-pc-cygwin exit ;; *:MINGW*:*) echo ${UNAME_MACHINE}-pc-mingw32 exit ;; i*:windows32*:*) # uname -m includes "-pc" on this system. echo ${UNAME_MACHINE}-mingw32 exit ;; i*:PW*:*) echo ${UNAME_MACHINE}-pc-pw32 exit ;; *:Interix*:*) case ${UNAME_MACHINE} in x86) echo i586-pc-interix${UNAME_RELEASE} exit ;; authenticamd | genuineintel | EM64T) echo x86_64-unknown-interix${UNAME_RELEASE} exit ;; IA64) echo ia64-unknown-interix${UNAME_RELEASE} exit ;; esac ;; [345]86:Windows_95:* | [345]86:Windows_98:* | [345]86:Windows_NT:*) echo i${UNAME_MACHINE}-pc-mks exit ;; 8664:Windows_NT:*) echo x86_64-pc-mks exit ;; i*:Windows_NT*:* | Pentium*:Windows_NT*:*) # How do we know it's Interix rather than the generic POSIX subsystem? # It also conflicts with pre-2.0 versions of AT&T UWIN. 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EV67) UNAME_MACHINE=alphaev67 ;; EV68*) UNAME_MACHINE=alphaev68 ;; esac objdump --private-headers /bin/sh | grep -q ld.so.1 if test "$?" = 0 ; then LIBC="libc1" ; else LIBC="" ; fi echo ${UNAME_MACHINE}-unknown-linux-gnu${LIBC} exit ;; arm*:Linux:*:*) eval $set_cc_for_build if echo __ARM_EABI__ | $CC_FOR_BUILD -E - 2>/dev/null \ | grep -q __ARM_EABI__ then echo ${UNAME_MACHINE}-unknown-linux-gnu else echo ${UNAME_MACHINE}-unknown-linux-gnueabi fi exit ;; avr32*:Linux:*:*) echo ${UNAME_MACHINE}-unknown-linux-gnu exit ;; cris:Linux:*:*) echo cris-axis-linux-gnu exit ;; crisv32:Linux:*:*) echo crisv32-axis-linux-gnu exit ;; frv:Linux:*:*) echo frv-unknown-linux-gnu exit ;; i*86:Linux:*:*) LIBC=gnu eval $set_cc_for_build sed 's/^ //' << EOF >$dummy.c #ifdef __dietlibc__ LIBC=dietlibc #endif EOF eval `$CC_FOR_BUILD -E $dummy.c 2>/dev/null | grep '^LIBC'` echo "${UNAME_MACHINE}-pc-linux-${LIBC}" exit ;; ia64:Linux:*:*) echo ${UNAME_MACHINE}-unknown-linux-gnu exit ;; m32r*:Linux:*:*) echo ${UNAME_MACHINE}-unknown-linux-gnu exit ;; m68*:Linux:*:*) echo ${UNAME_MACHINE}-unknown-linux-gnu exit ;; mips:Linux:*:* | mips64:Linux:*:*) eval $set_cc_for_build sed 's/^ //' << EOF >$dummy.c #undef CPU #undef ${UNAME_MACHINE} #undef ${UNAME_MACHINE}el #if defined(__MIPSEL__) || defined(__MIPSEL) || defined(_MIPSEL) || defined(MIPSEL) CPU=${UNAME_MACHINE}el #else #if defined(__MIPSEB__) || defined(__MIPSEB) || defined(_MIPSEB) || defined(MIPSEB) CPU=${UNAME_MACHINE} #else CPU= #endif #endif EOF eval `$CC_FOR_BUILD -E $dummy.c 2>/dev/null | grep '^CPU'` test x"${CPU}" != x && { echo "${CPU}-unknown-linux-gnu"; exit; } ;; or32:Linux:*:*) echo or32-unknown-linux-gnu exit ;; padre:Linux:*:*) echo sparc-unknown-linux-gnu exit ;; parisc64:Linux:*:* | hppa64:Linux:*:*) echo hppa64-unknown-linux-gnu exit ;; parisc:Linux:*:* | hppa:Linux:*:*) # Look for CPU level case `grep '^cpu[^a-z]*:' /proc/cpuinfo 2>/dev/null | cut -d' ' -f2` in PA7*) echo hppa1.1-unknown-linux-gnu ;; PA8*) echo hppa2.0-unknown-linux-gnu ;; *) echo hppa-unknown-linux-gnu ;; esac exit ;; ppc64:Linux:*:*) echo powerpc64-unknown-linux-gnu exit ;; ppc:Linux:*:*) echo powerpc-unknown-linux-gnu exit ;; s390:Linux:*:* | s390x:Linux:*:*) echo ${UNAME_MACHINE}-ibm-linux exit ;; sh64*:Linux:*:*) echo ${UNAME_MACHINE}-unknown-linux-gnu exit ;; sh*:Linux:*:*) echo ${UNAME_MACHINE}-unknown-linux-gnu exit ;; sparc:Linux:*:* | sparc64:Linux:*:*) echo ${UNAME_MACHINE}-unknown-linux-gnu exit ;; vax:Linux:*:*) echo ${UNAME_MACHINE}-dec-linux-gnu exit ;; x86_64:Linux:*:*) echo x86_64-unknown-linux-gnu exit ;; xtensa*:Linux:*:*) echo ${UNAME_MACHINE}-unknown-linux-gnu exit ;; i*86:DYNIX/ptx:4*:*) # ptx 4.0 does uname -s correctly, with DYNIX/ptx in there. # earlier versions are messed up and put the nodename in both # sysname and nodename. echo i386-sequent-sysv4 exit ;; i*86:UNIX_SV:4.2MP:2.*) # Unixware is an offshoot of SVR4, but it has its own version # number series starting with 2... # I am not positive that other SVR4 systems won't match this, # I just have to hope. -- rms. # Use sysv4.2uw... so that sysv4* matches it. echo ${UNAME_MACHINE}-pc-sysv4.2uw${UNAME_VERSION} exit ;; i*86:OS/2:*:*) # If we were able to find `uname', then EMX Unix compatibility # is probably installed. echo ${UNAME_MACHINE}-pc-os2-emx exit ;; i*86:XTS-300:*:STOP) echo ${UNAME_MACHINE}-unknown-stop exit ;; i*86:atheos:*:*) echo ${UNAME_MACHINE}-unknown-atheos exit ;; i*86:syllable:*:*) echo ${UNAME_MACHINE}-pc-syllable exit ;; i*86:LynxOS:2.*:* | i*86:LynxOS:3.[01]*:* | i*86:LynxOS:4.[02]*:*) echo i386-unknown-lynxos${UNAME_RELEASE} exit ;; i*86:*DOS:*:*) echo ${UNAME_MACHINE}-pc-msdosdjgpp exit ;; i*86:*:4.*:* | i*86:SYSTEM_V:4.*:*) UNAME_REL=`echo ${UNAME_RELEASE} | sed 's/\/MP$//'` if grep Novell /usr/include/link.h >/dev/null 2>/dev/null; then echo ${UNAME_MACHINE}-univel-sysv${UNAME_REL} else echo ${UNAME_MACHINE}-pc-sysv${UNAME_REL} fi exit ;; i*86:*:5:[678]*) # UnixWare 7.x, OpenUNIX and OpenServer 6. case `/bin/uname -X | grep "^Machine"` in *486*) UNAME_MACHINE=i486 ;; *Pentium) UNAME_MACHINE=i586 ;; *Pent*|*Celeron) UNAME_MACHINE=i686 ;; esac echo ${UNAME_MACHINE}-unknown-sysv${UNAME_RELEASE}${UNAME_SYSTEM}${UNAME_VERSION} exit ;; i*86:*:3.2:*) if test -f /usr/options/cb.name; then UNAME_REL=`sed -n 's/.*Version //p' /dev/null >/dev/null ; then UNAME_REL=`(/bin/uname -X|grep Release|sed -e 's/.*= //')` (/bin/uname -X|grep i80486 >/dev/null) && UNAME_MACHINE=i486 (/bin/uname -X|grep '^Machine.*Pentium' >/dev/null) \ && UNAME_MACHINE=i586 (/bin/uname -X|grep '^Machine.*Pent *II' >/dev/null) \ && UNAME_MACHINE=i686 (/bin/uname -X|grep '^Machine.*Pentium Pro' >/dev/null) \ && UNAME_MACHINE=i686 echo ${UNAME_MACHINE}-pc-sco$UNAME_REL else echo ${UNAME_MACHINE}-pc-sysv32 fi exit ;; pc:*:*:*) # Left here for compatibility: # uname -m prints for DJGPP always 'pc', but it prints nothing about # the processor, so we play safe by assuming i586. # Note: whatever this is, it MUST be the same as what config.sub # prints for the "djgpp" host, or else GDB configury will decide that # this is a cross-build. echo i586-pc-msdosdjgpp exit ;; Intel:Mach:3*:*) echo i386-pc-mach3 exit ;; paragon:*:*:*) echo i860-intel-osf1 exit ;; i860:*:4.*:*) # i860-SVR4 if grep Stardent /usr/include/sys/uadmin.h >/dev/null 2>&1 ; then echo i860-stardent-sysv${UNAME_RELEASE} # Stardent Vistra i860-SVR4 else # Add other i860-SVR4 vendors below as they are discovered. echo i860-unknown-sysv${UNAME_RELEASE} # Unknown i860-SVR4 fi exit ;; mini*:CTIX:SYS*5:*) # "miniframe" echo m68010-convergent-sysv exit ;; mc68k:UNIX:SYSTEM5:3.51m) echo m68k-convergent-sysv exit ;; M680?0:D-NIX:5.3:*) echo m68k-diab-dnix exit ;; M68*:*:R3V[5678]*:*) test -r /sysV68 && { echo 'm68k-motorola-sysv'; exit; } ;; 3[345]??:*:4.0:3.0 | 3[34]??A:*:4.0:3.0 | 3[34]??,*:*:4.0:3.0 | 3[34]??/*:*:4.0:3.0 | 4400:*:4.0:3.0 | 4850:*:4.0:3.0 | SKA40:*:4.0:3.0 | SDS2:*:4.0:3.0 | SHG2:*:4.0:3.0 | S7501*:*:4.0:3.0) OS_REL='' test -r /etc/.relid \ && OS_REL=.`sed -n 's/[^ ]* [^ ]* \([0-9][0-9]\).*/\1/p' < /etc/.relid` /bin/uname -p 2>/dev/null | grep 86 >/dev/null \ && { echo i486-ncr-sysv4.3${OS_REL}; exit; } /bin/uname -p 2>/dev/null | /bin/grep entium >/dev/null \ && { echo i586-ncr-sysv4.3${OS_REL}; exit; } ;; 3[34]??:*:4.0:* | 3[34]??,*:*:4.0:*) /bin/uname -p 2>/dev/null | grep 86 >/dev/null \ && { echo i486-ncr-sysv4; exit; } ;; NCR*:*:4.2:* | MPRAS*:*:4.2:*) OS_REL='.3' test -r /etc/.relid \ && OS_REL=.`sed -n 's/[^ ]* [^ ]* \([0-9][0-9]\).*/\1/p' < /etc/.relid` /bin/uname -p 2>/dev/null | grep 86 >/dev/null \ && { echo i486-ncr-sysv4.3${OS_REL}; exit; } /bin/uname -p 2>/dev/null | /bin/grep entium >/dev/null \ && { echo i586-ncr-sysv4.3${OS_REL}; exit; } /bin/uname -p 2>/dev/null | /bin/grep pteron >/dev/null \ && { echo i586-ncr-sysv4.3${OS_REL}; exit; } ;; m68*:LynxOS:2.*:* | m68*:LynxOS:3.0*:*) echo m68k-unknown-lynxos${UNAME_RELEASE} exit ;; mc68030:UNIX_System_V:4.*:*) echo m68k-atari-sysv4 exit ;; TSUNAMI:LynxOS:2.*:*) echo sparc-unknown-lynxos${UNAME_RELEASE} exit ;; rs6000:LynxOS:2.*:*) echo rs6000-unknown-lynxos${UNAME_RELEASE} exit ;; PowerPC:LynxOS:2.*:* | PowerPC:LynxOS:3.[01]*:* | PowerPC:LynxOS:4.[02]*:*) echo powerpc-unknown-lynxos${UNAME_RELEASE} exit ;; SM[BE]S:UNIX_SV:*:*) echo mips-dde-sysv${UNAME_RELEASE} exit ;; RM*:ReliantUNIX-*:*:*) echo mips-sni-sysv4 exit ;; RM*:SINIX-*:*:*) echo mips-sni-sysv4 exit ;; *:SINIX-*:*:*) if uname -p 2>/dev/null >/dev/null ; then UNAME_MACHINE=`(uname -p) 2>/dev/null` echo ${UNAME_MACHINE}-sni-sysv4 else echo ns32k-sni-sysv fi exit ;; PENTIUM:*:4.0*:*) # Unisys `ClearPath HMP IX 4000' SVR4/MP effort # says echo i586-unisys-sysv4 exit ;; *:UNIX_System_V:4*:FTX*) # From Gerald Hewes . # How about differentiating between stratus architectures? -djm echo hppa1.1-stratus-sysv4 exit ;; *:*:*:FTX*) # From seanf@swdc.stratus.com. echo i860-stratus-sysv4 exit ;; i*86:VOS:*:*) # From Paul.Green@stratus.com. echo ${UNAME_MACHINE}-stratus-vos exit ;; *:VOS:*:*) # From Paul.Green@stratus.com. echo hppa1.1-stratus-vos exit ;; mc68*:A/UX:*:*) echo m68k-apple-aux${UNAME_RELEASE} exit ;; news*:NEWS-OS:6*:*) echo mips-sony-newsos6 exit ;; R[34]000:*System_V*:*:* | R4000:UNIX_SYSV:*:* | R*000:UNIX_SV:*:*) if [ -d /usr/nec ]; then echo mips-nec-sysv${UNAME_RELEASE} else echo mips-unknown-sysv${UNAME_RELEASE} fi exit ;; BeBox:BeOS:*:*) # BeOS running on hardware made by Be, PPC only. echo powerpc-be-beos exit ;; BeMac:BeOS:*:*) # BeOS running on Mac or Mac clone, PPC only. echo powerpc-apple-beos exit ;; BePC:BeOS:*:*) # BeOS running on Intel PC compatible. echo i586-pc-beos exit ;; BePC:Haiku:*:*) # Haiku running on Intel PC compatible. echo i586-pc-haiku exit ;; SX-4:SUPER-UX:*:*) echo sx4-nec-superux${UNAME_RELEASE} exit ;; SX-5:SUPER-UX:*:*) echo sx5-nec-superux${UNAME_RELEASE} exit ;; SX-6:SUPER-UX:*:*) echo sx6-nec-superux${UNAME_RELEASE} exit ;; SX-7:SUPER-UX:*:*) echo sx7-nec-superux${UNAME_RELEASE} exit ;; SX-8:SUPER-UX:*:*) echo sx8-nec-superux${UNAME_RELEASE} exit ;; SX-8R:SUPER-UX:*:*) echo sx8r-nec-superux${UNAME_RELEASE} exit ;; Power*:Rhapsody:*:*) echo powerpc-apple-rhapsody${UNAME_RELEASE} exit ;; *:Rhapsody:*:*) echo ${UNAME_MACHINE}-apple-rhapsody${UNAME_RELEASE} exit ;; *:Darwin:*:*) UNAME_PROCESSOR=`uname -p` || UNAME_PROCESSOR=unknown case $UNAME_PROCESSOR in i386) eval $set_cc_for_build if [ "$CC_FOR_BUILD" != 'no_compiler_found' ]; then if (echo '#ifdef __LP64__'; echo IS_64BIT_ARCH; echo '#endif') | \ (CCOPTS= $CC_FOR_BUILD -E - 2>/dev/null) | \ grep IS_64BIT_ARCH >/dev/null then UNAME_PROCESSOR="x86_64" fi fi ;; unknown) UNAME_PROCESSOR=powerpc ;; esac echo ${UNAME_PROCESSOR}-apple-darwin${UNAME_RELEASE} exit ;; *:procnto*:*:* | *:QNX:[0123456789]*:*) UNAME_PROCESSOR=`uname -p` if test "$UNAME_PROCESSOR" = "x86"; then UNAME_PROCESSOR=i386 UNAME_MACHINE=pc fi echo ${UNAME_PROCESSOR}-${UNAME_MACHINE}-nto-qnx${UNAME_RELEASE} exit ;; *:QNX:*:4*) echo i386-pc-qnx exit ;; NSE-?:NONSTOP_KERNEL:*:*) echo nse-tandem-nsk${UNAME_RELEASE} exit ;; NSR-?:NONSTOP_KERNEL:*:*) echo nsr-tandem-nsk${UNAME_RELEASE} exit ;; *:NonStop-UX:*:*) echo mips-compaq-nonstopux exit ;; BS2000:POSIX*:*:*) echo bs2000-siemens-sysv exit ;; DS/*:UNIX_System_V:*:*) echo ${UNAME_MACHINE}-${UNAME_SYSTEM}-${UNAME_RELEASE} exit ;; *:Plan9:*:*) # "uname -m" is not consistent, so use $cputype instead. 386 # is converted to i386 for consistency with other x86 # operating systems. if test "$cputype" = "386"; then UNAME_MACHINE=i386 else UNAME_MACHINE="$cputype" fi echo ${UNAME_MACHINE}-unknown-plan9 exit ;; *:TOPS-10:*:*) echo pdp10-unknown-tops10 exit ;; *:TENEX:*:*) echo pdp10-unknown-tenex exit ;; KS10:TOPS-20:*:* | KL10:TOPS-20:*:* | TYPE4:TOPS-20:*:*) echo pdp10-dec-tops20 exit ;; XKL-1:TOPS-20:*:* | TYPE5:TOPS-20:*:*) echo pdp10-xkl-tops20 exit ;; *:TOPS-20:*:*) echo pdp10-unknown-tops20 exit ;; *:ITS:*:*) echo pdp10-unknown-its exit ;; SEI:*:*:SEIUX) echo mips-sei-seiux${UNAME_RELEASE} exit ;; *:DragonFly:*:*) echo ${UNAME_MACHINE}-unknown-dragonfly`echo ${UNAME_RELEASE}|sed -e 's/[-(].*//'` exit ;; *:*VMS:*:*) UNAME_MACHINE=`(uname -p) 2>/dev/null` case "${UNAME_MACHINE}" in A*) echo alpha-dec-vms ; exit ;; I*) echo ia64-dec-vms ; exit ;; V*) echo vax-dec-vms ; exit ;; esac ;; *:XENIX:*:SysV) echo i386-pc-xenix exit ;; i*86:skyos:*:*) echo ${UNAME_MACHINE}-pc-skyos`echo ${UNAME_RELEASE}` | sed -e 's/ .*$//' exit ;; i*86:rdos:*:*) echo ${UNAME_MACHINE}-pc-rdos exit ;; i*86:AROS:*:*) echo ${UNAME_MACHINE}-pc-aros exit ;; esac #echo '(No uname command or uname output not recognized.)' 1>&2 #echo "${UNAME_MACHINE}:${UNAME_SYSTEM}:${UNAME_RELEASE}:${UNAME_VERSION}" 1>&2 eval $set_cc_for_build cat >$dummy.c < # include #endif main () { #if defined (sony) #if defined (MIPSEB) /* BFD wants "bsd" instead of "newsos". Perhaps BFD should be changed, I don't know.... */ printf ("mips-sony-bsd\n"); exit (0); #else #include printf ("m68k-sony-newsos%s\n", #ifdef NEWSOS4 "4" #else "" #endif ); exit (0); #endif #endif #if defined (__arm) && defined (__acorn) && defined (__unix) printf ("arm-acorn-riscix\n"); exit (0); #endif #if defined (hp300) && !defined (hpux) printf ("m68k-hp-bsd\n"); exit (0); #endif #if defined (NeXT) #if !defined (__ARCHITECTURE__) #define __ARCHITECTURE__ "m68k" #endif int version; version=`(hostinfo | sed -n 's/.*NeXT Mach \([0-9]*\).*/\1/p') 2>/dev/null`; if (version < 4) printf ("%s-next-nextstep%d\n", __ARCHITECTURE__, version); else printf ("%s-next-openstep%d\n", __ARCHITECTURE__, version); exit (0); #endif #if defined (MULTIMAX) || defined (n16) #if defined (UMAXV) printf ("ns32k-encore-sysv\n"); exit (0); #else #if defined (CMU) printf ("ns32k-encore-mach\n"); exit (0); #else printf ("ns32k-encore-bsd\n"); exit (0); #endif #endif #endif #if defined (__386BSD__) printf ("i386-pc-bsd\n"); exit (0); #endif #if defined (sequent) #if defined (i386) printf ("i386-sequent-dynix\n"); exit (0); #endif #if defined (ns32000) printf ("ns32k-sequent-dynix\n"); exit (0); #endif #endif #if defined (_SEQUENT_) struct utsname un; uname(&un); if (strncmp(un.version, "V2", 2) == 0) { printf ("i386-sequent-ptx2\n"); exit (0); } if (strncmp(un.version, "V1", 2) == 0) { /* XXX is V1 correct? */ printf ("i386-sequent-ptx1\n"); exit (0); } printf ("i386-sequent-ptx\n"); exit (0); #endif #if defined (vax) # if !defined (ultrix) # include # if defined (BSD) # if BSD == 43 printf ("vax-dec-bsd4.3\n"); exit (0); # else # if BSD == 199006 printf ("vax-dec-bsd4.3reno\n"); exit (0); # else printf ("vax-dec-bsd\n"); exit (0); # endif # endif # else printf ("vax-dec-bsd\n"); exit (0); # endif # else printf ("vax-dec-ultrix\n"); exit (0); # endif #endif #if defined (alliant) && defined (i860) printf ("i860-alliant-bsd\n"); exit (0); #endif exit (1); } EOF $CC_FOR_BUILD -o $dummy $dummy.c 2>/dev/null && SYSTEM_NAME=`$dummy` && { echo "$SYSTEM_NAME"; exit; } # Apollos put the system type in the environment. test -d /usr/apollo && { echo ${ISP}-apollo-${SYSTYPE}; exit; } # Convex versions that predate uname can use getsysinfo(1) if [ -x /usr/convex/getsysinfo ] then case `getsysinfo -f cpu_type` in c1*) echo c1-convex-bsd exit ;; c2*) if getsysinfo -f scalar_acc then echo c32-convex-bsd else echo c2-convex-bsd fi exit ;; c34*) echo c34-convex-bsd exit ;; c38*) echo c38-convex-bsd exit ;; c4*) echo c4-convex-bsd exit ;; esac fi cat >&2 < in order to provide the needed information to handle your system. config.guess timestamp = $timestamp uname -m = `(uname -m) 2>/dev/null || echo unknown` uname -r = `(uname -r) 2>/dev/null || echo unknown` uname -s = `(uname -s) 2>/dev/null || echo unknown` uname -v = `(uname -v) 2>/dev/null || echo unknown` /usr/bin/uname -p = `(/usr/bin/uname -p) 2>/dev/null` /bin/uname -X = `(/bin/uname -X) 2>/dev/null` hostinfo = `(hostinfo) 2>/dev/null` /bin/universe = `(/bin/universe) 2>/dev/null` /usr/bin/arch -k = `(/usr/bin/arch -k) 2>/dev/null` /bin/arch = `(/bin/arch) 2>/dev/null` /usr/bin/oslevel = `(/usr/bin/oslevel) 2>/dev/null` /usr/convex/getsysinfo = `(/usr/convex/getsysinfo) 2>/dev/null` UNAME_MACHINE = ${UNAME_MACHINE} UNAME_RELEASE = ${UNAME_RELEASE} UNAME_SYSTEM = ${UNAME_SYSTEM} UNAME_VERSION = ${UNAME_VERSION} EOF exit 1 # Local variables: # eval: (add-hook 'write-file-hooks 'time-stamp) # time-stamp-start: "timestamp='" # time-stamp-format: "%:y-%02m-%02d" # time-stamp-end: "'" # End: arpack-0.92.1/UTIL/0000755000175000017500000000000011540551571010626 500000000000000arpack-0.92.1/UTIL/icnteq.f0000644000175000017500000000060410776001577012206 00000000000000c c----------------------------------------------------------------------- c c Count the number of elements equal to a specified integer value. c integer function icnteq (n, array, value) c integer n, value integer array(*) c k = 0 do 10 i = 1, n if (array(i) .eq. value) k = k + 1 10 continue icnteq = k c return end arpack-0.92.1/UTIL/dmout.f0000644000175000017500000001265710776001577012066 00000000000000*----------------------------------------------------------------------- * Routine: DMOUT * * Purpose: Real matrix output routine. * * Usage: CALL DMOUT (LOUT, M, N, A, LDA, IDIGIT, IFMT) * * Arguments * M - Number of rows of A. (Input) * N - Number of columns of A. (Input) * A - Real M by N matrix to be printed. (Input) * LDA - Leading dimension of A exactly as specified in the * dimension statement of the calling program. (Input) * IFMT - Format to be used in printing matrix A. (Input) * IDIGIT - Print up to IABS(IDIGIT) decimal digits per number. (In) * If IDIGIT .LT. 0, printing is done with 72 columns. * If IDIGIT .GT. 0, printing is done with 132 columns. * *----------------------------------------------------------------------- * SUBROUTINE DMOUT( LOUT, M, N, A, LDA, IDIGIT, IFMT ) * ... * ... SPECIFICATIONS FOR ARGUMENTS * ... * ... SPECIFICATIONS FOR LOCAL VARIABLES * .. Scalar Arguments .. CHARACTER*( * ) IFMT INTEGER IDIGIT, LDA, LOUT, M, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ) * .. * .. Local Scalars .. CHARACTER*80 LINE INTEGER I, J, K1, K2, LLL, NDIGIT * .. * .. Local Arrays .. CHARACTER ICOL( 3 ) * .. * .. Intrinsic Functions .. INTRINSIC LEN, MIN, MIN0 * .. * .. Data statements .. DATA ICOL( 1 ), ICOL( 2 ), ICOL( 3 ) / 'C', 'o', $ 'l' / * .. * .. Executable Statements .. * ... * ... FIRST EXECUTABLE STATEMENT * LLL = MIN( LEN( IFMT ), 80 ) DO 10 I = 1, LLL LINE( I: I ) = '-' 10 CONTINUE * DO 20 I = LLL + 1, 80 LINE( I: I ) = ' ' 20 CONTINUE * WRITE( LOUT, FMT = 9999 )IFMT, LINE( 1: LLL ) 9999 FORMAT( / 1X, A, / 1X, A ) * IF( M.LE.0 .OR. N.LE.0 .OR. LDA.LE.0 ) $ RETURN NDIGIT = IDIGIT IF( IDIGIT.EQ.0 ) $ NDIGIT = 4 * *======================================================================= * CODE FOR OUTPUT USING 72 COLUMNS FORMAT *======================================================================= * IF( IDIGIT.LT.0 ) THEN NDIGIT = -IDIGIT IF( NDIGIT.LE.4 ) THEN DO 40 K1 = 1, N, 5 K2 = MIN0( N, K1+4 ) WRITE( LOUT, FMT = 9998 )( ICOL, I, I = K1, K2 ) DO 30 I = 1, M WRITE( LOUT, FMT = 9994 )I, ( A( I, J ), J = K1, K2 ) 30 CONTINUE 40 CONTINUE * ELSE IF( NDIGIT.LE.6 ) THEN DO 60 K1 = 1, N, 4 K2 = MIN0( N, K1+3 ) WRITE( LOUT, FMT = 9997 )( ICOL, I, I = K1, K2 ) DO 50 I = 1, M WRITE( LOUT, FMT = 9993 )I, ( A( I, J ), J = K1, K2 ) 50 CONTINUE 60 CONTINUE * ELSE IF( NDIGIT.LE.10 ) THEN DO 80 K1 = 1, N, 3 K2 = MIN0( N, K1+2 ) WRITE( LOUT, FMT = 9996 )( ICOL, I, I = K1, K2 ) DO 70 I = 1, M WRITE( LOUT, FMT = 9992 )I, ( A( I, J ), J = K1, K2 ) 70 CONTINUE 80 CONTINUE * ELSE DO 100 K1 = 1, N, 2 K2 = MIN0( N, K1+1 ) WRITE( LOUT, FMT = 9995 )( ICOL, I, I = K1, K2 ) DO 90 I = 1, M WRITE( LOUT, FMT = 9991 )I, ( A( I, J ), J = K1, K2 ) 90 CONTINUE 100 CONTINUE END IF * *======================================================================= * CODE FOR OUTPUT USING 132 COLUMNS FORMAT *======================================================================= * ELSE IF( NDIGIT.LE.4 ) THEN DO 120 K1 = 1, N, 10 K2 = MIN0( N, K1+9 ) WRITE( LOUT, FMT = 9998 )( ICOL, I, I = K1, K2 ) DO 110 I = 1, M WRITE( LOUT, FMT = 9994 )I, ( A( I, J ), J = K1, K2 ) 110 CONTINUE 120 CONTINUE * ELSE IF( NDIGIT.LE.6 ) THEN DO 140 K1 = 1, N, 8 K2 = MIN0( N, K1+7 ) WRITE( LOUT, FMT = 9997 )( ICOL, I, I = K1, K2 ) DO 130 I = 1, M WRITE( LOUT, FMT = 9993 )I, ( A( I, J ), J = K1, K2 ) 130 CONTINUE 140 CONTINUE * ELSE IF( NDIGIT.LE.10 ) THEN DO 160 K1 = 1, N, 6 K2 = MIN0( N, K1+5 ) WRITE( LOUT, FMT = 9996 )( ICOL, I, I = K1, K2 ) DO 150 I = 1, M WRITE( LOUT, FMT = 9992 )I, ( A( I, J ), J = K1, K2 ) 150 CONTINUE 160 CONTINUE * ELSE DO 180 K1 = 1, N, 5 K2 = MIN0( N, K1+4 ) WRITE( LOUT, FMT = 9995 )( ICOL, I, I = K1, K2 ) DO 170 I = 1, M WRITE( LOUT, FMT = 9991 )I, ( A( I, J ), J = K1, K2 ) 170 CONTINUE 180 CONTINUE END IF END IF WRITE( LOUT, FMT = 9990 ) * 9998 FORMAT( 10X, 10( 4X, 3A1, I4, 1X ) ) 9997 FORMAT( 10X, 8( 5X, 3A1, I4, 2X ) ) 9996 FORMAT( 10X, 6( 7X, 3A1, I4, 4X ) ) 9995 FORMAT( 10X, 5( 9X, 3A1, I4, 6X ) ) 9994 FORMAT( 1X, ' Row', I4, ':', 1X, 1P, 10D12.3 ) 9993 FORMAT( 1X, ' Row', I4, ':', 1X, 1P, 8D14.5 ) 9992 FORMAT( 1X, ' Row', I4, ':', 1X, 1P, 6D18.9 ) 9991 FORMAT( 1X, ' Row', I4, ':', 1X, 1P, 5D22.13 ) 9990 FORMAT( 1X, ' ' ) * RETURN END arpack-0.92.1/UTIL/cmout.f0000644000175000017500000002106310776001577012054 00000000000000* * Routine: CMOUT * * Purpose: Complex matrix output routine. * * Usage: CALL CMOUT (LOUT, M, N, A, LDA, IDIGIT, IFMT) * * Arguments * M - Number of rows of A. (Input) * N - Number of columns of A. (Input) * A - Complex M by N matrix to be printed. (Input) * LDA - Leading dimension of A exactly as specified in the * dimension statement of the calling program. (Input) * IFMT - Format to be used in printing matrix A. (Input) * IDIGIT - Print up to IABS(IDIGIT) decimal digits per number. (In) * If IDIGIT .LT. 0, printing is done with 72 columns. * If IDIGIT .GT. 0, printing is done with 132 columns. * *\SCCS Information: @(#) * FILE: cmout.f SID: 2.1 DATE OF SID: 11/16/95 RELEASE: 2 * *----------------------------------------------------------------------- * SUBROUTINE CMOUT( LOUT, M, N, A, LDA, IDIGIT, IFMT ) * ... * ... SPECIFICATIONS FOR ARGUMENTS INTEGER M, N, IDIGIT, LDA, LOUT Complex & A( LDA, * ) CHARACTER IFMT*( * ) * ... * ... SPECIFICATIONS FOR LOCAL VARIABLES INTEGER I, J, NDIGIT, K1, K2, LLL CHARACTER*1 ICOL( 3 ) CHARACTER*80 LINE * ... * ... SPECIFICATIONS INTRINSICS INTRINSIC MIN * DATA ICOL( 1 ), ICOL( 2 ), ICOL( 3 ) / 'C', 'o', $ 'l' / * ... * ... FIRST EXECUTABLE STATEMENT * LLL = MIN( LEN( IFMT ), 80 ) DO 10 I = 1, LLL LINE( I: I ) = '-' 10 CONTINUE * DO 20 I = LLL + 1, 80 LINE( I: I ) = ' ' 20 CONTINUE * WRITE( LOUT, 9999 )IFMT, LINE( 1: LLL ) 9999 FORMAT( / 1X, A / 1X, A ) * IF( M.LE.0 .OR. N.LE.0 .OR. LDA.LE.0 ) $ RETURN NDIGIT = IDIGIT IF( IDIGIT.EQ.0 ) $ NDIGIT = 4 * *======================================================================= * CODE FOR OUTPUT USING 72 COLUMNS FORMAT *======================================================================= * IF( IDIGIT.LT.0 ) THEN NDIGIT = -IDIGIT IF( NDIGIT.LE.4 ) THEN DO 40 K1 = 1, N, 2 K2 = MIN0( N, K1+1 ) WRITE( LOUT, 9998 )( ICOL, I, I = K1, K2 ) DO 30 I = 1, M IF (K1.NE.N) THEN WRITE( LOUT, 9994 )I, ( A( I, J ), J = K1, K2 ) ELSE WRITE( LOUT, 9984 )I, ( A( I, J ), J = K1, K2 ) END IF 30 CONTINUE 40 CONTINUE * ELSE IF( NDIGIT.LE.6 ) THEN DO 60 K1 = 1, N, 2 K2 = MIN0( N, K1+1 ) WRITE( LOUT, 9997 )( ICOL, I, I = K1, K2 ) DO 50 I = 1, M IF (K1.NE.N) THEN WRITE( LOUT, 9993 )I, ( A( I, J ), J = K1, K2 ) ELSE WRITE( LOUT, 9983 )I, ( A( I, J ), J = K1, K2 ) END IF 50 CONTINUE 60 CONTINUE * ELSE IF( NDIGIT.LE.8 ) THEN DO 80 K1 = 1, N, 2 K2 = MIN0( N, K1+1 ) WRITE( LOUT, 9996 )( ICOL, I, I = K1, K2 ) DO 70 I = 1, M IF (K1.NE.N) THEN WRITE( LOUT, 9992 )I, ( A( I, J ), J = K1, K2 ) ELSE WRITE( LOUT, 9982 )I, ( A( I, J ), J = K1, K2 ) END IF 70 CONTINUE 80 CONTINUE * ELSE DO 100 K1 = 1, N WRITE( LOUT, 9995 ) ICOL, K1 DO 90 I = 1, M WRITE( LOUT, 9991 )I, A( I, K1 ) 90 CONTINUE 100 CONTINUE END IF * *======================================================================= * CODE FOR OUTPUT USING 132 COLUMNS FORMAT *======================================================================= * ELSE IF( NDIGIT.LE.4 ) THEN DO 120 K1 = 1, N, 4 K2 = MIN0( N, K1+3 ) WRITE( LOUT, 9998 )( ICOL, I, I = K1, K2 ) DO 110 I = 1, M IF ((K1+3).LE.N) THEN WRITE( LOUT, 9974 )I, ( A( I, J ), J = K1, K2 ) ELSE IF ((K1+3-N).EQ.1) THEN WRITE( LOUT, 9964 )I, ( A( I, J ), J = k1, K2 ) ELSE IF ((K1+3-N).EQ.2) THEN WRITE( LOUT, 9954 )I, ( A( I, J ), J = K1, K2 ) ELSE IF ((K1+3-N).EQ.3) THEN WRITE( LOUT, 9944 )I, ( A( I, J ), J = K1, K2 ) END IF 110 CONTINUE 120 CONTINUE * ELSE IF( NDIGIT.LE.6 ) THEN DO 140 K1 = 1, N, 3 K2 = MIN0( N, K1+ 2) WRITE( LOUT, 9997 )( ICOL, I, I = K1, K2 ) DO 130 I = 1, M IF ((K1+2).LE.N) THEN WRITE( LOUT, 9973 )I, ( A( I, J ), J = K1, K2 ) ELSE IF ((K1+2-N).EQ.1) THEN WRITE( LOUT, 9963 )I, ( A( I, J ), J = K1, K2 ) ELSE IF ((K1+2-N).EQ.2) THEN WRITE( LOUT, 9953 )I, ( A( I, J ), J = K1, K2 ) END IF 130 CONTINUE 140 CONTINUE * ELSE IF( NDIGIT.LE.8 ) THEN DO 160 K1 = 1, N, 3 K2 = MIN0( N, K1+2 ) WRITE( LOUT, 9996 )( ICOL, I, I = K1, K2 ) DO 150 I = 1, M IF ((K1+2).LE.N) THEN WRITE( LOUT, 9972 )I, ( A( I, J ), J = K1, K2 ) ELSE IF ((K1+2-N).EQ.1) THEN WRITE( LOUT, 9962 )I, ( A( I, J ), J = K1, K2 ) ELSE IF ((K1+2-N).EQ.2) THEN WRITE( LOUT, 9952 )I, ( A( I, J ), J = K1, K2 ) END IF 150 CONTINUE 160 CONTINUE * ELSE DO 180 K1 = 1, N, 2 K2 = MIN0( N, K1+1 ) WRITE( LOUT, 9995 )( ICOL, I, I = K1, K2 ) DO 170 I = 1, M IF ((K1+1).LE.N) THEN WRITE( LOUT, 9971 )I, ( A( I, J ), J = K1, K2 ) ELSE WRITE( LOUT, 9961 )I, ( A( I, J ), J = K1, K2 ) END IF 170 CONTINUE 180 CONTINUE END IF END IF WRITE( LOUT, 9990 ) * 9998 FORMAT( 11X, 4( 9X, 3A1, I4, 9X ) ) 9997 FORMAT( 10X, 4( 11X, 3A1, I4, 11X ) ) 9996 FORMAT( 10X, 3( 13X, 3A1, I4, 13X ) ) 9995 FORMAT( 12X, 2( 18x, 3A1, I4, 18X ) ) * *======================================================== * FORMAT FOR 72 COLUMN *======================================================== * * DISPLAY 4 SIGNIFICANT DIGITS * 9994 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,2('(',E10.3,',',E10.3,') ') ) 9984 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,1('(',E10.3,',',E10.3,') ') ) * * DISPLAY 6 SIGNIFICANT DIGITS * 9993 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,2('(',E12.5,',',E12.5,') ') ) 9983 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,1('(',E12.5,',',E12.5,') ') ) * * DISPLAY 8 SIGNIFICANT DIGITS * 9992 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,2('(',E14.7,',',E14.7,') ') ) 9982 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,1('(',E14.7,',',E14.7,') ') ) * * DISPLAY 13 SIGNIFICANT DIGITS * 9991 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,1('(',E20.13,',',E20.13,')') ) 9990 FORMAT( 1X, ' ' ) * * *======================================================== * FORMAT FOR 132 COLUMN *======================================================== * * DISPLAY 4 SIGNIFICANT DIGIT * 9974 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,4('(',E10.3,',',E10.3,') ') ) 9964 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,3('(',E10.3,',',E10.3,') ') ) 9954 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,2('(',E10.3,',',E10.3,') ') ) 9944 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,1('(',E10.3,',',E10.3,') ') ) * * DISPLAY 6 SIGNIFICANT DIGIT * 9973 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,3('(',E12.5,',',E12.5,') ') ) 9963 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,2('(',E12.5,',',E12.5,') ') ) 9953 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,1('(',E12.5,',',E12.5,') ') ) * * DISPLAY 8 SIGNIFICANT DIGIT * 9972 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,3('(',E14.7,',',E14.7,') ') ) 9962 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,2('(',E14.7,',',E14.7,') ') ) 9952 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,1('(',E14.7,',',E14.7,') ') ) * * DISPLAY 13 SIGNIFICANT DIGIT * 9971 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,2('(',E20.13,',',E20.13, & ') ')) 9961 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,1('(',E20.13,',',E20.13, & ') ')) * * * * RETURN END arpack-0.92.1/UTIL/ivout.f0000644000175000017500000000645710776001577012105 00000000000000C----------------------------------------------------------------------- C Routine: IVOUT C C Purpose: Integer vector output routine. C C Usage: CALL IVOUT (LOUT, N, IX, IDIGIT, IFMT) C C Arguments C N - Length of array IX. (Input) C IX - Integer array to be printed. (Input) C IFMT - Format to be used in printing array IX. (Input) C IDIGIT - Print up to ABS(IDIGIT) decimal digits / number. (Input) C If IDIGIT .LT. 0, printing is done with 72 columns. C If IDIGIT .GT. 0, printing is done with 132 columns. C C----------------------------------------------------------------------- C SUBROUTINE IVOUT (LOUT, N, IX, IDIGIT, IFMT) C ... C ... SPECIFICATIONS FOR ARGUMENTS INTEGER IX(*), N, IDIGIT, LOUT CHARACTER IFMT*(*) C ... C ... SPECIFICATIONS FOR LOCAL VARIABLES INTEGER I, NDIGIT, K1, K2, LLL CHARACTER*80 LINE * ... * ... SPECIFICATIONS INTRINSICS INTRINSIC MIN * C LLL = MIN ( LEN ( IFMT ), 80 ) DO 1 I = 1, LLL LINE(I:I) = '-' 1 CONTINUE C DO 2 I = LLL+1, 80 LINE(I:I) = ' ' 2 CONTINUE C WRITE ( LOUT, 2000 ) IFMT, LINE(1:LLL) 2000 FORMAT ( /1X, A /1X, A ) C IF (N .LE. 0) RETURN NDIGIT = IDIGIT IF (IDIGIT .EQ. 0) NDIGIT = 4 C C======================================================================= C CODE FOR OUTPUT USING 72 COLUMNS FORMAT C======================================================================= C IF (IDIGIT .LT. 0) THEN C NDIGIT = -IDIGIT IF (NDIGIT .LE. 4) THEN DO 10 K1 = 1, N, 10 K2 = MIN0(N,K1+9) WRITE(LOUT,1000) K1,K2,(IX(I),I=K1,K2) 10 CONTINUE C ELSE IF (NDIGIT .LE. 6) THEN DO 30 K1 = 1, N, 7 K2 = MIN0(N,K1+6) WRITE(LOUT,1001) K1,K2,(IX(I),I=K1,K2) 30 CONTINUE C ELSE IF (NDIGIT .LE. 10) THEN DO 50 K1 = 1, N, 5 K2 = MIN0(N,K1+4) WRITE(LOUT,1002) K1,K2,(IX(I),I=K1,K2) 50 CONTINUE C ELSE DO 70 K1 = 1, N, 3 K2 = MIN0(N,K1+2) WRITE(LOUT,1003) K1,K2,(IX(I),I=K1,K2) 70 CONTINUE END IF C C======================================================================= C CODE FOR OUTPUT USING 132 COLUMNS FORMAT C======================================================================= C ELSE C IF (NDIGIT .LE. 4) THEN DO 90 K1 = 1, N, 20 K2 = MIN0(N,K1+19) WRITE(LOUT,1000) K1,K2,(IX(I),I=K1,K2) 90 CONTINUE C ELSE IF (NDIGIT .LE. 6) THEN DO 110 K1 = 1, N, 15 K2 = MIN0(N,K1+14) WRITE(LOUT,1001) K1,K2,(IX(I),I=K1,K2) 110 CONTINUE C ELSE IF (NDIGIT .LE. 10) THEN DO 130 K1 = 1, N, 10 K2 = MIN0(N,K1+9) WRITE(LOUT,1002) K1,K2,(IX(I),I=K1,K2) 130 CONTINUE C ELSE DO 150 K1 = 1, N, 7 K2 = MIN0(N,K1+6) WRITE(LOUT,1003) K1,K2,(IX(I),I=K1,K2) 150 CONTINUE END IF END IF WRITE (LOUT,1004) C 1000 FORMAT(1X,I4,' - ',I4,':',20(1X,I5)) 1001 FORMAT(1X,I4,' - ',I4,':',15(1X,I7)) 1002 FORMAT(1X,I4,' - ',I4,':',10(1X,I11)) 1003 FORMAT(1X,I4,' - ',I4,':',7(1X,I15)) 1004 FORMAT(1X,' ') C RETURN END arpack-0.92.1/UTIL/arscnd.f0000644000175000017500000000143110776001577012174 00000000000000 SUBROUTINE ARSCND( T ) * REAL T * * -- LAPACK auxiliary routine (preliminary version) -- * Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., * Courant Institute, Argonne National Lab, and Rice University * July 26, 1991 * * Purpose * ======= * * ARSCND returns the user time for a process in seconds. * This version gets the time from the system function ETIME. * * .. Local Scalars .. REAL T1 * .. * .. Local Arrays .. REAL TARRAY( 2 ) * .. * .. External Functions .. REAL ETIME EXTERNAL ETIME * .. * .. Executable Statements .. * * T1 = ETIME( TARRAY ) * T = TARRAY( 1 ) T = 0 RETURN * * End of ARSCND * END arpack-0.92.1/UTIL/iswap.f0000644000175000017500000000231310776001577012045 00000000000000 subroutine iswap (n,sx,incx,sy,incy) c c interchanges two vectors. c uses unrolled loops for increments equal to 1. c jack dongarra, linpack, 3/11/78. c integer sx(1),sy(1),stemp integer i,incx,incy,ix,iy,m,mp1,n c if(n.le.0)return if(incx.eq.1.and.incy.eq.1)go to 20 c c code for unequal increments or equal increments not equal c to 1 c ix = 1 iy = 1 if(incx.lt.0)ix = (-n+1)*incx + 1 if(incy.lt.0)iy = (-n+1)*incy + 1 do 10 i = 1,n stemp = sx(ix) sx(ix) = sy(iy) sy(iy) = stemp ix = ix + incx iy = iy + incy 10 continue return c c code for both increments equal to 1 c c c clean-up loop c 20 m = mod(n,3) if( m .eq. 0 ) go to 40 do 30 i = 1,m stemp = sx(i) sx(i) = sy(i) sy(i) = stemp 30 continue if( n .lt. 3 ) return 40 mp1 = m + 1 do 50 i = mp1,n,3 stemp = sx(i) sx(i) = sy(i) sy(i) = stemp stemp = sx(i + 1) sx(i + 1) = sy(i + 1) sy(i + 1) = stemp stemp = sx(i + 2) sx(i + 2) = sy(i + 2) sy(i + 2) = stemp 50 continue return end arpack-0.92.1/UTIL/zmout.f0000644000175000017500000002107410776001577012105 00000000000000* * Routine: ZMOUT * * Purpose: Complex*16 matrix output routine. * * Usage: CALL ZMOUT (LOUT, M, N, A, LDA, IDIGIT, IFMT) * * Arguments * M - Number of rows of A. (Input) * N - Number of columns of A. (Input) * A - Complex*16 M by N matrix to be printed. (Input) * LDA - Leading dimension of A exactly as specified in the * dimension statement of the calling program. (Input) * IFMT - Format to be used in printing matrix A. (Input) * IDIGIT - Print up to IABS(IDIGIT) decimal digits per number. (In) * If IDIGIT .LT. 0, printing is done with 72 columns. * If IDIGIT .GT. 0, printing is done with 132 columns. * *\SCCS Information: @(#) * FILE: zmout.f SID: 2.1 DATE OF SID: 11/16/95 RELEASE: 2 * *----------------------------------------------------------------------- * SUBROUTINE ZMOUT( LOUT, M, N, A, LDA, IDIGIT, IFMT ) * ... * ... SPECIFICATIONS FOR ARGUMENTS INTEGER M, N, IDIGIT, LDA, LOUT Complex*16 & A( LDA, * ) CHARACTER IFMT*( * ) * ... * ... SPECIFICATIONS FOR LOCAL VARIABLES INTEGER I, J, NDIGIT, K1, K2, LLL CHARACTER*1 ICOL( 3 ) CHARACTER*80 LINE * ... * ... SPECIFICATIONS INTRINSICS INTRINSIC MIN * DATA ICOL( 1 ), ICOL( 2 ), ICOL( 3 ) / 'C', 'o', $ 'l' / * ... * ... FIRST EXECUTABLE STATEMENT * LLL = MIN( LEN( IFMT ), 80 ) DO 10 I = 1, LLL LINE( I: I ) = '-' 10 CONTINUE * DO 20 I = LLL + 1, 80 LINE( I: I ) = ' ' 20 CONTINUE * WRITE( LOUT, 9999 )IFMT, LINE( 1: LLL ) 9999 FORMAT( / 1X, A / 1X, A ) * IF( M.LE.0 .OR. N.LE.0 .OR. LDA.LE.0 ) $ RETURN NDIGIT = IDIGIT IF( IDIGIT.EQ.0 ) $ NDIGIT = 4 * *======================================================================= * CODE FOR OUTPUT USING 72 COLUMNS FORMAT *======================================================================= * IF( IDIGIT.LT.0 ) THEN NDIGIT = -IDIGIT IF( NDIGIT.LE.4 ) THEN DO 40 K1 = 1, N, 2 K2 = MIN0( N, K1+1 ) WRITE( LOUT, 9998 )( ICOL, I, I = K1, K2 ) DO 30 I = 1, M IF (K1.NE.N) THEN WRITE( LOUT, 9994 )I, ( A( I, J ), J = K1, K2 ) ELSE WRITE( LOUT, 9984 )I, ( A( I, J ), J = K1, K2 ) END IF 30 CONTINUE 40 CONTINUE * ELSE IF( NDIGIT.LE.6 ) THEN DO 60 K1 = 1, N, 2 K2 = MIN0( N, K1+1 ) WRITE( LOUT, 9997 )( ICOL, I, I = K1, K2 ) DO 50 I = 1, M IF (K1.NE.N) THEN WRITE( LOUT, 9993 )I, ( A( I, J ), J = K1, K2 ) ELSE WRITE( LOUT, 9983 )I, ( A( I, J ), J = K1, K2 ) END IF 50 CONTINUE 60 CONTINUE * ELSE IF( NDIGIT.LE.8 ) THEN DO 80 K1 = 1, N, 2 K2 = MIN0( N, K1+1 ) WRITE( LOUT, 9996 )( ICOL, I, I = K1, K2 ) DO 70 I = 1, M IF (K1.NE.N) THEN WRITE( LOUT, 9992 )I, ( A( I, J ), J = K1, K2 ) ELSE WRITE( LOUT, 9982 )I, ( A( I, J ), J = K1, K2 ) END IF 70 CONTINUE 80 CONTINUE * ELSE DO 100 K1 = 1, N WRITE( LOUT, 9995 ) ICOL, K1 DO 90 I = 1, M WRITE( LOUT, 9991 )I, A( I, K1 ) 90 CONTINUE 100 CONTINUE END IF * *======================================================================= * CODE FOR OUTPUT USING 132 COLUMNS FORMAT *======================================================================= * ELSE IF( NDIGIT.LE.4 ) THEN DO 120 K1 = 1, N, 4 K2 = MIN0( N, K1+3 ) WRITE( LOUT, 9998 )( ICOL, I, I = K1, K2 ) DO 110 I = 1, M IF ((K1+3).LE.N) THEN WRITE( LOUT, 9974 )I, ( A( I, J ), J = K1, K2 ) ELSE IF ((K1+3-N).EQ.1) THEN WRITE( LOUT, 9964 )I, ( A( I, J ), J = k1, K2 ) ELSE IF ((K1+3-N).EQ.2) THEN WRITE( LOUT, 9954 )I, ( A( I, J ), J = K1, K2 ) ELSE IF ((K1+3-N).EQ.3) THEN WRITE( LOUT, 9944 )I, ( A( I, J ), J = K1, K2 ) END IF 110 CONTINUE 120 CONTINUE * ELSE IF( NDIGIT.LE.6 ) THEN DO 140 K1 = 1, N, 3 K2 = MIN0( N, K1+ 2) WRITE( LOUT, 9997 )( ICOL, I, I = K1, K2 ) DO 130 I = 1, M IF ((K1+2).LE.N) THEN WRITE( LOUT, 9973 )I, ( A( I, J ), J = K1, K2 ) ELSE IF ((K1+2-N).EQ.1) THEN WRITE( LOUT, 9963 )I, ( A( I, J ), J = K1, K2 ) ELSE IF ((K1+2-N).EQ.2) THEN WRITE( LOUT, 9953 )I, ( A( I, J ), J = K1, K2 ) END IF 130 CONTINUE 140 CONTINUE * ELSE IF( NDIGIT.LE.8 ) THEN DO 160 K1 = 1, N, 3 K2 = MIN0( N, K1+2 ) WRITE( LOUT, 9996 )( ICOL, I, I = K1, K2 ) DO 150 I = 1, M IF ((K1+2).LE.N) THEN WRITE( LOUT, 9972 )I, ( A( I, J ), J = K1, K2 ) ELSE IF ((K1+2-N).EQ.1) THEN WRITE( LOUT, 9962 )I, ( A( I, J ), J = K1, K2 ) ELSE IF ((K1+2-N).EQ.2) THEN WRITE( LOUT, 9952 )I, ( A( I, J ), J = K1, K2 ) END IF 150 CONTINUE 160 CONTINUE * ELSE DO 180 K1 = 1, N, 2 K2 = MIN0( N, K1+1 ) WRITE( LOUT, 9995 )( ICOL, I, I = K1, K2 ) DO 170 I = 1, M IF ((K1+1).LE.N) THEN WRITE( LOUT, 9971 )I, ( A( I, J ), J = K1, K2 ) ELSE WRITE( LOUT, 9961 )I, ( A( I, J ), J = K1, K2 ) END IF 170 CONTINUE 180 CONTINUE END IF END IF WRITE( LOUT, 9990 ) * 9998 FORMAT( 11X, 4( 9X, 3A1, I4, 9X ) ) 9997 FORMAT( 10X, 4( 11X, 3A1, I4, 11X ) ) 9996 FORMAT( 10X, 3( 13X, 3A1, I4, 13X ) ) 9995 FORMAT( 12X, 2( 18x, 3A1, I4, 18X ) ) * *======================================================== * FORMAT FOR 72 COLUMN *======================================================== * * DISPLAY 4 SIGNIFICANT DIGITS * 9994 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,2('(',D10.3,',',D10.3,') ') ) 9984 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,1('(',D10.3,',',D10.3,') ') ) * * DISPLAY 6 SIGNIFICANT DIGITS * 9993 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,2('(',D12.5,',',D12.5,') ') ) 9983 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,1('(',D12.5,',',D12.5,') ') ) * * DISPLAY 8 SIGNIFICANT DIGITS * 9992 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,2('(',D14.7,',',D14.7,') ') ) 9982 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,1('(',D14.7,',',D14.7,') ') ) * * DISPLAY 13 SIGNIFICANT DIGITS * 9991 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,1('(',D20.13,',',D20.13,')') ) 9990 FORMAT( 1X, ' ' ) * * *======================================================== * FORMAT FOR 132 COLUMN *======================================================== * * DISPLAY 4 SIGNIFICANT DIGIT * 9974 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,4('(',D10.3,',',D10.3,') ') ) 9964 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,3('(',D10.3,',',D10.3,') ') ) 9954 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,2('(',D10.3,',',D10.3,') ') ) 9944 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,1('(',D10.3,',',D10.3,') ') ) * * DISPLAY 6 SIGNIFICANT DIGIT * 9973 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,3('(',D12.5,',',D12.5,') ') ) 9963 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,2('(',D12.5,',',D12.5,') ') ) 9953 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,1('(',D12.5,',',D12.5,') ') ) * * DISPLAY 8 SIGNIFICANT DIGIT * 9972 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,3('(',D14.7,',',D14.7,') ') ) 9962 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,2('(',D14.7,',',D14.7,') ') ) 9952 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,1('(',D14.7,',',D14.7,') ') ) * * DISPLAY 13 SIGNIFICANT DIGIT * 9971 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,2('(',D20.13,',',D20.13, & ') ')) 9961 FORMAT( 1X, ' Row', I4, ':', 1X, 1P,1('(',D20.13,',',D20.13, & ') ')) * * * * RETURN END arpack-0.92.1/UTIL/svout.f0000644000175000017500000000714410776001577012111 00000000000000*----------------------------------------------------------------------- * Routine: SVOUT * * Purpose: Real vector output routine. * * Usage: CALL SVOUT (LOUT, N, SX, IDIGIT, IFMT) * * Arguments * N - Length of array SX. (Input) * SX - Real array to be printed. (Input) * IFMT - Format to be used in printing array SX. (Input) * IDIGIT - Print up to IABS(IDIGIT) decimal digits per number. (In) * If IDIGIT .LT. 0, printing is done with 72 columns. * If IDIGIT .GT. 0, printing is done with 132 columns. * *----------------------------------------------------------------------- * SUBROUTINE SVOUT( LOUT, N, SX, IDIGIT, IFMT ) * ... * ... SPECIFICATIONS FOR ARGUMENTS INTEGER N, IDIGIT, LOUT REAL SX( * ) CHARACTER IFMT*( * ) * ... * ... SPECIFICATIONS FOR LOCAL VARIABLES INTEGER I, NDIGIT, K1, K2, LLL CHARACTER*80 LINE * ... * ... FIRST EXECUTABLE STATEMENT * * LLL = MIN( LEN( IFMT ), 80 ) DO 10 I = 1, LLL LINE( I: I ) = '-' 10 CONTINUE * DO 20 I = LLL + 1, 80 LINE( I: I ) = ' ' 20 CONTINUE * WRITE( LOUT, 9999 )IFMT, LINE( 1: LLL ) 9999 FORMAT( / 1X, A / 1X, A ) * IF( N.LE.0 ) $ RETURN NDIGIT = IDIGIT IF( IDIGIT.EQ.0 ) $ NDIGIT = 4 * *======================================================================= * CODE FOR OUTPUT USING 72 COLUMNS FORMAT *======================================================================= * IF( IDIGIT.LT.0 ) THEN NDIGIT = -IDIGIT IF( NDIGIT.LE.4 ) THEN DO 30 K1 = 1, N, 5 K2 = MIN0( N, K1+4 ) WRITE( LOUT, 9998 )K1, K2, ( SX( I ), I = K1, K2 ) 30 CONTINUE ELSE IF( NDIGIT.LE.6 ) THEN DO 40 K1 = 1, N, 4 K2 = MIN0( N, K1+3 ) WRITE( LOUT, 9997 )K1, K2, ( SX( I ), I = K1, K2 ) 40 CONTINUE ELSE IF( NDIGIT.LE.10 ) THEN DO 50 K1 = 1, N, 3 K2 = MIN0( N, K1+2 ) WRITE( LOUT, 9996 )K1, K2, ( SX( I ), I = K1, K2 ) 50 CONTINUE ELSE DO 60 K1 = 1, N, 2 K2 = MIN0( N, K1+1 ) WRITE( LOUT, 9995 )K1, K2, ( SX( I ), I = K1, K2 ) 60 CONTINUE END IF * *======================================================================= * CODE FOR OUTPUT USING 132 COLUMNS FORMAT *======================================================================= * ELSE IF( NDIGIT.LE.4 ) THEN DO 70 K1 = 1, N, 10 K2 = MIN0( N, K1+9 ) WRITE( LOUT, 9998 )K1, K2, ( SX( I ), I = K1, K2 ) 70 CONTINUE ELSE IF( NDIGIT.LE.6 ) THEN DO 80 K1 = 1, N, 8 K2 = MIN0( N, K1+7 ) WRITE( LOUT, 9997 )K1, K2, ( SX( I ), I = K1, K2 ) 80 CONTINUE ELSE IF( NDIGIT.LE.10 ) THEN DO 90 K1 = 1, N, 6 K2 = MIN0( N, K1+5 ) WRITE( LOUT, 9996 )K1, K2, ( SX( I ), I = K1, K2 ) 90 CONTINUE ELSE DO 100 K1 = 1, N, 5 K2 = MIN0( N, K1+4 ) WRITE( LOUT, 9995 )K1, K2, ( SX( I ), I = K1, K2 ) 100 CONTINUE END IF END IF WRITE( LOUT, 9994 ) RETURN 9998 FORMAT( 1X, I4, ' - ', I4, ':', 1P10E12.3 ) 9997 FORMAT( 1X, I4, ' - ', I4, ':', 1X, 1P8E14.5 ) 9996 FORMAT( 1X, I4, ' - ', I4, ':', 1X, 1P6E18.9 ) 9995 FORMAT( 1X, I4, ' - ', I4, ':', 1X, 1P5E24.13 ) 9994 FORMAT( 1X, ' ' ) END arpack-0.92.1/UTIL/cvout.f0000644000175000017500000002001510776001577012061 00000000000000c----------------------------------------------------------------------- c c\SCCS Information: @(#) c FILE: cvout.f SID: 2.1 DATE OF SID: 11/16/95 RELEASE: 2 c *----------------------------------------------------------------------- * Routine: CVOUT * * Purpose: Complex vector output routine. * * Usage: CALL CVOUT (LOUT, N, CX, IDIGIT, IFMT) * * Arguments * N - Length of array CX. (Input) * CX - Complex array to be printed. (Input) * IFMT - Format to be used in printing array CX. (Input) * IDIGIT - Print up to IABS(IDIGIT) decimal digits per number. (In) * If IDIGIT .LT. 0, printing is done with 72 columns. * If IDIGIT .GT. 0, printing is done with 132 columns. * *----------------------------------------------------------------------- * SUBROUTINE CVOUT( LOUT, N, CX, IDIGIT, IFMT ) * ... * ... SPECIFICATIONS FOR ARGUMENTS INTEGER N, IDIGIT, LOUT Complex & CX( * ) CHARACTER IFMT*( * ) * ... * ... SPECIFICATIONS FOR LOCAL VARIABLES INTEGER I, NDIGIT, K1, K2, LLL CHARACTER*80 LINE * ... * ... FIRST EXECUTABLE STATEMENT * * LLL = MIN( LEN( IFMT ), 80 ) DO 10 I = 1, LLL LINE( I: I ) = '-' 10 CONTINUE * DO 20 I = LLL + 1, 80 LINE( I: I ) = ' ' 20 CONTINUE * WRITE( LOUT, 9999 )IFMT, LINE( 1: LLL ) 9999 FORMAT( / 1X, A / 1X, A ) * IF( N.LE.0 ) $ RETURN NDIGIT = IDIGIT IF( IDIGIT.EQ.0 ) $ NDIGIT = 4 * *======================================================================= * CODE FOR OUTPUT USING 72 COLUMNS FORMAT *======================================================================= * IF( IDIGIT.LT.0 ) THEN NDIGIT = -IDIGIT IF( NDIGIT.LE.4 ) THEN DO 30 K1 = 1, N, 2 K2 = MIN0( N, K1+1 ) IF (K1.NE.N) THEN WRITE( LOUT, 9998 )K1, K2, ( CX( I ), $ I = K1, K2 ) ELSE WRITE( LOUT, 9997 )K1, K2, ( CX( I ), $ I = K1, K2 ) END IF 30 CONTINUE ELSE IF( NDIGIT.LE.6 ) THEN DO 40 K1 = 1, N, 2 K2 = MIN0( N, K1+1 ) IF (K1.NE.N) THEN WRITE( LOUT, 9988 )K1, K2, ( CX( I ), $ I = K1, K2 ) ELSE WRITE( LOUT, 9987 )K1, K2, ( CX( I ), $ I = K1, K2 ) END IF 40 CONTINUE ELSE IF( NDIGIT.LE.8 ) THEN DO 50 K1 = 1, N, 2 K2 = MIN0( N, K1+1 ) IF (K1.NE.N) THEN WRITE( LOUT, 9978 )K1, K2, ( CX( I ), $ I = K1, K2 ) ELSE WRITE( LOUT, 9977 )K1, K2, ( CX( I ), $ I = K1, K2 ) END IF 50 CONTINUE ELSE DO 60 K1 = 1, N WRITE( LOUT, 9968 )K1, K1, CX( I ) 60 CONTINUE END IF * *======================================================================= * CODE FOR OUTPUT USING 132 COLUMNS FORMAT *======================================================================= * ELSE IF( NDIGIT.LE.4 ) THEN DO 70 K1 = 1, N, 4 K2 = MIN0( N, K1+3 ) IF ((K1+3).LE.N) THEN WRITE( LOUT, 9958 )K1, K2, ( CX( I ), $ I = K1, K2 ) ELSE IF ((K1+3-N) .EQ. 1) THEN WRITE( LOUT, 9957 )K1, K2, ( CX( I ), $ I = K1, K2 ) ELSE IF ((K1+3-N) .EQ. 2) THEN WRITE( LOUT, 9956 )K1, K2, ( CX( I ), $ I = K1, K2 ) ELSE IF ((K1+3-N) .EQ. 1) THEN WRITE( LOUT, 9955 )K1, K2, ( CX( I ), $ I = K1, K2 ) END IF 70 CONTINUE ELSE IF( NDIGIT.LE.6 ) THEN DO 80 K1 = 1, N, 3 K2 = MIN0( N, K1+2 ) IF ((K1+2).LE.N) THEN WRITE( LOUT, 9948 )K1, K2, ( CX( I ), $ I = K1, K2 ) ELSE IF ((K1+2-N) .EQ. 1) THEN WRITE( LOUT, 9947 )K1, K2, ( CX( I ), $ I = K1, K2 ) ELSE IF ((K1+2-N) .EQ. 2) THEN WRITE( LOUT, 9946 )K1, K2, ( CX( I ), $ I = K1, K2 ) END IF 80 CONTINUE ELSE IF( NDIGIT.LE.8 ) THEN DO 90 K1 = 1, N, 3 K2 = MIN0( N, K1+2 ) IF ((K1+2).LE.N) THEN WRITE( LOUT, 9938 )K1, K2, ( CX( I ), $ I = K1, K2 ) ELSE IF ((K1+2-N) .EQ. 1) THEN WRITE( LOUT, 9937 )K1, K2, ( CX( I ), $ I = K1, K2 ) ELSE IF ((K1+2-N) .EQ. 2) THEN WRITE( LOUT, 9936 )K1, K2, ( CX( I ), $ I = K1, K2 ) END IF 90 CONTINUE ELSE DO 100 K1 = 1, N, 2 K2 = MIN0( N, K1+1 ) IF ((K1+2).LE.N) THEN WRITE( LOUT, 9928 )K1, K2, ( CX( I ), $ I = K1, K2 ) ELSE IF ((K1+2-N) .EQ. 1) THEN WRITE( LOUT, 9927 )K1, K2, ( CX( I ), $ I = K1, K2 ) END IF 100 CONTINUE END IF END IF WRITE( LOUT, 9994 ) RETURN * *======================================================================= * FORMAT FOR 72 COLUMNS *======================================================================= * * DISPLAY 4 SIGNIFICANT DIGITS * 9998 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,2('(',E10.3,',',E10.3,') ') ) 9997 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,1('(',E10.3,',',E10.3,') ') ) * * DISPLAY 6 SIGNIFICANT DIGITS * 9988 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,2('(',E12.5,',',E12.5,') ') ) 9987 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,1('(',E12.5,',',E12.5,') ') ) * * DISPLAY 8 SIGNIFICANT DIGITS * 9978 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,2('(',E14.7,',',E14.7,') ') ) 9977 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,1('(',E14.7,',',E14.7,') ') ) * * DISPLAY 13 SIGNIFICANT DIGITS * 9968 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,1('(',E20.13,',',E20.13,') ') ) * *========================================================================= * FORMAT FOR 132 COLUMNS *========================================================================= * * DISPLAY 4 SIGNIFICANT DIGITS * 9958 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,4('(',E10.3,',',E10.3,') ') ) 9957 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,3('(',E10.3,',',E10.3,') ') ) 9956 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,2('(',E10.3,',',E10.3,') ') ) 9955 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,1('(',E10.3,',',E10.3,') ') ) * * DISPLAY 6 SIGNIFICANT DIGITS * 9948 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,3('(',E12.5,',',E12.5,') ') ) 9947 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,2('(',E12.5,',',E12.5,') ') ) 9946 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,1('(',E12.5,',',E12.5,') ') ) * * DISPLAY 8 SIGNIFICANT DIGITS * 9938 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,3('(',E14.7,',',E14.7,') ') ) 9937 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,2('(',E14.7,',',E14.7,') ') ) 9936 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,1('(',E14.7,',',E14.7,') ') ) * * DISPLAY 13 SIGNIFICANT DIGITS * 9928 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,2('(',E20.13,',',E20.13,') ') ) 9927 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,1('(',E20.13,',',E20.13,') ') ) * * * 9994 FORMAT( 1X, ' ' ) END arpack-0.92.1/UTIL/iset.f0000644000175000017500000000050510776001577011667 00000000000000c c----------------------------------------------------------------------- c c Only work with increment equal to 1 right now. c subroutine iset (n, value, array, inc) c integer n, value, inc integer array(*) c do 10 i = 1, n array(i) = value 10 continue c return end arpack-0.92.1/UTIL/smout.f0000644000175000017500000001214510776001577012075 00000000000000*----------------------------------------------------------------------- * Routine: SMOUT * * Purpose: Real matrix output routine. * * Usage: CALL SMOUT (LOUT, M, N, A, LDA, IDIGIT, IFMT) * * Arguments * M - Number of rows of A. (Input) * N - Number of columns of A. (Input) * A - Real M by N matrix to be printed. (Input) * LDA - Leading dimension of A exactly as specified in the * dimension statement of the calling program. (Input) * IFMT - Format to be used in printing matrix A. (Input) * IDIGIT - Print up to IABS(IDIGIT) decimal digits per number. (In) * If IDIGIT .LT. 0, printing is done with 72 columns. * If IDIGIT .GT. 0, printing is done with 132 columns. * *----------------------------------------------------------------------- * SUBROUTINE SMOUT( LOUT, M, N, A, LDA, IDIGIT, IFMT ) * ... * ... SPECIFICATIONS FOR ARGUMENTS INTEGER M, N, IDIGIT, LDA, LOUT REAL A( LDA, * ) CHARACTER IFMT*( * ) * ... * ... SPECIFICATIONS FOR LOCAL VARIABLES INTEGER I, J, NDIGIT, K1, K2, LLL CHARACTER*1 ICOL( 3 ) CHARACTER*80 LINE * ... * ... SPECIFICATIONS INTRINSICS INTRINSIC MIN * DATA ICOL( 1 ), ICOL( 2 ), ICOL( 3 ) / 'C', 'o', $ 'l' / * ... * ... FIRST EXECUTABLE STATEMENT * LLL = MIN( LEN( IFMT ), 80 ) DO 10 I = 1, LLL LINE( I: I ) = '-' 10 CONTINUE * DO 20 I = LLL + 1, 80 LINE( I: I ) = ' ' 20 CONTINUE * WRITE( LOUT, 9999 )IFMT, LINE( 1: LLL ) 9999 FORMAT( / 1X, A / 1X, A ) * IF( M.LE.0 .OR. N.LE.0 .OR. LDA.LE.0 ) $ RETURN NDIGIT = IDIGIT IF( IDIGIT.EQ.0 ) $ NDIGIT = 4 * *======================================================================= * CODE FOR OUTPUT USING 72 COLUMNS FORMAT *======================================================================= * IF( IDIGIT.LT.0 ) THEN NDIGIT = -IDIGIT IF( NDIGIT.LE.4 ) THEN DO 40 K1 = 1, N, 5 K2 = MIN0( N, K1+4 ) WRITE( LOUT, 9998 )( ICOL, I, I = K1, K2 ) DO 30 I = 1, M WRITE( LOUT, 9994 )I, ( A( I, J ), J = K1, K2 ) 30 CONTINUE 40 CONTINUE * ELSE IF( NDIGIT.LE.6 ) THEN DO 60 K1 = 1, N, 4 K2 = MIN0( N, K1+3 ) WRITE( LOUT, 9997 )( ICOL, I, I = K1, K2 ) DO 50 I = 1, M WRITE( LOUT, 9993 )I, ( A( I, J ), J = K1, K2 ) 50 CONTINUE 60 CONTINUE * ELSE IF( NDIGIT.LE.10 ) THEN DO 80 K1 = 1, N, 3 K2 = MIN0( N, K1+2 ) WRITE( LOUT, 9996 )( ICOL, I, I = K1, K2 ) DO 70 I = 1, M WRITE( LOUT, 9992 )I, ( A( I, J ), J = K1, K2 ) 70 CONTINUE 80 CONTINUE * ELSE DO 100 K1 = 1, N, 2 K2 = MIN0( N, K1+1 ) WRITE( LOUT, 9995 )( ICOL, I, I = K1, K2 ) DO 90 I = 1, M WRITE( LOUT, 9991 )I, ( A( I, J ), J = K1, K2 ) 90 CONTINUE 100 CONTINUE END IF * *======================================================================= * CODE FOR OUTPUT USING 132 COLUMNS FORMAT *======================================================================= * ELSE IF( NDIGIT.LE.4 ) THEN DO 120 K1 = 1, N, 10 K2 = MIN0( N, K1+9 ) WRITE( LOUT, 9998 )( ICOL, I, I = K1, K2 ) DO 110 I = 1, M WRITE( LOUT, 9994 )I, ( A( I, J ), J = K1, K2 ) 110 CONTINUE 120 CONTINUE * ELSE IF( NDIGIT.LE.6 ) THEN DO 140 K1 = 1, N, 8 K2 = MIN0( N, K1+7 ) WRITE( LOUT, 9997 )( ICOL, I, I = K1, K2 ) DO 130 I = 1, M WRITE( LOUT, 9993 )I, ( A( I, J ), J = K1, K2 ) 130 CONTINUE 140 CONTINUE * ELSE IF( NDIGIT.LE.10 ) THEN DO 160 K1 = 1, N, 6 K2 = MIN0( N, K1+5 ) WRITE( LOUT, 9996 )( ICOL, I, I = K1, K2 ) DO 150 I = 1, M WRITE( LOUT, 9992 )I, ( A( I, J ), J = K1, K2 ) 150 CONTINUE 160 CONTINUE * ELSE DO 180 K1 = 1, N, 5 K2 = MIN0( N, K1+4 ) WRITE( LOUT, 9995 )( ICOL, I, I = K1, K2 ) DO 170 I = 1, M WRITE( LOUT, 9991 )I, ( A( I, J ), J = K1, K2 ) 170 CONTINUE 180 CONTINUE END IF END IF WRITE( LOUT, 9990 ) * 9998 FORMAT( 10X, 10( 4X, 3A1, I4, 1X ) ) 9997 FORMAT( 10X, 8( 5X, 3A1, I4, 2X ) ) 9996 FORMAT( 10X, 6( 7X, 3A1, I4, 4X ) ) 9995 FORMAT( 10X, 5( 9X, 3A1, I4, 6X ) ) 9994 FORMAT( 1X, ' Row', I4, ':', 1X, 1P10E12.3 ) 9993 FORMAT( 1X, ' Row', I4, ':', 1X, 1P8E14.5 ) 9992 FORMAT( 1X, ' Row', I4, ':', 1X, 1P6E18.9 ) 9991 FORMAT( 1X, ' Row', I4, ':', 1X, 1P5E22.13 ) 9990 FORMAT( 1X, ' ' ) * RETURN END arpack-0.92.1/UTIL/icopy.f0000644000175000017500000000363510776001577012055 00000000000000*-------------------------------------------------------------------- *\Documentation * *\Name: ICOPY * *\Description: * ICOPY copies an integer vector lx to an integer vector ly. * *\Usage: * call icopy ( n, lx, inc, ly, incy ) * *\Arguments: * n integer (input) * On entry, n is the number of elements of lx to be c copied to ly. * * lx integer array (input) * On entry, lx is the integer vector to be copied. * * incx integer (input) * On entry, incx is the increment between elements of lx. * * ly integer array (input) * On exit, ly is the integer vector that contains the * copy of lx. * * incy integer (input) * On entry, incy is the increment between elements of ly. * *\Enddoc * *-------------------------------------------------------------------- * subroutine icopy( n, lx, incx, ly, incy ) * * ---------------------------- * Specifications for arguments * ---------------------------- integer incx, incy, n integer lx( 1 ), ly( 1 ) * * ---------------------------------- * Specifications for local variables * ---------------------------------- integer i, ix, iy * * -------------------------- * First executable statement * -------------------------- if( n.le.0 ) $ return if( incx.eq.1 .and. incy.eq.1 ) $ go to 20 c c.....code for unequal increments or equal increments c not equal to 1 ix = 1 iy = 1 if( incx.lt.0 ) $ ix = ( -n+1 )*incx + 1 if( incy.lt.0 ) $ iy = ( -n+1 )*incy + 1 do 10 i = 1, n ly( iy ) = lx( ix ) ix = ix + incx iy = iy + incy 10 continue return c c.....code for both increments equal to 1 c 20 continue do 30 i = 1, n ly( i ) = lx( i ) 30 continue return end arpack-0.92.1/UTIL/dvout.f0000644000175000017500000000760410776001577012073 00000000000000*----------------------------------------------------------------------- * Routine: DVOUT * * Purpose: Real vector output routine. * * Usage: CALL DVOUT (LOUT, N, SX, IDIGIT, IFMT) * * Arguments * N - Length of array SX. (Input) * SX - Real array to be printed. (Input) * IFMT - Format to be used in printing array SX. (Input) * IDIGIT - Print up to IABS(IDIGIT) decimal digits per number. (In) * If IDIGIT .LT. 0, printing is done with 72 columns. * If IDIGIT .GT. 0, printing is done with 132 columns. * *----------------------------------------------------------------------- * SUBROUTINE DVOUT( LOUT, N, SX, IDIGIT, IFMT ) * ... * ... SPECIFICATIONS FOR ARGUMENTS * ... * ... SPECIFICATIONS FOR LOCAL VARIABLES * .. Scalar Arguments .. CHARACTER*( * ) IFMT INTEGER IDIGIT, LOUT, N * .. * .. Array Arguments .. DOUBLE PRECISION SX( * ) * .. * .. Local Scalars .. CHARACTER*80 LINE INTEGER I, K1, K2, LLL, NDIGIT * .. * .. Intrinsic Functions .. INTRINSIC LEN, MIN, MIN0 * .. * .. Executable Statements .. * ... * ... FIRST EXECUTABLE STATEMENT * * LLL = MIN( LEN( IFMT ), 80 ) DO 10 I = 1, LLL LINE( I: I ) = '-' 10 CONTINUE * DO 20 I = LLL + 1, 80 LINE( I: I ) = ' ' 20 CONTINUE * WRITE( LOUT, FMT = 9999 )IFMT, LINE( 1: LLL ) 9999 FORMAT( / 1X, A, / 1X, A ) * IF( N.LE.0 ) $ RETURN NDIGIT = IDIGIT IF( IDIGIT.EQ.0 ) $ NDIGIT = 4 * *======================================================================= * CODE FOR OUTPUT USING 72 COLUMNS FORMAT *======================================================================= * IF( IDIGIT.LT.0 ) THEN NDIGIT = -IDIGIT IF( NDIGIT.LE.4 ) THEN DO 30 K1 = 1, N, 5 K2 = MIN0( N, K1+4 ) WRITE( LOUT, FMT = 9998 )K1, K2, ( SX( I ), I = K1, K2 ) 30 CONTINUE ELSE IF( NDIGIT.LE.6 ) THEN DO 40 K1 = 1, N, 4 K2 = MIN0( N, K1+3 ) WRITE( LOUT, FMT = 9997 )K1, K2, ( SX( I ), I = K1, K2 ) 40 CONTINUE ELSE IF( NDIGIT.LE.10 ) THEN DO 50 K1 = 1, N, 3 K2 = MIN0( N, K1+2 ) WRITE( LOUT, FMT = 9996 )K1, K2, ( SX( I ), I = K1, K2 ) 50 CONTINUE ELSE DO 60 K1 = 1, N, 2 K2 = MIN0( N, K1+1 ) WRITE( LOUT, FMT = 9995 )K1, K2, ( SX( I ), I = K1, K2 ) 60 CONTINUE END IF * *======================================================================= * CODE FOR OUTPUT USING 132 COLUMNS FORMAT *======================================================================= * ELSE IF( NDIGIT.LE.4 ) THEN DO 70 K1 = 1, N, 10 K2 = MIN0( N, K1+9 ) WRITE( LOUT, FMT = 9998 )K1, K2, ( SX( I ), I = K1, K2 ) 70 CONTINUE ELSE IF( NDIGIT.LE.6 ) THEN DO 80 K1 = 1, N, 8 K2 = MIN0( N, K1+7 ) WRITE( LOUT, FMT = 9997 )K1, K2, ( SX( I ), I = K1, K2 ) 80 CONTINUE ELSE IF( NDIGIT.LE.10 ) THEN DO 90 K1 = 1, N, 6 K2 = MIN0( N, K1+5 ) WRITE( LOUT, FMT = 9996 )K1, K2, ( SX( I ), I = K1, K2 ) 90 CONTINUE ELSE DO 100 K1 = 1, N, 5 K2 = MIN0( N, K1+4 ) WRITE( LOUT, FMT = 9995 )K1, K2, ( SX( I ), I = K1, K2 ) 100 CONTINUE END IF END IF WRITE( LOUT, FMT = 9994 ) RETURN 9998 FORMAT( 1X, I4, ' - ', I4, ':', 1P, 10D12.3 ) 9997 FORMAT( 1X, I4, ' - ', I4, ':', 1X, 1P, 8D14.5 ) 9996 FORMAT( 1X, I4, ' - ', I4, ':', 1X, 1P, 6D18.9 ) 9995 FORMAT( 1X, I4, ' - ', I4, ':', 1X, 1P, 5D24.13 ) 9994 FORMAT( 1X, ' ' ) END arpack-0.92.1/UTIL/zvout.f0000644000175000017500000002002610776001577012112 00000000000000c----------------------------------------------------------------------- c c\SCCS Information: @(#) c FILE: zvout.f SID: 2.1 DATE OF SID: 11/16/95 RELEASE: 2 c *----------------------------------------------------------------------- * Routine: ZVOUT * * Purpose: Complex*16 vector output routine. * * Usage: CALL ZVOUT (LOUT, N, CX, IDIGIT, IFMT) * * Arguments * N - Length of array CX. (Input) * CX - Complex*16 array to be printed. (Input) * IFMT - Format to be used in printing array CX. (Input) * IDIGIT - Print up to IABS(IDIGIT) decimal digits per number. (In) * If IDIGIT .LT. 0, printing is done with 72 columns. * If IDIGIT .GT. 0, printing is done with 132 columns. * *----------------------------------------------------------------------- * SUBROUTINE ZVOUT( LOUT, N, CX, IDIGIT, IFMT ) * ... * ... SPECIFICATIONS FOR ARGUMENTS INTEGER N, IDIGIT, LOUT Complex*16 & CX( * ) CHARACTER IFMT*( * ) * ... * ... SPECIFICATIONS FOR LOCAL VARIABLES INTEGER I, NDIGIT, K1, K2, LLL CHARACTER*80 LINE * ... * ... FIRST EXECUTABLE STATEMENT * * LLL = MIN( LEN( IFMT ), 80 ) DO 10 I = 1, LLL LINE( I: I ) = '-' 10 CONTINUE * DO 20 I = LLL + 1, 80 LINE( I: I ) = ' ' 20 CONTINUE * WRITE( LOUT, 9999 )IFMT, LINE( 1: LLL ) 9999 FORMAT( / 1X, A / 1X, A ) * IF( N.LE.0 ) $ RETURN NDIGIT = IDIGIT IF( IDIGIT.EQ.0 ) $ NDIGIT = 4 * *======================================================================= * CODE FOR OUTPUT USING 72 COLUMNS FORMAT *======================================================================= * IF( IDIGIT.LT.0 ) THEN NDIGIT = -IDIGIT IF( NDIGIT.LE.4 ) THEN DO 30 K1 = 1, N, 2 K2 = MIN0( N, K1+1 ) IF (K1.NE.N) THEN WRITE( LOUT, 9998 )K1, K2, ( CX( I ), $ I = K1, K2 ) ELSE WRITE( LOUT, 9997 )K1, K2, ( CX( I ), $ I = K1, K2 ) END IF 30 CONTINUE ELSE IF( NDIGIT.LE.6 ) THEN DO 40 K1 = 1, N, 2 K2 = MIN0( N, K1+1 ) IF (K1.NE.N) THEN WRITE( LOUT, 9988 )K1, K2, ( CX( I ), $ I = K1, K2 ) ELSE WRITE( LOUT, 9987 )K1, K2, ( CX( I ), $ I = K1, K2 ) END IF 40 CONTINUE ELSE IF( NDIGIT.LE.8 ) THEN DO 50 K1 = 1, N, 2 K2 = MIN0( N, K1+1 ) IF (K1.NE.N) THEN WRITE( LOUT, 9978 )K1, K2, ( CX( I ), $ I = K1, K2 ) ELSE WRITE( LOUT, 9977 )K1, K2, ( CX( I ), $ I = K1, K2 ) END IF 50 CONTINUE ELSE DO 60 K1 = 1, N WRITE( LOUT, 9968 )K1, K1, CX( I ) 60 CONTINUE END IF * *======================================================================= * CODE FOR OUTPUT USING 132 COLUMNS FORMAT *======================================================================= * ELSE IF( NDIGIT.LE.4 ) THEN DO 70 K1 = 1, N, 4 K2 = MIN0( N, K1+3 ) IF ((K1+3).LE.N) THEN WRITE( LOUT, 9958 )K1, K2, ( CX( I ), $ I = K1, K2 ) ELSE IF ((K1+3-N) .EQ. 1) THEN WRITE( LOUT, 9957 )K1, K2, ( CX( I ), $ I = K1, K2 ) ELSE IF ((K1+3-N) .EQ. 2) THEN WRITE( LOUT, 9956 )K1, K2, ( CX( I ), $ I = K1, K2 ) ELSE IF ((K1+3-N) .EQ. 1) THEN WRITE( LOUT, 9955 )K1, K2, ( CX( I ), $ I = K1, K2 ) END IF 70 CONTINUE ELSE IF( NDIGIT.LE.6 ) THEN DO 80 K1 = 1, N, 3 K2 = MIN0( N, K1+2 ) IF ((K1+2).LE.N) THEN WRITE( LOUT, 9948 )K1, K2, ( CX( I ), $ I = K1, K2 ) ELSE IF ((K1+2-N) .EQ. 1) THEN WRITE( LOUT, 9947 )K1, K2, ( CX( I ), $ I = K1, K2 ) ELSE IF ((K1+2-N) .EQ. 2) THEN WRITE( LOUT, 9946 )K1, K2, ( CX( I ), $ I = K1, K2 ) END IF 80 CONTINUE ELSE IF( NDIGIT.LE.8 ) THEN DO 90 K1 = 1, N, 3 K2 = MIN0( N, K1+2 ) IF ((K1+2).LE.N) THEN WRITE( LOUT, 9938 )K1, K2, ( CX( I ), $ I = K1, K2 ) ELSE IF ((K1+2-N) .EQ. 1) THEN WRITE( LOUT, 9937 )K1, K2, ( CX( I ), $ I = K1, K2 ) ELSE IF ((K1+2-N) .EQ. 2) THEN WRITE( LOUT, 9936 )K1, K2, ( CX( I ), $ I = K1, K2 ) END IF 90 CONTINUE ELSE DO 100 K1 = 1, N, 2 K2 = MIN0( N, K1+1 ) IF ((K1+2).LE.N) THEN WRITE( LOUT, 9928 )K1, K2, ( CX( I ), $ I = K1, K2 ) ELSE IF ((K1+2-N) .EQ. 1) THEN WRITE( LOUT, 9927 )K1, K2, ( CX( I ), $ I = K1, K2 ) END IF 100 CONTINUE END IF END IF WRITE( LOUT, 9994 ) RETURN * *======================================================================= * FORMAT FOR 72 COLUMNS *======================================================================= * * DISPLAY 4 SIGNIFICANT DIGITS * 9998 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,2('(',D10.3,',',D10.3,') ') ) 9997 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,1('(',D10.3,',',D10.3,') ') ) * * DISPLAY 6 SIGNIFICANT DIGITS * 9988 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,2('(',D12.5,',',D12.5,') ') ) 9987 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,1('(',D12.5,',',D12.5,') ') ) * * DISPLAY 8 SIGNIFICANT DIGITS * 9978 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,2('(',D14.7,',',D14.7,') ') ) 9977 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,1('(',D14.7,',',D14.7,') ') ) * * DISPLAY 13 SIGNIFICANT DIGITS * 9968 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,1('(',D20.13,',',D20.13,') ') ) * *========================================================================= * FORMAT FOR 132 COLUMNS *========================================================================= * * DISPLAY 4 SIGNIFICANT DIGITS * 9958 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,4('(',D10.3,',',D10.3,') ') ) 9957 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,3('(',D10.3,',',D10.3,') ') ) 9956 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,2('(',D10.3,',',D10.3,') ') ) 9955 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,1('(',D10.3,',',D10.3,') ') ) * * DISPLAY 6 SIGNIFICANT DIGITS * 9948 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,3('(',D12.5,',',D12.5,') ') ) 9947 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,2('(',D12.5,',',D12.5,') ') ) 9946 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,1('(',D12.5,',',D12.5,') ') ) * * DISPLAY 8 SIGNIFICANT DIGITS * 9938 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,3('(',D14.7,',',D14.7,') ') ) 9937 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,2('(',D14.7,',',D14.7,') ') ) 9936 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,1('(',D14.7,',',D14.7,') ') ) * * DISPLAY 13 SIGNIFICANT DIGITS * 9928 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,2('(',D20.13,',',D20.13,') ') ) 9927 FORMAT( 1X, I4, ' - ', I4, ':', 1X, $ 1P,1('(',D20.13,',',D20.13,') ') ) * * * 9994 FORMAT( 1X, ' ' ) END arpack-0.92.1/SRC/0000755000175000017500000000000011540551571010500 500000000000000arpack-0.92.1/SRC/snapps.f0000644000175000017500000005551510776001577012114 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: snapps c c\Description: c Given the Arnoldi factorization c c A*V_{k} - V_{k}*H_{k} = r_{k+p}*e_{k+p}^T, c c apply NP implicit shifts resulting in c c A*(V_{k}*Q) - (V_{k}*Q)*(Q^T* H_{k}*Q) = r_{k+p}*e_{k+p}^T * Q c c where Q is an orthogonal matrix which is the product of rotations c and reflections resulting from the NP bulge chage sweeps. c The updated Arnoldi factorization becomes: c c A*VNEW_{k} - VNEW_{k}*HNEW_{k} = rnew_{k}*e_{k}^T. c c\Usage: c call snapps c ( N, KEV, NP, SHIFTR, SHIFTI, V, LDV, H, LDH, RESID, Q, LDQ, c WORKL, WORKD ) c c\Arguments c N Integer. (INPUT) c Problem size, i.e. size of matrix A. c c KEV Integer. (INPUT/OUTPUT) c KEV+NP is the size of the input matrix H. c KEV is the size of the updated matrix HNEW. KEV is only c updated on ouput when fewer than NP shifts are applied in c order to keep the conjugate pair together. c c NP Integer. (INPUT) c Number of implicit shifts to be applied. c c SHIFTR, Real array of length NP. (INPUT) c SHIFTI Real and imaginary part of the shifts to be applied. c Upon, entry to snapps, the shifts must be sorted so that the c conjugate pairs are in consecutive locations. c c V Real N by (KEV+NP) array. (INPUT/OUTPUT) c On INPUT, V contains the current KEV+NP Arnoldi vectors. c On OUTPUT, V contains the updated KEV Arnoldi vectors c in the first KEV columns of V. c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling c program. c c H Real (KEV+NP) by (KEV+NP) array. (INPUT/OUTPUT) c On INPUT, H contains the current KEV+NP by KEV+NP upper c Hessenber matrix of the Arnoldi factorization. c On OUTPUT, H contains the updated KEV by KEV upper Hessenberg c matrix in the KEV leading submatrix. c c LDH Integer. (INPUT) c Leading dimension of H exactly as declared in the calling c program. c c RESID Real array of length N. (INPUT/OUTPUT) c On INPUT, RESID contains the the residual vector r_{k+p}. c On OUTPUT, RESID is the update residual vector rnew_{k} c in the first KEV locations. c c Q Real KEV+NP by KEV+NP work array. (WORKSPACE) c Work array used to accumulate the rotations and reflections c during the bulge chase sweep. c c LDQ Integer. (INPUT) c Leading dimension of Q exactly as declared in the calling c program. c c WORKL Real work array of length (KEV+NP). (WORKSPACE) c Private (replicated) array on each PE or array allocated on c the front end. c c WORKD Real work array of length 2*N. (WORKSPACE) c Distributed array used in the application of the accumulated c orthogonal matrix Q. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx real c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c c\Routines called: c ivout ARPACK utility routine that prints integers. c arscnd ARPACK utility routine for timing. c smout ARPACK utility routine that prints matrices. c svout ARPACK utility routine that prints vectors. c slabad LAPACK routine that computes machine constants. c slacpy LAPACK matrix copy routine. c slamch LAPACK routine that determines machine constants. c slanhs LAPACK routine that computes various norms of a matrix. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c slarf LAPACK routine that applies Householder reflection to c a matrix. c slarfg LAPACK Householder reflection construction routine. c slartg LAPACK Givens rotation construction routine. c slaset LAPACK matrix initialization routine. c sgemv Level 2 BLAS routine for matrix vector multiplication. c saxpy Level 1 BLAS that computes a vector triad. c scopy Level 1 BLAS that copies one vector to another . c sscal Level 1 BLAS that scales a vector. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c xx/xx/92: Version ' 2.4' c c\SCCS Information: @(#) c FILE: napps.F SID: 2.4 DATE OF SID: 3/28/97 RELEASE: 2 c c\Remarks c 1. In this version, each shift is applied to all the sublocks of c the Hessenberg matrix H and not just to the submatrix that it c comes from. Deflation as in LAPACK routine slahqr (QR algorithm c for upper Hessenberg matrices ) is used. c The subdiagonals of H are enforced to be non-negative. c c\EndLib c c----------------------------------------------------------------------- c subroutine snapps & ( n, kev, np, shiftr, shifti, v, ldv, h, ldh, resid, q, ldq, & workl, workd ) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c integer kev, ldh, ldq, ldv, n, np c c %-----------------% c | Array Arguments | c %-----------------% c Real & h(ldh,kev+np), resid(n), shifti(np), shiftr(np), & v(ldv,kev+np), q(ldq,kev+np), workd(2*n), workl(kev+np) c c %------------% c | Parameters | c %------------% c Real & one, zero parameter (one = 1.0E+0, zero = 0.0E+0) c c %------------------------% c | Local Scalars & Arrays | c %------------------------% c integer i, iend, ir, istart, j, jj, kplusp, msglvl, nr logical cconj, first Real & c, f, g, h11, h12, h21, h22, h32, ovfl, r, s, sigmai, & sigmar, smlnum, ulp, unfl, u(3), t, tau, tst1 save first, ovfl, smlnum, ulp, unfl c c %----------------------% c | External Subroutines | c %----------------------% c external saxpy, scopy, sscal, slacpy, slarfg, slarf, & slaset, slabad, arscnd, slartg c c %--------------------% c | External Functions | c %--------------------% c Real & slamch, slanhs, slapy2 external slamch, slanhs, slapy2 c c %----------------------% c | Intrinsics Functions | c %----------------------% c intrinsic abs, max, min c c %----------------% c | Data statments | c %----------------% c data first / .true. / c c %-----------------------% c | Executable Statements | c %-----------------------% c if (first) then c c %-----------------------------------------------% c | Set machine-dependent constants for the | c | stopping criterion. If norm(H) <= sqrt(OVFL), | c | overflow should not occur. | c | REFERENCE: LAPACK subroutine slahqr | c %-----------------------------------------------% c unfl = slamch( 'safe minimum' ) ovfl = one / unfl call slabad( unfl, ovfl ) ulp = slamch( 'precision' ) smlnum = unfl*( n / ulp ) first = .false. end if c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call arscnd (t0) msglvl = mnapps kplusp = kev + np c c %--------------------------------------------% c | Initialize Q to the identity to accumulate | c | the rotations and reflections | c %--------------------------------------------% c call slaset ('All', kplusp, kplusp, zero, one, q, ldq) c c %----------------------------------------------% c | Quick return if there are no shifts to apply | c %----------------------------------------------% c if (np .eq. 0) go to 9000 c c %----------------------------------------------% c | Chase the bulge with the application of each | c | implicit shift. Each shift is applied to the | c | whole matrix including each block. | c %----------------------------------------------% c cconj = .false. do 110 jj = 1, np sigmar = shiftr(jj) sigmai = shifti(jj) c if (msglvl .gt. 2 ) then call ivout (logfil, 1, jj, ndigit, & '_napps: shift number.') call svout (logfil, 1, sigmar, ndigit, & '_napps: The real part of the shift ') call svout (logfil, 1, sigmai, ndigit, & '_napps: The imaginary part of the shift ') end if c c %-------------------------------------------------% c | The following set of conditionals is necessary | c | in order that complex conjugate pairs of shifts | c | are applied together or not at all. | c %-------------------------------------------------% c if ( cconj ) then c c %-----------------------------------------% c | cconj = .true. means the previous shift | c | had non-zero imaginary part. | c %-----------------------------------------% c cconj = .false. go to 110 else if ( jj .lt. np .and. abs( sigmai ) .gt. zero ) then c c %------------------------------------% c | Start of a complex conjugate pair. | c %------------------------------------% c cconj = .true. else if ( jj .eq. np .and. abs( sigmai ) .gt. zero ) then c c %----------------------------------------------% c | The last shift has a nonzero imaginary part. | c | Don't apply it; thus the order of the | c | compressed H is order KEV+1 since only np-1 | c | were applied. | c %----------------------------------------------% c kev = kev + 1 go to 110 end if istart = 1 20 continue c c %--------------------------------------------------% c | if sigmai = 0 then | c | Apply the jj-th shift ... | c | else | c | Apply the jj-th and (jj+1)-th together ... | c | (Note that jj < np at this point in the code) | c | end | c | to the current block of H. The next do loop | c | determines the current block ; | c %--------------------------------------------------% c do 30 i = istart, kplusp-1 c c %----------------------------------------% c | Check for splitting and deflation. Use | c | a standard test as in the QR algorithm | c | REFERENCE: LAPACK subroutine slahqr | c %----------------------------------------% c tst1 = abs( h( i, i ) ) + abs( h( i+1, i+1 ) ) if( tst1.eq.zero ) & tst1 = slanhs( '1', kplusp-jj+1, h, ldh, workl ) if( abs( h( i+1,i ) ).le.max( ulp*tst1, smlnum ) ) then if (msglvl .gt. 0) then call ivout (logfil, 1, i, ndigit, & '_napps: matrix splitting at row/column no.') call ivout (logfil, 1, jj, ndigit, & '_napps: matrix splitting with shift number.') call svout (logfil, 1, h(i+1,i), ndigit, & '_napps: off diagonal element.') end if iend = i h(i+1,i) = zero go to 40 end if 30 continue iend = kplusp 40 continue c if (msglvl .gt. 2) then call ivout (logfil, 1, istart, ndigit, & '_napps: Start of current block ') call ivout (logfil, 1, iend, ndigit, & '_napps: End of current block ') end if c c %------------------------------------------------% c | No reason to apply a shift to block of order 1 | c %------------------------------------------------% c if ( istart .eq. iend ) go to 100 c c %------------------------------------------------------% c | If istart + 1 = iend then no reason to apply a | c | complex conjugate pair of shifts on a 2 by 2 matrix. | c %------------------------------------------------------% c if ( istart + 1 .eq. iend .and. abs( sigmai ) .gt. zero ) & go to 100 c h11 = h(istart,istart) h21 = h(istart+1,istart) if ( abs( sigmai ) .le. zero ) then c c %---------------------------------------------% c | Real-valued shift ==> apply single shift QR | c %---------------------------------------------% c f = h11 - sigmar g = h21 c do 80 i = istart, iend-1 c c %-----------------------------------------------------% c | Contruct the plane rotation G to zero out the bulge | c %-----------------------------------------------------% c call slartg (f, g, c, s, r) if (i .gt. istart) then c c %-------------------------------------------% c | The following ensures that h(1:iend-1,1), | c | the first iend-2 off diagonal of elements | c | H, remain non negative. | c %-------------------------------------------% c if (r .lt. zero) then r = -r c = -c s = -s end if h(i,i-1) = r h(i+1,i-1) = zero end if c c %---------------------------------------------% c | Apply rotation to the left of H; H <- G'*H | c %---------------------------------------------% c do 50 j = i, kplusp t = c*h(i,j) + s*h(i+1,j) h(i+1,j) = -s*h(i,j) + c*h(i+1,j) h(i,j) = t 50 continue c c %---------------------------------------------% c | Apply rotation to the right of H; H <- H*G | c %---------------------------------------------% c do 60 j = 1, min(i+2,iend) t = c*h(j,i) + s*h(j,i+1) h(j,i+1) = -s*h(j,i) + c*h(j,i+1) h(j,i) = t 60 continue c c %----------------------------------------------------% c | Accumulate the rotation in the matrix Q; Q <- Q*G | c %----------------------------------------------------% c do 70 j = 1, min( i+jj, kplusp ) t = c*q(j,i) + s*q(j,i+1) q(j,i+1) = - s*q(j,i) + c*q(j,i+1) q(j,i) = t 70 continue c c %---------------------------% c | Prepare for next rotation | c %---------------------------% c if (i .lt. iend-1) then f = h(i+1,i) g = h(i+2,i) end if 80 continue c c %-----------------------------------% c | Finished applying the real shift. | c %-----------------------------------% c else c c %----------------------------------------------------% c | Complex conjugate shifts ==> apply double shift QR | c %----------------------------------------------------% c h12 = h(istart,istart+1) h22 = h(istart+1,istart+1) h32 = h(istart+2,istart+1) c c %---------------------------------------------------------% c | Compute 1st column of (H - shift*I)*(H - conj(shift)*I) | c %---------------------------------------------------------% c s = 2.0*sigmar t = slapy2 ( sigmar, sigmai ) u(1) = ( h11 * (h11 - s) + t * t ) / h21 + h12 u(2) = h11 + h22 - s u(3) = h32 c do 90 i = istart, iend-1 c nr = min ( 3, iend-i+1 ) c c %-----------------------------------------------------% c | Construct Householder reflector G to zero out u(1). | c | G is of the form I - tau*( 1 u )' * ( 1 u' ). | c %-----------------------------------------------------% c call slarfg ( nr, u(1), u(2), 1, tau ) c if (i .gt. istart) then h(i,i-1) = u(1) h(i+1,i-1) = zero if (i .lt. iend-1) h(i+2,i-1) = zero end if u(1) = one c c %--------------------------------------% c | Apply the reflector to the left of H | c %--------------------------------------% c call slarf ('Left', nr, kplusp-i+1, u, 1, tau, & h(i,i), ldh, workl) c c %---------------------------------------% c | Apply the reflector to the right of H | c %---------------------------------------% c ir = min ( i+3, iend ) call slarf ('Right', ir, nr, u, 1, tau, & h(1,i), ldh, workl) c c %-----------------------------------------------------% c | Accumulate the reflector in the matrix Q; Q <- Q*G | c %-----------------------------------------------------% c call slarf ('Right', kplusp, nr, u, 1, tau, & q(1,i), ldq, workl) c c %----------------------------% c | Prepare for next reflector | c %----------------------------% c if (i .lt. iend-1) then u(1) = h(i+1,i) u(2) = h(i+2,i) if (i .lt. iend-2) u(3) = h(i+3,i) end if c 90 continue c c %--------------------------------------------% c | Finished applying a complex pair of shifts | c | to the current block | c %--------------------------------------------% c end if c 100 continue c c %---------------------------------------------------------% c | Apply the same shift to the next block if there is any. | c %---------------------------------------------------------% c istart = iend + 1 if (iend .lt. kplusp) go to 20 c c %---------------------------------------------% c | Loop back to the top to get the next shift. | c %---------------------------------------------% c 110 continue c c %--------------------------------------------------% c | Perform a similarity transformation that makes | c | sure that H will have non negative sub diagonals | c %--------------------------------------------------% c do 120 j=1,kev if ( h(j+1,j) .lt. zero ) then call sscal( kplusp-j+1, -one, h(j+1,j), ldh ) call sscal( min(j+2, kplusp), -one, h(1,j+1), 1 ) call sscal( min(j+np+1,kplusp), -one, q(1,j+1), 1 ) end if 120 continue c do 130 i = 1, kev c c %--------------------------------------------% c | Final check for splitting and deflation. | c | Use a standard test as in the QR algorithm | c | REFERENCE: LAPACK subroutine slahqr | c %--------------------------------------------% c tst1 = abs( h( i, i ) ) + abs( h( i+1, i+1 ) ) if( tst1.eq.zero ) & tst1 = slanhs( '1', kev, h, ldh, workl ) if( h( i+1,i ) .le. max( ulp*tst1, smlnum ) ) & h(i+1,i) = zero 130 continue c c %-------------------------------------------------% c | Compute the (kev+1)-st column of (V*Q) and | c | temporarily store the result in WORKD(N+1:2*N). | c | This is needed in the residual update since we | c | cannot GUARANTEE that the corresponding entry | c | of H would be zero as in exact arithmetic. | c %-------------------------------------------------% c if (h(kev+1,kev) .gt. zero) & call sgemv ('N', n, kplusp, one, v, ldv, q(1,kev+1), 1, zero, & workd(n+1), 1) c c %----------------------------------------------------------% c | Compute column 1 to kev of (V*Q) in backward order | c | taking advantage of the upper Hessenberg structure of Q. | c %----------------------------------------------------------% c do 140 i = 1, kev call sgemv ('N', n, kplusp-i+1, one, v, ldv, & q(1,kev-i+1), 1, zero, workd, 1) call scopy (n, workd, 1, v(1,kplusp-i+1), 1) 140 continue c c %-------------------------------------------------% c | Move v(:,kplusp-kev+1:kplusp) into v(:,1:kev). | c %-------------------------------------------------% c call slacpy ('A', n, kev, v(1,kplusp-kev+1), ldv, v, ldv) c c %--------------------------------------------------------------% c | Copy the (kev+1)-st column of (V*Q) in the appropriate place | c %--------------------------------------------------------------% c if (h(kev+1,kev) .gt. zero) & call scopy (n, workd(n+1), 1, v(1,kev+1), 1) c c %-------------------------------------% c | Update the residual vector: | c | r <- sigmak*r + betak*v(:,kev+1) | c | where | c | sigmak = (e_{kplusp}'*Q)*e_{kev} | c | betak = e_{kev+1}'*H*e_{kev} | c %-------------------------------------% c call sscal (n, q(kplusp,kev), resid, 1) if (h(kev+1,kev) .gt. zero) & call saxpy (n, h(kev+1,kev), v(1,kev+1), 1, resid, 1) c if (msglvl .gt. 1) then call svout (logfil, 1, q(kplusp,kev), ndigit, & '_napps: sigmak = (e_{kev+p}^T*Q)*e_{kev}') call svout (logfil, 1, h(kev+1,kev), ndigit, & '_napps: betak = e_{kev+1}^T*H*e_{kev}') call ivout (logfil, 1, kev, ndigit, & '_napps: Order of the final Hessenberg matrix ') if (msglvl .gt. 2) then call smout (logfil, kev, kev, h, ldh, ndigit, & '_napps: updated Hessenberg matrix H for next iteration') end if c end if c 9000 continue call arscnd (t1) tnapps = tnapps + (t1 - t0) c return c c %---------------% c | End of snapps | c %---------------% c end arpack-0.92.1/SRC/Makefile.am0000644000175000017500000000210210776003057012450 00000000000000lib_LTLIBRARIES = libarpack.la libarpack_la_LDFLAGS = -version-info 2 libarpack_la_SOURCES = \ debug.h stat.h version.h \ \ sgetv0.f slaqrb.f sstqrb.f ssortc.f ssortr.f sstatn.f sstats.f \ snaitr.f snapps.f snaup2.f snaupd.f snconv.f sneigh.f sngets.f \ ssaitr.f ssapps.f ssaup2.f ssaupd.f ssconv.f sseigt.f ssgets.f \ sneupd.f sseupd.f ssesrt.f \ \ dgetv0.f dlaqrb.f dstqrb.f dsortc.f dsortr.f dstatn.f dstats.f \ dnaitr.f dnapps.f dnaup2.f dnaupd.f dnconv.f dneigh.f dngets.f \ dsaitr.f dsapps.f dsaup2.f dsaupd.f dsconv.f dseigt.f dsgets.f \ dneupd.f dseupd.f dsesrt.f \ \ cnaitr.f cnapps.f cnaup2.f cnaupd.f cneigh.f cneupd.f cngets.f \ cgetv0.f csortc.f cstatn.f \ \ znaitr.f znapps.f znaup2.f znaupd.f zneigh.f zneupd.f zngets.f \ zgetv0.f zsortc.f zstatn.f \ ../UTIL/arscnd.f ../UTIL/dvout.f ../UTIL/iswap.f ../UTIL/zmout.f \ ../UTIL/cmout.f ../UTIL/icnteq.f ../UTIL/ivout.f ../UTIL/zvout.f \ ../UTIL/cvout.f ../UTIL/icopy.f ../UTIL/smout.f \ ../UTIL/dmout.f ../UTIL/iset.f ../UTIL/svout.f arpack-0.92.1/SRC/zneupd.f0000644000175000017500000010411010776001577012077 00000000000000c\BeginDoc c c\Name: zneupd c c\Description: c This subroutine returns the converged approximations to eigenvalues c of A*z = lambda*B*z and (optionally): c c (1) The corresponding approximate eigenvectors; c c (2) An orthonormal basis for the associated approximate c invariant subspace; c c (3) Both. c c There is negligible additional cost to obtain eigenvectors. An orthonormal c basis is always computed. There is an additional storage cost of n*nev c if both are requested (in this case a separate array Z must be supplied). c c The approximate eigenvalues and eigenvectors of A*z = lambda*B*z c are derived from approximate eigenvalues and eigenvectors of c of the linear operator OP prescribed by the MODE selection in the c call to ZNAUPD. ZNAUPD must be called before this routine is called. c These approximate eigenvalues and vectors are commonly called Ritz c values and Ritz vectors respectively. They are referred to as such c in the comments that follow. The computed orthonormal basis for the c invariant subspace corresponding to these Ritz values is referred to as a c Schur basis. c c The definition of OP as well as other terms and the relation of computed c Ritz values and vectors of OP with respect to the given problem c A*z = lambda*B*z may be found in the header of ZNAUPD. For a brief c description, see definitions of IPARAM(7), MODE and WHICH in the c documentation of ZNAUPD. c c\Usage: c call zneupd c ( RVEC, HOWMNY, SELECT, D, Z, LDZ, SIGMA, WORKEV, BMAT, c N, WHICH, NEV, TOL, RESID, NCV, V, LDV, IPARAM, IPNTR, WORKD, c WORKL, LWORKL, RWORK, INFO ) c c\Arguments: c RVEC LOGICAL (INPUT) c Specifies whether a basis for the invariant subspace corresponding c to the converged Ritz value approximations for the eigenproblem c A*z = lambda*B*z is computed. c c RVEC = .FALSE. Compute Ritz values only. c c RVEC = .TRUE. Compute Ritz vectors or Schur vectors. c See Remarks below. c c HOWMNY Character*1 (INPUT) c Specifies the form of the basis for the invariant subspace c corresponding to the converged Ritz values that is to be computed. c c = 'A': Compute NEV Ritz vectors; c = 'P': Compute NEV Schur vectors; c = 'S': compute some of the Ritz vectors, specified c by the logical array SELECT. c c SELECT Logical array of dimension NCV. (INPUT) c If HOWMNY = 'S', SELECT specifies the Ritz vectors to be c computed. To select the Ritz vector corresponding to a c Ritz value D(j), SELECT(j) must be set to .TRUE.. c If HOWMNY = 'A' or 'P', SELECT need not be initialized c but it is used as internal workspace. c c D Complex*16 array of dimension NEV+1. (OUTPUT) c On exit, D contains the Ritz approximations c to the eigenvalues lambda for A*z = lambda*B*z. c c Z Complex*16 N by NEV array (OUTPUT) c On exit, if RVEC = .TRUE. and HOWMNY = 'A', then the columns of c Z represents approximate eigenvectors (Ritz vectors) corresponding c to the NCONV=IPARAM(5) Ritz values for eigensystem c A*z = lambda*B*z. c c If RVEC = .FALSE. or HOWMNY = 'P', then Z is NOT REFERENCED. c c NOTE: If if RVEC = .TRUE. and a Schur basis is not required, c the array Z may be set equal to first NEV+1 columns of the Arnoldi c basis array V computed by ZNAUPD. In this case the Arnoldi basis c will be destroyed and overwritten with the eigenvector basis. c c LDZ Integer. (INPUT) c The leading dimension of the array Z. If Ritz vectors are c desired, then LDZ .ge. max( 1, N ) is required. c In any case, LDZ .ge. 1 is required. c c SIGMA Complex*16 (INPUT) c If IPARAM(7) = 3 then SIGMA represents the shift. c Not referenced if IPARAM(7) = 1 or 2. c c WORKEV Complex*16 work array of dimension 2*NCV. (WORKSPACE) c c **** The remaining arguments MUST be the same as for the **** c **** call to ZNAUPD that was just completed. **** c c NOTE: The remaining arguments c c BMAT, N, WHICH, NEV, TOL, RESID, NCV, V, LDV, IPARAM, IPNTR, c WORKD, WORKL, LWORKL, RWORK, INFO c c must be passed directly to ZNEUPD following the last call c to ZNAUPD. These arguments MUST NOT BE MODIFIED between c the the last call to ZNAUPD and the call to ZNEUPD. c c Three of these parameters (V, WORKL and INFO) are also output parameters: c c V Complex*16 N by NCV array. (INPUT/OUTPUT) c c Upon INPUT: the NCV columns of V contain the Arnoldi basis c vectors for OP as constructed by ZNAUPD . c c Upon OUTPUT: If RVEC = .TRUE. the first NCONV=IPARAM(5) columns c contain approximate Schur vectors that span the c desired invariant subspace. c c NOTE: If the array Z has been set equal to first NEV+1 columns c of the array V and RVEC=.TRUE. and HOWMNY= 'A', then the c Arnoldi basis held by V has been overwritten by the desired c Ritz vectors. If a separate array Z has been passed then c the first NCONV=IPARAM(5) columns of V will contain approximate c Schur vectors that span the desired invariant subspace. c c WORKL Double precision work array of length LWORKL. (OUTPUT/WORKSPACE) c WORKL(1:ncv*ncv+2*ncv) contains information obtained in c znaupd. They are not changed by zneupd. c WORKL(ncv*ncv+2*ncv+1:3*ncv*ncv+4*ncv) holds the c untransformed Ritz values, the untransformed error estimates of c the Ritz values, the upper triangular matrix for H, and the c associated matrix representation of the invariant subspace for H. c c Note: IPNTR(9:13) contains the pointer into WORKL for addresses c of the above information computed by zneupd. c ------------------------------------------------------------- c IPNTR(9): pointer to the NCV RITZ values of the c original system. c IPNTR(10): Not used c IPNTR(11): pointer to the NCV corresponding error estimates. c IPNTR(12): pointer to the NCV by NCV upper triangular c Schur matrix for H. c IPNTR(13): pointer to the NCV by NCV matrix of eigenvectors c of the upper Hessenberg matrix H. Only referenced by c zneupd if RVEC = .TRUE. See Remark 2 below. c ------------------------------------------------------------- c c INFO Integer. (OUTPUT) c Error flag on output. c = 0: Normal exit. c c = 1: The Schur form computed by LAPACK routine csheqr c could not be reordered by LAPACK routine ztrsen. c Re-enter subroutine zneupd with IPARAM(5)=NCV and c increase the size of the array D to have c dimension at least dimension NCV and allocate at least NCV c columns for Z. NOTE: Not necessary if Z and V share c the same space. Please notify the authors if this error c occurs. c c = -1: N must be positive. c = -2: NEV must be positive. c = -3: NCV-NEV >= 1 and less than or equal to N. c = -5: WHICH must be one of 'LM', 'SM', 'LR', 'SR', 'LI', 'SI' c = -6: BMAT must be one of 'I' or 'G'. c = -7: Length of private work WORKL array is not sufficient. c = -8: Error return from LAPACK eigenvalue calculation. c This should never happened. c = -9: Error return from calculation of eigenvectors. c Informational error from LAPACK routine ztrevc. c = -10: IPARAM(7) must be 1,2,3 c = -11: IPARAM(7) = 1 and BMAT = 'G' are incompatible. c = -12: HOWMNY = 'S' not yet implemented c = -13: HOWMNY must be one of 'A' or 'P' if RVEC = .true. c = -14: ZNAUPD did not find any eigenvalues to sufficient c accuracy. c = -15: ZNEUPD got a different count of the number of converged c Ritz values than ZNAUPD got. This indicates the user c probably made an error in passing data from ZNAUPD to c ZNEUPD or that the data was modified before entering c ZNEUPD c c\BeginLib c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly c Restarted Arnoldi Iteration", Rice University Technical Report c TR95-13, Department of Computational and Applied Mathematics. c 3. B. Nour-Omid, B. N. Parlett, T. Ericsson and P. S. Jensen, c "How to Implement the Spectral Transformation", Math Comp., c Vol. 48, No. 178, April, 1987 pp. 664-673. c c\Routines called: c ivout ARPACK utility routine that prints integers. c zmout ARPACK utility routine that prints matrices c zvout ARPACK utility routine that prints vectors. c zgeqr2 LAPACK routine that computes the QR factorization of c a matrix. c zlacpy LAPACK matrix copy routine. c zlahqr LAPACK routine that computes the Schur form of a c upper Hessenberg matrix. c zlaset LAPACK matrix initialization routine. c ztrevc LAPACK routine to compute the eigenvectors of a matrix c in upper triangular form. c ztrsen LAPACK routine that re-orders the Schur form. c zunm2r LAPACK routine that applies an orthogonal matrix in c factored form. c dlamch LAPACK routine that determines machine constants. c ztrmm Level 3 BLAS matrix times an upper triangular matrix. c zgeru Level 2 BLAS rank one update to a matrix. c zcopy Level 1 BLAS that copies one vector to another . c zscal Level 1 BLAS that scales a vector. c zdscal Level 1 BLAS that scales a complex vector by a real number. c dznrm2 Level 1 BLAS that computes the norm of a complex vector. c c\Remarks c c 1. Currently only HOWMNY = 'A' and 'P' are implemented. c c 2. Schur vectors are an orthogonal representation for the basis of c Ritz vectors. Thus, their numerical properties are often superior. c If RVEC = .true. then the relationship c A * V(:,1:IPARAM(5)) = V(:,1:IPARAM(5)) * T, and c transpose( V(:,1:IPARAM(5)) ) * V(:,1:IPARAM(5)) = I c are approximately satisfied. c Here T is the leading submatrix of order IPARAM(5) of the c upper triangular matrix stored workl(ipntr(12)). c c\Authors c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Chao Yang Houston, Texas c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: neupd.F SID: 2.8 DATE OF SID: 07/21/02 RELEASE: 2 c c\EndLib c c----------------------------------------------------------------------- subroutine zneupd(rvec , howmny, select, d , & z , ldz , sigma , workev, & bmat , n , which , nev , & tol , resid , ncv , v , & ldv , iparam, ipntr , workd , & workl, lworkl, rwork , info ) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character bmat, howmny, which*2 logical rvec integer info, ldz, ldv, lworkl, n, ncv, nev Complex*16 & sigma Double precision & tol c c %-----------------% c | Array Arguments | c %-----------------% c integer iparam(11), ipntr(14) logical select(ncv) Double precision & rwork(ncv) Complex*16 & d(nev) , resid(n) , v(ldv,ncv), & z(ldz, nev), & workd(3*n) , workl(lworkl), workev(2*ncv) c c %------------% c | Parameters | c %------------% c Complex*16 & one, zero parameter (one = (1.0D+0, 0.0D+0), zero = (0.0D+0, 0.0D+0)) c c %---------------% c | Local Scalars | c %---------------% c character type*6 integer bounds, ierr , ih , ihbds, iheig , nconv , & invsub, iuptri, iwev , j , ldh , ldq , & mode , msglvl, ritz , wr , k , irz , & ibd , outncv, iq , np , numcnv, jj , & ishift Complex*16 & rnorm, temp, vl(1) Double precision & conds, sep, rtemp, eps23 logical reord c c %----------------------% c | External Subroutines | c %----------------------% c external zcopy , zgeru, zgeqr2, zlacpy, zmout, & zunm2r, ztrmm, zvout, ivout, & zlahqr c c %--------------------% c | External Functions | c %--------------------% c Double precision & dznrm2, dlamch, dlapy2 external dznrm2, dlamch, dlapy2 c Complex*16 & zdotc external zdotc c c %-----------------------% c | Executable Statements | c %-----------------------% c c %------------------------% c | Set default parameters | c %------------------------% c msglvl = mceupd mode = iparam(7) nconv = iparam(5) info = 0 c c c %---------------------------------% c | Get machine dependent constant. | c %---------------------------------% c eps23 = dlamch('Epsilon-Machine') eps23 = eps23**(2.0D+0 / 3.0D+0) c c %-------------------------------% c | Quick return | c | Check for incompatible input | c %-------------------------------% c ierr = 0 c if (nconv .le. 0) then ierr = -14 else if (n .le. 0) then ierr = -1 else if (nev .le. 0) then ierr = -2 else if (ncv .le. nev .or. ncv .gt. n) then ierr = -3 else if (which .ne. 'LM' .and. & which .ne. 'SM' .and. & which .ne. 'LR' .and. & which .ne. 'SR' .and. & which .ne. 'LI' .and. & which .ne. 'SI') then ierr = -5 else if (bmat .ne. 'I' .and. bmat .ne. 'G') then ierr = -6 else if (lworkl .lt. 3*ncv**2 + 4*ncv) then ierr = -7 else if ( (howmny .ne. 'A' .and. & howmny .ne. 'P' .and. & howmny .ne. 'S') .and. rvec ) then ierr = -13 else if (howmny .eq. 'S' ) then ierr = -12 end if c if (mode .eq. 1 .or. mode .eq. 2) then type = 'REGULR' else if (mode .eq. 3 ) then type = 'SHIFTI' else ierr = -10 end if if (mode .eq. 1 .and. bmat .eq. 'G') ierr = -11 c c %------------% c | Error Exit | c %------------% c if (ierr .ne. 0) then info = ierr go to 9000 end if c c %--------------------------------------------------------% c | Pointer into WORKL for address of H, RITZ, WORKEV, Q | c | etc... and the remaining workspace. | c | Also update pointer to be used on output. | c | Memory is laid out as follows: | c | workl(1:ncv*ncv) := generated Hessenberg matrix | c | workl(ncv*ncv+1:ncv*ncv+ncv) := ritz values | c | workl(ncv*ncv+ncv+1:ncv*ncv+2*ncv) := error bounds | c %--------------------------------------------------------% c c %-----------------------------------------------------------% c | The following is used and set by ZNEUPD. | c | workl(ncv*ncv+2*ncv+1:ncv*ncv+3*ncv) := The untransformed | c | Ritz values. | c | workl(ncv*ncv+3*ncv+1:ncv*ncv+4*ncv) := The untransformed | c | error bounds of | c | the Ritz values | c | workl(ncv*ncv+4*ncv+1:2*ncv*ncv+4*ncv) := Holds the upper | c | triangular matrix | c | for H. | c | workl(2*ncv*ncv+4*ncv+1: 3*ncv*ncv+4*ncv) := Holds the | c | associated matrix | c | representation of | c | the invariant | c | subspace for H. | c | GRAND total of NCV * ( 3 * NCV + 4 ) locations. | c %-----------------------------------------------------------% c ih = ipntr(5) ritz = ipntr(6) iq = ipntr(7) bounds = ipntr(8) ldh = ncv ldq = ncv iheig = bounds + ldh ihbds = iheig + ldh iuptri = ihbds + ldh invsub = iuptri + ldh*ncv ipntr(9) = iheig ipntr(11) = ihbds ipntr(12) = iuptri ipntr(13) = invsub wr = 1 iwev = wr + ncv c c %-----------------------------------------% c | irz points to the Ritz values computed | c | by _neigh before exiting _naup2. | c | ibd points to the Ritz estimates | c | computed by _neigh before exiting | c | _naup2. | c %-----------------------------------------% c irz = ipntr(14) + ncv*ncv ibd = irz + ncv c c %------------------------------------% c | RNORM is B-norm of the RESID(1:N). | c %------------------------------------% c rnorm = workl(ih+2) workl(ih+2) = zero c if (msglvl .gt. 2) then call zvout(logfil, ncv, workl(irz), ndigit, & '_neupd: Ritz values passed in from _NAUPD.') call zvout(logfil, ncv, workl(ibd), ndigit, & '_neupd: Ritz estimates passed in from _NAUPD.') end if c if (rvec) then c reord = .false. c c %---------------------------------------------------% c | Use the temporary bounds array to store indices | c | These will be used to mark the select array later | c %---------------------------------------------------% c do 10 j = 1,ncv workl(bounds+j-1) = j select(j) = .false. 10 continue c c %-------------------------------------% c | Select the wanted Ritz values. | c | Sort the Ritz values so that the | c | wanted ones appear at the tailing | c | NEV positions of workl(irr) and | c | workl(iri). Move the corresponding | c | error estimates in workl(ibd) | c | accordingly. | c %-------------------------------------% c np = ncv - nev ishift = 0 call zngets(ishift, which , nev , & np , workl(irz), workl(bounds)) c if (msglvl .gt. 2) then call zvout (logfil, ncv, workl(irz), ndigit, & '_neupd: Ritz values after calling _NGETS.') call zvout (logfil, ncv, workl(bounds), ndigit, & '_neupd: Ritz value indices after calling _NGETS.') end if c c %-----------------------------------------------------% c | Record indices of the converged wanted Ritz values | c | Mark the select array for possible reordering | c %-----------------------------------------------------% c numcnv = 0 do 11 j = 1,ncv rtemp = max(eps23, & dlapy2 ( dble(workl(irz+ncv-j)), & dimag(workl(irz+ncv-j)) )) jj = workl(bounds + ncv - j) if (numcnv .lt. nconv .and. & dlapy2( dble(workl(ibd+jj-1)), & dimag(workl(ibd+jj-1)) ) & .le. tol*rtemp) then select(jj) = .true. numcnv = numcnv + 1 if (jj .gt. nev) reord = .true. endif 11 continue c c %-----------------------------------------------------------% c | Check the count (numcnv) of converged Ritz values with | c | the number (nconv) reported by dnaupd. If these two | c | are different then there has probably been an error | c | caused by incorrect passing of the dnaupd data. | c %-----------------------------------------------------------% c if (msglvl .gt. 2) then call ivout(logfil, 1, numcnv, ndigit, & '_neupd: Number of specified eigenvalues') call ivout(logfil, 1, nconv, ndigit, & '_neupd: Number of "converged" eigenvalues') end if c if (numcnv .ne. nconv) then info = -15 go to 9000 end if c c %-------------------------------------------------------% c | Call LAPACK routine zlahqr to compute the Schur form | c | of the upper Hessenberg matrix returned by ZNAUPD. | c | Make a copy of the upper Hessenberg matrix. | c | Initialize the Schur vector matrix Q to the identity. | c %-------------------------------------------------------% c call zcopy(ldh*ncv, workl(ih), 1, workl(iuptri), 1) call zlaset('All', ncv, ncv , & zero , one, workl(invsub), & ldq) call zlahqr(.true., .true. , ncv , & 1 , ncv , workl(iuptri), & ldh , workl(iheig) , 1 , & ncv , workl(invsub), ldq , & ierr) call zcopy(ncv , workl(invsub+ncv-1), ldq, & workl(ihbds), 1) c if (ierr .ne. 0) then info = -8 go to 9000 end if c if (msglvl .gt. 1) then call zvout (logfil, ncv, workl(iheig), ndigit, & '_neupd: Eigenvalues of H') call zvout (logfil, ncv, workl(ihbds), ndigit, & '_neupd: Last row of the Schur vector matrix') if (msglvl .gt. 3) then call zmout (logfil , ncv, ncv , & workl(iuptri), ldh, ndigit, & '_neupd: The upper triangular matrix ') end if end if c if (reord) then c c %-----------------------------------------------% c | Reorder the computed upper triangular matrix. | c %-----------------------------------------------% c call ztrsen('None' , 'V' , select , & ncv , workl(iuptri), ldh , & workl(invsub), ldq , workl(iheig), & nconv , conds , sep , & workev , ncv , ierr) c if (ierr .eq. 1) then info = 1 go to 9000 end if c if (msglvl .gt. 2) then call zvout (logfil, ncv, workl(iheig), ndigit, & '_neupd: Eigenvalues of H--reordered') if (msglvl .gt. 3) then call zmout(logfil , ncv, ncv , & workl(iuptri), ldq, ndigit, & '_neupd: Triangular matrix after re-ordering') end if end if c end if c c %---------------------------------------------% c | Copy the last row of the Schur basis matrix | c | to workl(ihbds). This vector will be used | c | to compute the Ritz estimates of converged | c | Ritz values. | c %---------------------------------------------% c call zcopy(ncv , workl(invsub+ncv-1), ldq, & workl(ihbds), 1) c c %--------------------------------------------% c | Place the computed eigenvalues of H into D | c | if a spectral transformation was not used. | c %--------------------------------------------% c if (type .eq. 'REGULR') then call zcopy(nconv, workl(iheig), 1, d, 1) end if c c %----------------------------------------------------------% c | Compute the QR factorization of the matrix representing | c | the wanted invariant subspace located in the first NCONV | c | columns of workl(invsub,ldq). | c %----------------------------------------------------------% c call zgeqr2(ncv , nconv , workl(invsub), & ldq , workev, workev(ncv+1), & ierr) c c %--------------------------------------------------------% c | * Postmultiply V by Q using zunm2r. | c | * Copy the first NCONV columns of VQ into Z. | c | * Postmultiply Z by R. | c | The N by NCONV matrix Z is now a matrix representation | c | of the approximate invariant subspace associated with | c | the Ritz values in workl(iheig). The first NCONV | c | columns of V are now approximate Schur vectors | c | associated with the upper triangular matrix of order | c | NCONV in workl(iuptri). | c %--------------------------------------------------------% c call zunm2r('Right', 'Notranspose', n , & ncv , nconv , workl(invsub), & ldq , workev , v , & ldv , workd(n+1) , ierr) call zlacpy('All', n, nconv, v, ldv, z, ldz) c do 20 j=1, nconv c c %---------------------------------------------------% c | Perform both a column and row scaling if the | c | diagonal element of workl(invsub,ldq) is negative | c | I'm lazy and don't take advantage of the upper | c | triangular form of workl(iuptri,ldq). | c | Note that since Q is orthogonal, R is a diagonal | c | matrix consisting of plus or minus ones. | c %---------------------------------------------------% c if ( dble( workl(invsub+(j-1)*ldq+j-1) ) .lt. & dble(zero) ) then call zscal(nconv, -one, workl(iuptri+j-1), ldq) call zscal(nconv, -one, workl(iuptri+(j-1)*ldq), 1) end if c 20 continue c if (howmny .eq. 'A') then c c %--------------------------------------------% c | Compute the NCONV wanted eigenvectors of T | c | located in workl(iuptri,ldq). | c %--------------------------------------------% c do 30 j=1, ncv if (j .le. nconv) then select(j) = .true. else select(j) = .false. end if 30 continue c call ztrevc('Right', 'Select' , select , & ncv , workl(iuptri), ldq , & vl , 1 , workl(invsub), & ldq , ncv , outncv , & workev , rwork , ierr) c if (ierr .ne. 0) then info = -9 go to 9000 end if c c %------------------------------------------------% c | Scale the returning eigenvectors so that their | c | Euclidean norms are all one. LAPACK subroutine | c | ztrevc returns each eigenvector normalized so | c | that the element of largest magnitude has | c | magnitude 1. | c %------------------------------------------------% c do 40 j=1, nconv rtemp = dznrm2(ncv, workl(invsub+(j-1)*ldq), 1) rtemp = dble(one) / rtemp call zdscal ( ncv, rtemp, & workl(invsub+(j-1)*ldq), 1 ) c c %------------------------------------------% c | Ritz estimates can be obtained by taking | c | the inner product of the last row of the | c | Schur basis of H with eigenvectors of T. | c | Note that the eigenvector matrix of T is | c | upper triangular, thus the length of the | c | inner product can be set to j. | c %------------------------------------------% c workev(j) = zdotc(j, workl(ihbds), 1, & workl(invsub+(j-1)*ldq), 1) 40 continue c if (msglvl .gt. 2) then call zcopy(nconv, workl(invsub+ncv-1), ldq, & workl(ihbds), 1) call zvout (logfil, nconv, workl(ihbds), ndigit, & '_neupd: Last row of the eigenvector matrix for T') if (msglvl .gt. 3) then call zmout(logfil , ncv, ncv , & workl(invsub), ldq, ndigit, & '_neupd: The eigenvector matrix for T') end if end if c c %---------------------------------------% c | Copy Ritz estimates into workl(ihbds) | c %---------------------------------------% c call zcopy(nconv, workev, 1, workl(ihbds), 1) c c %----------------------------------------------% c | The eigenvector matrix Q of T is triangular. | c | Form Z*Q. | c %----------------------------------------------% c call ztrmm('Right' , 'Upper' , 'No transpose', & 'Non-unit', n , nconv , & one , workl(invsub), ldq , & z , ldz) end if c else c c %--------------------------------------------------% c | An approximate invariant subspace is not needed. | c | Place the Ritz values computed ZNAUPD into D. | c %--------------------------------------------------% c call zcopy(nconv, workl(ritz), 1, d, 1) call zcopy(nconv, workl(ritz), 1, workl(iheig), 1) call zcopy(nconv, workl(bounds), 1, workl(ihbds), 1) c end if c c %------------------------------------------------% c | Transform the Ritz values and possibly vectors | c | and corresponding error bounds of OP to those | c | of A*x = lambda*B*x. | c %------------------------------------------------% c if (type .eq. 'REGULR') then c if (rvec) & call zscal(ncv, rnorm, workl(ihbds), 1) c else c c %---------------------------------------% c | A spectral transformation was used. | c | * Determine the Ritz estimates of the | c | Ritz values in the original system. | c %---------------------------------------% c if (rvec) & call zscal(ncv, rnorm, workl(ihbds), 1) c do 50 k=1, ncv temp = workl(iheig+k-1) workl(ihbds+k-1) = workl(ihbds+k-1) / temp / temp 50 continue c end if c c %-----------------------------------------------------------% c | * Transform the Ritz values back to the original system. | c | For TYPE = 'SHIFTI' the transformation is | c | lambda = 1/theta + sigma | c | NOTES: | c | *The Ritz vectors are not affected by the transformation. | c %-----------------------------------------------------------% c if (type .eq. 'SHIFTI') then do 60 k=1, nconv d(k) = one / workl(iheig+k-1) + sigma 60 continue end if c if (type .ne. 'REGULR' .and. msglvl .gt. 1) then call zvout (logfil, nconv, d, ndigit, & '_neupd: Untransformed Ritz values.') call zvout (logfil, nconv, workl(ihbds), ndigit, & '_neupd: Ritz estimates of the untransformed Ritz values.') else if ( msglvl .gt. 1) then call zvout (logfil, nconv, d, ndigit, & '_neupd: Converged Ritz values.') call zvout (logfil, nconv, workl(ihbds), ndigit, & '_neupd: Associated Ritz estimates.') end if c c %-------------------------------------------------% c | Eigenvector Purification step. Formally perform | c | one of inverse subspace iteration. Only used | c | for MODE = 3. See reference 3. | c %-------------------------------------------------% c if (rvec .and. howmny .eq. 'A' .and. type .eq. 'SHIFTI') then c c %------------------------------------------------% c | Purify the computed Ritz vectors by adding a | c | little bit of the residual vector: | c | T | c | resid(:)*( e s ) / theta | c | NCV | c | where H s = s theta. | c %------------------------------------------------% c do 100 j=1, nconv if (workl(iheig+j-1) .ne. zero) then workev(j) = workl(invsub+(j-1)*ldq+ncv-1) / & workl(iheig+j-1) endif 100 continue c %---------------------------------------% c | Perform a rank one update to Z and | c | purify all the Ritz vectors together. | c %---------------------------------------% c call zgeru (n, nconv, one, resid, 1, workev, 1, z, ldz) c end if c 9000 continue c return c c %---------------% c | End of zneupd| c %---------------% c end arpack-0.92.1/SRC/zstatn.f0000644000175000017500000000230510776001577012120 00000000000000c c\SCCS Information: @(#) c FILE: statn.F SID: 2.2 DATE OF SID: 4/20/96 RELEASE: 2 c c %---------------------------------------------% c | Initialize statistic and timing information | c | for complex nonsymmetric Arnoldi code. | c %---------------------------------------------% subroutine zstatn c c %--------------------------------% c | See stat.doc for documentation | c %--------------------------------% c include 'stat.h' c %-----------------------% c | Executable Statements | c %-----------------------% nopx = 0 nbx = 0 nrorth = 0 nitref = 0 nrstrt = 0 tcaupd = 0.0D+0 tcaup2 = 0.0D+0 tcaitr = 0.0D+0 tceigh = 0.0D+0 tcgets = 0.0D+0 tcapps = 0.0D+0 tcconv = 0.0D+0 titref = 0.0D+0 tgetv0 = 0.0D+0 trvec = 0.0D+0 c %----------------------------------------------------% c | User time including reverse communication overhead | c %----------------------------------------------------% tmvopx = 0.0D+0 tmvbx = 0.0D+0 return c c %---------------% c | End of zstatn | c %---------------% c end arpack-0.92.1/SRC/ssaupd.f0000644000175000017500000007037210776001577012105 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: ssaupd c c\Description: c c Reverse communication interface for the Implicitly Restarted Arnoldi c Iteration. For symmetric problems this reduces to a variant of the Lanczos c method. This method has been designed to compute approximations to a c few eigenpairs of a linear operator OP that is real and symmetric c with respect to a real positive semi-definite symmetric matrix B, c i.e. c c B*OP = (OP`)*B. c c Another way to express this condition is c c < x,OPy > = < OPx,y > where < z,w > = z`Bw . c c In the standard eigenproblem B is the identity matrix. c ( A` denotes transpose of A) c c The computed approximate eigenvalues are called Ritz values and c the corresponding approximate eigenvectors are called Ritz vectors. c c ssaupd is usually called iteratively to solve one of the c following problems: c c Mode 1: A*x = lambda*x, A symmetric c ===> OP = A and B = I. c c Mode 2: A*x = lambda*M*x, A symmetric, M symmetric positive definite c ===> OP = inv[M]*A and B = M. c ===> (If M can be factored see remark 3 below) c c Mode 3: K*x = lambda*M*x, K symmetric, M symmetric positive semi-definite c ===> OP = (inv[K - sigma*M])*M and B = M. c ===> Shift-and-Invert mode c c Mode 4: K*x = lambda*KG*x, K symmetric positive semi-definite, c KG symmetric indefinite c ===> OP = (inv[K - sigma*KG])*K and B = K. c ===> Buckling mode c c Mode 5: A*x = lambda*M*x, A symmetric, M symmetric positive semi-definite c ===> OP = inv[A - sigma*M]*[A + sigma*M] and B = M. c ===> Cayley transformed mode c c NOTE: The action of w <- inv[A - sigma*M]*v or w <- inv[M]*v c should be accomplished either by a direct method c using a sparse matrix factorization and solving c c [A - sigma*M]*w = v or M*w = v, c c or through an iterative method for solving these c systems. If an iterative method is used, the c convergence test must be more stringent than c the accuracy requirements for the eigenvalue c approximations. c c\Usage: c call ssaupd c ( IDO, BMAT, N, WHICH, NEV, TOL, RESID, NCV, V, LDV, IPARAM, c IPNTR, WORKD, WORKL, LWORKL, INFO ) c c\Arguments c IDO Integer. (INPUT/OUTPUT) c Reverse communication flag. IDO must be zero on the first c call to ssaupd. IDO will be set internally to c indicate the type of operation to be performed. Control is c then given back to the calling routine which has the c responsibility to carry out the requested operation and call c ssaupd with the result. The operand is given in c WORKD(IPNTR(1)), the result must be put in WORKD(IPNTR(2)). c (If Mode = 2 see remark 5 below) c ------------------------------------------------------------- c IDO = 0: first call to the reverse communication interface c IDO = -1: compute Y = OP * X where c IPNTR(1) is the pointer into WORKD for X, c IPNTR(2) is the pointer into WORKD for Y. c This is for the initialization phase to force the c starting vector into the range of OP. c IDO = 1: compute Y = OP * X where c IPNTR(1) is the pointer into WORKD for X, c IPNTR(2) is the pointer into WORKD for Y. c In mode 3,4 and 5, the vector B * X is already c available in WORKD(ipntr(3)). It does not c need to be recomputed in forming OP * X. c IDO = 2: compute Y = B * X where c IPNTR(1) is the pointer into WORKD for X, c IPNTR(2) is the pointer into WORKD for Y. c IDO = 3: compute the IPARAM(8) shifts where c IPNTR(11) is the pointer into WORKL for c placing the shifts. See remark 6 below. c IDO = 99: done c ------------------------------------------------------------- c c BMAT Character*1. (INPUT) c BMAT specifies the type of the matrix B that defines the c semi-inner product for the operator OP. c B = 'I' -> standard eigenvalue problem A*x = lambda*x c B = 'G' -> generalized eigenvalue problem A*x = lambda*B*x c c N Integer. (INPUT) c Dimension of the eigenproblem. c c WHICH Character*2. (INPUT) c Specify which of the Ritz values of OP to compute. c c 'LA' - compute the NEV largest (algebraic) eigenvalues. c 'SA' - compute the NEV smallest (algebraic) eigenvalues. c 'LM' - compute the NEV largest (in magnitude) eigenvalues. c 'SM' - compute the NEV smallest (in magnitude) eigenvalues. c 'BE' - compute NEV eigenvalues, half from each end of the c spectrum. When NEV is odd, compute one more from the c high end than from the low end. c (see remark 1 below) c c NEV Integer. (INPUT) c Number of eigenvalues of OP to be computed. 0 < NEV < N. c c TOL Real scalar. (INPUT) c Stopping criterion: the relative accuracy of the Ritz value c is considered acceptable if BOUNDS(I) .LE. TOL*ABS(RITZ(I)). c If TOL .LE. 0. is passed a default is set: c DEFAULT = SLAMCH('EPS') (machine precision as computed c by the LAPACK auxiliary subroutine SLAMCH). c c RESID Real array of length N. (INPUT/OUTPUT) c On INPUT: c If INFO .EQ. 0, a random initial residual vector is used. c If INFO .NE. 0, RESID contains the initial residual vector, c possibly from a previous run. c On OUTPUT: c RESID contains the final residual vector. c c NCV Integer. (INPUT) c Number of columns of the matrix V (less than or equal to N). c This will indicate how many Lanczos vectors are generated c at each iteration. After the startup phase in which NEV c Lanczos vectors are generated, the algorithm generates c NCV-NEV Lanczos vectors at each subsequent update iteration. c Most of the cost in generating each Lanczos vector is in the c matrix-vector product OP*x. (See remark 4 below). c c V Real N by NCV array. (OUTPUT) c The NCV columns of V contain the Lanczos basis vectors. c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling c program. c c IPARAM Integer array of length 11. (INPUT/OUTPUT) c IPARAM(1) = ISHIFT: method for selecting the implicit shifts. c The shifts selected at each iteration are used to restart c the Arnoldi iteration in an implicit fashion. c ------------------------------------------------------------- c ISHIFT = 0: the shifts are provided by the user via c reverse communication. The NCV eigenvalues of c the current tridiagonal matrix T are returned in c the part of WORKL array corresponding to RITZ. c See remark 6 below. c ISHIFT = 1: exact shifts with respect to the reduced c tridiagonal matrix T. This is equivalent to c restarting the iteration with a starting vector c that is a linear combination of Ritz vectors c associated with the "wanted" Ritz values. c ------------------------------------------------------------- c c IPARAM(2) = LEVEC c No longer referenced. See remark 2 below. c c IPARAM(3) = MXITER c On INPUT: maximum number of Arnoldi update iterations allowed. c On OUTPUT: actual number of Arnoldi update iterations taken. c c IPARAM(4) = NB: blocksize to be used in the recurrence. c The code currently works only for NB = 1. c c IPARAM(5) = NCONV: number of "converged" Ritz values. c This represents the number of Ritz values that satisfy c the convergence criterion. c c IPARAM(6) = IUPD c No longer referenced. Implicit restarting is ALWAYS used. c c IPARAM(7) = MODE c On INPUT determines what type of eigenproblem is being solved. c Must be 1,2,3,4,5; See under \Description of ssaupd for the c five modes available. c c IPARAM(8) = NP c When ido = 3 and the user provides shifts through reverse c communication (IPARAM(1)=0), ssaupd returns NP, the number c of shifts the user is to provide. 0 < NP <=NCV-NEV. See Remark c 6 below. c c IPARAM(9) = NUMOP, IPARAM(10) = NUMOPB, IPARAM(11) = NUMREO, c OUTPUT: NUMOP = total number of OP*x operations, c NUMOPB = total number of B*x operations if BMAT='G', c NUMREO = total number of steps of re-orthogonalization. c c IPNTR Integer array of length 11. (OUTPUT) c Pointer to mark the starting locations in the WORKD and WORKL c arrays for matrices/vectors used by the Lanczos iteration. c ------------------------------------------------------------- c IPNTR(1): pointer to the current operand vector X in WORKD. c IPNTR(2): pointer to the current result vector Y in WORKD. c IPNTR(3): pointer to the vector B * X in WORKD when used in c the shift-and-invert mode. c IPNTR(4): pointer to the next available location in WORKL c that is untouched by the program. c IPNTR(5): pointer to the NCV by 2 tridiagonal matrix T in WORKL. c IPNTR(6): pointer to the NCV RITZ values array in WORKL. c IPNTR(7): pointer to the Ritz estimates in array WORKL associated c with the Ritz values located in RITZ in WORKL. c IPNTR(11): pointer to the NP shifts in WORKL. See Remark 6 below. c c Note: IPNTR(8:10) is only referenced by sseupd. See Remark 2. c IPNTR(8): pointer to the NCV RITZ values of the original system. c IPNTR(9): pointer to the NCV corresponding error bounds. c IPNTR(10): pointer to the NCV by NCV matrix of eigenvectors c of the tridiagonal matrix T. Only referenced by c sseupd if RVEC = .TRUE. See Remarks. c ------------------------------------------------------------- c c WORKD Real work array of length 3*N. (REVERSE COMMUNICATION) c Distributed array to be used in the basic Arnoldi iteration c for reverse communication. The user should not use WORKD c as temporary workspace during the iteration. Upon termination c WORKD(1:N) contains B*RESID(1:N). If the Ritz vectors are desired c subroutine sseupd uses this output. c See Data Distribution Note below. c c WORKL Real work array of length LWORKL. (OUTPUT/WORKSPACE) c Private (replicated) array on each PE or array allocated on c the front end. See Data Distribution Note below. c c LWORKL Integer. (INPUT) c LWORKL must be at least NCV**2 + 8*NCV . c c INFO Integer. (INPUT/OUTPUT) c If INFO .EQ. 0, a randomly initial residual vector is used. c If INFO .NE. 0, RESID contains the initial residual vector, c possibly from a previous run. c Error flag on output. c = 0: Normal exit. c = 1: Maximum number of iterations taken. c All possible eigenvalues of OP has been found. IPARAM(5) c returns the number of wanted converged Ritz values. c = 2: No longer an informational error. Deprecated starting c with release 2 of ARPACK. c = 3: No shifts could be applied during a cycle of the c Implicitly restarted Arnoldi iteration. One possibility c is to increase the size of NCV relative to NEV. c See remark 4 below. c = -1: N must be positive. c = -2: NEV must be positive. c = -3: NCV must be greater than NEV and less than or equal to N. c = -4: The maximum number of Arnoldi update iterations allowed c must be greater than zero. c = -5: WHICH must be one of 'LM', 'SM', 'LA', 'SA' or 'BE'. c = -6: BMAT must be one of 'I' or 'G'. c = -7: Length of private work array WORKL is not sufficient. c = -8: Error return from trid. eigenvalue calculation; c Informatinal error from LAPACK routine ssteqr. c = -9: Starting vector is zero. c = -10: IPARAM(7) must be 1,2,3,4,5. c = -11: IPARAM(7) = 1 and BMAT = 'G' are incompatable. c = -12: IPARAM(1) must be equal to 0 or 1. c = -13: NEV and WHICH = 'BE' are incompatable. c = -9999: Could not build an Arnoldi factorization. c IPARAM(5) returns the size of the current Arnoldi c factorization. The user is advised to check that c enough workspace and array storage has been allocated. c c c\Remarks c 1. The converged Ritz values are always returned in ascending c algebraic order. The computed Ritz values are approximate c eigenvalues of OP. The selection of WHICH should be made c with this in mind when Mode = 3,4,5. After convergence, c approximate eigenvalues of the original problem may be obtained c with the ARPACK subroutine sseupd. c c 2. If the Ritz vectors corresponding to the converged Ritz values c are needed, the user must call sseupd immediately following completion c of ssaupd. This is new starting with version 2.1 of ARPACK. c c 3. If M can be factored into a Cholesky factorization M = LL` c then Mode = 2 should not be selected. Instead one should use c Mode = 1 with OP = inv(L)*A*inv(L`). Appropriate triangular c linear systems should be solved with L and L` rather c than computing inverses. After convergence, an approximate c eigenvector z of the original problem is recovered by solving c L`z = x where x is a Ritz vector of OP. c c 4. At present there is no a-priori analysis to guide the selection c of NCV relative to NEV. The only formal requrement is that NCV > NEV. c However, it is recommended that NCV .ge. 2*NEV. If many problems of c the same type are to be solved, one should experiment with increasing c NCV while keeping NEV fixed for a given test problem. This will c usually decrease the required number of OP*x operations but it c also increases the work and storage required to maintain the orthogonal c basis vectors. The optimal "cross-over" with respect to CPU time c is problem dependent and must be determined empirically. c c 5. If IPARAM(7) = 2 then in the Reverse commuication interface the user c must do the following. When IDO = 1, Y = OP * X is to be computed. c When IPARAM(7) = 2 OP = inv(B)*A. After computing A*X the user c must overwrite X with A*X. Y is then the solution to the linear set c of equations B*Y = A*X. c c 6. When IPARAM(1) = 0, and IDO = 3, the user needs to provide the c NP = IPARAM(8) shifts in locations: c 1 WORKL(IPNTR(11)) c 2 WORKL(IPNTR(11)+1) c . c . c . c NP WORKL(IPNTR(11)+NP-1). c c The eigenvalues of the current tridiagonal matrix are located in c WORKL(IPNTR(6)) through WORKL(IPNTR(6)+NCV-1). They are in the c order defined by WHICH. The associated Ritz estimates are located in c WORKL(IPNTR(8)), WORKL(IPNTR(8)+1), ... , WORKL(IPNTR(8)+NCV-1). c c----------------------------------------------------------------------- c c\Data Distribution Note: c c Fortran-D syntax: c ================ c REAL RESID(N), V(LDV,NCV), WORKD(3*N), WORKL(LWORKL) c DECOMPOSE D1(N), D2(N,NCV) c ALIGN RESID(I) with D1(I) c ALIGN V(I,J) with D2(I,J) c ALIGN WORKD(I) with D1(I) range (1:N) c ALIGN WORKD(I) with D1(I-N) range (N+1:2*N) c ALIGN WORKD(I) with D1(I-2*N) range (2*N+1:3*N) c DISTRIBUTE D1(BLOCK), D2(BLOCK,:) c REPLICATED WORKL(LWORKL) c c Cray MPP syntax: c =============== c REAL RESID(N), V(LDV,NCV), WORKD(N,3), WORKL(LWORKL) c SHARED RESID(BLOCK), V(BLOCK,:), WORKD(BLOCK,:) c REPLICATED WORKL(LWORKL) c c c\BeginLib c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly c Restarted Arnoldi Iteration", Rice University Technical Report c TR95-13, Department of Computational and Applied Mathematics. c 3. B.N. Parlett, "The Symmetric Eigenvalue Problem". Prentice-Hall, c 1980. c 4. B.N. Parlett, B. Nour-Omid, "Towards a Black Box Lanczos Program", c Computer Physics Communications, 53 (1989), pp 169-179. c 5. B. Nour-Omid, B.N. Parlett, T. Ericson, P.S. Jensen, "How to c Implement the Spectral Transformation", Math. Comp., 48 (1987), c pp 663-673. c 6. R.G. Grimes, J.G. Lewis and H.D. Simon, "A Shifted Block Lanczos c Algorithm for Solving Sparse Symmetric Generalized Eigenproblems", c SIAM J. Matr. Anal. Apps., January (1993). c 7. L. Reichel, W.B. Gragg, "Algorithm 686: FORTRAN Subroutines c for Updating the QR decomposition", ACM TOMS, December 1990, c Volume 16 Number 4, pp 369-377. c 8. R.B. Lehoucq, D.C. Sorensen, "Implementation of Some Spectral c Transformations in a k-Step Arnoldi Method". In Preparation. c c\Routines called: c ssaup2 ARPACK routine that implements the Implicitly Restarted c Arnoldi Iteration. c sstats ARPACK routine that initialize timing and other statistics c variables. c ivout ARPACK utility routine that prints integers. c arscnd ARPACK utility routine for timing. c svout ARPACK utility routine that prints vectors. c slamch LAPACK routine that determines machine constants. c c\Authors c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c 12/15/93: Version ' 2.4' c c\SCCS Information: @(#) c FILE: saupd.F SID: 2.8 DATE OF SID: 04/10/01 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c----------------------------------------------------------------------- c subroutine ssaupd & ( ido, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam, & ipntr, workd, workl, lworkl, info ) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character bmat*1, which*2 integer ido, info, ldv, lworkl, n, ncv, nev Real & tol c c %-----------------% c | Array Arguments | c %-----------------% c integer iparam(11), ipntr(11) Real & resid(n), v(ldv,ncv), workd(3*n), workl(lworkl) c c %------------% c | Parameters | c %------------% c Real & one, zero parameter (one = 1.0E+0 , zero = 0.0E+0 ) c c %---------------% c | Local Scalars | c %---------------% c integer bounds, ierr, ih, iq, ishift, iupd, iw, & ldh, ldq, msglvl, mxiter, mode, nb, & nev0, next, np, ritz, j save bounds, ierr, ih, iq, ishift, iupd, iw, & ldh, ldq, msglvl, mxiter, mode, nb, & nev0, next, np, ritz c c %----------------------% c | External Subroutines | c %----------------------% c external ssaup2, svout, ivout, arscnd, sstats c c %--------------------% c | External Functions | c %--------------------% c Real & slamch external slamch c c %-----------------------% c | Executable Statements | c %-----------------------% c if (ido .eq. 0) then c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call sstats call arscnd (t0) msglvl = msaupd c ierr = 0 ishift = iparam(1) mxiter = iparam(3) c nb = iparam(4) nb = 1 c c %--------------------------------------------% c | Revision 2 performs only implicit restart. | c %--------------------------------------------% c iupd = 1 mode = iparam(7) c c %----------------% c | Error checking | c %----------------% c if (n .le. 0) then ierr = -1 else if (nev .le. 0) then ierr = -2 else if (ncv .le. nev .or. ncv .gt. n) then ierr = -3 end if c c %----------------------------------------------% c | NP is the number of additional steps to | c | extend the length NEV Lanczos factorization. | c %----------------------------------------------% c np = ncv - nev c if (mxiter .le. 0) ierr = -4 if (which .ne. 'LM' .and. & which .ne. 'SM' .and. & which .ne. 'LA' .and. & which .ne. 'SA' .and. & which .ne. 'BE') ierr = -5 if (bmat .ne. 'I' .and. bmat .ne. 'G') ierr = -6 c if (lworkl .lt. ncv**2 + 8*ncv) ierr = -7 if (mode .lt. 1 .or. mode .gt. 5) then ierr = -10 else if (mode .eq. 1 .and. bmat .eq. 'G') then ierr = -11 else if (ishift .lt. 0 .or. ishift .gt. 1) then ierr = -12 else if (nev .eq. 1 .and. which .eq. 'BE') then ierr = -13 end if c c %------------% c | Error Exit | c %------------% c if (ierr .ne. 0) then info = ierr ido = 99 go to 9000 end if c c %------------------------% c | Set default parameters | c %------------------------% c if (nb .le. 0) nb = 1 if (tol .le. zero) tol = slamch('EpsMach') c c %----------------------------------------------% c | NP is the number of additional steps to | c | extend the length NEV Lanczos factorization. | c | NEV0 is the local variable designating the | c | size of the invariant subspace desired. | c %----------------------------------------------% c np = ncv - nev nev0 = nev c c %-----------------------------% c | Zero out internal workspace | c %-----------------------------% c do 10 j = 1, ncv**2 + 8*ncv workl(j) = zero 10 continue c c %-------------------------------------------------------% c | Pointer into WORKL for address of H, RITZ, BOUNDS, Q | c | etc... and the remaining workspace. | c | Also update pointer to be used on output. | c | Memory is laid out as follows: | c | workl(1:2*ncv) := generated tridiagonal matrix | c | workl(2*ncv+1:2*ncv+ncv) := ritz values | c | workl(3*ncv+1:3*ncv+ncv) := computed error bounds | c | workl(4*ncv+1:4*ncv+ncv*ncv) := rotation matrix Q | c | workl(4*ncv+ncv*ncv+1:7*ncv+ncv*ncv) := workspace | c %-------------------------------------------------------% c ldh = ncv ldq = ncv ih = 1 ritz = ih + 2*ldh bounds = ritz + ncv iq = bounds + ncv iw = iq + ncv**2 next = iw + 3*ncv c ipntr(4) = next ipntr(5) = ih ipntr(6) = ritz ipntr(7) = bounds ipntr(11) = iw end if c c %-------------------------------------------------------% c | Carry out the Implicitly restarted Lanczos Iteration. | c %-------------------------------------------------------% c call ssaup2 & ( ido, bmat, n, which, nev0, np, tol, resid, mode, iupd, & ishift, mxiter, v, ldv, workl(ih), ldh, workl(ritz), & workl(bounds), workl(iq), ldq, workl(iw), ipntr, workd, & info ) c c %--------------------------------------------------% c | ido .ne. 99 implies use of reverse communication | c | to compute operations involving OP or shifts. | c %--------------------------------------------------% c if (ido .eq. 3) iparam(8) = np if (ido .ne. 99) go to 9000 c iparam(3) = mxiter iparam(5) = np iparam(9) = nopx iparam(10) = nbx iparam(11) = nrorth c c %------------------------------------% c | Exit if there was an informational | c | error within ssaup2. | c %------------------------------------% c if (info .lt. 0) go to 9000 if (info .eq. 2) info = 3 c if (msglvl .gt. 0) then call ivout (logfil, 1, mxiter, ndigit, & '_saupd: number of update iterations taken') call ivout (logfil, 1, np, ndigit, & '_saupd: number of "converged" Ritz values') call svout (logfil, np, workl(Ritz), ndigit, & '_saupd: final Ritz values') call svout (logfil, np, workl(Bounds), ndigit, & '_saupd: corresponding error bounds') end if c call arscnd (t1) tsaupd = t1 - t0 c if (msglvl .gt. 0) then c c %--------------------------------------------------------% c | Version Number & Version Date are defined in version.h | c %--------------------------------------------------------% c write (6,1000) write (6,1100) mxiter, nopx, nbx, nrorth, nitref, nrstrt, & tmvopx, tmvbx, tsaupd, tsaup2, tsaitr, titref, & tgetv0, tseigt, tsgets, tsapps, tsconv 1000 format (//, & 5x, '==========================================',/ & 5x, '= Symmetric implicit Arnoldi update code =',/ & 5x, '= Version Number:', ' 2.4' , 19x, ' =',/ & 5x, '= Version Date: ', ' 07/31/96' , 14x, ' =',/ & 5x, '==========================================',/ & 5x, '= Summary of timing statistics =',/ & 5x, '==========================================',//) 1100 format ( & 5x, 'Total number update iterations = ', i5,/ & 5x, 'Total number of OP*x operations = ', i5,/ & 5x, 'Total number of B*x operations = ', i5,/ & 5x, 'Total number of reorthogonalization steps = ', i5,/ & 5x, 'Total number of iterative refinement steps = ', i5,/ & 5x, 'Total number of restart steps = ', i5,/ & 5x, 'Total time in user OP*x operation = ', f12.6,/ & 5x, 'Total time in user B*x operation = ', f12.6,/ & 5x, 'Total time in Arnoldi update routine = ', f12.6,/ & 5x, 'Total time in saup2 routine = ', f12.6,/ & 5x, 'Total time in basic Arnoldi iteration loop = ', f12.6,/ & 5x, 'Total time in reorthogonalization phase = ', f12.6,/ & 5x, 'Total time in (re)start vector generation = ', f12.6,/ & 5x, 'Total time in trid eigenvalue subproblem = ', f12.6,/ & 5x, 'Total time in getting the shifts = ', f12.6,/ & 5x, 'Total time in applying the shifts = ', f12.6,/ & 5x, 'Total time in convergence testing = ', f12.6) end if c 9000 continue c return c c %---------------% c | End of ssaupd | c %---------------% c end arpack-0.92.1/SRC/dneigh.f0000644000175000017500000002424110776001577012036 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: dneigh c c\Description: c Compute the eigenvalues of the current upper Hessenberg matrix c and the corresponding Ritz estimates given the current residual norm. c c\Usage: c call dneigh c ( RNORM, N, H, LDH, RITZR, RITZI, BOUNDS, Q, LDQ, WORKL, IERR ) c c\Arguments c RNORM Double precision scalar. (INPUT) c Residual norm corresponding to the current upper Hessenberg c matrix H. c c N Integer. (INPUT) c Size of the matrix H. c c H Double precision N by N array. (INPUT) c H contains the current upper Hessenberg matrix. c c LDH Integer. (INPUT) c Leading dimension of H exactly as declared in the calling c program. c c RITZR, Double precision arrays of length N. (OUTPUT) c RITZI On output, RITZR(1:N) (resp. RITZI(1:N)) contains the real c (respectively imaginary) parts of the eigenvalues of H. c c BOUNDS Double precision array of length N. (OUTPUT) c On output, BOUNDS contains the Ritz estimates associated with c the eigenvalues RITZR and RITZI. This is equal to RNORM c times the last components of the eigenvectors corresponding c to the eigenvalues in RITZR and RITZI. c c Q Double precision N by N array. (WORKSPACE) c Workspace needed to store the eigenvectors of H. c c LDQ Integer. (INPUT) c Leading dimension of Q exactly as declared in the calling c program. c c WORKL Double precision work array of length N**2 + 3*N. (WORKSPACE) c Private (replicated) array on each PE or array allocated on c the front end. This is needed to keep the full Schur form c of H and also in the calculation of the eigenvectors of H. c c IERR Integer. (OUTPUT) c Error exit flag from dlaqrb or dtrevc. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx real c c\Routines called: c dlaqrb ARPACK routine to compute the real Schur form of an c upper Hessenberg matrix and last row of the Schur vectors. c arscnd ARPACK utility routine for timing. c dmout ARPACK utility routine that prints matrices c dvout ARPACK utility routine that prints vectors. c dlacpy LAPACK matrix copy routine. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c dtrevc LAPACK routine to compute the eigenvectors of a matrix c in upper quasi-triangular form c dgemv Level 2 BLAS routine for matrix vector multiplication. c dcopy Level 1 BLAS that copies one vector to another . c dnrm2 Level 1 BLAS that computes the norm of a vector. c dscal Level 1 BLAS that scales a vector. c c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c xx/xx/92: Version ' 2.1' c c\SCCS Information: @(#) c FILE: neigh.F SID: 2.3 DATE OF SID: 4/20/96 RELEASE: 2 c c\Remarks c None c c\EndLib c c----------------------------------------------------------------------- c subroutine dneigh (rnorm, n, h, ldh, ritzr, ritzi, bounds, & q, ldq, workl, ierr) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c integer ierr, n, ldh, ldq Double precision & rnorm c c %-----------------% c | Array Arguments | c %-----------------% c Double precision & bounds(n), h(ldh,n), q(ldq,n), ritzi(n), ritzr(n), & workl(n*(n+3)) c c %------------% c | Parameters | c %------------% c Double precision & one, zero parameter (one = 1.0D+0, zero = 0.0D+0) c c %------------------------% c | Local Scalars & Arrays | c %------------------------% c logical select(1) integer i, iconj, msglvl Double precision & temp, vl(1) c c %----------------------% c | External Subroutines | c %----------------------% c external dcopy, dlacpy, dlaqrb, dtrevc, dvout, arscnd c c %--------------------% c | External Functions | c %--------------------% c Double precision & dlapy2, dnrm2 external dlapy2, dnrm2 c c %---------------------% c | Intrinsic Functions | c %---------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call arscnd (t0) msglvl = mneigh c if (msglvl .gt. 2) then call dmout (logfil, n, n, h, ldh, ndigit, & '_neigh: Entering upper Hessenberg matrix H ') end if c c %-----------------------------------------------------------% c | 1. Compute the eigenvalues, the last components of the | c | corresponding Schur vectors and the full Schur form T | c | of the current upper Hessenberg matrix H. | c | dlaqrb returns the full Schur form of H in WORKL(1:N**2) | c | and the last components of the Schur vectors in BOUNDS. | c %-----------------------------------------------------------% c call dlacpy ('All', n, n, h, ldh, workl, n) call dlaqrb (.true., n, 1, n, workl, n, ritzr, ritzi, bounds, & ierr) if (ierr .ne. 0) go to 9000 c if (msglvl .gt. 1) then call dvout (logfil, n, bounds, ndigit, & '_neigh: last row of the Schur matrix for H') end if c c %-----------------------------------------------------------% c | 2. Compute the eigenvectors of the full Schur form T and | c | apply the last components of the Schur vectors to get | c | the last components of the corresponding eigenvectors. | c | Remember that if the i-th and (i+1)-st eigenvalues are | c | complex conjugate pairs, then the real & imaginary part | c | of the eigenvector components are split across adjacent | c | columns of Q. | c %-----------------------------------------------------------% c call dtrevc ('R', 'A', select, n, workl, n, vl, n, q, ldq, & n, n, workl(n*n+1), ierr) c if (ierr .ne. 0) go to 9000 c c %------------------------------------------------% c | Scale the returning eigenvectors so that their | c | euclidean norms are all one. LAPACK subroutine | c | dtrevc returns each eigenvector normalized so | c | that the element of largest magnitude has | c | magnitude 1; here the magnitude of a complex | c | number (x,y) is taken to be |x| + |y|. | c %------------------------------------------------% c iconj = 0 do 10 i=1, n if ( abs( ritzi(i) ) .le. zero ) then c c %----------------------% c | Real eigenvalue case | c %----------------------% c temp = dnrm2( n, q(1,i), 1 ) call dscal ( n, one / temp, q(1,i), 1 ) else c c %-------------------------------------------% c | Complex conjugate pair case. Note that | c | since the real and imaginary part of | c | the eigenvector are stored in consecutive | c | columns, we further normalize by the | c | square root of two. | c %-------------------------------------------% c if (iconj .eq. 0) then temp = dlapy2( dnrm2( n, q(1,i), 1 ), & dnrm2( n, q(1,i+1), 1 ) ) call dscal ( n, one / temp, q(1,i), 1 ) call dscal ( n, one / temp, q(1,i+1), 1 ) iconj = 1 else iconj = 0 end if end if 10 continue c call dgemv ('T', n, n, one, q, ldq, bounds, 1, zero, workl, 1) c if (msglvl .gt. 1) then call dvout (logfil, n, workl, ndigit, & '_neigh: Last row of the eigenvector matrix for H') end if c c %----------------------------% c | Compute the Ritz estimates | c %----------------------------% c iconj = 0 do 20 i = 1, n if ( abs( ritzi(i) ) .le. zero ) then c c %----------------------% c | Real eigenvalue case | c %----------------------% c bounds(i) = rnorm * abs( workl(i) ) else c c %-------------------------------------------% c | Complex conjugate pair case. Note that | c | since the real and imaginary part of | c | the eigenvector are stored in consecutive | c | columns, we need to take the magnitude | c | of the last components of the two vectors | c %-------------------------------------------% c if (iconj .eq. 0) then bounds(i) = rnorm * dlapy2( workl(i), workl(i+1) ) bounds(i+1) = bounds(i) iconj = 1 else iconj = 0 end if end if 20 continue c if (msglvl .gt. 2) then call dvout (logfil, n, ritzr, ndigit, & '_neigh: Real part of the eigenvalues of H') call dvout (logfil, n, ritzi, ndigit, & '_neigh: Imaginary part of the eigenvalues of H') call dvout (logfil, n, bounds, ndigit, & '_neigh: Ritz estimates for the eigenvalues of H') end if c call arscnd (t1) tneigh = tneigh + (t1 - t0) c 9000 continue return c c %---------------% c | End of dneigh | c %---------------% c end arpack-0.92.1/SRC/sneigh.f0000644000175000017500000002403510776001577012056 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: sneigh c c\Description: c Compute the eigenvalues of the current upper Hessenberg matrix c and the corresponding Ritz estimates given the current residual norm. c c\Usage: c call sneigh c ( RNORM, N, H, LDH, RITZR, RITZI, BOUNDS, Q, LDQ, WORKL, IERR ) c c\Arguments c RNORM Real scalar. (INPUT) c Residual norm corresponding to the current upper Hessenberg c matrix H. c c N Integer. (INPUT) c Size of the matrix H. c c H Real N by N array. (INPUT) c H contains the current upper Hessenberg matrix. c c LDH Integer. (INPUT) c Leading dimension of H exactly as declared in the calling c program. c c RITZR, Real arrays of length N. (OUTPUT) c RITZI On output, RITZR(1:N) (resp. RITZI(1:N)) contains the real c (respectively imaginary) parts of the eigenvalues of H. c c BOUNDS Real array of length N. (OUTPUT) c On output, BOUNDS contains the Ritz estimates associated with c the eigenvalues RITZR and RITZI. This is equal to RNORM c times the last components of the eigenvectors corresponding c to the eigenvalues in RITZR and RITZI. c c Q Real N by N array. (WORKSPACE) c Workspace needed to store the eigenvectors of H. c c LDQ Integer. (INPUT) c Leading dimension of Q exactly as declared in the calling c program. c c WORKL Real work array of length N**2 + 3*N. (WORKSPACE) c Private (replicated) array on each PE or array allocated on c the front end. This is needed to keep the full Schur form c of H and also in the calculation of the eigenvectors of H. c c IERR Integer. (OUTPUT) c Error exit flag from slaqrb or strevc. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx real c c\Routines called: c slaqrb ARPACK routine to compute the real Schur form of an c upper Hessenberg matrix and last row of the Schur vectors. c arscnd ARPACK utility routine for timing. c smout ARPACK utility routine that prints matrices c svout ARPACK utility routine that prints vectors. c slacpy LAPACK matrix copy routine. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c strevc LAPACK routine to compute the eigenvectors of a matrix c in upper quasi-triangular form c sgemv Level 2 BLAS routine for matrix vector multiplication. c scopy Level 1 BLAS that copies one vector to another . c snrm2 Level 1 BLAS that computes the norm of a vector. c sscal Level 1 BLAS that scales a vector. c c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c xx/xx/92: Version ' 2.1' c c\SCCS Information: @(#) c FILE: neigh.F SID: 2.3 DATE OF SID: 4/20/96 RELEASE: 2 c c\Remarks c None c c\EndLib c c----------------------------------------------------------------------- c subroutine sneigh (rnorm, n, h, ldh, ritzr, ritzi, bounds, & q, ldq, workl, ierr) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c integer ierr, n, ldh, ldq Real & rnorm c c %-----------------% c | Array Arguments | c %-----------------% c Real & bounds(n), h(ldh,n), q(ldq,n), ritzi(n), ritzr(n), & workl(n*(n+3)) c c %------------% c | Parameters | c %------------% c Real & one, zero parameter (one = 1.0E+0, zero = 0.0E+0) c c %------------------------% c | Local Scalars & Arrays | c %------------------------% c logical select(1) integer i, iconj, msglvl Real & temp, vl(1) c c %----------------------% c | External Subroutines | c %----------------------% c external scopy, slacpy, slaqrb, strevc, svout, arscnd c c %--------------------% c | External Functions | c %--------------------% c Real & slapy2, snrm2 external slapy2, snrm2 c c %---------------------% c | Intrinsic Functions | c %---------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call arscnd (t0) msglvl = mneigh c if (msglvl .gt. 2) then call smout (logfil, n, n, h, ldh, ndigit, & '_neigh: Entering upper Hessenberg matrix H ') end if c c %-----------------------------------------------------------% c | 1. Compute the eigenvalues, the last components of the | c | corresponding Schur vectors and the full Schur form T | c | of the current upper Hessenberg matrix H. | c | slaqrb returns the full Schur form of H in WORKL(1:N**2) | c | and the last components of the Schur vectors in BOUNDS. | c %-----------------------------------------------------------% c call slacpy ('All', n, n, h, ldh, workl, n) call slaqrb (.true., n, 1, n, workl, n, ritzr, ritzi, bounds, & ierr) if (ierr .ne. 0) go to 9000 c if (msglvl .gt. 1) then call svout (logfil, n, bounds, ndigit, & '_neigh: last row of the Schur matrix for H') end if c c %-----------------------------------------------------------% c | 2. Compute the eigenvectors of the full Schur form T and | c | apply the last components of the Schur vectors to get | c | the last components of the corresponding eigenvectors. | c | Remember that if the i-th and (i+1)-st eigenvalues are | c | complex conjugate pairs, then the real & imaginary part | c | of the eigenvector components are split across adjacent | c | columns of Q. | c %-----------------------------------------------------------% c call strevc ('R', 'A', select, n, workl, n, vl, n, q, ldq, & n, n, workl(n*n+1), ierr) c if (ierr .ne. 0) go to 9000 c c %------------------------------------------------% c | Scale the returning eigenvectors so that their | c | euclidean norms are all one. LAPACK subroutine | c | strevc returns each eigenvector normalized so | c | that the element of largest magnitude has | c | magnitude 1; here the magnitude of a complex | c | number (x,y) is taken to be |x| + |y|. | c %------------------------------------------------% c iconj = 0 do 10 i=1, n if ( abs( ritzi(i) ) .le. zero ) then c c %----------------------% c | Real eigenvalue case | c %----------------------% c temp = snrm2( n, q(1,i), 1 ) call sscal ( n, one / temp, q(1,i), 1 ) else c c %-------------------------------------------% c | Complex conjugate pair case. Note that | c | since the real and imaginary part of | c | the eigenvector are stored in consecutive | c | columns, we further normalize by the | c | square root of two. | c %-------------------------------------------% c if (iconj .eq. 0) then temp = slapy2( snrm2( n, q(1,i), 1 ), & snrm2( n, q(1,i+1), 1 ) ) call sscal ( n, one / temp, q(1,i), 1 ) call sscal ( n, one / temp, q(1,i+1), 1 ) iconj = 1 else iconj = 0 end if end if 10 continue c call sgemv ('T', n, n, one, q, ldq, bounds, 1, zero, workl, 1) c if (msglvl .gt. 1) then call svout (logfil, n, workl, ndigit, & '_neigh: Last row of the eigenvector matrix for H') end if c c %----------------------------% c | Compute the Ritz estimates | c %----------------------------% c iconj = 0 do 20 i = 1, n if ( abs( ritzi(i) ) .le. zero ) then c c %----------------------% c | Real eigenvalue case | c %----------------------% c bounds(i) = rnorm * abs( workl(i) ) else c c %-------------------------------------------% c | Complex conjugate pair case. Note that | c | since the real and imaginary part of | c | the eigenvector are stored in consecutive | c | columns, we need to take the magnitude | c | of the last components of the two vectors | c %-------------------------------------------% c if (iconj .eq. 0) then bounds(i) = rnorm * slapy2( workl(i), workl(i+1) ) bounds(i+1) = bounds(i) iconj = 1 else iconj = 0 end if end if 20 continue c if (msglvl .gt. 2) then call svout (logfil, n, ritzr, ndigit, & '_neigh: Real part of the eigenvalues of H') call svout (logfil, n, ritzi, ndigit, & '_neigh: Imaginary part of the eigenvalues of H') call svout (logfil, n, bounds, ndigit, & '_neigh: Ritz estimates for the eigenvalues of H') end if c call arscnd (t1) tneigh = tneigh + (t1 - t0) c 9000 continue return c c %---------------% c | End of sneigh | c %---------------% c end arpack-0.92.1/SRC/Makefile.in0000644000175000017500000004725111540551555012500 00000000000000# Makefile.in generated by automake 1.11.1 from Makefile.am. # 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install-info-am \ install-libLTLIBRARIES install-man install-pdf install-pdf-am \ install-ps install-ps-am install-strip installcheck \ installcheck-am installdirs maintainer-clean \ maintainer-clean-generic mostlyclean mostlyclean-compile \ mostlyclean-generic mostlyclean-libtool pdf pdf-am ps ps-am \ tags uninstall uninstall-am uninstall-libLTLIBRARIES # Tell versions [3.59,3.63) of GNU make to not export all variables. # Otherwise a system limit (for SysV at least) may be exceeded. .NOEXPORT: arpack-0.92.1/SRC/dsaup2.f0000644000175000017500000007712710776001577012011 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: dsaup2 c c\Description: c Intermediate level interface called by dsaupd. c c\Usage: c call dsaup2 c ( IDO, BMAT, N, WHICH, NEV, NP, TOL, RESID, MODE, IUPD, c ISHIFT, MXITER, V, LDV, H, LDH, RITZ, BOUNDS, Q, LDQ, WORKL, c IPNTR, WORKD, INFO ) c c\Arguments c c IDO, BMAT, N, WHICH, NEV, TOL, RESID: same as defined in dsaupd. c MODE, ISHIFT, MXITER: see the definition of IPARAM in dsaupd. c c NP Integer. (INPUT/OUTPUT) c Contains the number of implicit shifts to apply during c each Arnoldi/Lanczos iteration. c If ISHIFT=1, NP is adjusted dynamically at each iteration c to accelerate convergence and prevent stagnation. c This is also roughly equal to the number of matrix-vector c products (involving the operator OP) per Arnoldi iteration. c The logic for adjusting is contained within the current c subroutine. c If ISHIFT=0, NP is the number of shifts the user needs c to provide via reverse comunication. 0 < NP < NCV-NEV. c NP may be less than NCV-NEV since a leading block of the current c upper Tridiagonal matrix has split off and contains "unwanted" c Ritz values. c Upon termination of the IRA iteration, NP contains the number c of "converged" wanted Ritz values. c c IUPD Integer. (INPUT) c IUPD .EQ. 0: use explicit restart instead implicit update. c IUPD .NE. 0: use implicit update. c c V Double precision N by (NEV+NP) array. (INPUT/OUTPUT) c The Lanczos basis vectors. c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling c program. c c H Double precision (NEV+NP) by 2 array. (OUTPUT) c H is used to store the generated symmetric tridiagonal matrix c The subdiagonal is stored in the first column of H starting c at H(2,1). The main diagonal is stored in the second column c of H starting at H(1,2). If dsaup2 converges store the c B-norm of the final residual vector in H(1,1). c c LDH Integer. (INPUT) c Leading dimension of H exactly as declared in the calling c program. c c RITZ Double precision array of length NEV+NP. (OUTPUT) c RITZ(1:NEV) contains the computed Ritz values of OP. c c BOUNDS Double precision array of length NEV+NP. (OUTPUT) c BOUNDS(1:NEV) contain the error bounds corresponding to RITZ. c c Q Double precision (NEV+NP) by (NEV+NP) array. (WORKSPACE) c Private (replicated) work array used to accumulate the c rotation in the shift application step. c c LDQ Integer. (INPUT) c Leading dimension of Q exactly as declared in the calling c program. c c WORKL Double precision array of length at least 3*(NEV+NP). (INPUT/WORKSPACE) c Private (replicated) array on each PE or array allocated on c the front end. It is used in the computation of the c tridiagonal eigenvalue problem, the calculation and c application of the shifts and convergence checking. c If ISHIFT .EQ. O and IDO .EQ. 3, the first NP locations c of WORKL are used in reverse communication to hold the user c supplied shifts. c c IPNTR Integer array of length 3. (OUTPUT) c Pointer to mark the starting locations in the WORKD for c vectors used by the Lanczos iteration. c ------------------------------------------------------------- c IPNTR(1): pointer to the current operand vector X. c IPNTR(2): pointer to the current result vector Y. c IPNTR(3): pointer to the vector B * X when used in one of c the spectral transformation modes. X is the current c operand. c ------------------------------------------------------------- c c WORKD Double precision work array of length 3*N. (REVERSE COMMUNICATION) c Distributed array to be used in the basic Lanczos iteration c for reverse communication. The user should not use WORKD c as temporary workspace during the iteration !!!!!!!!!! c See Data Distribution Note in dsaupd. c c INFO Integer. (INPUT/OUTPUT) c If INFO .EQ. 0, a randomly initial residual vector is used. c If INFO .NE. 0, RESID contains the initial residual vector, c possibly from a previous run. c Error flag on output. c = 0: Normal return. c = 1: All possible eigenvalues of OP has been found. c NP returns the size of the invariant subspace c spanning the operator OP. c = 2: No shifts could be applied. c = -8: Error return from trid. eigenvalue calculation; c This should never happen. c = -9: Starting vector is zero. c = -9999: Could not build an Lanczos factorization. c Size that was built in returned in NP. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly c Restarted Arnoldi Iteration", Rice University Technical Report c TR95-13, Department of Computational and Applied Mathematics. c 3. B.N. Parlett, "The Symmetric Eigenvalue Problem". Prentice-Hall, c 1980. c 4. B.N. Parlett, B. Nour-Omid, "Towards a Black Box Lanczos Program", c Computer Physics Communications, 53 (1989), pp 169-179. c 5. B. Nour-Omid, B.N. Parlett, T. Ericson, P.S. Jensen, "How to c Implement the Spectral Transformation", Math. Comp., 48 (1987), c pp 663-673. c 6. R.G. Grimes, J.G. Lewis and H.D. Simon, "A Shifted Block Lanczos c Algorithm for Solving Sparse Symmetric Generalized Eigenproblems", c SIAM J. Matr. Anal. Apps., January (1993). c 7. L. Reichel, W.B. Gragg, "Algorithm 686: FORTRAN Subroutines c for Updating the QR decomposition", ACM TOMS, December 1990, c Volume 16 Number 4, pp 369-377. c c\Routines called: c dgetv0 ARPACK initial vector generation routine. c dsaitr ARPACK Lanczos factorization routine. c dsapps ARPACK application of implicit shifts routine. c dsconv ARPACK convergence of Ritz values routine. c dseigt ARPACK compute Ritz values and error bounds routine. c dsgets ARPACK reorder Ritz values and error bounds routine. c dsortr ARPACK sorting routine. c ivout ARPACK utility routine that prints integers. c arscnd ARPACK utility routine for timing. c dvout ARPACK utility routine that prints vectors. c dlamch LAPACK routine that determines machine constants. c dcopy Level 1 BLAS that copies one vector to another. c ddot Level 1 BLAS that computes the scalar product of two vectors. c dnrm2 Level 1 BLAS that computes the norm of a vector. c dscal Level 1 BLAS that scales a vector. c dswap Level 1 BLAS that swaps two vectors. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c 12/15/93: Version ' 2.4' c xx/xx/95: Version ' 2.4'. (R.B. Lehoucq) c c\SCCS Information: @(#) c FILE: saup2.F SID: 2.7 DATE OF SID: 5/19/98 RELEASE: 2 c c\EndLib c c----------------------------------------------------------------------- c subroutine dsaup2 & ( ido, bmat, n, which, nev, np, tol, resid, mode, iupd, & ishift, mxiter, v, ldv, h, ldh, ritz, bounds, & q, ldq, workl, ipntr, workd, info ) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character bmat*1, which*2 integer ido, info, ishift, iupd, ldh, ldq, ldv, mxiter, & n, mode, nev, np Double precision & tol c c %-----------------% c | Array Arguments | c %-----------------% c integer ipntr(3) Double precision & bounds(nev+np), h(ldh,2), q(ldq,nev+np), resid(n), & ritz(nev+np), v(ldv,nev+np), workd(3*n), & workl(3*(nev+np)) c c %------------% c | Parameters | c %------------% c Double precision & one, zero parameter (one = 1.0D+0, zero = 0.0D+0) c c %---------------% c | Local Scalars | c %---------------% c character wprime*2 logical cnorm, getv0, initv, update, ushift integer ierr, iter, j, kplusp, msglvl, nconv, nevbef, nev0, & np0, nptemp, nevd2, nevm2, kp(3) Double precision & rnorm, temp, eps23 save cnorm, getv0, initv, update, ushift, & iter, kplusp, msglvl, nconv, nev0, np0, & rnorm, eps23 c c %----------------------% c | External Subroutines | c %----------------------% c external dcopy, dgetv0, dsaitr, dscal, dsconv, dseigt, dsgets, & dsapps, dsortr, dvout, ivout, arscnd, dswap c c %--------------------% c | External Functions | c %--------------------% c Double precision & ddot, dnrm2, dlamch external ddot, dnrm2, dlamch c c %---------------------% c | Intrinsic Functions | c %---------------------% c intrinsic min c c %-----------------------% c | Executable Statements | c %-----------------------% c if (ido .eq. 0) then c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call arscnd (t0) msglvl = msaup2 c c %---------------------------------% c | Set machine dependent constant. | c %---------------------------------% c eps23 = dlamch('Epsilon-Machine') eps23 = eps23**(2.0D+0/3.0D+0) c c %-------------------------------------% c | nev0 and np0 are integer variables | c | hold the initial values of NEV & NP | c %-------------------------------------% c nev0 = nev np0 = np c c %-------------------------------------% c | kplusp is the bound on the largest | c | Lanczos factorization built. | c | nconv is the current number of | c | "converged" eigenvlues. | c | iter is the counter on the current | c | iteration step. | c %-------------------------------------% c kplusp = nev0 + np0 nconv = 0 iter = 0 c c %--------------------------------------------% c | Set flags for computing the first NEV steps | c | of the Lanczos factorization. | c %--------------------------------------------% c getv0 = .true. update = .false. ushift = .false. cnorm = .false. c if (info .ne. 0) then c c %--------------------------------------------% c | User provides the initial residual vector. | c %--------------------------------------------% c initv = .true. info = 0 else initv = .false. end if end if c c %---------------------------------------------% c | Get a possibly random starting vector and | c | force it into the range of the operator OP. | c %---------------------------------------------% c 10 continue c if (getv0) then call dgetv0 (ido, bmat, 1, initv, n, 1, v, ldv, resid, rnorm, & ipntr, workd, info) c if (ido .ne. 99) go to 9000 c if (rnorm .eq. zero) then c c %-----------------------------------------% c | The initial vector is zero. Error exit. | c %-----------------------------------------% c info = -9 go to 1200 end if getv0 = .false. ido = 0 end if c c %------------------------------------------------------------% c | Back from reverse communication: continue with update step | c %------------------------------------------------------------% c if (update) go to 20 c c %-------------------------------------------% c | Back from computing user specified shifts | c %-------------------------------------------% c if (ushift) go to 50 c c %-------------------------------------% c | Back from computing residual norm | c | at the end of the current iteration | c %-------------------------------------% c if (cnorm) go to 100 c c %----------------------------------------------------------% c | Compute the first NEV steps of the Lanczos factorization | c %----------------------------------------------------------% c call dsaitr (ido, bmat, n, 0, nev0, mode, resid, rnorm, v, ldv, & h, ldh, ipntr, workd, info) c c %---------------------------------------------------% c | ido .ne. 99 implies use of reverse communication | c | to compute operations involving OP and possibly B | c %---------------------------------------------------% c if (ido .ne. 99) go to 9000 c if (info .gt. 0) then c c %-----------------------------------------------------% c | dsaitr was unable to build an Lanczos factorization | c | of length NEV0. INFO is returned with the size of | c | the factorization built. Exit main loop. | c %-----------------------------------------------------% c np = info mxiter = iter info = -9999 go to 1200 end if c c %--------------------------------------------------------------% c | | c | M A I N LANCZOS I T E R A T I O N L O O P | c | Each iteration implicitly restarts the Lanczos | c | factorization in place. | c | | c %--------------------------------------------------------------% c 1000 continue c iter = iter + 1 c if (msglvl .gt. 0) then call ivout (logfil, 1, iter, ndigit, & '_saup2: **** Start of major iteration number ****') end if if (msglvl .gt. 1) then call ivout (logfil, 1, nev, ndigit, & '_saup2: The length of the current Lanczos factorization') call ivout (logfil, 1, np, ndigit, & '_saup2: Extend the Lanczos factorization by') end if c c %------------------------------------------------------------% c | Compute NP additional steps of the Lanczos factorization. | c %------------------------------------------------------------% c ido = 0 20 continue update = .true. c call dsaitr (ido, bmat, n, nev, np, mode, resid, rnorm, v, & ldv, h, ldh, ipntr, workd, info) c c %---------------------------------------------------% c | ido .ne. 99 implies use of reverse communication | c | to compute operations involving OP and possibly B | c %---------------------------------------------------% c if (ido .ne. 99) go to 9000 c if (info .gt. 0) then c c %-----------------------------------------------------% c | dsaitr was unable to build an Lanczos factorization | c | of length NEV0+NP0. INFO is returned with the size | c | of the factorization built. Exit main loop. | c %-----------------------------------------------------% c np = info mxiter = iter info = -9999 go to 1200 end if update = .false. c if (msglvl .gt. 1) then call dvout (logfil, 1, rnorm, ndigit, & '_saup2: Current B-norm of residual for factorization') end if c c %--------------------------------------------------------% c | Compute the eigenvalues and corresponding error bounds | c | of the current symmetric tridiagonal matrix. | c %--------------------------------------------------------% c call dseigt (rnorm, kplusp, h, ldh, ritz, bounds, workl, ierr) c if (ierr .ne. 0) then info = -8 go to 1200 end if c c %----------------------------------------------------% c | Make a copy of eigenvalues and corresponding error | c | bounds obtained from _seigt. | c %----------------------------------------------------% c call dcopy(kplusp, ritz, 1, workl(kplusp+1), 1) call dcopy(kplusp, bounds, 1, workl(2*kplusp+1), 1) c c %---------------------------------------------------% c | Select the wanted Ritz values and their bounds | c | to be used in the convergence test. | c | The selection is based on the requested number of | c | eigenvalues instead of the current NEV and NP to | c | prevent possible misconvergence. | c | * Wanted Ritz values := RITZ(NP+1:NEV+NP) | c | * Shifts := RITZ(1:NP) := WORKL(1:NP) | c %---------------------------------------------------% c nev = nev0 np = np0 call dsgets (ishift, which, nev, np, ritz, bounds, workl) c c %-------------------% c | Convergence test. | c %-------------------% c call dcopy (nev, bounds(np+1), 1, workl(np+1), 1) call dsconv (nev, ritz(np+1), workl(np+1), tol, nconv) c if (msglvl .gt. 2) then kp(1) = nev kp(2) = np kp(3) = nconv call ivout (logfil, 3, kp, ndigit, & '_saup2: NEV, NP, NCONV are') call dvout (logfil, kplusp, ritz, ndigit, & '_saup2: The eigenvalues of H') call dvout (logfil, kplusp, bounds, ndigit, & '_saup2: Ritz estimates of the current NCV Ritz values') end if c c %---------------------------------------------------------% c | Count the number of unwanted Ritz values that have zero | c | Ritz estimates. If any Ritz estimates are equal to zero | c | then a leading block of H of order equal to at least | c | the number of Ritz values with zero Ritz estimates has | c | split off. None of these Ritz values may be removed by | c | shifting. Decrease NP the number of shifts to apply. If | c | no shifts may be applied, then prepare to exit | c %---------------------------------------------------------% c nptemp = np do 30 j=1, nptemp if (bounds(j) .eq. zero) then np = np - 1 nev = nev + 1 end if 30 continue c if ( (nconv .ge. nev0) .or. & (iter .gt. mxiter) .or. & (np .eq. 0) ) then c c %------------------------------------------------% c | Prepare to exit. Put the converged Ritz values | c | and corresponding bounds in RITZ(1:NCONV) and | c | BOUNDS(1:NCONV) respectively. Then sort. Be | c | careful when NCONV > NP since we don't want to | c | swap overlapping locations. | c %------------------------------------------------% c if (which .eq. 'BE') then c c %-----------------------------------------------------% c | Both ends of the spectrum are requested. | c | Sort the eigenvalues into algebraically decreasing | c | order first then swap low end of the spectrum next | c | to high end in appropriate locations. | c | NOTE: when np < floor(nev/2) be careful not to swap | c | overlapping locations. | c %-----------------------------------------------------% c wprime = 'SA' call dsortr (wprime, .true., kplusp, ritz, bounds) nevd2 = nev0 / 2 nevm2 = nev0 - nevd2 if ( nev .gt. 1 ) then call dswap ( min(nevd2,np), ritz(nevm2+1), 1, & ritz( max(kplusp-nevd2+1,kplusp-np+1) ), 1) call dswap ( min(nevd2,np), bounds(nevm2+1), 1, & bounds( max(kplusp-nevd2+1,kplusp-np+1)), 1) end if c else c c %--------------------------------------------------% c | LM, SM, LA, SA case. | c | Sort the eigenvalues of H into the an order that | c | is opposite to WHICH, and apply the resulting | c | order to BOUNDS. The eigenvalues are sorted so | c | that the wanted part are always within the first | c | NEV locations. | c %--------------------------------------------------% c if (which .eq. 'LM') wprime = 'SM' if (which .eq. 'SM') wprime = 'LM' if (which .eq. 'LA') wprime = 'SA' if (which .eq. 'SA') wprime = 'LA' c call dsortr (wprime, .true., kplusp, ritz, bounds) c end if c c %--------------------------------------------------% c | Scale the Ritz estimate of each Ritz value | c | by 1 / max(eps23,magnitude of the Ritz value). | c %--------------------------------------------------% c do 35 j = 1, nev0 temp = max( eps23, abs(ritz(j)) ) bounds(j) = bounds(j)/temp 35 continue c c %----------------------------------------------------% c | Sort the Ritz values according to the scaled Ritz | c | esitmates. This will push all the converged ones | c | towards the front of ritzr, ritzi, bounds | c | (in the case when NCONV < NEV.) | c %----------------------------------------------------% c wprime = 'LA' call dsortr(wprime, .true., nev0, bounds, ritz) c c %----------------------------------------------% c | Scale the Ritz estimate back to its original | c | value. | c %----------------------------------------------% c do 40 j = 1, nev0 temp = max( eps23, abs(ritz(j)) ) bounds(j) = bounds(j)*temp 40 continue c c %--------------------------------------------------% c | Sort the "converged" Ritz values again so that | c | the "threshold" values and their associated Ritz | c | estimates appear at the appropriate position in | c | ritz and bound. | c %--------------------------------------------------% c if (which .eq. 'BE') then c c %------------------------------------------------% c | Sort the "converged" Ritz values in increasing | c | order. The "threshold" values are in the | c | middle. | c %------------------------------------------------% c wprime = 'LA' call dsortr(wprime, .true., nconv, ritz, bounds) c else c c %----------------------------------------------% c | In LM, SM, LA, SA case, sort the "converged" | c | Ritz values according to WHICH so that the | c | "threshold" value appears at the front of | c | ritz. | c %----------------------------------------------% call dsortr(which, .true., nconv, ritz, bounds) c end if c c %------------------------------------------% c | Use h( 1,1 ) as storage to communicate | c | rnorm to _seupd if needed | c %------------------------------------------% c h(1,1) = rnorm c if (msglvl .gt. 1) then call dvout (logfil, kplusp, ritz, ndigit, & '_saup2: Sorted Ritz values.') call dvout (logfil, kplusp, bounds, ndigit, & '_saup2: Sorted ritz estimates.') end if c c %------------------------------------% c | Max iterations have been exceeded. | c %------------------------------------% c if (iter .gt. mxiter .and. nconv .lt. nev) info = 1 c c %---------------------% c | No shifts to apply. | c %---------------------% c if (np .eq. 0 .and. nconv .lt. nev0) info = 2 c np = nconv go to 1100 c else if (nconv .lt. nev .and. ishift .eq. 1) then c c %---------------------------------------------------% c | Do not have all the requested eigenvalues yet. | c | To prevent possible stagnation, adjust the number | c | of Ritz values and the shifts. | c %---------------------------------------------------% c nevbef = nev nev = nev + min (nconv, np/2) if (nev .eq. 1 .and. kplusp .ge. 6) then nev = kplusp / 2 else if (nev .eq. 1 .and. kplusp .gt. 2) then nev = 2 end if np = kplusp - nev c c %---------------------------------------% c | If the size of NEV was just increased | c | resort the eigenvalues. | c %---------------------------------------% c if (nevbef .lt. nev) & call dsgets (ishift, which, nev, np, ritz, bounds, & workl) c end if c if (msglvl .gt. 0) then call ivout (logfil, 1, nconv, ndigit, & '_saup2: no. of "converged" Ritz values at this iter.') if (msglvl .gt. 1) then kp(1) = nev kp(2) = np call ivout (logfil, 2, kp, ndigit, & '_saup2: NEV and NP are') call dvout (logfil, nev, ritz(np+1), ndigit, & '_saup2: "wanted" Ritz values.') call dvout (logfil, nev, bounds(np+1), ndigit, & '_saup2: Ritz estimates of the "wanted" values ') end if end if c if (ishift .eq. 0) then c c %-----------------------------------------------------% c | User specified shifts: reverse communication to | c | compute the shifts. They are returned in the first | c | NP locations of WORKL. | c %-----------------------------------------------------% c ushift = .true. ido = 3 go to 9000 end if c 50 continue c c %------------------------------------% c | Back from reverse communication; | c | User specified shifts are returned | c | in WORKL(1:*NP) | c %------------------------------------% c ushift = .false. c c c %---------------------------------------------------------% c | Move the NP shifts to the first NP locations of RITZ to | c | free up WORKL. This is for the non-exact shift case; | c | in the exact shift case, dsgets already handles this. | c %---------------------------------------------------------% c if (ishift .eq. 0) call dcopy (np, workl, 1, ritz, 1) c if (msglvl .gt. 2) then call ivout (logfil, 1, np, ndigit, & '_saup2: The number of shifts to apply ') call dvout (logfil, np, workl, ndigit, & '_saup2: shifts selected') if (ishift .eq. 1) then call dvout (logfil, np, bounds, ndigit, & '_saup2: corresponding Ritz estimates') end if end if c c %---------------------------------------------------------% c | Apply the NP0 implicit shifts by QR bulge chasing. | c | Each shift is applied to the entire tridiagonal matrix. | c | The first 2*N locations of WORKD are used as workspace. | c | After dsapps is done, we have a Lanczos | c | factorization of length NEV. | c %---------------------------------------------------------% c call dsapps (n, nev, np, ritz, v, ldv, h, ldh, resid, q, ldq, & workd) c c %---------------------------------------------% c | Compute the B-norm of the updated residual. | c | Keep B*RESID in WORKD(1:N) to be used in | c | the first step of the next call to dsaitr. | c %---------------------------------------------% c cnorm = .true. call arscnd (t2) if (bmat .eq. 'G') then nbx = nbx + 1 call dcopy (n, resid, 1, workd(n+1), 1) ipntr(1) = n + 1 ipntr(2) = 1 ido = 2 c c %----------------------------------% c | Exit in order to compute B*RESID | c %----------------------------------% c go to 9000 else if (bmat .eq. 'I') then call dcopy (n, resid, 1, workd, 1) end if c 100 continue c c %----------------------------------% c | Back from reverse communication; | c | WORKD(1:N) := B*RESID | c %----------------------------------% c if (bmat .eq. 'G') then call arscnd (t3) tmvbx = tmvbx + (t3 - t2) end if c if (bmat .eq. 'G') then rnorm = ddot (n, resid, 1, workd, 1) rnorm = sqrt(abs(rnorm)) else if (bmat .eq. 'I') then rnorm = dnrm2(n, resid, 1) end if cnorm = .false. 130 continue c if (msglvl .gt. 2) then call dvout (logfil, 1, rnorm, ndigit, & '_saup2: B-norm of residual for NEV factorization') call dvout (logfil, nev, h(1,2), ndigit, & '_saup2: main diagonal of compressed H matrix') call dvout (logfil, nev-1, h(2,1), ndigit, & '_saup2: subdiagonal of compressed H matrix') end if c go to 1000 c c %---------------------------------------------------------------% c | | c | E N D O F M A I N I T E R A T I O N L O O P | c | | c %---------------------------------------------------------------% c 1100 continue c mxiter = iter nev = nconv c 1200 continue ido = 99 c c %------------% c | Error exit | c %------------% c call arscnd (t1) tsaup2 = t1 - t0 c 9000 continue return c c %---------------% c | End of dsaup2 | c %---------------% c end arpack-0.92.1/SRC/dlaqrb.f0000644000175000017500000004402010776001577012042 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: dlaqrb c c\Description: c Compute the eigenvalues and the Schur decomposition of an upper c Hessenberg submatrix in rows and columns ILO to IHI. Only the c last component of the Schur vectors are computed. c c This is mostly a modification of the LAPACK routine dlahqr. c c\Usage: c call dlaqrb c ( WANTT, N, ILO, IHI, H, LDH, WR, WI, Z, INFO ) c c\Arguments c WANTT Logical variable. (INPUT) c = .TRUE. : the full Schur form T is required; c = .FALSE.: only eigenvalues are required. c c N Integer. (INPUT) c The order of the matrix H. N >= 0. c c ILO Integer. (INPUT) c IHI Integer. (INPUT) c It is assumed that H is already upper quasi-triangular in c rows and columns IHI+1:N, and that H(ILO,ILO-1) = 0 (unless c ILO = 1). SLAQRB works primarily with the Hessenberg c submatrix in rows and columns ILO to IHI, but applies c transformations to all of H if WANTT is .TRUE.. c 1 <= ILO <= max(1,IHI); IHI <= N. c c H Double precision array, dimension (LDH,N). (INPUT/OUTPUT) c On entry, the upper Hessenberg matrix H. c On exit, if WANTT is .TRUE., H is upper quasi-triangular in c rows and columns ILO:IHI, with any 2-by-2 diagonal blocks in c standard form. If WANTT is .FALSE., the contents of H are c unspecified on exit. c c LDH Integer. (INPUT) c The leading dimension of the array H. LDH >= max(1,N). c c WR Double precision array, dimension (N). (OUTPUT) c WI Double precision array, dimension (N). (OUTPUT) c The real and imaginary parts, respectively, of the computed c eigenvalues ILO to IHI are stored in the corresponding c elements of WR and WI. If two eigenvalues are computed as a c complex conjugate pair, they are stored in consecutive c elements of WR and WI, say the i-th and (i+1)th, with c WI(i) > 0 and WI(i+1) < 0. If WANTT is .TRUE., the c eigenvalues are stored in the same order as on the diagonal c of the Schur form returned in H, with WR(i) = H(i,i), and, if c H(i:i+1,i:i+1) is a 2-by-2 diagonal block, c WI(i) = sqrt(H(i+1,i)*H(i,i+1)) and WI(i+1) = -WI(i). c c Z Double precision array, dimension (N). (OUTPUT) c On exit Z contains the last components of the Schur vectors. c c INFO Integer. (OUPUT) c = 0: successful exit c > 0: SLAQRB failed to compute all the eigenvalues ILO to IHI c in a total of 30*(IHI-ILO+1) iterations; if INFO = i, c elements i+1:ihi of WR and WI contain those eigenvalues c which have been successfully computed. c c\Remarks c 1. None. c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx real c c\Routines called: c dlabad LAPACK routine that computes machine constants. c dlamch LAPACK routine that determines machine constants. c dlanhs LAPACK routine that computes various norms of a matrix. c dlanv2 LAPACK routine that computes the Schur factorization of c 2 by 2 nonsymmetric matrix in standard form. c dlarfg LAPACK Householder reflection construction routine. c dcopy Level 1 BLAS that copies one vector to another. c drot Level 1 BLAS that applies a rotation to a 2 by 2 matrix. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c xx/xx/92: Version ' 2.4' c Modified from the LAPACK routine dlahqr so that only the c last component of the Schur vectors are computed. c c\SCCS Information: @(#) c FILE: laqrb.F SID: 2.2 DATE OF SID: 8/27/96 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c----------------------------------------------------------------------- c subroutine dlaqrb ( wantt, n, ilo, ihi, h, ldh, wr, wi, & z, info ) c c %------------------% c | Scalar Arguments | c %------------------% c logical wantt integer ihi, ilo, info, ldh, n c c %-----------------% c | Array Arguments | c %-----------------% c Double precision & h( ldh, * ), wi( * ), wr( * ), z( * ) c c %------------% c | Parameters | c %------------% c Double precision & zero, one, dat1, dat2 parameter (zero = 0.0D+0, one = 1.0D+0, dat1 = 7.5D-1, & dat2 = -4.375D-1) c c %------------------------% c | Local Scalars & Arrays | c %------------------------% c integer i, i1, i2, itn, its, j, k, l, m, nh, nr Double precision & cs, h00, h10, h11, h12, h21, h22, h33, h33s, & h43h34, h44, h44s, ovfl, s, smlnum, sn, sum, & t1, t2, t3, tst1, ulp, unfl, v1, v2, v3 Double precision & v( 3 ), work( 1 ) c c %--------------------% c | External Functions | c %--------------------% c Double precision & dlamch, dlanhs external dlamch, dlanhs c c %----------------------% c | External Subroutines | c %----------------------% c external dcopy, dlabad, dlanv2, dlarfg, drot c c %-----------------------% c | Executable Statements | c %-----------------------% c info = 0 c c %--------------------------% c | Quick return if possible | c %--------------------------% c if( n.eq.0 ) & return if( ilo.eq.ihi ) then wr( ilo ) = h( ilo, ilo ) wi( ilo ) = zero return end if c c %---------------------------------------------% c | Initialize the vector of last components of | c | the Schur vectors for accumulation. | c %---------------------------------------------% c do 5 j = 1, n-1 z(j) = zero 5 continue z(n) = one c nh = ihi - ilo + 1 c c %-------------------------------------------------------------% c | Set machine-dependent constants for the stopping criterion. | c | If norm(H) <= sqrt(OVFL), overflow should not occur. | c %-------------------------------------------------------------% c unfl = dlamch( 'safe minimum' ) ovfl = one / unfl call dlabad( unfl, ovfl ) ulp = dlamch( 'precision' ) smlnum = unfl*( nh / ulp ) c c %---------------------------------------------------------------% c | I1 and I2 are the indices of the first row and last column | c | of H to which transformations must be applied. If eigenvalues | c | only are computed, I1 and I2 are set inside the main loop. | c | Zero out H(J+2,J) = ZERO for J=1:N if WANTT = .TRUE. | c | else H(J+2,J) for J=ILO:IHI-ILO-1 if WANTT = .FALSE. | c %---------------------------------------------------------------% c if( wantt ) then i1 = 1 i2 = n do 8 i=1,i2-2 h(i1+i+1,i) = zero 8 continue else do 9 i=1, ihi-ilo-1 h(ilo+i+1,ilo+i-1) = zero 9 continue end if c c %---------------------------------------------------% c | ITN is the total number of QR iterations allowed. | c %---------------------------------------------------% c itn = 30*nh c c ------------------------------------------------------------------ c The main loop begins here. I is the loop index and decreases from c IHI to ILO in steps of 1 or 2. Each iteration of the loop works c with the active submatrix in rows and columns L to I. c Eigenvalues I+1 to IHI have already converged. Either L = ILO or c H(L,L-1) is negligible so that the matrix splits. c ------------------------------------------------------------------ c i = ihi 10 continue l = ilo if( i.lt.ilo ) & go to 150 c %--------------------------------------------------------------% c | Perform QR iterations on rows and columns ILO to I until a | c | submatrix of order 1 or 2 splits off at the bottom because a | c | subdiagonal element has become negligible. | c %--------------------------------------------------------------% do 130 its = 0, itn c c %----------------------------------------------% c | Look for a single small subdiagonal element. | c %----------------------------------------------% c do 20 k = i, l + 1, -1 tst1 = abs( h( k-1, k-1 ) ) + abs( h( k, k ) ) if( tst1.eq.zero ) & tst1 = dlanhs( '1', i-l+1, h( l, l ), ldh, work ) if( abs( h( k, k-1 ) ).le.max( ulp*tst1, smlnum ) ) & go to 30 20 continue 30 continue l = k if( l.gt.ilo ) then c c %------------------------% c | H(L,L-1) is negligible | c %------------------------% c h( l, l-1 ) = zero end if c c %-------------------------------------------------------------% c | Exit from loop if a submatrix of order 1 or 2 has split off | c %-------------------------------------------------------------% c if( l.ge.i-1 ) & go to 140 c c %---------------------------------------------------------% c | Now the active submatrix is in rows and columns L to I. | c | If eigenvalues only are being computed, only the active | c | submatrix need be transformed. | c %---------------------------------------------------------% c if( .not.wantt ) then i1 = l i2 = i end if c if( its.eq.10 .or. its.eq.20 ) then c c %-------------------% c | Exceptional shift | c %-------------------% c s = abs( h( i, i-1 ) ) + abs( h( i-1, i-2 ) ) h44 = dat1*s h33 = h44 h43h34 = dat2*s*s c else c c %-----------------------------------------% c | Prepare to use Wilkinson's double shift | c %-----------------------------------------% c h44 = h( i, i ) h33 = h( i-1, i-1 ) h43h34 = h( i, i-1 )*h( i-1, i ) end if c c %-----------------------------------------------------% c | Look for two consecutive small subdiagonal elements | c %-----------------------------------------------------% c do 40 m = i - 2, l, -1 c c %---------------------------------------------------------% c | Determine the effect of starting the double-shift QR | c | iteration at row M, and see if this would make H(M,M-1) | c | negligible. | c %---------------------------------------------------------% c h11 = h( m, m ) h22 = h( m+1, m+1 ) h21 = h( m+1, m ) h12 = h( m, m+1 ) h44s = h44 - h11 h33s = h33 - h11 v1 = ( h33s*h44s-h43h34 ) / h21 + h12 v2 = h22 - h11 - h33s - h44s v3 = h( m+2, m+1 ) s = abs( v1 ) + abs( v2 ) + abs( v3 ) v1 = v1 / s v2 = v2 / s v3 = v3 / s v( 1 ) = v1 v( 2 ) = v2 v( 3 ) = v3 if( m.eq.l ) & go to 50 h00 = h( m-1, m-1 ) h10 = h( m, m-1 ) tst1 = abs( v1 )*( abs( h00 )+abs( h11 )+abs( h22 ) ) if( abs( h10 )*( abs( v2 )+abs( v3 ) ).le.ulp*tst1 ) & go to 50 40 continue 50 continue c c %----------------------% c | Double-shift QR step | c %----------------------% c do 120 k = m, i - 1 c c ------------------------------------------------------------ c The first iteration of this loop determines a reflection G c from the vector V and applies it from left and right to H, c thus creating a nonzero bulge below the subdiagonal. c c Each subsequent iteration determines a reflection G to c restore the Hessenberg form in the (K-1)th column, and thus c chases the bulge one step toward the bottom of the active c submatrix. NR is the order of G. c ------------------------------------------------------------ c nr = min( 3, i-k+1 ) if( k.gt.m ) & call dcopy( nr, h( k, k-1 ), 1, v, 1 ) call dlarfg( nr, v( 1 ), v( 2 ), 1, t1 ) if( k.gt.m ) then h( k, k-1 ) = v( 1 ) h( k+1, k-1 ) = zero if( k.lt.i-1 ) & h( k+2, k-1 ) = zero else if( m.gt.l ) then h( k, k-1 ) = -h( k, k-1 ) end if v2 = v( 2 ) t2 = t1*v2 if( nr.eq.3 ) then v3 = v( 3 ) t3 = t1*v3 c c %------------------------------------------------% c | Apply G from the left to transform the rows of | c | the matrix in columns K to I2. | c %------------------------------------------------% c do 60 j = k, i2 sum = h( k, j ) + v2*h( k+1, j ) + v3*h( k+2, j ) h( k, j ) = h( k, j ) - sum*t1 h( k+1, j ) = h( k+1, j ) - sum*t2 h( k+2, j ) = h( k+2, j ) - sum*t3 60 continue c c %----------------------------------------------------% c | Apply G from the right to transform the columns of | c | the matrix in rows I1 to min(K+3,I). | c %----------------------------------------------------% c do 70 j = i1, min( k+3, i ) sum = h( j, k ) + v2*h( j, k+1 ) + v3*h( j, k+2 ) h( j, k ) = h( j, k ) - sum*t1 h( j, k+1 ) = h( j, k+1 ) - sum*t2 h( j, k+2 ) = h( j, k+2 ) - sum*t3 70 continue c c %----------------------------------% c | Accumulate transformations for Z | c %----------------------------------% c sum = z( k ) + v2*z( k+1 ) + v3*z( k+2 ) z( k ) = z( k ) - sum*t1 z( k+1 ) = z( k+1 ) - sum*t2 z( k+2 ) = z( k+2 ) - sum*t3 else if( nr.eq.2 ) then c c %------------------------------------------------% c | Apply G from the left to transform the rows of | c | the matrix in columns K to I2. | c %------------------------------------------------% c do 90 j = k, i2 sum = h( k, j ) + v2*h( k+1, j ) h( k, j ) = h( k, j ) - sum*t1 h( k+1, j ) = h( k+1, j ) - sum*t2 90 continue c c %----------------------------------------------------% c | Apply G from the right to transform the columns of | c | the matrix in rows I1 to min(K+3,I). | c %----------------------------------------------------% c do 100 j = i1, i sum = h( j, k ) + v2*h( j, k+1 ) h( j, k ) = h( j, k ) - sum*t1 h( j, k+1 ) = h( j, k+1 ) - sum*t2 100 continue c c %----------------------------------% c | Accumulate transformations for Z | c %----------------------------------% c sum = z( k ) + v2*z( k+1 ) z( k ) = z( k ) - sum*t1 z( k+1 ) = z( k+1 ) - sum*t2 end if 120 continue 130 continue c c %-------------------------------------------------------% c | Failure to converge in remaining number of iterations | c %-------------------------------------------------------% c info = i return 140 continue if( l.eq.i ) then c c %------------------------------------------------------% c | H(I,I-1) is negligible: one eigenvalue has converged | c %------------------------------------------------------% c wr( i ) = h( i, i ) wi( i ) = zero else if( l.eq.i-1 ) then c c %--------------------------------------------------------% c | H(I-1,I-2) is negligible; | c | a pair of eigenvalues have converged. | c | | c | Transform the 2-by-2 submatrix to standard Schur form, | c | and compute and store the eigenvalues. | c %--------------------------------------------------------% c call dlanv2( h( i-1, i-1 ), h( i-1, i ), h( i, i-1 ), & h( i, i ), wr( i-1 ), wi( i-1 ), wr( i ), wi( i ), & cs, sn ) if( wantt ) then c c %-----------------------------------------------------% c | Apply the transformation to the rest of H and to Z, | c | as required. | c %-----------------------------------------------------% c if( i2.gt.i ) & call drot( i2-i, h( i-1, i+1 ), ldh, h( i, i+1 ), ldh, & cs, sn ) call drot( i-i1-1, h( i1, i-1 ), 1, h( i1, i ), 1, cs, sn ) sum = cs*z( i-1 ) + sn*z( i ) z( i ) = cs*z( i ) - sn*z( i-1 ) z( i-1 ) = sum end if end if c c %---------------------------------------------------------% c | Decrement number of remaining iterations, and return to | c | start of the main loop with new value of I. | c %---------------------------------------------------------% c itn = itn - its i = l - 1 go to 10 150 continue return c c %---------------% c | End of dlaqrb | c %---------------% c end arpack-0.92.1/SRC/snaupd.f0000644000175000017500000007161710776001577012103 00000000000000c\BeginDoc c c\Name: snaupd c c\Description: c Reverse communication interface for the Implicitly Restarted Arnoldi c iteration. This subroutine computes approximations to a few eigenpairs c of a linear operator "OP" with respect to a semi-inner product defined by c a symmetric positive semi-definite real matrix B. B may be the identity c matrix. NOTE: If the linear operator "OP" is real and symmetric c with respect to the real positive semi-definite symmetric matrix B, c i.e. B*OP = (OP`)*B, then subroutine ssaupd should be used instead. c c The computed approximate eigenvalues are called Ritz values and c the corresponding approximate eigenvectors are called Ritz vectors. c c snaupd is usually called iteratively to solve one of the c following problems: c c Mode 1: A*x = lambda*x. c ===> OP = A and B = I. c c Mode 2: A*x = lambda*M*x, M symmetric positive definite c ===> OP = inv[M]*A and B = M. c ===> (If M can be factored see remark 3 below) c c Mode 3: A*x = lambda*M*x, M symmetric semi-definite c ===> OP = Real_Part{ inv[A - sigma*M]*M } and B = M. c ===> shift-and-invert mode (in real arithmetic) c If OP*x = amu*x, then c amu = 1/2 * [ 1/(lambda-sigma) + 1/(lambda-conjg(sigma)) ]. c Note: If sigma is real, i.e. imaginary part of sigma is zero; c Real_Part{ inv[A - sigma*M]*M } == inv[A - sigma*M]*M c amu == 1/(lambda-sigma). c c Mode 4: A*x = lambda*M*x, M symmetric semi-definite c ===> OP = Imaginary_Part{ inv[A - sigma*M]*M } and B = M. c ===> shift-and-invert mode (in real arithmetic) c If OP*x = amu*x, then c amu = 1/2i * [ 1/(lambda-sigma) - 1/(lambda-conjg(sigma)) ]. c c Both mode 3 and 4 give the same enhancement to eigenvalues close to c the (complex) shift sigma. However, as lambda goes to infinity, c the operator OP in mode 4 dampens the eigenvalues more strongly than c does OP defined in mode 3. c c NOTE: The action of w <- inv[A - sigma*M]*v or w <- inv[M]*v c should be accomplished either by a direct method c using a sparse matrix factorization and solving c c [A - sigma*M]*w = v or M*w = v, c c or through an iterative method for solving these c systems. If an iterative method is used, the c convergence test must be more stringent than c the accuracy requirements for the eigenvalue c approximations. c c\Usage: c call snaupd c ( IDO, BMAT, N, WHICH, NEV, TOL, RESID, NCV, V, LDV, IPARAM, c IPNTR, WORKD, WORKL, LWORKL, INFO ) c c\Arguments c IDO Integer. (INPUT/OUTPUT) c Reverse communication flag. IDO must be zero on the first c call to snaupd. IDO will be set internally to c indicate the type of operation to be performed. Control is c then given back to the calling routine which has the c responsibility to carry out the requested operation and call c snaupd with the result. The operand is given in c WORKD(IPNTR(1)), the result must be put in WORKD(IPNTR(2)). c ------------------------------------------------------------- c IDO = 0: first call to the reverse communication interface c IDO = -1: compute Y = OP * X where c IPNTR(1) is the pointer into WORKD for X, c IPNTR(2) is the pointer into WORKD for Y. c This is for the initialization phase to force the c starting vector into the range of OP. c IDO = 1: compute Y = OP * X where c IPNTR(1) is the pointer into WORKD for X, c IPNTR(2) is the pointer into WORKD for Y. c In mode 3 and 4, the vector B * X is already c available in WORKD(ipntr(3)). It does not c need to be recomputed in forming OP * X. c IDO = 2: compute Y = B * X where c IPNTR(1) is the pointer into WORKD for X, c IPNTR(2) is the pointer into WORKD for Y. c IDO = 3: compute the IPARAM(8) real and imaginary parts c of the shifts where INPTR(14) is the pointer c into WORKL for placing the shifts. See Remark c 5 below. c IDO = 99: done c ------------------------------------------------------------- c c BMAT Character*1. (INPUT) c BMAT specifies the type of the matrix B that defines the c semi-inner product for the operator OP. c BMAT = 'I' -> standard eigenvalue problem A*x = lambda*x c BMAT = 'G' -> generalized eigenvalue problem A*x = lambda*B*x c c N Integer. (INPUT) c Dimension of the eigenproblem. c c WHICH Character*2. (INPUT) c 'LM' -> want the NEV eigenvalues of largest magnitude. c 'SM' -> want the NEV eigenvalues of smallest magnitude. c 'LR' -> want the NEV eigenvalues of largest real part. c 'SR' -> want the NEV eigenvalues of smallest real part. c 'LI' -> want the NEV eigenvalues of largest imaginary part. c 'SI' -> want the NEV eigenvalues of smallest imaginary part. c c NEV Integer. (INPUT/OUTPUT) c Number of eigenvalues of OP to be computed. 0 < NEV < N-1. c c TOL Real scalar. (INPUT) c Stopping criterion: the relative accuracy of the Ritz value c is considered acceptable if BOUNDS(I) .LE. TOL*ABS(RITZ(I)) c where ABS(RITZ(I)) is the magnitude when RITZ(I) is complex. c DEFAULT = SLAMCH('EPS') (machine precision as computed c by the LAPACK auxiliary subroutine SLAMCH). c c RESID Real array of length N. (INPUT/OUTPUT) c On INPUT: c If INFO .EQ. 0, a random initial residual vector is used. c If INFO .NE. 0, RESID contains the initial residual vector, c possibly from a previous run. c On OUTPUT: c RESID contains the final residual vector. c c NCV Integer. (INPUT) c Number of columns of the matrix V. NCV must satisfy the two c inequalities 2 <= NCV-NEV and NCV <= N. c This will indicate how many Arnoldi vectors are generated c at each iteration. After the startup phase in which NEV c Arnoldi vectors are generated, the algorithm generates c approximately NCV-NEV Arnoldi vectors at each subsequent update c iteration. Most of the cost in generating each Arnoldi vector is c in the matrix-vector operation OP*x. c NOTE: 2 <= NCV-NEV in order that complex conjugate pairs of Ritz c values are kept together. (See remark 4 below) c c V Real array N by NCV. (OUTPUT) c Contains the final set of Arnoldi basis vectors. c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling program. c c IPARAM Integer array of length 11. (INPUT/OUTPUT) c IPARAM(1) = ISHIFT: method for selecting the implicit shifts. c The shifts selected at each iteration are used to restart c the Arnoldi iteration in an implicit fashion. c ------------------------------------------------------------- c ISHIFT = 0: the shifts are provided by the user via c reverse communication. The real and imaginary c parts of the NCV eigenvalues of the Hessenberg c matrix H are returned in the part of the WORKL c array corresponding to RITZR and RITZI. See remark c 5 below. c ISHIFT = 1: exact shifts with respect to the current c Hessenberg matrix H. This is equivalent to c restarting the iteration with a starting vector c that is a linear combination of approximate Schur c vectors associated with the "wanted" Ritz values. c ------------------------------------------------------------- c c IPARAM(2) = No longer referenced. c c IPARAM(3) = MXITER c On INPUT: maximum number of Arnoldi update iterations allowed. c On OUTPUT: actual number of Arnoldi update iterations taken. c c IPARAM(4) = NB: blocksize to be used in the recurrence. c The code currently works only for NB = 1. c c IPARAM(5) = NCONV: number of "converged" Ritz values. c This represents the number of Ritz values that satisfy c the convergence criterion. c c IPARAM(6) = IUPD c No longer referenced. Implicit restarting is ALWAYS used. c c IPARAM(7) = MODE c On INPUT determines what type of eigenproblem is being solved. c Must be 1,2,3,4; See under \Description of snaupd for the c four modes available. c c IPARAM(8) = NP c When ido = 3 and the user provides shifts through reverse c communication (IPARAM(1)=0), snaupd returns NP, the number c of shifts the user is to provide. 0 < NP <=NCV-NEV. See Remark c 5 below. c c IPARAM(9) = NUMOP, IPARAM(10) = NUMOPB, IPARAM(11) = NUMREO, c OUTPUT: NUMOP = total number of OP*x operations, c NUMOPB = total number of B*x operations if BMAT='G', c NUMREO = total number of steps of re-orthogonalization. c c IPNTR Integer array of length 14. (OUTPUT) c Pointer to mark the starting locations in the WORKD and WORKL c arrays for matrices/vectors used by the Arnoldi iteration. c ------------------------------------------------------------- c IPNTR(1): pointer to the current operand vector X in WORKD. c IPNTR(2): pointer to the current result vector Y in WORKD. c IPNTR(3): pointer to the vector B * X in WORKD when used in c the shift-and-invert mode. c IPNTR(4): pointer to the next available location in WORKL c that is untouched by the program. c IPNTR(5): pointer to the NCV by NCV upper Hessenberg matrix c H in WORKL. c IPNTR(6): pointer to the real part of the ritz value array c RITZR in WORKL. c IPNTR(7): pointer to the imaginary part of the ritz value array c RITZI in WORKL. c IPNTR(8): pointer to the Ritz estimates in array WORKL associated c with the Ritz values located in RITZR and RITZI in WORKL. c c IPNTR(14): pointer to the NP shifts in WORKL. See Remark 5 below. c c Note: IPNTR(9:13) is only referenced by sneupd. See Remark 2 below. c c IPNTR(9): pointer to the real part of the NCV RITZ values of the c original system. c IPNTR(10): pointer to the imaginary part of the NCV RITZ values of c the original system. c IPNTR(11): pointer to the NCV corresponding error bounds. c IPNTR(12): pointer to the NCV by NCV upper quasi-triangular c Schur matrix for H. c IPNTR(13): pointer to the NCV by NCV matrix of eigenvectors c of the upper Hessenberg matrix H. Only referenced by c sneupd if RVEC = .TRUE. See Remark 2 below. c ------------------------------------------------------------- c c WORKD Real work array of length 3*N. (REVERSE COMMUNICATION) c Distributed array to be used in the basic Arnoldi iteration c for reverse communication. The user should not use WORKD c as temporary workspace during the iteration. Upon termination c WORKD(1:N) contains B*RESID(1:N). If an invariant subspace c associated with the converged Ritz values is desired, see remark c 2 below, subroutine sneupd uses this output. c See Data Distribution Note below. c c WORKL Real work array of length LWORKL. (OUTPUT/WORKSPACE) c Private (replicated) array on each PE or array allocated on c the front end. See Data Distribution Note below. c c LWORKL Integer. (INPUT) c LWORKL must be at least 3*NCV**2 + 6*NCV. c c INFO Integer. (INPUT/OUTPUT) c If INFO .EQ. 0, a randomly initial residual vector is used. c If INFO .NE. 0, RESID contains the initial residual vector, c possibly from a previous run. c Error flag on output. c = 0: Normal exit. c = 1: Maximum number of iterations taken. c All possible eigenvalues of OP has been found. IPARAM(5) c returns the number of wanted converged Ritz values. c = 2: No longer an informational error. Deprecated starting c with release 2 of ARPACK. c = 3: No shifts could be applied during a cycle of the c Implicitly restarted Arnoldi iteration. One possibility c is to increase the size of NCV relative to NEV. c See remark 4 below. c = -1: N must be positive. c = -2: NEV must be positive. c = -3: NCV-NEV >= 2 and less than or equal to N. c = -4: The maximum number of Arnoldi update iteration c must be greater than zero. c = -5: WHICH must be one of 'LM', 'SM', 'LR', 'SR', 'LI', 'SI' c = -6: BMAT must be one of 'I' or 'G'. c = -7: Length of private work array is not sufficient. c = -8: Error return from LAPACK eigenvalue calculation; c = -9: Starting vector is zero. c = -10: IPARAM(7) must be 1,2,3,4. c = -11: IPARAM(7) = 1 and BMAT = 'G' are incompatable. c = -12: IPARAM(1) must be equal to 0 or 1. c = -9999: Could not build an Arnoldi factorization. c IPARAM(5) returns the size of the current Arnoldi c factorization. c c\Remarks c 1. The computed Ritz values are approximate eigenvalues of OP. The c selection of WHICH should be made with this in mind when c Mode = 3 and 4. After convergence, approximate eigenvalues of the c original problem may be obtained with the ARPACK subroutine sneupd. c c 2. If a basis for the invariant subspace corresponding to the converged Ritz c values is needed, the user must call sneupd immediately following c completion of snaupd. This is new starting with release 2 of ARPACK. c c 3. If M can be factored into a Cholesky factorization M = LL` c then Mode = 2 should not be selected. Instead one should use c Mode = 1 with OP = inv(L)*A*inv(L`). Appropriate triangular c linear systems should be solved with L and L` rather c than computing inverses. After convergence, an approximate c eigenvector z of the original problem is recovered by solving c L`z = x where x is a Ritz vector of OP. c c 4. At present there is no a-priori analysis to guide the selection c of NCV relative to NEV. The only formal requrement is that NCV > NEV + 2. c However, it is recommended that NCV .ge. 2*NEV+1. If many problems of c the same type are to be solved, one should experiment with increasing c NCV while keeping NEV fixed for a given test problem. This will c usually decrease the required number of OP*x operations but it c also increases the work and storage required to maintain the orthogonal c basis vectors. The optimal "cross-over" with respect to CPU time c is problem dependent and must be determined empirically. c See Chapter 8 of Reference 2 for further information. c c 5. When IPARAM(1) = 0, and IDO = 3, the user needs to provide the c NP = IPARAM(8) real and imaginary parts of the shifts in locations c real part imaginary part c ----------------------- -------------- c 1 WORKL(IPNTR(14)) WORKL(IPNTR(14)+NP) c 2 WORKL(IPNTR(14)+1) WORKL(IPNTR(14)+NP+1) c . . c . . c . . c NP WORKL(IPNTR(14)+NP-1) WORKL(IPNTR(14)+2*NP-1). c c Only complex conjugate pairs of shifts may be applied and the pairs c must be placed in consecutive locations. The real part of the c eigenvalues of the current upper Hessenberg matrix are located in c WORKL(IPNTR(6)) through WORKL(IPNTR(6)+NCV-1) and the imaginary part c in WORKL(IPNTR(7)) through WORKL(IPNTR(7)+NCV-1). They are ordered c according to the order defined by WHICH. The complex conjugate c pairs are kept together and the associated Ritz estimates are located in c WORKL(IPNTR(8)), WORKL(IPNTR(8)+1), ... , WORKL(IPNTR(8)+NCV-1). c c----------------------------------------------------------------------- c c\Data Distribution Note: c c Fortran-D syntax: c ================ c Real resid(n), v(ldv,ncv), workd(3*n), workl(lworkl) c decompose d1(n), d2(n,ncv) c align resid(i) with d1(i) c align v(i,j) with d2(i,j) c align workd(i) with d1(i) range (1:n) c align workd(i) with d1(i-n) range (n+1:2*n) c align workd(i) with d1(i-2*n) range (2*n+1:3*n) c distribute d1(block), d2(block,:) c replicated workl(lworkl) c c Cray MPP syntax: c =============== c Real resid(n), v(ldv,ncv), workd(n,3), workl(lworkl) c shared resid(block), v(block,:), workd(block,:) c replicated workl(lworkl) c c CM2/CM5 syntax: c ============== c c----------------------------------------------------------------------- c c include 'ex-nonsym.doc' c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx real c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly c Restarted Arnoldi Iteration", Rice University Technical Report c TR95-13, Department of Computational and Applied Mathematics. c 3. B.N. Parlett & Y. Saad, "Complex Shift and Invert Strategies for c Real Matrices", Linear Algebra and its Applications, vol 88/89, c pp 575-595, (1987). c c\Routines called: c snaup2 ARPACK routine that implements the Implicitly Restarted c Arnoldi Iteration. c ivout ARPACK utility routine that prints integers. c arscnd ARPACK utility routine for timing. c svout ARPACK utility routine that prints vectors. c slamch LAPACK routine that determines machine constants. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c 12/16/93: Version '1.1' c c\SCCS Information: @(#) c FILE: naupd.F SID: 2.10 DATE OF SID: 08/23/02 RELEASE: 2 c c\Remarks c c\EndLib c c----------------------------------------------------------------------- c subroutine snaupd & ( ido, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam, & ipntr, workd, workl, lworkl, info ) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character bmat*1, which*2 integer ido, info, ldv, lworkl, n, ncv, nev Real & tol c c %-----------------% c | Array Arguments | c %-----------------% c integer iparam(11), ipntr(14) Real & resid(n), v(ldv,ncv), workd(3*n), workl(lworkl) c c %------------% c | Parameters | c %------------% c Real & one, zero parameter (one = 1.0E+0, zero = 0.0E+0) c c %---------------% c | Local Scalars | c %---------------% c integer bounds, ierr, ih, iq, ishift, iupd, iw, & ldh, ldq, levec, mode, msglvl, mxiter, nb, & nev0, next, np, ritzi, ritzr, j save bounds, ih, iq, ishift, iupd, iw, ldh, ldq, & levec, mode, msglvl, mxiter, nb, nev0, next, & np, ritzi, ritzr c c %----------------------% c | External Subroutines | c %----------------------% c external snaup2, svout, ivout, arscnd, sstatn c c %--------------------% c | External Functions | c %--------------------% c Real & slamch external slamch c c %-----------------------% c | Executable Statements | c %-----------------------% c if (ido .eq. 0) then c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call sstatn call arscnd (t0) msglvl = mnaupd c c %----------------% c | Error checking | c %----------------% c ierr = 0 ishift = iparam(1) c levec = iparam(2) mxiter = iparam(3) c nb = iparam(4) nb = 1 c c %--------------------------------------------% c | Revision 2 performs only implicit restart. | c %--------------------------------------------% c iupd = 1 mode = iparam(7) c if (n .le. 0) then ierr = -1 else if (nev .le. 0) then ierr = -2 else if (ncv .le. nev+1 .or. ncv .gt. n) then ierr = -3 else if (mxiter .le. 0) then ierr = 4 else if (which .ne. 'LM' .and. & which .ne. 'SM' .and. & which .ne. 'LR' .and. & which .ne. 'SR' .and. & which .ne. 'LI' .and. & which .ne. 'SI') then ierr = -5 else if (bmat .ne. 'I' .and. bmat .ne. 'G') then ierr = -6 else if (lworkl .lt. 3*ncv**2 + 6*ncv) then ierr = -7 else if (mode .lt. 1 .or. mode .gt. 4) then ierr = -10 else if (mode .eq. 1 .and. bmat .eq. 'G') then ierr = -11 else if (ishift .lt. 0 .or. ishift .gt. 1) then ierr = -12 end if c c %------------% c | Error Exit | c %------------% c if (ierr .ne. 0) then info = ierr ido = 99 go to 9000 end if c c %------------------------% c | Set default parameters | c %------------------------% c if (nb .le. 0) nb = 1 if (tol .le. zero) tol = slamch('EpsMach') c c %----------------------------------------------% c | NP is the number of additional steps to | c | extend the length NEV Lanczos factorization. | c | NEV0 is the local variable designating the | c | size of the invariant subspace desired. | c %----------------------------------------------% c np = ncv - nev nev0 = nev c c %-----------------------------% c | Zero out internal workspace | c %-----------------------------% c do 10 j = 1, 3*ncv**2 + 6*ncv workl(j) = zero 10 continue c c %-------------------------------------------------------------% c | Pointer into WORKL for address of H, RITZ, BOUNDS, Q | c | etc... and the remaining workspace. | c | Also update pointer to be used on output. | c | Memory is laid out as follows: | c | workl(1:ncv*ncv) := generated Hessenberg matrix | c | workl(ncv*ncv+1:ncv*ncv+2*ncv) := real and imaginary | c | parts of ritz values | c | workl(ncv*ncv+2*ncv+1:ncv*ncv+3*ncv) := error bounds | c | workl(ncv*ncv+3*ncv+1:2*ncv*ncv+3*ncv) := rotation matrix Q | c | workl(2*ncv*ncv+3*ncv+1:3*ncv*ncv+6*ncv) := workspace | c | The final workspace is needed by subroutine sneigh called | c | by snaup2. Subroutine sneigh calls LAPACK routines for | c | calculating eigenvalues and the last row of the eigenvector | c | matrix. | c %-------------------------------------------------------------% c ldh = ncv ldq = ncv ih = 1 ritzr = ih + ldh*ncv ritzi = ritzr + ncv bounds = ritzi + ncv iq = bounds + ncv iw = iq + ldq*ncv next = iw + ncv**2 + 3*ncv c ipntr(4) = next ipntr(5) = ih ipntr(6) = ritzr ipntr(7) = ritzi ipntr(8) = bounds ipntr(14) = iw c end if c c %-------------------------------------------------------% c | Carry out the Implicitly restarted Arnoldi Iteration. | c %-------------------------------------------------------% c call snaup2 & ( ido, bmat, n, which, nev0, np, tol, resid, mode, iupd, & ishift, mxiter, v, ldv, workl(ih), ldh, workl(ritzr), & workl(ritzi), workl(bounds), workl(iq), ldq, workl(iw), & ipntr, workd, info ) c c %--------------------------------------------------% c | ido .ne. 99 implies use of reverse communication | c | to compute operations involving OP or shifts. | c %--------------------------------------------------% c if (ido .eq. 3) iparam(8) = np if (ido .ne. 99) go to 9000 c iparam(3) = mxiter iparam(5) = np iparam(9) = nopx iparam(10) = nbx iparam(11) = nrorth c c %------------------------------------% c | Exit if there was an informational | c | error within snaup2. | c %------------------------------------% c if (info .lt. 0) go to 9000 if (info .eq. 2) info = 3 c if (msglvl .gt. 0) then call ivout (logfil, 1, mxiter, ndigit, & '_naupd: Number of update iterations taken') call ivout (logfil, 1, np, ndigit, & '_naupd: Number of wanted "converged" Ritz values') call svout (logfil, np, workl(ritzr), ndigit, & '_naupd: Real part of the final Ritz values') call svout (logfil, np, workl(ritzi), ndigit, & '_naupd: Imaginary part of the final Ritz values') call svout (logfil, np, workl(bounds), ndigit, & '_naupd: Associated Ritz estimates') end if c call arscnd (t1) tnaupd = t1 - t0 c if (msglvl .gt. 0) then c c %--------------------------------------------------------% c | Version Number & Version Date are defined in version.h | c %--------------------------------------------------------% c write (6,1000) write (6,1100) mxiter, nopx, nbx, nrorth, nitref, nrstrt, & tmvopx, tmvbx, tnaupd, tnaup2, tnaitr, titref, & tgetv0, tneigh, tngets, tnapps, tnconv, trvec 1000 format (//, & 5x, '=============================================',/ & 5x, '= Nonsymmetric implicit Arnoldi update code =',/ & 5x, '= Version Number: ', ' 2.4', 21x, ' =',/ & 5x, '= Version Date: ', ' 07/31/96', 16x, ' =',/ & 5x, '=============================================',/ & 5x, '= Summary of timing statistics =',/ & 5x, '=============================================',//) 1100 format ( & 5x, 'Total number update iterations = ', i5,/ & 5x, 'Total number of OP*x operations = ', i5,/ & 5x, 'Total number of B*x operations = ', i5,/ & 5x, 'Total number of reorthogonalization steps = ', i5,/ & 5x, 'Total number of iterative refinement steps = ', i5,/ & 5x, 'Total number of restart steps = ', i5,/ & 5x, 'Total time in user OP*x operation = ', f12.6,/ & 5x, 'Total time in user B*x operation = ', f12.6,/ & 5x, 'Total time in Arnoldi update routine = ', f12.6,/ & 5x, 'Total time in naup2 routine = ', f12.6,/ & 5x, 'Total time in basic Arnoldi iteration loop = ', f12.6,/ & 5x, 'Total time in reorthogonalization phase = ', f12.6,/ & 5x, 'Total time in (re)start vector generation = ', f12.6,/ & 5x, 'Total time in Hessenberg eig. subproblem = ', f12.6,/ & 5x, 'Total time in getting the shifts = ', f12.6,/ & 5x, 'Total time in applying the shifts = ', f12.6,/ & 5x, 'Total time in convergence testing = ', f12.6,/ & 5x, 'Total time in computing final Ritz vectors = ', f12.6/) end if c 9000 continue c return c c %---------------% c | End of snaupd | c %---------------% c end arpack-0.92.1/SRC/zneigh.f0000644000175000017500000002007010776001577012060 00000000000000c\BeginDoc c c\Name: zneigh c c\Description: c Compute the eigenvalues of the current upper Hessenberg matrix c and the corresponding Ritz estimates given the current residual norm. c c\Usage: c call zneigh c ( RNORM, N, H, LDH, RITZ, BOUNDS, Q, LDQ, WORKL, RWORK, IERR ) c c\Arguments c RNORM Double precision scalar. (INPUT) c Residual norm corresponding to the current upper Hessenberg c matrix H. c c N Integer. (INPUT) c Size of the matrix H. c c H Complex*16 N by N array. (INPUT) c H contains the current upper Hessenberg matrix. c c LDH Integer. (INPUT) c Leading dimension of H exactly as declared in the calling c program. c c RITZ Complex*16 array of length N. (OUTPUT) c On output, RITZ(1:N) contains the eigenvalues of H. c c BOUNDS Complex*16 array of length N. (OUTPUT) c On output, BOUNDS contains the Ritz estimates associated with c the eigenvalues held in RITZ. This is equal to RNORM c times the last components of the eigenvectors corresponding c to the eigenvalues in RITZ. c c Q Complex*16 N by N array. (WORKSPACE) c Workspace needed to store the eigenvectors of H. c c LDQ Integer. (INPUT) c Leading dimension of Q exactly as declared in the calling c program. c c WORKL Complex*16 work array of length N**2 + 3*N. (WORKSPACE) c Private (replicated) array on each PE or array allocated on c the front end. This is needed to keep the full Schur form c of H and also in the calculation of the eigenvectors of H. c c RWORK Double precision work array of length N (WORKSPACE) c Private (replicated) array on each PE or array allocated on c the front end. c c IERR Integer. (OUTPUT) c Error exit flag from zlahqr or ztrevc. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx Complex*16 c c\Routines called: c ivout ARPACK utility routine that prints integers. c arscnd ARPACK utility routine for timing. c zmout ARPACK utility routine that prints matrices c zvout ARPACK utility routine that prints vectors. c dvout ARPACK utility routine that prints vectors. c zlacpy LAPACK matrix copy routine. c zlahqr LAPACK routine to compute the Schur form of an c upper Hessenberg matrix. c zlaset LAPACK matrix initialization routine. c ztrevc LAPACK routine to compute the eigenvectors of a matrix c in upper triangular form c zcopy Level 1 BLAS that copies one vector to another. c zdscal Level 1 BLAS that scales a complex vector by a real number. c dznrm2 Level 1 BLAS that computes the norm of a vector. c c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: neigh.F SID: 2.2 DATE OF SID: 4/20/96 RELEASE: 2 c c\Remarks c None c c\EndLib c c----------------------------------------------------------------------- c subroutine zneigh (rnorm, n, h, ldh, ritz, bounds, & q, ldq, workl, rwork, ierr) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c integer ierr, n, ldh, ldq Double precision & rnorm c c %-----------------% c | Array Arguments | c %-----------------% c Complex*16 & bounds(n), h(ldh,n), q(ldq,n), ritz(n), & workl(n*(n+3)) Double precision & rwork(n) c c %------------% c | Parameters | c %------------% c Complex*16 & one, zero Double precision & rone parameter (one = (1.0D+0, 0.0D+0), zero = (0.0D+0, 0.0D+0), & rone = 1.0D+0) c c %------------------------% c | Local Scalars & Arrays | c %------------------------% c logical select(1) integer j, msglvl Complex*16 & vl(1) Double precision & temp c c %----------------------% c | External Subroutines | c %----------------------% c external zlacpy, zlahqr, ztrevc, zcopy, & zdscal, zmout, zvout, arscnd c c %--------------------% c | External Functions | c %--------------------% c Double precision & dznrm2 external dznrm2 c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call arscnd (t0) msglvl = mceigh c if (msglvl .gt. 2) then call zmout (logfil, n, n, h, ldh, ndigit, & '_neigh: Entering upper Hessenberg matrix H ') end if c c %----------------------------------------------------------% c | 1. Compute the eigenvalues, the last components of the | c | corresponding Schur vectors and the full Schur form T | c | of the current upper Hessenberg matrix H. | c | zlahqr returns the full Schur form of H | c | in WORKL(1:N**2), and the Schur vectors in q. | c %----------------------------------------------------------% c call zlacpy ('All', n, n, h, ldh, workl, n) call zlaset ('All', n, n, zero, one, q, ldq) call zlahqr (.true., .true., n, 1, n, workl, ldh, ritz, & 1, n, q, ldq, ierr) if (ierr .ne. 0) go to 9000 c call zcopy (n, q(n-1,1), ldq, bounds, 1) if (msglvl .gt. 1) then call zvout (logfil, n, bounds, ndigit, & '_neigh: last row of the Schur matrix for H') end if c c %----------------------------------------------------------% c | 2. Compute the eigenvectors of the full Schur form T and | c | apply the Schur vectors to get the corresponding | c | eigenvectors. | c %----------------------------------------------------------% c call ztrevc ('Right', 'Back', select, n, workl, n, vl, n, q, & ldq, n, n, workl(n*n+1), rwork, ierr) c if (ierr .ne. 0) go to 9000 c c %------------------------------------------------% c | Scale the returning eigenvectors so that their | c | Euclidean norms are all one. LAPACK subroutine | c | ztrevc returns each eigenvector normalized so | c | that the element of largest magnitude has | c | magnitude 1; here the magnitude of a complex | c | number (x,y) is taken to be |x| + |y|. | c %------------------------------------------------% c do 10 j=1, n temp = dznrm2( n, q(1,j), 1 ) call zdscal ( n, rone / temp, q(1,j), 1 ) 10 continue c if (msglvl .gt. 1) then call zcopy(n, q(n,1), ldq, workl, 1) call zvout (logfil, n, workl, ndigit, & '_neigh: Last row of the eigenvector matrix for H') end if c c %----------------------------% c | Compute the Ritz estimates | c %----------------------------% c call zcopy(n, q(n,1), n, bounds, 1) call zdscal(n, rnorm, bounds, 1) c if (msglvl .gt. 2) then call zvout (logfil, n, ritz, ndigit, & '_neigh: The eigenvalues of H') call zvout (logfil, n, bounds, ndigit, & '_neigh: Ritz estimates for the eigenvalues of H') end if c call arscnd(t1) tceigh = tceigh + (t1 - t0) c 9000 continue return c c %---------------% c | End of zneigh | c %---------------% c end arpack-0.92.1/SRC/dngets.f0000644000175000017500000001753410776001577012073 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: dngets c c\Description: c Given the eigenvalues of the upper Hessenberg matrix H, c computes the NP shifts AMU that are zeros of the polynomial of c degree NP which filters out components of the unwanted eigenvectors c corresponding to the AMU's based on some given criteria. c c NOTE: call this even in the case of user specified shifts in order c to sort the eigenvalues, and error bounds of H for later use. c c\Usage: c call dngets c ( ISHIFT, WHICH, KEV, NP, RITZR, RITZI, BOUNDS, SHIFTR, SHIFTI ) c c\Arguments c ISHIFT Integer. (INPUT) c Method for selecting the implicit shifts at each iteration. c ISHIFT = 0: user specified shifts c ISHIFT = 1: exact shift with respect to the matrix H. c c WHICH Character*2. (INPUT) c Shift selection criteria. c 'LM' -> want the KEV eigenvalues of largest magnitude. c 'SM' -> want the KEV eigenvalues of smallest magnitude. c 'LR' -> want the KEV eigenvalues of largest real part. c 'SR' -> want the KEV eigenvalues of smallest real part. c 'LI' -> want the KEV eigenvalues of largest imaginary part. c 'SI' -> want the KEV eigenvalues of smallest imaginary part. c c KEV Integer. (INPUT/OUTPUT) c INPUT: KEV+NP is the size of the matrix H. c OUTPUT: Possibly increases KEV by one to keep complex conjugate c pairs together. c c NP Integer. (INPUT/OUTPUT) c Number of implicit shifts to be computed. c OUTPUT: Possibly decreases NP by one to keep complex conjugate c pairs together. c c RITZR, Double precision array of length KEV+NP. (INPUT/OUTPUT) c RITZI On INPUT, RITZR and RITZI contain the real and imaginary c parts of the eigenvalues of H. c On OUTPUT, RITZR and RITZI are sorted so that the unwanted c eigenvalues are in the first NP locations and the wanted c portion is in the last KEV locations. When exact shifts are c selected, the unwanted part corresponds to the shifts to c be applied. Also, if ISHIFT .eq. 1, the unwanted eigenvalues c are further sorted so that the ones with largest Ritz values c are first. c c BOUNDS Double precision array of length KEV+NP. (INPUT/OUTPUT) c Error bounds corresponding to the ordering in RITZ. c c SHIFTR, SHIFTI *** USE deprecated as of version 2.1. *** c c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx real c c\Routines called: c dsortc ARPACK sorting routine. c dcopy Level 1 BLAS that copies one vector to another . c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c xx/xx/92: Version ' 2.1' c c\SCCS Information: @(#) c FILE: ngets.F SID: 2.3 DATE OF SID: 4/20/96 RELEASE: 2 c c\Remarks c 1. xxxx c c\EndLib c c----------------------------------------------------------------------- c subroutine dngets ( ishift, which, kev, np, ritzr, ritzi, bounds, & shiftr, shifti ) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character*2 which integer ishift, kev, np c c %-----------------% c | Array Arguments | c %-----------------% c Double precision & bounds(kev+np), ritzr(kev+np), ritzi(kev+np), & shiftr(1), shifti(1) c c %------------% c | Parameters | c %------------% c Double precision & one, zero parameter (one = 1.0, zero = 0.0) c c %---------------% c | Local Scalars | c %---------------% c integer msglvl c c %----------------------% c | External Subroutines | c %----------------------% c external dcopy, dsortc, arscnd c c %----------------------% c | Intrinsics Functions | c %----------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call arscnd (t0) msglvl = mngets c c %----------------------------------------------------% c | LM, SM, LR, SR, LI, SI case. | c | Sort the eigenvalues of H into the desired order | c | and apply the resulting order to BOUNDS. | c | The eigenvalues are sorted so that the wanted part | c | are always in the last KEV locations. | c | We first do a pre-processing sort in order to keep | c | complex conjugate pairs together | c %----------------------------------------------------% c if (which .eq. 'LM') then call dsortc ('LR', .true., kev+np, ritzr, ritzi, bounds) else if (which .eq. 'SM') then call dsortc ('SR', .true., kev+np, ritzr, ritzi, bounds) else if (which .eq. 'LR') then call dsortc ('LM', .true., kev+np, ritzr, ritzi, bounds) else if (which .eq. 'SR') then call dsortc ('SM', .true., kev+np, ritzr, ritzi, bounds) else if (which .eq. 'LI') then call dsortc ('LM', .true., kev+np, ritzr, ritzi, bounds) else if (which .eq. 'SI') then call dsortc ('SM', .true., kev+np, ritzr, ritzi, bounds) end if c call dsortc (which, .true., kev+np, ritzr, ritzi, bounds) c c %-------------------------------------------------------% c | Increase KEV by one if the ( ritzr(np),ritzi(np) ) | c | = ( ritzr(np+1),-ritzi(np+1) ) and ritz(np) .ne. zero | c | Accordingly decrease NP by one. In other words keep | c | complex conjugate pairs together. | c %-------------------------------------------------------% c if ( ( ritzr(np+1) - ritzr(np) ) .eq. zero & .and. ( ritzi(np+1) + ritzi(np) ) .eq. zero ) then np = np - 1 kev = kev + 1 end if c if ( ishift .eq. 1 ) then c c %-------------------------------------------------------% c | Sort the unwanted Ritz values used as shifts so that | c | the ones with largest Ritz estimates are first | c | This will tend to minimize the effects of the | c | forward instability of the iteration when they shifts | c | are applied in subroutine dnapps. | c | Be careful and use 'SR' since we want to sort BOUNDS! | c %-------------------------------------------------------% c call dsortc ( 'SR', .true., np, bounds, ritzr, ritzi ) end if c call arscnd (t1) tngets = tngets + (t1 - t0) c if (msglvl .gt. 0) then call ivout (logfil, 1, kev, ndigit, '_ngets: KEV is') call ivout (logfil, 1, np, ndigit, '_ngets: NP is') call dvout (logfil, kev+np, ritzr, ndigit, & '_ngets: Eigenvalues of current H matrix -- real part') call dvout (logfil, kev+np, ritzi, ndigit, & '_ngets: Eigenvalues of current H matrix -- imag part') call dvout (logfil, kev+np, bounds, ndigit, & '_ngets: Ritz estimates of the current KEV+NP Ritz values') end if c return c c %---------------% c | End of dngets | c %---------------% c end arpack-0.92.1/SRC/dstqrb.f0000644000175000017500000004062410776001577012102 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: dstqrb c c\Description: c Computes all eigenvalues and the last component of the eigenvectors c of a symmetric tridiagonal matrix using the implicit QL or QR method. c c This is mostly a modification of the LAPACK routine dsteqr. c See Remarks. c c\Usage: c call dstqrb c ( N, D, E, Z, WORK, INFO ) c c\Arguments c N Integer. (INPUT) c The number of rows and columns in the matrix. N >= 0. c c D Double precision array, dimension (N). (INPUT/OUTPUT) c On entry, D contains the diagonal elements of the c tridiagonal matrix. c On exit, D contains the eigenvalues, in ascending order. c If an error exit is made, the eigenvalues are correct c for indices 1,2,...,INFO-1, but they are unordered and c may not be the smallest eigenvalues of the matrix. c c E Double precision array, dimension (N-1). (INPUT/OUTPUT) c On entry, E contains the subdiagonal elements of the c tridiagonal matrix in positions 1 through N-1. c On exit, E has been destroyed. c c Z Double precision array, dimension (N). (OUTPUT) c On exit, Z contains the last row of the orthonormal c eigenvector matrix of the symmetric tridiagonal matrix. c If an error exit is made, Z contains the last row of the c eigenvector matrix associated with the stored eigenvalues. c c WORK Double precision array, dimension (max(1,2*N-2)). (WORKSPACE) c Workspace used in accumulating the transformation for c computing the last components of the eigenvectors. c c INFO Integer. (OUTPUT) c = 0: normal return. c < 0: if INFO = -i, the i-th argument had an illegal value. c > 0: if INFO = +i, the i-th eigenvalue has not converged c after a total of 30*N iterations. c c\Remarks c 1. None. c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx real c c\Routines called: c daxpy Level 1 BLAS that computes a vector triad. c dcopy Level 1 BLAS that copies one vector to another. c dswap Level 1 BLAS that swaps the contents of two vectors. c lsame LAPACK character comparison routine. c dlae2 LAPACK routine that computes the eigenvalues of a 2-by-2 c symmetric matrix. c dlaev2 LAPACK routine that eigendecomposition of a 2-by-2 symmetric c matrix. c dlamch LAPACK routine that determines machine constants. c dlanst LAPACK routine that computes the norm of a matrix. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c dlartg LAPACK Givens rotation construction routine. c dlascl LAPACK routine for careful scaling of a matrix. c dlaset LAPACK matrix initialization routine. c dlasr LAPACK routine that applies an orthogonal transformation to c a matrix. c dlasrt LAPACK sorting routine. c dsteqr LAPACK routine that computes eigenvalues and eigenvectors c of a symmetric tridiagonal matrix. c xerbla LAPACK error handler routine. c c\Authors c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: stqrb.F SID: 2.5 DATE OF SID: 8/27/96 RELEASE: 2 c c\Remarks c 1. Starting with version 2.5, this routine is a modified version c of LAPACK version 2.0 subroutine SSTEQR. No lines are deleted, c only commeted out and new lines inserted. c All lines commented out have "c$$$" at the beginning. c Note that the LAPACK version 1.0 subroutine SSTEQR contained c bugs. c c\EndLib c c----------------------------------------------------------------------- c subroutine dstqrb ( n, d, e, z, work, info ) c c %------------------% c | Scalar Arguments | c %------------------% c integer info, n c c %-----------------% c | Array Arguments | c %-----------------% c Double precision & d( n ), e( n-1 ), z( n ), work( 2*n-2 ) c c .. parameters .. Double precision & zero, one, two, three parameter ( zero = 0.0D+0, one = 1.0D+0, & two = 2.0D+0, three = 3.0D+0 ) integer maxit parameter ( maxit = 30 ) c .. c .. local scalars .. integer i, icompz, ii, iscale, j, jtot, k, l, l1, lend, & lendm1, lendp1, lendsv, lm1, lsv, m, mm, mm1, & nm1, nmaxit Double precision & anorm, b, c, eps, eps2, f, g, p, r, rt1, rt2, & s, safmax, safmin, ssfmax, ssfmin, tst c .. c .. external functions .. logical lsame Double precision & dlamch, dlanst, dlapy2 external lsame, dlamch, dlanst, dlapy2 c .. c .. external subroutines .. external dlae2, dlaev2, dlartg, dlascl, dlaset, dlasr, & dlasrt, dswap, xerbla c .. c .. intrinsic functions .. intrinsic abs, max, sign, sqrt c .. c .. executable statements .. c c test the input parameters. c info = 0 c c$$$ IF( LSAME( COMPZ, 'N' ) ) THEN c$$$ ICOMPZ = 0 c$$$ ELSE IF( LSAME( COMPZ, 'V' ) ) THEN c$$$ ICOMPZ = 1 c$$$ ELSE IF( LSAME( COMPZ, 'I' ) ) THEN c$$$ ICOMPZ = 2 c$$$ ELSE c$$$ ICOMPZ = -1 c$$$ END IF c$$$ IF( ICOMPZ.LT.0 ) THEN c$$$ INFO = -1 c$$$ ELSE IF( N.LT.0 ) THEN c$$$ INFO = -2 c$$$ ELSE IF( ( LDZ.LT.1 ) .OR. ( ICOMPZ.GT.0 .AND. LDZ.LT.MAX( 1, c$$$ $ N ) ) ) THEN c$$$ INFO = -6 c$$$ END IF c$$$ IF( INFO.NE.0 ) THEN c$$$ CALL XERBLA( 'SSTEQR', -INFO ) c$$$ RETURN c$$$ END IF c c *** New starting with version 2.5 *** c icompz = 2 c ************************************* c c quick return if possible c if( n.eq.0 ) $ return c if( n.eq.1 ) then if( icompz.eq.2 ) z( 1 ) = one return end if c c determine the unit roundoff and over/underflow thresholds. c eps = dlamch( 'e' ) eps2 = eps**2 safmin = dlamch( 's' ) safmax = one / safmin ssfmax = sqrt( safmax ) / three ssfmin = sqrt( safmin ) / eps2 c c compute the eigenvalues and eigenvectors of the tridiagonal c matrix. c c$$ if( icompz.eq.2 ) c$$$ $ call dlaset( 'full', n, n, zero, one, z, ldz ) c c *** New starting with version 2.5 *** c if ( icompz .eq. 2 ) then do 5 j = 1, n-1 z(j) = zero 5 continue z( n ) = one end if c ************************************* c nmaxit = n*maxit jtot = 0 c c determine where the matrix splits and choose ql or qr iteration c for each block, according to whether top or bottom diagonal c element is smaller. c l1 = 1 nm1 = n - 1 c 10 continue if( l1.gt.n ) $ go to 160 if( l1.gt.1 ) $ e( l1-1 ) = zero if( l1.le.nm1 ) then do 20 m = l1, nm1 tst = abs( e( m ) ) if( tst.eq.zero ) $ go to 30 if( tst.le.( sqrt( abs( d( m ) ) )*sqrt( abs( d( m+ $ 1 ) ) ) )*eps ) then e( m ) = zero go to 30 end if 20 continue end if m = n c 30 continue l = l1 lsv = l lend = m lendsv = lend l1 = m + 1 if( lend.eq.l ) $ go to 10 c c scale submatrix in rows and columns l to lend c anorm = dlanst( 'i', lend-l+1, d( l ), e( l ) ) iscale = 0 if( anorm.eq.zero ) $ go to 10 if( anorm.gt.ssfmax ) then iscale = 1 call dlascl( 'g', 0, 0, anorm, ssfmax, lend-l+1, 1, d( l ), n, $ info ) call dlascl( 'g', 0, 0, anorm, ssfmax, lend-l, 1, e( l ), n, $ info ) else if( anorm.lt.ssfmin ) then iscale = 2 call dlascl( 'g', 0, 0, anorm, ssfmin, lend-l+1, 1, d( l ), n, $ info ) call dlascl( 'g', 0, 0, anorm, ssfmin, lend-l, 1, e( l ), n, $ info ) end if c c choose between ql and qr iteration c if( abs( d( lend ) ).lt.abs( d( l ) ) ) then lend = lsv l = lendsv end if c if( lend.gt.l ) then c c ql iteration c c look for small subdiagonal element. c 40 continue if( l.ne.lend ) then lendm1 = lend - 1 do 50 m = l, lendm1 tst = abs( e( m ) )**2 if( tst.le.( eps2*abs( d( m ) ) )*abs( d( m+1 ) )+ $ safmin )go to 60 50 continue end if c m = lend c 60 continue if( m.lt.lend ) $ e( m ) = zero p = d( l ) if( m.eq.l ) $ go to 80 c c if remaining matrix is 2-by-2, use dlae2 or dlaev2 c to compute its eigensystem. c if( m.eq.l+1 ) then if( icompz.gt.0 ) then call dlaev2( d( l ), e( l ), d( l+1 ), rt1, rt2, c, s ) work( l ) = c work( n-1+l ) = s c$$$ call dlasr( 'r', 'v', 'b', n, 2, work( l ), c$$$ $ work( n-1+l ), z( 1, l ), ldz ) c c *** New starting with version 2.5 *** c tst = z(l+1) z(l+1) = c*tst - s*z(l) z(l) = s*tst + c*z(l) c ************************************* else call dlae2( d( l ), e( l ), d( l+1 ), rt1, rt2 ) end if d( l ) = rt1 d( l+1 ) = rt2 e( l ) = zero l = l + 2 if( l.le.lend ) $ go to 40 go to 140 end if c if( jtot.eq.nmaxit ) $ go to 140 jtot = jtot + 1 c c form shift. c g = ( d( l+1 )-p ) / ( two*e( l ) ) r = dlapy2( g, one ) g = d( m ) - p + ( e( l ) / ( g+sign( r, g ) ) ) c s = one c = one p = zero c c inner loop c mm1 = m - 1 do 70 i = mm1, l, -1 f = s*e( i ) b = c*e( i ) call dlartg( g, f, c, s, r ) if( i.ne.m-1 ) $ e( i+1 ) = r g = d( i+1 ) - p r = ( d( i )-g )*s + two*c*b p = s*r d( i+1 ) = g + p g = c*r - b c c if eigenvectors are desired, then save rotations. c if( icompz.gt.0 ) then work( i ) = c work( n-1+i ) = -s end if c 70 continue c c if eigenvectors are desired, then apply saved rotations. c if( icompz.gt.0 ) then mm = m - l + 1 c$$$ call dlasr( 'r', 'v', 'b', n, mm, work( l ), work( n-1+l ), c$$$ $ z( 1, l ), ldz ) c c *** New starting with version 2.5 *** c call dlasr( 'r', 'v', 'b', 1, mm, work( l ), & work( n-1+l ), z( l ), 1 ) c ************************************* end if c d( l ) = d( l ) - p e( l ) = g go to 40 c c eigenvalue found. c 80 continue d( l ) = p c l = l + 1 if( l.le.lend ) $ go to 40 go to 140 c else c c qr iteration c c look for small superdiagonal element. c 90 continue if( l.ne.lend ) then lendp1 = lend + 1 do 100 m = l, lendp1, -1 tst = abs( e( m-1 ) )**2 if( tst.le.( eps2*abs( d( m ) ) )*abs( d( m-1 ) )+ $ safmin )go to 110 100 continue end if c m = lend c 110 continue if( m.gt.lend ) $ e( m-1 ) = zero p = d( l ) if( m.eq.l ) $ go to 130 c c if remaining matrix is 2-by-2, use dlae2 or dlaev2 c to compute its eigensystem. c if( m.eq.l-1 ) then if( icompz.gt.0 ) then call dlaev2( d( l-1 ), e( l-1 ), d( l ), rt1, rt2, c, s ) c$$$ work( m ) = c c$$$ work( n-1+m ) = s c$$$ call dlasr( 'r', 'v', 'f', n, 2, work( m ), c$$$ $ work( n-1+m ), z( 1, l-1 ), ldz ) c c *** New starting with version 2.5 *** c tst = z(l) z(l) = c*tst - s*z(l-1) z(l-1) = s*tst + c*z(l-1) c ************************************* else call dlae2( d( l-1 ), e( l-1 ), d( l ), rt1, rt2 ) end if d( l-1 ) = rt1 d( l ) = rt2 e( l-1 ) = zero l = l - 2 if( l.ge.lend ) $ go to 90 go to 140 end if c if( jtot.eq.nmaxit ) $ go to 140 jtot = jtot + 1 c c form shift. c g = ( d( l-1 )-p ) / ( two*e( l-1 ) ) r = dlapy2( g, one ) g = d( m ) - p + ( e( l-1 ) / ( g+sign( r, g ) ) ) c s = one c = one p = zero c c inner loop c lm1 = l - 1 do 120 i = m, lm1 f = s*e( i ) b = c*e( i ) call dlartg( g, f, c, s, r ) if( i.ne.m ) $ e( i-1 ) = r g = d( i ) - p r = ( d( i+1 )-g )*s + two*c*b p = s*r d( i ) = g + p g = c*r - b c c if eigenvectors are desired, then save rotations. c if( icompz.gt.0 ) then work( i ) = c work( n-1+i ) = s end if c 120 continue c c if eigenvectors are desired, then apply saved rotations. c if( icompz.gt.0 ) then mm = l - m + 1 c$$$ call dlasr( 'r', 'v', 'f', n, mm, work( m ), work( n-1+m ), c$$$ $ z( 1, m ), ldz ) c c *** New starting with version 2.5 *** c call dlasr( 'r', 'v', 'f', 1, mm, work( m ), work( n-1+m ), & z( m ), 1 ) c ************************************* end if c d( l ) = d( l ) - p e( lm1 ) = g go to 90 c c eigenvalue found. c 130 continue d( l ) = p c l = l - 1 if( l.ge.lend ) $ go to 90 go to 140 c end if c c undo scaling if necessary c 140 continue if( iscale.eq.1 ) then call dlascl( 'g', 0, 0, ssfmax, anorm, lendsv-lsv+1, 1, $ d( lsv ), n, info ) call dlascl( 'g', 0, 0, ssfmax, anorm, lendsv-lsv, 1, e( lsv ), $ n, info ) else if( iscale.eq.2 ) then call dlascl( 'g', 0, 0, ssfmin, anorm, lendsv-lsv+1, 1, $ d( lsv ), n, info ) call dlascl( 'g', 0, 0, ssfmin, anorm, lendsv-lsv, 1, e( lsv ), $ n, info ) end if c c check for no convergence to an eigenvalue after a total c of n*maxit iterations. c if( jtot.lt.nmaxit ) $ go to 10 do 150 i = 1, n - 1 if( e( i ).ne.zero ) $ info = info + 1 150 continue go to 190 c c order eigenvalues and eigenvectors. c 160 continue if( icompz.eq.0 ) then c c use quick sort c call dlasrt( 'i', n, d, info ) c else c c use selection sort to minimize swaps of eigenvectors c do 180 ii = 2, n i = ii - 1 k = i p = d( i ) do 170 j = ii, n if( d( j ).lt.p ) then k = j p = d( j ) end if 170 continue if( k.ne.i ) then d( k ) = d( i ) d( i ) = p c$$$ call dswap( n, z( 1, i ), 1, z( 1, k ), 1 ) c *** New starting with version 2.5 *** c p = z(k) z(k) = z(i) z(i) = p c ************************************* end if 180 continue end if c 190 continue return c c %---------------% c | End of dstqrb | c %---------------% c end arpack-0.92.1/SRC/dsaitr.f0000644000175000017500000007413310776001577012073 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: dsaitr c c\Description: c Reverse communication interface for applying NP additional steps to c a K step symmetric Arnoldi factorization. c c Input: OP*V_{k} - V_{k}*H = r_{k}*e_{k}^T c c with (V_{k}^T)*B*V_{k} = I, (V_{k}^T)*B*r_{k} = 0. c c Output: OP*V_{k+p} - V_{k+p}*H = r_{k+p}*e_{k+p}^T c c with (V_{k+p}^T)*B*V_{k+p} = I, (V_{k+p}^T)*B*r_{k+p} = 0. c c where OP and B are as in dsaupd. The B-norm of r_{k+p} is also c computed and returned. c c\Usage: c call dsaitr c ( IDO, BMAT, N, K, NP, MODE, RESID, RNORM, V, LDV, H, LDH, c IPNTR, WORKD, INFO ) c c\Arguments c IDO Integer. (INPUT/OUTPUT) c Reverse communication flag. c ------------------------------------------------------------- c IDO = 0: first call to the reverse communication interface c IDO = -1: compute Y = OP * X where c IPNTR(1) is the pointer into WORK for X, c IPNTR(2) is the pointer into WORK for Y. c This is for the restart phase to force the new c starting vector into the range of OP. c IDO = 1: compute Y = OP * X where c IPNTR(1) is the pointer into WORK for X, c IPNTR(2) is the pointer into WORK for Y, c IPNTR(3) is the pointer into WORK for B * X. c IDO = 2: compute Y = B * X where c IPNTR(1) is the pointer into WORK for X, c IPNTR(2) is the pointer into WORK for Y. c IDO = 99: done c ------------------------------------------------------------- c When the routine is used in the "shift-and-invert" mode, the c vector B * Q is already available and does not need to be c recomputed in forming OP * Q. c c BMAT Character*1. (INPUT) c BMAT specifies the type of matrix B that defines the c semi-inner product for the operator OP. See dsaupd. c B = 'I' -> standard eigenvalue problem A*x = lambda*x c B = 'G' -> generalized eigenvalue problem A*x = lambda*M*x c c N Integer. (INPUT) c Dimension of the eigenproblem. c c K Integer. (INPUT) c Current order of H and the number of columns of V. c c NP Integer. (INPUT) c Number of additional Arnoldi steps to take. c c MODE Integer. (INPUT) c Signifies which form for "OP". If MODE=2 then c a reduction in the number of B matrix vector multiplies c is possible since the B-norm of OP*x is equivalent to c the inv(B)-norm of A*x. c c RESID Double precision array of length N. (INPUT/OUTPUT) c On INPUT: RESID contains the residual vector r_{k}. c On OUTPUT: RESID contains the residual vector r_{k+p}. c c RNORM Double precision scalar. (INPUT/OUTPUT) c On INPUT the B-norm of r_{k}. c On OUTPUT the B-norm of the updated residual r_{k+p}. c c V Double precision N by K+NP array. (INPUT/OUTPUT) c On INPUT: V contains the Arnoldi vectors in the first K c columns. c On OUTPUT: V contains the new NP Arnoldi vectors in the next c NP columns. The first K columns are unchanged. c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling c program. c c H Double precision (K+NP) by 2 array. (INPUT/OUTPUT) c H is used to store the generated symmetric tridiagonal matrix c with the subdiagonal in the first column starting at H(2,1) c and the main diagonal in the second column. c c LDH Integer. (INPUT) c Leading dimension of H exactly as declared in the calling c program. c c IPNTR Integer array of length 3. (OUTPUT) c Pointer to mark the starting locations in the WORK for c vectors used by the Arnoldi iteration. c ------------------------------------------------------------- c IPNTR(1): pointer to the current operand vector X. c IPNTR(2): pointer to the current result vector Y. c IPNTR(3): pointer to the vector B * X when used in the c shift-and-invert mode. X is the current operand. c ------------------------------------------------------------- c c WORKD Double precision work array of length 3*N. (REVERSE COMMUNICATION) c Distributed array to be used in the basic Arnoldi iteration c for reverse communication. The calling program should not c use WORKD as temporary workspace during the iteration !!!!!! c On INPUT, WORKD(1:N) = B*RESID where RESID is associated c with the K step Arnoldi factorization. Used to save some c computation at the first step. c On OUTPUT, WORKD(1:N) = B*RESID where RESID is associated c with the K+NP step Arnoldi factorization. c c INFO Integer. (OUTPUT) c = 0: Normal exit. c > 0: Size of an invariant subspace of OP is found that is c less than K + NP. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx real c c\Routines called: c dgetv0 ARPACK routine to generate the initial vector. c ivout ARPACK utility routine that prints integers. c dmout ARPACK utility routine that prints matrices. c dvout ARPACK utility routine that prints vectors. c dlamch LAPACK routine that determines machine constants. c dlascl LAPACK routine for careful scaling of a matrix. c dgemv Level 2 BLAS routine for matrix vector multiplication. c daxpy Level 1 BLAS that computes a vector triad. c dscal Level 1 BLAS that scales a vector. c dcopy Level 1 BLAS that copies one vector to another . c ddot Level 1 BLAS that computes the scalar product of two vectors. c dnrm2 Level 1 BLAS that computes the norm of a vector. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c xx/xx/93: Version ' 2.4' c c\SCCS Information: @(#) c FILE: saitr.F SID: 2.6 DATE OF SID: 8/28/96 RELEASE: 2 c c\Remarks c The algorithm implemented is: c c restart = .false. c Given V_{k} = [v_{1}, ..., v_{k}], r_{k}; c r_{k} contains the initial residual vector even for k = 0; c Also assume that rnorm = || B*r_{k} || and B*r_{k} are already c computed by the calling program. c c betaj = rnorm ; p_{k+1} = B*r_{k} ; c For j = k+1, ..., k+np Do c 1) if ( betaj < tol ) stop or restart depending on j. c if ( restart ) generate a new starting vector. c 2) v_{j} = r(j-1)/betaj; V_{j} = [V_{j-1}, v_{j}]; c p_{j} = p_{j}/betaj c 3) r_{j} = OP*v_{j} where OP is defined as in dsaupd c For shift-invert mode p_{j} = B*v_{j} is already available. c wnorm = || OP*v_{j} || c 4) Compute the j-th step residual vector. c w_{j} = V_{j}^T * B * OP * v_{j} c r_{j} = OP*v_{j} - V_{j} * w_{j} c alphaj <- j-th component of w_{j} c rnorm = || r_{j} || c betaj+1 = rnorm c If (rnorm > 0.717*wnorm) accept step and go back to 1) c 5) Re-orthogonalization step: c s = V_{j}'*B*r_{j} c r_{j} = r_{j} - V_{j}*s; rnorm1 = || r_{j} || c alphaj = alphaj + s_{j}; c 6) Iterative refinement step: c If (rnorm1 > 0.717*rnorm) then c rnorm = rnorm1 c accept step and go back to 1) c Else c rnorm = rnorm1 c If this is the first time in step 6), go to 5) c Else r_{j} lies in the span of V_{j} numerically. c Set r_{j} = 0 and rnorm = 0; go to 1) c EndIf c End Do c c\EndLib c c----------------------------------------------------------------------- c subroutine dsaitr & (ido, bmat, n, k, np, mode, resid, rnorm, v, ldv, h, ldh, & ipntr, workd, info) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character bmat*1 integer ido, info, k, ldh, ldv, n, mode, np Double precision & rnorm c c %-----------------% c | Array Arguments | c %-----------------% c integer ipntr(3) Double precision & h(ldh,2), resid(n), v(ldv,k+np), workd(3*n) c c %------------% c | Parameters | c %------------% c Double precision & one, zero parameter (one = 1.0D+0, zero = 0.0D+0) c c %---------------% c | Local Scalars | c %---------------% c logical first, orth1, orth2, rstart, step3, step4 integer i, ierr, ipj, irj, ivj, iter, itry, j, msglvl, & infol, jj Double precision & rnorm1, wnorm, safmin, temp1 save orth1, orth2, rstart, step3, step4, & ierr, ipj, irj, ivj, iter, itry, j, msglvl, & rnorm1, safmin, wnorm c c %-----------------------% c | Local Array Arguments | c %-----------------------% c Double precision & xtemp(2) c c %----------------------% c | External Subroutines | c %----------------------% c external daxpy, dcopy, dscal, dgemv, dgetv0, dvout, dmout, & dlascl, ivout, arscnd c c %--------------------% c | External Functions | c %--------------------% c Double precision & ddot, dnrm2, dlamch external ddot, dnrm2, dlamch c c %-----------------% c | Data statements | c %-----------------% c data first / .true. / c c %-----------------------% c | Executable Statements | c %-----------------------% c if (first) then first = .false. c c %--------------------------------% c | safmin = safe minimum is such | c | that 1/sfmin does not overflow | c %--------------------------------% c safmin = dlamch('safmin') end if c if (ido .eq. 0) then c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call arscnd (t0) msglvl = msaitr c c %------------------------------% c | Initial call to this routine | c %------------------------------% c info = 0 step3 = .false. step4 = .false. rstart = .false. orth1 = .false. orth2 = .false. c c %--------------------------------% c | Pointer to the current step of | c | the factorization to build | c %--------------------------------% c j = k + 1 c c %------------------------------------------% c | Pointers used for reverse communication | c | when using WORKD. | c %------------------------------------------% c ipj = 1 irj = ipj + n ivj = irj + n end if c c %-------------------------------------------------% c | When in reverse communication mode one of: | c | STEP3, STEP4, ORTH1, ORTH2, RSTART | c | will be .true. | c | STEP3: return from computing OP*v_{j}. | c | STEP4: return from computing B-norm of OP*v_{j} | c | ORTH1: return from computing B-norm of r_{j+1} | c | ORTH2: return from computing B-norm of | c | correction to the residual vector. | c | RSTART: return from OP computations needed by | c | dgetv0. | c %-------------------------------------------------% c if (step3) go to 50 if (step4) go to 60 if (orth1) go to 70 if (orth2) go to 90 if (rstart) go to 30 c c %------------------------------% c | Else this is the first step. | c %------------------------------% c c %--------------------------------------------------------------% c | | c | A R N O L D I I T E R A T I O N L O O P | c | | c | Note: B*r_{j-1} is already in WORKD(1:N)=WORKD(IPJ:IPJ+N-1) | c %--------------------------------------------------------------% c 1000 continue c if (msglvl .gt. 2) then call ivout (logfil, 1, j, ndigit, & '_saitr: generating Arnoldi vector no.') call dvout (logfil, 1, rnorm, ndigit, & '_saitr: B-norm of the current residual =') end if c c %---------------------------------------------------------% c | Check for exact zero. Equivalent to determing whether a | c | j-step Arnoldi factorization is present. | c %---------------------------------------------------------% c if (rnorm .gt. zero) go to 40 c c %---------------------------------------------------% c | Invariant subspace found, generate a new starting | c | vector which is orthogonal to the current Arnoldi | c | basis and continue the iteration. | c %---------------------------------------------------% c if (msglvl .gt. 0) then call ivout (logfil, 1, j, ndigit, & '_saitr: ****** restart at step ******') end if c c %---------------------------------------------% c | ITRY is the loop variable that controls the | c | maximum amount of times that a restart is | c | attempted. NRSTRT is used by stat.h | c %---------------------------------------------% c nrstrt = nrstrt + 1 itry = 1 20 continue rstart = .true. ido = 0 30 continue c c %--------------------------------------% c | If in reverse communication mode and | c | RSTART = .true. flow returns here. | c %--------------------------------------% c call dgetv0 (ido, bmat, itry, .false., n, j, v, ldv, & resid, rnorm, ipntr, workd, ierr) if (ido .ne. 99) go to 9000 if (ierr .lt. 0) then itry = itry + 1 if (itry .le. 3) go to 20 c c %------------------------------------------------% c | Give up after several restart attempts. | c | Set INFO to the size of the invariant subspace | c | which spans OP and exit. | c %------------------------------------------------% c info = j - 1 call arscnd (t1) tsaitr = tsaitr + (t1 - t0) ido = 99 go to 9000 end if c 40 continue c c %---------------------------------------------------------% c | STEP 2: v_{j} = r_{j-1}/rnorm and p_{j} = p_{j}/rnorm | c | Note that p_{j} = B*r_{j-1}. In order to avoid overflow | c | when reciprocating a small RNORM, test against lower | c | machine bound. | c %---------------------------------------------------------% c call dcopy (n, resid, 1, v(1,j), 1) if (rnorm .ge. safmin) then temp1 = one / rnorm call dscal (n, temp1, v(1,j), 1) call dscal (n, temp1, workd(ipj), 1) else c c %-----------------------------------------% c | To scale both v_{j} and p_{j} carefully | c | use LAPACK routine SLASCL | c %-----------------------------------------% c call dlascl ('General', i, i, rnorm, one, n, 1, & v(1,j), n, infol) call dlascl ('General', i, i, rnorm, one, n, 1, & workd(ipj), n, infol) end if c c %------------------------------------------------------% c | STEP 3: r_{j} = OP*v_{j}; Note that p_{j} = B*v_{j} | c | Note that this is not quite yet r_{j}. See STEP 4 | c %------------------------------------------------------% c step3 = .true. nopx = nopx + 1 call arscnd (t2) call dcopy (n, v(1,j), 1, workd(ivj), 1) ipntr(1) = ivj ipntr(2) = irj ipntr(3) = ipj ido = 1 c c %-----------------------------------% c | Exit in order to compute OP*v_{j} | c %-----------------------------------% c go to 9000 50 continue c c %-----------------------------------% c | Back from reverse communication; | c | WORKD(IRJ:IRJ+N-1) := OP*v_{j}. | c %-----------------------------------% c call arscnd (t3) tmvopx = tmvopx + (t3 - t2) c step3 = .false. c c %------------------------------------------% c | Put another copy of OP*v_{j} into RESID. | c %------------------------------------------% c call dcopy (n, workd(irj), 1, resid, 1) c c %-------------------------------------------% c | STEP 4: Finish extending the symmetric | c | Arnoldi to length j. If MODE = 2 | c | then B*OP = B*inv(B)*A = A and | c | we don't need to compute B*OP. | c | NOTE: If MODE = 2 WORKD(IVJ:IVJ+N-1) is | c | assumed to have A*v_{j}. | c %-------------------------------------------% c if (mode .eq. 2) go to 65 call arscnd (t2) if (bmat .eq. 'G') then nbx = nbx + 1 step4 = .true. ipntr(1) = irj ipntr(2) = ipj ido = 2 c c %-------------------------------------% c | Exit in order to compute B*OP*v_{j} | c %-------------------------------------% c go to 9000 else if (bmat .eq. 'I') then call dcopy(n, resid, 1 , workd(ipj), 1) end if 60 continue c c %-----------------------------------% c | Back from reverse communication; | c | WORKD(IPJ:IPJ+N-1) := B*OP*v_{j}. | c %-----------------------------------% c if (bmat .eq. 'G') then call arscnd (t3) tmvbx = tmvbx + (t3 - t2) end if c step4 = .false. c c %-------------------------------------% c | The following is needed for STEP 5. | c | Compute the B-norm of OP*v_{j}. | c %-------------------------------------% c 65 continue if (mode .eq. 2) then c c %----------------------------------% c | Note that the B-norm of OP*v_{j} | c | is the inv(B)-norm of A*v_{j}. | c %----------------------------------% c wnorm = ddot (n, resid, 1, workd(ivj), 1) wnorm = sqrt(abs(wnorm)) else if (bmat .eq. 'G') then wnorm = ddot (n, resid, 1, workd(ipj), 1) wnorm = sqrt(abs(wnorm)) else if (bmat .eq. 'I') then wnorm = dnrm2(n, resid, 1) end if c c %-----------------------------------------% c | Compute the j-th residual corresponding | c | to the j step factorization. | c | Use Classical Gram Schmidt and compute: | c | w_{j} <- V_{j}^T * B * OP * v_{j} | c | r_{j} <- OP*v_{j} - V_{j} * w_{j} | c %-----------------------------------------% c c c %------------------------------------------% c | Compute the j Fourier coefficients w_{j} | c | WORKD(IPJ:IPJ+N-1) contains B*OP*v_{j}. | c %------------------------------------------% c if (mode .ne. 2 ) then call dgemv('T', n, j, one, v, ldv, workd(ipj), 1, zero, & workd(irj), 1) else if (mode .eq. 2) then call dgemv('T', n, j, one, v, ldv, workd(ivj), 1, zero, & workd(irj), 1) end if c c %--------------------------------------% c | Orthgonalize r_{j} against V_{j}. | c | RESID contains OP*v_{j}. See STEP 3. | c %--------------------------------------% c call dgemv('N', n, j, -one, v, ldv, workd(irj), 1, one, & resid, 1) c c %--------------------------------------% c | Extend H to have j rows and columns. | c %--------------------------------------% c h(j,2) = workd(irj + j - 1) if (j .eq. 1 .or. rstart) then h(j,1) = zero else h(j,1) = rnorm end if call arscnd (t4) c orth1 = .true. iter = 0 c call arscnd (t2) if (bmat .eq. 'G') then nbx = nbx + 1 call dcopy (n, resid, 1, workd(irj), 1) ipntr(1) = irj ipntr(2) = ipj ido = 2 c c %----------------------------------% c | Exit in order to compute B*r_{j} | c %----------------------------------% c go to 9000 else if (bmat .eq. 'I') then call dcopy (n, resid, 1, workd(ipj), 1) end if 70 continue c c %---------------------------------------------------% c | Back from reverse communication if ORTH1 = .true. | c | WORKD(IPJ:IPJ+N-1) := B*r_{j}. | c %---------------------------------------------------% c if (bmat .eq. 'G') then call arscnd (t3) tmvbx = tmvbx + (t3 - t2) end if c orth1 = .false. c c %------------------------------% c | Compute the B-norm of r_{j}. | c %------------------------------% c if (bmat .eq. 'G') then rnorm = ddot (n, resid, 1, workd(ipj), 1) rnorm = sqrt(abs(rnorm)) else if (bmat .eq. 'I') then rnorm = dnrm2(n, resid, 1) end if c c %-----------------------------------------------------------% c | STEP 5: Re-orthogonalization / Iterative refinement phase | c | Maximum NITER_ITREF tries. | c | | c | s = V_{j}^T * B * r_{j} | c | r_{j} = r_{j} - V_{j}*s | c | alphaj = alphaj + s_{j} | c | | c | The stopping criteria used for iterative refinement is | c | discussed in Parlett's book SEP, page 107 and in Gragg & | c | Reichel ACM TOMS paper; Algorithm 686, Dec. 1990. | c | Determine if we need to correct the residual. The goal is | c | to enforce ||v(:,1:j)^T * r_{j}|| .le. eps * || r_{j} || | c %-----------------------------------------------------------% c if (rnorm .gt. 0.717*wnorm) go to 100 nrorth = nrorth + 1 c c %---------------------------------------------------% c | Enter the Iterative refinement phase. If further | c | refinement is necessary, loop back here. The loop | c | variable is ITER. Perform a step of Classical | c | Gram-Schmidt using all the Arnoldi vectors V_{j} | c %---------------------------------------------------% c 80 continue c if (msglvl .gt. 2) then xtemp(1) = wnorm xtemp(2) = rnorm call dvout (logfil, 2, xtemp, ndigit, & '_saitr: re-orthonalization ; wnorm and rnorm are') end if c c %----------------------------------------------------% c | Compute V_{j}^T * B * r_{j}. | c | WORKD(IRJ:IRJ+J-1) = v(:,1:J)'*WORKD(IPJ:IPJ+N-1). | c %----------------------------------------------------% c call dgemv ('T', n, j, one, v, ldv, workd(ipj), 1, & zero, workd(irj), 1) c c %----------------------------------------------% c | Compute the correction to the residual: | c | r_{j} = r_{j} - V_{j} * WORKD(IRJ:IRJ+J-1). | c | The correction to H is v(:,1:J)*H(1:J,1:J) + | c | v(:,1:J)*WORKD(IRJ:IRJ+J-1)*e'_j, but only | c | H(j,j) is updated. | c %----------------------------------------------% c call dgemv ('N', n, j, -one, v, ldv, workd(irj), 1, & one, resid, 1) c if (j .eq. 1 .or. rstart) h(j,1) = zero h(j,2) = h(j,2) + workd(irj + j - 1) c orth2 = .true. call arscnd (t2) if (bmat .eq. 'G') then nbx = nbx + 1 call dcopy (n, resid, 1, workd(irj), 1) ipntr(1) = irj ipntr(2) = ipj ido = 2 c c %-----------------------------------% c | Exit in order to compute B*r_{j}. | c | r_{j} is the corrected residual. | c %-----------------------------------% c go to 9000 else if (bmat .eq. 'I') then call dcopy (n, resid, 1, workd(ipj), 1) end if 90 continue c c %---------------------------------------------------% c | Back from reverse communication if ORTH2 = .true. | c %---------------------------------------------------% c if (bmat .eq. 'G') then call arscnd (t3) tmvbx = tmvbx + (t3 - t2) end if c c %-----------------------------------------------------% c | Compute the B-norm of the corrected residual r_{j}. | c %-----------------------------------------------------% c if (bmat .eq. 'G') then rnorm1 = ddot (n, resid, 1, workd(ipj), 1) rnorm1 = sqrt(abs(rnorm1)) else if (bmat .eq. 'I') then rnorm1 = dnrm2(n, resid, 1) end if c if (msglvl .gt. 0 .and. iter .gt. 0) then call ivout (logfil, 1, j, ndigit, & '_saitr: Iterative refinement for Arnoldi residual') if (msglvl .gt. 2) then xtemp(1) = rnorm xtemp(2) = rnorm1 call dvout (logfil, 2, xtemp, ndigit, & '_saitr: iterative refinement ; rnorm and rnorm1 are') end if end if c c %-----------------------------------------% c | Determine if we need to perform another | c | step of re-orthogonalization. | c %-----------------------------------------% c if (rnorm1 .gt. 0.717*rnorm) then c c %--------------------------------% c | No need for further refinement | c %--------------------------------% c rnorm = rnorm1 c else c c %-------------------------------------------% c | Another step of iterative refinement step | c | is required. NITREF is used by stat.h | c %-------------------------------------------% c nitref = nitref + 1 rnorm = rnorm1 iter = iter + 1 if (iter .le. 1) go to 80 c c %-------------------------------------------------% c | Otherwise RESID is numerically in the span of V | c %-------------------------------------------------% c do 95 jj = 1, n resid(jj) = zero 95 continue rnorm = zero end if c c %----------------------------------------------% c | Branch here directly if iterative refinement | c | wasn't necessary or after at most NITER_REF | c | steps of iterative refinement. | c %----------------------------------------------% c 100 continue c rstart = .false. orth2 = .false. c call arscnd (t5) titref = titref + (t5 - t4) c c %----------------------------------------------------------% c | Make sure the last off-diagonal element is non negative | c | If not perform a similarity transformation on H(1:j,1:j) | c | and scale v(:,j) by -1. | c %----------------------------------------------------------% c if (h(j,1) .lt. zero) then h(j,1) = -h(j,1) if ( j .lt. k+np) then call dscal(n, -one, v(1,j+1), 1) else call dscal(n, -one, resid, 1) end if end if c c %------------------------------------% c | STEP 6: Update j = j+1; Continue | c %------------------------------------% c j = j + 1 if (j .gt. k+np) then call arscnd (t1) tsaitr = tsaitr + (t1 - t0) ido = 99 c if (msglvl .gt. 1) then call dvout (logfil, k+np, h(1,2), ndigit, & '_saitr: main diagonal of matrix H of step K+NP.') if (k+np .gt. 1) then call dvout (logfil, k+np-1, h(2,1), ndigit, & '_saitr: sub diagonal of matrix H of step K+NP.') end if end if c go to 9000 end if c c %--------------------------------------------------------% c | Loop back to extend the factorization by another step. | c %--------------------------------------------------------% c go to 1000 c c %---------------------------------------------------------------% c | | c | E N D O F M A I N I T E R A T I O N L O O P | c | | c %---------------------------------------------------------------% c 9000 continue return c c %---------------% c | End of dsaitr | c %---------------% c end arpack-0.92.1/SRC/ssortc.f0000644000175000017500000002175210776001577012121 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: ssortc c c\Description: c Sorts the complex array in XREAL and XIMAG into the order c specified by WHICH and optionally applies the permutation to the c real array Y. It is assumed that if an element of XIMAG is c nonzero, then its negative is also an element. In other words, c both members of a complex conjugate pair are to be sorted and the c pairs are kept adjacent to each other. c c\Usage: c call ssortc c ( WHICH, APPLY, N, XREAL, XIMAG, Y ) c c\Arguments c WHICH Character*2. (Input) c 'LM' -> sort XREAL,XIMAG into increasing order of magnitude. c 'SM' -> sort XREAL,XIMAG into decreasing order of magnitude. c 'LR' -> sort XREAL into increasing order of algebraic. c 'SR' -> sort XREAL into decreasing order of algebraic. c 'LI' -> sort XIMAG into increasing order of magnitude. c 'SI' -> sort XIMAG into decreasing order of magnitude. c NOTE: If an element of XIMAG is non-zero, then its negative c is also an element. c c APPLY Logical. (Input) c APPLY = .TRUE. -> apply the sorted order to array Y. c APPLY = .FALSE. -> do not apply the sorted order to array Y. c c N Integer. (INPUT) c Size of the arrays. c c XREAL, Real array of length N. (INPUT/OUTPUT) c XIMAG Real and imaginary part of the array to be sorted. c c Y Real array of length N. (INPUT/OUTPUT) c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c xx/xx/92: Version ' 2.1' c Adapted from the sort routine in LANSO. c c\SCCS Information: @(#) c FILE: sortc.F SID: 2.3 DATE OF SID: 4/20/96 RELEASE: 2 c c\EndLib c c----------------------------------------------------------------------- c subroutine ssortc (which, apply, n, xreal, ximag, y) c c %------------------% c | Scalar Arguments | c %------------------% c character*2 which logical apply integer n c c %-----------------% c | Array Arguments | c %-----------------% c Real & xreal(0:n-1), ximag(0:n-1), y(0:n-1) c c %---------------% c | Local Scalars | c %---------------% c integer i, igap, j Real & temp, temp1, temp2 c c %--------------------% c | External Functions | c %--------------------% c Real & slapy2 external slapy2 c c %-----------------------% c | Executable Statements | c %-----------------------% c igap = n / 2 c if (which .eq. 'LM') then c c %------------------------------------------------------% c | Sort XREAL,XIMAG into increasing order of magnitude. | c %------------------------------------------------------% c 10 continue if (igap .eq. 0) go to 9000 c do 30 i = igap, n-1 j = i-igap 20 continue c if (j.lt.0) go to 30 c temp1 = slapy2(xreal(j),ximag(j)) temp2 = slapy2(xreal(j+igap),ximag(j+igap)) c if (temp1.gt.temp2) then temp = xreal(j) xreal(j) = xreal(j+igap) xreal(j+igap) = temp c temp = ximag(j) ximag(j) = ximag(j+igap) ximag(j+igap) = temp c if (apply) then temp = y(j) y(j) = y(j+igap) y(j+igap) = temp end if else go to 30 end if j = j-igap go to 20 30 continue igap = igap / 2 go to 10 c else if (which .eq. 'SM') then c c %------------------------------------------------------% c | Sort XREAL,XIMAG into decreasing order of magnitude. | c %------------------------------------------------------% c 40 continue if (igap .eq. 0) go to 9000 c do 60 i = igap, n-1 j = i-igap 50 continue c if (j .lt. 0) go to 60 c temp1 = slapy2(xreal(j),ximag(j)) temp2 = slapy2(xreal(j+igap),ximag(j+igap)) c if (temp1.lt.temp2) then temp = xreal(j) xreal(j) = xreal(j+igap) xreal(j+igap) = temp c temp = ximag(j) ximag(j) = ximag(j+igap) ximag(j+igap) = temp c if (apply) then temp = y(j) y(j) = y(j+igap) y(j+igap) = temp end if else go to 60 endif j = j-igap go to 50 60 continue igap = igap / 2 go to 40 c else if (which .eq. 'LR') then c c %------------------------------------------------% c | Sort XREAL into increasing order of algebraic. | c %------------------------------------------------% c 70 continue if (igap .eq. 0) go to 9000 c do 90 i = igap, n-1 j = i-igap 80 continue c if (j.lt.0) go to 90 c if (xreal(j).gt.xreal(j+igap)) then temp = xreal(j) xreal(j) = xreal(j+igap) xreal(j+igap) = temp c temp = ximag(j) ximag(j) = ximag(j+igap) ximag(j+igap) = temp c if (apply) then temp = y(j) y(j) = y(j+igap) y(j+igap) = temp end if else go to 90 endif j = j-igap go to 80 90 continue igap = igap / 2 go to 70 c else if (which .eq. 'SR') then c c %------------------------------------------------% c | Sort XREAL into decreasing order of algebraic. | c %------------------------------------------------% c 100 continue if (igap .eq. 0) go to 9000 do 120 i = igap, n-1 j = i-igap 110 continue c if (j.lt.0) go to 120 c if (xreal(j).lt.xreal(j+igap)) then temp = xreal(j) xreal(j) = xreal(j+igap) xreal(j+igap) = temp c temp = ximag(j) ximag(j) = ximag(j+igap) ximag(j+igap) = temp c if (apply) then temp = y(j) y(j) = y(j+igap) y(j+igap) = temp end if else go to 120 endif j = j-igap go to 110 120 continue igap = igap / 2 go to 100 c else if (which .eq. 'LI') then c c %------------------------------------------------% c | Sort XIMAG into increasing order of magnitude. | c %------------------------------------------------% c 130 continue if (igap .eq. 0) go to 9000 do 150 i = igap, n-1 j = i-igap 140 continue c if (j.lt.0) go to 150 c if (abs(ximag(j)).gt.abs(ximag(j+igap))) then temp = xreal(j) xreal(j) = xreal(j+igap) xreal(j+igap) = temp c temp = ximag(j) ximag(j) = ximag(j+igap) ximag(j+igap) = temp c if (apply) then temp = y(j) y(j) = y(j+igap) y(j+igap) = temp end if else go to 150 endif j = j-igap go to 140 150 continue igap = igap / 2 go to 130 c else if (which .eq. 'SI') then c c %------------------------------------------------% c | Sort XIMAG into decreasing order of magnitude. | c %------------------------------------------------% c 160 continue if (igap .eq. 0) go to 9000 do 180 i = igap, n-1 j = i-igap 170 continue c if (j.lt.0) go to 180 c if (abs(ximag(j)).lt.abs(ximag(j+igap))) then temp = xreal(j) xreal(j) = xreal(j+igap) xreal(j+igap) = temp c temp = ximag(j) ximag(j) = ximag(j+igap) ximag(j+igap) = temp c if (apply) then temp = y(j) y(j) = y(j+igap) y(j+igap) = temp end if else go to 180 endif j = j-igap go to 170 180 continue igap = igap / 2 go to 160 end if c 9000 continue return c c %---------------% c | End of ssortc | c %---------------% c end arpack-0.92.1/SRC/snconv.f0000644000175000017500000000764110776001577012113 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: snconv c c\Description: c Convergence testing for the nonsymmetric Arnoldi eigenvalue routine. c c\Usage: c call snconv c ( N, RITZR, RITZI, BOUNDS, TOL, NCONV ) c c\Arguments c N Integer. (INPUT) c Number of Ritz values to check for convergence. c c RITZR, Real arrays of length N. (INPUT) c RITZI Real and imaginary parts of the Ritz values to be checked c for convergence. c BOUNDS Real array of length N. (INPUT) c Ritz estimates for the Ritz values in RITZR and RITZI. c c TOL Real scalar. (INPUT) c Desired backward error for a Ritz value to be considered c "converged". c c NCONV Integer scalar. (OUTPUT) c Number of "converged" Ritz values. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx real c c\Routines called: c arscnd ARPACK utility routine for timing. c slamch LAPACK routine that determines machine constants. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c xx/xx/92: Version ' 2.1' c c\SCCS Information: @(#) c FILE: nconv.F SID: 2.3 DATE OF SID: 4/20/96 RELEASE: 2 c c\Remarks c 1. xxxx c c\EndLib c c----------------------------------------------------------------------- c subroutine snconv (n, ritzr, ritzi, bounds, tol, nconv) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c integer n, nconv Real & tol c c %-----------------% c | Array Arguments | c %-----------------% Real & ritzr(n), ritzi(n), bounds(n) c c %---------------% c | Local Scalars | c %---------------% c integer i Real & temp, eps23 c c %--------------------% c | External Functions | c %--------------------% c Real & slapy2, slamch external slapy2, slamch c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------------------------------------% c | Convergence test: unlike in the symmetric code, I am not | c | using things like refined error bounds and gap condition | c | because I don't know the exact equivalent concept. | c | | c | Instead the i-th Ritz value is considered "converged" when: | c | | c | bounds(i) .le. ( TOL * | ritz | ) | c | | c | for some appropriate choice of norm. | c %-------------------------------------------------------------% c call arscnd (t0) c c %---------------------------------% c | Get machine dependent constant. | c %---------------------------------% c eps23 = slamch('Epsilon-Machine') eps23 = eps23**(2.0E+0 / 3.0E+0) c nconv = 0 do 20 i = 1, n temp = max( eps23, slapy2( ritzr(i), ritzi(i) ) ) if (bounds(i) .le. tol*temp) nconv = nconv + 1 20 continue c call arscnd (t1) tnconv = tnconv + (t1 - t0) c return c c %---------------% c | End of snconv | c %---------------% c end arpack-0.92.1/SRC/dsesrt.f0000644000175000017500000001237010776001577012104 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: dsesrt c c\Description: c Sort the array X in the order specified by WHICH and optionally c apply the permutation to the columns of the matrix A. c c\Usage: c call dsesrt c ( WHICH, APPLY, N, X, NA, A, LDA) c c\Arguments c WHICH Character*2. (Input) c 'LM' -> X is sorted into increasing order of magnitude. c 'SM' -> X is sorted into decreasing order of magnitude. c 'LA' -> X is sorted into increasing order of algebraic. c 'SA' -> X is sorted into decreasing order of algebraic. c c APPLY Logical. (Input) c APPLY = .TRUE. -> apply the sorted order to A. c APPLY = .FALSE. -> do not apply the sorted order to A. c c N Integer. (INPUT) c Dimension of the array X. c c X Double precision array of length N. (INPUT/OUTPUT) c The array to be sorted. c c NA Integer. (INPUT) c Number of rows of the matrix A. c c A Double precision array of length NA by N. (INPUT/OUTPUT) c c LDA Integer. (INPUT) c Leading dimension of A. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Routines c dswap Level 1 BLAS that swaps the contents of two vectors. c c\Authors c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c 12/15/93: Version ' 2.1'. c Adapted from the sort routine in LANSO and c the ARPACK code dsortr c c\SCCS Information: @(#) c FILE: sesrt.F SID: 2.3 DATE OF SID: 4/19/96 RELEASE: 2 c c\EndLib c c----------------------------------------------------------------------- c subroutine dsesrt (which, apply, n, x, na, a, lda) c c %------------------% c | Scalar Arguments | c %------------------% c character*2 which logical apply integer lda, n, na c c %-----------------% c | Array Arguments | c %-----------------% c Double precision & x(0:n-1), a(lda, 0:n-1) c c %---------------% c | Local Scalars | c %---------------% c integer i, igap, j Double precision & temp c c %----------------------% c | External Subroutines | c %----------------------% c external dswap c c %-----------------------% c | Executable Statements | c %-----------------------% c igap = n / 2 c if (which .eq. 'SA') then c c X is sorted into decreasing order of algebraic. c 10 continue if (igap .eq. 0) go to 9000 do 30 i = igap, n-1 j = i-igap 20 continue c if (j.lt.0) go to 30 c if (x(j).lt.x(j+igap)) then temp = x(j) x(j) = x(j+igap) x(j+igap) = temp if (apply) call dswap( na, a(1, j), 1, a(1,j+igap), 1) else go to 30 endif j = j-igap go to 20 30 continue igap = igap / 2 go to 10 c else if (which .eq. 'SM') then c c X is sorted into decreasing order of magnitude. c 40 continue if (igap .eq. 0) go to 9000 do 60 i = igap, n-1 j = i-igap 50 continue c if (j.lt.0) go to 60 c if (abs(x(j)).lt.abs(x(j+igap))) then temp = x(j) x(j) = x(j+igap) x(j+igap) = temp if (apply) call dswap( na, a(1, j), 1, a(1,j+igap), 1) else go to 60 endif j = j-igap go to 50 60 continue igap = igap / 2 go to 40 c else if (which .eq. 'LA') then c c X is sorted into increasing order of algebraic. c 70 continue if (igap .eq. 0) go to 9000 do 90 i = igap, n-1 j = i-igap 80 continue c if (j.lt.0) go to 90 c if (x(j).gt.x(j+igap)) then temp = x(j) x(j) = x(j+igap) x(j+igap) = temp if (apply) call dswap( na, a(1, j), 1, a(1,j+igap), 1) else go to 90 endif j = j-igap go to 80 90 continue igap = igap / 2 go to 70 c else if (which .eq. 'LM') then c c X is sorted into increasing order of magnitude. c 100 continue if (igap .eq. 0) go to 9000 do 120 i = igap, n-1 j = i-igap 110 continue c if (j.lt.0) go to 120 c if (abs(x(j)).gt.abs(x(j+igap))) then temp = x(j) x(j) = x(j+igap) x(j+igap) = temp if (apply) call dswap( na, a(1, j), 1, a(1,j+igap), 1) else go to 120 endif j = j-igap go to 110 120 continue igap = igap / 2 go to 100 end if c 9000 continue return c c %---------------% c | End of dsesrt | c %---------------% c end arpack-0.92.1/SRC/zngets.f0000644000175000017500000001271210776001577012112 00000000000000c\BeginDoc c c\Name: zngets c c\Description: c Given the eigenvalues of the upper Hessenberg matrix H, c computes the NP shifts AMU that are zeros of the polynomial of c degree NP which filters out components of the unwanted eigenvectors c corresponding to the AMU's based on some given criteria. c c NOTE: call this even in the case of user specified shifts in order c to sort the eigenvalues, and error bounds of H for later use. c c\Usage: c call zngets c ( ISHIFT, WHICH, KEV, NP, RITZ, BOUNDS ) c c\Arguments c ISHIFT Integer. (INPUT) c Method for selecting the implicit shifts at each iteration. c ISHIFT = 0: user specified shifts c ISHIFT = 1: exact shift with respect to the matrix H. c c WHICH Character*2. (INPUT) c Shift selection criteria. c 'LM' -> want the KEV eigenvalues of largest magnitude. c 'SM' -> want the KEV eigenvalues of smallest magnitude. c 'LR' -> want the KEV eigenvalues of largest REAL part. c 'SR' -> want the KEV eigenvalues of smallest REAL part. c 'LI' -> want the KEV eigenvalues of largest imaginary part. c 'SI' -> want the KEV eigenvalues of smallest imaginary part. c c KEV Integer. (INPUT) c The number of desired eigenvalues. c c NP Integer. (INPUT) c The number of shifts to compute. c c RITZ Complex*16 array of length KEV+NP. (INPUT/OUTPUT) c On INPUT, RITZ contains the the eigenvalues of H. c On OUTPUT, RITZ are sorted so that the unwanted c eigenvalues are in the first NP locations and the wanted c portion is in the last KEV locations. When exact shifts are c selected, the unwanted part corresponds to the shifts to c be applied. Also, if ISHIFT .eq. 1, the unwanted eigenvalues c are further sorted so that the ones with largest Ritz values c are first. c c BOUNDS Complex*16 array of length KEV+NP. (INPUT/OUTPUT) c Error bounds corresponding to the ordering in RITZ. c c c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx Complex*16 c c\Routines called: c zsortc ARPACK sorting routine. c ivout ARPACK utility routine that prints integers. c arscnd ARPACK utility routine for timing. c zvout ARPACK utility routine that prints vectors. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: ngets.F SID: 2.2 DATE OF SID: 4/20/96 RELEASE: 2 c c\Remarks c 1. This routine does not keep complex conjugate pairs of c eigenvalues together. c c\EndLib c c----------------------------------------------------------------------- c subroutine zngets ( ishift, which, kev, np, ritz, bounds) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character*2 which integer ishift, kev, np c c %-----------------% c | Array Arguments | c %-----------------% c Complex*16 & bounds(kev+np), ritz(kev+np) c c %------------% c | Parameters | c %------------% c Complex*16 & one, zero parameter (one = (1.0D+0, 0.0D+0), zero = (0.0D+0, 0.0D+0)) c c %---------------% c | Local Scalars | c %---------------% c integer msglvl c c %----------------------% c | External Subroutines | c %----------------------% c external zvout, zsortc, arscnd c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call arscnd (t0) msglvl = mcgets c call zsortc (which, .true., kev+np, ritz, bounds) c if ( ishift .eq. 1 ) then c c %-------------------------------------------------------% c | Sort the unwanted Ritz values used as shifts so that | c | the ones with largest Ritz estimates are first | c | This will tend to minimize the effects of the | c | forward instability of the iteration when the shifts | c | are applied in subroutine znapps. | c | Be careful and use 'SM' since we want to sort BOUNDS! | c %-------------------------------------------------------% c call zsortc ( 'SM', .true., np, bounds, ritz ) c end if c call arscnd (t1) tcgets = tcgets + (t1 - t0) c if (msglvl .gt. 0) then call ivout (logfil, 1, kev, ndigit, '_ngets: KEV is') call ivout (logfil, 1, np, ndigit, '_ngets: NP is') call zvout (logfil, kev+np, ritz, ndigit, & '_ngets: Eigenvalues of current H matrix ') call zvout (logfil, kev+np, bounds, ndigit, & '_ngets: Ritz estimates of the current KEV+NP Ritz values') end if c return c c %---------------% c | End of zngets | c %---------------% c end arpack-0.92.1/SRC/ssapps.f0000644000175000017500000004373210776001577012117 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: ssapps c c\Description: c Given the Arnoldi factorization c c A*V_{k} - V_{k}*H_{k} = r_{k+p}*e_{k+p}^T, c c apply NP shifts implicitly resulting in c c A*(V_{k}*Q) - (V_{k}*Q)*(Q^T* H_{k}*Q) = r_{k+p}*e_{k+p}^T * Q c c where Q is an orthogonal matrix of order KEV+NP. Q is the product of c rotations resulting from the NP bulge chasing sweeps. The updated Arnoldi c factorization becomes: c c A*VNEW_{k} - VNEW_{k}*HNEW_{k} = rnew_{k}*e_{k}^T. c c\Usage: c call ssapps c ( N, KEV, NP, SHIFT, V, LDV, H, LDH, RESID, Q, LDQ, WORKD ) c c\Arguments c N Integer. (INPUT) c Problem size, i.e. dimension of matrix A. c c KEV Integer. (INPUT) c INPUT: KEV+NP is the size of the input matrix H. c OUTPUT: KEV is the size of the updated matrix HNEW. c c NP Integer. (INPUT) c Number of implicit shifts to be applied. c c SHIFT Real array of length NP. (INPUT) c The shifts to be applied. c c V Real N by (KEV+NP) array. (INPUT/OUTPUT) c INPUT: V contains the current KEV+NP Arnoldi vectors. c OUTPUT: VNEW = V(1:n,1:KEV); the updated Arnoldi vectors c are in the first KEV columns of V. c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling c program. c c H Real (KEV+NP) by 2 array. (INPUT/OUTPUT) c INPUT: H contains the symmetric tridiagonal matrix of the c Arnoldi factorization with the subdiagonal in the 1st column c starting at H(2,1) and the main diagonal in the 2nd column. c OUTPUT: H contains the updated tridiagonal matrix in the c KEV leading submatrix. c c LDH Integer. (INPUT) c Leading dimension of H exactly as declared in the calling c program. c c RESID Real array of length (N). (INPUT/OUTPUT) c INPUT: RESID contains the the residual vector r_{k+p}. c OUTPUT: RESID is the updated residual vector rnew_{k}. c c Q Real KEV+NP by KEV+NP work array. (WORKSPACE) c Work array used to accumulate the rotations during the bulge c chase sweep. c c LDQ Integer. (INPUT) c Leading dimension of Q exactly as declared in the calling c program. c c WORKD Real work array of length 2*N. (WORKSPACE) c Distributed array used in the application of the accumulated c orthogonal matrix Q. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx real c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly c Restarted Arnoldi Iteration", Rice University Technical Report c TR95-13, Department of Computational and Applied Mathematics. c c\Routines called: c ivout ARPACK utility routine that prints integers. c arscnd ARPACK utility routine for timing. c svout ARPACK utility routine that prints vectors. c slamch LAPACK routine that determines machine constants. c slartg LAPACK Givens rotation construction routine. c slacpy LAPACK matrix copy routine. c slaset LAPACK matrix initialization routine. c sgemv Level 2 BLAS routine for matrix vector multiplication. c saxpy Level 1 BLAS that computes a vector triad. c scopy Level 1 BLAS that copies one vector to another. c sscal Level 1 BLAS that scales a vector. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c 12/16/93: Version ' 2.4' c c\SCCS Information: @(#) c FILE: sapps.F SID: 2.6 DATE OF SID: 3/28/97 RELEASE: 2 c c\Remarks c 1. In this version, each shift is applied to all the subblocks of c the tridiagonal matrix H and not just to the submatrix that it c comes from. This routine assumes that the subdiagonal elements c of H that are stored in h(1:kev+np,1) are nonegative upon input c and enforce this condition upon output. This version incorporates c deflation. See code for documentation. c c\EndLib c c----------------------------------------------------------------------- c subroutine ssapps & ( n, kev, np, shift, v, ldv, h, ldh, resid, q, ldq, workd ) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c integer kev, ldh, ldq, ldv, n, np c c %-----------------% c | Array Arguments | c %-----------------% c Real & h(ldh,2), q(ldq,kev+np), resid(n), shift(np), & v(ldv,kev+np), workd(2*n) c c %------------% c | Parameters | c %------------% c Real & one, zero parameter (one = 1.0E+0, zero = 0.0E+0) c c %---------------% c | Local Scalars | c %---------------% c integer i, iend, istart, itop, j, jj, kplusp, msglvl logical first Real & a1, a2, a3, a4, big, c, epsmch, f, g, r, s save epsmch, first c c c %----------------------% c | External Subroutines | c %----------------------% c external saxpy, scopy, sscal, slacpy, slartg, slaset, svout, & ivout, arscnd, sgemv c c %--------------------% c | External Functions | c %--------------------% c Real & slamch external slamch c c %----------------------% c | Intrinsics Functions | c %----------------------% c intrinsic abs c c %----------------% c | Data statments | c %----------------% c data first / .true. / c c %-----------------------% c | Executable Statements | c %-----------------------% c if (first) then epsmch = slamch('Epsilon-Machine') first = .false. end if itop = 1 c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call arscnd (t0) msglvl = msapps c kplusp = kev + np c c %----------------------------------------------% c | Initialize Q to the identity matrix of order | c | kplusp used to accumulate the rotations. | c %----------------------------------------------% c call slaset ('All', kplusp, kplusp, zero, one, q, ldq) c c %----------------------------------------------% c | Quick return if there are no shifts to apply | c %----------------------------------------------% c if (np .eq. 0) go to 9000 c c %----------------------------------------------------------% c | Apply the np shifts implicitly. Apply each shift to the | c | whole matrix and not just to the submatrix from which it | c | comes. | c %----------------------------------------------------------% c do 90 jj = 1, np c istart = itop c c %----------------------------------------------------------% c | Check for splitting and deflation. Currently we consider | c | an off-diagonal element h(i+1,1) negligible if | c | h(i+1,1) .le. epsmch*( |h(i,2)| + |h(i+1,2)| ) | c | for i=1:KEV+NP-1. | c | If above condition tests true then we set h(i+1,1) = 0. | c | Note that h(1:KEV+NP,1) are assumed to be non negative. | c %----------------------------------------------------------% c 20 continue c c %------------------------------------------------% c | The following loop exits early if we encounter | c | a negligible off diagonal element. | c %------------------------------------------------% c do 30 i = istart, kplusp-1 big = abs(h(i,2)) + abs(h(i+1,2)) if (h(i+1,1) .le. epsmch*big) then if (msglvl .gt. 0) then call ivout (logfil, 1, i, ndigit, & '_sapps: deflation at row/column no.') call ivout (logfil, 1, jj, ndigit, & '_sapps: occured before shift number.') call svout (logfil, 1, h(i+1,1), ndigit, & '_sapps: the corresponding off diagonal element') end if h(i+1,1) = zero iend = i go to 40 end if 30 continue iend = kplusp 40 continue c if (istart .lt. iend) then c c %--------------------------------------------------------% c | Construct the plane rotation G'(istart,istart+1,theta) | c | that attempts to drive h(istart+1,1) to zero. | c %--------------------------------------------------------% c f = h(istart,2) - shift(jj) g = h(istart+1,1) call slartg (f, g, c, s, r) c c %-------------------------------------------------------% c | Apply rotation to the left and right of H; | c | H <- G' * H * G, where G = G(istart,istart+1,theta). | c | This will create a "bulge". | c %-------------------------------------------------------% c a1 = c*h(istart,2) + s*h(istart+1,1) a2 = c*h(istart+1,1) + s*h(istart+1,2) a4 = c*h(istart+1,2) - s*h(istart+1,1) a3 = c*h(istart+1,1) - s*h(istart,2) h(istart,2) = c*a1 + s*a2 h(istart+1,2) = c*a4 - s*a3 h(istart+1,1) = c*a3 + s*a4 c c %----------------------------------------------------% c | Accumulate the rotation in the matrix Q; Q <- Q*G | c %----------------------------------------------------% c do 60 j = 1, min(istart+jj,kplusp) a1 = c*q(j,istart) + s*q(j,istart+1) q(j,istart+1) = - s*q(j,istart) + c*q(j,istart+1) q(j,istart) = a1 60 continue c c c %----------------------------------------------% c | The following loop chases the bulge created. | c | Note that the previous rotation may also be | c | done within the following loop. But it is | c | kept separate to make the distinction among | c | the bulge chasing sweeps and the first plane | c | rotation designed to drive h(istart+1,1) to | c | zero. | c %----------------------------------------------% c do 70 i = istart+1, iend-1 c c %----------------------------------------------% c | Construct the plane rotation G'(i,i+1,theta) | c | that zeros the i-th bulge that was created | c | by G(i-1,i,theta). g represents the bulge. | c %----------------------------------------------% c f = h(i,1) g = s*h(i+1,1) c c %----------------------------------% c | Final update with G(i-1,i,theta) | c %----------------------------------% c h(i+1,1) = c*h(i+1,1) call slartg (f, g, c, s, r) c c %-------------------------------------------% c | The following ensures that h(1:iend-1,1), | c | the first iend-2 off diagonal of elements | c | H, remain non negative. | c %-------------------------------------------% c if (r .lt. zero) then r = -r c = -c s = -s end if c c %--------------------------------------------% c | Apply rotation to the left and right of H; | c | H <- G * H * G', where G = G(i,i+1,theta) | c %--------------------------------------------% c h(i,1) = r c a1 = c*h(i,2) + s*h(i+1,1) a2 = c*h(i+1,1) + s*h(i+1,2) a3 = c*h(i+1,1) - s*h(i,2) a4 = c*h(i+1,2) - s*h(i+1,1) c h(i,2) = c*a1 + s*a2 h(i+1,2) = c*a4 - s*a3 h(i+1,1) = c*a3 + s*a4 c c %----------------------------------------------------% c | Accumulate the rotation in the matrix Q; Q <- Q*G | c %----------------------------------------------------% c do 50 j = 1, min( i+jj, kplusp ) a1 = c*q(j,i) + s*q(j,i+1) q(j,i+1) = - s*q(j,i) + c*q(j,i+1) q(j,i) = a1 50 continue c 70 continue c end if c c %--------------------------% c | Update the block pointer | c %--------------------------% c istart = iend + 1 c c %------------------------------------------% c | Make sure that h(iend,1) is non-negative | c | If not then set h(iend,1) <-- -h(iend,1) | c | and negate the last column of Q. | c | We have effectively carried out a | c | similarity on transformation H | c %------------------------------------------% c if (h(iend,1) .lt. zero) then h(iend,1) = -h(iend,1) call sscal(kplusp, -one, q(1,iend), 1) end if c c %--------------------------------------------------------% c | Apply the same shift to the next block if there is any | c %--------------------------------------------------------% c if (iend .lt. kplusp) go to 20 c c %-----------------------------------------------------% c | Check if we can increase the the start of the block | c %-----------------------------------------------------% c do 80 i = itop, kplusp-1 if (h(i+1,1) .gt. zero) go to 90 itop = itop + 1 80 continue c c %-----------------------------------% c | Finished applying the jj-th shift | c %-----------------------------------% c 90 continue c c %------------------------------------------% c | All shifts have been applied. Check for | c | more possible deflation that might occur | c | after the last shift is applied. | c %------------------------------------------% c do 100 i = itop, kplusp-1 big = abs(h(i,2)) + abs(h(i+1,2)) if (h(i+1,1) .le. epsmch*big) then if (msglvl .gt. 0) then call ivout (logfil, 1, i, ndigit, & '_sapps: deflation at row/column no.') call svout (logfil, 1, h(i+1,1), ndigit, & '_sapps: the corresponding off diagonal element') end if h(i+1,1) = zero end if 100 continue c c %-------------------------------------------------% c | Compute the (kev+1)-st column of (V*Q) and | c | temporarily store the result in WORKD(N+1:2*N). | c | This is not necessary if h(kev+1,1) = 0. | c %-------------------------------------------------% c if ( h(kev+1,1) .gt. zero ) & call sgemv ('N', n, kplusp, one, v, ldv, & q(1,kev+1), 1, zero, workd(n+1), 1) c c %-------------------------------------------------------% c | Compute column 1 to kev of (V*Q) in backward order | c | taking advantage that Q is an upper triangular matrix | c | with lower bandwidth np. | c | Place results in v(:,kplusp-kev:kplusp) temporarily. | c %-------------------------------------------------------% c do 130 i = 1, kev call sgemv ('N', n, kplusp-i+1, one, v, ldv, & q(1,kev-i+1), 1, zero, workd, 1) call scopy (n, workd, 1, v(1,kplusp-i+1), 1) 130 continue c c %-------------------------------------------------% c | Move v(:,kplusp-kev+1:kplusp) into v(:,1:kev). | c %-------------------------------------------------% c call slacpy ('All', n, kev, v(1,np+1), ldv, v, ldv) c c %--------------------------------------------% c | Copy the (kev+1)-st column of (V*Q) in the | c | appropriate place if h(kev+1,1) .ne. zero. | c %--------------------------------------------% c if ( h(kev+1,1) .gt. zero ) & call scopy (n, workd(n+1), 1, v(1,kev+1), 1) c c %-------------------------------------% c | Update the residual vector: | c | r <- sigmak*r + betak*v(:,kev+1) | c | where | c | sigmak = (e_{kev+p}'*Q)*e_{kev} | c | betak = e_{kev+1}'*H*e_{kev} | c %-------------------------------------% c call sscal (n, q(kplusp,kev), resid, 1) if (h(kev+1,1) .gt. zero) & call saxpy (n, h(kev+1,1), v(1,kev+1), 1, resid, 1) c if (msglvl .gt. 1) then call svout (logfil, 1, q(kplusp,kev), ndigit, & '_sapps: sigmak of the updated residual vector') call svout (logfil, 1, h(kev+1,1), ndigit, & '_sapps: betak of the updated residual vector') call svout (logfil, kev, h(1,2), ndigit, & '_sapps: updated main diagonal of H for next iteration') if (kev .gt. 1) then call svout (logfil, kev-1, h(2,1), ndigit, & '_sapps: updated sub diagonal of H for next iteration') end if end if c call arscnd (t1) tsapps = tsapps + (t1 - t0) c 9000 continue return c c %---------------% c | End of ssapps | c %---------------% c end arpack-0.92.1/SRC/cnaupd.f0000644000175000017500000006615210776001577012061 00000000000000c\BeginDoc c c\Name: cnaupd c c\Description: c Reverse communication interface for the Implicitly Restarted Arnoldi c iteration. This is intended to be used to find a few eigenpairs of a c complex linear operator OP with respect to a semi-inner product defined c by a hermitian positive semi-definite real matrix B. B may be the identity c matrix. NOTE: if both OP and B are real, then ssaupd or snaupd should c be used. c c c The computed approximate eigenvalues are called Ritz values and c the corresponding approximate eigenvectors are called Ritz vectors. c c cnaupd is usually called iteratively to solve one of the c following problems: c c Mode 1: A*x = lambda*x. c ===> OP = A and B = I. c c Mode 2: A*x = lambda*M*x, M hermitian positive definite c ===> OP = inv[M]*A and B = M. c ===> (If M can be factored see remark 3 below) c c Mode 3: A*x = lambda*M*x, M hermitian semi-definite c ===> OP = inv[A - sigma*M]*M and B = M. c ===> shift-and-invert mode c If OP*x = amu*x, then lambda = sigma + 1/amu. c c c NOTE: The action of w <- inv[A - sigma*M]*v or w <- inv[M]*v c should be accomplished either by a direct method c using a sparse matrix factorization and solving c c [A - sigma*M]*w = v or M*w = v, c c or through an iterative method for solving these c systems. If an iterative method is used, the c convergence test must be more stringent than c the accuracy requirements for the eigenvalue c approximations. c c\Usage: c call cnaupd c ( IDO, BMAT, N, WHICH, NEV, TOL, RESID, NCV, V, LDV, IPARAM, c IPNTR, WORKD, WORKL, LWORKL, RWORK, INFO ) c c\Arguments c IDO Integer. (INPUT/OUTPUT) c Reverse communication flag. IDO must be zero on the first c call to cnaupd. IDO will be set internally to c indicate the type of operation to be performed. Control is c then given back to the calling routine which has the c responsibility to carry out the requested operation and call c cnaupd with the result. The operand is given in c WORKD(IPNTR(1)), the result must be put in WORKD(IPNTR(2)). c ------------------------------------------------------------- c IDO = 0: first call to the reverse communication interface c IDO = -1: compute Y = OP * X where c IPNTR(1) is the pointer into WORKD for X, c IPNTR(2) is the pointer into WORKD for Y. c This is for the initialization phase to force the c starting vector into the range of OP. c IDO = 1: compute Y = OP * X where c IPNTR(1) is the pointer into WORKD for X, c IPNTR(2) is the pointer into WORKD for Y. c In mode 3, the vector B * X is already c available in WORKD(ipntr(3)). It does not c need to be recomputed in forming OP * X. c IDO = 2: compute Y = M * X where c IPNTR(1) is the pointer into WORKD for X, c IPNTR(2) is the pointer into WORKD for Y. c IDO = 3: compute and return the shifts in the first c NP locations of WORKL. c IDO = 99: done c ------------------------------------------------------------- c After the initialization phase, when the routine is used in c the "shift-and-invert" mode, the vector M * X is already c available and does not need to be recomputed in forming OP*X. c c BMAT Character*1. (INPUT) c BMAT specifies the type of the matrix B that defines the c semi-inner product for the operator OP. c BMAT = 'I' -> standard eigenvalue problem A*x = lambda*x c BMAT = 'G' -> generalized eigenvalue problem A*x = lambda*M*x c c N Integer. (INPUT) c Dimension of the eigenproblem. c c WHICH Character*2. (INPUT) c 'LM' -> want the NEV eigenvalues of largest magnitude. c 'SM' -> want the NEV eigenvalues of smallest magnitude. c 'LR' -> want the NEV eigenvalues of largest real part. c 'SR' -> want the NEV eigenvalues of smallest real part. c 'LI' -> want the NEV eigenvalues of largest imaginary part. c 'SI' -> want the NEV eigenvalues of smallest imaginary part. c c NEV Integer. (INPUT) c Number of eigenvalues of OP to be computed. 0 < NEV < N-1. c c TOL Real scalar. (INPUT) c Stopping criteria: the relative accuracy of the Ritz value c is considered acceptable if BOUNDS(I) .LE. TOL*ABS(RITZ(I)) c where ABS(RITZ(I)) is the magnitude when RITZ(I) is complex. c DEFAULT = slamch('EPS') (machine precision as computed c by the LAPACK auxiliary subroutine slamch). c c RESID Complex array of length N. (INPUT/OUTPUT) c On INPUT: c If INFO .EQ. 0, a random initial residual vector is used. c If INFO .NE. 0, RESID contains the initial residual vector, c possibly from a previous run. c On OUTPUT: c RESID contains the final residual vector. c c NCV Integer. (INPUT) c Number of columns of the matrix V. NCV must satisfy the two c inequalities 1 <= NCV-NEV and NCV <= N. c This will indicate how many Arnoldi vectors are generated c at each iteration. After the startup phase in which NEV c Arnoldi vectors are generated, the algorithm generates c approximately NCV-NEV Arnoldi vectors at each subsequent update c iteration. Most of the cost in generating each Arnoldi vector is c in the matrix-vector operation OP*x. (See remark 4 below.) c c V Complex array N by NCV. (OUTPUT) c Contains the final set of Arnoldi basis vectors. c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling program. c c IPARAM Integer array of length 11. (INPUT/OUTPUT) c IPARAM(1) = ISHIFT: method for selecting the implicit shifts. c The shifts selected at each iteration are used to filter out c the components of the unwanted eigenvector. c ------------------------------------------------------------- c ISHIFT = 0: the shifts are to be provided by the user via c reverse communication. The NCV eigenvalues of c the Hessenberg matrix H are returned in the part c of WORKL array corresponding to RITZ. c ISHIFT = 1: exact shifts with respect to the current c Hessenberg matrix H. This is equivalent to c restarting the iteration from the beginning c after updating the starting vector with a linear c combination of Ritz vectors associated with the c "wanted" eigenvalues. c ISHIFT = 2: other choice of internal shift to be defined. c ------------------------------------------------------------- c c IPARAM(2) = No longer referenced c c IPARAM(3) = MXITER c On INPUT: maximum number of Arnoldi update iterations allowed. c On OUTPUT: actual number of Arnoldi update iterations taken. c c IPARAM(4) = NB: blocksize to be used in the recurrence. c The code currently works only for NB = 1. c c IPARAM(5) = NCONV: number of "converged" Ritz values. c This represents the number of Ritz values that satisfy c the convergence criterion. c c IPARAM(6) = IUPD c No longer referenced. Implicit restarting is ALWAYS used. c c IPARAM(7) = MODE c On INPUT determines what type of eigenproblem is being solved. c Must be 1,2,3; See under \Description of cnaupd for the c four modes available. c c IPARAM(8) = NP c When ido = 3 and the user provides shifts through reverse c communication (IPARAM(1)=0), _naupd returns NP, the number c of shifts the user is to provide. 0 < NP < NCV-NEV. c c IPARAM(9) = NUMOP, IPARAM(10) = NUMOPB, IPARAM(11) = NUMREO, c OUTPUT: NUMOP = total number of OP*x operations, c NUMOPB = total number of B*x operations if BMAT='G', c NUMREO = total number of steps of re-orthogonalization. c c IPNTR Integer array of length 14. (OUTPUT) c Pointer to mark the starting locations in the WORKD and WORKL c arrays for matrices/vectors used by the Arnoldi iteration. c ------------------------------------------------------------- c IPNTR(1): pointer to the current operand vector X in WORKD. c IPNTR(2): pointer to the current result vector Y in WORKD. c IPNTR(3): pointer to the vector B * X in WORKD when used in c the shift-and-invert mode. c IPNTR(4): pointer to the next available location in WORKL c that is untouched by the program. c IPNTR(5): pointer to the NCV by NCV upper Hessenberg c matrix H in WORKL. c IPNTR(6): pointer to the ritz value array RITZ c IPNTR(7): pointer to the (projected) ritz vector array Q c IPNTR(8): pointer to the error BOUNDS array in WORKL. c IPNTR(14): pointer to the NP shifts in WORKL. See Remark 5 below. c c Note: IPNTR(9:13) is only referenced by cneupd. See Remark 2 below. c c IPNTR(9): pointer to the NCV RITZ values of the c original system. c IPNTR(10): Not Used c IPNTR(11): pointer to the NCV corresponding error bounds. c IPNTR(12): pointer to the NCV by NCV upper triangular c Schur matrix for H. c IPNTR(13): pointer to the NCV by NCV matrix of eigenvectors c of the upper Hessenberg matrix H. Only referenced by c cneupd if RVEC = .TRUE. See Remark 2 below. c c ------------------------------------------------------------- c c WORKD Complex work array of length 3*N. (REVERSE COMMUNICATION) c Distributed array to be used in the basic Arnoldi iteration c for reverse communication. The user should not use WORKD c as temporary workspace during the iteration !!!!!!!!!! c See Data Distribution Note below. c c WORKL Complex work array of length LWORKL. (OUTPUT/WORKSPACE) c Private (replicated) array on each PE or array allocated on c the front end. See Data Distribution Note below. c c LWORKL Integer. (INPUT) c LWORKL must be at least 3*NCV**2 + 5*NCV. c c RWORK Real work array of length NCV (WORKSPACE) c Private (replicated) array on each PE or array allocated on c the front end. c c c INFO Integer. (INPUT/OUTPUT) c If INFO .EQ. 0, a randomly initial residual vector is used. c If INFO .NE. 0, RESID contains the initial residual vector, c possibly from a previous run. c Error flag on output. c = 0: Normal exit. c = 1: Maximum number of iterations taken. c All possible eigenvalues of OP has been found. IPARAM(5) c returns the number of wanted converged Ritz values. c = 2: No longer an informational error. Deprecated starting c with release 2 of ARPACK. c = 3: No shifts could be applied during a cycle of the c Implicitly restarted Arnoldi iteration. One possibility c is to increase the size of NCV relative to NEV. c See remark 4 below. c = -1: N must be positive. c = -2: NEV must be positive. c = -3: NCV-NEV >= 1 and less than or equal to N. c = -4: The maximum number of Arnoldi update iteration c must be greater than zero. c = -5: WHICH must be one of 'LM', 'SM', 'LR', 'SR', 'LI', 'SI' c = -6: BMAT must be one of 'I' or 'G'. c = -7: Length of private work array is not sufficient. c = -8: Error return from LAPACK eigenvalue calculation; c = -9: Starting vector is zero. c = -10: IPARAM(7) must be 1,2,3. c = -11: IPARAM(7) = 1 and BMAT = 'G' are incompatible. c = -12: IPARAM(1) must be equal to 0 or 1. c = -9999: Could not build an Arnoldi factorization. c User input error highly likely. Please c check actual array dimensions and layout. c IPARAM(5) returns the size of the current Arnoldi c factorization. c c\Remarks c 1. The computed Ritz values are approximate eigenvalues of OP. The c selection of WHICH should be made with this in mind when using c Mode = 3. When operating in Mode = 3 setting WHICH = 'LM' will c compute the NEV eigenvalues of the original problem that are c closest to the shift SIGMA . After convergence, approximate eigenvalues c of the original problem may be obtained with the ARPACK subroutine cneupd. c c 2. If a basis for the invariant subspace corresponding to the converged Ritz c values is needed, the user must call cneupd immediately following c completion of cnaupd. This is new starting with release 2 of ARPACK. c c 3. If M can be factored into a Cholesky factorization M = LL` c then Mode = 2 should not be selected. Instead one should use c Mode = 1 with OP = inv(L)*A*inv(L`). Appropriate triangular c linear systems should be solved with L and L` rather c than computing inverses. After convergence, an approximate c eigenvector z of the original problem is recovered by solving c L`z = x where x is a Ritz vector of OP. c c 4. At present there is no a-priori analysis to guide the selection c of NCV relative to NEV. The only formal requirement is that NCV > NEV + 1. c However, it is recommended that NCV .ge. 2*NEV. If many problems of c the same type are to be solved, one should experiment with increasing c NCV while keeping NEV fixed for a given test problem. This will c usually decrease the required number of OP*x operations but it c also increases the work and storage required to maintain the orthogonal c basis vectors. The optimal "cross-over" with respect to CPU time c is problem dependent and must be determined empirically. c See Chapter 8 of Reference 2 for further information. c c 5. When IPARAM(1) = 0, and IDO = 3, the user needs to provide the c NP = IPARAM(8) complex shifts in locations c WORKL(IPNTR(14)), WORKL(IPNTR(14)+1), ... , WORKL(IPNTR(14)+NP). c Eigenvalues of the current upper Hessenberg matrix are located in c WORKL(IPNTR(6)) through WORKL(IPNTR(6)+NCV-1). They are ordered c according to the order defined by WHICH. The associated Ritz estimates c are located in WORKL(IPNTR(8)), WORKL(IPNTR(8)+1), ... , c WORKL(IPNTR(8)+NCV-1). c c----------------------------------------------------------------------- c c\Data Distribution Note: c c Fortran-D syntax: c ================ c Complex resid(n), v(ldv,ncv), workd(3*n), workl(lworkl) c decompose d1(n), d2(n,ncv) c align resid(i) with d1(i) c align v(i,j) with d2(i,j) c align workd(i) with d1(i) range (1:n) c align workd(i) with d1(i-n) range (n+1:2*n) c align workd(i) with d1(i-2*n) range (2*n+1:3*n) c distribute d1(block), d2(block,:) c replicated workl(lworkl) c c Cray MPP syntax: c =============== c Complex resid(n), v(ldv,ncv), workd(n,3), workl(lworkl) c shared resid(block), v(block,:), workd(block,:) c replicated workl(lworkl) c c CM2/CM5 syntax: c ============== c c----------------------------------------------------------------------- c c include 'ex-nonsym.doc' c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx Complex c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly c Restarted Arnoldi Iteration", Rice University Technical Report c TR95-13, Department of Computational and Applied Mathematics. c 3. B.N. Parlett & Y. Saad, "_Complex_ Shift and Invert Strategies for c Real Matrices", Linear Algebra and its Applications, vol 88/89, c pp 575-595, (1987). c c\Routines called: c cnaup2 ARPACK routine that implements the Implicitly Restarted c Arnoldi Iteration. c cstatn ARPACK routine that initializes the timing variables. c ivout ARPACK utility routine that prints integers. c cvout ARPACK utility routine that prints vectors. c arscnd ARPACK utility routine for timing. c slamch LAPACK routine that determines machine constants. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: naupd.F SID: 2.9 DATE OF SID: 07/21/02 RELEASE: 2 c c\Remarks c c\EndLib c c----------------------------------------------------------------------- c subroutine cnaupd & ( ido, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam, & ipntr, workd, workl, lworkl, rwork, info ) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character bmat*1, which*2 integer ido, info, ldv, lworkl, n, ncv, nev Real & tol c c %-----------------% c | Array Arguments | c %-----------------% c integer iparam(11), ipntr(14) Complex & resid(n), v(ldv,ncv), workd(3*n), workl(lworkl) Real & rwork(ncv) c c %------------% c | Parameters | c %------------% c Complex & one, zero parameter (one = (1.0E+0, 0.0E+0), zero = (0.0E+0, 0.0E+0)) c c %---------------% c | Local Scalars | c %---------------% c integer bounds, ierr, ih, iq, ishift, iupd, iw, & ldh, ldq, levec, mode, msglvl, mxiter, nb, & nev0, next, np, ritz, j save bounds, ih, iq, ishift, iupd, iw, & ldh, ldq, levec, mode, msglvl, mxiter, nb, & nev0, next, np, ritz c c %----------------------% c | External Subroutines | c %----------------------% c external cnaup2, cvout, ivout, arscnd, cstatn c c %--------------------% c | External Functions | c %--------------------% c Real & slamch external slamch c c %-----------------------% c | Executable Statements | c %-----------------------% c if (ido .eq. 0) then c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call cstatn call arscnd (t0) msglvl = mcaupd c c %----------------% c | Error checking | c %----------------% c ierr = 0 ishift = iparam(1) c levec = iparam(2) mxiter = iparam(3) c nb = iparam(4) nb = 1 c c %--------------------------------------------% c | Revision 2 performs only implicit restart. | c %--------------------------------------------% c iupd = 1 mode = iparam(7) c if (n .le. 0) then ierr = -1 else if (nev .le. 0) then ierr = -2 else if (ncv .le. nev .or. ncv .gt. n) then ierr = -3 else if (mxiter .le. 0) then ierr = -4 else if (which .ne. 'LM' .and. & which .ne. 'SM' .and. & which .ne. 'LR' .and. & which .ne. 'SR' .and. & which .ne. 'LI' .and. & which .ne. 'SI') then ierr = -5 else if (bmat .ne. 'I' .and. bmat .ne. 'G') then ierr = -6 else if (lworkl .lt. 3*ncv**2 + 5*ncv) then ierr = -7 else if (mode .lt. 1 .or. mode .gt. 3) then ierr = -10 else if (mode .eq. 1 .and. bmat .eq. 'G') then ierr = -11 end if c c %------------% c | Error Exit | c %------------% c if (ierr .ne. 0) then info = ierr ido = 99 go to 9000 end if c c %------------------------% c | Set default parameters | c %------------------------% c if (nb .le. 0) nb = 1 if (tol .le. 0.0E+0 ) tol = slamch('EpsMach') if (ishift .ne. 0 .and. & ishift .ne. 1 .and. & ishift .ne. 2) ishift = 1 c c %----------------------------------------------% c | NP is the number of additional steps to | c | extend the length NEV Lanczos factorization. | c | NEV0 is the local variable designating the | c | size of the invariant subspace desired. | c %----------------------------------------------% c np = ncv - nev nev0 = nev c c %-----------------------------% c | Zero out internal workspace | c %-----------------------------% c do 10 j = 1, 3*ncv**2 + 5*ncv workl(j) = zero 10 continue c c %-------------------------------------------------------------% c | Pointer into WORKL for address of H, RITZ, BOUNDS, Q | c | etc... and the remaining workspace. | c | Also update pointer to be used on output. | c | Memory is laid out as follows: | c | workl(1:ncv*ncv) := generated Hessenberg matrix | c | workl(ncv*ncv+1:ncv*ncv+ncv) := the ritz values | c | workl(ncv*ncv+ncv+1:ncv*ncv+2*ncv) := error bounds | c | workl(ncv*ncv+2*ncv+1:2*ncv*ncv+2*ncv) := rotation matrix Q | c | workl(2*ncv*ncv+2*ncv+1:3*ncv*ncv+5*ncv) := workspace | c | The final workspace is needed by subroutine cneigh called | c | by cnaup2. Subroutine cneigh calls LAPACK routines for | c | calculating eigenvalues and the last row of the eigenvector | c | matrix. | c %-------------------------------------------------------------% c ldh = ncv ldq = ncv ih = 1 ritz = ih + ldh*ncv bounds = ritz + ncv iq = bounds + ncv iw = iq + ldq*ncv next = iw + ncv**2 + 3*ncv c ipntr(4) = next ipntr(5) = ih ipntr(6) = ritz ipntr(7) = iq ipntr(8) = bounds ipntr(14) = iw end if c c %-------------------------------------------------------% c | Carry out the Implicitly restarted Arnoldi Iteration. | c %-------------------------------------------------------% c call cnaup2 & ( ido, bmat, n, which, nev0, np, tol, resid, mode, iupd, & ishift, mxiter, v, ldv, workl(ih), ldh, workl(ritz), & workl(bounds), workl(iq), ldq, workl(iw), & ipntr, workd, rwork, info ) c c %--------------------------------------------------% c | ido .ne. 99 implies use of reverse communication | c | to compute operations involving OP. | c %--------------------------------------------------% c if (ido .eq. 3) iparam(8) = np if (ido .ne. 99) go to 9000 c iparam(3) = mxiter iparam(5) = np iparam(9) = nopx iparam(10) = nbx iparam(11) = nrorth c c %------------------------------------% c | Exit if there was an informational | c | error within cnaup2. | c %------------------------------------% c if (info .lt. 0) go to 9000 if (info .eq. 2) info = 3 c if (msglvl .gt. 0) then call ivout (logfil, 1, mxiter, ndigit, & '_naupd: Number of update iterations taken') call ivout (logfil, 1, np, ndigit, & '_naupd: Number of wanted "converged" Ritz values') call cvout (logfil, np, workl(ritz), ndigit, & '_naupd: The final Ritz values') call cvout (logfil, np, workl(bounds), ndigit, & '_naupd: Associated Ritz estimates') end if c call arscnd (t1) tcaupd = t1 - t0 c if (msglvl .gt. 0) then c c %--------------------------------------------------------% c | Version Number & Version Date are defined in version.h | c %--------------------------------------------------------% c write (6,1000) write (6,1100) mxiter, nopx, nbx, nrorth, nitref, nrstrt, & tmvopx, tmvbx, tcaupd, tcaup2, tcaitr, titref, & tgetv0, tceigh, tcgets, tcapps, tcconv, trvec 1000 format (//, & 5x, '=============================================',/ & 5x, '= Complex implicit Arnoldi update code =',/ & 5x, '= Version Number: ', ' 2.3', 21x, ' =',/ & 5x, '= Version Date: ', ' 07/31/96', 16x, ' =',/ & 5x, '=============================================',/ & 5x, '= Summary of timing statistics =',/ & 5x, '=============================================',//) 1100 format ( & 5x, 'Total number update iterations = ', i5,/ & 5x, 'Total number of OP*x operations = ', i5,/ & 5x, 'Total number of B*x operations = ', i5,/ & 5x, 'Total number of reorthogonalization steps = ', i5,/ & 5x, 'Total number of iterative refinement steps = ', i5,/ & 5x, 'Total number of restart steps = ', i5,/ & 5x, 'Total time in user OP*x operation = ', f12.6,/ & 5x, 'Total time in user B*x operation = ', f12.6,/ & 5x, 'Total time in Arnoldi update routine = ', f12.6,/ & 5x, 'Total time in naup2 routine = ', f12.6,/ & 5x, 'Total time in basic Arnoldi iteration loop = ', f12.6,/ & 5x, 'Total time in reorthogonalization phase = ', f12.6,/ & 5x, 'Total time in (re)start vector generation = ', f12.6,/ & 5x, 'Total time in Hessenberg eig. subproblem = ', f12.6,/ & 5x, 'Total time in getting the shifts = ', f12.6,/ & 5x, 'Total time in applying the shifts = ', f12.6,/ & 5x, 'Total time in convergence testing = ', f12.6,/ & 5x, 'Total time in computing final Ritz vectors = ', f12.6/) end if c 9000 continue c return c c %---------------% c | End of cnaupd | c %---------------% c end arpack-0.92.1/SRC/dnconv.f0000644000175000017500000000776510776001577012103 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: dnconv c c\Description: c Convergence testing for the nonsymmetric Arnoldi eigenvalue routine. c c\Usage: c call dnconv c ( N, RITZR, RITZI, BOUNDS, TOL, NCONV ) c c\Arguments c N Integer. (INPUT) c Number of Ritz values to check for convergence. c c RITZR, Double precision arrays of length N. (INPUT) c RITZI Real and imaginary parts of the Ritz values to be checked c for convergence. c BOUNDS Double precision array of length N. (INPUT) c Ritz estimates for the Ritz values in RITZR and RITZI. c c TOL Double precision scalar. (INPUT) c Desired backward error for a Ritz value to be considered c "converged". c c NCONV Integer scalar. (OUTPUT) c Number of "converged" Ritz values. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx real c c\Routines called: c arscnd ARPACK utility routine for timing. c dlamch LAPACK routine that determines machine constants. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c xx/xx/92: Version ' 2.1' c c\SCCS Information: @(#) c FILE: nconv.F SID: 2.3 DATE OF SID: 4/20/96 RELEASE: 2 c c\Remarks c 1. xxxx c c\EndLib c c----------------------------------------------------------------------- c subroutine dnconv (n, ritzr, ritzi, bounds, tol, nconv) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c integer n, nconv Double precision & tol c c %-----------------% c | Array Arguments | c %-----------------% Double precision & ritzr(n), ritzi(n), bounds(n) c c %---------------% c | Local Scalars | c %---------------% c integer i Double precision & temp, eps23 c c %--------------------% c | External Functions | c %--------------------% c Double precision & dlapy2, dlamch external dlapy2, dlamch c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------------------------------------% c | Convergence test: unlike in the symmetric code, I am not | c | using things like refined error bounds and gap condition | c | because I don't know the exact equivalent concept. | c | | c | Instead the i-th Ritz value is considered "converged" when: | c | | c | bounds(i) .le. ( TOL * | ritz | ) | c | | c | for some appropriate choice of norm. | c %-------------------------------------------------------------% c call arscnd (t0) c c %---------------------------------% c | Get machine dependent constant. | c %---------------------------------% c eps23 = dlamch('Epsilon-Machine') eps23 = eps23**(2.0D+0 / 3.0D+0) c nconv = 0 do 20 i = 1, n temp = max( eps23, dlapy2( ritzr(i), ritzi(i) ) ) if (bounds(i) .le. tol*temp) nconv = nconv + 1 20 continue c call arscnd (t1) tnconv = tnconv + (t1 - t0) c return c c %---------------% c | End of dnconv | c %---------------% c end arpack-0.92.1/SRC/ssaitr.f0000644000175000017500000007372710776001577012122 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: ssaitr c c\Description: c Reverse communication interface for applying NP additional steps to c a K step symmetric Arnoldi factorization. c c Input: OP*V_{k} - V_{k}*H = r_{k}*e_{k}^T c c with (V_{k}^T)*B*V_{k} = I, (V_{k}^T)*B*r_{k} = 0. c c Output: OP*V_{k+p} - V_{k+p}*H = r_{k+p}*e_{k+p}^T c c with (V_{k+p}^T)*B*V_{k+p} = I, (V_{k+p}^T)*B*r_{k+p} = 0. c c where OP and B are as in ssaupd. The B-norm of r_{k+p} is also c computed and returned. c c\Usage: c call ssaitr c ( IDO, BMAT, N, K, NP, MODE, RESID, RNORM, V, LDV, H, LDH, c IPNTR, WORKD, INFO ) c c\Arguments c IDO Integer. (INPUT/OUTPUT) c Reverse communication flag. c ------------------------------------------------------------- c IDO = 0: first call to the reverse communication interface c IDO = -1: compute Y = OP * X where c IPNTR(1) is the pointer into WORK for X, c IPNTR(2) is the pointer into WORK for Y. c This is for the restart phase to force the new c starting vector into the range of OP. c IDO = 1: compute Y = OP * X where c IPNTR(1) is the pointer into WORK for X, c IPNTR(2) is the pointer into WORK for Y, c IPNTR(3) is the pointer into WORK for B * X. c IDO = 2: compute Y = B * X where c IPNTR(1) is the pointer into WORK for X, c IPNTR(2) is the pointer into WORK for Y. c IDO = 99: done c ------------------------------------------------------------- c When the routine is used in the "shift-and-invert" mode, the c vector B * Q is already available and does not need to be c recomputed in forming OP * Q. c c BMAT Character*1. (INPUT) c BMAT specifies the type of matrix B that defines the c semi-inner product for the operator OP. See ssaupd. c B = 'I' -> standard eigenvalue problem A*x = lambda*x c B = 'G' -> generalized eigenvalue problem A*x = lambda*M*x c c N Integer. (INPUT) c Dimension of the eigenproblem. c c K Integer. (INPUT) c Current order of H and the number of columns of V. c c NP Integer. (INPUT) c Number of additional Arnoldi steps to take. c c MODE Integer. (INPUT) c Signifies which form for "OP". If MODE=2 then c a reduction in the number of B matrix vector multiplies c is possible since the B-norm of OP*x is equivalent to c the inv(B)-norm of A*x. c c RESID Real array of length N. (INPUT/OUTPUT) c On INPUT: RESID contains the residual vector r_{k}. c On OUTPUT: RESID contains the residual vector r_{k+p}. c c RNORM Real scalar. (INPUT/OUTPUT) c On INPUT the B-norm of r_{k}. c On OUTPUT the B-norm of the updated residual r_{k+p}. c c V Real N by K+NP array. (INPUT/OUTPUT) c On INPUT: V contains the Arnoldi vectors in the first K c columns. c On OUTPUT: V contains the new NP Arnoldi vectors in the next c NP columns. The first K columns are unchanged. c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling c program. c c H Real (K+NP) by 2 array. (INPUT/OUTPUT) c H is used to store the generated symmetric tridiagonal matrix c with the subdiagonal in the first column starting at H(2,1) c and the main diagonal in the second column. c c LDH Integer. (INPUT) c Leading dimension of H exactly as declared in the calling c program. c c IPNTR Integer array of length 3. (OUTPUT) c Pointer to mark the starting locations in the WORK for c vectors used by the Arnoldi iteration. c ------------------------------------------------------------- c IPNTR(1): pointer to the current operand vector X. c IPNTR(2): pointer to the current result vector Y. c IPNTR(3): pointer to the vector B * X when used in the c shift-and-invert mode. X is the current operand. c ------------------------------------------------------------- c c WORKD Real work array of length 3*N. (REVERSE COMMUNICATION) c Distributed array to be used in the basic Arnoldi iteration c for reverse communication. The calling program should not c use WORKD as temporary workspace during the iteration !!!!!! c On INPUT, WORKD(1:N) = B*RESID where RESID is associated c with the K step Arnoldi factorization. Used to save some c computation at the first step. c On OUTPUT, WORKD(1:N) = B*RESID where RESID is associated c with the K+NP step Arnoldi factorization. c c INFO Integer. (OUTPUT) c = 0: Normal exit. c > 0: Size of an invariant subspace of OP is found that is c less than K + NP. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx real c c\Routines called: c sgetv0 ARPACK routine to generate the initial vector. c ivout ARPACK utility routine that prints integers. c smout ARPACK utility routine that prints matrices. c svout ARPACK utility routine that prints vectors. c slamch LAPACK routine that determines machine constants. c slascl LAPACK routine for careful scaling of a matrix. c sgemv Level 2 BLAS routine for matrix vector multiplication. c saxpy Level 1 BLAS that computes a vector triad. c sscal Level 1 BLAS that scales a vector. c scopy Level 1 BLAS that copies one vector to another . c sdot Level 1 BLAS that computes the scalar product of two vectors. c snrm2 Level 1 BLAS that computes the norm of a vector. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c xx/xx/93: Version ' 2.4' c c\SCCS Information: @(#) c FILE: saitr.F SID: 2.6 DATE OF SID: 8/28/96 RELEASE: 2 c c\Remarks c The algorithm implemented is: c c restart = .false. c Given V_{k} = [v_{1}, ..., v_{k}], r_{k}; c r_{k} contains the initial residual vector even for k = 0; c Also assume that rnorm = || B*r_{k} || and B*r_{k} are already c computed by the calling program. c c betaj = rnorm ; p_{k+1} = B*r_{k} ; c For j = k+1, ..., k+np Do c 1) if ( betaj < tol ) stop or restart depending on j. c if ( restart ) generate a new starting vector. c 2) v_{j} = r(j-1)/betaj; V_{j} = [V_{j-1}, v_{j}]; c p_{j} = p_{j}/betaj c 3) r_{j} = OP*v_{j} where OP is defined as in ssaupd c For shift-invert mode p_{j} = B*v_{j} is already available. c wnorm = || OP*v_{j} || c 4) Compute the j-th step residual vector. c w_{j} = V_{j}^T * B * OP * v_{j} c r_{j} = OP*v_{j} - V_{j} * w_{j} c alphaj <- j-th component of w_{j} c rnorm = || r_{j} || c betaj+1 = rnorm c If (rnorm > 0.717*wnorm) accept step and go back to 1) c 5) Re-orthogonalization step: c s = V_{j}'*B*r_{j} c r_{j} = r_{j} - V_{j}*s; rnorm1 = || r_{j} || c alphaj = alphaj + s_{j}; c 6) Iterative refinement step: c If (rnorm1 > 0.717*rnorm) then c rnorm = rnorm1 c accept step and go back to 1) c Else c rnorm = rnorm1 c If this is the first time in step 6), go to 5) c Else r_{j} lies in the span of V_{j} numerically. c Set r_{j} = 0 and rnorm = 0; go to 1) c EndIf c End Do c c\EndLib c c----------------------------------------------------------------------- c subroutine ssaitr & (ido, bmat, n, k, np, mode, resid, rnorm, v, ldv, h, ldh, & ipntr, workd, info) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character bmat*1 integer ido, info, k, ldh, ldv, n, mode, np Real & rnorm c c %-----------------% c | Array Arguments | c %-----------------% c integer ipntr(3) Real & h(ldh,2), resid(n), v(ldv,k+np), workd(3*n) c c %------------% c | Parameters | c %------------% c Real & one, zero parameter (one = 1.0E+0, zero = 0.0E+0) c c %---------------% c | Local Scalars | c %---------------% c logical first, orth1, orth2, rstart, step3, step4 integer i, ierr, ipj, irj, ivj, iter, itry, j, msglvl, & infol, jj Real & rnorm1, wnorm, safmin, temp1 save orth1, orth2, rstart, step3, step4, & ierr, ipj, irj, ivj, iter, itry, j, msglvl, & rnorm1, safmin, wnorm c c %-----------------------% c | Local Array Arguments | c %-----------------------% c Real & xtemp(2) c c %----------------------% c | External Subroutines | c %----------------------% c external saxpy, scopy, sscal, sgemv, sgetv0, svout, smout, & slascl, ivout, arscnd c c %--------------------% c | External Functions | c %--------------------% c Real & sdot, snrm2, slamch external sdot, snrm2, slamch c c %-----------------% c | Data statements | c %-----------------% c data first / .true. / c c %-----------------------% c | Executable Statements | c %-----------------------% c if (first) then first = .false. c c %--------------------------------% c | safmin = safe minimum is such | c | that 1/sfmin does not overflow | c %--------------------------------% c safmin = slamch('safmin') end if c if (ido .eq. 0) then c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call arscnd (t0) msglvl = msaitr c c %------------------------------% c | Initial call to this routine | c %------------------------------% c info = 0 step3 = .false. step4 = .false. rstart = .false. orth1 = .false. orth2 = .false. c c %--------------------------------% c | Pointer to the current step of | c | the factorization to build | c %--------------------------------% c j = k + 1 c c %------------------------------------------% c | Pointers used for reverse communication | c | when using WORKD. | c %------------------------------------------% c ipj = 1 irj = ipj + n ivj = irj + n end if c c %-------------------------------------------------% c | When in reverse communication mode one of: | c | STEP3, STEP4, ORTH1, ORTH2, RSTART | c | will be .true. | c | STEP3: return from computing OP*v_{j}. | c | STEP4: return from computing B-norm of OP*v_{j} | c | ORTH1: return from computing B-norm of r_{j+1} | c | ORTH2: return from computing B-norm of | c | correction to the residual vector. | c | RSTART: return from OP computations needed by | c | sgetv0. | c %-------------------------------------------------% c if (step3) go to 50 if (step4) go to 60 if (orth1) go to 70 if (orth2) go to 90 if (rstart) go to 30 c c %------------------------------% c | Else this is the first step. | c %------------------------------% c c %--------------------------------------------------------------% c | | c | A R N O L D I I T E R A T I O N L O O P | c | | c | Note: B*r_{j-1} is already in WORKD(1:N)=WORKD(IPJ:IPJ+N-1) | c %--------------------------------------------------------------% c 1000 continue c if (msglvl .gt. 2) then call ivout (logfil, 1, j, ndigit, & '_saitr: generating Arnoldi vector no.') call svout (logfil, 1, rnorm, ndigit, & '_saitr: B-norm of the current residual =') end if c c %---------------------------------------------------------% c | Check for exact zero. Equivalent to determing whether a | c | j-step Arnoldi factorization is present. | c %---------------------------------------------------------% c if (rnorm .gt. zero) go to 40 c c %---------------------------------------------------% c | Invariant subspace found, generate a new starting | c | vector which is orthogonal to the current Arnoldi | c | basis and continue the iteration. | c %---------------------------------------------------% c if (msglvl .gt. 0) then call ivout (logfil, 1, j, ndigit, & '_saitr: ****** restart at step ******') end if c c %---------------------------------------------% c | ITRY is the loop variable that controls the | c | maximum amount of times that a restart is | c | attempted. NRSTRT is used by stat.h | c %---------------------------------------------% c nrstrt = nrstrt + 1 itry = 1 20 continue rstart = .true. ido = 0 30 continue c c %--------------------------------------% c | If in reverse communication mode and | c | RSTART = .true. flow returns here. | c %--------------------------------------% c call sgetv0 (ido, bmat, itry, .false., n, j, v, ldv, & resid, rnorm, ipntr, workd, ierr) if (ido .ne. 99) go to 9000 if (ierr .lt. 0) then itry = itry + 1 if (itry .le. 3) go to 20 c c %------------------------------------------------% c | Give up after several restart attempts. | c | Set INFO to the size of the invariant subspace | c | which spans OP and exit. | c %------------------------------------------------% c info = j - 1 call arscnd (t1) tsaitr = tsaitr + (t1 - t0) ido = 99 go to 9000 end if c 40 continue c c %---------------------------------------------------------% c | STEP 2: v_{j} = r_{j-1}/rnorm and p_{j} = p_{j}/rnorm | c | Note that p_{j} = B*r_{j-1}. In order to avoid overflow | c | when reciprocating a small RNORM, test against lower | c | machine bound. | c %---------------------------------------------------------% c call scopy (n, resid, 1, v(1,j), 1) if (rnorm .ge. safmin) then temp1 = one / rnorm call sscal (n, temp1, v(1,j), 1) call sscal (n, temp1, workd(ipj), 1) else c c %-----------------------------------------% c | To scale both v_{j} and p_{j} carefully | c | use LAPACK routine SLASCL | c %-----------------------------------------% c call slascl ('General', i, i, rnorm, one, n, 1, & v(1,j), n, infol) call slascl ('General', i, i, rnorm, one, n, 1, & workd(ipj), n, infol) end if c c %------------------------------------------------------% c | STEP 3: r_{j} = OP*v_{j}; Note that p_{j} = B*v_{j} | c | Note that this is not quite yet r_{j}. See STEP 4 | c %------------------------------------------------------% c step3 = .true. nopx = nopx + 1 call arscnd (t2) call scopy (n, v(1,j), 1, workd(ivj), 1) ipntr(1) = ivj ipntr(2) = irj ipntr(3) = ipj ido = 1 c c %-----------------------------------% c | Exit in order to compute OP*v_{j} | c %-----------------------------------% c go to 9000 50 continue c c %-----------------------------------% c | Back from reverse communication; | c | WORKD(IRJ:IRJ+N-1) := OP*v_{j}. | c %-----------------------------------% c call arscnd (t3) tmvopx = tmvopx + (t3 - t2) c step3 = .false. c c %------------------------------------------% c | Put another copy of OP*v_{j} into RESID. | c %------------------------------------------% c call scopy (n, workd(irj), 1, resid, 1) c c %-------------------------------------------% c | STEP 4: Finish extending the symmetric | c | Arnoldi to length j. If MODE = 2 | c | then B*OP = B*inv(B)*A = A and | c | we don't need to compute B*OP. | c | NOTE: If MODE = 2 WORKD(IVJ:IVJ+N-1) is | c | assumed to have A*v_{j}. | c %-------------------------------------------% c if (mode .eq. 2) go to 65 call arscnd (t2) if (bmat .eq. 'G') then nbx = nbx + 1 step4 = .true. ipntr(1) = irj ipntr(2) = ipj ido = 2 c c %-------------------------------------% c | Exit in order to compute B*OP*v_{j} | c %-------------------------------------% c go to 9000 else if (bmat .eq. 'I') then call scopy(n, resid, 1 , workd(ipj), 1) end if 60 continue c c %-----------------------------------% c | Back from reverse communication; | c | WORKD(IPJ:IPJ+N-1) := B*OP*v_{j}. | c %-----------------------------------% c if (bmat .eq. 'G') then call arscnd (t3) tmvbx = tmvbx + (t3 - t2) end if c step4 = .false. c c %-------------------------------------% c | The following is needed for STEP 5. | c | Compute the B-norm of OP*v_{j}. | c %-------------------------------------% c 65 continue if (mode .eq. 2) then c c %----------------------------------% c | Note that the B-norm of OP*v_{j} | c | is the inv(B)-norm of A*v_{j}. | c %----------------------------------% c wnorm = sdot (n, resid, 1, workd(ivj), 1) wnorm = sqrt(abs(wnorm)) else if (bmat .eq. 'G') then wnorm = sdot (n, resid, 1, workd(ipj), 1) wnorm = sqrt(abs(wnorm)) else if (bmat .eq. 'I') then wnorm = snrm2(n, resid, 1) end if c c %-----------------------------------------% c | Compute the j-th residual corresponding | c | to the j step factorization. | c | Use Classical Gram Schmidt and compute: | c | w_{j} <- V_{j}^T * B * OP * v_{j} | c | r_{j} <- OP*v_{j} - V_{j} * w_{j} | c %-----------------------------------------% c c c %------------------------------------------% c | Compute the j Fourier coefficients w_{j} | c | WORKD(IPJ:IPJ+N-1) contains B*OP*v_{j}. | c %------------------------------------------% c if (mode .ne. 2 ) then call sgemv('T', n, j, one, v, ldv, workd(ipj), 1, zero, & workd(irj), 1) else if (mode .eq. 2) then call sgemv('T', n, j, one, v, ldv, workd(ivj), 1, zero, & workd(irj), 1) end if c c %--------------------------------------% c | Orthgonalize r_{j} against V_{j}. | c | RESID contains OP*v_{j}. See STEP 3. | c %--------------------------------------% c call sgemv('N', n, j, -one, v, ldv, workd(irj), 1, one, & resid, 1) c c %--------------------------------------% c | Extend H to have j rows and columns. | c %--------------------------------------% c h(j,2) = workd(irj + j - 1) if (j .eq. 1 .or. rstart) then h(j,1) = zero else h(j,1) = rnorm end if call arscnd (t4) c orth1 = .true. iter = 0 c call arscnd (t2) if (bmat .eq. 'G') then nbx = nbx + 1 call scopy (n, resid, 1, workd(irj), 1) ipntr(1) = irj ipntr(2) = ipj ido = 2 c c %----------------------------------% c | Exit in order to compute B*r_{j} | c %----------------------------------% c go to 9000 else if (bmat .eq. 'I') then call scopy (n, resid, 1, workd(ipj), 1) end if 70 continue c c %---------------------------------------------------% c | Back from reverse communication if ORTH1 = .true. | c | WORKD(IPJ:IPJ+N-1) := B*r_{j}. | c %---------------------------------------------------% c if (bmat .eq. 'G') then call arscnd (t3) tmvbx = tmvbx + (t3 - t2) end if c orth1 = .false. c c %------------------------------% c | Compute the B-norm of r_{j}. | c %------------------------------% c if (bmat .eq. 'G') then rnorm = sdot (n, resid, 1, workd(ipj), 1) rnorm = sqrt(abs(rnorm)) else if (bmat .eq. 'I') then rnorm = snrm2(n, resid, 1) end if c c %-----------------------------------------------------------% c | STEP 5: Re-orthogonalization / Iterative refinement phase | c | Maximum NITER_ITREF tries. | c | | c | s = V_{j}^T * B * r_{j} | c | r_{j} = r_{j} - V_{j}*s | c | alphaj = alphaj + s_{j} | c | | c | The stopping criteria used for iterative refinement is | c | discussed in Parlett's book SEP, page 107 and in Gragg & | c | Reichel ACM TOMS paper; Algorithm 686, Dec. 1990. | c | Determine if we need to correct the residual. The goal is | c | to enforce ||v(:,1:j)^T * r_{j}|| .le. eps * || r_{j} || | c %-----------------------------------------------------------% c if (rnorm .gt. 0.717*wnorm) go to 100 nrorth = nrorth + 1 c c %---------------------------------------------------% c | Enter the Iterative refinement phase. If further | c | refinement is necessary, loop back here. The loop | c | variable is ITER. Perform a step of Classical | c | Gram-Schmidt using all the Arnoldi vectors V_{j} | c %---------------------------------------------------% c 80 continue c if (msglvl .gt. 2) then xtemp(1) = wnorm xtemp(2) = rnorm call svout (logfil, 2, xtemp, ndigit, & '_saitr: re-orthonalization ; wnorm and rnorm are') end if c c %----------------------------------------------------% c | Compute V_{j}^T * B * r_{j}. | c | WORKD(IRJ:IRJ+J-1) = v(:,1:J)'*WORKD(IPJ:IPJ+N-1). | c %----------------------------------------------------% c call sgemv ('T', n, j, one, v, ldv, workd(ipj), 1, & zero, workd(irj), 1) c c %----------------------------------------------% c | Compute the correction to the residual: | c | r_{j} = r_{j} - V_{j} * WORKD(IRJ:IRJ+J-1). | c | The correction to H is v(:,1:J)*H(1:J,1:J) + | c | v(:,1:J)*WORKD(IRJ:IRJ+J-1)*e'_j, but only | c | H(j,j) is updated. | c %----------------------------------------------% c call sgemv ('N', n, j, -one, v, ldv, workd(irj), 1, & one, resid, 1) c if (j .eq. 1 .or. rstart) h(j,1) = zero h(j,2) = h(j,2) + workd(irj + j - 1) c orth2 = .true. call arscnd (t2) if (bmat .eq. 'G') then nbx = nbx + 1 call scopy (n, resid, 1, workd(irj), 1) ipntr(1) = irj ipntr(2) = ipj ido = 2 c c %-----------------------------------% c | Exit in order to compute B*r_{j}. | c | r_{j} is the corrected residual. | c %-----------------------------------% c go to 9000 else if (bmat .eq. 'I') then call scopy (n, resid, 1, workd(ipj), 1) end if 90 continue c c %---------------------------------------------------% c | Back from reverse communication if ORTH2 = .true. | c %---------------------------------------------------% c if (bmat .eq. 'G') then call arscnd (t3) tmvbx = tmvbx + (t3 - t2) end if c c %-----------------------------------------------------% c | Compute the B-norm of the corrected residual r_{j}. | c %-----------------------------------------------------% c if (bmat .eq. 'G') then rnorm1 = sdot (n, resid, 1, workd(ipj), 1) rnorm1 = sqrt(abs(rnorm1)) else if (bmat .eq. 'I') then rnorm1 = snrm2(n, resid, 1) end if c if (msglvl .gt. 0 .and. iter .gt. 0) then call ivout (logfil, 1, j, ndigit, & '_saitr: Iterative refinement for Arnoldi residual') if (msglvl .gt. 2) then xtemp(1) = rnorm xtemp(2) = rnorm1 call svout (logfil, 2, xtemp, ndigit, & '_saitr: iterative refinement ; rnorm and rnorm1 are') end if end if c c %-----------------------------------------% c | Determine if we need to perform another | c | step of re-orthogonalization. | c %-----------------------------------------% c if (rnorm1 .gt. 0.717*rnorm) then c c %--------------------------------% c | No need for further refinement | c %--------------------------------% c rnorm = rnorm1 c else c c %-------------------------------------------% c | Another step of iterative refinement step | c | is required. NITREF is used by stat.h | c %-------------------------------------------% c nitref = nitref + 1 rnorm = rnorm1 iter = iter + 1 if (iter .le. 1) go to 80 c c %-------------------------------------------------% c | Otherwise RESID is numerically in the span of V | c %-------------------------------------------------% c do 95 jj = 1, n resid(jj) = zero 95 continue rnorm = zero end if c c %----------------------------------------------% c | Branch here directly if iterative refinement | c | wasn't necessary or after at most NITER_REF | c | steps of iterative refinement. | c %----------------------------------------------% c 100 continue c rstart = .false. orth2 = .false. c call arscnd (t5) titref = titref + (t5 - t4) c c %----------------------------------------------------------% c | Make sure the last off-diagonal element is non negative | c | If not perform a similarity transformation on H(1:j,1:j) | c | and scale v(:,j) by -1. | c %----------------------------------------------------------% c if (h(j,1) .lt. zero) then h(j,1) = -h(j,1) if ( j .lt. k+np) then call sscal(n, -one, v(1,j+1), 1) else call sscal(n, -one, resid, 1) end if end if c c %------------------------------------% c | STEP 6: Update j = j+1; Continue | c %------------------------------------% c j = j + 1 if (j .gt. k+np) then call arscnd (t1) tsaitr = tsaitr + (t1 - t0) ido = 99 c if (msglvl .gt. 1) then call svout (logfil, k+np, h(1,2), ndigit, & '_saitr: main diagonal of matrix H of step K+NP.') if (k+np .gt. 1) then call svout (logfil, k+np-1, h(2,1), ndigit, & '_saitr: sub diagonal of matrix H of step K+NP.') end if end if c go to 9000 end if c c %--------------------------------------------------------% c | Loop back to extend the factorization by another step. | c %--------------------------------------------------------% c go to 1000 c c %---------------------------------------------------------------% c | | c | E N D O F M A I N I T E R A T I O N L O O P | c | | c %---------------------------------------------------------------% c 9000 continue return c c %---------------% c | End of ssaitr | c %---------------% c end arpack-0.92.1/SRC/cstatn.f0000644000175000017500000000230510776001577012071 00000000000000c c\SCCS Information: @(#) c FILE: statn.F SID: 2.2 DATE OF SID: 4/20/96 RELEASE: 2 c c %---------------------------------------------% c | Initialize statistic and timing information | c | for complex nonsymmetric Arnoldi code. | c %---------------------------------------------% subroutine cstatn c c %--------------------------------% c | See stat.doc for documentation | c %--------------------------------% c include 'stat.h' c %-----------------------% c | Executable Statements | c %-----------------------% nopx = 0 nbx = 0 nrorth = 0 nitref = 0 nrstrt = 0 tcaupd = 0.0E+0 tcaup2 = 0.0E+0 tcaitr = 0.0E+0 tceigh = 0.0E+0 tcgets = 0.0E+0 tcapps = 0.0E+0 tcconv = 0.0E+0 titref = 0.0E+0 tgetv0 = 0.0E+0 trvec = 0.0E+0 c %----------------------------------------------------% c | User time including reverse communication overhead | c %----------------------------------------------------% tmvopx = 0.0E+0 tmvbx = 0.0E+0 return c c %---------------% c | End of cstatn | c %---------------% c end arpack-0.92.1/SRC/dsconv.f0000644000175000017500000000660210776001577012075 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: dsconv c c\Description: c Convergence testing for the symmetric Arnoldi eigenvalue routine. c c\Usage: c call dsconv c ( N, RITZ, BOUNDS, TOL, NCONV ) c c\Arguments c N Integer. (INPUT) c Number of Ritz values to check for convergence. c c RITZ Double precision array of length N. (INPUT) c The Ritz values to be checked for convergence. c c BOUNDS Double precision array of length N. (INPUT) c Ritz estimates associated with the Ritz values in RITZ. c c TOL Double precision scalar. (INPUT) c Desired relative accuracy for a Ritz value to be considered c "converged". c c NCONV Integer scalar. (OUTPUT) c Number of "converged" Ritz values. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Routines called: c arscnd ARPACK utility routine for timing. c dlamch LAPACK routine that determines machine constants. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: sconv.F SID: 2.4 DATE OF SID: 4/19/96 RELEASE: 2 c c\Remarks c 1. Starting with version 2.4, this routine no longer uses the c Parlett strategy using the gap conditions. c c\EndLib c c----------------------------------------------------------------------- c subroutine dsconv (n, ritz, bounds, tol, nconv) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c integer n, nconv Double precision & tol c c %-----------------% c | Array Arguments | c %-----------------% c Double precision & ritz(n), bounds(n) c c %---------------% c | Local Scalars | c %---------------% c integer i Double precision & temp, eps23 c c %-------------------% c | External routines | c %-------------------% c Double precision & dlamch external dlamch c %---------------------% c | Intrinsic Functions | c %---------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c call arscnd (t0) c eps23 = dlamch('Epsilon-Machine') eps23 = eps23**(2.0D+0 / 3.0D+0) c nconv = 0 do 10 i = 1, n c c %-----------------------------------------------------% c | The i-th Ritz value is considered "converged" | c | when: bounds(i) .le. TOL*max(eps23, abs(ritz(i))) | c %-----------------------------------------------------% c temp = max( eps23, abs(ritz(i)) ) if ( bounds(i) .le. tol*temp ) then nconv = nconv + 1 end if c 10 continue c call arscnd (t1) tsconv = tsconv + (t1 - t0) c return c c %---------------% c | End of dsconv | c %---------------% c end arpack-0.92.1/SRC/cneigh.f0000644000175000017500000001771110776001577012041 00000000000000c\BeginDoc c c\Name: cneigh c c\Description: c Compute the eigenvalues of the current upper Hessenberg matrix c and the corresponding Ritz estimates given the current residual norm. c c\Usage: c call cneigh c ( RNORM, N, H, LDH, RITZ, BOUNDS, Q, LDQ, WORKL, RWORK, IERR ) c c\Arguments c RNORM Real scalar. (INPUT) c Residual norm corresponding to the current upper Hessenberg c matrix H. c c N Integer. (INPUT) c Size of the matrix H. c c H Complex N by N array. (INPUT) c H contains the current upper Hessenberg matrix. c c LDH Integer. (INPUT) c Leading dimension of H exactly as declared in the calling c program. c c RITZ Complex array of length N. (OUTPUT) c On output, RITZ(1:N) contains the eigenvalues of H. c c BOUNDS Complex array of length N. (OUTPUT) c On output, BOUNDS contains the Ritz estimates associated with c the eigenvalues held in RITZ. This is equal to RNORM c times the last components of the eigenvectors corresponding c to the eigenvalues in RITZ. c c Q Complex N by N array. (WORKSPACE) c Workspace needed to store the eigenvectors of H. c c LDQ Integer. (INPUT) c Leading dimension of Q exactly as declared in the calling c program. c c WORKL Complex work array of length N**2 + 3*N. (WORKSPACE) c Private (replicated) array on each PE or array allocated on c the front end. This is needed to keep the full Schur form c of H and also in the calculation of the eigenvectors of H. c c RWORK Real work array of length N (WORKSPACE) c Private (replicated) array on each PE or array allocated on c the front end. c c IERR Integer. (OUTPUT) c Error exit flag from clahqr or ctrevc. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx Complex c c\Routines called: c ivout ARPACK utility routine that prints integers. c arscnd ARPACK utility routine for timing. c cmout ARPACK utility routine that prints matrices c cvout ARPACK utility routine that prints vectors. c svout ARPACK utility routine that prints vectors. c clacpy LAPACK matrix copy routine. c clahqr LAPACK routine to compute the Schur form of an c upper Hessenberg matrix. c claset LAPACK matrix initialization routine. c ctrevc LAPACK routine to compute the eigenvectors of a matrix c in upper triangular form c ccopy Level 1 BLAS that copies one vector to another. c csscal Level 1 BLAS that scales a complex vector by a real number. c scnrm2 Level 1 BLAS that computes the norm of a vector. c c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: neigh.F SID: 2.2 DATE OF SID: 4/20/96 RELEASE: 2 c c\Remarks c None c c\EndLib c c----------------------------------------------------------------------- c subroutine cneigh (rnorm, n, h, ldh, ritz, bounds, & q, ldq, workl, rwork, ierr) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c integer ierr, n, ldh, ldq Real & rnorm c c %-----------------% c | Array Arguments | c %-----------------% c Complex & bounds(n), h(ldh,n), q(ldq,n), ritz(n), & workl(n*(n+3)) Real & rwork(n) c c %------------% c | Parameters | c %------------% c Complex & one, zero Real & rone parameter (one = (1.0E+0, 0.0E+0), zero = (0.0E+0, 0.0E+0), & rone = 1.0E+0) c c %------------------------% c | Local Scalars & Arrays | c %------------------------% c logical select(1) integer j, msglvl Complex & vl(1) Real & temp c c %----------------------% c | External Subroutines | c %----------------------% c external clacpy, clahqr, ctrevc, ccopy, & csscal, cmout, cvout, arscnd c c %--------------------% c | External Functions | c %--------------------% c Real & scnrm2 external scnrm2 c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call arscnd (t0) msglvl = mceigh c if (msglvl .gt. 2) then call cmout (logfil, n, n, h, ldh, ndigit, & '_neigh: Entering upper Hessenberg matrix H ') end if c c %----------------------------------------------------------% c | 1. Compute the eigenvalues, the last components of the | c | corresponding Schur vectors and the full Schur form T | c | of the current upper Hessenberg matrix H. | c | clahqr returns the full Schur form of H | c | in WORKL(1:N**2), and the Schur vectors in q. | c %----------------------------------------------------------% c call clacpy ('All', n, n, h, ldh, workl, n) call claset ('All', n, n, zero, one, q, ldq) call clahqr (.true., .true., n, 1, n, workl, ldh, ritz, & 1, n, q, ldq, ierr) if (ierr .ne. 0) go to 9000 c call ccopy (n, q(n-1,1), ldq, bounds, 1) if (msglvl .gt. 1) then call cvout (logfil, n, bounds, ndigit, & '_neigh: last row of the Schur matrix for H') end if c c %----------------------------------------------------------% c | 2. Compute the eigenvectors of the full Schur form T and | c | apply the Schur vectors to get the corresponding | c | eigenvectors. | c %----------------------------------------------------------% c call ctrevc ('Right', 'Back', select, n, workl, n, vl, n, q, & ldq, n, n, workl(n*n+1), rwork, ierr) c if (ierr .ne. 0) go to 9000 c c %------------------------------------------------% c | Scale the returning eigenvectors so that their | c | Euclidean norms are all one. LAPACK subroutine | c | ctrevc returns each eigenvector normalized so | c | that the element of largest magnitude has | c | magnitude 1; here the magnitude of a complex | c | number (x,y) is taken to be |x| + |y|. | c %------------------------------------------------% c do 10 j=1, n temp = scnrm2( n, q(1,j), 1 ) call csscal ( n, rone / temp, q(1,j), 1 ) 10 continue c if (msglvl .gt. 1) then call ccopy(n, q(n,1), ldq, workl, 1) call cvout (logfil, n, workl, ndigit, & '_neigh: Last row of the eigenvector matrix for H') end if c c %----------------------------% c | Compute the Ritz estimates | c %----------------------------% c call ccopy(n, q(n,1), n, bounds, 1) call csscal(n, rnorm, bounds, 1) c if (msglvl .gt. 2) then call cvout (logfil, n, ritz, ndigit, & '_neigh: The eigenvalues of H') call cvout (logfil, n, bounds, ndigit, & '_neigh: Ritz estimates for the eigenvalues of H') end if c call arscnd(t1) tceigh = tceigh + (t1 - t0) c 9000 continue return c c %---------------% c | End of cneigh | c %---------------% c end arpack-0.92.1/SRC/debug.h0000644000175000017500000000135110776001577011665 00000000000000c c\SCCS Information: @(#) c FILE: debug.h SID: 2.3 DATE OF SID: 11/16/95 RELEASE: 2 c c %---------------------------------% c | See debug.doc for documentation | c %---------------------------------% integer logfil, ndigit, mgetv0, & msaupd, msaup2, msaitr, mseigt, msapps, msgets, mseupd, & mnaupd, mnaup2, mnaitr, mneigh, mnapps, mngets, mneupd, & mcaupd, mcaup2, mcaitr, mceigh, mcapps, mcgets, mceupd common /debug/ & logfil, ndigit, mgetv0, & msaupd, msaup2, msaitr, mseigt, msapps, msgets, mseupd, & mnaupd, mnaup2, mnaitr, mneigh, mnapps, mngets, mneupd, & mcaupd, mcaup2, mcaitr, mceigh, mcapps, mcgets, mceupd arpack-0.92.1/SRC/ssesrt.f0000644000175000017500000001231010776001577012115 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: ssesrt c c\Description: c Sort the array X in the order specified by WHICH and optionally c apply the permutation to the columns of the matrix A. c c\Usage: c call ssesrt c ( WHICH, APPLY, N, X, NA, A, LDA) c c\Arguments c WHICH Character*2. (Input) c 'LM' -> X is sorted into increasing order of magnitude. c 'SM' -> X is sorted into decreasing order of magnitude. c 'LA' -> X is sorted into increasing order of algebraic. c 'SA' -> X is sorted into decreasing order of algebraic. c c APPLY Logical. (Input) c APPLY = .TRUE. -> apply the sorted order to A. c APPLY = .FALSE. -> do not apply the sorted order to A. c c N Integer. (INPUT) c Dimension of the array X. c c X Real array of length N. (INPUT/OUTPUT) c The array to be sorted. c c NA Integer. (INPUT) c Number of rows of the matrix A. c c A Real array of length NA by N. (INPUT/OUTPUT) c c LDA Integer. (INPUT) c Leading dimension of A. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Routines c sswap Level 1 BLAS that swaps the contents of two vectors. c c\Authors c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c 12/15/93: Version ' 2.1'. c Adapted from the sort routine in LANSO and c the ARPACK code ssortr c c\SCCS Information: @(#) c FILE: sesrt.F SID: 2.3 DATE OF SID: 4/19/96 RELEASE: 2 c c\EndLib c c----------------------------------------------------------------------- c subroutine ssesrt (which, apply, n, x, na, a, lda) c c %------------------% c | Scalar Arguments | c %------------------% c character*2 which logical apply integer lda, n, na c c %-----------------% c | Array Arguments | c %-----------------% c Real & x(0:n-1), a(lda, 0:n-1) c c %---------------% c | Local Scalars | c %---------------% c integer i, igap, j Real & temp c c %----------------------% c | External Subroutines | c %----------------------% c external sswap c c %-----------------------% c | Executable Statements | c %-----------------------% c igap = n / 2 c if (which .eq. 'SA') then c c X is sorted into decreasing order of algebraic. c 10 continue if (igap .eq. 0) go to 9000 do 30 i = igap, n-1 j = i-igap 20 continue c if (j.lt.0) go to 30 c if (x(j).lt.x(j+igap)) then temp = x(j) x(j) = x(j+igap) x(j+igap) = temp if (apply) call sswap( na, a(1, j), 1, a(1,j+igap), 1) else go to 30 endif j = j-igap go to 20 30 continue igap = igap / 2 go to 10 c else if (which .eq. 'SM') then c c X is sorted into decreasing order of magnitude. c 40 continue if (igap .eq. 0) go to 9000 do 60 i = igap, n-1 j = i-igap 50 continue c if (j.lt.0) go to 60 c if (abs(x(j)).lt.abs(x(j+igap))) then temp = x(j) x(j) = x(j+igap) x(j+igap) = temp if (apply) call sswap( na, a(1, j), 1, a(1,j+igap), 1) else go to 60 endif j = j-igap go to 50 60 continue igap = igap / 2 go to 40 c else if (which .eq. 'LA') then c c X is sorted into increasing order of algebraic. c 70 continue if (igap .eq. 0) go to 9000 do 90 i = igap, n-1 j = i-igap 80 continue c if (j.lt.0) go to 90 c if (x(j).gt.x(j+igap)) then temp = x(j) x(j) = x(j+igap) x(j+igap) = temp if (apply) call sswap( na, a(1, j), 1, a(1,j+igap), 1) else go to 90 endif j = j-igap go to 80 90 continue igap = igap / 2 go to 70 c else if (which .eq. 'LM') then c c X is sorted into increasing order of magnitude. c 100 continue if (igap .eq. 0) go to 9000 do 120 i = igap, n-1 j = i-igap 110 continue c if (j.lt.0) go to 120 c if (abs(x(j)).gt.abs(x(j+igap))) then temp = x(j) x(j) = x(j+igap) x(j+igap) = temp if (apply) call sswap( na, a(1, j), 1, a(1,j+igap), 1) else go to 120 endif j = j-igap go to 110 120 continue igap = igap / 2 go to 100 end if c 9000 continue return c c %---------------% c | End of ssesrt | c %---------------% c end arpack-0.92.1/SRC/stat.h0000644000175000017500000000171310776001577011554 00000000000000c %--------------------------------% c | See stat.doc for documentation | c %--------------------------------% c c\SCCS Information: @(#) c FILE: stat.h SID: 2.2 DATE OF SID: 11/16/95 RELEASE: 2 c real t0, t1, t2, t3, t4, t5 save t0, t1, t2, t3, t4, t5 c integer nopx, nbx, nrorth, nitref, nrstrt real tsaupd, tsaup2, tsaitr, tseigt, tsgets, tsapps, tsconv, & tnaupd, tnaup2, tnaitr, tneigh, tngets, tnapps, tnconv, & tcaupd, tcaup2, tcaitr, tceigh, tcgets, tcapps, tcconv, & tmvopx, tmvbx, tgetv0, titref, trvec common /timing/ & nopx, nbx, nrorth, nitref, nrstrt, & tsaupd, tsaup2, tsaitr, tseigt, tsgets, tsapps, tsconv, & tnaupd, tnaup2, tnaitr, tneigh, tngets, tnapps, tnconv, & tcaupd, tcaup2, tcaitr, tceigh, tcgets, tcapps, tcconv, & tmvopx, tmvbx, tgetv0, titref, trvec arpack-0.92.1/SRC/dsgets.f0000644000175000017500000001643510776001577012077 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: dsgets c c\Description: c Given the eigenvalues of the symmetric tridiagonal matrix H, c computes the NP shifts AMU that are zeros of the polynomial of c degree NP which filters out components of the unwanted eigenvectors c corresponding to the AMU's based on some given criteria. c c NOTE: This is called even in the case of user specified shifts in c order to sort the eigenvalues, and error bounds of H for later use. c c\Usage: c call dsgets c ( ISHIFT, WHICH, KEV, NP, RITZ, BOUNDS, SHIFTS ) c c\Arguments c ISHIFT Integer. (INPUT) c Method for selecting the implicit shifts at each iteration. c ISHIFT = 0: user specified shifts c ISHIFT = 1: exact shift with respect to the matrix H. c c WHICH Character*2. (INPUT) c Shift selection criteria. c 'LM' -> KEV eigenvalues of largest magnitude are retained. c 'SM' -> KEV eigenvalues of smallest magnitude are retained. c 'LA' -> KEV eigenvalues of largest value are retained. c 'SA' -> KEV eigenvalues of smallest value are retained. c 'BE' -> KEV eigenvalues, half from each end of the spectrum. c If KEV is odd, compute one more from the high end. c c KEV Integer. (INPUT) c KEV+NP is the size of the matrix H. c c NP Integer. (INPUT) c Number of implicit shifts to be computed. c c RITZ Double precision array of length KEV+NP. (INPUT/OUTPUT) c On INPUT, RITZ contains the eigenvalues of H. c On OUTPUT, RITZ are sorted so that the unwanted eigenvalues c are in the first NP locations and the wanted part is in c the last KEV locations. When exact shifts are selected, the c unwanted part corresponds to the shifts to be applied. c c BOUNDS Double precision array of length KEV+NP. (INPUT/OUTPUT) c Error bounds corresponding to the ordering in RITZ. c c SHIFTS Double precision array of length NP. (INPUT/OUTPUT) c On INPUT: contains the user specified shifts if ISHIFT = 0. c On OUTPUT: contains the shifts sorted into decreasing order c of magnitude with respect to the Ritz estimates contained in c BOUNDS. If ISHIFT = 0, SHIFTS is not modified on exit. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx real c c\Routines called: c dsortr ARPACK utility sorting routine. c ivout ARPACK utility routine that prints integers. c arscnd ARPACK utility routine for timing. c dvout ARPACK utility routine that prints vectors. c dcopy Level 1 BLAS that copies one vector to another. c dswap Level 1 BLAS that swaps the contents of two vectors. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c xx/xx/93: Version ' 2.1' c c\SCCS Information: @(#) c FILE: sgets.F SID: 2.4 DATE OF SID: 4/19/96 RELEASE: 2 c c\Remarks c c\EndLib c c----------------------------------------------------------------------- c subroutine dsgets ( ishift, which, kev, np, ritz, bounds, shifts ) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character*2 which integer ishift, kev, np c c %-----------------% c | Array Arguments | c %-----------------% c Double precision & bounds(kev+np), ritz(kev+np), shifts(np) c c %------------% c | Parameters | c %------------% c Double precision & one, zero parameter (one = 1.0D+0, zero = 0.0D+0) c c %---------------% c | Local Scalars | c %---------------% c integer kevd2, msglvl c c %----------------------% c | External Subroutines | c %----------------------% c external dswap, dcopy, dsortr, arscnd c c %---------------------% c | Intrinsic Functions | c %---------------------% c intrinsic max, min c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call arscnd (t0) msglvl = msgets c if (which .eq. 'BE') then c c %-----------------------------------------------------% c | Both ends of the spectrum are requested. | c | Sort the eigenvalues into algebraically increasing | c | order first then swap high end of the spectrum next | c | to low end in appropriate locations. | c | NOTE: when np < floor(kev/2) be careful not to swap | c | overlapping locations. | c %-----------------------------------------------------% c call dsortr ('LA', .true., kev+np, ritz, bounds) kevd2 = kev / 2 if ( kev .gt. 1 ) then call dswap ( min(kevd2,np), ritz, 1, & ritz( max(kevd2,np)+1 ), 1) call dswap ( min(kevd2,np), bounds, 1, & bounds( max(kevd2,np)+1 ), 1) end if c else c c %----------------------------------------------------% c | LM, SM, LA, SA case. | c | Sort the eigenvalues of H into the desired order | c | and apply the resulting order to BOUNDS. | c | The eigenvalues are sorted so that the wanted part | c | are always in the last KEV locations. | c %----------------------------------------------------% c call dsortr (which, .true., kev+np, ritz, bounds) end if c if (ishift .eq. 1 .and. np .gt. 0) then c c %-------------------------------------------------------% c | Sort the unwanted Ritz values used as shifts so that | c | the ones with largest Ritz estimates are first. | c | This will tend to minimize the effects of the | c | forward instability of the iteration when the shifts | c | are applied in subroutine dsapps. | c %-------------------------------------------------------% c call dsortr ('SM', .true., np, bounds, ritz) call dcopy (np, ritz, 1, shifts, 1) end if c call arscnd (t1) tsgets = tsgets + (t1 - t0) c if (msglvl .gt. 0) then call ivout (logfil, 1, kev, ndigit, '_sgets: KEV is') call ivout (logfil, 1, np, ndigit, '_sgets: NP is') call dvout (logfil, kev+np, ritz, ndigit, & '_sgets: Eigenvalues of current H matrix') call dvout (logfil, kev+np, bounds, ndigit, & '_sgets: Associated Ritz estimates') end if c return c c %---------------% c | End of dsgets | c %---------------% c end arpack-0.92.1/SRC/znaupd.f0000644000175000017500000006631510776001577012111 00000000000000c\BeginDoc c c\Name: znaupd c c\Description: c Reverse communication interface for the Implicitly Restarted Arnoldi c iteration. This is intended to be used to find a few eigenpairs of a c complex linear operator OP with respect to a semi-inner product defined c by a hermitian positive semi-definite real matrix B. B may be the identity c matrix. NOTE: if both OP and B are real, then dsaupd or dnaupd should c be used. c c c The computed approximate eigenvalues are called Ritz values and c the corresponding approximate eigenvectors are called Ritz vectors. c c znaupd is usually called iteratively to solve one of the c following problems: c c Mode 1: A*x = lambda*x. c ===> OP = A and B = I. c c Mode 2: A*x = lambda*M*x, M hermitian positive definite c ===> OP = inv[M]*A and B = M. c ===> (If M can be factored see remark 3 below) c c Mode 3: A*x = lambda*M*x, M hermitian semi-definite c ===> OP = inv[A - sigma*M]*M and B = M. c ===> shift-and-invert mode c If OP*x = amu*x, then lambda = sigma + 1/amu. c c c NOTE: The action of w <- inv[A - sigma*M]*v or w <- inv[M]*v c should be accomplished either by a direct method c using a sparse matrix factorization and solving c c [A - sigma*M]*w = v or M*w = v, c c or through an iterative method for solving these c systems. If an iterative method is used, the c convergence test must be more stringent than c the accuracy requirements for the eigenvalue c approximations. c c\Usage: c call znaupd c ( IDO, BMAT, N, WHICH, NEV, TOL, RESID, NCV, V, LDV, IPARAM, c IPNTR, WORKD, WORKL, LWORKL, RWORK, INFO ) c c\Arguments c IDO Integer. (INPUT/OUTPUT) c Reverse communication flag. IDO must be zero on the first c call to znaupd. IDO will be set internally to c indicate the type of operation to be performed. Control is c then given back to the calling routine which has the c responsibility to carry out the requested operation and call c znaupd with the result. The operand is given in c WORKD(IPNTR(1)), the result must be put in WORKD(IPNTR(2)). c ------------------------------------------------------------- c IDO = 0: first call to the reverse communication interface c IDO = -1: compute Y = OP * X where c IPNTR(1) is the pointer into WORKD for X, c IPNTR(2) is the pointer into WORKD for Y. c This is for the initialization phase to force the c starting vector into the range of OP. c IDO = 1: compute Y = OP * X where c IPNTR(1) is the pointer into WORKD for X, c IPNTR(2) is the pointer into WORKD for Y. c In mode 3, the vector B * X is already c available in WORKD(ipntr(3)). It does not c need to be recomputed in forming OP * X. c IDO = 2: compute Y = M * X where c IPNTR(1) is the pointer into WORKD for X, c IPNTR(2) is the pointer into WORKD for Y. c IDO = 3: compute and return the shifts in the first c NP locations of WORKL. c IDO = 99: done c ------------------------------------------------------------- c After the initialization phase, when the routine is used in c the "shift-and-invert" mode, the vector M * X is already c available and does not need to be recomputed in forming OP*X. c c BMAT Character*1. (INPUT) c BMAT specifies the type of the matrix B that defines the c semi-inner product for the operator OP. c BMAT = 'I' -> standard eigenvalue problem A*x = lambda*x c BMAT = 'G' -> generalized eigenvalue problem A*x = lambda*M*x c c N Integer. (INPUT) c Dimension of the eigenproblem. c c WHICH Character*2. (INPUT) c 'LM' -> want the NEV eigenvalues of largest magnitude. c 'SM' -> want the NEV eigenvalues of smallest magnitude. c 'LR' -> want the NEV eigenvalues of largest real part. c 'SR' -> want the NEV eigenvalues of smallest real part. c 'LI' -> want the NEV eigenvalues of largest imaginary part. c 'SI' -> want the NEV eigenvalues of smallest imaginary part. c c NEV Integer. (INPUT) c Number of eigenvalues of OP to be computed. 0 < NEV < N-1. c c TOL Double precision scalar. (INPUT) c Stopping criteria: the relative accuracy of the Ritz value c is considered acceptable if BOUNDS(I) .LE. TOL*ABS(RITZ(I)) c where ABS(RITZ(I)) is the magnitude when RITZ(I) is complex. c DEFAULT = dlamch('EPS') (machine precision as computed c by the LAPACK auxiliary subroutine dlamch). c c RESID Complex*16 array of length N. (INPUT/OUTPUT) c On INPUT: c If INFO .EQ. 0, a random initial residual vector is used. c If INFO .NE. 0, RESID contains the initial residual vector, c possibly from a previous run. c On OUTPUT: c RESID contains the final residual vector. c c NCV Integer. (INPUT) c Number of columns of the matrix V. NCV must satisfy the two c inequalities 1 <= NCV-NEV and NCV <= N. c This will indicate how many Arnoldi vectors are generated c at each iteration. After the startup phase in which NEV c Arnoldi vectors are generated, the algorithm generates c approximately NCV-NEV Arnoldi vectors at each subsequent update c iteration. Most of the cost in generating each Arnoldi vector is c in the matrix-vector operation OP*x. (See remark 4 below.) c c V Complex*16 array N by NCV. (OUTPUT) c Contains the final set of Arnoldi basis vectors. c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling program. c c IPARAM Integer array of length 11. (INPUT/OUTPUT) c IPARAM(1) = ISHIFT: method for selecting the implicit shifts. c The shifts selected at each iteration are used to filter out c the components of the unwanted eigenvector. c ------------------------------------------------------------- c ISHIFT = 0: the shifts are to be provided by the user via c reverse communication. The NCV eigenvalues of c the Hessenberg matrix H are returned in the part c of WORKL array corresponding to RITZ. c ISHIFT = 1: exact shifts with respect to the current c Hessenberg matrix H. This is equivalent to c restarting the iteration from the beginning c after updating the starting vector with a linear c combination of Ritz vectors associated with the c "wanted" eigenvalues. c ISHIFT = 2: other choice of internal shift to be defined. c ------------------------------------------------------------- c c IPARAM(2) = No longer referenced c c IPARAM(3) = MXITER c On INPUT: maximum number of Arnoldi update iterations allowed. c On OUTPUT: actual number of Arnoldi update iterations taken. c c IPARAM(4) = NB: blocksize to be used in the recurrence. c The code currently works only for NB = 1. c c IPARAM(5) = NCONV: number of "converged" Ritz values. c This represents the number of Ritz values that satisfy c the convergence criterion. c c IPARAM(6) = IUPD c No longer referenced. Implicit restarting is ALWAYS used. c c IPARAM(7) = MODE c On INPUT determines what type of eigenproblem is being solved. c Must be 1,2,3; See under \Description of znaupd for the c four modes available. c c IPARAM(8) = NP c When ido = 3 and the user provides shifts through reverse c communication (IPARAM(1)=0), _naupd returns NP, the number c of shifts the user is to provide. 0 < NP < NCV-NEV. c c IPARAM(9) = NUMOP, IPARAM(10) = NUMOPB, IPARAM(11) = NUMREO, c OUTPUT: NUMOP = total number of OP*x operations, c NUMOPB = total number of B*x operations if BMAT='G', c NUMREO = total number of steps of re-orthogonalization. c c IPNTR Integer array of length 14. (OUTPUT) c Pointer to mark the starting locations in the WORKD and WORKL c arrays for matrices/vectors used by the Arnoldi iteration. c ------------------------------------------------------------- c IPNTR(1): pointer to the current operand vector X in WORKD. c IPNTR(2): pointer to the current result vector Y in WORKD. c IPNTR(3): pointer to the vector B * X in WORKD when used in c the shift-and-invert mode. c IPNTR(4): pointer to the next available location in WORKL c that is untouched by the program. c IPNTR(5): pointer to the NCV by NCV upper Hessenberg c matrix H in WORKL. c IPNTR(6): pointer to the ritz value array RITZ c IPNTR(7): pointer to the (projected) ritz vector array Q c IPNTR(8): pointer to the error BOUNDS array in WORKL. c IPNTR(14): pointer to the NP shifts in WORKL. See Remark 5 below. c c Note: IPNTR(9:13) is only referenced by zneupd. See Remark 2 below. c c IPNTR(9): pointer to the NCV RITZ values of the c original system. c IPNTR(10): Not Used c IPNTR(11): pointer to the NCV corresponding error bounds. c IPNTR(12): pointer to the NCV by NCV upper triangular c Schur matrix for H. c IPNTR(13): pointer to the NCV by NCV matrix of eigenvectors c of the upper Hessenberg matrix H. Only referenced by c zneupd if RVEC = .TRUE. See Remark 2 below. c c ------------------------------------------------------------- c c WORKD Complex*16 work array of length 3*N. (REVERSE COMMUNICATION) c Distributed array to be used in the basic Arnoldi iteration c for reverse communication. The user should not use WORKD c as temporary workspace during the iteration !!!!!!!!!! c See Data Distribution Note below. c c WORKL Complex*16 work array of length LWORKL. (OUTPUT/WORKSPACE) c Private (replicated) array on each PE or array allocated on c the front end. See Data Distribution Note below. c c LWORKL Integer. (INPUT) c LWORKL must be at least 3*NCV**2 + 5*NCV. c c RWORK Double precision work array of length NCV (WORKSPACE) c Private (replicated) array on each PE or array allocated on c the front end. c c c INFO Integer. (INPUT/OUTPUT) c If INFO .EQ. 0, a randomly initial residual vector is used. c If INFO .NE. 0, RESID contains the initial residual vector, c possibly from a previous run. c Error flag on output. c = 0: Normal exit. c = 1: Maximum number of iterations taken. c All possible eigenvalues of OP has been found. IPARAM(5) c returns the number of wanted converged Ritz values. c = 2: No longer an informational error. Deprecated starting c with release 2 of ARPACK. c = 3: No shifts could be applied during a cycle of the c Implicitly restarted Arnoldi iteration. One possibility c is to increase the size of NCV relative to NEV. c See remark 4 below. c = -1: N must be positive. c = -2: NEV must be positive. c = -3: NCV-NEV >= 1 and less than or equal to N. c = -4: The maximum number of Arnoldi update iteration c must be greater than zero. c = -5: WHICH must be one of 'LM', 'SM', 'LR', 'SR', 'LI', 'SI' c = -6: BMAT must be one of 'I' or 'G'. c = -7: Length of private work array is not sufficient. c = -8: Error return from LAPACK eigenvalue calculation; c = -9: Starting vector is zero. c = -10: IPARAM(7) must be 1,2,3. c = -11: IPARAM(7) = 1 and BMAT = 'G' are incompatible. c = -12: IPARAM(1) must be equal to 0 or 1. c = -9999: Could not build an Arnoldi factorization. c User input error highly likely. Please c check actual array dimensions and layout. c IPARAM(5) returns the size of the current Arnoldi c factorization. c c\Remarks c 1. The computed Ritz values are approximate eigenvalues of OP. The c selection of WHICH should be made with this in mind when using c Mode = 3. When operating in Mode = 3 setting WHICH = 'LM' will c compute the NEV eigenvalues of the original problem that are c closest to the shift SIGMA . After convergence, approximate eigenvalues c of the original problem may be obtained with the ARPACK subroutine zneupd. c c 2. If a basis for the invariant subspace corresponding to the converged Ritz c values is needed, the user must call zneupd immediately following c completion of znaupd. This is new starting with release 2 of ARPACK. c c 3. If M can be factored into a Cholesky factorization M = LL` c then Mode = 2 should not be selected. Instead one should use c Mode = 1 with OP = inv(L)*A*inv(L`). Appropriate triangular c linear systems should be solved with L and L` rather c than computing inverses. After convergence, an approximate c eigenvector z of the original problem is recovered by solving c L`z = x where x is a Ritz vector of OP. c c 4. At present there is no a-priori analysis to guide the selection c of NCV relative to NEV. The only formal requirement is that NCV > NEV + 1. c However, it is recommended that NCV .ge. 2*NEV. If many problems of c the same type are to be solved, one should experiment with increasing c NCV while keeping NEV fixed for a given test problem. This will c usually decrease the required number of OP*x operations but it c also increases the work and storage required to maintain the orthogonal c basis vectors. The optimal "cross-over" with respect to CPU time c is problem dependent and must be determined empirically. c See Chapter 8 of Reference 2 for further information. c c 5. When IPARAM(1) = 0, and IDO = 3, the user needs to provide the c NP = IPARAM(8) complex shifts in locations c WORKL(IPNTR(14)), WORKL(IPNTR(14)+1), ... , WORKL(IPNTR(14)+NP). c Eigenvalues of the current upper Hessenberg matrix are located in c WORKL(IPNTR(6)) through WORKL(IPNTR(6)+NCV-1). They are ordered c according to the order defined by WHICH. The associated Ritz estimates c are located in WORKL(IPNTR(8)), WORKL(IPNTR(8)+1), ... , c WORKL(IPNTR(8)+NCV-1). c c----------------------------------------------------------------------- c c\Data Distribution Note: c c Fortran-D syntax: c ================ c Complex*16 resid(n), v(ldv,ncv), workd(3*n), workl(lworkl) c decompose d1(n), d2(n,ncv) c align resid(i) with d1(i) c align v(i,j) with d2(i,j) c align workd(i) with d1(i) range (1:n) c align workd(i) with d1(i-n) range (n+1:2*n) c align workd(i) with d1(i-2*n) range (2*n+1:3*n) c distribute d1(block), d2(block,:) c replicated workl(lworkl) c c Cray MPP syntax: c =============== c Complex*16 resid(n), v(ldv,ncv), workd(n,3), workl(lworkl) c shared resid(block), v(block,:), workd(block,:) c replicated workl(lworkl) c c CM2/CM5 syntax: c ============== c c----------------------------------------------------------------------- c c include 'ex-nonsym.doc' c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx Complex*16 c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly c Restarted Arnoldi Iteration", Rice University Technical Report c TR95-13, Department of Computational and Applied Mathematics. c 3. B.N. Parlett & Y. Saad, "_Complex_ Shift and Invert Strategies for c Double precision Matrices", Linear Algebra and its Applications, vol 88/89, c pp 575-595, (1987). c c\Routines called: c znaup2 ARPACK routine that implements the Implicitly Restarted c Arnoldi Iteration. c zstatn ARPACK routine that initializes the timing variables. c ivout ARPACK utility routine that prints integers. c zvout ARPACK utility routine that prints vectors. c arscnd ARPACK utility routine for timing. c dlamch LAPACK routine that determines machine constants. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: naupd.F SID: 2.9 DATE OF SID: 07/21/02 RELEASE: 2 c c\Remarks c c\EndLib c c----------------------------------------------------------------------- c subroutine znaupd & ( ido, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam, & ipntr, workd, workl, lworkl, rwork, info ) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character bmat*1, which*2 integer ido, info, ldv, lworkl, n, ncv, nev Double precision & tol c c %-----------------% c | Array Arguments | c %-----------------% c integer iparam(11), ipntr(14) Complex*16 & resid(n), v(ldv,ncv), workd(3*n), workl(lworkl) Double precision & rwork(ncv) c c %------------% c | Parameters | c %------------% c Complex*16 & one, zero parameter (one = (1.0D+0, 0.0D+0), zero = (0.0D+0, 0.0D+0)) c c %---------------% c | Local Scalars | c %---------------% c integer bounds, ierr, ih, iq, ishift, iupd, iw, & ldh, ldq, levec, mode, msglvl, mxiter, nb, & nev0, next, np, ritz, j save bounds, ih, iq, ishift, iupd, iw, & ldh, ldq, levec, mode, msglvl, mxiter, nb, & nev0, next, np, ritz c c %----------------------% c | External Subroutines | c %----------------------% c external znaup2, zvout, ivout, arscnd, zstatn c c %--------------------% c | External Functions | c %--------------------% c Double precision & dlamch external dlamch c c %-----------------------% c | Executable Statements | c %-----------------------% c if (ido .eq. 0) then c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call zstatn call arscnd (t0) msglvl = mcaupd c c %----------------% c | Error checking | c %----------------% c ierr = 0 ishift = iparam(1) c levec = iparam(2) mxiter = iparam(3) c nb = iparam(4) nb = 1 c c %--------------------------------------------% c | Revision 2 performs only implicit restart. | c %--------------------------------------------% c iupd = 1 mode = iparam(7) c if (n .le. 0) then ierr = -1 else if (nev .le. 0) then ierr = -2 else if (ncv .le. nev .or. ncv .gt. n) then ierr = -3 else if (mxiter .le. 0) then ierr = -4 else if (which .ne. 'LM' .and. & which .ne. 'SM' .and. & which .ne. 'LR' .and. & which .ne. 'SR' .and. & which .ne. 'LI' .and. & which .ne. 'SI') then ierr = -5 else if (bmat .ne. 'I' .and. bmat .ne. 'G') then ierr = -6 else if (lworkl .lt. 3*ncv**2 + 5*ncv) then ierr = -7 else if (mode .lt. 1 .or. mode .gt. 3) then ierr = -10 else if (mode .eq. 1 .and. bmat .eq. 'G') then ierr = -11 end if c c %------------% c | Error Exit | c %------------% c if (ierr .ne. 0) then info = ierr ido = 99 go to 9000 end if c c %------------------------% c | Set default parameters | c %------------------------% c if (nb .le. 0) nb = 1 if (tol .le. 0.0D+0 ) tol = dlamch('EpsMach') if (ishift .ne. 0 .and. & ishift .ne. 1 .and. & ishift .ne. 2) ishift = 1 c c %----------------------------------------------% c | NP is the number of additional steps to | c | extend the length NEV Lanczos factorization. | c | NEV0 is the local variable designating the | c | size of the invariant subspace desired. | c %----------------------------------------------% c np = ncv - nev nev0 = nev c c %-----------------------------% c | Zero out internal workspace | c %-----------------------------% c do 10 j = 1, 3*ncv**2 + 5*ncv workl(j) = zero 10 continue c c %-------------------------------------------------------------% c | Pointer into WORKL for address of H, RITZ, BOUNDS, Q | c | etc... and the remaining workspace. | c | Also update pointer to be used on output. | c | Memory is laid out as follows: | c | workl(1:ncv*ncv) := generated Hessenberg matrix | c | workl(ncv*ncv+1:ncv*ncv+ncv) := the ritz values | c | workl(ncv*ncv+ncv+1:ncv*ncv+2*ncv) := error bounds | c | workl(ncv*ncv+2*ncv+1:2*ncv*ncv+2*ncv) := rotation matrix Q | c | workl(2*ncv*ncv+2*ncv+1:3*ncv*ncv+5*ncv) := workspace | c | The final workspace is needed by subroutine zneigh called | c | by znaup2. Subroutine zneigh calls LAPACK routines for | c | calculating eigenvalues and the last row of the eigenvector | c | matrix. | c %-------------------------------------------------------------% c ldh = ncv ldq = ncv ih = 1 ritz = ih + ldh*ncv bounds = ritz + ncv iq = bounds + ncv iw = iq + ldq*ncv next = iw + ncv**2 + 3*ncv c ipntr(4) = next ipntr(5) = ih ipntr(6) = ritz ipntr(7) = iq ipntr(8) = bounds ipntr(14) = iw end if c c %-------------------------------------------------------% c | Carry out the Implicitly restarted Arnoldi Iteration. | c %-------------------------------------------------------% c call znaup2 & ( ido, bmat, n, which, nev0, np, tol, resid, mode, iupd, & ishift, mxiter, v, ldv, workl(ih), ldh, workl(ritz), & workl(bounds), workl(iq), ldq, workl(iw), & ipntr, workd, rwork, info ) c c %--------------------------------------------------% c | ido .ne. 99 implies use of reverse communication | c | to compute operations involving OP. | c %--------------------------------------------------% c if (ido .eq. 3) iparam(8) = np if (ido .ne. 99) go to 9000 c iparam(3) = mxiter iparam(5) = np iparam(9) = nopx iparam(10) = nbx iparam(11) = nrorth c c %------------------------------------% c | Exit if there was an informational | c | error within znaup2. | c %------------------------------------% c if (info .lt. 0) go to 9000 if (info .eq. 2) info = 3 c if (msglvl .gt. 0) then call ivout (logfil, 1, mxiter, ndigit, & '_naupd: Number of update iterations taken') call ivout (logfil, 1, np, ndigit, & '_naupd: Number of wanted "converged" Ritz values') call zvout (logfil, np, workl(ritz), ndigit, & '_naupd: The final Ritz values') call zvout (logfil, np, workl(bounds), ndigit, & '_naupd: Associated Ritz estimates') end if c call arscnd (t1) tcaupd = t1 - t0 c if (msglvl .gt. 0) then c c %--------------------------------------------------------% c | Version Number & Version Date are defined in version.h | c %--------------------------------------------------------% c write (6,1000) write (6,1100) mxiter, nopx, nbx, nrorth, nitref, nrstrt, & tmvopx, tmvbx, tcaupd, tcaup2, tcaitr, titref, & tgetv0, tceigh, tcgets, tcapps, tcconv, trvec 1000 format (//, & 5x, '=============================================',/ & 5x, '= Complex implicit Arnoldi update code =',/ & 5x, '= Version Number: ', ' 2.3', 21x, ' =',/ & 5x, '= Version Date: ', ' 07/31/96', 16x, ' =',/ & 5x, '=============================================',/ & 5x, '= Summary of timing statistics =',/ & 5x, '=============================================',//) 1100 format ( & 5x, 'Total number update iterations = ', i5,/ & 5x, 'Total number of OP*x operations = ', i5,/ & 5x, 'Total number of B*x operations = ', i5,/ & 5x, 'Total number of reorthogonalization steps = ', i5,/ & 5x, 'Total number of iterative refinement steps = ', i5,/ & 5x, 'Total number of restart steps = ', i5,/ & 5x, 'Total time in user OP*x operation = ', f12.6,/ & 5x, 'Total time in user B*x operation = ', f12.6,/ & 5x, 'Total time in Arnoldi update routine = ', f12.6,/ & 5x, 'Total time in naup2 routine = ', f12.6,/ & 5x, 'Total time in basic Arnoldi iteration loop = ', f12.6,/ & 5x, 'Total time in reorthogonalization phase = ', f12.6,/ & 5x, 'Total time in (re)start vector generation = ', f12.6,/ & 5x, 'Total time in Hessenberg eig. subproblem = ', f12.6,/ & 5x, 'Total time in getting the shifts = ', f12.6,/ & 5x, 'Total time in applying the shifts = ', f12.6,/ & 5x, 'Total time in convergence testing = ', f12.6,/ & 5x, 'Total time in computing final Ritz vectors = ', f12.6/) end if c 9000 continue c return c c %---------------% c | End of znaupd | c %---------------% c end arpack-0.92.1/SRC/csortc.f0000644000175000017500000001757510776001577012111 00000000000000c\BeginDoc c c\Name: csortc c c\Description: c Sorts the Complex array in X into the order c specified by WHICH and optionally applies the permutation to the c Real array Y. c c\Usage: c call csortc c ( WHICH, APPLY, N, X, Y ) c c\Arguments c WHICH Character*2. (Input) c 'LM' -> sort X into increasing order of magnitude. c 'SM' -> sort X into decreasing order of magnitude. c 'LR' -> sort X with real(X) in increasing algebraic order c 'SR' -> sort X with real(X) in decreasing algebraic order c 'LI' -> sort X with imag(X) in increasing algebraic order c 'SI' -> sort X with imag(X) in decreasing algebraic order c c APPLY Logical. (Input) c APPLY = .TRUE. -> apply the sorted order to array Y. c APPLY = .FALSE. -> do not apply the sorted order to array Y. c c N Integer. (INPUT) c Size of the arrays. c c X Complex array of length N. (INPUT/OUTPUT) c This is the array to be sorted. c c Y Complex array of length N. (INPUT/OUTPUT) c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Routines called: c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c Adapted from the sort routine in LANSO. c c\SCCS Information: @(#) c FILE: sortc.F SID: 2.2 DATE OF SID: 4/20/96 RELEASE: 2 c c\EndLib c c----------------------------------------------------------------------- c subroutine csortc (which, apply, n, x, y) c c %------------------% c | Scalar Arguments | c %------------------% c character*2 which logical apply integer n c c %-----------------% c | Array Arguments | c %-----------------% c Complex & x(0:n-1), y(0:n-1) c c %---------------% c | Local Scalars | c %---------------% c integer i, igap, j Complex & temp Real & temp1, temp2 c c %--------------------% c | External functions | c %--------------------% c Real & slapy2 c c %--------------------% c | Intrinsic Functions | c %--------------------% Intrinsic & real, aimag c c %-----------------------% c | Executable Statements | c %-----------------------% c igap = n / 2 c if (which .eq. 'LM') then c c %--------------------------------------------% c | Sort X into increasing order of magnitude. | c %--------------------------------------------% c 10 continue if (igap .eq. 0) go to 9000 c do 30 i = igap, n-1 j = i-igap 20 continue c if (j.lt.0) go to 30 c temp1 = slapy2(real(x(j)),aimag(x(j))) temp2 = slapy2(real(x(j+igap)),aimag(x(j+igap))) c if (temp1.gt.temp2) then temp = x(j) x(j) = x(j+igap) x(j+igap) = temp c if (apply) then temp = y(j) y(j) = y(j+igap) y(j+igap) = temp end if else go to 30 end if j = j-igap go to 20 30 continue igap = igap / 2 go to 10 c else if (which .eq. 'SM') then c c %--------------------------------------------% c | Sort X into decreasing order of magnitude. | c %--------------------------------------------% c 40 continue if (igap .eq. 0) go to 9000 c do 60 i = igap, n-1 j = i-igap 50 continue c if (j .lt. 0) go to 60 c temp1 = slapy2(real(x(j)),aimag(x(j))) temp2 = slapy2(real(x(j+igap)),aimag(x(j+igap))) c if (temp1.lt.temp2) then temp = x(j) x(j) = x(j+igap) x(j+igap) = temp c if (apply) then temp = y(j) y(j) = y(j+igap) y(j+igap) = temp end if else go to 60 endif j = j-igap go to 50 60 continue igap = igap / 2 go to 40 c else if (which .eq. 'LR') then c c %------------------------------------------------% c | Sort XREAL into increasing order of algebraic. | c %------------------------------------------------% c 70 continue if (igap .eq. 0) go to 9000 c do 90 i = igap, n-1 j = i-igap 80 continue c if (j.lt.0) go to 90 c if (real(x(j)).gt.real(x(j+igap))) then temp = x(j) x(j) = x(j+igap) x(j+igap) = temp c if (apply) then temp = y(j) y(j) = y(j+igap) y(j+igap) = temp end if else go to 90 endif j = j-igap go to 80 90 continue igap = igap / 2 go to 70 c else if (which .eq. 'SR') then c c %------------------------------------------------% c | Sort XREAL into decreasing order of algebraic. | c %------------------------------------------------% c 100 continue if (igap .eq. 0) go to 9000 do 120 i = igap, n-1 j = i-igap 110 continue c if (j.lt.0) go to 120 c if (real(x(j)).lt.real(x(j+igap))) then temp = x(j) x(j) = x(j+igap) x(j+igap) = temp c if (apply) then temp = y(j) y(j) = y(j+igap) y(j+igap) = temp end if else go to 120 endif j = j-igap go to 110 120 continue igap = igap / 2 go to 100 c else if (which .eq. 'LI') then c c %--------------------------------------------% c | Sort XIMAG into increasing algebraic order | c %--------------------------------------------% c 130 continue if (igap .eq. 0) go to 9000 do 150 i = igap, n-1 j = i-igap 140 continue c if (j.lt.0) go to 150 c if (aimag(x(j)).gt.aimag(x(j+igap))) then temp = x(j) x(j) = x(j+igap) x(j+igap) = temp c if (apply) then temp = y(j) y(j) = y(j+igap) y(j+igap) = temp end if else go to 150 endif j = j-igap go to 140 150 continue igap = igap / 2 go to 130 c else if (which .eq. 'SI') then c c %---------------------------------------------% c | Sort XIMAG into decreasing algebraic order | c %---------------------------------------------% c 160 continue if (igap .eq. 0) go to 9000 do 180 i = igap, n-1 j = i-igap 170 continue c if (j.lt.0) go to 180 c if (aimag(x(j)).lt.aimag(x(j+igap))) then temp = x(j) x(j) = x(j+igap) x(j+igap) = temp c if (apply) then temp = y(j) y(j) = y(j+igap) y(j+igap) = temp end if else go to 180 endif j = j-igap go to 170 180 continue igap = igap / 2 go to 160 end if c 9000 continue return c c %---------------% c | End of csortc | c %---------------% c end arpack-0.92.1/SRC/ssaup2.f0000644000175000017500000007670710776001577012033 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: ssaup2 c c\Description: c Intermediate level interface called by ssaupd. c c\Usage: c call ssaup2 c ( IDO, BMAT, N, WHICH, NEV, NP, TOL, RESID, MODE, IUPD, c ISHIFT, MXITER, V, LDV, H, LDH, RITZ, BOUNDS, Q, LDQ, WORKL, c IPNTR, WORKD, INFO ) c c\Arguments c c IDO, BMAT, N, WHICH, NEV, TOL, RESID: same as defined in ssaupd. c MODE, ISHIFT, MXITER: see the definition of IPARAM in ssaupd. c c NP Integer. (INPUT/OUTPUT) c Contains the number of implicit shifts to apply during c each Arnoldi/Lanczos iteration. c If ISHIFT=1, NP is adjusted dynamically at each iteration c to accelerate convergence and prevent stagnation. c This is also roughly equal to the number of matrix-vector c products (involving the operator OP) per Arnoldi iteration. c The logic for adjusting is contained within the current c subroutine. c If ISHIFT=0, NP is the number of shifts the user needs c to provide via reverse comunication. 0 < NP < NCV-NEV. c NP may be less than NCV-NEV since a leading block of the current c upper Tridiagonal matrix has split off and contains "unwanted" c Ritz values. c Upon termination of the IRA iteration, NP contains the number c of "converged" wanted Ritz values. c c IUPD Integer. (INPUT) c IUPD .EQ. 0: use explicit restart instead implicit update. c IUPD .NE. 0: use implicit update. c c V Real N by (NEV+NP) array. (INPUT/OUTPUT) c The Lanczos basis vectors. c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling c program. c c H Real (NEV+NP) by 2 array. (OUTPUT) c H is used to store the generated symmetric tridiagonal matrix c The subdiagonal is stored in the first column of H starting c at H(2,1). The main diagonal is stored in the second column c of H starting at H(1,2). If ssaup2 converges store the c B-norm of the final residual vector in H(1,1). c c LDH Integer. (INPUT) c Leading dimension of H exactly as declared in the calling c program. c c RITZ Real array of length NEV+NP. (OUTPUT) c RITZ(1:NEV) contains the computed Ritz values of OP. c c BOUNDS Real array of length NEV+NP. (OUTPUT) c BOUNDS(1:NEV) contain the error bounds corresponding to RITZ. c c Q Real (NEV+NP) by (NEV+NP) array. (WORKSPACE) c Private (replicated) work array used to accumulate the c rotation in the shift application step. c c LDQ Integer. (INPUT) c Leading dimension of Q exactly as declared in the calling c program. c c WORKL Real array of length at least 3*(NEV+NP). (INPUT/WORKSPACE) c Private (replicated) array on each PE or array allocated on c the front end. It is used in the computation of the c tridiagonal eigenvalue problem, the calculation and c application of the shifts and convergence checking. c If ISHIFT .EQ. O and IDO .EQ. 3, the first NP locations c of WORKL are used in reverse communication to hold the user c supplied shifts. c c IPNTR Integer array of length 3. (OUTPUT) c Pointer to mark the starting locations in the WORKD for c vectors used by the Lanczos iteration. c ------------------------------------------------------------- c IPNTR(1): pointer to the current operand vector X. c IPNTR(2): pointer to the current result vector Y. c IPNTR(3): pointer to the vector B * X when used in one of c the spectral transformation modes. X is the current c operand. c ------------------------------------------------------------- c c WORKD Real work array of length 3*N. (REVERSE COMMUNICATION) c Distributed array to be used in the basic Lanczos iteration c for reverse communication. The user should not use WORKD c as temporary workspace during the iteration !!!!!!!!!! c See Data Distribution Note in ssaupd. c c INFO Integer. (INPUT/OUTPUT) c If INFO .EQ. 0, a randomly initial residual vector is used. c If INFO .NE. 0, RESID contains the initial residual vector, c possibly from a previous run. c Error flag on output. c = 0: Normal return. c = 1: All possible eigenvalues of OP has been found. c NP returns the size of the invariant subspace c spanning the operator OP. c = 2: No shifts could be applied. c = -8: Error return from trid. eigenvalue calculation; c This should never happen. c = -9: Starting vector is zero. c = -9999: Could not build an Lanczos factorization. c Size that was built in returned in NP. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly c Restarted Arnoldi Iteration", Rice University Technical Report c TR95-13, Department of Computational and Applied Mathematics. c 3. B.N. Parlett, "The Symmetric Eigenvalue Problem". Prentice-Hall, c 1980. c 4. B.N. Parlett, B. Nour-Omid, "Towards a Black Box Lanczos Program", c Computer Physics Communications, 53 (1989), pp 169-179. c 5. B. Nour-Omid, B.N. Parlett, T. Ericson, P.S. Jensen, "How to c Implement the Spectral Transformation", Math. Comp., 48 (1987), c pp 663-673. c 6. R.G. Grimes, J.G. Lewis and H.D. Simon, "A Shifted Block Lanczos c Algorithm for Solving Sparse Symmetric Generalized Eigenproblems", c SIAM J. Matr. Anal. Apps., January (1993). c 7. L. Reichel, W.B. Gragg, "Algorithm 686: FORTRAN Subroutines c for Updating the QR decomposition", ACM TOMS, December 1990, c Volume 16 Number 4, pp 369-377. c c\Routines called: c sgetv0 ARPACK initial vector generation routine. c ssaitr ARPACK Lanczos factorization routine. c ssapps ARPACK application of implicit shifts routine. c ssconv ARPACK convergence of Ritz values routine. c sseigt ARPACK compute Ritz values and error bounds routine. c ssgets ARPACK reorder Ritz values and error bounds routine. c ssortr ARPACK sorting routine. c ivout ARPACK utility routine that prints integers. c arscnd ARPACK utility routine for timing. c svout ARPACK utility routine that prints vectors. c slamch LAPACK routine that determines machine constants. c scopy Level 1 BLAS that copies one vector to another. c sdot Level 1 BLAS that computes the scalar product of two vectors. c snrm2 Level 1 BLAS that computes the norm of a vector. c sscal Level 1 BLAS that scales a vector. c sswap Level 1 BLAS that swaps two vectors. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c 12/15/93: Version ' 2.4' c xx/xx/95: Version ' 2.4'. (R.B. Lehoucq) c c\SCCS Information: @(#) c FILE: saup2.F SID: 2.7 DATE OF SID: 5/19/98 RELEASE: 2 c c\EndLib c c----------------------------------------------------------------------- c subroutine ssaup2 & ( ido, bmat, n, which, nev, np, tol, resid, mode, iupd, & ishift, mxiter, v, ldv, h, ldh, ritz, bounds, & q, ldq, workl, ipntr, workd, info ) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character bmat*1, which*2 integer ido, info, ishift, iupd, ldh, ldq, ldv, mxiter, & n, mode, nev, np Real & tol c c %-----------------% c | Array Arguments | c %-----------------% c integer ipntr(3) Real & bounds(nev+np), h(ldh,2), q(ldq,nev+np), resid(n), & ritz(nev+np), v(ldv,nev+np), workd(3*n), & workl(3*(nev+np)) c c %------------% c | Parameters | c %------------% c Real & one, zero parameter (one = 1.0E+0, zero = 0.0E+0) c c %---------------% c | Local Scalars | c %---------------% c character wprime*2 logical cnorm, getv0, initv, update, ushift integer ierr, iter, j, kplusp, msglvl, nconv, nevbef, nev0, & np0, nptemp, nevd2, nevm2, kp(3) Real & rnorm, temp, eps23 save cnorm, getv0, initv, update, ushift, & iter, kplusp, msglvl, nconv, nev0, np0, & rnorm, eps23 c c %----------------------% c | External Subroutines | c %----------------------% c external scopy, sgetv0, ssaitr, sscal, ssconv, sseigt, ssgets, & ssapps, ssortr, svout, ivout, arscnd, sswap c c %--------------------% c | External Functions | c %--------------------% c Real & sdot, snrm2, slamch external sdot, snrm2, slamch c c %---------------------% c | Intrinsic Functions | c %---------------------% c intrinsic min c c %-----------------------% c | Executable Statements | c %-----------------------% c if (ido .eq. 0) then c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call arscnd (t0) msglvl = msaup2 c c %---------------------------------% c | Set machine dependent constant. | c %---------------------------------% c eps23 = slamch('Epsilon-Machine') eps23 = eps23**(2.0E+0/3.0E+0) c c %-------------------------------------% c | nev0 and np0 are integer variables | c | hold the initial values of NEV & NP | c %-------------------------------------% c nev0 = nev np0 = np c c %-------------------------------------% c | kplusp is the bound on the largest | c | Lanczos factorization built. | c | nconv is the current number of | c | "converged" eigenvlues. | c | iter is the counter on the current | c | iteration step. | c %-------------------------------------% c kplusp = nev0 + np0 nconv = 0 iter = 0 c c %--------------------------------------------% c | Set flags for computing the first NEV steps | c | of the Lanczos factorization. | c %--------------------------------------------% c getv0 = .true. update = .false. ushift = .false. cnorm = .false. c if (info .ne. 0) then c c %--------------------------------------------% c | User provides the initial residual vector. | c %--------------------------------------------% c initv = .true. info = 0 else initv = .false. end if end if c c %---------------------------------------------% c | Get a possibly random starting vector and | c | force it into the range of the operator OP. | c %---------------------------------------------% c 10 continue c if (getv0) then call sgetv0 (ido, bmat, 1, initv, n, 1, v, ldv, resid, rnorm, & ipntr, workd, info) c if (ido .ne. 99) go to 9000 c if (rnorm .eq. zero) then c c %-----------------------------------------% c | The initial vector is zero. Error exit. | c %-----------------------------------------% c info = -9 go to 1200 end if getv0 = .false. ido = 0 end if c c %------------------------------------------------------------% c | Back from reverse communication: continue with update step | c %------------------------------------------------------------% c if (update) go to 20 c c %-------------------------------------------% c | Back from computing user specified shifts | c %-------------------------------------------% c if (ushift) go to 50 c c %-------------------------------------% c | Back from computing residual norm | c | at the end of the current iteration | c %-------------------------------------% c if (cnorm) go to 100 c c %----------------------------------------------------------% c | Compute the first NEV steps of the Lanczos factorization | c %----------------------------------------------------------% c call ssaitr (ido, bmat, n, 0, nev0, mode, resid, rnorm, v, ldv, & h, ldh, ipntr, workd, info) c c %---------------------------------------------------% c | ido .ne. 99 implies use of reverse communication | c | to compute operations involving OP and possibly B | c %---------------------------------------------------% c if (ido .ne. 99) go to 9000 c if (info .gt. 0) then c c %-----------------------------------------------------% c | ssaitr was unable to build an Lanczos factorization | c | of length NEV0. INFO is returned with the size of | c | the factorization built. Exit main loop. | c %-----------------------------------------------------% c np = info mxiter = iter info = -9999 go to 1200 end if c c %--------------------------------------------------------------% c | | c | M A I N LANCZOS I T E R A T I O N L O O P | c | Each iteration implicitly restarts the Lanczos | c | factorization in place. | c | | c %--------------------------------------------------------------% c 1000 continue c iter = iter + 1 c if (msglvl .gt. 0) then call ivout (logfil, 1, iter, ndigit, & '_saup2: **** Start of major iteration number ****') end if if (msglvl .gt. 1) then call ivout (logfil, 1, nev, ndigit, & '_saup2: The length of the current Lanczos factorization') call ivout (logfil, 1, np, ndigit, & '_saup2: Extend the Lanczos factorization by') end if c c %------------------------------------------------------------% c | Compute NP additional steps of the Lanczos factorization. | c %------------------------------------------------------------% c ido = 0 20 continue update = .true. c call ssaitr (ido, bmat, n, nev, np, mode, resid, rnorm, v, & ldv, h, ldh, ipntr, workd, info) c c %---------------------------------------------------% c | ido .ne. 99 implies use of reverse communication | c | to compute operations involving OP and possibly B | c %---------------------------------------------------% c if (ido .ne. 99) go to 9000 c if (info .gt. 0) then c c %-----------------------------------------------------% c | ssaitr was unable to build an Lanczos factorization | c | of length NEV0+NP0. INFO is returned with the size | c | of the factorization built. Exit main loop. | c %-----------------------------------------------------% c np = info mxiter = iter info = -9999 go to 1200 end if update = .false. c if (msglvl .gt. 1) then call svout (logfil, 1, rnorm, ndigit, & '_saup2: Current B-norm of residual for factorization') end if c c %--------------------------------------------------------% c | Compute the eigenvalues and corresponding error bounds | c | of the current symmetric tridiagonal matrix. | c %--------------------------------------------------------% c call sseigt (rnorm, kplusp, h, ldh, ritz, bounds, workl, ierr) c if (ierr .ne. 0) then info = -8 go to 1200 end if c c %----------------------------------------------------% c | Make a copy of eigenvalues and corresponding error | c | bounds obtained from _seigt. | c %----------------------------------------------------% c call scopy(kplusp, ritz, 1, workl(kplusp+1), 1) call scopy(kplusp, bounds, 1, workl(2*kplusp+1), 1) c c %---------------------------------------------------% c | Select the wanted Ritz values and their bounds | c | to be used in the convergence test. | c | The selection is based on the requested number of | c | eigenvalues instead of the current NEV and NP to | c | prevent possible misconvergence. | c | * Wanted Ritz values := RITZ(NP+1:NEV+NP) | c | * Shifts := RITZ(1:NP) := WORKL(1:NP) | c %---------------------------------------------------% c nev = nev0 np = np0 call ssgets (ishift, which, nev, np, ritz, bounds, workl) c c %-------------------% c | Convergence test. | c %-------------------% c call scopy (nev, bounds(np+1), 1, workl(np+1), 1) call ssconv (nev, ritz(np+1), workl(np+1), tol, nconv) c if (msglvl .gt. 2) then kp(1) = nev kp(2) = np kp(3) = nconv call ivout (logfil, 3, kp, ndigit, & '_saup2: NEV, NP, NCONV are') call svout (logfil, kplusp, ritz, ndigit, & '_saup2: The eigenvalues of H') call svout (logfil, kplusp, bounds, ndigit, & '_saup2: Ritz estimates of the current NCV Ritz values') end if c c %---------------------------------------------------------% c | Count the number of unwanted Ritz values that have zero | c | Ritz estimates. If any Ritz estimates are equal to zero | c | then a leading block of H of order equal to at least | c | the number of Ritz values with zero Ritz estimates has | c | split off. None of these Ritz values may be removed by | c | shifting. Decrease NP the number of shifts to apply. If | c | no shifts may be applied, then prepare to exit | c %---------------------------------------------------------% c nptemp = np do 30 j=1, nptemp if (bounds(j) .eq. zero) then np = np - 1 nev = nev + 1 end if 30 continue c if ( (nconv .ge. nev0) .or. & (iter .gt. mxiter) .or. & (np .eq. 0) ) then c c %------------------------------------------------% c | Prepare to exit. Put the converged Ritz values | c | and corresponding bounds in RITZ(1:NCONV) and | c | BOUNDS(1:NCONV) respectively. Then sort. Be | c | careful when NCONV > NP since we don't want to | c | swap overlapping locations. | c %------------------------------------------------% c if (which .eq. 'BE') then c c %-----------------------------------------------------% c | Both ends of the spectrum are requested. | c | Sort the eigenvalues into algebraically decreasing | c | order first then swap low end of the spectrum next | c | to high end in appropriate locations. | c | NOTE: when np < floor(nev/2) be careful not to swap | c | overlapping locations. | c %-----------------------------------------------------% c wprime = 'SA' call ssortr (wprime, .true., kplusp, ritz, bounds) nevd2 = nev0 / 2 nevm2 = nev0 - nevd2 if ( nev .gt. 1 ) then call sswap ( min(nevd2,np), ritz(nevm2+1), 1, & ritz( max(kplusp-nevd2+1,kplusp-np+1) ), 1) call sswap ( min(nevd2,np), bounds(nevm2+1), 1, & bounds( max(kplusp-nevd2+1,kplusp-np+1)), 1) end if c else c c %--------------------------------------------------% c | LM, SM, LA, SA case. | c | Sort the eigenvalues of H into the an order that | c | is opposite to WHICH, and apply the resulting | c | order to BOUNDS. The eigenvalues are sorted so | c | that the wanted part are always within the first | c | NEV locations. | c %--------------------------------------------------% c if (which .eq. 'LM') wprime = 'SM' if (which .eq. 'SM') wprime = 'LM' if (which .eq. 'LA') wprime = 'SA' if (which .eq. 'SA') wprime = 'LA' c call ssortr (wprime, .true., kplusp, ritz, bounds) c end if c c %--------------------------------------------------% c | Scale the Ritz estimate of each Ritz value | c | by 1 / max(eps23,magnitude of the Ritz value). | c %--------------------------------------------------% c do 35 j = 1, nev0 temp = max( eps23, abs(ritz(j)) ) bounds(j) = bounds(j)/temp 35 continue c c %----------------------------------------------------% c | Sort the Ritz values according to the scaled Ritz | c | esitmates. This will push all the converged ones | c | towards the front of ritzr, ritzi, bounds | c | (in the case when NCONV < NEV.) | c %----------------------------------------------------% c wprime = 'LA' call ssortr(wprime, .true., nev0, bounds, ritz) c c %----------------------------------------------% c | Scale the Ritz estimate back to its original | c | value. | c %----------------------------------------------% c do 40 j = 1, nev0 temp = max( eps23, abs(ritz(j)) ) bounds(j) = bounds(j)*temp 40 continue c c %--------------------------------------------------% c | Sort the "converged" Ritz values again so that | c | the "threshold" values and their associated Ritz | c | estimates appear at the appropriate position in | c | ritz and bound. | c %--------------------------------------------------% c if (which .eq. 'BE') then c c %------------------------------------------------% c | Sort the "converged" Ritz values in increasing | c | order. The "threshold" values are in the | c | middle. | c %------------------------------------------------% c wprime = 'LA' call ssortr(wprime, .true., nconv, ritz, bounds) c else c c %----------------------------------------------% c | In LM, SM, LA, SA case, sort the "converged" | c | Ritz values according to WHICH so that the | c | "threshold" value appears at the front of | c | ritz. | c %----------------------------------------------% call ssortr(which, .true., nconv, ritz, bounds) c end if c c %------------------------------------------% c | Use h( 1,1 ) as storage to communicate | c | rnorm to _seupd if needed | c %------------------------------------------% c h(1,1) = rnorm c if (msglvl .gt. 1) then call svout (logfil, kplusp, ritz, ndigit, & '_saup2: Sorted Ritz values.') call svout (logfil, kplusp, bounds, ndigit, & '_saup2: Sorted ritz estimates.') end if c c %------------------------------------% c | Max iterations have been exceeded. | c %------------------------------------% c if (iter .gt. mxiter .and. nconv .lt. nev) info = 1 c c %---------------------% c | No shifts to apply. | c %---------------------% c if (np .eq. 0 .and. nconv .lt. nev0) info = 2 c np = nconv go to 1100 c else if (nconv .lt. nev .and. ishift .eq. 1) then c c %---------------------------------------------------% c | Do not have all the requested eigenvalues yet. | c | To prevent possible stagnation, adjust the number | c | of Ritz values and the shifts. | c %---------------------------------------------------% c nevbef = nev nev = nev + min (nconv, np/2) if (nev .eq. 1 .and. kplusp .ge. 6) then nev = kplusp / 2 else if (nev .eq. 1 .and. kplusp .gt. 2) then nev = 2 end if np = kplusp - nev c c %---------------------------------------% c | If the size of NEV was just increased | c | resort the eigenvalues. | c %---------------------------------------% c if (nevbef .lt. nev) & call ssgets (ishift, which, nev, np, ritz, bounds, & workl) c end if c if (msglvl .gt. 0) then call ivout (logfil, 1, nconv, ndigit, & '_saup2: no. of "converged" Ritz values at this iter.') if (msglvl .gt. 1) then kp(1) = nev kp(2) = np call ivout (logfil, 2, kp, ndigit, & '_saup2: NEV and NP are') call svout (logfil, nev, ritz(np+1), ndigit, & '_saup2: "wanted" Ritz values.') call svout (logfil, nev, bounds(np+1), ndigit, & '_saup2: Ritz estimates of the "wanted" values ') end if end if c if (ishift .eq. 0) then c c %-----------------------------------------------------% c | User specified shifts: reverse communication to | c | compute the shifts. They are returned in the first | c | NP locations of WORKL. | c %-----------------------------------------------------% c ushift = .true. ido = 3 go to 9000 end if c 50 continue c c %------------------------------------% c | Back from reverse communication; | c | User specified shifts are returned | c | in WORKL(1:*NP) | c %------------------------------------% c ushift = .false. c c c %---------------------------------------------------------% c | Move the NP shifts to the first NP locations of RITZ to | c | free up WORKL. This is for the non-exact shift case; | c | in the exact shift case, ssgets already handles this. | c %---------------------------------------------------------% c if (ishift .eq. 0) call scopy (np, workl, 1, ritz, 1) c if (msglvl .gt. 2) then call ivout (logfil, 1, np, ndigit, & '_saup2: The number of shifts to apply ') call svout (logfil, np, workl, ndigit, & '_saup2: shifts selected') if (ishift .eq. 1) then call svout (logfil, np, bounds, ndigit, & '_saup2: corresponding Ritz estimates') end if end if c c %---------------------------------------------------------% c | Apply the NP0 implicit shifts by QR bulge chasing. | c | Each shift is applied to the entire tridiagonal matrix. | c | The first 2*N locations of WORKD are used as workspace. | c | After ssapps is done, we have a Lanczos | c | factorization of length NEV. | c %---------------------------------------------------------% c call ssapps (n, nev, np, ritz, v, ldv, h, ldh, resid, q, ldq, & workd) c c %---------------------------------------------% c | Compute the B-norm of the updated residual. | c | Keep B*RESID in WORKD(1:N) to be used in | c | the first step of the next call to ssaitr. | c %---------------------------------------------% c cnorm = .true. call arscnd (t2) if (bmat .eq. 'G') then nbx = nbx + 1 call scopy (n, resid, 1, workd(n+1), 1) ipntr(1) = n + 1 ipntr(2) = 1 ido = 2 c c %----------------------------------% c | Exit in order to compute B*RESID | c %----------------------------------% c go to 9000 else if (bmat .eq. 'I') then call scopy (n, resid, 1, workd, 1) end if c 100 continue c c %----------------------------------% c | Back from reverse communication; | c | WORKD(1:N) := B*RESID | c %----------------------------------% c if (bmat .eq. 'G') then call arscnd (t3) tmvbx = tmvbx + (t3 - t2) end if c if (bmat .eq. 'G') then rnorm = sdot (n, resid, 1, workd, 1) rnorm = sqrt(abs(rnorm)) else if (bmat .eq. 'I') then rnorm = snrm2(n, resid, 1) end if cnorm = .false. 130 continue c if (msglvl .gt. 2) then call svout (logfil, 1, rnorm, ndigit, & '_saup2: B-norm of residual for NEV factorization') call svout (logfil, nev, h(1,2), ndigit, & '_saup2: main diagonal of compressed H matrix') call svout (logfil, nev-1, h(2,1), ndigit, & '_saup2: subdiagonal of compressed H matrix') end if c go to 1000 c c %---------------------------------------------------------------% c | | c | E N D O F M A I N I T E R A T I O N L O O P | c | | c %---------------------------------------------------------------% c 1100 continue c mxiter = iter nev = nconv c 1200 continue ido = 99 c c %------------% c | Error exit | c %------------% c call arscnd (t1) tsaup2 = t1 - t0 c 9000 continue return c c %---------------% c | End of ssaup2 | c %---------------% c end arpack-0.92.1/SRC/cgetv0.f0000644000175000017500000003115010776001577011765 00000000000000c\BeginDoc c c\Name: cgetv0 c c\Description: c Generate a random initial residual vector for the Arnoldi process. c Force the residual vector to be in the range of the operator OP. c c\Usage: c call cgetv0 c ( IDO, BMAT, ITRY, INITV, N, J, V, LDV, RESID, RNORM, c IPNTR, WORKD, IERR ) c c\Arguments c IDO Integer. (INPUT/OUTPUT) c Reverse communication flag. IDO must be zero on the first c call to cgetv0. c ------------------------------------------------------------- c IDO = 0: first call to the reverse communication interface c IDO = -1: compute Y = OP * X where c IPNTR(1) is the pointer into WORKD for X, c IPNTR(2) is the pointer into WORKD for Y. c This is for the initialization phase to force the c starting vector into the range of OP. c IDO = 2: compute Y = B * X where c IPNTR(1) is the pointer into WORKD for X, c IPNTR(2) is the pointer into WORKD for Y. c IDO = 99: done c ------------------------------------------------------------- c c BMAT Character*1. (INPUT) c BMAT specifies the type of the matrix B in the (generalized) c eigenvalue problem A*x = lambda*B*x. c B = 'I' -> standard eigenvalue problem A*x = lambda*x c B = 'G' -> generalized eigenvalue problem A*x = lambda*B*x c c ITRY Integer. (INPUT) c ITRY counts the number of times that cgetv0 is called. c It should be set to 1 on the initial call to cgetv0. c c INITV Logical variable. (INPUT) c .TRUE. => the initial residual vector is given in RESID. c .FALSE. => generate a random initial residual vector. c c N Integer. (INPUT) c Dimension of the problem. c c J Integer. (INPUT) c Index of the residual vector to be generated, with respect to c the Arnoldi process. J > 1 in case of a "restart". c c V Complex N by J array. (INPUT) c The first J-1 columns of V contain the current Arnoldi basis c if this is a "restart". c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling c program. c c RESID Complex array of length N. (INPUT/OUTPUT) c Initial residual vector to be generated. If RESID is c provided, force RESID into the range of the operator OP. c c RNORM Real scalar. (OUTPUT) c B-norm of the generated residual. c c IPNTR Integer array of length 3. (OUTPUT) c c WORKD Complex work array of length 2*N. (REVERSE COMMUNICATION). c On exit, WORK(1:N) = B*RESID to be used in SSAITR. c c IERR Integer. (OUTPUT) c = 0: Normal exit. c = -1: Cannot generate a nontrivial restarted residual vector c in the range of the operator OP. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx Complex c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c c\Routines called: c arscnd ARPACK utility routine for timing. c cvout ARPACK utility routine that prints vectors. c clarnv LAPACK routine for generating a random vector. c cgemv Level 2 BLAS routine for matrix vector multiplication. c ccopy Level 1 BLAS that copies one vector to another. c cdotc Level 1 BLAS that computes the scalar product of two vectors. c scnrm2 Level 1 BLAS that computes the norm of a vector. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: getv0.F SID: 2.3 DATE OF SID: 08/27/96 RELEASE: 2 c c\EndLib c c----------------------------------------------------------------------- c subroutine cgetv0 & ( ido, bmat, itry, initv, n, j, v, ldv, resid, rnorm, & ipntr, workd, ierr ) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character bmat*1 logical initv integer ido, ierr, itry, j, ldv, n Real & rnorm c c %-----------------% c | Array Arguments | c %-----------------% c integer ipntr(3) Complex & resid(n), v(ldv,j), workd(2*n) c c %------------% c | Parameters | c %------------% c Complex & one, zero Real & rzero parameter (one = (1.0E+0, 0.0E+0), zero = (0.0E+0, 0.0E+0), & rzero = 0.0E+0) c c %------------------------% c | Local Scalars & Arrays | c %------------------------% c logical first, inits, orth integer idist, iseed(4), iter, msglvl, jj Real & rnorm0 Complex & cnorm save first, iseed, inits, iter, msglvl, orth, rnorm0 c c %----------------------% c | External Subroutines | c %----------------------% c external ccopy, cgemv, clarnv, cvout, arscnd c c %--------------------% c | External Functions | c %--------------------% c Real & scnrm2, slapy2 Complex & cdotc external cdotc, scnrm2, slapy2 c c %-----------------% c | Data Statements | c %-----------------% c data inits /.true./ c c %-----------------------% c | Executable Statements | c %-----------------------% c c c %-----------------------------------% c | Initialize the seed of the LAPACK | c | random number generator | c %-----------------------------------% c if (inits) then iseed(1) = 1 iseed(2) = 3 iseed(3) = 5 iseed(4) = 7 inits = .false. end if c if (ido .eq. 0) then c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call arscnd (t0) msglvl = mgetv0 c ierr = 0 iter = 0 first = .FALSE. orth = .FALSE. c c %-----------------------------------------------------% c | Possibly generate a random starting vector in RESID | c | Use a LAPACK random number generator used by the | c | matrix generation routines. | c | idist = 1: uniform (0,1) distribution; | c | idist = 2: uniform (-1,1) distribution; | c | idist = 3: normal (0,1) distribution; | c %-----------------------------------------------------% c if (.not.initv) then idist = 2 call clarnv (idist, iseed, n, resid) end if c c %----------------------------------------------------------% c | Force the starting vector into the range of OP to handle | c | the generalized problem when B is possibly (singular). | c %----------------------------------------------------------% c call arscnd (t2) if (bmat .eq. 'G') then nopx = nopx + 1 ipntr(1) = 1 ipntr(2) = n + 1 call ccopy (n, resid, 1, workd, 1) ido = -1 go to 9000 end if end if c c %----------------------------------------% c | Back from computing B*(initial-vector) | c %----------------------------------------% c if (first) go to 20 c c %-----------------------------------------------% c | Back from computing B*(orthogonalized-vector) | c %-----------------------------------------------% c if (orth) go to 40 c call arscnd (t3) tmvopx = tmvopx + (t3 - t2) c c %------------------------------------------------------% c | Starting vector is now in the range of OP; r = OP*r; | c | Compute B-norm of starting vector. | c %------------------------------------------------------% c call arscnd (t2) first = .TRUE. if (bmat .eq. 'G') then nbx = nbx + 1 call ccopy (n, workd(n+1), 1, resid, 1) ipntr(1) = n + 1 ipntr(2) = 1 ido = 2 go to 9000 else if (bmat .eq. 'I') then call ccopy (n, resid, 1, workd, 1) end if c 20 continue c if (bmat .eq. 'G') then call arscnd (t3) tmvbx = tmvbx + (t3 - t2) end if c first = .FALSE. if (bmat .eq. 'G') then cnorm = cdotc (n, resid, 1, workd, 1) rnorm0 = sqrt(slapy2(real(cnorm),aimag(cnorm))) else if (bmat .eq. 'I') then rnorm0 = scnrm2(n, resid, 1) end if rnorm = rnorm0 c c %---------------------------------------------% c | Exit if this is the very first Arnoldi step | c %---------------------------------------------% c if (j .eq. 1) go to 50 c c %---------------------------------------------------------------- c | Otherwise need to B-orthogonalize the starting vector against | c | the current Arnoldi basis using Gram-Schmidt with iter. ref. | c | This is the case where an invariant subspace is encountered | c | in the middle of the Arnoldi factorization. | c | | c | s = V^{T}*B*r; r = r - V*s; | c | | c | Stopping criteria used for iter. ref. is discussed in | c | Parlett's book, page 107 and in Gragg & Reichel TOMS paper. | c %---------------------------------------------------------------% c orth = .TRUE. 30 continue c call cgemv ('C', n, j-1, one, v, ldv, workd, 1, & zero, workd(n+1), 1) call cgemv ('N', n, j-1, -one, v, ldv, workd(n+1), 1, & one, resid, 1) c c %----------------------------------------------------------% c | Compute the B-norm of the orthogonalized starting vector | c %----------------------------------------------------------% c call arscnd (t2) if (bmat .eq. 'G') then nbx = nbx + 1 call ccopy (n, resid, 1, workd(n+1), 1) ipntr(1) = n + 1 ipntr(2) = 1 ido = 2 go to 9000 else if (bmat .eq. 'I') then call ccopy (n, resid, 1, workd, 1) end if c 40 continue c if (bmat .eq. 'G') then call arscnd (t3) tmvbx = tmvbx + (t3 - t2) end if c if (bmat .eq. 'G') then cnorm = cdotc (n, resid, 1, workd, 1) rnorm = sqrt(slapy2(real(cnorm),aimag(cnorm))) else if (bmat .eq. 'I') then rnorm = scnrm2(n, resid, 1) end if c c %--------------------------------------% c | Check for further orthogonalization. | c %--------------------------------------% c if (msglvl .gt. 2) then call svout (logfil, 1, rnorm0, ndigit, & '_getv0: re-orthonalization ; rnorm0 is') call svout (logfil, 1, rnorm, ndigit, & '_getv0: re-orthonalization ; rnorm is') end if c if (rnorm .gt. 0.717*rnorm0) go to 50 c iter = iter + 1 if (iter .le. 1) then c c %-----------------------------------% c | Perform iterative refinement step | c %-----------------------------------% c rnorm0 = rnorm go to 30 else c c %------------------------------------% c | Iterative refinement step "failed" | c %------------------------------------% c do 45 jj = 1, n resid(jj) = zero 45 continue rnorm = rzero ierr = -1 end if c 50 continue c if (msglvl .gt. 0) then call svout (logfil, 1, rnorm, ndigit, & '_getv0: B-norm of initial / restarted starting vector') end if if (msglvl .gt. 2) then call cvout (logfil, n, resid, ndigit, & '_getv0: initial / restarted starting vector') end if ido = 99 c call arscnd (t1) tgetv0 = tgetv0 + (t1 - t0) c 9000 continue return c c %---------------% c | End of cgetv0 | c %---------------% c end arpack-0.92.1/SRC/cngets.f0000644000175000017500000001267310776001577012071 00000000000000c\BeginDoc c c\Name: cngets c c\Description: c Given the eigenvalues of the upper Hessenberg matrix H, c computes the NP shifts AMU that are zeros of the polynomial of c degree NP which filters out components of the unwanted eigenvectors c corresponding to the AMU's based on some given criteria. c c NOTE: call this even in the case of user specified shifts in order c to sort the eigenvalues, and error bounds of H for later use. c c\Usage: c call cngets c ( ISHIFT, WHICH, KEV, NP, RITZ, BOUNDS ) c c\Arguments c ISHIFT Integer. (INPUT) c Method for selecting the implicit shifts at each iteration. c ISHIFT = 0: user specified shifts c ISHIFT = 1: exact shift with respect to the matrix H. c c WHICH Character*2. (INPUT) c Shift selection criteria. c 'LM' -> want the KEV eigenvalues of largest magnitude. c 'SM' -> want the KEV eigenvalues of smallest magnitude. c 'LR' -> want the KEV eigenvalues of largest REAL part. c 'SR' -> want the KEV eigenvalues of smallest REAL part. c 'LI' -> want the KEV eigenvalues of largest imaginary part. c 'SI' -> want the KEV eigenvalues of smallest imaginary part. c c KEV Integer. (INPUT) c The number of desired eigenvalues. c c NP Integer. (INPUT) c The number of shifts to compute. c c RITZ Complex array of length KEV+NP. (INPUT/OUTPUT) c On INPUT, RITZ contains the the eigenvalues of H. c On OUTPUT, RITZ are sorted so that the unwanted c eigenvalues are in the first NP locations and the wanted c portion is in the last KEV locations. When exact shifts are c selected, the unwanted part corresponds to the shifts to c be applied. Also, if ISHIFT .eq. 1, the unwanted eigenvalues c are further sorted so that the ones with largest Ritz values c are first. c c BOUNDS Complex array of length KEV+NP. (INPUT/OUTPUT) c Error bounds corresponding to the ordering in RITZ. c c c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx Complex c c\Routines called: c csortc ARPACK sorting routine. c ivout ARPACK utility routine that prints integers. c arscnd ARPACK utility routine for timing. c cvout ARPACK utility routine that prints vectors. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: ngets.F SID: 2.2 DATE OF SID: 4/20/96 RELEASE: 2 c c\Remarks c 1. This routine does not keep complex conjugate pairs of c eigenvalues together. c c\EndLib c c----------------------------------------------------------------------- c subroutine cngets ( ishift, which, kev, np, ritz, bounds) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character*2 which integer ishift, kev, np c c %-----------------% c | Array Arguments | c %-----------------% c Complex & bounds(kev+np), ritz(kev+np) c c %------------% c | Parameters | c %------------% c Complex & one, zero parameter (one = (1.0E+0, 0.0E+0), zero = (0.0E+0, 0.0E+0)) c c %---------------% c | Local Scalars | c %---------------% c integer msglvl c c %----------------------% c | External Subroutines | c %----------------------% c external cvout, csortc, arscnd c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call arscnd (t0) msglvl = mcgets c call csortc (which, .true., kev+np, ritz, bounds) c if ( ishift .eq. 1 ) then c c %-------------------------------------------------------% c | Sort the unwanted Ritz values used as shifts so that | c | the ones with largest Ritz estimates are first | c | This will tend to minimize the effects of the | c | forward instability of the iteration when the shifts | c | are applied in subroutine cnapps. | c | Be careful and use 'SM' since we want to sort BOUNDS! | c %-------------------------------------------------------% c call csortc ( 'SM', .true., np, bounds, ritz ) c end if c call arscnd (t1) tcgets = tcgets + (t1 - t0) c if (msglvl .gt. 0) then call ivout (logfil, 1, kev, ndigit, '_ngets: KEV is') call ivout (logfil, 1, np, ndigit, '_ngets: NP is') call cvout (logfil, kev+np, ritz, ndigit, & '_ngets: Eigenvalues of current H matrix ') call cvout (logfil, kev+np, bounds, ndigit, & '_ngets: Ritz estimates of the current KEV+NP Ritz values') end if c return c c %---------------% c | End of cngets | c %---------------% c end arpack-0.92.1/SRC/sstqrb.f0000644000175000017500000004046410776001577012123 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: sstqrb c c\Description: c Computes all eigenvalues and the last component of the eigenvectors c of a symmetric tridiagonal matrix using the implicit QL or QR method. c c This is mostly a modification of the LAPACK routine ssteqr. c See Remarks. c c\Usage: c call sstqrb c ( N, D, E, Z, WORK, INFO ) c c\Arguments c N Integer. (INPUT) c The number of rows and columns in the matrix. N >= 0. c c D Real array, dimension (N). (INPUT/OUTPUT) c On entry, D contains the diagonal elements of the c tridiagonal matrix. c On exit, D contains the eigenvalues, in ascending order. c If an error exit is made, the eigenvalues are correct c for indices 1,2,...,INFO-1, but they are unordered and c may not be the smallest eigenvalues of the matrix. c c E Real array, dimension (N-1). (INPUT/OUTPUT) c On entry, E contains the subdiagonal elements of the c tridiagonal matrix in positions 1 through N-1. c On exit, E has been destroyed. c c Z Real array, dimension (N). (OUTPUT) c On exit, Z contains the last row of the orthonormal c eigenvector matrix of the symmetric tridiagonal matrix. c If an error exit is made, Z contains the last row of the c eigenvector matrix associated with the stored eigenvalues. c c WORK Real array, dimension (max(1,2*N-2)). (WORKSPACE) c Workspace used in accumulating the transformation for c computing the last components of the eigenvectors. c c INFO Integer. (OUTPUT) c = 0: normal return. c < 0: if INFO = -i, the i-th argument had an illegal value. c > 0: if INFO = +i, the i-th eigenvalue has not converged c after a total of 30*N iterations. c c\Remarks c 1. None. c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx real c c\Routines called: c saxpy Level 1 BLAS that computes a vector triad. c scopy Level 1 BLAS that copies one vector to another. c sswap Level 1 BLAS that swaps the contents of two vectors. c lsame LAPACK character comparison routine. c slae2 LAPACK routine that computes the eigenvalues of a 2-by-2 c symmetric matrix. c slaev2 LAPACK routine that eigendecomposition of a 2-by-2 symmetric c matrix. c slamch LAPACK routine that determines machine constants. c slanst LAPACK routine that computes the norm of a matrix. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c slartg LAPACK Givens rotation construction routine. c slascl LAPACK routine for careful scaling of a matrix. c slaset LAPACK matrix initialization routine. c slasr LAPACK routine that applies an orthogonal transformation to c a matrix. c slasrt LAPACK sorting routine. c ssteqr LAPACK routine that computes eigenvalues and eigenvectors c of a symmetric tridiagonal matrix. c xerbla LAPACK error handler routine. c c\Authors c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: stqrb.F SID: 2.5 DATE OF SID: 8/27/96 RELEASE: 2 c c\Remarks c 1. Starting with version 2.5, this routine is a modified version c of LAPACK version 2.0 subroutine SSTEQR. No lines are deleted, c only commeted out and new lines inserted. c All lines commented out have "c$$$" at the beginning. c Note that the LAPACK version 1.0 subroutine SSTEQR contained c bugs. c c\EndLib c c----------------------------------------------------------------------- c subroutine sstqrb ( n, d, e, z, work, info ) c c %------------------% c | Scalar Arguments | c %------------------% c integer info, n c c %-----------------% c | Array Arguments | c %-----------------% c Real & d( n ), e( n-1 ), z( n ), work( 2*n-2 ) c c .. parameters .. Real & zero, one, two, three parameter ( zero = 0.0E+0, one = 1.0E+0, & two = 2.0E+0, three = 3.0E+0 ) integer maxit parameter ( maxit = 30 ) c .. c .. local scalars .. integer i, icompz, ii, iscale, j, jtot, k, l, l1, lend, & lendm1, lendp1, lendsv, lm1, lsv, m, mm, mm1, & nm1, nmaxit Real & anorm, b, c, eps, eps2, f, g, p, r, rt1, rt2, & s, safmax, safmin, ssfmax, ssfmin, tst c .. c .. external functions .. logical lsame Real & slamch, slanst, slapy2 external lsame, slamch, slanst, slapy2 c .. c .. external subroutines .. external slae2, slaev2, slartg, slascl, slaset, slasr, & slasrt, sswap, xerbla c .. c .. intrinsic functions .. intrinsic abs, max, sign, sqrt c .. c .. executable statements .. c c test the input parameters. c info = 0 c c$$$ IF( LSAME( COMPZ, 'N' ) ) THEN c$$$ ICOMPZ = 0 c$$$ ELSE IF( LSAME( COMPZ, 'V' ) ) THEN c$$$ ICOMPZ = 1 c$$$ ELSE IF( LSAME( COMPZ, 'I' ) ) THEN c$$$ ICOMPZ = 2 c$$$ ELSE c$$$ ICOMPZ = -1 c$$$ END IF c$$$ IF( ICOMPZ.LT.0 ) THEN c$$$ INFO = -1 c$$$ ELSE IF( N.LT.0 ) THEN c$$$ INFO = -2 c$$$ ELSE IF( ( LDZ.LT.1 ) .OR. ( ICOMPZ.GT.0 .AND. LDZ.LT.MAX( 1, c$$$ $ N ) ) ) THEN c$$$ INFO = -6 c$$$ END IF c$$$ IF( INFO.NE.0 ) THEN c$$$ CALL XERBLA( 'SSTEQR', -INFO ) c$$$ RETURN c$$$ END IF c c *** New starting with version 2.5 *** c icompz = 2 c ************************************* c c quick return if possible c if( n.eq.0 ) $ return c if( n.eq.1 ) then if( icompz.eq.2 ) z( 1 ) = one return end if c c determine the unit roundoff and over/underflow thresholds. c eps = slamch( 'e' ) eps2 = eps**2 safmin = slamch( 's' ) safmax = one / safmin ssfmax = sqrt( safmax ) / three ssfmin = sqrt( safmin ) / eps2 c c compute the eigenvalues and eigenvectors of the tridiagonal c matrix. c c$$ if( icompz.eq.2 ) c$$$ $ call slaset( 'full', n, n, zero, one, z, ldz ) c c *** New starting with version 2.5 *** c if ( icompz .eq. 2 ) then do 5 j = 1, n-1 z(j) = zero 5 continue z( n ) = one end if c ************************************* c nmaxit = n*maxit jtot = 0 c c determine where the matrix splits and choose ql or qr iteration c for each block, according to whether top or bottom diagonal c element is smaller. c l1 = 1 nm1 = n - 1 c 10 continue if( l1.gt.n ) $ go to 160 if( l1.gt.1 ) $ e( l1-1 ) = zero if( l1.le.nm1 ) then do 20 m = l1, nm1 tst = abs( e( m ) ) if( tst.eq.zero ) $ go to 30 if( tst.le.( sqrt( abs( d( m ) ) )*sqrt( abs( d( m+ $ 1 ) ) ) )*eps ) then e( m ) = zero go to 30 end if 20 continue end if m = n c 30 continue l = l1 lsv = l lend = m lendsv = lend l1 = m + 1 if( lend.eq.l ) $ go to 10 c c scale submatrix in rows and columns l to lend c anorm = slanst( 'i', lend-l+1, d( l ), e( l ) ) iscale = 0 if( anorm.eq.zero ) $ go to 10 if( anorm.gt.ssfmax ) then iscale = 1 call slascl( 'g', 0, 0, anorm, ssfmax, lend-l+1, 1, d( l ), n, $ info ) call slascl( 'g', 0, 0, anorm, ssfmax, lend-l, 1, e( l ), n, $ info ) else if( anorm.lt.ssfmin ) then iscale = 2 call slascl( 'g', 0, 0, anorm, ssfmin, lend-l+1, 1, d( l ), n, $ info ) call slascl( 'g', 0, 0, anorm, ssfmin, lend-l, 1, e( l ), n, $ info ) end if c c choose between ql and qr iteration c if( abs( d( lend ) ).lt.abs( d( l ) ) ) then lend = lsv l = lendsv end if c if( lend.gt.l ) then c c ql iteration c c look for small subdiagonal element. c 40 continue if( l.ne.lend ) then lendm1 = lend - 1 do 50 m = l, lendm1 tst = abs( e( m ) )**2 if( tst.le.( eps2*abs( d( m ) ) )*abs( d( m+1 ) )+ $ safmin )go to 60 50 continue end if c m = lend c 60 continue if( m.lt.lend ) $ e( m ) = zero p = d( l ) if( m.eq.l ) $ go to 80 c c if remaining matrix is 2-by-2, use slae2 or slaev2 c to compute its eigensystem. c if( m.eq.l+1 ) then if( icompz.gt.0 ) then call slaev2( d( l ), e( l ), d( l+1 ), rt1, rt2, c, s ) work( l ) = c work( n-1+l ) = s c$$$ call slasr( 'r', 'v', 'b', n, 2, work( l ), c$$$ $ work( n-1+l ), z( 1, l ), ldz ) c c *** New starting with version 2.5 *** c tst = z(l+1) z(l+1) = c*tst - s*z(l) z(l) = s*tst + c*z(l) c ************************************* else call slae2( d( l ), e( l ), d( l+1 ), rt1, rt2 ) end if d( l ) = rt1 d( l+1 ) = rt2 e( l ) = zero l = l + 2 if( l.le.lend ) $ go to 40 go to 140 end if c if( jtot.eq.nmaxit ) $ go to 140 jtot = jtot + 1 c c form shift. c g = ( d( l+1 )-p ) / ( two*e( l ) ) r = slapy2( g, one ) g = d( m ) - p + ( e( l ) / ( g+sign( r, g ) ) ) c s = one c = one p = zero c c inner loop c mm1 = m - 1 do 70 i = mm1, l, -1 f = s*e( i ) b = c*e( i ) call slartg( g, f, c, s, r ) if( i.ne.m-1 ) $ e( i+1 ) = r g = d( i+1 ) - p r = ( d( i )-g )*s + two*c*b p = s*r d( i+1 ) = g + p g = c*r - b c c if eigenvectors are desired, then save rotations. c if( icompz.gt.0 ) then work( i ) = c work( n-1+i ) = -s end if c 70 continue c c if eigenvectors are desired, then apply saved rotations. c if( icompz.gt.0 ) then mm = m - l + 1 c$$$ call slasr( 'r', 'v', 'b', n, mm, work( l ), work( n-1+l ), c$$$ $ z( 1, l ), ldz ) c c *** New starting with version 2.5 *** c call slasr( 'r', 'v', 'b', 1, mm, work( l ), & work( n-1+l ), z( l ), 1 ) c ************************************* end if c d( l ) = d( l ) - p e( l ) = g go to 40 c c eigenvalue found. c 80 continue d( l ) = p c l = l + 1 if( l.le.lend ) $ go to 40 go to 140 c else c c qr iteration c c look for small superdiagonal element. c 90 continue if( l.ne.lend ) then lendp1 = lend + 1 do 100 m = l, lendp1, -1 tst = abs( e( m-1 ) )**2 if( tst.le.( eps2*abs( d( m ) ) )*abs( d( m-1 ) )+ $ safmin )go to 110 100 continue end if c m = lend c 110 continue if( m.gt.lend ) $ e( m-1 ) = zero p = d( l ) if( m.eq.l ) $ go to 130 c c if remaining matrix is 2-by-2, use slae2 or slaev2 c to compute its eigensystem. c if( m.eq.l-1 ) then if( icompz.gt.0 ) then call slaev2( d( l-1 ), e( l-1 ), d( l ), rt1, rt2, c, s ) c$$$ work( m ) = c c$$$ work( n-1+m ) = s c$$$ call slasr( 'r', 'v', 'f', n, 2, work( m ), c$$$ $ work( n-1+m ), z( 1, l-1 ), ldz ) c c *** New starting with version 2.5 *** c tst = z(l) z(l) = c*tst - s*z(l-1) z(l-1) = s*tst + c*z(l-1) c ************************************* else call slae2( d( l-1 ), e( l-1 ), d( l ), rt1, rt2 ) end if d( l-1 ) = rt1 d( l ) = rt2 e( l-1 ) = zero l = l - 2 if( l.ge.lend ) $ go to 90 go to 140 end if c if( jtot.eq.nmaxit ) $ go to 140 jtot = jtot + 1 c c form shift. c g = ( d( l-1 )-p ) / ( two*e( l-1 ) ) r = slapy2( g, one ) g = d( m ) - p + ( e( l-1 ) / ( g+sign( r, g ) ) ) c s = one c = one p = zero c c inner loop c lm1 = l - 1 do 120 i = m, lm1 f = s*e( i ) b = c*e( i ) call slartg( g, f, c, s, r ) if( i.ne.m ) $ e( i-1 ) = r g = d( i ) - p r = ( d( i+1 )-g )*s + two*c*b p = s*r d( i ) = g + p g = c*r - b c c if eigenvectors are desired, then save rotations. c if( icompz.gt.0 ) then work( i ) = c work( n-1+i ) = s end if c 120 continue c c if eigenvectors are desired, then apply saved rotations. c if( icompz.gt.0 ) then mm = l - m + 1 c$$$ call slasr( 'r', 'v', 'f', n, mm, work( m ), work( n-1+m ), c$$$ $ z( 1, m ), ldz ) c c *** New starting with version 2.5 *** c call slasr( 'r', 'v', 'f', 1, mm, work( m ), work( n-1+m ), & z( m ), 1 ) c ************************************* end if c d( l ) = d( l ) - p e( lm1 ) = g go to 90 c c eigenvalue found. c 130 continue d( l ) = p c l = l - 1 if( l.ge.lend ) $ go to 90 go to 140 c end if c c undo scaling if necessary c 140 continue if( iscale.eq.1 ) then call slascl( 'g', 0, 0, ssfmax, anorm, lendsv-lsv+1, 1, $ d( lsv ), n, info ) call slascl( 'g', 0, 0, ssfmax, anorm, lendsv-lsv, 1, e( lsv ), $ n, info ) else if( iscale.eq.2 ) then call slascl( 'g', 0, 0, ssfmin, anorm, lendsv-lsv+1, 1, $ d( lsv ), n, info ) call slascl( 'g', 0, 0, ssfmin, anorm, lendsv-lsv, 1, e( lsv ), $ n, info ) end if c c check for no convergence to an eigenvalue after a total c of n*maxit iterations. c if( jtot.lt.nmaxit ) $ go to 10 do 150 i = 1, n - 1 if( e( i ).ne.zero ) $ info = info + 1 150 continue go to 190 c c order eigenvalues and eigenvectors. c 160 continue if( icompz.eq.0 ) then c c use quick sort c call slasrt( 'i', n, d, info ) c else c c use selection sort to minimize swaps of eigenvectors c do 180 ii = 2, n i = ii - 1 k = i p = d( i ) do 170 j = ii, n if( d( j ).lt.p ) then k = j p = d( j ) end if 170 continue if( k.ne.i ) then d( k ) = d( i ) d( i ) = p c$$$ call sswap( n, z( 1, i ), 1, z( 1, k ), 1 ) c *** New starting with version 2.5 *** c p = z(k) z(k) = z(i) z(i) = p c ************************************* end if 180 continue end if c 190 continue return c c %---------------% c | End of sstqrb | c %---------------% c end arpack-0.92.1/SRC/dnaup2.f0000644000175000017500000007536510776001577012006 00000000000000c\BeginDoc c c\Name: dnaup2 c c\Description: c Intermediate level interface called by dnaupd. c c\Usage: c call dnaup2 c ( IDO, BMAT, N, WHICH, NEV, NP, TOL, RESID, MODE, IUPD, c ISHIFT, MXITER, V, LDV, H, LDH, RITZR, RITZI, BOUNDS, c Q, LDQ, WORKL, IPNTR, WORKD, INFO ) c c\Arguments c c IDO, BMAT, N, WHICH, NEV, TOL, RESID: same as defined in dnaupd. c MODE, ISHIFT, MXITER: see the definition of IPARAM in dnaupd. c c NP Integer. (INPUT/OUTPUT) c Contains the number of implicit shifts to apply during c each Arnoldi iteration. c If ISHIFT=1, NP is adjusted dynamically at each iteration c to accelerate convergence and prevent stagnation. c This is also roughly equal to the number of matrix-vector c products (involving the operator OP) per Arnoldi iteration. c The logic for adjusting is contained within the current c subroutine. c If ISHIFT=0, NP is the number of shifts the user needs c to provide via reverse comunication. 0 < NP < NCV-NEV. c NP may be less than NCV-NEV for two reasons. The first, is c to keep complex conjugate pairs of "wanted" Ritz values c together. The second, is that a leading block of the current c upper Hessenberg matrix has split off and contains "unwanted" c Ritz values. c Upon termination of the IRA iteration, NP contains the number c of "converged" wanted Ritz values. c c IUPD Integer. (INPUT) c IUPD .EQ. 0: use explicit restart instead implicit update. c IUPD .NE. 0: use implicit update. c c V Double precision N by (NEV+NP) array. (INPUT/OUTPUT) c The Arnoldi basis vectors are returned in the first NEV c columns of V. c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling c program. c c H Double precision (NEV+NP) by (NEV+NP) array. (OUTPUT) c H is used to store the generated upper Hessenberg matrix c c LDH Integer. (INPUT) c Leading dimension of H exactly as declared in the calling c program. c c RITZR, Double precision arrays of length NEV+NP. (OUTPUT) c RITZI RITZR(1:NEV) (resp. RITZI(1:NEV)) contains the real (resp. c imaginary) part of the computed Ritz values of OP. c c BOUNDS Double precision array of length NEV+NP. (OUTPUT) c BOUNDS(1:NEV) contain the error bounds corresponding to c the computed Ritz values. c c Q Double precision (NEV+NP) by (NEV+NP) array. (WORKSPACE) c Private (replicated) work array used to accumulate the c rotation in the shift application step. c c LDQ Integer. (INPUT) c Leading dimension of Q exactly as declared in the calling c program. c c WORKL Double precision work array of length at least c (NEV+NP)**2 + 3*(NEV+NP). (INPUT/WORKSPACE) c Private (replicated) array on each PE or array allocated on c the front end. It is used in shifts calculation, shifts c application and convergence checking. c c On exit, the last 3*(NEV+NP) locations of WORKL contain c the Ritz values (real,imaginary) and associated Ritz c estimates of the current Hessenberg matrix. They are c listed in the same order as returned from dneigh. c c If ISHIFT .EQ. O and IDO .EQ. 3, the first 2*NP locations c of WORKL are used in reverse communication to hold the user c supplied shifts. c c IPNTR Integer array of length 3. (OUTPUT) c Pointer to mark the starting locations in the WORKD for c vectors used by the Arnoldi iteration. c ------------------------------------------------------------- c IPNTR(1): pointer to the current operand vector X. c IPNTR(2): pointer to the current result vector Y. c IPNTR(3): pointer to the vector B * X when used in the c shift-and-invert mode. X is the current operand. c ------------------------------------------------------------- c c WORKD Double precision work array of length 3*N. (WORKSPACE) c Distributed array to be used in the basic Arnoldi iteration c for reverse communication. The user should not use WORKD c as temporary workspace during the iteration !!!!!!!!!! c See Data Distribution Note in DNAUPD. c c INFO Integer. (INPUT/OUTPUT) c If INFO .EQ. 0, a randomly initial residual vector is used. c If INFO .NE. 0, RESID contains the initial residual vector, c possibly from a previous run. c Error flag on output. c = 0: Normal return. c = 1: Maximum number of iterations taken. c All possible eigenvalues of OP has been found. c NP returns the number of converged Ritz values. c = 2: No shifts could be applied. c = -8: Error return from LAPACK eigenvalue calculation; c This should never happen. c = -9: Starting vector is zero. c = -9999: Could not build an Arnoldi factorization. c Size that was built in returned in NP. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx real c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly c Restarted Arnoldi Iteration", Rice University Technical Report c TR95-13, Department of Computational and Applied Mathematics. c c\Routines called: c dgetv0 ARPACK initial vector generation routine. c dnaitr ARPACK Arnoldi factorization routine. c dnapps ARPACK application of implicit shifts routine. c dnconv ARPACK convergence of Ritz values routine. c dneigh ARPACK compute Ritz values and error bounds routine. c dngets ARPACK reorder Ritz values and error bounds routine. c dsortc ARPACK sorting routine. c ivout ARPACK utility routine that prints integers. c arscnd ARPACK utility routine for timing. c dmout ARPACK utility routine that prints matrices c dvout ARPACK utility routine that prints vectors. c dlamch LAPACK routine that determines machine constants. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c dcopy Level 1 BLAS that copies one vector to another . c ddot Level 1 BLAS that computes the scalar product of two vectors. c dnrm2 Level 1 BLAS that computes the norm of a vector. c dswap Level 1 BLAS that swaps two vectors. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: naup2.F SID: 2.8 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c----------------------------------------------------------------------- c subroutine dnaup2 & ( ido, bmat, n, which, nev, np, tol, resid, mode, iupd, & ishift, mxiter, v, ldv, h, ldh, ritzr, ritzi, bounds, & q, ldq, workl, ipntr, workd, info ) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character bmat*1, which*2 integer ido, info, ishift, iupd, mode, ldh, ldq, ldv, mxiter, & n, nev, np Double precision & tol c c %-----------------% c | Array Arguments | c %-----------------% c integer ipntr(13) Double precision & bounds(nev+np), h(ldh,nev+np), q(ldq,nev+np), resid(n), & ritzi(nev+np), ritzr(nev+np), v(ldv,nev+np), & workd(3*n), workl( (nev+np)*(nev+np+3) ) c c %------------% c | Parameters | c %------------% c Double precision & one, zero parameter (one = 1.0D+0, zero = 0.0D+0) c c %---------------% c | Local Scalars | c %---------------% c character wprime*2 logical cnorm , getv0, initv, update, ushift integer ierr , iter , j , kplusp, msglvl, nconv, & nevbef, nev0 , np0 , nptemp, numcnv Double precision & rnorm , temp , eps23 save cnorm , getv0, initv, update, ushift, & rnorm , iter , eps23, kplusp, msglvl, nconv , & nevbef, nev0 , np0 , numcnv c c %-----------------------% c | Local array arguments | c %-----------------------% c integer kp(4) c c %----------------------% c | External Subroutines | c %----------------------% c external dcopy , dgetv0, dnaitr, dnconv, dneigh, & dngets, dnapps, dvout , ivout , arscnd c c %--------------------% c | External Functions | c %--------------------% c Double precision & ddot, dnrm2, dlapy2, dlamch external ddot, dnrm2, dlapy2, dlamch c c %---------------------% c | Intrinsic Functions | c %---------------------% c intrinsic min, max, abs, sqrt c c %-----------------------% c | Executable Statements | c %-----------------------% c if (ido .eq. 0) then c call arscnd (t0) c msglvl = mnaup2 c c %-------------------------------------% c | Get the machine dependent constant. | c %-------------------------------------% c eps23 = dlamch('Epsilon-Machine') eps23 = eps23**(2.0D+0 / 3.0D+0) c nev0 = nev np0 = np c c %-------------------------------------% c | kplusp is the bound on the largest | c | Lanczos factorization built. | c | nconv is the current number of | c | "converged" eigenvlues. | c | iter is the counter on the current | c | iteration step. | c %-------------------------------------% c kplusp = nev + np nconv = 0 iter = 0 c c %---------------------------------------% c | Set flags for computing the first NEV | c | steps of the Arnoldi factorization. | c %---------------------------------------% c getv0 = .true. update = .false. ushift = .false. cnorm = .false. c if (info .ne. 0) then c c %--------------------------------------------% c | User provides the initial residual vector. | c %--------------------------------------------% c initv = .true. info = 0 else initv = .false. end if end if c c %---------------------------------------------% c | Get a possibly random starting vector and | c | force it into the range of the operator OP. | c %---------------------------------------------% c 10 continue c if (getv0) then call dgetv0 (ido, bmat, 1, initv, n, 1, v, ldv, resid, rnorm, & ipntr, workd, info) c if (ido .ne. 99) go to 9000 c if (rnorm .eq. zero) then c c %-----------------------------------------% c | The initial vector is zero. Error exit. | c %-----------------------------------------% c info = -9 go to 1100 end if getv0 = .false. ido = 0 end if c c %-----------------------------------% c | Back from reverse communication : | c | continue with update step | c %-----------------------------------% c if (update) go to 20 c c %-------------------------------------------% c | Back from computing user specified shifts | c %-------------------------------------------% c if (ushift) go to 50 c c %-------------------------------------% c | Back from computing residual norm | c | at the end of the current iteration | c %-------------------------------------% c if (cnorm) go to 100 c c %----------------------------------------------------------% c | Compute the first NEV steps of the Arnoldi factorization | c %----------------------------------------------------------% c call dnaitr (ido, bmat, n, 0, nev, mode, resid, rnorm, v, ldv, & h, ldh, ipntr, workd, info) c c %---------------------------------------------------% c | ido .ne. 99 implies use of reverse communication | c | to compute operations involving OP and possibly B | c %---------------------------------------------------% c if (ido .ne. 99) go to 9000 c if (info .gt. 0) then np = info mxiter = iter info = -9999 go to 1200 end if c c %--------------------------------------------------------------% c | | c | M A I N ARNOLDI I T E R A T I O N L O O P | c | Each iteration implicitly restarts the Arnoldi | c | factorization in place. | c | | c %--------------------------------------------------------------% c 1000 continue c iter = iter + 1 c if (msglvl .gt. 0) then call ivout (logfil, 1, iter, ndigit, & '_naup2: **** Start of major iteration number ****') end if c c %-----------------------------------------------------------% c | Compute NP additional steps of the Arnoldi factorization. | c | Adjust NP since NEV might have been updated by last call | c | to the shift application routine dnapps. | c %-----------------------------------------------------------% c np = kplusp - nev c if (msglvl .gt. 1) then call ivout (logfil, 1, nev, ndigit, & '_naup2: The length of the current Arnoldi factorization') call ivout (logfil, 1, np, ndigit, & '_naup2: Extend the Arnoldi factorization by') end if c c %-----------------------------------------------------------% c | Compute NP additional steps of the Arnoldi factorization. | c %-----------------------------------------------------------% c ido = 0 20 continue update = .true. c call dnaitr (ido , bmat, n , nev, np , mode , resid, & rnorm, v , ldv, h , ldh, ipntr, workd, & info) c c %---------------------------------------------------% c | ido .ne. 99 implies use of reverse communication | c | to compute operations involving OP and possibly B | c %---------------------------------------------------% c if (ido .ne. 99) go to 9000 c if (info .gt. 0) then np = info mxiter = iter info = -9999 go to 1200 end if update = .false. c if (msglvl .gt. 1) then call dvout (logfil, 1, rnorm, ndigit, & '_naup2: Corresponding B-norm of the residual') end if c c %--------------------------------------------------------% c | Compute the eigenvalues and corresponding error bounds | c | of the current upper Hessenberg matrix. | c %--------------------------------------------------------% c call dneigh (rnorm, kplusp, h, ldh, ritzr, ritzi, bounds, & q, ldq, workl, ierr) c if (ierr .ne. 0) then info = -8 go to 1200 end if c c %----------------------------------------------------% c | Make a copy of eigenvalues and corresponding error | c | bounds obtained from dneigh. | c %----------------------------------------------------% c call dcopy(kplusp, ritzr, 1, workl(kplusp**2+1), 1) call dcopy(kplusp, ritzi, 1, workl(kplusp**2+kplusp+1), 1) call dcopy(kplusp, bounds, 1, workl(kplusp**2+2*kplusp+1), 1) c c %---------------------------------------------------% c | Select the wanted Ritz values and their bounds | c | to be used in the convergence test. | c | The wanted part of the spectrum and corresponding | c | error bounds are in the last NEV loc. of RITZR, | c | RITZI and BOUNDS respectively. The variables NEV | c | and NP may be updated if the NEV-th wanted Ritz | c | value has a non zero imaginary part. In this case | c | NEV is increased by one and NP decreased by one. | c | NOTE: The last two arguments of dngets are no | c | longer used as of version 2.1. | c %---------------------------------------------------% c nev = nev0 np = np0 numcnv = nev call dngets (ishift, which, nev, np, ritzr, ritzi, & bounds, workl, workl(np+1)) if (nev .eq. nev0+1) numcnv = nev0+1 c c %-------------------% c | Convergence test. | c %-------------------% c call dcopy (nev, bounds(np+1), 1, workl(2*np+1), 1) call dnconv (nev, ritzr(np+1), ritzi(np+1), workl(2*np+1), & tol, nconv) c if (msglvl .gt. 2) then kp(1) = nev kp(2) = np kp(3) = numcnv kp(4) = nconv call ivout (logfil, 4, kp, ndigit, & '_naup2: NEV, NP, NUMCNV, NCONV are') call dvout (logfil, kplusp, ritzr, ndigit, & '_naup2: Real part of the eigenvalues of H') call dvout (logfil, kplusp, ritzi, ndigit, & '_naup2: Imaginary part of the eigenvalues of H') call dvout (logfil, kplusp, bounds, ndigit, & '_naup2: Ritz estimates of the current NCV Ritz values') end if c c %---------------------------------------------------------% c | Count the number of unwanted Ritz values that have zero | c | Ritz estimates. If any Ritz estimates are equal to zero | c | then a leading block of H of order equal to at least | c | the number of Ritz values with zero Ritz estimates has | c | split off. None of these Ritz values may be removed by | c | shifting. Decrease NP the number of shifts to apply. If | c | no shifts may be applied, then prepare to exit | c %---------------------------------------------------------% c nptemp = np do 30 j=1, nptemp if (bounds(j) .eq. zero) then np = np - 1 nev = nev + 1 end if 30 continue c if ( (nconv .ge. numcnv) .or. & (iter .gt. mxiter) .or. & (np .eq. 0) ) then c if (msglvl .gt. 4) then call dvout(logfil, kplusp, workl(kplusp**2+1), ndigit, & '_naup2: Real part of the eig computed by _neigh:') call dvout(logfil, kplusp, workl(kplusp**2+kplusp+1), & ndigit, & '_naup2: Imag part of the eig computed by _neigh:') call dvout(logfil, kplusp, workl(kplusp**2+kplusp*2+1), & ndigit, & '_naup2: Ritz eistmates computed by _neigh:') end if c c %------------------------------------------------% c | Prepare to exit. Put the converged Ritz values | c | and corresponding bounds in RITZ(1:NCONV) and | c | BOUNDS(1:NCONV) respectively. Then sort. Be | c | careful when NCONV > NP | c %------------------------------------------------% c c %------------------------------------------% c | Use h( 3,1 ) as storage to communicate | c | rnorm to _neupd if needed | c %------------------------------------------% h(3,1) = rnorm c c %----------------------------------------------% c | To be consistent with dngets, we first do a | c | pre-processing sort in order to keep complex | c | conjugate pairs together. This is similar | c | to the pre-processing sort used in dngets | c | except that the sort is done in the opposite | c | order. | c %----------------------------------------------% c if (which .eq. 'LM') wprime = 'SR' if (which .eq. 'SM') wprime = 'LR' if (which .eq. 'LR') wprime = 'SM' if (which .eq. 'SR') wprime = 'LM' if (which .eq. 'LI') wprime = 'SM' if (which .eq. 'SI') wprime = 'LM' c call dsortc (wprime, .true., kplusp, ritzr, ritzi, bounds) c c %----------------------------------------------% c | Now sort Ritz values so that converged Ritz | c | values appear within the first NEV locations | c | of ritzr, ritzi and bounds, and the most | c | desired one appears at the front. | c %----------------------------------------------% c if (which .eq. 'LM') wprime = 'SM' if (which .eq. 'SM') wprime = 'LM' if (which .eq. 'LR') wprime = 'SR' if (which .eq. 'SR') wprime = 'LR' if (which .eq. 'LI') wprime = 'SI' if (which .eq. 'SI') wprime = 'LI' c call dsortc(wprime, .true., kplusp, ritzr, ritzi, bounds) c c %--------------------------------------------------% c | Scale the Ritz estimate of each Ritz value | c | by 1 / max(eps23,magnitude of the Ritz value). | c %--------------------------------------------------% c do 35 j = 1, numcnv temp = max(eps23,dlapy2(ritzr(j), & ritzi(j))) bounds(j) = bounds(j)/temp 35 continue c c %----------------------------------------------------% c | Sort the Ritz values according to the scaled Ritz | c | esitmates. This will push all the converged ones | c | towards the front of ritzr, ritzi, bounds | c | (in the case when NCONV < NEV.) | c %----------------------------------------------------% c wprime = 'LR' call dsortc(wprime, .true., numcnv, bounds, ritzr, ritzi) c c %----------------------------------------------% c | Scale the Ritz estimate back to its original | c | value. | c %----------------------------------------------% c do 40 j = 1, numcnv temp = max(eps23, dlapy2(ritzr(j), & ritzi(j))) bounds(j) = bounds(j)*temp 40 continue c c %------------------------------------------------% c | Sort the converged Ritz values again so that | c | the "threshold" value appears at the front of | c | ritzr, ritzi and bound. | c %------------------------------------------------% c call dsortc(which, .true., nconv, ritzr, ritzi, bounds) c if (msglvl .gt. 1) then call dvout (logfil, kplusp, ritzr, ndigit, & '_naup2: Sorted real part of the eigenvalues') call dvout (logfil, kplusp, ritzi, ndigit, & '_naup2: Sorted imaginary part of the eigenvalues') call dvout (logfil, kplusp, bounds, ndigit, & '_naup2: Sorted ritz estimates.') end if c c %------------------------------------% c | Max iterations have been exceeded. | c %------------------------------------% c if (iter .gt. mxiter .and. nconv .lt. numcnv) info = 1 c c %---------------------% c | No shifts to apply. | c %---------------------% c if (np .eq. 0 .and. nconv .lt. numcnv) info = 2 c np = nconv go to 1100 c else if ( (nconv .lt. numcnv) .and. (ishift .eq. 1) ) then c c %-------------------------------------------------% c | Do not have all the requested eigenvalues yet. | c | To prevent possible stagnation, adjust the size | c | of NEV. | c %-------------------------------------------------% c nevbef = nev nev = nev + min(nconv, np/2) if (nev .eq. 1 .and. kplusp .ge. 6) then nev = kplusp / 2 else if (nev .eq. 1 .and. kplusp .gt. 3) then nev = 2 end if np = kplusp - nev c c %---------------------------------------% c | If the size of NEV was just increased | c | resort the eigenvalues. | c %---------------------------------------% c if (nevbef .lt. nev) & call dngets (ishift, which, nev, np, ritzr, ritzi, & bounds, workl, workl(np+1)) c end if c if (msglvl .gt. 0) then call ivout (logfil, 1, nconv, ndigit, & '_naup2: no. of "converged" Ritz values at this iter.') if (msglvl .gt. 1) then kp(1) = nev kp(2) = np call ivout (logfil, 2, kp, ndigit, & '_naup2: NEV and NP are') call dvout (logfil, nev, ritzr(np+1), ndigit, & '_naup2: "wanted" Ritz values -- real part') call dvout (logfil, nev, ritzi(np+1), ndigit, & '_naup2: "wanted" Ritz values -- imag part') call dvout (logfil, nev, bounds(np+1), ndigit, & '_naup2: Ritz estimates of the "wanted" values ') end if end if c if (ishift .eq. 0) then c c %-------------------------------------------------------% c | User specified shifts: reverse comminucation to | c | compute the shifts. They are returned in the first | c | 2*NP locations of WORKL. | c %-------------------------------------------------------% c ushift = .true. ido = 3 go to 9000 end if c 50 continue c c %------------------------------------% c | Back from reverse communication; | c | User specified shifts are returned | c | in WORKL(1:2*NP) | c %------------------------------------% c ushift = .false. c if ( ishift .eq. 0 ) then c c %----------------------------------% c | Move the NP shifts from WORKL to | c | RITZR, RITZI to free up WORKL | c | for non-exact shift case. | c %----------------------------------% c call dcopy (np, workl, 1, ritzr, 1) call dcopy (np, workl(np+1), 1, ritzi, 1) end if c if (msglvl .gt. 2) then call ivout (logfil, 1, np, ndigit, & '_naup2: The number of shifts to apply ') call dvout (logfil, np, ritzr, ndigit, & '_naup2: Real part of the shifts') call dvout (logfil, np, ritzi, ndigit, & '_naup2: Imaginary part of the shifts') if ( ishift .eq. 1 ) & call dvout (logfil, np, bounds, ndigit, & '_naup2: Ritz estimates of the shifts') end if c c %---------------------------------------------------------% c | Apply the NP implicit shifts by QR bulge chasing. | c | Each shift is applied to the whole upper Hessenberg | c | matrix H. | c | The first 2*N locations of WORKD are used as workspace. | c %---------------------------------------------------------% c call dnapps (n, nev, np, ritzr, ritzi, v, ldv, & h, ldh, resid, q, ldq, workl, workd) c c %---------------------------------------------% c | Compute the B-norm of the updated residual. | c | Keep B*RESID in WORKD(1:N) to be used in | c | the first step of the next call to dnaitr. | c %---------------------------------------------% c cnorm = .true. call arscnd (t2) if (bmat .eq. 'G') then nbx = nbx + 1 call dcopy (n, resid, 1, workd(n+1), 1) ipntr(1) = n + 1 ipntr(2) = 1 ido = 2 c c %----------------------------------% c | Exit in order to compute B*RESID | c %----------------------------------% c go to 9000 else if (bmat .eq. 'I') then call dcopy (n, resid, 1, workd, 1) end if c 100 continue c c %----------------------------------% c | Back from reverse communication; | c | WORKD(1:N) := B*RESID | c %----------------------------------% c if (bmat .eq. 'G') then call arscnd (t3) tmvbx = tmvbx + (t3 - t2) end if c if (bmat .eq. 'G') then rnorm = ddot (n, resid, 1, workd, 1) rnorm = sqrt(abs(rnorm)) else if (bmat .eq. 'I') then rnorm = dnrm2(n, resid, 1) end if cnorm = .false. c if (msglvl .gt. 2) then call dvout (logfil, 1, rnorm, ndigit, & '_naup2: B-norm of residual for compressed factorization') call dmout (logfil, nev, nev, h, ldh, ndigit, & '_naup2: Compressed upper Hessenberg matrix H') end if c go to 1000 c c %---------------------------------------------------------------% c | | c | E N D O F M A I N I T E R A T I O N L O O P | c | | c %---------------------------------------------------------------% c 1100 continue c mxiter = iter nev = numcnv c 1200 continue ido = 99 c c %------------% c | Error Exit | c %------------% c call arscnd (t1) tnaup2 = t1 - t0 c 9000 continue c c %---------------% c | End of dnaup2 | c %---------------% c return end arpack-0.92.1/SRC/dnaupd.f0000644000175000017500000007202310776001577012054 00000000000000c\BeginDoc c c\Name: dnaupd c c\Description: c Reverse communication interface for the Implicitly Restarted Arnoldi c iteration. This subroutine computes approximations to a few eigenpairs c of a linear operator "OP" with respect to a semi-inner product defined by c a symmetric positive semi-definite real matrix B. B may be the identity c matrix. NOTE: If the linear operator "OP" is real and symmetric c with respect to the real positive semi-definite symmetric matrix B, c i.e. B*OP = (OP`)*B, then subroutine dsaupd should be used instead. c c The computed approximate eigenvalues are called Ritz values and c the corresponding approximate eigenvectors are called Ritz vectors. c c dnaupd is usually called iteratively to solve one of the c following problems: c c Mode 1: A*x = lambda*x. c ===> OP = A and B = I. c c Mode 2: A*x = lambda*M*x, M symmetric positive definite c ===> OP = inv[M]*A and B = M. c ===> (If M can be factored see remark 3 below) c c Mode 3: A*x = lambda*M*x, M symmetric semi-definite c ===> OP = Real_Part{ inv[A - sigma*M]*M } and B = M. c ===> shift-and-invert mode (in real arithmetic) c If OP*x = amu*x, then c amu = 1/2 * [ 1/(lambda-sigma) + 1/(lambda-conjg(sigma)) ]. c Note: If sigma is real, i.e. imaginary part of sigma is zero; c Real_Part{ inv[A - sigma*M]*M } == inv[A - sigma*M]*M c amu == 1/(lambda-sigma). c c Mode 4: A*x = lambda*M*x, M symmetric semi-definite c ===> OP = Imaginary_Part{ inv[A - sigma*M]*M } and B = M. c ===> shift-and-invert mode (in real arithmetic) c If OP*x = amu*x, then c amu = 1/2i * [ 1/(lambda-sigma) - 1/(lambda-conjg(sigma)) ]. c c Both mode 3 and 4 give the same enhancement to eigenvalues close to c the (complex) shift sigma. However, as lambda goes to infinity, c the operator OP in mode 4 dampens the eigenvalues more strongly than c does OP defined in mode 3. c c NOTE: The action of w <- inv[A - sigma*M]*v or w <- inv[M]*v c should be accomplished either by a direct method c using a sparse matrix factorization and solving c c [A - sigma*M]*w = v or M*w = v, c c or through an iterative method for solving these c systems. If an iterative method is used, the c convergence test must be more stringent than c the accuracy requirements for the eigenvalue c approximations. c c\Usage: c call dnaupd c ( IDO, BMAT, N, WHICH, NEV, TOL, RESID, NCV, V, LDV, IPARAM, c IPNTR, WORKD, WORKL, LWORKL, INFO ) c c\Arguments c IDO Integer. (INPUT/OUTPUT) c Reverse communication flag. IDO must be zero on the first c call to dnaupd. IDO will be set internally to c indicate the type of operation to be performed. Control is c then given back to the calling routine which has the c responsibility to carry out the requested operation and call c dnaupd with the result. The operand is given in c WORKD(IPNTR(1)), the result must be put in WORKD(IPNTR(2)). c ------------------------------------------------------------- c IDO = 0: first call to the reverse communication interface c IDO = -1: compute Y = OP * X where c IPNTR(1) is the pointer into WORKD for X, c IPNTR(2) is the pointer into WORKD for Y. c This is for the initialization phase to force the c starting vector into the range of OP. c IDO = 1: compute Y = OP * X where c IPNTR(1) is the pointer into WORKD for X, c IPNTR(2) is the pointer into WORKD for Y. c In mode 3 and 4, the vector B * X is already c available in WORKD(ipntr(3)). It does not c need to be recomputed in forming OP * X. c IDO = 2: compute Y = B * X where c IPNTR(1) is the pointer into WORKD for X, c IPNTR(2) is the pointer into WORKD for Y. c IDO = 3: compute the IPARAM(8) real and imaginary parts c of the shifts where INPTR(14) is the pointer c into WORKL for placing the shifts. See Remark c 5 below. c IDO = 99: done c ------------------------------------------------------------- c c BMAT Character*1. (INPUT) c BMAT specifies the type of the matrix B that defines the c semi-inner product for the operator OP. c BMAT = 'I' -> standard eigenvalue problem A*x = lambda*x c BMAT = 'G' -> generalized eigenvalue problem A*x = lambda*B*x c c N Integer. (INPUT) c Dimension of the eigenproblem. c c WHICH Character*2. (INPUT) c 'LM' -> want the NEV eigenvalues of largest magnitude. c 'SM' -> want the NEV eigenvalues of smallest magnitude. c 'LR' -> want the NEV eigenvalues of largest real part. c 'SR' -> want the NEV eigenvalues of smallest real part. c 'LI' -> want the NEV eigenvalues of largest imaginary part. c 'SI' -> want the NEV eigenvalues of smallest imaginary part. c c NEV Integer. (INPUT/OUTPUT) c Number of eigenvalues of OP to be computed. 0 < NEV < N-1. c c TOL Double precision scalar. (INPUT) c Stopping criterion: the relative accuracy of the Ritz value c is considered acceptable if BOUNDS(I) .LE. TOL*ABS(RITZ(I)) c where ABS(RITZ(I)) is the magnitude when RITZ(I) is complex. c DEFAULT = DLAMCH('EPS') (machine precision as computed c by the LAPACK auxiliary subroutine DLAMCH). c c RESID Double precision array of length N. (INPUT/OUTPUT) c On INPUT: c If INFO .EQ. 0, a random initial residual vector is used. c If INFO .NE. 0, RESID contains the initial residual vector, c possibly from a previous run. c On OUTPUT: c RESID contains the final residual vector. c c NCV Integer. (INPUT) c Number of columns of the matrix V. NCV must satisfy the two c inequalities 2 <= NCV-NEV and NCV <= N. c This will indicate how many Arnoldi vectors are generated c at each iteration. After the startup phase in which NEV c Arnoldi vectors are generated, the algorithm generates c approximately NCV-NEV Arnoldi vectors at each subsequent update c iteration. Most of the cost in generating each Arnoldi vector is c in the matrix-vector operation OP*x. c NOTE: 2 <= NCV-NEV in order that complex conjugate pairs of Ritz c values are kept together. (See remark 4 below) c c V Double precision array N by NCV. (OUTPUT) c Contains the final set of Arnoldi basis vectors. c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling program. c c IPARAM Integer array of length 11. (INPUT/OUTPUT) c IPARAM(1) = ISHIFT: method for selecting the implicit shifts. c The shifts selected at each iteration are used to restart c the Arnoldi iteration in an implicit fashion. c ------------------------------------------------------------- c ISHIFT = 0: the shifts are provided by the user via c reverse communication. The real and imaginary c parts of the NCV eigenvalues of the Hessenberg c matrix H are returned in the part of the WORKL c array corresponding to RITZR and RITZI. See remark c 5 below. c ISHIFT = 1: exact shifts with respect to the current c Hessenberg matrix H. This is equivalent to c restarting the iteration with a starting vector c that is a linear combination of approximate Schur c vectors associated with the "wanted" Ritz values. c ------------------------------------------------------------- c c IPARAM(2) = No longer referenced. c c IPARAM(3) = MXITER c On INPUT: maximum number of Arnoldi update iterations allowed. c On OUTPUT: actual number of Arnoldi update iterations taken. c c IPARAM(4) = NB: blocksize to be used in the recurrence. c The code currently works only for NB = 1. c c IPARAM(5) = NCONV: number of "converged" Ritz values. c This represents the number of Ritz values that satisfy c the convergence criterion. c c IPARAM(6) = IUPD c No longer referenced. Implicit restarting is ALWAYS used. c c IPARAM(7) = MODE c On INPUT determines what type of eigenproblem is being solved. c Must be 1,2,3,4; See under \Description of dnaupd for the c four modes available. c c IPARAM(8) = NP c When ido = 3 and the user provides shifts through reverse c communication (IPARAM(1)=0), dnaupd returns NP, the number c of shifts the user is to provide. 0 < NP <=NCV-NEV. See Remark c 5 below. c c IPARAM(9) = NUMOP, IPARAM(10) = NUMOPB, IPARAM(11) = NUMREO, c OUTPUT: NUMOP = total number of OP*x operations, c NUMOPB = total number of B*x operations if BMAT='G', c NUMREO = total number of steps of re-orthogonalization. c c IPNTR Integer array of length 14. (OUTPUT) c Pointer to mark the starting locations in the WORKD and WORKL c arrays for matrices/vectors used by the Arnoldi iteration. c ------------------------------------------------------------- c IPNTR(1): pointer to the current operand vector X in WORKD. c IPNTR(2): pointer to the current result vector Y in WORKD. c IPNTR(3): pointer to the vector B * X in WORKD when used in c the shift-and-invert mode. c IPNTR(4): pointer to the next available location in WORKL c that is untouched by the program. c IPNTR(5): pointer to the NCV by NCV upper Hessenberg matrix c H in WORKL. c IPNTR(6): pointer to the real part of the ritz value array c RITZR in WORKL. c IPNTR(7): pointer to the imaginary part of the ritz value array c RITZI in WORKL. c IPNTR(8): pointer to the Ritz estimates in array WORKL associated c with the Ritz values located in RITZR and RITZI in WORKL. c c IPNTR(14): pointer to the NP shifts in WORKL. See Remark 5 below. c c Note: IPNTR(9:13) is only referenced by dneupd. See Remark 2 below. c c IPNTR(9): pointer to the real part of the NCV RITZ values of the c original system. c IPNTR(10): pointer to the imaginary part of the NCV RITZ values of c the original system. c IPNTR(11): pointer to the NCV corresponding error bounds. c IPNTR(12): pointer to the NCV by NCV upper quasi-triangular c Schur matrix for H. c IPNTR(13): pointer to the NCV by NCV matrix of eigenvectors c of the upper Hessenberg matrix H. Only referenced by c dneupd if RVEC = .TRUE. See Remark 2 below. c ------------------------------------------------------------- c c WORKD Double precision work array of length 3*N. (REVERSE COMMUNICATION) c Distributed array to be used in the basic Arnoldi iteration c for reverse communication. The user should not use WORKD c as temporary workspace during the iteration. Upon termination c WORKD(1:N) contains B*RESID(1:N). If an invariant subspace c associated with the converged Ritz values is desired, see remark c 2 below, subroutine dneupd uses this output. c See Data Distribution Note below. c c WORKL Double precision work array of length LWORKL. (OUTPUT/WORKSPACE) c Private (replicated) array on each PE or array allocated on c the front end. See Data Distribution Note below. c c LWORKL Integer. (INPUT) c LWORKL must be at least 3*NCV**2 + 6*NCV. c c INFO Integer. (INPUT/OUTPUT) c If INFO .EQ. 0, a randomly initial residual vector is used. c If INFO .NE. 0, RESID contains the initial residual vector, c possibly from a previous run. c Error flag on output. c = 0: Normal exit. c = 1: Maximum number of iterations taken. c All possible eigenvalues of OP has been found. IPARAM(5) c returns the number of wanted converged Ritz values. c = 2: No longer an informational error. Deprecated starting c with release 2 of ARPACK. c = 3: No shifts could be applied during a cycle of the c Implicitly restarted Arnoldi iteration. One possibility c is to increase the size of NCV relative to NEV. c See remark 4 below. c = -1: N must be positive. c = -2: NEV must be positive. c = -3: NCV-NEV >= 2 and less than or equal to N. c = -4: The maximum number of Arnoldi update iteration c must be greater than zero. c = -5: WHICH must be one of 'LM', 'SM', 'LR', 'SR', 'LI', 'SI' c = -6: BMAT must be one of 'I' or 'G'. c = -7: Length of private work array is not sufficient. c = -8: Error return from LAPACK eigenvalue calculation; c = -9: Starting vector is zero. c = -10: IPARAM(7) must be 1,2,3,4. c = -11: IPARAM(7) = 1 and BMAT = 'G' are incompatable. c = -12: IPARAM(1) must be equal to 0 or 1. c = -9999: Could not build an Arnoldi factorization. c IPARAM(5) returns the size of the current Arnoldi c factorization. c c\Remarks c 1. The computed Ritz values are approximate eigenvalues of OP. The c selection of WHICH should be made with this in mind when c Mode = 3 and 4. After convergence, approximate eigenvalues of the c original problem may be obtained with the ARPACK subroutine dneupd. c c 2. If a basis for the invariant subspace corresponding to the converged Ritz c values is needed, the user must call dneupd immediately following c completion of dnaupd. This is new starting with release 2 of ARPACK. c c 3. If M can be factored into a Cholesky factorization M = LL` c then Mode = 2 should not be selected. Instead one should use c Mode = 1 with OP = inv(L)*A*inv(L`). Appropriate triangular c linear systems should be solved with L and L` rather c than computing inverses. After convergence, an approximate c eigenvector z of the original problem is recovered by solving c L`z = x where x is a Ritz vector of OP. c c 4. At present there is no a-priori analysis to guide the selection c of NCV relative to NEV. The only formal requrement is that NCV > NEV + 2. c However, it is recommended that NCV .ge. 2*NEV+1. If many problems of c the same type are to be solved, one should experiment with increasing c NCV while keeping NEV fixed for a given test problem. This will c usually decrease the required number of OP*x operations but it c also increases the work and storage required to maintain the orthogonal c basis vectors. The optimal "cross-over" with respect to CPU time c is problem dependent and must be determined empirically. c See Chapter 8 of Reference 2 for further information. c c 5. When IPARAM(1) = 0, and IDO = 3, the user needs to provide the c NP = IPARAM(8) real and imaginary parts of the shifts in locations c real part imaginary part c ----------------------- -------------- c 1 WORKL(IPNTR(14)) WORKL(IPNTR(14)+NP) c 2 WORKL(IPNTR(14)+1) WORKL(IPNTR(14)+NP+1) c . . c . . c . . c NP WORKL(IPNTR(14)+NP-1) WORKL(IPNTR(14)+2*NP-1). c c Only complex conjugate pairs of shifts may be applied and the pairs c must be placed in consecutive locations. The real part of the c eigenvalues of the current upper Hessenberg matrix are located in c WORKL(IPNTR(6)) through WORKL(IPNTR(6)+NCV-1) and the imaginary part c in WORKL(IPNTR(7)) through WORKL(IPNTR(7)+NCV-1). They are ordered c according to the order defined by WHICH. The complex conjugate c pairs are kept together and the associated Ritz estimates are located in c WORKL(IPNTR(8)), WORKL(IPNTR(8)+1), ... , WORKL(IPNTR(8)+NCV-1). c c----------------------------------------------------------------------- c c\Data Distribution Note: c c Fortran-D syntax: c ================ c Double precision resid(n), v(ldv,ncv), workd(3*n), workl(lworkl) c decompose d1(n), d2(n,ncv) c align resid(i) with d1(i) c align v(i,j) with d2(i,j) c align workd(i) with d1(i) range (1:n) c align workd(i) with d1(i-n) range (n+1:2*n) c align workd(i) with d1(i-2*n) range (2*n+1:3*n) c distribute d1(block), d2(block,:) c replicated workl(lworkl) c c Cray MPP syntax: c =============== c Double precision resid(n), v(ldv,ncv), workd(n,3), workl(lworkl) c shared resid(block), v(block,:), workd(block,:) c replicated workl(lworkl) c c CM2/CM5 syntax: c ============== c c----------------------------------------------------------------------- c c include 'ex-nonsym.doc' c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx real c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly c Restarted Arnoldi Iteration", Rice University Technical Report c TR95-13, Department of Computational and Applied Mathematics. c 3. B.N. Parlett & Y. Saad, "Complex Shift and Invert Strategies for c Real Matrices", Linear Algebra and its Applications, vol 88/89, c pp 575-595, (1987). c c\Routines called: c dnaup2 ARPACK routine that implements the Implicitly Restarted c Arnoldi Iteration. c ivout ARPACK utility routine that prints integers. c arscnd ARPACK utility routine for timing. c dvout ARPACK utility routine that prints vectors. c dlamch LAPACK routine that determines machine constants. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c 12/16/93: Version '1.1' c c\SCCS Information: @(#) c FILE: naupd.F SID: 2.10 DATE OF SID: 08/23/02 RELEASE: 2 c c\Remarks c c\EndLib c c----------------------------------------------------------------------- c subroutine dnaupd & ( ido, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam, & ipntr, workd, workl, lworkl, info ) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character bmat*1, which*2 integer ido, info, ldv, lworkl, n, ncv, nev Double precision & tol c c %-----------------% c | Array Arguments | c %-----------------% c integer iparam(11), ipntr(14) Double precision & resid(n), v(ldv,ncv), workd(3*n), workl(lworkl) c c %------------% c | Parameters | c %------------% c Double precision & one, zero parameter (one = 1.0D+0, zero = 0.0D+0) c c %---------------% c | Local Scalars | c %---------------% c integer bounds, ierr, ih, iq, ishift, iupd, iw, & ldh, ldq, levec, mode, msglvl, mxiter, nb, & nev0, next, np, ritzi, ritzr, j save bounds, ih, iq, ishift, iupd, iw, ldh, ldq, & levec, mode, msglvl, mxiter, nb, nev0, next, & np, ritzi, ritzr c c %----------------------% c | External Subroutines | c %----------------------% c external dnaup2, dvout, ivout, arscnd, dstatn c c %--------------------% c | External Functions | c %--------------------% c Double precision & dlamch external dlamch c c %-----------------------% c | Executable Statements | c %-----------------------% c if (ido .eq. 0) then c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call dstatn call arscnd (t0) msglvl = mnaupd c c %----------------% c | Error checking | c %----------------% c ierr = 0 ishift = iparam(1) c levec = iparam(2) mxiter = iparam(3) c nb = iparam(4) nb = 1 c c %--------------------------------------------% c | Revision 2 performs only implicit restart. | c %--------------------------------------------% c iupd = 1 mode = iparam(7) c if (n .le. 0) then ierr = -1 else if (nev .le. 0) then ierr = -2 else if (ncv .le. nev+1 .or. ncv .gt. n) then ierr = -3 else if (mxiter .le. 0) then ierr = 4 else if (which .ne. 'LM' .and. & which .ne. 'SM' .and. & which .ne. 'LR' .and. & which .ne. 'SR' .and. & which .ne. 'LI' .and. & which .ne. 'SI') then ierr = -5 else if (bmat .ne. 'I' .and. bmat .ne. 'G') then ierr = -6 else if (lworkl .lt. 3*ncv**2 + 6*ncv) then ierr = -7 else if (mode .lt. 1 .or. mode .gt. 4) then ierr = -10 else if (mode .eq. 1 .and. bmat .eq. 'G') then ierr = -11 else if (ishift .lt. 0 .or. ishift .gt. 1) then ierr = -12 end if c c %------------% c | Error Exit | c %------------% c if (ierr .ne. 0) then info = ierr ido = 99 go to 9000 end if c c %------------------------% c | Set default parameters | c %------------------------% c if (nb .le. 0) nb = 1 if (tol .le. zero) tol = dlamch('EpsMach') c c %----------------------------------------------% c | NP is the number of additional steps to | c | extend the length NEV Lanczos factorization. | c | NEV0 is the local variable designating the | c | size of the invariant subspace desired. | c %----------------------------------------------% c np = ncv - nev nev0 = nev c c %-----------------------------% c | Zero out internal workspace | c %-----------------------------% c do 10 j = 1, 3*ncv**2 + 6*ncv workl(j) = zero 10 continue c c %-------------------------------------------------------------% c | Pointer into WORKL for address of H, RITZ, BOUNDS, Q | c | etc... and the remaining workspace. | c | Also update pointer to be used on output. | c | Memory is laid out as follows: | c | workl(1:ncv*ncv) := generated Hessenberg matrix | c | workl(ncv*ncv+1:ncv*ncv+2*ncv) := real and imaginary | c | parts of ritz values | c | workl(ncv*ncv+2*ncv+1:ncv*ncv+3*ncv) := error bounds | c | workl(ncv*ncv+3*ncv+1:2*ncv*ncv+3*ncv) := rotation matrix Q | c | workl(2*ncv*ncv+3*ncv+1:3*ncv*ncv+6*ncv) := workspace | c | The final workspace is needed by subroutine dneigh called | c | by dnaup2. Subroutine dneigh calls LAPACK routines for | c | calculating eigenvalues and the last row of the eigenvector | c | matrix. | c %-------------------------------------------------------------% c ldh = ncv ldq = ncv ih = 1 ritzr = ih + ldh*ncv ritzi = ritzr + ncv bounds = ritzi + ncv iq = bounds + ncv iw = iq + ldq*ncv next = iw + ncv**2 + 3*ncv c ipntr(4) = next ipntr(5) = ih ipntr(6) = ritzr ipntr(7) = ritzi ipntr(8) = bounds ipntr(14) = iw c end if c c %-------------------------------------------------------% c | Carry out the Implicitly restarted Arnoldi Iteration. | c %-------------------------------------------------------% c call dnaup2 & ( ido, bmat, n, which, nev0, np, tol, resid, mode, iupd, & ishift, mxiter, v, ldv, workl(ih), ldh, workl(ritzr), & workl(ritzi), workl(bounds), workl(iq), ldq, workl(iw), & ipntr, workd, info ) c c %--------------------------------------------------% c | ido .ne. 99 implies use of reverse communication | c | to compute operations involving OP or shifts. | c %--------------------------------------------------% c if (ido .eq. 3) iparam(8) = np if (ido .ne. 99) go to 9000 c iparam(3) = mxiter iparam(5) = np iparam(9) = nopx iparam(10) = nbx iparam(11) = nrorth c c %------------------------------------% c | Exit if there was an informational | c | error within dnaup2. | c %------------------------------------% c if (info .lt. 0) go to 9000 if (info .eq. 2) info = 3 c if (msglvl .gt. 0) then call ivout (logfil, 1, mxiter, ndigit, & '_naupd: Number of update iterations taken') call ivout (logfil, 1, np, ndigit, & '_naupd: Number of wanted "converged" Ritz values') call dvout (logfil, np, workl(ritzr), ndigit, & '_naupd: Real part of the final Ritz values') call dvout (logfil, np, workl(ritzi), ndigit, & '_naupd: Imaginary part of the final Ritz values') call dvout (logfil, np, workl(bounds), ndigit, & '_naupd: Associated Ritz estimates') end if c call arscnd (t1) tnaupd = t1 - t0 c if (msglvl .gt. 0) then c c %--------------------------------------------------------% c | Version Number & Version Date are defined in version.h | c %--------------------------------------------------------% c write (6,1000) write (6,1100) mxiter, nopx, nbx, nrorth, nitref, nrstrt, & tmvopx, tmvbx, tnaupd, tnaup2, tnaitr, titref, & tgetv0, tneigh, tngets, tnapps, tnconv, trvec 1000 format (//, & 5x, '=============================================',/ & 5x, '= Nonsymmetric implicit Arnoldi update code =',/ & 5x, '= Version Number: ', ' 2.4', 21x, ' =',/ & 5x, '= Version Date: ', ' 07/31/96', 16x, ' =',/ & 5x, '=============================================',/ & 5x, '= Summary of timing statistics =',/ & 5x, '=============================================',//) 1100 format ( & 5x, 'Total number update iterations = ', i5,/ & 5x, 'Total number of OP*x operations = ', i5,/ & 5x, 'Total number of B*x operations = ', i5,/ & 5x, 'Total number of reorthogonalization steps = ', i5,/ & 5x, 'Total number of iterative refinement steps = ', i5,/ & 5x, 'Total number of restart steps = ', i5,/ & 5x, 'Total time in user OP*x operation = ', f12.6,/ & 5x, 'Total time in user B*x operation = ', f12.6,/ & 5x, 'Total time in Arnoldi update routine = ', f12.6,/ & 5x, 'Total time in naup2 routine = ', f12.6,/ & 5x, 'Total time in basic Arnoldi iteration loop = ', f12.6,/ & 5x, 'Total time in reorthogonalization phase = ', f12.6,/ & 5x, 'Total time in (re)start vector generation = ', f12.6,/ & 5x, 'Total time in Hessenberg eig. subproblem = ', f12.6,/ & 5x, 'Total time in getting the shifts = ', f12.6,/ & 5x, 'Total time in applying the shifts = ', f12.6,/ & 5x, 'Total time in convergence testing = ', f12.6,/ & 5x, 'Total time in computing final Ritz vectors = ', f12.6/) end if c 9000 continue c return c c %---------------% c | End of dnaupd | c %---------------% c end arpack-0.92.1/SRC/dsortc.f0000644000175000017500000002204610776001577012077 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: dsortc c c\Description: c Sorts the complex array in XREAL and XIMAG into the order c specified by WHICH and optionally applies the permutation to the c real array Y. It is assumed that if an element of XIMAG is c nonzero, then its negative is also an element. In other words, c both members of a complex conjugate pair are to be sorted and the c pairs are kept adjacent to each other. c c\Usage: c call dsortc c ( WHICH, APPLY, N, XREAL, XIMAG, Y ) c c\Arguments c WHICH Character*2. (Input) c 'LM' -> sort XREAL,XIMAG into increasing order of magnitude. c 'SM' -> sort XREAL,XIMAG into decreasing order of magnitude. c 'LR' -> sort XREAL into increasing order of algebraic. c 'SR' -> sort XREAL into decreasing order of algebraic. c 'LI' -> sort XIMAG into increasing order of magnitude. c 'SI' -> sort XIMAG into decreasing order of magnitude. c NOTE: If an element of XIMAG is non-zero, then its negative c is also an element. c c APPLY Logical. (Input) c APPLY = .TRUE. -> apply the sorted order to array Y. c APPLY = .FALSE. -> do not apply the sorted order to array Y. c c N Integer. (INPUT) c Size of the arrays. c c XREAL, Double precision array of length N. (INPUT/OUTPUT) c XIMAG Real and imaginary part of the array to be sorted. c c Y Double precision array of length N. (INPUT/OUTPUT) c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c xx/xx/92: Version ' 2.1' c Adapted from the sort routine in LANSO. c c\SCCS Information: @(#) c FILE: sortc.F SID: 2.3 DATE OF SID: 4/20/96 RELEASE: 2 c c\EndLib c c----------------------------------------------------------------------- c subroutine dsortc (which, apply, n, xreal, ximag, y) c c %------------------% c | Scalar Arguments | c %------------------% c character*2 which logical apply integer n c c %-----------------% c | Array Arguments | c %-----------------% c Double precision & xreal(0:n-1), ximag(0:n-1), y(0:n-1) c c %---------------% c | Local Scalars | c %---------------% c integer i, igap, j Double precision & temp, temp1, temp2 c c %--------------------% c | External Functions | c %--------------------% c Double precision & dlapy2 external dlapy2 c c %-----------------------% c | Executable Statements | c %-----------------------% c igap = n / 2 c if (which .eq. 'LM') then c c %------------------------------------------------------% c | Sort XREAL,XIMAG into increasing order of magnitude. | c %------------------------------------------------------% c 10 continue if (igap .eq. 0) go to 9000 c do 30 i = igap, n-1 j = i-igap 20 continue c if (j.lt.0) go to 30 c temp1 = dlapy2(xreal(j),ximag(j)) temp2 = dlapy2(xreal(j+igap),ximag(j+igap)) c if (temp1.gt.temp2) then temp = xreal(j) xreal(j) = xreal(j+igap) xreal(j+igap) = temp c temp = ximag(j) ximag(j) = ximag(j+igap) ximag(j+igap) = temp c if (apply) then temp = y(j) y(j) = y(j+igap) y(j+igap) = temp end if else go to 30 end if j = j-igap go to 20 30 continue igap = igap / 2 go to 10 c else if (which .eq. 'SM') then c c %------------------------------------------------------% c | Sort XREAL,XIMAG into decreasing order of magnitude. | c %------------------------------------------------------% c 40 continue if (igap .eq. 0) go to 9000 c do 60 i = igap, n-1 j = i-igap 50 continue c if (j .lt. 0) go to 60 c temp1 = dlapy2(xreal(j),ximag(j)) temp2 = dlapy2(xreal(j+igap),ximag(j+igap)) c if (temp1.lt.temp2) then temp = xreal(j) xreal(j) = xreal(j+igap) xreal(j+igap) = temp c temp = ximag(j) ximag(j) = ximag(j+igap) ximag(j+igap) = temp c if (apply) then temp = y(j) y(j) = y(j+igap) y(j+igap) = temp end if else go to 60 endif j = j-igap go to 50 60 continue igap = igap / 2 go to 40 c else if (which .eq. 'LR') then c c %------------------------------------------------% c | Sort XREAL into increasing order of algebraic. | c %------------------------------------------------% c 70 continue if (igap .eq. 0) go to 9000 c do 90 i = igap, n-1 j = i-igap 80 continue c if (j.lt.0) go to 90 c if (xreal(j).gt.xreal(j+igap)) then temp = xreal(j) xreal(j) = xreal(j+igap) xreal(j+igap) = temp c temp = ximag(j) ximag(j) = ximag(j+igap) ximag(j+igap) = temp c if (apply) then temp = y(j) y(j) = y(j+igap) y(j+igap) = temp end if else go to 90 endif j = j-igap go to 80 90 continue igap = igap / 2 go to 70 c else if (which .eq. 'SR') then c c %------------------------------------------------% c | Sort XREAL into decreasing order of algebraic. | c %------------------------------------------------% c 100 continue if (igap .eq. 0) go to 9000 do 120 i = igap, n-1 j = i-igap 110 continue c if (j.lt.0) go to 120 c if (xreal(j).lt.xreal(j+igap)) then temp = xreal(j) xreal(j) = xreal(j+igap) xreal(j+igap) = temp c temp = ximag(j) ximag(j) = ximag(j+igap) ximag(j+igap) = temp c if (apply) then temp = y(j) y(j) = y(j+igap) y(j+igap) = temp end if else go to 120 endif j = j-igap go to 110 120 continue igap = igap / 2 go to 100 c else if (which .eq. 'LI') then c c %------------------------------------------------% c | Sort XIMAG into increasing order of magnitude. | c %------------------------------------------------% c 130 continue if (igap .eq. 0) go to 9000 do 150 i = igap, n-1 j = i-igap 140 continue c if (j.lt.0) go to 150 c if (abs(ximag(j)).gt.abs(ximag(j+igap))) then temp = xreal(j) xreal(j) = xreal(j+igap) xreal(j+igap) = temp c temp = ximag(j) ximag(j) = ximag(j+igap) ximag(j+igap) = temp c if (apply) then temp = y(j) y(j) = y(j+igap) y(j+igap) = temp end if else go to 150 endif j = j-igap go to 140 150 continue igap = igap / 2 go to 130 c else if (which .eq. 'SI') then c c %------------------------------------------------% c | Sort XIMAG into decreasing order of magnitude. | c %------------------------------------------------% c 160 continue if (igap .eq. 0) go to 9000 do 180 i = igap, n-1 j = i-igap 170 continue c if (j.lt.0) go to 180 c if (abs(ximag(j)).lt.abs(ximag(j+igap))) then temp = xreal(j) xreal(j) = xreal(j+igap) xreal(j+igap) = temp c temp = ximag(j) ximag(j) = ximag(j+igap) ximag(j+igap) = temp c if (apply) then temp = y(j) y(j) = y(j+igap) y(j+igap) = temp end if else go to 180 endif j = j-igap go to 170 180 continue igap = igap / 2 go to 160 end if c 9000 continue return c c %---------------% c | End of dsortc | c %---------------% c end arpack-0.92.1/SRC/znaitr.f0000644000175000017500000007463310776001577012121 00000000000000c\BeginDoc c c\Name: znaitr c c\Description: c Reverse communication interface for applying NP additional steps to c a K step nonsymmetric Arnoldi factorization. c c Input: OP*V_{k} - V_{k}*H = r_{k}*e_{k}^T c c with (V_{k}^T)*B*V_{k} = I, (V_{k}^T)*B*r_{k} = 0. c c Output: OP*V_{k+p} - V_{k+p}*H = r_{k+p}*e_{k+p}^T c c with (V_{k+p}^T)*B*V_{k+p} = I, (V_{k+p}^T)*B*r_{k+p} = 0. c c where OP and B are as in znaupd. The B-norm of r_{k+p} is also c computed and returned. c c\Usage: c call znaitr c ( IDO, BMAT, N, K, NP, NB, RESID, RNORM, V, LDV, H, LDH, c IPNTR, WORKD, INFO ) c c\Arguments c IDO Integer. (INPUT/OUTPUT) c Reverse communication flag. c ------------------------------------------------------------- c IDO = 0: first call to the reverse communication interface c IDO = -1: compute Y = OP * X where c IPNTR(1) is the pointer into WORK for X, c IPNTR(2) is the pointer into WORK for Y. c This is for the restart phase to force the new c starting vector into the range of OP. c IDO = 1: compute Y = OP * X where c IPNTR(1) is the pointer into WORK for X, c IPNTR(2) is the pointer into WORK for Y, c IPNTR(3) is the pointer into WORK for B * X. c IDO = 2: compute Y = B * X where c IPNTR(1) is the pointer into WORK for X, c IPNTR(2) is the pointer into WORK for Y. c IDO = 99: done c ------------------------------------------------------------- c When the routine is used in the "shift-and-invert" mode, the c vector B * Q is already available and do not need to be c recomputed in forming OP * Q. c c BMAT Character*1. (INPUT) c BMAT specifies the type of the matrix B that defines the c semi-inner product for the operator OP. See znaupd. c B = 'I' -> standard eigenvalue problem A*x = lambda*x c B = 'G' -> generalized eigenvalue problem A*x = lambda*M**x c c N Integer. (INPUT) c Dimension of the eigenproblem. c c K Integer. (INPUT) c Current size of V and H. c c NP Integer. (INPUT) c Number of additional Arnoldi steps to take. c c NB Integer. (INPUT) c Blocksize to be used in the recurrence. c Only work for NB = 1 right now. The goal is to have a c program that implement both the block and non-block method. c c RESID Complex*16 array of length N. (INPUT/OUTPUT) c On INPUT: RESID contains the residual vector r_{k}. c On OUTPUT: RESID contains the residual vector r_{k+p}. c c RNORM Double precision scalar. (INPUT/OUTPUT) c B-norm of the starting residual on input. c B-norm of the updated residual r_{k+p} on output. c c V Complex*16 N by K+NP array. (INPUT/OUTPUT) c On INPUT: V contains the Arnoldi vectors in the first K c columns. c On OUTPUT: V contains the new NP Arnoldi vectors in the next c NP columns. The first K columns are unchanged. c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling c program. c c H Complex*16 (K+NP) by (K+NP) array. (INPUT/OUTPUT) c H is used to store the generated upper Hessenberg matrix. c c LDH Integer. (INPUT) c Leading dimension of H exactly as declared in the calling c program. c c IPNTR Integer array of length 3. (OUTPUT) c Pointer to mark the starting locations in the WORK for c vectors used by the Arnoldi iteration. c ------------------------------------------------------------- c IPNTR(1): pointer to the current operand vector X. c IPNTR(2): pointer to the current result vector Y. c IPNTR(3): pointer to the vector B * X when used in the c shift-and-invert mode. X is the current operand. c ------------------------------------------------------------- c c WORKD Complex*16 work array of length 3*N. (REVERSE COMMUNICATION) c Distributed array to be used in the basic Arnoldi iteration c for reverse communication. The calling program should not c use WORKD as temporary workspace during the iteration !!!!!! c On input, WORKD(1:N) = B*RESID and is used to save some c computation at the first step. c c INFO Integer. (OUTPUT) c = 0: Normal exit. c > 0: Size of the spanning invariant subspace of OP found. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx Complex*16 c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly c Restarted Arnoldi Iteration", Rice University Technical Report c TR95-13, Department of Computational and Applied Mathematics. c c\Routines called: c zgetv0 ARPACK routine to generate the initial vector. c ivout ARPACK utility routine that prints integers. c arscnd ARPACK utility routine for timing. c zmout ARPACK utility routine that prints matrices c zvout ARPACK utility routine that prints vectors. c zlanhs LAPACK routine that computes various norms of a matrix. c zlascl LAPACK routine for careful scaling of a matrix. c dlabad LAPACK routine for defining the underflow and overflow c limits. c dlamch LAPACK routine that determines machine constants. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c zgemv Level 2 BLAS routine for matrix vector multiplication. c zaxpy Level 1 BLAS that computes a vector triad. c zcopy Level 1 BLAS that copies one vector to another . c zdotc Level 1 BLAS that computes the scalar product of two vectors. c zscal Level 1 BLAS that scales a vector. c zdscal Level 1 BLAS that scales a complex vector by a real number. c dznrm2 Level 1 BLAS that computes the norm of a vector. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: naitr.F SID: 2.3 DATE OF SID: 8/27/96 RELEASE: 2 c c\Remarks c The algorithm implemented is: c c restart = .false. c Given V_{k} = [v_{1}, ..., v_{k}], r_{k}; c r_{k} contains the initial residual vector even for k = 0; c Also assume that rnorm = || B*r_{k} || and B*r_{k} are already c computed by the calling program. c c betaj = rnorm ; p_{k+1} = B*r_{k} ; c For j = k+1, ..., k+np Do c 1) if ( betaj < tol ) stop or restart depending on j. c ( At present tol is zero ) c if ( restart ) generate a new starting vector. c 2) v_{j} = r(j-1)/betaj; V_{j} = [V_{j-1}, v_{j}]; c p_{j} = p_{j}/betaj c 3) r_{j} = OP*v_{j} where OP is defined as in znaupd c For shift-invert mode p_{j} = B*v_{j} is already available. c wnorm = || OP*v_{j} || c 4) Compute the j-th step residual vector. c w_{j} = V_{j}^T * B * OP * v_{j} c r_{j} = OP*v_{j} - V_{j} * w_{j} c H(:,j) = w_{j}; c H(j,j-1) = rnorm c rnorm = || r_(j) || c If (rnorm > 0.717*wnorm) accept step and go back to 1) c 5) Re-orthogonalization step: c s = V_{j}'*B*r_{j} c r_{j} = r_{j} - V_{j}*s; rnorm1 = || r_{j} || c alphaj = alphaj + s_{j}; c 6) Iterative refinement step: c If (rnorm1 > 0.717*rnorm) then c rnorm = rnorm1 c accept step and go back to 1) c Else c rnorm = rnorm1 c If this is the first time in step 6), go to 5) c Else r_{j} lies in the span of V_{j} numerically. c Set r_{j} = 0 and rnorm = 0; go to 1) c EndIf c End Do c c\EndLib c c----------------------------------------------------------------------- c subroutine znaitr & (ido, bmat, n, k, np, nb, resid, rnorm, v, ldv, h, ldh, & ipntr, workd, info) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character bmat*1 integer ido, info, k, ldh, ldv, n, nb, np Double precision & rnorm c c %-----------------% c | Array Arguments | c %-----------------% c integer ipntr(3) Complex*16 & h(ldh,k+np), resid(n), v(ldv,k+np), workd(3*n) c c %------------% c | Parameters | c %------------% c Complex*16 & one, zero Double precision & rone, rzero parameter (one = (1.0D+0, 0.0D+0), zero = (0.0D+0, 0.0D+0), & rone = 1.0D+0, rzero = 0.0D+0) c c %--------------% c | Local Arrays | c %--------------% c Double precision & rtemp(2) c c %---------------% c | Local Scalars | c %---------------% c logical first, orth1, orth2, rstart, step3, step4 integer ierr, i, infol, ipj, irj, ivj, iter, itry, j, msglvl, & jj Double precision & ovfl, smlnum, tst1, ulp, unfl, betaj, & temp1, rnorm1, wnorm Complex*16 & cnorm c save first, orth1, orth2, rstart, step3, step4, & ierr, ipj, irj, ivj, iter, itry, j, msglvl, ovfl, & betaj, rnorm1, smlnum, ulp, unfl, wnorm c c %----------------------% c | External Subroutines | c %----------------------% c external zaxpy, zcopy, zscal, zdscal, zgemv, zgetv0, & dlabad, zvout, zmout, ivout, arscnd c c %--------------------% c | External Functions | c %--------------------% c Complex*16 & zdotc Double precision & dlamch, dznrm2, zlanhs, dlapy2 external zdotc, dznrm2, zlanhs, dlamch, dlapy2 c c %---------------------% c | Intrinsic Functions | c %---------------------% c intrinsic dimag, dble, max, sqrt c c %-----------------% c | Data statements | c %-----------------% c data first / .true. / c c %-----------------------% c | Executable Statements | c %-----------------------% c if (first) then c c %-----------------------------------------% c | Set machine-dependent constants for the | c | the splitting and deflation criterion. | c | If norm(H) <= sqrt(OVFL), | c | overflow should not occur. | c | REFERENCE: LAPACK subroutine zlahqr | c %-----------------------------------------% c unfl = dlamch( 'safe minimum' ) ovfl = dble(one / unfl) call dlabad( unfl, ovfl ) ulp = dlamch( 'precision' ) smlnum = unfl*( n / ulp ) first = .false. end if c if (ido .eq. 0) then c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call arscnd (t0) msglvl = mcaitr c c %------------------------------% c | Initial call to this routine | c %------------------------------% c info = 0 step3 = .false. step4 = .false. rstart = .false. orth1 = .false. orth2 = .false. j = k + 1 ipj = 1 irj = ipj + n ivj = irj + n end if c c %-------------------------------------------------% c | When in reverse communication mode one of: | c | STEP3, STEP4, ORTH1, ORTH2, RSTART | c | will be .true. when .... | c | STEP3: return from computing OP*v_{j}. | c | STEP4: return from computing B-norm of OP*v_{j} | c | ORTH1: return from computing B-norm of r_{j+1} | c | ORTH2: return from computing B-norm of | c | correction to the residual vector. | c | RSTART: return from OP computations needed by | c | zgetv0. | c %-------------------------------------------------% c if (step3) go to 50 if (step4) go to 60 if (orth1) go to 70 if (orth2) go to 90 if (rstart) go to 30 c c %-----------------------------% c | Else this is the first step | c %-----------------------------% c c %--------------------------------------------------------------% c | | c | A R N O L D I I T E R A T I O N L O O P | c | | c | Note: B*r_{j-1} is already in WORKD(1:N)=WORKD(IPJ:IPJ+N-1) | c %--------------------------------------------------------------% 1000 continue c if (msglvl .gt. 1) then call ivout (logfil, 1, j, ndigit, & '_naitr: generating Arnoldi vector number') call dvout (logfil, 1, rnorm, ndigit, & '_naitr: B-norm of the current residual is') end if c c %---------------------------------------------------% c | STEP 1: Check if the B norm of j-th residual | c | vector is zero. Equivalent to determine whether | c | an exact j-step Arnoldi factorization is present. | c %---------------------------------------------------% c betaj = rnorm if (rnorm .gt. rzero) go to 40 c c %---------------------------------------------------% c | Invariant subspace found, generate a new starting | c | vector which is orthogonal to the current Arnoldi | c | basis and continue the iteration. | c %---------------------------------------------------% c if (msglvl .gt. 0) then call ivout (logfil, 1, j, ndigit, & '_naitr: ****** RESTART AT STEP ******') end if c c %---------------------------------------------% c | ITRY is the loop variable that controls the | c | maximum amount of times that a restart is | c | attempted. NRSTRT is used by stat.h | c %---------------------------------------------% c betaj = rzero nrstrt = nrstrt + 1 itry = 1 20 continue rstart = .true. ido = 0 30 continue c c %--------------------------------------% c | If in reverse communication mode and | c | RSTART = .true. flow returns here. | c %--------------------------------------% c call zgetv0 (ido, bmat, itry, .false., n, j, v, ldv, & resid, rnorm, ipntr, workd, ierr) if (ido .ne. 99) go to 9000 if (ierr .lt. 0) then itry = itry + 1 if (itry .le. 3) go to 20 c c %------------------------------------------------% c | Give up after several restart attempts. | c | Set INFO to the size of the invariant subspace | c | which spans OP and exit. | c %------------------------------------------------% c info = j - 1 call arscnd (t1) tcaitr = tcaitr + (t1 - t0) ido = 99 go to 9000 end if c 40 continue c c %---------------------------------------------------------% c | STEP 2: v_{j} = r_{j-1}/rnorm and p_{j} = p_{j}/rnorm | c | Note that p_{j} = B*r_{j-1}. In order to avoid overflow | c | when reciprocating a small RNORM, test against lower | c | machine bound. | c %---------------------------------------------------------% c call zcopy (n, resid, 1, v(1,j), 1) if ( rnorm .ge. unfl) then temp1 = rone / rnorm call zdscal (n, temp1, v(1,j), 1) call zdscal (n, temp1, workd(ipj), 1) else c c %-----------------------------------------% c | To scale both v_{j} and p_{j} carefully | c | use LAPACK routine zlascl | c %-----------------------------------------% c call zlascl ('General', i, i, rnorm, rone, & n, 1, v(1,j), n, infol) call zlascl ('General', i, i, rnorm, rone, & n, 1, workd(ipj), n, infol) end if c c %------------------------------------------------------% c | STEP 3: r_{j} = OP*v_{j}; Note that p_{j} = B*v_{j} | c | Note that this is not quite yet r_{j}. See STEP 4 | c %------------------------------------------------------% c step3 = .true. nopx = nopx + 1 call arscnd (t2) call zcopy (n, v(1,j), 1, workd(ivj), 1) ipntr(1) = ivj ipntr(2) = irj ipntr(3) = ipj ido = 1 c c %-----------------------------------% c | Exit in order to compute OP*v_{j} | c %-----------------------------------% c go to 9000 50 continue c c %----------------------------------% c | Back from reverse communication; | c | WORKD(IRJ:IRJ+N-1) := OP*v_{j} | c | if step3 = .true. | c %----------------------------------% c call arscnd (t3) tmvopx = tmvopx + (t3 - t2) step3 = .false. c c %------------------------------------------% c | Put another copy of OP*v_{j} into RESID. | c %------------------------------------------% c call zcopy (n, workd(irj), 1, resid, 1) c c %---------------------------------------% c | STEP 4: Finish extending the Arnoldi | c | factorization to length j. | c %---------------------------------------% c call arscnd (t2) if (bmat .eq. 'G') then nbx = nbx + 1 step4 = .true. ipntr(1) = irj ipntr(2) = ipj ido = 2 c c %-------------------------------------% c | Exit in order to compute B*OP*v_{j} | c %-------------------------------------% c go to 9000 else if (bmat .eq. 'I') then call zcopy (n, resid, 1, workd(ipj), 1) end if 60 continue c c %----------------------------------% c | Back from reverse communication; | c | WORKD(IPJ:IPJ+N-1) := B*OP*v_{j} | c | if step4 = .true. | c %----------------------------------% c if (bmat .eq. 'G') then call arscnd (t3) tmvbx = tmvbx + (t3 - t2) end if c step4 = .false. c c %-------------------------------------% c | The following is needed for STEP 5. | c | Compute the B-norm of OP*v_{j}. | c %-------------------------------------% c if (bmat .eq. 'G') then cnorm = zdotc (n, resid, 1, workd(ipj), 1) wnorm = sqrt( dlapy2(dble(cnorm),dimag(cnorm)) ) else if (bmat .eq. 'I') then wnorm = dznrm2(n, resid, 1) end if c c %-----------------------------------------% c | Compute the j-th residual corresponding | c | to the j step factorization. | c | Use Classical Gram Schmidt and compute: | c | w_{j} <- V_{j}^T * B * OP * v_{j} | c | r_{j} <- OP*v_{j} - V_{j} * w_{j} | c %-----------------------------------------% c c c %------------------------------------------% c | Compute the j Fourier coefficients w_{j} | c | WORKD(IPJ:IPJ+N-1) contains B*OP*v_{j}. | c %------------------------------------------% c call zgemv ('C', n, j, one, v, ldv, workd(ipj), 1, & zero, h(1,j), 1) c c %--------------------------------------% c | Orthogonalize r_{j} against V_{j}. | c | RESID contains OP*v_{j}. See STEP 3. | c %--------------------------------------% c call zgemv ('N', n, j, -one, v, ldv, h(1,j), 1, & one, resid, 1) c if (j .gt. 1) h(j,j-1) = dcmplx(betaj, rzero) c call arscnd (t4) c orth1 = .true. c call arscnd (t2) if (bmat .eq. 'G') then nbx = nbx + 1 call zcopy (n, resid, 1, workd(irj), 1) ipntr(1) = irj ipntr(2) = ipj ido = 2 c c %----------------------------------% c | Exit in order to compute B*r_{j} | c %----------------------------------% c go to 9000 else if (bmat .eq. 'I') then call zcopy (n, resid, 1, workd(ipj), 1) end if 70 continue c c %---------------------------------------------------% c | Back from reverse communication if ORTH1 = .true. | c | WORKD(IPJ:IPJ+N-1) := B*r_{j}. | c %---------------------------------------------------% c if (bmat .eq. 'G') then call arscnd (t3) tmvbx = tmvbx + (t3 - t2) end if c orth1 = .false. c c %------------------------------% c | Compute the B-norm of r_{j}. | c %------------------------------% c if (bmat .eq. 'G') then cnorm = zdotc (n, resid, 1, workd(ipj), 1) rnorm = sqrt( dlapy2(dble(cnorm),dimag(cnorm)) ) else if (bmat .eq. 'I') then rnorm = dznrm2(n, resid, 1) end if c c %-----------------------------------------------------------% c | STEP 5: Re-orthogonalization / Iterative refinement phase | c | Maximum NITER_ITREF tries. | c | | c | s = V_{j}^T * B * r_{j} | c | r_{j} = r_{j} - V_{j}*s | c | alphaj = alphaj + s_{j} | c | | c | The stopping criteria used for iterative refinement is | c | discussed in Parlett's book SEP, page 107 and in Gragg & | c | Reichel ACM TOMS paper; Algorithm 686, Dec. 1990. | c | Determine if we need to correct the residual. The goal is | c | to enforce ||v(:,1:j)^T * r_{j}|| .le. eps * || r_{j} || | c | The following test determines whether the sine of the | c | angle between OP*x and the computed residual is less | c | than or equal to 0.717. | c %-----------------------------------------------------------% c if ( rnorm .gt. 0.717*wnorm ) go to 100 c iter = 0 nrorth = nrorth + 1 c c %---------------------------------------------------% c | Enter the Iterative refinement phase. If further | c | refinement is necessary, loop back here. The loop | c | variable is ITER. Perform a step of Classical | c | Gram-Schmidt using all the Arnoldi vectors V_{j} | c %---------------------------------------------------% c 80 continue c if (msglvl .gt. 2) then rtemp(1) = wnorm rtemp(2) = rnorm call dvout (logfil, 2, rtemp, ndigit, & '_naitr: re-orthogonalization; wnorm and rnorm are') call zvout (logfil, j, h(1,j), ndigit, & '_naitr: j-th column of H') end if c c %----------------------------------------------------% c | Compute V_{j}^T * B * r_{j}. | c | WORKD(IRJ:IRJ+J-1) = v(:,1:J)'*WORKD(IPJ:IPJ+N-1). | c %----------------------------------------------------% c call zgemv ('C', n, j, one, v, ldv, workd(ipj), 1, & zero, workd(irj), 1) c c %---------------------------------------------% c | Compute the correction to the residual: | c | r_{j} = r_{j} - V_{j} * WORKD(IRJ:IRJ+J-1). | c | The correction to H is v(:,1:J)*H(1:J,1:J) | c | + v(:,1:J)*WORKD(IRJ:IRJ+J-1)*e'_j. | c %---------------------------------------------% c call zgemv ('N', n, j, -one, v, ldv, workd(irj), 1, & one, resid, 1) call zaxpy (j, one, workd(irj), 1, h(1,j), 1) c orth2 = .true. call arscnd (t2) if (bmat .eq. 'G') then nbx = nbx + 1 call zcopy (n, resid, 1, workd(irj), 1) ipntr(1) = irj ipntr(2) = ipj ido = 2 c c %-----------------------------------% c | Exit in order to compute B*r_{j}. | c | r_{j} is the corrected residual. | c %-----------------------------------% c go to 9000 else if (bmat .eq. 'I') then call zcopy (n, resid, 1, workd(ipj), 1) end if 90 continue c c %---------------------------------------------------% c | Back from reverse communication if ORTH2 = .true. | c %---------------------------------------------------% c if (bmat .eq. 'G') then call arscnd (t3) tmvbx = tmvbx + (t3 - t2) end if c c %-----------------------------------------------------% c | Compute the B-norm of the corrected residual r_{j}. | c %-----------------------------------------------------% c if (bmat .eq. 'G') then cnorm = zdotc (n, resid, 1, workd(ipj), 1) rnorm1 = sqrt( dlapy2(dble(cnorm),dimag(cnorm)) ) else if (bmat .eq. 'I') then rnorm1 = dznrm2(n, resid, 1) end if c if (msglvl .gt. 0 .and. iter .gt. 0 ) then call ivout (logfil, 1, j, ndigit, & '_naitr: Iterative refinement for Arnoldi residual') if (msglvl .gt. 2) then rtemp(1) = rnorm rtemp(2) = rnorm1 call dvout (logfil, 2, rtemp, ndigit, & '_naitr: iterative refinement ; rnorm and rnorm1 are') end if end if c c %-----------------------------------------% c | Determine if we need to perform another | c | step of re-orthogonalization. | c %-----------------------------------------% c if ( rnorm1 .gt. 0.717*rnorm ) then c c %---------------------------------------% c | No need for further refinement. | c | The cosine of the angle between the | c | corrected residual vector and the old | c | residual vector is greater than 0.717 | c | In other words the corrected residual | c | and the old residual vector share an | c | angle of less than arcCOS(0.717) | c %---------------------------------------% c rnorm = rnorm1 c else c c %-------------------------------------------% c | Another step of iterative refinement step | c | is required. NITREF is used by stat.h | c %-------------------------------------------% c nitref = nitref + 1 rnorm = rnorm1 iter = iter + 1 if (iter .le. 1) go to 80 c c %-------------------------------------------------% c | Otherwise RESID is numerically in the span of V | c %-------------------------------------------------% c do 95 jj = 1, n resid(jj) = zero 95 continue rnorm = rzero end if c c %----------------------------------------------% c | Branch here directly if iterative refinement | c | wasn't necessary or after at most NITER_REF | c | steps of iterative refinement. | c %----------------------------------------------% c 100 continue c rstart = .false. orth2 = .false. c call arscnd (t5) titref = titref + (t5 - t4) c c %------------------------------------% c | STEP 6: Update j = j+1; Continue | c %------------------------------------% c j = j + 1 if (j .gt. k+np) then call arscnd (t1) tcaitr = tcaitr + (t1 - t0) ido = 99 do 110 i = max(1,k), k+np-1 c c %--------------------------------------------% c | Check for splitting and deflation. | c | Use a standard test as in the QR algorithm | c | REFERENCE: LAPACK subroutine zlahqr | c %--------------------------------------------% c tst1 = dlapy2(dble(h(i,i)),dimag(h(i,i))) & + dlapy2(dble(h(i+1,i+1)), dimag(h(i+1,i+1))) if( tst1.eq.dble(zero) ) & tst1 = zlanhs( '1', k+np, h, ldh, workd(n+1) ) if( dlapy2(dble(h(i+1,i)),dimag(h(i+1,i))) .le. & max( ulp*tst1, smlnum ) ) & h(i+1,i) = zero 110 continue c if (msglvl .gt. 2) then call zmout (logfil, k+np, k+np, h, ldh, ndigit, & '_naitr: Final upper Hessenberg matrix H of order K+NP') end if c go to 9000 end if c c %--------------------------------------------------------% c | Loop back to extend the factorization by another step. | c %--------------------------------------------------------% c go to 1000 c c %---------------------------------------------------------------% c | | c | E N D O F M A I N I T E R A T I O N L O O P | c | | c %---------------------------------------------------------------% c 9000 continue return c c %---------------% c | End of znaitr | c %---------------% c end arpack-0.92.1/SRC/dstatn.f0000644000175000017500000000271010776001577012072 00000000000000c c %---------------------------------------------% c | Initialize statistic and timing information | c | for nonsymmetric Arnoldi code. | c %---------------------------------------------% c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: statn.F SID: 2.4 DATE OF SID: 4/20/96 RELEASE: 2 c subroutine dstatn c c %--------------------------------% c | See stat.doc for documentation | c %--------------------------------% c include 'stat.h' c c %-----------------------% c | Executable Statements | c %-----------------------% c nopx = 0 nbx = 0 nrorth = 0 nitref = 0 nrstrt = 0 c tnaupd = 0.0D+0 tnaup2 = 0.0D+0 tnaitr = 0.0D+0 tneigh = 0.0D+0 tngets = 0.0D+0 tnapps = 0.0D+0 tnconv = 0.0D+0 titref = 0.0D+0 tgetv0 = 0.0D+0 trvec = 0.0D+0 c c %----------------------------------------------------% c | User time including reverse communication overhead | c %----------------------------------------------------% c tmvopx = 0.0D+0 tmvbx = 0.0D+0 c return c c c %---------------% c | End of dstatn | c %---------------% c end arpack-0.92.1/SRC/sneupd.f0000644000175000017500000012577510776001577012114 00000000000000c\BeginDoc c c\Name: sneupd c c\Description: c c This subroutine returns the converged approximations to eigenvalues c of A*z = lambda*B*z and (optionally): c c (1) The corresponding approximate eigenvectors; c c (2) An orthonormal basis for the associated approximate c invariant subspace; c c (3) Both. c c There is negligible additional cost to obtain eigenvectors. An orthonormal c basis is always computed. There is an additional storage cost of n*nev c if both are requested (in this case a separate array Z must be supplied). c c The approximate eigenvalues and eigenvectors of A*z = lambda*B*z c are derived from approximate eigenvalues and eigenvectors of c of the linear operator OP prescribed by the MODE selection in the c call to SNAUPD. SNAUPD must be called before this routine is called. c These approximate eigenvalues and vectors are commonly called Ritz c values and Ritz vectors respectively. They are referred to as such c in the comments that follow. The computed orthonormal basis for the c invariant subspace corresponding to these Ritz values is referred to as a c Schur basis. c c See documentation in the header of the subroutine SNAUPD for c definition of OP as well as other terms and the relation of computed c Ritz values and Ritz vectors of OP with respect to the given problem c A*z = lambda*B*z. For a brief description, see definitions of c IPARAM(7), MODE and WHICH in the documentation of SNAUPD. c c\Usage: c call sneupd c ( RVEC, HOWMNY, SELECT, DR, DI, Z, LDZ, SIGMAR, SIGMAI, WORKEV, BMAT, c N, WHICH, NEV, TOL, RESID, NCV, V, LDV, IPARAM, IPNTR, WORKD, WORKL, c LWORKL, INFO ) c c\Arguments: c RVEC LOGICAL (INPUT) c Specifies whether a basis for the invariant subspace corresponding c to the converged Ritz value approximations for the eigenproblem c A*z = lambda*B*z is computed. c c RVEC = .FALSE. Compute Ritz values only. c c RVEC = .TRUE. Compute the Ritz vectors or Schur vectors. c See Remarks below. c c HOWMNY Character*1 (INPUT) c Specifies the form of the basis for the invariant subspace c corresponding to the converged Ritz values that is to be computed. c c = 'A': Compute NEV Ritz vectors; c = 'P': Compute NEV Schur vectors; c = 'S': compute some of the Ritz vectors, specified c by the logical array SELECT. c c SELECT Logical array of dimension NCV. (INPUT) c If HOWMNY = 'S', SELECT specifies the Ritz vectors to be c computed. To select the Ritz vector corresponding to a c Ritz value (DR(j), DI(j)), SELECT(j) must be set to .TRUE.. c If HOWMNY = 'A' or 'P', SELECT is used as internal workspace. c c DR Real array of dimension NEV+1. (OUTPUT) c If IPARAM(7) = 1,2 or 3 and SIGMAI=0.0 then on exit: DR contains c the real part of the Ritz approximations to the eigenvalues of c A*z = lambda*B*z. c If IPARAM(7) = 3, 4 and SIGMAI is not equal to zero, then on exit: c DR contains the real part of the Ritz values of OP computed by c SNAUPD. A further computation must be performed by the user c to transform the Ritz values computed for OP by SNAUPD to those c of the original system A*z = lambda*B*z. See remark 3 below. c c DI Real array of dimension NEV+1. (OUTPUT) c On exit, DI contains the imaginary part of the Ritz value c approximations to the eigenvalues of A*z = lambda*B*z associated c with DR. c c NOTE: When Ritz values are complex, they will come in complex c conjugate pairs. If eigenvectors are requested, the c corresponding Ritz vectors will also come in conjugate c pairs and the real and imaginary parts of these are c represented in two consecutive columns of the array Z c (see below). c c Z Real N by NEV+1 array if RVEC = .TRUE. and HOWMNY = 'A'. (OUTPUT) c On exit, if RVEC = .TRUE. and HOWMNY = 'A', then the columns of c Z represent approximate eigenvectors (Ritz vectors) corresponding c to the NCONV=IPARAM(5) Ritz values for eigensystem c A*z = lambda*B*z. c c The complex Ritz vector associated with the Ritz value c with positive imaginary part is stored in two consecutive c columns. The first column holds the real part of the Ritz c vector and the second column holds the imaginary part. The c Ritz vector associated with the Ritz value with negative c imaginary part is simply the complex conjugate of the Ritz vector c associated with the positive imaginary part. c c If RVEC = .FALSE. or HOWMNY = 'P', then Z is not referenced. c c NOTE: If if RVEC = .TRUE. and a Schur basis is not required, c the array Z may be set equal to first NEV+1 columns of the Arnoldi c basis array V computed by SNAUPD. In this case the Arnoldi basis c will be destroyed and overwritten with the eigenvector basis. c c LDZ Integer. (INPUT) c The leading dimension of the array Z. If Ritz vectors are c desired, then LDZ >= max( 1, N ). In any case, LDZ >= 1. c c SIGMAR Real (INPUT) c If IPARAM(7) = 3 or 4, represents the real part of the shift. c Not referenced if IPARAM(7) = 1 or 2. c c SIGMAI Real (INPUT) c If IPARAM(7) = 3 or 4, represents the imaginary part of the shift. c Not referenced if IPARAM(7) = 1 or 2. See remark 3 below. c c WORKEV Real work array of dimension 3*NCV. (WORKSPACE) c c **** The remaining arguments MUST be the same as for the **** c **** call to SNAUPD that was just completed. **** c c NOTE: The remaining arguments c c BMAT, N, WHICH, NEV, TOL, RESID, NCV, V, LDV, IPARAM, IPNTR, c WORKD, WORKL, LWORKL, INFO c c must be passed directly to SNEUPD following the last call c to SNAUPD. These arguments MUST NOT BE MODIFIED between c the the last call to SNAUPD and the call to SNEUPD. c c Three of these parameters (V, WORKL, INFO) are also output parameters: c c V Real N by NCV array. (INPUT/OUTPUT) c c Upon INPUT: the NCV columns of V contain the Arnoldi basis c vectors for OP as constructed by SNAUPD . c c Upon OUTPUT: If RVEC = .TRUE. the first NCONV=IPARAM(5) columns c contain approximate Schur vectors that span the c desired invariant subspace. See Remark 2 below. c c NOTE: If the array Z has been set equal to first NEV+1 columns c of the array V and RVEC=.TRUE. and HOWMNY= 'A', then the c Arnoldi basis held by V has been overwritten by the desired c Ritz vectors. If a separate array Z has been passed then c the first NCONV=IPARAM(5) columns of V will contain approximate c Schur vectors that span the desired invariant subspace. c c WORKL Real work array of length LWORKL. (OUTPUT/WORKSPACE) c WORKL(1:ncv*ncv+3*ncv) contains information obtained in c snaupd. They are not changed by sneupd. c WORKL(ncv*ncv+3*ncv+1:3*ncv*ncv+6*ncv) holds the c real and imaginary part of the untransformed Ritz values, c the upper quasi-triangular matrix for H, and the c associated matrix representation of the invariant subspace for H. c c Note: IPNTR(9:13) contains the pointer into WORKL for addresses c of the above information computed by sneupd. c ------------------------------------------------------------- c IPNTR(9): pointer to the real part of the NCV RITZ values of the c original system. c IPNTR(10): pointer to the imaginary part of the NCV RITZ values of c the original system. c IPNTR(11): pointer to the NCV corresponding error bounds. c IPNTR(12): pointer to the NCV by NCV upper quasi-triangular c Schur matrix for H. c IPNTR(13): pointer to the NCV by NCV matrix of eigenvectors c of the upper Hessenberg matrix H. Only referenced by c sneupd if RVEC = .TRUE. See Remark 2 below. c ------------------------------------------------------------- c c INFO Integer. (OUTPUT) c Error flag on output. c c = 0: Normal exit. c c = 1: The Schur form computed by LAPACK routine slahqr c could not be reordered by LAPACK routine strsen. c Re-enter subroutine sneupd with IPARAM(5)=NCV and c increase the size of the arrays DR and DI to have c dimension at least dimension NCV and allocate at least NCV c columns for Z. NOTE: Not necessary if Z and V share c the same space. Please notify the authors if this error c occurs. c c = -1: N must be positive. c = -2: NEV must be positive. c = -3: NCV-NEV >= 2 and less than or equal to N. c = -5: WHICH must be one of 'LM', 'SM', 'LR', 'SR', 'LI', 'SI' c = -6: BMAT must be one of 'I' or 'G'. c = -7: Length of private work WORKL array is not sufficient. c = -8: Error return from calculation of a real Schur form. c Informational error from LAPACK routine slahqr. c = -9: Error return from calculation of eigenvectors. c Informational error from LAPACK routine strevc. c = -10: IPARAM(7) must be 1,2,3,4. c = -11: IPARAM(7) = 1 and BMAT = 'G' are incompatible. c = -12: HOWMNY = 'S' not yet implemented c = -13: HOWMNY must be one of 'A' or 'P' if RVEC = .true. c = -14: SNAUPD did not find any eigenvalues to sufficient c accuracy. c = -15: DNEUPD got a different count of the number of converged c Ritz values than DNAUPD got. This indicates the user c probably made an error in passing data from DNAUPD to c DNEUPD or that the data was modified before entering c DNEUPD c c\BeginLib c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly c Restarted Arnoldi Iteration", Rice University Technical Report c TR95-13, Department of Computational and Applied Mathematics. c 3. B.N. Parlett & Y. Saad, "Complex Shift and Invert Strategies for c Real Matrices", Linear Algebra and its Applications, vol 88/89, c pp 575-595, (1987). c c\Routines called: c ivout ARPACK utility routine that prints integers. c smout ARPACK utility routine that prints matrices c svout ARPACK utility routine that prints vectors. c sgeqr2 LAPACK routine that computes the QR factorization of c a matrix. c slacpy LAPACK matrix copy routine. c slahqr LAPACK routine to compute the real Schur form of an c upper Hessenberg matrix. c slamch LAPACK routine that determines machine constants. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c slaset LAPACK matrix initialization routine. c sorm2r LAPACK routine that applies an orthogonal matrix in c factored form. c strevc LAPACK routine to compute the eigenvectors of a matrix c in upper quasi-triangular form. c strsen LAPACK routine that re-orders the Schur form. c strmm Level 3 BLAS matrix times an upper triangular matrix. c sger Level 2 BLAS rank one update to a matrix. c scopy Level 1 BLAS that copies one vector to another . c sdot Level 1 BLAS that computes the scalar product of two vectors. c snrm2 Level 1 BLAS that computes the norm of a vector. c sscal Level 1 BLAS that scales a vector. c c\Remarks c c 1. Currently only HOWMNY = 'A' and 'P' are implemented. c c Let trans(X) denote the transpose of X. c c 2. Schur vectors are an orthogonal representation for the basis of c Ritz vectors. Thus, their numerical properties are often superior. c If RVEC = .TRUE. then the relationship c A * V(:,1:IPARAM(5)) = V(:,1:IPARAM(5)) * T, and c trans(V(:,1:IPARAM(5))) * V(:,1:IPARAM(5)) = I are approximately c satisfied. Here T is the leading submatrix of order IPARAM(5) of the c real upper quasi-triangular matrix stored workl(ipntr(12)). That is, c T is block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; c each 2-by-2 diagonal block has its diagonal elements equal and its c off-diagonal elements of opposite sign. Corresponding to each 2-by-2 c diagonal block is a complex conjugate pair of Ritz values. The real c Ritz values are stored on the diagonal of T. c c 3. If IPARAM(7) = 3 or 4 and SIGMAI is not equal zero, then the user must c form the IPARAM(5) Rayleigh quotients in order to transform the Ritz c values computed by SNAUPD for OP to those of A*z = lambda*B*z. c Set RVEC = .true. and HOWMNY = 'A', and c compute c trans(Z(:,I)) * A * Z(:,I) if DI(I) = 0. c If DI(I) is not equal to zero and DI(I+1) = - D(I), c then the desired real and imaginary parts of the Ritz value are c trans(Z(:,I)) * A * Z(:,I) + trans(Z(:,I+1)) * A * Z(:,I+1), c trans(Z(:,I)) * A * Z(:,I+1) - trans(Z(:,I+1)) * A * Z(:,I), c respectively. c Another possibility is to set RVEC = .true. and HOWMNY = 'P' and c compute trans(V(:,1:IPARAM(5))) * A * V(:,1:IPARAM(5)) and then an upper c quasi-triangular matrix of order IPARAM(5) is computed. See remark c 2 above. c c\Authors c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Chao Yang Houston, Texas c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: neupd.F SID: 2.7 DATE OF SID: 09/20/00 RELEASE: 2 c c\EndLib c c----------------------------------------------------------------------- subroutine sneupd(rvec , howmny, select, dr , di, & z , ldz , sigmar, sigmai, workev, & bmat , n , which , nev , tol, & resid, ncv , v , ldv , iparam, & ipntr, workd , workl , lworkl, info) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character bmat, howmny, which*2 logical rvec integer info, ldz, ldv, lworkl, n, ncv, nev Real & sigmar, sigmai, tol c c %-----------------% c | Array Arguments | c %-----------------% c integer iparam(11), ipntr(14) logical select(ncv) Real & dr(nev+1) , di(nev+1), resid(n) , & v(ldv,ncv) , z(ldz,*) , workd(3*n), & workl(lworkl), workev(3*ncv) c c %------------% c | Parameters | c %------------% c Real & one, zero parameter (one = 1.0E+0 , zero = 0.0E+0 ) c c %---------------% c | Local Scalars | c %---------------% c character type*6 integer bounds, ierr , ih , ihbds , & iheigr, iheigi, iconj , nconv , & invsub, iuptri, iwev , iwork(1), & j , k , ldh , ldq , & mode , msglvl, outncv, ritzr , & ritzi , wri , wrr , irr , & iri , ibd , ishift, numcnv , & np , jj logical reord Real & conds , rnorm, sep , temp, & vl(1,1), temp1, eps23 c c %----------------------% c | External Subroutines | c %----------------------% c external scopy , sger , sgeqr2, slacpy, & slahqr, slaset, smout , sorm2r, & strevc, strmm , strsen, sscal , & svout , ivout c c %--------------------% c | External Functions | c %--------------------% c Real & slapy2, snrm2, slamch, sdot external slapy2, snrm2, slamch, sdot c c %---------------------% c | Intrinsic Functions | c %---------------------% c intrinsic abs, min, sqrt c c %-----------------------% c | Executable Statements | c %-----------------------% c c %------------------------% c | Set default parameters | c %------------------------% c msglvl = mneupd mode = iparam(7) nconv = iparam(5) info = 0 c c %---------------------------------% c | Get machine dependent constant. | c %---------------------------------% c eps23 = slamch('Epsilon-Machine') eps23 = eps23**(2.0E+0 / 3.0E+0 ) c c %--------------% c | Quick return | c %--------------% c ierr = 0 c if (nconv .le. 0) then ierr = -14 else if (n .le. 0) then ierr = -1 else if (nev .le. 0) then ierr = -2 else if (ncv .le. nev+1 .or. ncv .gt. n) then ierr = -3 else if (which .ne. 'LM' .and. & which .ne. 'SM' .and. & which .ne. 'LR' .and. & which .ne. 'SR' .and. & which .ne. 'LI' .and. & which .ne. 'SI') then ierr = -5 else if (bmat .ne. 'I' .and. bmat .ne. 'G') then ierr = -6 else if (lworkl .lt. 3*ncv**2 + 6*ncv) then ierr = -7 else if ( (howmny .ne. 'A' .and. & howmny .ne. 'P' .and. & howmny .ne. 'S') .and. rvec ) then ierr = -13 else if (howmny .eq. 'S' ) then ierr = -12 end if c if (mode .eq. 1 .or. mode .eq. 2) then type = 'REGULR' else if (mode .eq. 3 .and. sigmai .eq. zero) then type = 'SHIFTI' else if (mode .eq. 3 ) then type = 'REALPT' else if (mode .eq. 4 ) then type = 'IMAGPT' else ierr = -10 end if if (mode .eq. 1 .and. bmat .eq. 'G') ierr = -11 c c %------------% c | Error Exit | c %------------% c if (ierr .ne. 0) then info = ierr go to 9000 end if c c %--------------------------------------------------------% c | Pointer into WORKL for address of H, RITZ, BOUNDS, Q | c | etc... and the remaining workspace. | c | Also update pointer to be used on output. | c | Memory is laid out as follows: | c | workl(1:ncv*ncv) := generated Hessenberg matrix | c | workl(ncv*ncv+1:ncv*ncv+2*ncv) := real and imaginary | c | parts of ritz values | c | workl(ncv*ncv+2*ncv+1:ncv*ncv+3*ncv) := error bounds | c %--------------------------------------------------------% c c %-----------------------------------------------------------% c | The following is used and set by SNEUPD. | c | workl(ncv*ncv+3*ncv+1:ncv*ncv+4*ncv) := The untransformed | c | real part of the Ritz values. | c | workl(ncv*ncv+4*ncv+1:ncv*ncv+5*ncv) := The untransformed | c | imaginary part of the Ritz values. | c | workl(ncv*ncv+5*ncv+1:ncv*ncv+6*ncv) := The untransformed | c | error bounds of the Ritz values | c | workl(ncv*ncv+6*ncv+1:2*ncv*ncv+6*ncv) := Holds the upper | c | quasi-triangular matrix for H | c | workl(2*ncv*ncv+6*ncv+1: 3*ncv*ncv+6*ncv) := Holds the | c | associated matrix representation of the invariant | c | subspace for H. | c | GRAND total of NCV * ( 3 * NCV + 6 ) locations. | c %-----------------------------------------------------------% c ih = ipntr(5) ritzr = ipntr(6) ritzi = ipntr(7) bounds = ipntr(8) ldh = ncv ldq = ncv iheigr = bounds + ldh iheigi = iheigr + ldh ihbds = iheigi + ldh iuptri = ihbds + ldh invsub = iuptri + ldh*ncv ipntr(9) = iheigr ipntr(10) = iheigi ipntr(11) = ihbds ipntr(12) = iuptri ipntr(13) = invsub wrr = 1 wri = ncv + 1 iwev = wri + ncv c c %-----------------------------------------% c | irr points to the REAL part of the Ritz | c | values computed by _neigh before | c | exiting _naup2. | c | iri points to the IMAGINARY part of the | c | Ritz values computed by _neigh | c | before exiting _naup2. | c | ibd points to the Ritz estimates | c | computed by _neigh before exiting | c | _naup2. | c %-----------------------------------------% c irr = ipntr(14)+ncv*ncv iri = irr+ncv ibd = iri+ncv c c %------------------------------------% c | RNORM is B-norm of the RESID(1:N). | c %------------------------------------% c rnorm = workl(ih+2) workl(ih+2) = zero c if (msglvl .gt. 2) then call svout(logfil, ncv, workl(irr), ndigit, & '_neupd: Real part of Ritz values passed in from _NAUPD.') call svout(logfil, ncv, workl(iri), ndigit, & '_neupd: Imag part of Ritz values passed in from _NAUPD.') call svout(logfil, ncv, workl(ibd), ndigit, & '_neupd: Ritz estimates passed in from _NAUPD.') end if c if (rvec) then c reord = .false. c c %---------------------------------------------------% c | Use the temporary bounds array to store indices | c | These will be used to mark the select array later | c %---------------------------------------------------% c do 10 j = 1,ncv workl(bounds+j-1) = j select(j) = .false. 10 continue c c %-------------------------------------% c | Select the wanted Ritz values. | c | Sort the Ritz values so that the | c | wanted ones appear at the tailing | c | NEV positions of workl(irr) and | c | workl(iri). Move the corresponding | c | error estimates in workl(bound) | c | accordingly. | c %-------------------------------------% c np = ncv - nev ishift = 0 call sngets(ishift , which , nev , & np , workl(irr), workl(iri), & workl(bounds), workl , workl(np+1)) c if (msglvl .gt. 2) then call svout(logfil, ncv, workl(irr), ndigit, & '_neupd: Real part of Ritz values after calling _NGETS.') call svout(logfil, ncv, workl(iri), ndigit, & '_neupd: Imag part of Ritz values after calling _NGETS.') call svout(logfil, ncv, workl(bounds), ndigit, & '_neupd: Ritz value indices after calling _NGETS.') end if c c %-----------------------------------------------------% c | Record indices of the converged wanted Ritz values | c | Mark the select array for possible reordering | c %-----------------------------------------------------% c numcnv = 0 do 11 j = 1,ncv temp1 = max(eps23, & slapy2( workl(irr+ncv-j), workl(iri+ncv-j) )) jj = workl(bounds + ncv - j) if (numcnv .lt. nconv .and. & workl(ibd+jj-1) .le. tol*temp1) then select(jj) = .true. numcnv = numcnv + 1 if (jj .gt. nev) reord = .true. endif 11 continue c c %-----------------------------------------------------------% c | Check the count (numcnv) of converged Ritz values with | c | the number (nconv) reported by dnaupd. If these two | c | are different then there has probably been an error | c | caused by incorrect passing of the dnaupd data. | c %-----------------------------------------------------------% c if (msglvl .gt. 2) then call ivout(logfil, 1, numcnv, ndigit, & '_neupd: Number of specified eigenvalues') call ivout(logfil, 1, nconv, ndigit, & '_neupd: Number of "converged" eigenvalues') end if c if (numcnv .ne. nconv) then info = -15 go to 9000 end if c c %-----------------------------------------------------------% c | Call LAPACK routine slahqr to compute the real Schur form | c | of the upper Hessenberg matrix returned by SNAUPD. | c | Make a copy of the upper Hessenberg matrix. | c | Initialize the Schur vector matrix Q to the identity. | c %-----------------------------------------------------------% c call scopy(ldh*ncv, workl(ih), 1, workl(iuptri), 1) call slaset('All', ncv, ncv, & zero , one, workl(invsub), & ldq) call slahqr(.true., .true. , ncv, & 1 , ncv , workl(iuptri), & ldh , workl(iheigr), workl(iheigi), & 1 , ncv , workl(invsub), & ldq , ierr) call scopy(ncv , workl(invsub+ncv-1), ldq, & workl(ihbds), 1) c if (ierr .ne. 0) then info = -8 go to 9000 end if c if (msglvl .gt. 1) then call svout(logfil, ncv, workl(iheigr), ndigit, & '_neupd: Real part of the eigenvalues of H') call svout(logfil, ncv, workl(iheigi), ndigit, & '_neupd: Imaginary part of the Eigenvalues of H') call svout(logfil, ncv, workl(ihbds), ndigit, & '_neupd: Last row of the Schur vector matrix') if (msglvl .gt. 3) then call smout(logfil , ncv, ncv , & workl(iuptri), ldh, ndigit, & '_neupd: The upper quasi-triangular matrix ') end if end if c if (reord) then c c %-----------------------------------------------------% c | Reorder the computed upper quasi-triangular matrix. | c %-----------------------------------------------------% c call strsen('None' , 'V' , & select , ncv , & workl(iuptri), ldh , & workl(invsub), ldq , & workl(iheigr), workl(iheigi), & nconv , conds , & sep , workl(ihbds) , & ncv , iwork , & 1 , ierr) c if (ierr .eq. 1) then info = 1 go to 9000 end if c if (msglvl .gt. 2) then call svout(logfil, ncv, workl(iheigr), ndigit, & '_neupd: Real part of the eigenvalues of H--reordered') call svout(logfil, ncv, workl(iheigi), ndigit, & '_neupd: Imag part of the eigenvalues of H--reordered') if (msglvl .gt. 3) then call smout(logfil , ncv, ncv , & workl(iuptri), ldq, ndigit, & '_neupd: Quasi-triangular matrix after re-ordering') end if end if c end if c c %---------------------------------------% c | Copy the last row of the Schur vector | c | into workl(ihbds). This will be used | c | to compute the Ritz estimates of | c | converged Ritz values. | c %---------------------------------------% c call scopy(ncv, workl(invsub+ncv-1), ldq, workl(ihbds), 1) c c %----------------------------------------------------% c | Place the computed eigenvalues of H into DR and DI | c | if a spectral transformation was not used. | c %----------------------------------------------------% c if (type .eq. 'REGULR') then call scopy(nconv, workl(iheigr), 1, dr, 1) call scopy(nconv, workl(iheigi), 1, di, 1) end if c c %----------------------------------------------------------% c | Compute the QR factorization of the matrix representing | c | the wanted invariant subspace located in the first NCONV | c | columns of workl(invsub,ldq). | c %----------------------------------------------------------% c call sgeqr2(ncv, nconv , workl(invsub), & ldq, workev, workev(ncv+1), & ierr) c c %---------------------------------------------------------% c | * Postmultiply V by Q using sorm2r. | c | * Copy the first NCONV columns of VQ into Z. | c | * Postmultiply Z by R. | c | The N by NCONV matrix Z is now a matrix representation | c | of the approximate invariant subspace associated with | c | the Ritz values in workl(iheigr) and workl(iheigi) | c | The first NCONV columns of V are now approximate Schur | c | vectors associated with the real upper quasi-triangular | c | matrix of order NCONV in workl(iuptri) | c %---------------------------------------------------------% c call sorm2r('Right', 'Notranspose', n , & ncv , nconv , workl(invsub), & ldq , workev , v , & ldv , workd(n+1) , ierr) call slacpy('All', n, nconv, v, ldv, z, ldz) c do 20 j=1, nconv c c %---------------------------------------------------% c | Perform both a column and row scaling if the | c | diagonal element of workl(invsub,ldq) is negative | c | I'm lazy and don't take advantage of the upper | c | quasi-triangular form of workl(iuptri,ldq) | c | Note that since Q is orthogonal, R is a diagonal | c | matrix consisting of plus or minus ones | c %---------------------------------------------------% c if (workl(invsub+(j-1)*ldq+j-1) .lt. zero) then call sscal(nconv, -one, workl(iuptri+j-1), ldq) call sscal(nconv, -one, workl(iuptri+(j-1)*ldq), 1) end if c 20 continue c if (howmny .eq. 'A') then c c %--------------------------------------------% c | Compute the NCONV wanted eigenvectors of T | c | located in workl(iuptri,ldq). | c %--------------------------------------------% c do 30 j=1, ncv if (j .le. nconv) then select(j) = .true. else select(j) = .false. end if 30 continue c call strevc('Right', 'Select' , select , & ncv , workl(iuptri), ldq , & vl , 1 , workl(invsub), & ldq , ncv , outncv , & workev , ierr) c if (ierr .ne. 0) then info = -9 go to 9000 end if c c %------------------------------------------------% c | Scale the returning eigenvectors so that their | c | Euclidean norms are all one. LAPACK subroutine | c | strevc returns each eigenvector normalized so | c | that the element of largest magnitude has | c | magnitude 1; | c %------------------------------------------------% c iconj = 0 do 40 j=1, nconv c if ( workl(iheigi+j-1) .eq. zero ) then c c %----------------------% c | real eigenvalue case | c %----------------------% c temp = snrm2( ncv, workl(invsub+(j-1)*ldq), 1 ) call sscal( ncv, one / temp, & workl(invsub+(j-1)*ldq), 1 ) c else c c %-------------------------------------------% c | Complex conjugate pair case. Note that | c | since the real and imaginary part of | c | the eigenvector are stored in consecutive | c | columns, we further normalize by the | c | square root of two. | c %-------------------------------------------% c if (iconj .eq. 0) then temp = slapy2(snrm2(ncv, & workl(invsub+(j-1)*ldq), & 1), & snrm2(ncv, & workl(invsub+j*ldq), & 1)) call sscal(ncv, one/temp, & workl(invsub+(j-1)*ldq), 1 ) call sscal(ncv, one/temp, & workl(invsub+j*ldq), 1 ) iconj = 1 else iconj = 0 end if c end if c 40 continue c call sgemv('T', ncv, nconv, one, workl(invsub), & ldq, workl(ihbds), 1, zero, workev, 1) c iconj = 0 do 45 j=1, nconv if (workl(iheigi+j-1) .ne. zero) then c c %-------------------------------------------% c | Complex conjugate pair case. Note that | c | since the real and imaginary part of | c | the eigenvector are stored in consecutive | c %-------------------------------------------% c if (iconj .eq. 0) then workev(j) = slapy2(workev(j), workev(j+1)) workev(j+1) = workev(j) iconj = 1 else iconj = 0 end if end if 45 continue c if (msglvl .gt. 2) then call scopy(ncv, workl(invsub+ncv-1), ldq, & workl(ihbds), 1) call svout(logfil, ncv, workl(ihbds), ndigit, & '_neupd: Last row of the eigenvector matrix for T') if (msglvl .gt. 3) then call smout(logfil, ncv, ncv, workl(invsub), ldq, & ndigit, '_neupd: The eigenvector matrix for T') end if end if c c %---------------------------------------% c | Copy Ritz estimates into workl(ihbds) | c %---------------------------------------% c call scopy(nconv, workev, 1, workl(ihbds), 1) c c %---------------------------------------------------------% c | Compute the QR factorization of the eigenvector matrix | c | associated with leading portion of T in the first NCONV | c | columns of workl(invsub,ldq). | c %---------------------------------------------------------% c call sgeqr2(ncv, nconv , workl(invsub), & ldq, workev, workev(ncv+1), & ierr) c c %----------------------------------------------% c | * Postmultiply Z by Q. | c | * Postmultiply Z by R. | c | The N by NCONV matrix Z is now contains the | c | Ritz vectors associated with the Ritz values | c | in workl(iheigr) and workl(iheigi). | c %----------------------------------------------% c call sorm2r('Right', 'Notranspose', n , & ncv , nconv , workl(invsub), & ldq , workev , z , & ldz , workd(n+1) , ierr) c call strmm('Right' , 'Upper' , 'No transpose', & 'Non-unit', n , nconv , & one , workl(invsub), ldq , & z , ldz) c end if c else c c %------------------------------------------------------% c | An approximate invariant subspace is not needed. | c | Place the Ritz values computed SNAUPD into DR and DI | c %------------------------------------------------------% c call scopy(nconv, workl(ritzr), 1, dr, 1) call scopy(nconv, workl(ritzi), 1, di, 1) call scopy(nconv, workl(ritzr), 1, workl(iheigr), 1) call scopy(nconv, workl(ritzi), 1, workl(iheigi), 1) call scopy(nconv, workl(bounds), 1, workl(ihbds), 1) end if c c %------------------------------------------------% c | Transform the Ritz values and possibly vectors | c | and corresponding error bounds of OP to those | c | of A*x = lambda*B*x. | c %------------------------------------------------% c if (type .eq. 'REGULR') then c if (rvec) & call sscal(ncv, rnorm, workl(ihbds), 1) c else c c %---------------------------------------% c | A spectral transformation was used. | c | * Determine the Ritz estimates of the | c | Ritz values in the original system. | c %---------------------------------------% c if (type .eq. 'SHIFTI') then c if (rvec) & call sscal(ncv, rnorm, workl(ihbds), 1) c do 50 k=1, ncv temp = slapy2( workl(iheigr+k-1), & workl(iheigi+k-1) ) workl(ihbds+k-1) = abs( workl(ihbds+k-1) ) & / temp / temp 50 continue c else if (type .eq. 'REALPT') then c do 60 k=1, ncv 60 continue c else if (type .eq. 'IMAGPT') then c do 70 k=1, ncv 70 continue c end if c c %-----------------------------------------------------------% c | * Transform the Ritz values back to the original system. | c | For TYPE = 'SHIFTI' the transformation is | c | lambda = 1/theta + sigma | c | For TYPE = 'REALPT' or 'IMAGPT' the user must from | c | Rayleigh quotients or a projection. See remark 3 above.| c | NOTES: | c | *The Ritz vectors are not affected by the transformation. | c %-----------------------------------------------------------% c if (type .eq. 'SHIFTI') then c do 80 k=1, ncv temp = slapy2( workl(iheigr+k-1), & workl(iheigi+k-1) ) workl(iheigr+k-1) = workl(iheigr+k-1)/temp/temp & + sigmar workl(iheigi+k-1) = -workl(iheigi+k-1)/temp/temp & + sigmai 80 continue c call scopy(nconv, workl(iheigr), 1, dr, 1) call scopy(nconv, workl(iheigi), 1, di, 1) c else if (type .eq. 'REALPT' .or. type .eq. 'IMAGPT') then c call scopy(nconv, workl(iheigr), 1, dr, 1) call scopy(nconv, workl(iheigi), 1, di, 1) c end if c end if c if (type .eq. 'SHIFTI' .and. msglvl .gt. 1) then call svout(logfil, nconv, dr, ndigit, & '_neupd: Untransformed real part of the Ritz valuess.') call svout (logfil, nconv, di, ndigit, & '_neupd: Untransformed imag part of the Ritz valuess.') call svout(logfil, nconv, workl(ihbds), ndigit, & '_neupd: Ritz estimates of untransformed Ritz values.') else if (type .eq. 'REGULR' .and. msglvl .gt. 1) then call svout(logfil, nconv, dr, ndigit, & '_neupd: Real parts of converged Ritz values.') call svout (logfil, nconv, di, ndigit, & '_neupd: Imag parts of converged Ritz values.') call svout(logfil, nconv, workl(ihbds), ndigit, & '_neupd: Associated Ritz estimates.') end if c c %-------------------------------------------------% c | Eigenvector Purification step. Formally perform | c | one of inverse subspace iteration. Only used | c | for MODE = 2. | c %-------------------------------------------------% c if (rvec .and. howmny .eq. 'A' .and. type .eq. 'SHIFTI') then c c %------------------------------------------------% c | Purify the computed Ritz vectors by adding a | c | little bit of the residual vector: | c | T | c | resid(:)*( e s ) / theta | c | NCV | c | where H s = s theta. Remember that when theta | c | has nonzero imaginary part, the corresponding | c | Ritz vector is stored across two columns of Z. | c %------------------------------------------------% c iconj = 0 do 110 j=1, nconv if (workl(iheigi+j-1) .eq. zero) then workev(j) = workl(invsub+(j-1)*ldq+ncv-1) / & workl(iheigr+j-1) else if (iconj .eq. 0) then temp = slapy2( workl(iheigr+j-1), workl(iheigi+j-1) ) workev(j) = ( workl(invsub+(j-1)*ldq+ncv-1) * & workl(iheigr+j-1) + & workl(invsub+j*ldq+ncv-1) * & workl(iheigi+j-1) ) / temp / temp workev(j+1) = ( workl(invsub+j*ldq+ncv-1) * & workl(iheigr+j-1) - & workl(invsub+(j-1)*ldq+ncv-1) * & workl(iheigi+j-1) ) / temp / temp iconj = 1 else iconj = 0 end if 110 continue c c %---------------------------------------% c | Perform a rank one update to Z and | c | purify all the Ritz vectors together. | c %---------------------------------------% c call sger(n, nconv, one, resid, 1, workev, 1, z, ldz) c end if c 9000 continue c return c c %---------------% c | End of SNEUPD | c %---------------% c end arpack-0.92.1/SRC/znaup2.f0000644000175000017500000007134210776001577012023 00000000000000c\BeginDoc c c\Name: znaup2 c c\Description: c Intermediate level interface called by znaupd . c c\Usage: c call znaup2 c ( IDO, BMAT, N, WHICH, NEV, NP, TOL, RESID, MODE, IUPD, c ISHIFT, MXITER, V, LDV, H, LDH, RITZ, BOUNDS, c Q, LDQ, WORKL, IPNTR, WORKD, RWORK, INFO ) c c\Arguments c c IDO, BMAT, N, WHICH, NEV, TOL, RESID: same as defined in znaupd . c MODE, ISHIFT, MXITER: see the definition of IPARAM in znaupd . c c NP Integer. (INPUT/OUTPUT) c Contains the number of implicit shifts to apply during c each Arnoldi iteration. c If ISHIFT=1, NP is adjusted dynamically at each iteration c to accelerate convergence and prevent stagnation. c This is also roughly equal to the number of matrix-vector c products (involving the operator OP) per Arnoldi iteration. c The logic for adjusting is contained within the current c subroutine. c If ISHIFT=0, NP is the number of shifts the user needs c to provide via reverse comunication. 0 < NP < NCV-NEV. c NP may be less than NCV-NEV since a leading block of the current c upper Hessenberg matrix has split off and contains "unwanted" c Ritz values. c Upon termination of the IRA iteration, NP contains the number c of "converged" wanted Ritz values. c c IUPD Integer. (INPUT) c IUPD .EQ. 0: use explicit restart instead implicit update. c IUPD .NE. 0: use implicit update. c c V Complex*16 N by (NEV+NP) array. (INPUT/OUTPUT) c The Arnoldi basis vectors are returned in the first NEV c columns of V. c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling c program. c c H Complex*16 (NEV+NP) by (NEV+NP) array. (OUTPUT) c H is used to store the generated upper Hessenberg matrix c c LDH Integer. (INPUT) c Leading dimension of H exactly as declared in the calling c program. c c RITZ Complex*16 array of length NEV+NP. (OUTPUT) c RITZ(1:NEV) contains the computed Ritz values of OP. c c BOUNDS Complex*16 array of length NEV+NP. (OUTPUT) c BOUNDS(1:NEV) contain the error bounds corresponding to c the computed Ritz values. c c Q Complex*16 (NEV+NP) by (NEV+NP) array. (WORKSPACE) c Private (replicated) work array used to accumulate the c rotation in the shift application step. c c LDQ Integer. (INPUT) c Leading dimension of Q exactly as declared in the calling c program. c c WORKL Complex*16 work array of length at least c (NEV+NP)**2 + 3*(NEV+NP). (WORKSPACE) c Private (replicated) array on each PE or array allocated on c the front end. It is used in shifts calculation, shifts c application and convergence checking. c c c IPNTR Integer array of length 3. (OUTPUT) c Pointer to mark the starting locations in the WORKD for c vectors used by the Arnoldi iteration. c ------------------------------------------------------------- c IPNTR(1): pointer to the current operand vector X. c IPNTR(2): pointer to the current result vector Y. c IPNTR(3): pointer to the vector B * X when used in the c shift-and-invert mode. X is the current operand. c ------------------------------------------------------------- c c WORKD Complex*16 work array of length 3*N. (WORKSPACE) c Distributed array to be used in the basic Arnoldi iteration c for reverse communication. The user should not use WORKD c as temporary workspace during the iteration !!!!!!!!!! c See Data Distribution Note in ZNAUPD . c c RWORK Double precision work array of length NEV+NP ( WORKSPACE) c Private (replicated) array on each PE or array allocated on c the front end. c c INFO Integer. (INPUT/OUTPUT) c If INFO .EQ. 0, a randomly initial residual vector is used. c If INFO .NE. 0, RESID contains the initial residual vector, c possibly from a previous run. c Error flag on output. c = 0: Normal return. c = 1: Maximum number of iterations taken. c All possible eigenvalues of OP has been found. c NP returns the number of converged Ritz values. c = 2: No shifts could be applied. c = -8: Error return from LAPACK eigenvalue calculation; c This should never happen. c = -9: Starting vector is zero. c = -9999: Could not build an Arnoldi factorization. c Size that was built in returned in NP. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx Complex*16 c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly c Restarted Arnoldi Iteration", Rice University Technical Report c TR95-13, Department of Computational and Applied Mathematics. c c\Routines called: c zgetv0 ARPACK initial vector generation routine. c znaitr ARPACK Arnoldi factorization routine. c znapps ARPACK application of implicit shifts routine. c zneigh ARPACK compute Ritz values and error bounds routine. c zngets ARPACK reorder Ritz values and error bounds routine. c zsortc ARPACK sorting routine. c ivout ARPACK utility routine that prints integers. c arscnd ARPACK utility routine for timing. c zmout ARPACK utility routine that prints matrices c zvout ARPACK utility routine that prints vectors. c dvout ARPACK utility routine that prints vectors. c dlamch LAPACK routine that determines machine constants. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c zcopy Level 1 BLAS that copies one vector to another . c zdotc Level 1 BLAS that computes the scalar product of two vectors. c zswap Level 1 BLAS that swaps two vectors. c dznrm2 Level 1 BLAS that computes the norm of a vector. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice Universitya c Chao Yang Houston, Texas c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: naup2.F SID: 2.6 DATE OF SID: 06/01/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c----------------------------------------------------------------------- c subroutine znaup2 & ( ido, bmat, n, which, nev, np, tol, resid, mode, iupd, & ishift, mxiter, v, ldv, h, ldh, ritz, bounds, & q, ldq, workl, ipntr, workd, rwork, info ) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character bmat*1, which*2 integer ido, info, ishift, iupd, mode, ldh, ldq, ldv, mxiter, & n, nev, np Double precision & tol c c %-----------------% c | Array Arguments | c %-----------------% c integer ipntr(13) Complex*16 & bounds(nev+np), h(ldh,nev+np), q(ldq,nev+np), & resid(n), ritz(nev+np), v(ldv,nev+np), & workd(3*n), workl( (nev+np)*(nev+np+3) ) Double precision & rwork(nev+np) c c %------------% c | Parameters | c %------------% c Complex*16 & one, zero Double precision & rzero parameter (one = (1.0D+0, 0.0D+0) , zero = (0.0D+0, 0.0D+0) , & rzero = 0.0D+0 ) c c %---------------% c | Local Scalars | c %---------------% c logical cnorm , getv0, initv , update, ushift integer ierr , iter , kplusp, msglvl, nconv, & nevbef, nev0 , np0 , nptemp, i , & j Complex*16 & cmpnorm Double precision & rnorm , eps23, rtemp character wprime*2 c save cnorm, getv0, initv , update, ushift, & rnorm, iter , kplusp, msglvl, nconv , & nevbef, nev0 , np0 , eps23 c c c %-----------------------% c | Local array arguments | c %-----------------------% c integer kp(3) c c %----------------------% c | External Subroutines | c %----------------------% c external zcopy , zgetv0 , znaitr , zneigh , zngets , znapps , & zsortc , zswap , zmout , zvout , ivout, arscnd c c %--------------------% c | External functions | c %--------------------% c Complex*16 & zdotc Double precision & dznrm2 , dlamch , dlapy2 external zdotc , dznrm2 , dlamch , dlapy2 c c %---------------------% c | Intrinsic Functions | c %---------------------% c intrinsic dimag , dble , min, max c c %-----------------------% c | Executable Statements | c %-----------------------% c if (ido .eq. 0) then c call arscnd (t0) c msglvl = mcaup2 c nev0 = nev np0 = np c c %-------------------------------------% c | kplusp is the bound on the largest | c | Lanczos factorization built. | c | nconv is the current number of | c | "converged" eigenvalues. | c | iter is the counter on the current | c | iteration step. | c %-------------------------------------% c kplusp = nev + np nconv = 0 iter = 0 c c %---------------------------------% c | Get machine dependent constant. | c %---------------------------------% c eps23 = dlamch ('Epsilon-Machine') eps23 = eps23**(2.0D+0 / 3.0D+0 ) c c %---------------------------------------% c | Set flags for computing the first NEV | c | steps of the Arnoldi factorization. | c %---------------------------------------% c getv0 = .true. update = .false. ushift = .false. cnorm = .false. c if (info .ne. 0) then c c %--------------------------------------------% c | User provides the initial residual vector. | c %--------------------------------------------% c initv = .true. info = 0 else initv = .false. end if end if c c %---------------------------------------------% c | Get a possibly random starting vector and | c | force it into the range of the operator OP. | c %---------------------------------------------% c 10 continue c if (getv0) then call zgetv0 (ido, bmat, 1, initv, n, 1, v, ldv, resid, rnorm, & ipntr, workd, info) c if (ido .ne. 99) go to 9000 c if (rnorm .eq. rzero) then c c %-----------------------------------------% c | The initial vector is zero. Error exit. | c %-----------------------------------------% c info = -9 go to 1100 end if getv0 = .false. ido = 0 end if c c %-----------------------------------% c | Back from reverse communication : | c | continue with update step | c %-----------------------------------% c if (update) go to 20 c c %-------------------------------------------% c | Back from computing user specified shifts | c %-------------------------------------------% c if (ushift) go to 50 c c %-------------------------------------% c | Back from computing residual norm | c | at the end of the current iteration | c %-------------------------------------% c if (cnorm) go to 100 c c %----------------------------------------------------------% c | Compute the first NEV steps of the Arnoldi factorization | c %----------------------------------------------------------% c call znaitr (ido, bmat, n, 0, nev, mode, resid, rnorm, v, ldv, & h, ldh, ipntr, workd, info) c if (ido .ne. 99) go to 9000 c if (info .gt. 0) then np = info mxiter = iter info = -9999 go to 1200 end if c c %--------------------------------------------------------------% c | | c | M A I N ARNOLDI I T E R A T I O N L O O P | c | Each iteration implicitly restarts the Arnoldi | c | factorization in place. | c | | c %--------------------------------------------------------------% c 1000 continue c iter = iter + 1 c if (msglvl .gt. 0) then call ivout (logfil, 1, iter, ndigit, & '_naup2: **** Start of major iteration number ****') end if c c %-----------------------------------------------------------% c | Compute NP additional steps of the Arnoldi factorization. | c | Adjust NP since NEV might have been updated by last call | c | to the shift application routine znapps . | c %-----------------------------------------------------------% c np = kplusp - nev c if (msglvl .gt. 1) then call ivout (logfil, 1, nev, ndigit, & '_naup2: The length of the current Arnoldi factorization') call ivout (logfil, 1, np, ndigit, & '_naup2: Extend the Arnoldi factorization by') end if c c %-----------------------------------------------------------% c | Compute NP additional steps of the Arnoldi factorization. | c %-----------------------------------------------------------% c ido = 0 20 continue update = .true. c call znaitr (ido, bmat, n, nev, np, mode, resid, rnorm, & v , ldv , h, ldh, ipntr, workd, info) c if (ido .ne. 99) go to 9000 c if (info .gt. 0) then np = info mxiter = iter info = -9999 go to 1200 end if update = .false. c if (msglvl .gt. 1) then call dvout (logfil, 1, rnorm, ndigit, & '_naup2: Corresponding B-norm of the residual') end if c c %--------------------------------------------------------% c | Compute the eigenvalues and corresponding error bounds | c | of the current upper Hessenberg matrix. | c %--------------------------------------------------------% c call zneigh (rnorm, kplusp, h, ldh, ritz, bounds, & q, ldq, workl, rwork, ierr) c if (ierr .ne. 0) then info = -8 go to 1200 end if c c %---------------------------------------------------% c | Select the wanted Ritz values and their bounds | c | to be used in the convergence test. | c | The wanted part of the spectrum and corresponding | c | error bounds are in the last NEV loc. of RITZ, | c | and BOUNDS respectively. | c %---------------------------------------------------% c nev = nev0 np = np0 c c %--------------------------------------------------% c | Make a copy of Ritz values and the corresponding | c | Ritz estimates obtained from zneigh . | c %--------------------------------------------------% c call zcopy (kplusp,ritz,1,workl(kplusp**2+1),1) call zcopy (kplusp,bounds,1,workl(kplusp**2+kplusp+1),1) c c %---------------------------------------------------% c | Select the wanted Ritz values and their bounds | c | to be used in the convergence test. | c | The wanted part of the spectrum and corresponding | c | bounds are in the last NEV loc. of RITZ | c | BOUNDS respectively. | c %---------------------------------------------------% c call zngets (ishift, which, nev, np, ritz, bounds) c c %------------------------------------------------------------% c | Convergence test: currently we use the following criteria. | c | The relative accuracy of a Ritz value is considered | c | acceptable if: | c | | c | error_bounds(i) .le. tol*max(eps23, magnitude_of_ritz(i)). | c | | c %------------------------------------------------------------% c nconv = 0 c do 25 i = 1, nev rtemp = max( eps23, dlapy2 ( dble (ritz(np+i)), & dimag (ritz(np+i)) ) ) if ( dlapy2 (dble (bounds(np+i)),dimag (bounds(np+i))) & .le. tol*rtemp ) then nconv = nconv + 1 end if 25 continue c if (msglvl .gt. 2) then kp(1) = nev kp(2) = np kp(3) = nconv call ivout (logfil, 3, kp, ndigit, & '_naup2: NEV, NP, NCONV are') call zvout (logfil, kplusp, ritz, ndigit, & '_naup2: The eigenvalues of H') call zvout (logfil, kplusp, bounds, ndigit, & '_naup2: Ritz estimates of the current NCV Ritz values') end if c c %---------------------------------------------------------% c | Count the number of unwanted Ritz values that have zero | c | Ritz estimates. If any Ritz estimates are equal to zero | c | then a leading block of H of order equal to at least | c | the number of Ritz values with zero Ritz estimates has | c | split off. None of these Ritz values may be removed by | c | shifting. Decrease NP the number of shifts to apply. If | c | no shifts may be applied, then prepare to exit | c %---------------------------------------------------------% c nptemp = np do 30 j=1, nptemp if (bounds(j) .eq. zero) then np = np - 1 nev = nev + 1 end if 30 continue c if ( (nconv .ge. nev0) .or. & (iter .gt. mxiter) .or. & (np .eq. 0) ) then c if (msglvl .gt. 4) then call zvout (logfil, kplusp, workl(kplusp**2+1), ndigit, & '_naup2: Eigenvalues computed by _neigh:') call zvout (logfil, kplusp, workl(kplusp**2+kplusp+1), & ndigit, & '_naup2: Ritz estimates computed by _neigh:') end if c c %------------------------------------------------% c | Prepare to exit. Put the converged Ritz values | c | and corresponding bounds in RITZ(1:NCONV) and | c | BOUNDS(1:NCONV) respectively. Then sort. Be | c | careful when NCONV > NP | c %------------------------------------------------% c c %------------------------------------------% c | Use h( 3,1 ) as storage to communicate | c | rnorm to zneupd if needed | c %------------------------------------------% h(3,1) = dcmplx (rnorm,rzero) c c %----------------------------------------------% c | Sort Ritz values so that converged Ritz | c | values appear within the first NEV locations | c | of ritz and bounds, and the most desired one | c | appears at the front. | c %----------------------------------------------% c if (which .eq. 'LM') wprime = 'SM' if (which .eq. 'SM') wprime = 'LM' if (which .eq. 'LR') wprime = 'SR' if (which .eq. 'SR') wprime = 'LR' if (which .eq. 'LI') wprime = 'SI' if (which .eq. 'SI') wprime = 'LI' c call zsortc (wprime, .true., kplusp, ritz, bounds) c c %--------------------------------------------------% c | Scale the Ritz estimate of each Ritz value | c | by 1 / max(eps23, magnitude of the Ritz value). | c %--------------------------------------------------% c do 35 j = 1, nev0 rtemp = max( eps23, dlapy2 ( dble (ritz(j)), & dimag (ritz(j)) ) ) bounds(j) = bounds(j)/rtemp 35 continue c c %---------------------------------------------------% c | Sort the Ritz values according to the scaled Ritz | c | estimates. This will push all the converged ones | c | towards the front of ritz, bounds (in the case | c | when NCONV < NEV.) | c %---------------------------------------------------% c wprime = 'LM' call zsortc (wprime, .true., nev0, bounds, ritz) c c %----------------------------------------------% c | Scale the Ritz estimate back to its original | c | value. | c %----------------------------------------------% c do 40 j = 1, nev0 rtemp = max( eps23, dlapy2 ( dble (ritz(j)), & dimag (ritz(j)) ) ) bounds(j) = bounds(j)*rtemp 40 continue c c %-----------------------------------------------% c | Sort the converged Ritz values again so that | c | the "threshold" value appears at the front of | c | ritz and bound. | c %-----------------------------------------------% c call zsortc (which, .true., nconv, ritz, bounds) c if (msglvl .gt. 1) then call zvout (logfil, kplusp, ritz, ndigit, & '_naup2: Sorted eigenvalues') call zvout (logfil, kplusp, bounds, ndigit, & '_naup2: Sorted ritz estimates.') end if c c %------------------------------------% c | Max iterations have been exceeded. | c %------------------------------------% c if (iter .gt. mxiter .and. nconv .lt. nev0) info = 1 c c %---------------------% c | No shifts to apply. | c %---------------------% c if (np .eq. 0 .and. nconv .lt. nev0) info = 2 c np = nconv go to 1100 c else if ( (nconv .lt. nev0) .and. (ishift .eq. 1) ) then c c %-------------------------------------------------% c | Do not have all the requested eigenvalues yet. | c | To prevent possible stagnation, adjust the size | c | of NEV. | c %-------------------------------------------------% c nevbef = nev nev = nev + min(nconv, np/2) if (nev .eq. 1 .and. kplusp .ge. 6) then nev = kplusp / 2 else if (nev .eq. 1 .and. kplusp .gt. 3) then nev = 2 end if np = kplusp - nev c c %---------------------------------------% c | If the size of NEV was just increased | c | resort the eigenvalues. | c %---------------------------------------% c if (nevbef .lt. nev) & call zngets (ishift, which, nev, np, ritz, bounds) c end if c if (msglvl .gt. 0) then call ivout (logfil, 1, nconv, ndigit, & '_naup2: no. of "converged" Ritz values at this iter.') if (msglvl .gt. 1) then kp(1) = nev kp(2) = np call ivout (logfil, 2, kp, ndigit, & '_naup2: NEV and NP are') call zvout (logfil, nev, ritz(np+1), ndigit, & '_naup2: "wanted" Ritz values ') call zvout (logfil, nev, bounds(np+1), ndigit, & '_naup2: Ritz estimates of the "wanted" values ') end if end if c if (ishift .eq. 0) then c c %-------------------------------------------------------% c | User specified shifts: pop back out to get the shifts | c | and return them in the first 2*NP locations of WORKL. | c %-------------------------------------------------------% c ushift = .true. ido = 3 go to 9000 end if 50 continue ushift = .false. c if ( ishift .ne. 1 ) then c c %----------------------------------% c | Move the NP shifts from WORKL to | c | RITZ, to free up WORKL | c | for non-exact shift case. | c %----------------------------------% c call zcopy (np, workl, 1, ritz, 1) end if c if (msglvl .gt. 2) then call ivout (logfil, 1, np, ndigit, & '_naup2: The number of shifts to apply ') call zvout (logfil, np, ritz, ndigit, & '_naup2: values of the shifts') if ( ishift .eq. 1 ) & call zvout (logfil, np, bounds, ndigit, & '_naup2: Ritz estimates of the shifts') end if c c %---------------------------------------------------------% c | Apply the NP implicit shifts by QR bulge chasing. | c | Each shift is applied to the whole upper Hessenberg | c | matrix H. | c | The first 2*N locations of WORKD are used as workspace. | c %---------------------------------------------------------% c call znapps (n, nev, np, ritz, v, ldv, & h, ldh, resid, q, ldq, workl, workd) c c %---------------------------------------------% c | Compute the B-norm of the updated residual. | c | Keep B*RESID in WORKD(1:N) to be used in | c | the first step of the next call to znaitr . | c %---------------------------------------------% c cnorm = .true. call arscnd (t2) if (bmat .eq. 'G') then nbx = nbx + 1 call zcopy (n, resid, 1, workd(n+1), 1) ipntr(1) = n + 1 ipntr(2) = 1 ido = 2 c c %----------------------------------% c | Exit in order to compute B*RESID | c %----------------------------------% c go to 9000 else if (bmat .eq. 'I') then call zcopy (n, resid, 1, workd, 1) end if c 100 continue c c %----------------------------------% c | Back from reverse communication; | c | WORKD(1:N) := B*RESID | c %----------------------------------% c if (bmat .eq. 'G') then call arscnd (t3) tmvbx = tmvbx + (t3 - t2) end if c if (bmat .eq. 'G') then cmpnorm = zdotc (n, resid, 1, workd, 1) rnorm = sqrt(dlapy2 (dble (cmpnorm),dimag (cmpnorm))) else if (bmat .eq. 'I') then rnorm = dznrm2 (n, resid, 1) end if cnorm = .false. c if (msglvl .gt. 2) then call dvout (logfil, 1, rnorm, ndigit, & '_naup2: B-norm of residual for compressed factorization') call zmout (logfil, nev, nev, h, ldh, ndigit, & '_naup2: Compressed upper Hessenberg matrix H') end if c go to 1000 c c %---------------------------------------------------------------% c | | c | E N D O F M A I N I T E R A T I O N L O O P | c | | c %---------------------------------------------------------------% c 1100 continue c mxiter = iter nev = nconv c 1200 continue ido = 99 c c %------------% c | Error Exit | c %------------% c call arscnd (t1) tcaup2 = t1 - t0 c 9000 continue c c %---------------% c | End of znaup2 | c %---------------% c return end arpack-0.92.1/SRC/dnaitr.f0000644000175000017500000007367310776001577012076 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: dnaitr c c\Description: c Reverse communication interface for applying NP additional steps to c a K step nonsymmetric Arnoldi factorization. c c Input: OP*V_{k} - V_{k}*H = r_{k}*e_{k}^T c c with (V_{k}^T)*B*V_{k} = I, (V_{k}^T)*B*r_{k} = 0. c c Output: OP*V_{k+p} - V_{k+p}*H = r_{k+p}*e_{k+p}^T c c with (V_{k+p}^T)*B*V_{k+p} = I, (V_{k+p}^T)*B*r_{k+p} = 0. c c where OP and B are as in dnaupd. The B-norm of r_{k+p} is also c computed and returned. c c\Usage: c call dnaitr c ( IDO, BMAT, N, K, NP, NB, RESID, RNORM, V, LDV, H, LDH, c IPNTR, WORKD, INFO ) c c\Arguments c IDO Integer. (INPUT/OUTPUT) c Reverse communication flag. c ------------------------------------------------------------- c IDO = 0: first call to the reverse communication interface c IDO = -1: compute Y = OP * X where c IPNTR(1) is the pointer into WORK for X, c IPNTR(2) is the pointer into WORK for Y. c This is for the restart phase to force the new c starting vector into the range of OP. c IDO = 1: compute Y = OP * X where c IPNTR(1) is the pointer into WORK for X, c IPNTR(2) is the pointer into WORK for Y, c IPNTR(3) is the pointer into WORK for B * X. c IDO = 2: compute Y = B * X where c IPNTR(1) is the pointer into WORK for X, c IPNTR(2) is the pointer into WORK for Y. c IDO = 99: done c ------------------------------------------------------------- c When the routine is used in the "shift-and-invert" mode, the c vector B * Q is already available and do not need to be c recompute in forming OP * Q. c c BMAT Character*1. (INPUT) c BMAT specifies the type of the matrix B that defines the c semi-inner product for the operator OP. See dnaupd. c B = 'I' -> standard eigenvalue problem A*x = lambda*x c B = 'G' -> generalized eigenvalue problem A*x = lambda*M**x c c N Integer. (INPUT) c Dimension of the eigenproblem. c c K Integer. (INPUT) c Current size of V and H. c c NP Integer. (INPUT) c Number of additional Arnoldi steps to take. c c NB Integer. (INPUT) c Blocksize to be used in the recurrence. c Only work for NB = 1 right now. The goal is to have a c program that implement both the block and non-block method. c c RESID Double precision array of length N. (INPUT/OUTPUT) c On INPUT: RESID contains the residual vector r_{k}. c On OUTPUT: RESID contains the residual vector r_{k+p}. c c RNORM Double precision scalar. (INPUT/OUTPUT) c B-norm of the starting residual on input. c B-norm of the updated residual r_{k+p} on output. c c V Double precision N by K+NP array. (INPUT/OUTPUT) c On INPUT: V contains the Arnoldi vectors in the first K c columns. c On OUTPUT: V contains the new NP Arnoldi vectors in the next c NP columns. The first K columns are unchanged. c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling c program. c c H Double precision (K+NP) by (K+NP) array. (INPUT/OUTPUT) c H is used to store the generated upper Hessenberg matrix. c c LDH Integer. (INPUT) c Leading dimension of H exactly as declared in the calling c program. c c IPNTR Integer array of length 3. (OUTPUT) c Pointer to mark the starting locations in the WORK for c vectors used by the Arnoldi iteration. c ------------------------------------------------------------- c IPNTR(1): pointer to the current operand vector X. c IPNTR(2): pointer to the current result vector Y. c IPNTR(3): pointer to the vector B * X when used in the c shift-and-invert mode. X is the current operand. c ------------------------------------------------------------- c c WORKD Double precision work array of length 3*N. (REVERSE COMMUNICATION) c Distributed array to be used in the basic Arnoldi iteration c for reverse communication. The calling program should not c use WORKD as temporary workspace during the iteration !!!!!! c On input, WORKD(1:N) = B*RESID and is used to save some c computation at the first step. c c INFO Integer. (OUTPUT) c = 0: Normal exit. c > 0: Size of the spanning invariant subspace of OP found. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx real c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly c Restarted Arnoldi Iteration", Rice University Technical Report c TR95-13, Department of Computational and Applied Mathematics. c c\Routines called: c dgetv0 ARPACK routine to generate the initial vector. c ivout ARPACK utility routine that prints integers. c arscnd ARPACK utility routine for timing. c dmout ARPACK utility routine that prints matrices c dvout ARPACK utility routine that prints vectors. c dlabad LAPACK routine that computes machine constants. c dlamch LAPACK routine that determines machine constants. c dlascl LAPACK routine for careful scaling of a matrix. c dlanhs LAPACK routine that computes various norms of a matrix. c dgemv Level 2 BLAS routine for matrix vector multiplication. c daxpy Level 1 BLAS that computes a vector triad. c dscal Level 1 BLAS that scales a vector. c dcopy Level 1 BLAS that copies one vector to another . c ddot Level 1 BLAS that computes the scalar product of two vectors. c dnrm2 Level 1 BLAS that computes the norm of a vector. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c xx/xx/92: Version ' 2.4' c c\SCCS Information: @(#) c FILE: naitr.F SID: 2.4 DATE OF SID: 8/27/96 RELEASE: 2 c c\Remarks c The algorithm implemented is: c c restart = .false. c Given V_{k} = [v_{1}, ..., v_{k}], r_{k}; c r_{k} contains the initial residual vector even for k = 0; c Also assume that rnorm = || B*r_{k} || and B*r_{k} are already c computed by the calling program. c c betaj = rnorm ; p_{k+1} = B*r_{k} ; c For j = k+1, ..., k+np Do c 1) if ( betaj < tol ) stop or restart depending on j. c ( At present tol is zero ) c if ( restart ) generate a new starting vector. c 2) v_{j} = r(j-1)/betaj; V_{j} = [V_{j-1}, v_{j}]; c p_{j} = p_{j}/betaj c 3) r_{j} = OP*v_{j} where OP is defined as in dnaupd c For shift-invert mode p_{j} = B*v_{j} is already available. c wnorm = || OP*v_{j} || c 4) Compute the j-th step residual vector. c w_{j} = V_{j}^T * B * OP * v_{j} c r_{j} = OP*v_{j} - V_{j} * w_{j} c H(:,j) = w_{j}; c H(j,j-1) = rnorm c rnorm = || r_(j) || c If (rnorm > 0.717*wnorm) accept step and go back to 1) c 5) Re-orthogonalization step: c s = V_{j}'*B*r_{j} c r_{j} = r_{j} - V_{j}*s; rnorm1 = || r_{j} || c alphaj = alphaj + s_{j}; c 6) Iterative refinement step: c If (rnorm1 > 0.717*rnorm) then c rnorm = rnorm1 c accept step and go back to 1) c Else c rnorm = rnorm1 c If this is the first time in step 6), go to 5) c Else r_{j} lies in the span of V_{j} numerically. c Set r_{j} = 0 and rnorm = 0; go to 1) c EndIf c End Do c c\EndLib c c----------------------------------------------------------------------- c subroutine dnaitr & (ido, bmat, n, k, np, nb, resid, rnorm, v, ldv, h, ldh, & ipntr, workd, info) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character bmat*1 integer ido, info, k, ldh, ldv, n, nb, np Double precision & rnorm c c %-----------------% c | Array Arguments | c %-----------------% c integer ipntr(3) Double precision & h(ldh,k+np), resid(n), v(ldv,k+np), workd(3*n) c c %------------% c | Parameters | c %------------% c Double precision & one, zero parameter (one = 1.0D+0, zero = 0.0D+0) c c %---------------% c | Local Scalars | c %---------------% c logical first, orth1, orth2, rstart, step3, step4 integer ierr, i, infol, ipj, irj, ivj, iter, itry, j, msglvl, & jj Double precision & betaj, ovfl, temp1, rnorm1, smlnum, tst1, ulp, unfl, & wnorm save first, orth1, orth2, rstart, step3, step4, & ierr, ipj, irj, ivj, iter, itry, j, msglvl, ovfl, & betaj, rnorm1, smlnum, ulp, unfl, wnorm c c %-----------------------% c | Local Array Arguments | c %-----------------------% c Double precision & xtemp(2) c c %----------------------% c | External Subroutines | c %----------------------% c external daxpy, dcopy, dscal, dgemv, dgetv0, dlabad, & dvout, dmout, ivout, arscnd c c %--------------------% c | External Functions | c %--------------------% c Double precision & ddot, dnrm2, dlanhs, dlamch external ddot, dnrm2, dlanhs, dlamch c c %---------------------% c | Intrinsic Functions | c %---------------------% c intrinsic abs, sqrt c c %-----------------% c | Data statements | c %-----------------% c data first / .true. / c c %-----------------------% c | Executable Statements | c %-----------------------% c if (first) then c c %-----------------------------------------% c | Set machine-dependent constants for the | c | the splitting and deflation criterion. | c | If norm(H) <= sqrt(OVFL), | c | overflow should not occur. | c | REFERENCE: LAPACK subroutine dlahqr | c %-----------------------------------------% c unfl = dlamch( 'safe minimum' ) ovfl = one / unfl call dlabad( unfl, ovfl ) ulp = dlamch( 'precision' ) smlnum = unfl*( n / ulp ) first = .false. end if c if (ido .eq. 0) then c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call arscnd (t0) msglvl = mnaitr c c %------------------------------% c | Initial call to this routine | c %------------------------------% c info = 0 step3 = .false. step4 = .false. rstart = .false. orth1 = .false. orth2 = .false. j = k + 1 ipj = 1 irj = ipj + n ivj = irj + n end if c c %-------------------------------------------------% c | When in reverse communication mode one of: | c | STEP3, STEP4, ORTH1, ORTH2, RSTART | c | will be .true. when .... | c | STEP3: return from computing OP*v_{j}. | c | STEP4: return from computing B-norm of OP*v_{j} | c | ORTH1: return from computing B-norm of r_{j+1} | c | ORTH2: return from computing B-norm of | c | correction to the residual vector. | c | RSTART: return from OP computations needed by | c | dgetv0. | c %-------------------------------------------------% c if (step3) go to 50 if (step4) go to 60 if (orth1) go to 70 if (orth2) go to 90 if (rstart) go to 30 c c %-----------------------------% c | Else this is the first step | c %-----------------------------% c c %--------------------------------------------------------------% c | | c | A R N O L D I I T E R A T I O N L O O P | c | | c | Note: B*r_{j-1} is already in WORKD(1:N)=WORKD(IPJ:IPJ+N-1) | c %--------------------------------------------------------------% 1000 continue c if (msglvl .gt. 1) then call ivout (logfil, 1, j, ndigit, & '_naitr: generating Arnoldi vector number') call dvout (logfil, 1, rnorm, ndigit, & '_naitr: B-norm of the current residual is') end if c c %---------------------------------------------------% c | STEP 1: Check if the B norm of j-th residual | c | vector is zero. Equivalent to determing whether | c | an exact j-step Arnoldi factorization is present. | c %---------------------------------------------------% c betaj = rnorm if (rnorm .gt. zero) go to 40 c c %---------------------------------------------------% c | Invariant subspace found, generate a new starting | c | vector which is orthogonal to the current Arnoldi | c | basis and continue the iteration. | c %---------------------------------------------------% c if (msglvl .gt. 0) then call ivout (logfil, 1, j, ndigit, & '_naitr: ****** RESTART AT STEP ******') end if c c %---------------------------------------------% c | ITRY is the loop variable that controls the | c | maximum amount of times that a restart is | c | attempted. NRSTRT is used by stat.h | c %---------------------------------------------% c betaj = zero nrstrt = nrstrt + 1 itry = 1 20 continue rstart = .true. ido = 0 30 continue c c %--------------------------------------% c | If in reverse communication mode and | c | RSTART = .true. flow returns here. | c %--------------------------------------% c call dgetv0 (ido, bmat, itry, .false., n, j, v, ldv, & resid, rnorm, ipntr, workd, ierr) if (ido .ne. 99) go to 9000 if (ierr .lt. 0) then itry = itry + 1 if (itry .le. 3) go to 20 c c %------------------------------------------------% c | Give up after several restart attempts. | c | Set INFO to the size of the invariant subspace | c | which spans OP and exit. | c %------------------------------------------------% c info = j - 1 call arscnd (t1) tnaitr = tnaitr + (t1 - t0) ido = 99 go to 9000 end if c 40 continue c c %---------------------------------------------------------% c | STEP 2: v_{j} = r_{j-1}/rnorm and p_{j} = p_{j}/rnorm | c | Note that p_{j} = B*r_{j-1}. In order to avoid overflow | c | when reciprocating a small RNORM, test against lower | c | machine bound. | c %---------------------------------------------------------% c call dcopy (n, resid, 1, v(1,j), 1) if (rnorm .ge. unfl) then temp1 = one / rnorm call dscal (n, temp1, v(1,j), 1) call dscal (n, temp1, workd(ipj), 1) else c c %-----------------------------------------% c | To scale both v_{j} and p_{j} carefully | c | use LAPACK routine SLASCL | c %-----------------------------------------% c call dlascl ('General', i, i, rnorm, one, n, 1, & v(1,j), n, infol) call dlascl ('General', i, i, rnorm, one, n, 1, & workd(ipj), n, infol) end if c c %------------------------------------------------------% c | STEP 3: r_{j} = OP*v_{j}; Note that p_{j} = B*v_{j} | c | Note that this is not quite yet r_{j}. See STEP 4 | c %------------------------------------------------------% c step3 = .true. nopx = nopx + 1 call arscnd (t2) call dcopy (n, v(1,j), 1, workd(ivj), 1) ipntr(1) = ivj ipntr(2) = irj ipntr(3) = ipj ido = 1 c c %-----------------------------------% c | Exit in order to compute OP*v_{j} | c %-----------------------------------% c go to 9000 50 continue c c %----------------------------------% c | Back from reverse communication; | c | WORKD(IRJ:IRJ+N-1) := OP*v_{j} | c | if step3 = .true. | c %----------------------------------% c call arscnd (t3) tmvopx = tmvopx + (t3 - t2) step3 = .false. c c %------------------------------------------% c | Put another copy of OP*v_{j} into RESID. | c %------------------------------------------% c call dcopy (n, workd(irj), 1, resid, 1) c c %---------------------------------------% c | STEP 4: Finish extending the Arnoldi | c | factorization to length j. | c %---------------------------------------% c call arscnd (t2) if (bmat .eq. 'G') then nbx = nbx + 1 step4 = .true. ipntr(1) = irj ipntr(2) = ipj ido = 2 c c %-------------------------------------% c | Exit in order to compute B*OP*v_{j} | c %-------------------------------------% c go to 9000 else if (bmat .eq. 'I') then call dcopy (n, resid, 1, workd(ipj), 1) end if 60 continue c c %----------------------------------% c | Back from reverse communication; | c | WORKD(IPJ:IPJ+N-1) := B*OP*v_{j} | c | if step4 = .true. | c %----------------------------------% c if (bmat .eq. 'G') then call arscnd (t3) tmvbx = tmvbx + (t3 - t2) end if c step4 = .false. c c %-------------------------------------% c | The following is needed for STEP 5. | c | Compute the B-norm of OP*v_{j}. | c %-------------------------------------% c if (bmat .eq. 'G') then wnorm = ddot (n, resid, 1, workd(ipj), 1) wnorm = sqrt(abs(wnorm)) else if (bmat .eq. 'I') then wnorm = dnrm2(n, resid, 1) end if c c %-----------------------------------------% c | Compute the j-th residual corresponding | c | to the j step factorization. | c | Use Classical Gram Schmidt and compute: | c | w_{j} <- V_{j}^T * B * OP * v_{j} | c | r_{j} <- OP*v_{j} - V_{j} * w_{j} | c %-----------------------------------------% c c c %------------------------------------------% c | Compute the j Fourier coefficients w_{j} | c | WORKD(IPJ:IPJ+N-1) contains B*OP*v_{j}. | c %------------------------------------------% c call dgemv ('T', n, j, one, v, ldv, workd(ipj), 1, & zero, h(1,j), 1) c c %--------------------------------------% c | Orthogonalize r_{j} against V_{j}. | c | RESID contains OP*v_{j}. See STEP 3. | c %--------------------------------------% c call dgemv ('N', n, j, -one, v, ldv, h(1,j), 1, & one, resid, 1) c if (j .gt. 1) h(j,j-1) = betaj c call arscnd (t4) c orth1 = .true. c call arscnd (t2) if (bmat .eq. 'G') then nbx = nbx + 1 call dcopy (n, resid, 1, workd(irj), 1) ipntr(1) = irj ipntr(2) = ipj ido = 2 c c %----------------------------------% c | Exit in order to compute B*r_{j} | c %----------------------------------% c go to 9000 else if (bmat .eq. 'I') then call dcopy (n, resid, 1, workd(ipj), 1) end if 70 continue c c %---------------------------------------------------% c | Back from reverse communication if ORTH1 = .true. | c | WORKD(IPJ:IPJ+N-1) := B*r_{j}. | c %---------------------------------------------------% c if (bmat .eq. 'G') then call arscnd (t3) tmvbx = tmvbx + (t3 - t2) end if c orth1 = .false. c c %------------------------------% c | Compute the B-norm of r_{j}. | c %------------------------------% c if (bmat .eq. 'G') then rnorm = ddot (n, resid, 1, workd(ipj), 1) rnorm = sqrt(abs(rnorm)) else if (bmat .eq. 'I') then rnorm = dnrm2(n, resid, 1) end if c c %-----------------------------------------------------------% c | STEP 5: Re-orthogonalization / Iterative refinement phase | c | Maximum NITER_ITREF tries. | c | | c | s = V_{j}^T * B * r_{j} | c | r_{j} = r_{j} - V_{j}*s | c | alphaj = alphaj + s_{j} | c | | c | The stopping criteria used for iterative refinement is | c | discussed in Parlett's book SEP, page 107 and in Gragg & | c | Reichel ACM TOMS paper; Algorithm 686, Dec. 1990. | c | Determine if we need to correct the residual. The goal is | c | to enforce ||v(:,1:j)^T * r_{j}|| .le. eps * || r_{j} || | c | The following test determines whether the sine of the | c | angle between OP*x and the computed residual is less | c | than or equal to 0.717. | c %-----------------------------------------------------------% c if (rnorm .gt. 0.717*wnorm) go to 100 iter = 0 nrorth = nrorth + 1 c c %---------------------------------------------------% c | Enter the Iterative refinement phase. If further | c | refinement is necessary, loop back here. The loop | c | variable is ITER. Perform a step of Classical | c | Gram-Schmidt using all the Arnoldi vectors V_{j} | c %---------------------------------------------------% c 80 continue c if (msglvl .gt. 2) then xtemp(1) = wnorm xtemp(2) = rnorm call dvout (logfil, 2, xtemp, ndigit, & '_naitr: re-orthonalization; wnorm and rnorm are') call dvout (logfil, j, h(1,j), ndigit, & '_naitr: j-th column of H') end if c c %----------------------------------------------------% c | Compute V_{j}^T * B * r_{j}. | c | WORKD(IRJ:IRJ+J-1) = v(:,1:J)'*WORKD(IPJ:IPJ+N-1). | c %----------------------------------------------------% c call dgemv ('T', n, j, one, v, ldv, workd(ipj), 1, & zero, workd(irj), 1) c c %---------------------------------------------% c | Compute the correction to the residual: | c | r_{j} = r_{j} - V_{j} * WORKD(IRJ:IRJ+J-1). | c | The correction to H is v(:,1:J)*H(1:J,1:J) | c | + v(:,1:J)*WORKD(IRJ:IRJ+J-1)*e'_j. | c %---------------------------------------------% c call dgemv ('N', n, j, -one, v, ldv, workd(irj), 1, & one, resid, 1) call daxpy (j, one, workd(irj), 1, h(1,j), 1) c orth2 = .true. call arscnd (t2) if (bmat .eq. 'G') then nbx = nbx + 1 call dcopy (n, resid, 1, workd(irj), 1) ipntr(1) = irj ipntr(2) = ipj ido = 2 c c %-----------------------------------% c | Exit in order to compute B*r_{j}. | c | r_{j} is the corrected residual. | c %-----------------------------------% c go to 9000 else if (bmat .eq. 'I') then call dcopy (n, resid, 1, workd(ipj), 1) end if 90 continue c c %---------------------------------------------------% c | Back from reverse communication if ORTH2 = .true. | c %---------------------------------------------------% c if (bmat .eq. 'G') then call arscnd (t3) tmvbx = tmvbx + (t3 - t2) end if c c %-----------------------------------------------------% c | Compute the B-norm of the corrected residual r_{j}. | c %-----------------------------------------------------% c if (bmat .eq. 'G') then rnorm1 = ddot (n, resid, 1, workd(ipj), 1) rnorm1 = sqrt(abs(rnorm1)) else if (bmat .eq. 'I') then rnorm1 = dnrm2(n, resid, 1) end if c if (msglvl .gt. 0 .and. iter .gt. 0) then call ivout (logfil, 1, j, ndigit, & '_naitr: Iterative refinement for Arnoldi residual') if (msglvl .gt. 2) then xtemp(1) = rnorm xtemp(2) = rnorm1 call dvout (logfil, 2, xtemp, ndigit, & '_naitr: iterative refinement ; rnorm and rnorm1 are') end if end if c c %-----------------------------------------% c | Determine if we need to perform another | c | step of re-orthogonalization. | c %-----------------------------------------% c if (rnorm1 .gt. 0.717*rnorm) then c c %---------------------------------------% c | No need for further refinement. | c | The cosine of the angle between the | c | corrected residual vector and the old | c | residual vector is greater than 0.717 | c | In other words the corrected residual | c | and the old residual vector share an | c | angle of less than arcCOS(0.717) | c %---------------------------------------% c rnorm = rnorm1 c else c c %-------------------------------------------% c | Another step of iterative refinement step | c | is required. NITREF is used by stat.h | c %-------------------------------------------% c nitref = nitref + 1 rnorm = rnorm1 iter = iter + 1 if (iter .le. 1) go to 80 c c %-------------------------------------------------% c | Otherwise RESID is numerically in the span of V | c %-------------------------------------------------% c do 95 jj = 1, n resid(jj) = zero 95 continue rnorm = zero end if c c %----------------------------------------------% c | Branch here directly if iterative refinement | c | wasn't necessary or after at most NITER_REF | c | steps of iterative refinement. | c %----------------------------------------------% c 100 continue c rstart = .false. orth2 = .false. c call arscnd (t5) titref = titref + (t5 - t4) c c %------------------------------------% c | STEP 6: Update j = j+1; Continue | c %------------------------------------% c j = j + 1 if (j .gt. k+np) then call arscnd (t1) tnaitr = tnaitr + (t1 - t0) ido = 99 do 110 i = max(1,k), k+np-1 c c %--------------------------------------------% c | Check for splitting and deflation. | c | Use a standard test as in the QR algorithm | c | REFERENCE: LAPACK subroutine dlahqr | c %--------------------------------------------% c tst1 = abs( h( i, i ) ) + abs( h( i+1, i+1 ) ) if( tst1.eq.zero ) & tst1 = dlanhs( '1', k+np, h, ldh, workd(n+1) ) if( abs( h( i+1,i ) ).le.max( ulp*tst1, smlnum ) ) & h(i+1,i) = zero 110 continue c if (msglvl .gt. 2) then call dmout (logfil, k+np, k+np, h, ldh, ndigit, & '_naitr: Final upper Hessenberg matrix H of order K+NP') end if c go to 9000 end if c c %--------------------------------------------------------% c | Loop back to extend the factorization by another step. | c %--------------------------------------------------------% c go to 1000 c c %---------------------------------------------------------------% c | | c | E N D O F M A I N I T E R A T I O N L O O P | c | | c %---------------------------------------------------------------% c 9000 continue return c c %---------------% c | End of dnaitr | c %---------------% c end arpack-0.92.1/SRC/cnaitr.f0000644000175000017500000007446710776001577012077 00000000000000c\BeginDoc c c\Name: cnaitr c c\Description: c Reverse communication interface for applying NP additional steps to c a K step nonsymmetric Arnoldi factorization. c c Input: OP*V_{k} - V_{k}*H = r_{k}*e_{k}^T c c with (V_{k}^T)*B*V_{k} = I, (V_{k}^T)*B*r_{k} = 0. c c Output: OP*V_{k+p} - V_{k+p}*H = r_{k+p}*e_{k+p}^T c c with (V_{k+p}^T)*B*V_{k+p} = I, (V_{k+p}^T)*B*r_{k+p} = 0. c c where OP and B are as in cnaupd. The B-norm of r_{k+p} is also c computed and returned. c c\Usage: c call cnaitr c ( IDO, BMAT, N, K, NP, NB, RESID, RNORM, V, LDV, H, LDH, c IPNTR, WORKD, INFO ) c c\Arguments c IDO Integer. (INPUT/OUTPUT) c Reverse communication flag. c ------------------------------------------------------------- c IDO = 0: first call to the reverse communication interface c IDO = -1: compute Y = OP * X where c IPNTR(1) is the pointer into WORK for X, c IPNTR(2) is the pointer into WORK for Y. c This is for the restart phase to force the new c starting vector into the range of OP. c IDO = 1: compute Y = OP * X where c IPNTR(1) is the pointer into WORK for X, c IPNTR(2) is the pointer into WORK for Y, c IPNTR(3) is the pointer into WORK for B * X. c IDO = 2: compute Y = B * X where c IPNTR(1) is the pointer into WORK for X, c IPNTR(2) is the pointer into WORK for Y. c IDO = 99: done c ------------------------------------------------------------- c When the routine is used in the "shift-and-invert" mode, the c vector B * Q is already available and do not need to be c recomputed in forming OP * Q. c c BMAT Character*1. (INPUT) c BMAT specifies the type of the matrix B that defines the c semi-inner product for the operator OP. See cnaupd. c B = 'I' -> standard eigenvalue problem A*x = lambda*x c B = 'G' -> generalized eigenvalue problem A*x = lambda*M**x c c N Integer. (INPUT) c Dimension of the eigenproblem. c c K Integer. (INPUT) c Current size of V and H. c c NP Integer. (INPUT) c Number of additional Arnoldi steps to take. c c NB Integer. (INPUT) c Blocksize to be used in the recurrence. c Only work for NB = 1 right now. The goal is to have a c program that implement both the block and non-block method. c c RESID Complex array of length N. (INPUT/OUTPUT) c On INPUT: RESID contains the residual vector r_{k}. c On OUTPUT: RESID contains the residual vector r_{k+p}. c c RNORM Real scalar. (INPUT/OUTPUT) c B-norm of the starting residual on input. c B-norm of the updated residual r_{k+p} on output. c c V Complex N by K+NP array. (INPUT/OUTPUT) c On INPUT: V contains the Arnoldi vectors in the first K c columns. c On OUTPUT: V contains the new NP Arnoldi vectors in the next c NP columns. The first K columns are unchanged. c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling c program. c c H Complex (K+NP) by (K+NP) array. (INPUT/OUTPUT) c H is used to store the generated upper Hessenberg matrix. c c LDH Integer. (INPUT) c Leading dimension of H exactly as declared in the calling c program. c c IPNTR Integer array of length 3. (OUTPUT) c Pointer to mark the starting locations in the WORK for c vectors used by the Arnoldi iteration. c ------------------------------------------------------------- c IPNTR(1): pointer to the current operand vector X. c IPNTR(2): pointer to the current result vector Y. c IPNTR(3): pointer to the vector B * X when used in the c shift-and-invert mode. X is the current operand. c ------------------------------------------------------------- c c WORKD Complex work array of length 3*N. (REVERSE COMMUNICATION) c Distributed array to be used in the basic Arnoldi iteration c for reverse communication. The calling program should not c use WORKD as temporary workspace during the iteration !!!!!! c On input, WORKD(1:N) = B*RESID and is used to save some c computation at the first step. c c INFO Integer. (OUTPUT) c = 0: Normal exit. c > 0: Size of the spanning invariant subspace of OP found. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx Complex c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly c Restarted Arnoldi Iteration", Rice University Technical Report c TR95-13, Department of Computational and Applied Mathematics. c c\Routines called: c cgetv0 ARPACK routine to generate the initial vector. c ivout ARPACK utility routine that prints integers. c arscnd ARPACK utility routine for timing. c cmout ARPACK utility routine that prints matrices c cvout ARPACK utility routine that prints vectors. c clanhs LAPACK routine that computes various norms of a matrix. c clascl LAPACK routine for careful scaling of a matrix. c slabad LAPACK routine for defining the underflow and overflow c limits. c slamch LAPACK routine that determines machine constants. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c cgemv Level 2 BLAS routine for matrix vector multiplication. c caxpy Level 1 BLAS that computes a vector triad. c ccopy Level 1 BLAS that copies one vector to another . c cdotc Level 1 BLAS that computes the scalar product of two vectors. c cscal Level 1 BLAS that scales a vector. c csscal Level 1 BLAS that scales a complex vector by a real number. c scnrm2 Level 1 BLAS that computes the norm of a vector. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: naitr.F SID: 2.3 DATE OF SID: 8/27/96 RELEASE: 2 c c\Remarks c The algorithm implemented is: c c restart = .false. c Given V_{k} = [v_{1}, ..., v_{k}], r_{k}; c r_{k} contains the initial residual vector even for k = 0; c Also assume that rnorm = || B*r_{k} || and B*r_{k} are already c computed by the calling program. c c betaj = rnorm ; p_{k+1} = B*r_{k} ; c For j = k+1, ..., k+np Do c 1) if ( betaj < tol ) stop or restart depending on j. c ( At present tol is zero ) c if ( restart ) generate a new starting vector. c 2) v_{j} = r(j-1)/betaj; V_{j} = [V_{j-1}, v_{j}]; c p_{j} = p_{j}/betaj c 3) r_{j} = OP*v_{j} where OP is defined as in cnaupd c For shift-invert mode p_{j} = B*v_{j} is already available. c wnorm = || OP*v_{j} || c 4) Compute the j-th step residual vector. c w_{j} = V_{j}^T * B * OP * v_{j} c r_{j} = OP*v_{j} - V_{j} * w_{j} c H(:,j) = w_{j}; c H(j,j-1) = rnorm c rnorm = || r_(j) || c If (rnorm > 0.717*wnorm) accept step and go back to 1) c 5) Re-orthogonalization step: c s = V_{j}'*B*r_{j} c r_{j} = r_{j} - V_{j}*s; rnorm1 = || r_{j} || c alphaj = alphaj + s_{j}; c 6) Iterative refinement step: c If (rnorm1 > 0.717*rnorm) then c rnorm = rnorm1 c accept step and go back to 1) c Else c rnorm = rnorm1 c If this is the first time in step 6), go to 5) c Else r_{j} lies in the span of V_{j} numerically. c Set r_{j} = 0 and rnorm = 0; go to 1) c EndIf c End Do c c\EndLib c c----------------------------------------------------------------------- c subroutine cnaitr & (ido, bmat, n, k, np, nb, resid, rnorm, v, ldv, h, ldh, & ipntr, workd, info) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character bmat*1 integer ido, info, k, ldh, ldv, n, nb, np Real & rnorm c c %-----------------% c | Array Arguments | c %-----------------% c integer ipntr(3) Complex & h(ldh,k+np), resid(n), v(ldv,k+np), workd(3*n) c c %------------% c | Parameters | c %------------% c Complex & one, zero Real & rone, rzero parameter (one = (1.0E+0, 0.0E+0), zero = (0.0E+0, 0.0E+0), & rone = 1.0E+0, rzero = 0.0E+0) c c %--------------% c | Local Arrays | c %--------------% c Real & rtemp(2) c c %---------------% c | Local Scalars | c %---------------% c logical first, orth1, orth2, rstart, step3, step4 integer ierr, i, infol, ipj, irj, ivj, iter, itry, j, msglvl, & jj Real & ovfl, smlnum, tst1, ulp, unfl, betaj, & temp1, rnorm1, wnorm Complex & cnorm c save first, orth1, orth2, rstart, step3, step4, & ierr, ipj, irj, ivj, iter, itry, j, msglvl, ovfl, & betaj, rnorm1, smlnum, ulp, unfl, wnorm c c %----------------------% c | External Subroutines | c %----------------------% c external caxpy, ccopy, cscal, csscal, cgemv, cgetv0, & slabad, cvout, cmout, ivout, arscnd c c %--------------------% c | External Functions | c %--------------------% c Complex & cdotc Real & slamch, scnrm2, clanhs, slapy2 external cdotc, scnrm2, clanhs, slamch, slapy2 c c %---------------------% c | Intrinsic Functions | c %---------------------% c intrinsic aimag, real, max, sqrt c c %-----------------% c | Data statements | c %-----------------% c data first / .true. / c c %-----------------------% c | Executable Statements | c %-----------------------% c if (first) then c c %-----------------------------------------% c | Set machine-dependent constants for the | c | the splitting and deflation criterion. | c | If norm(H) <= sqrt(OVFL), | c | overflow should not occur. | c | REFERENCE: LAPACK subroutine clahqr | c %-----------------------------------------% c unfl = slamch( 'safe minimum' ) ovfl = real(one / unfl) call slabad( unfl, ovfl ) ulp = slamch( 'precision' ) smlnum = unfl*( n / ulp ) first = .false. end if c if (ido .eq. 0) then c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call arscnd (t0) msglvl = mcaitr c c %------------------------------% c | Initial call to this routine | c %------------------------------% c info = 0 step3 = .false. step4 = .false. rstart = .false. orth1 = .false. orth2 = .false. j = k + 1 ipj = 1 irj = ipj + n ivj = irj + n end if c c %-------------------------------------------------% c | When in reverse communication mode one of: | c | STEP3, STEP4, ORTH1, ORTH2, RSTART | c | will be .true. when .... | c | STEP3: return from computing OP*v_{j}. | c | STEP4: return from computing B-norm of OP*v_{j} | c | ORTH1: return from computing B-norm of r_{j+1} | c | ORTH2: return from computing B-norm of | c | correction to the residual vector. | c | RSTART: return from OP computations needed by | c | cgetv0. | c %-------------------------------------------------% c if (step3) go to 50 if (step4) go to 60 if (orth1) go to 70 if (orth2) go to 90 if (rstart) go to 30 c c %-----------------------------% c | Else this is the first step | c %-----------------------------% c c %--------------------------------------------------------------% c | | c | A R N O L D I I T E R A T I O N L O O P | c | | c | Note: B*r_{j-1} is already in WORKD(1:N)=WORKD(IPJ:IPJ+N-1) | c %--------------------------------------------------------------% 1000 continue c if (msglvl .gt. 1) then call ivout (logfil, 1, j, ndigit, & '_naitr: generating Arnoldi vector number') call svout (logfil, 1, rnorm, ndigit, & '_naitr: B-norm of the current residual is') end if c c %---------------------------------------------------% c | STEP 1: Check if the B norm of j-th residual | c | vector is zero. Equivalent to determine whether | c | an exact j-step Arnoldi factorization is present. | c %---------------------------------------------------% c betaj = rnorm if (rnorm .gt. rzero) go to 40 c c %---------------------------------------------------% c | Invariant subspace found, generate a new starting | c | vector which is orthogonal to the current Arnoldi | c | basis and continue the iteration. | c %---------------------------------------------------% c if (msglvl .gt. 0) then call ivout (logfil, 1, j, ndigit, & '_naitr: ****** RESTART AT STEP ******') end if c c %---------------------------------------------% c | ITRY is the loop variable that controls the | c | maximum amount of times that a restart is | c | attempted. NRSTRT is used by stat.h | c %---------------------------------------------% c betaj = rzero nrstrt = nrstrt + 1 itry = 1 20 continue rstart = .true. ido = 0 30 continue c c %--------------------------------------% c | If in reverse communication mode and | c | RSTART = .true. flow returns here. | c %--------------------------------------% c call cgetv0 (ido, bmat, itry, .false., n, j, v, ldv, & resid, rnorm, ipntr, workd, ierr) if (ido .ne. 99) go to 9000 if (ierr .lt. 0) then itry = itry + 1 if (itry .le. 3) go to 20 c c %------------------------------------------------% c | Give up after several restart attempts. | c | Set INFO to the size of the invariant subspace | c | which spans OP and exit. | c %------------------------------------------------% c info = j - 1 call arscnd (t1) tcaitr = tcaitr + (t1 - t0) ido = 99 go to 9000 end if c 40 continue c c %---------------------------------------------------------% c | STEP 2: v_{j} = r_{j-1}/rnorm and p_{j} = p_{j}/rnorm | c | Note that p_{j} = B*r_{j-1}. In order to avoid overflow | c | when reciprocating a small RNORM, test against lower | c | machine bound. | c %---------------------------------------------------------% c call ccopy (n, resid, 1, v(1,j), 1) if ( rnorm .ge. unfl) then temp1 = rone / rnorm call csscal (n, temp1, v(1,j), 1) call csscal (n, temp1, workd(ipj), 1) else c c %-----------------------------------------% c | To scale both v_{j} and p_{j} carefully | c | use LAPACK routine clascl | c %-----------------------------------------% c call clascl ('General', i, i, rnorm, rone, & n, 1, v(1,j), n, infol) call clascl ('General', i, i, rnorm, rone, & n, 1, workd(ipj), n, infol) end if c c %------------------------------------------------------% c | STEP 3: r_{j} = OP*v_{j}; Note that p_{j} = B*v_{j} | c | Note that this is not quite yet r_{j}. See STEP 4 | c %------------------------------------------------------% c step3 = .true. nopx = nopx + 1 call arscnd (t2) call ccopy (n, v(1,j), 1, workd(ivj), 1) ipntr(1) = ivj ipntr(2) = irj ipntr(3) = ipj ido = 1 c c %-----------------------------------% c | Exit in order to compute OP*v_{j} | c %-----------------------------------% c go to 9000 50 continue c c %----------------------------------% c | Back from reverse communication; | c | WORKD(IRJ:IRJ+N-1) := OP*v_{j} | c | if step3 = .true. | c %----------------------------------% c call arscnd (t3) tmvopx = tmvopx + (t3 - t2) step3 = .false. c c %------------------------------------------% c | Put another copy of OP*v_{j} into RESID. | c %------------------------------------------% c call ccopy (n, workd(irj), 1, resid, 1) c c %---------------------------------------% c | STEP 4: Finish extending the Arnoldi | c | factorization to length j. | c %---------------------------------------% c call arscnd (t2) if (bmat .eq. 'G') then nbx = nbx + 1 step4 = .true. ipntr(1) = irj ipntr(2) = ipj ido = 2 c c %-------------------------------------% c | Exit in order to compute B*OP*v_{j} | c %-------------------------------------% c go to 9000 else if (bmat .eq. 'I') then call ccopy (n, resid, 1, workd(ipj), 1) end if 60 continue c c %----------------------------------% c | Back from reverse communication; | c | WORKD(IPJ:IPJ+N-1) := B*OP*v_{j} | c | if step4 = .true. | c %----------------------------------% c if (bmat .eq. 'G') then call arscnd (t3) tmvbx = tmvbx + (t3 - t2) end if c step4 = .false. c c %-------------------------------------% c | The following is needed for STEP 5. | c | Compute the B-norm of OP*v_{j}. | c %-------------------------------------% c if (bmat .eq. 'G') then cnorm = cdotc (n, resid, 1, workd(ipj), 1) wnorm = sqrt( slapy2(real(cnorm),aimag(cnorm)) ) else if (bmat .eq. 'I') then wnorm = scnrm2(n, resid, 1) end if c c %-----------------------------------------% c | Compute the j-th residual corresponding | c | to the j step factorization. | c | Use Classical Gram Schmidt and compute: | c | w_{j} <- V_{j}^T * B * OP * v_{j} | c | r_{j} <- OP*v_{j} - V_{j} * w_{j} | c %-----------------------------------------% c c c %------------------------------------------% c | Compute the j Fourier coefficients w_{j} | c | WORKD(IPJ:IPJ+N-1) contains B*OP*v_{j}. | c %------------------------------------------% c call cgemv ('C', n, j, one, v, ldv, workd(ipj), 1, & zero, h(1,j), 1) c c %--------------------------------------% c | Orthogonalize r_{j} against V_{j}. | c | RESID contains OP*v_{j}. See STEP 3. | c %--------------------------------------% c call cgemv ('N', n, j, -one, v, ldv, h(1,j), 1, & one, resid, 1) c if (j .gt. 1) h(j,j-1) = cmplx(betaj, rzero) c call arscnd (t4) c orth1 = .true. c call arscnd (t2) if (bmat .eq. 'G') then nbx = nbx + 1 call ccopy (n, resid, 1, workd(irj), 1) ipntr(1) = irj ipntr(2) = ipj ido = 2 c c %----------------------------------% c | Exit in order to compute B*r_{j} | c %----------------------------------% c go to 9000 else if (bmat .eq. 'I') then call ccopy (n, resid, 1, workd(ipj), 1) end if 70 continue c c %---------------------------------------------------% c | Back from reverse communication if ORTH1 = .true. | c | WORKD(IPJ:IPJ+N-1) := B*r_{j}. | c %---------------------------------------------------% c if (bmat .eq. 'G') then call arscnd (t3) tmvbx = tmvbx + (t3 - t2) end if c orth1 = .false. c c %------------------------------% c | Compute the B-norm of r_{j}. | c %------------------------------% c if (bmat .eq. 'G') then cnorm = cdotc (n, resid, 1, workd(ipj), 1) rnorm = sqrt( slapy2(real(cnorm),aimag(cnorm)) ) else if (bmat .eq. 'I') then rnorm = scnrm2(n, resid, 1) end if c c %-----------------------------------------------------------% c | STEP 5: Re-orthogonalization / Iterative refinement phase | c | Maximum NITER_ITREF tries. | c | | c | s = V_{j}^T * B * r_{j} | c | r_{j} = r_{j} - V_{j}*s | c | alphaj = alphaj + s_{j} | c | | c | The stopping criteria used for iterative refinement is | c | discussed in Parlett's book SEP, page 107 and in Gragg & | c | Reichel ACM TOMS paper; Algorithm 686, Dec. 1990. | c | Determine if we need to correct the residual. The goal is | c | to enforce ||v(:,1:j)^T * r_{j}|| .le. eps * || r_{j} || | c | The following test determines whether the sine of the | c | angle between OP*x and the computed residual is less | c | than or equal to 0.717. | c %-----------------------------------------------------------% c if ( rnorm .gt. 0.717*wnorm ) go to 100 c iter = 0 nrorth = nrorth + 1 c c %---------------------------------------------------% c | Enter the Iterative refinement phase. If further | c | refinement is necessary, loop back here. The loop | c | variable is ITER. Perform a step of Classical | c | Gram-Schmidt using all the Arnoldi vectors V_{j} | c %---------------------------------------------------% c 80 continue c if (msglvl .gt. 2) then rtemp(1) = wnorm rtemp(2) = rnorm call svout (logfil, 2, rtemp, ndigit, & '_naitr: re-orthogonalization; wnorm and rnorm are') call cvout (logfil, j, h(1,j), ndigit, & '_naitr: j-th column of H') end if c c %----------------------------------------------------% c | Compute V_{j}^T * B * r_{j}. | c | WORKD(IRJ:IRJ+J-1) = v(:,1:J)'*WORKD(IPJ:IPJ+N-1). | c %----------------------------------------------------% c call cgemv ('C', n, j, one, v, ldv, workd(ipj), 1, & zero, workd(irj), 1) c c %---------------------------------------------% c | Compute the correction to the residual: | c | r_{j} = r_{j} - V_{j} * WORKD(IRJ:IRJ+J-1). | c | The correction to H is v(:,1:J)*H(1:J,1:J) | c | + v(:,1:J)*WORKD(IRJ:IRJ+J-1)*e'_j. | c %---------------------------------------------% c call cgemv ('N', n, j, -one, v, ldv, workd(irj), 1, & one, resid, 1) call caxpy (j, one, workd(irj), 1, h(1,j), 1) c orth2 = .true. call arscnd (t2) if (bmat .eq. 'G') then nbx = nbx + 1 call ccopy (n, resid, 1, workd(irj), 1) ipntr(1) = irj ipntr(2) = ipj ido = 2 c c %-----------------------------------% c | Exit in order to compute B*r_{j}. | c | r_{j} is the corrected residual. | c %-----------------------------------% c go to 9000 else if (bmat .eq. 'I') then call ccopy (n, resid, 1, workd(ipj), 1) end if 90 continue c c %---------------------------------------------------% c | Back from reverse communication if ORTH2 = .true. | c %---------------------------------------------------% c if (bmat .eq. 'G') then call arscnd (t3) tmvbx = tmvbx + (t3 - t2) end if c c %-----------------------------------------------------% c | Compute the B-norm of the corrected residual r_{j}. | c %-----------------------------------------------------% c if (bmat .eq. 'G') then cnorm = cdotc (n, resid, 1, workd(ipj), 1) rnorm1 = sqrt( slapy2(real(cnorm),aimag(cnorm)) ) else if (bmat .eq. 'I') then rnorm1 = scnrm2(n, resid, 1) end if c if (msglvl .gt. 0 .and. iter .gt. 0 ) then call ivout (logfil, 1, j, ndigit, & '_naitr: Iterative refinement for Arnoldi residual') if (msglvl .gt. 2) then rtemp(1) = rnorm rtemp(2) = rnorm1 call svout (logfil, 2, rtemp, ndigit, & '_naitr: iterative refinement ; rnorm and rnorm1 are') end if end if c c %-----------------------------------------% c | Determine if we need to perform another | c | step of re-orthogonalization. | c %-----------------------------------------% c if ( rnorm1 .gt. 0.717*rnorm ) then c c %---------------------------------------% c | No need for further refinement. | c | The cosine of the angle between the | c | corrected residual vector and the old | c | residual vector is greater than 0.717 | c | In other words the corrected residual | c | and the old residual vector share an | c | angle of less than arcCOS(0.717) | c %---------------------------------------% c rnorm = rnorm1 c else c c %-------------------------------------------% c | Another step of iterative refinement step | c | is required. NITREF is used by stat.h | c %-------------------------------------------% c nitref = nitref + 1 rnorm = rnorm1 iter = iter + 1 if (iter .le. 1) go to 80 c c %-------------------------------------------------% c | Otherwise RESID is numerically in the span of V | c %-------------------------------------------------% c do 95 jj = 1, n resid(jj) = zero 95 continue rnorm = rzero end if c c %----------------------------------------------% c | Branch here directly if iterative refinement | c | wasn't necessary or after at most NITER_REF | c | steps of iterative refinement. | c %----------------------------------------------% c 100 continue c rstart = .false. orth2 = .false. c call arscnd (t5) titref = titref + (t5 - t4) c c %------------------------------------% c | STEP 6: Update j = j+1; Continue | c %------------------------------------% c j = j + 1 if (j .gt. k+np) then call arscnd (t1) tcaitr = tcaitr + (t1 - t0) ido = 99 do 110 i = max(1,k), k+np-1 c c %--------------------------------------------% c | Check for splitting and deflation. | c | Use a standard test as in the QR algorithm | c | REFERENCE: LAPACK subroutine clahqr | c %--------------------------------------------% c tst1 = slapy2(real(h(i,i)),aimag(h(i,i))) & + slapy2(real(h(i+1,i+1)), aimag(h(i+1,i+1))) if( tst1.eq.real(zero) ) & tst1 = clanhs( '1', k+np, h, ldh, workd(n+1) ) if( slapy2(real(h(i+1,i)),aimag(h(i+1,i))) .le. & max( ulp*tst1, smlnum ) ) & h(i+1,i) = zero 110 continue c if (msglvl .gt. 2) then call cmout (logfil, k+np, k+np, h, ldh, ndigit, & '_naitr: Final upper Hessenberg matrix H of order K+NP') end if c go to 9000 end if c c %--------------------------------------------------------% c | Loop back to extend the factorization by another step. | c %--------------------------------------------------------% c go to 1000 c c %---------------------------------------------------------------% c | | c | E N D O F M A I N I T E R A T I O N L O O P | c | | c %---------------------------------------------------------------% c 9000 continue return c c %---------------% c | End of cnaitr | c %---------------% c end arpack-0.92.1/SRC/cneupd.f0000644000175000017500000010375610776001577012067 00000000000000c\BeginDoc c c\Name: cneupd c c\Description: c This subroutine returns the converged approximations to eigenvalues c of A*z = lambda*B*z and (optionally): c c (1) The corresponding approximate eigenvectors; c c (2) An orthonormal basis for the associated approximate c invariant subspace; c c (3) Both. c c There is negligible additional cost to obtain eigenvectors. An orthonormal c basis is always computed. There is an additional storage cost of n*nev c if both are requested (in this case a separate array Z must be supplied). c c The approximate eigenvalues and eigenvectors of A*z = lambda*B*z c are derived from approximate eigenvalues and eigenvectors of c of the linear operator OP prescribed by the MODE selection in the c call to CNAUPD. CNAUPD must be called before this routine is called. c These approximate eigenvalues and vectors are commonly called Ritz c values and Ritz vectors respectively. They are referred to as such c in the comments that follow. The computed orthonormal basis for the c invariant subspace corresponding to these Ritz values is referred to as a c Schur basis. c c The definition of OP as well as other terms and the relation of computed c Ritz values and vectors of OP with respect to the given problem c A*z = lambda*B*z may be found in the header of CNAUPD. For a brief c description, see definitions of IPARAM(7), MODE and WHICH in the c documentation of CNAUPD. c c\Usage: c call cneupd c ( RVEC, HOWMNY, SELECT, D, Z, LDZ, SIGMA, WORKEV, BMAT, c N, WHICH, NEV, TOL, RESID, NCV, V, LDV, IPARAM, IPNTR, WORKD, c WORKL, LWORKL, RWORK, INFO ) c c\Arguments: c RVEC LOGICAL (INPUT) c Specifies whether a basis for the invariant subspace corresponding c to the converged Ritz value approximations for the eigenproblem c A*z = lambda*B*z is computed. c c RVEC = .FALSE. Compute Ritz values only. c c RVEC = .TRUE. Compute Ritz vectors or Schur vectors. c See Remarks below. c c HOWMNY Character*1 (INPUT) c Specifies the form of the basis for the invariant subspace c corresponding to the converged Ritz values that is to be computed. c c = 'A': Compute NEV Ritz vectors; c = 'P': Compute NEV Schur vectors; c = 'S': compute some of the Ritz vectors, specified c by the logical array SELECT. c c SELECT Logical array of dimension NCV. (INPUT) c If HOWMNY = 'S', SELECT specifies the Ritz vectors to be c computed. To select the Ritz vector corresponding to a c Ritz value D(j), SELECT(j) must be set to .TRUE.. c If HOWMNY = 'A' or 'P', SELECT need not be initialized c but it is used as internal workspace. c c D Complex array of dimension NEV+1. (OUTPUT) c On exit, D contains the Ritz approximations c to the eigenvalues lambda for A*z = lambda*B*z. c c Z Complex N by NEV array (OUTPUT) c On exit, if RVEC = .TRUE. and HOWMNY = 'A', then the columns of c Z represents approximate eigenvectors (Ritz vectors) corresponding c to the NCONV=IPARAM(5) Ritz values for eigensystem c A*z = lambda*B*z. c c If RVEC = .FALSE. or HOWMNY = 'P', then Z is NOT REFERENCED. c c NOTE: If if RVEC = .TRUE. and a Schur basis is not required, c the array Z may be set equal to first NEV+1 columns of the Arnoldi c basis array V computed by CNAUPD. In this case the Arnoldi basis c will be destroyed and overwritten with the eigenvector basis. c c LDZ Integer. (INPUT) c The leading dimension of the array Z. If Ritz vectors are c desired, then LDZ .ge. max( 1, N ) is required. c In any case, LDZ .ge. 1 is required. c c SIGMA Complex (INPUT) c If IPARAM(7) = 3 then SIGMA represents the shift. c Not referenced if IPARAM(7) = 1 or 2. c c WORKEV Complex work array of dimension 2*NCV. (WORKSPACE) c c **** The remaining arguments MUST be the same as for the **** c **** call to CNAUPD that was just completed. **** c c NOTE: The remaining arguments c c BMAT, N, WHICH, NEV, TOL, RESID, NCV, V, LDV, IPARAM, IPNTR, c WORKD, WORKL, LWORKL, RWORK, INFO c c must be passed directly to CNEUPD following the last call c to CNAUPD. These arguments MUST NOT BE MODIFIED between c the the last call to CNAUPD and the call to CNEUPD. c c Three of these parameters (V, WORKL and INFO) are also output parameters: c c V Complex N by NCV array. (INPUT/OUTPUT) c c Upon INPUT: the NCV columns of V contain the Arnoldi basis c vectors for OP as constructed by CNAUPD . c c Upon OUTPUT: If RVEC = .TRUE. the first NCONV=IPARAM(5) columns c contain approximate Schur vectors that span the c desired invariant subspace. c c NOTE: If the array Z has been set equal to first NEV+1 columns c of the array V and RVEC=.TRUE. and HOWMNY= 'A', then the c Arnoldi basis held by V has been overwritten by the desired c Ritz vectors. If a separate array Z has been passed then c the first NCONV=IPARAM(5) columns of V will contain approximate c Schur vectors that span the desired invariant subspace. c c WORKL Real work array of length LWORKL. (OUTPUT/WORKSPACE) c WORKL(1:ncv*ncv+2*ncv) contains information obtained in c cnaupd. They are not changed by cneupd. c WORKL(ncv*ncv+2*ncv+1:3*ncv*ncv+4*ncv) holds the c untransformed Ritz values, the untransformed error estimates of c the Ritz values, the upper triangular matrix for H, and the c associated matrix representation of the invariant subspace for H. c c Note: IPNTR(9:13) contains the pointer into WORKL for addresses c of the above information computed by cneupd. c ------------------------------------------------------------- c IPNTR(9): pointer to the NCV RITZ values of the c original system. c IPNTR(10): Not used c IPNTR(11): pointer to the NCV corresponding error estimates. c IPNTR(12): pointer to the NCV by NCV upper triangular c Schur matrix for H. c IPNTR(13): pointer to the NCV by NCV matrix of eigenvectors c of the upper Hessenberg matrix H. Only referenced by c cneupd if RVEC = .TRUE. See Remark 2 below. c ------------------------------------------------------------- c c INFO Integer. (OUTPUT) c Error flag on output. c = 0: Normal exit. c c = 1: The Schur form computed by LAPACK routine csheqr c could not be reordered by LAPACK routine ctrsen. c Re-enter subroutine cneupd with IPARAM(5)=NCV and c increase the size of the array D to have c dimension at least dimension NCV and allocate at least NCV c columns for Z. NOTE: Not necessary if Z and V share c the same space. Please notify the authors if this error c occurs. c c = -1: N must be positive. c = -2: NEV must be positive. c = -3: NCV-NEV >= 1 and less than or equal to N. c = -5: WHICH must be one of 'LM', 'SM', 'LR', 'SR', 'LI', 'SI' c = -6: BMAT must be one of 'I' or 'G'. c = -7: Length of private work WORKL array is not sufficient. c = -8: Error return from LAPACK eigenvalue calculation. c This should never happened. c = -9: Error return from calculation of eigenvectors. c Informational error from LAPACK routine ctrevc. c = -10: IPARAM(7) must be 1,2,3 c = -11: IPARAM(7) = 1 and BMAT = 'G' are incompatible. c = -12: HOWMNY = 'S' not yet implemented c = -13: HOWMNY must be one of 'A' or 'P' if RVEC = .true. c = -14: CNAUPD did not find any eigenvalues to sufficient c accuracy. c = -15: CNEUPD got a different count of the number of converged c Ritz values than CNAUPD got. This indicates the user c probably made an error in passing data from CNAUPD to c CNEUPD or that the data was modified before entering c CNEUPD c c\BeginLib c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly c Restarted Arnoldi Iteration", Rice University Technical Report c TR95-13, Department of Computational and Applied Mathematics. c 3. B. Nour-Omid, B. N. Parlett, T. Ericsson and P. S. Jensen, c "How to Implement the Spectral Transformation", Math Comp., c Vol. 48, No. 178, April, 1987 pp. 664-673. c c\Routines called: c ivout ARPACK utility routine that prints integers. c cmout ARPACK utility routine that prints matrices c cvout ARPACK utility routine that prints vectors. c cgeqr2 LAPACK routine that computes the QR factorization of c a matrix. c clacpy LAPACK matrix copy routine. c clahqr LAPACK routine that computes the Schur form of a c upper Hessenberg matrix. c claset LAPACK matrix initialization routine. c ctrevc LAPACK routine to compute the eigenvectors of a matrix c in upper triangular form. c ctrsen LAPACK routine that re-orders the Schur form. c cunm2r LAPACK routine that applies an orthogonal matrix in c factored form. c slamch LAPACK routine that determines machine constants. c ctrmm Level 3 BLAS matrix times an upper triangular matrix. c cgeru Level 2 BLAS rank one update to a matrix. c ccopy Level 1 BLAS that copies one vector to another . c cscal Level 1 BLAS that scales a vector. c csscal Level 1 BLAS that scales a complex vector by a real number. c scnrm2 Level 1 BLAS that computes the norm of a complex vector. c c\Remarks c c 1. Currently only HOWMNY = 'A' and 'P' are implemented. c c 2. Schur vectors are an orthogonal representation for the basis of c Ritz vectors. Thus, their numerical properties are often superior. c If RVEC = .true. then the relationship c A * V(:,1:IPARAM(5)) = V(:,1:IPARAM(5)) * T, and c transpose( V(:,1:IPARAM(5)) ) * V(:,1:IPARAM(5)) = I c are approximately satisfied. c Here T is the leading submatrix of order IPARAM(5) of the c upper triangular matrix stored workl(ipntr(12)). c c\Authors c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Chao Yang Houston, Texas c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: neupd.F SID: 2.8 DATE OF SID: 07/21/02 RELEASE: 2 c c\EndLib c c----------------------------------------------------------------------- subroutine cneupd(rvec , howmny, select, d , & z , ldz , sigma , workev, & bmat , n , which , nev , & tol , resid , ncv , v , & ldv , iparam, ipntr , workd , & workl, lworkl, rwork , info ) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character bmat, howmny, which*2 logical rvec integer info, ldz, ldv, lworkl, n, ncv, nev Complex & sigma Real & tol c c %-----------------% c | Array Arguments | c %-----------------% c integer iparam(11), ipntr(14) logical select(ncv) Real & rwork(ncv) Complex & d(nev) , resid(n) , v(ldv,ncv), & z(ldz, nev), & workd(3*n) , workl(lworkl), workev(2*ncv) c c %------------% c | Parameters | c %------------% c Complex & one, zero parameter (one = (1.0E+0, 0.0E+0), zero = (0.0E+0, 0.0E+0)) c c %---------------% c | Local Scalars | c %---------------% c character type*6 integer bounds, ierr , ih , ihbds, iheig , nconv , & invsub, iuptri, iwev , j , ldh , ldq , & mode , msglvl, ritz , wr , k , irz , & ibd , outncv, iq , np , numcnv, jj , & ishift Complex & rnorm, temp, vl(1) Real & conds, sep, rtemp, eps23 logical reord c c %----------------------% c | External Subroutines | c %----------------------% c external ccopy , cgeru, cgeqr2, clacpy, cmout, & cunm2r, ctrmm, cvout, ivout, & clahqr c c %--------------------% c | External Functions | c %--------------------% c Real & scnrm2, slamch, slapy2 external scnrm2, slamch, slapy2 c Complex & cdotc external cdotc c c %-----------------------% c | Executable Statements | c %-----------------------% c c %------------------------% c | Set default parameters | c %------------------------% c msglvl = mceupd mode = iparam(7) nconv = iparam(5) info = 0 c c c %---------------------------------% c | Get machine dependent constant. | c %---------------------------------% c eps23 = slamch('Epsilon-Machine') eps23 = eps23**(2.0E+0 / 3.0E+0) c c %-------------------------------% c | Quick return | c | Check for incompatible input | c %-------------------------------% c ierr = 0 c if (nconv .le. 0) then ierr = -14 else if (n .le. 0) then ierr = -1 else if (nev .le. 0) then ierr = -2 else if (ncv .le. nev .or. ncv .gt. n) then ierr = -3 else if (which .ne. 'LM' .and. & which .ne. 'SM' .and. & which .ne. 'LR' .and. & which .ne. 'SR' .and. & which .ne. 'LI' .and. & which .ne. 'SI') then ierr = -5 else if (bmat .ne. 'I' .and. bmat .ne. 'G') then ierr = -6 else if (lworkl .lt. 3*ncv**2 + 4*ncv) then ierr = -7 else if ( (howmny .ne. 'A' .and. & howmny .ne. 'P' .and. & howmny .ne. 'S') .and. rvec ) then ierr = -13 else if (howmny .eq. 'S' ) then ierr = -12 end if c if (mode .eq. 1 .or. mode .eq. 2) then type = 'REGULR' else if (mode .eq. 3 ) then type = 'SHIFTI' else ierr = -10 end if if (mode .eq. 1 .and. bmat .eq. 'G') ierr = -11 c c %------------% c | Error Exit | c %------------% c if (ierr .ne. 0) then info = ierr go to 9000 end if c c %--------------------------------------------------------% c | Pointer into WORKL for address of H, RITZ, WORKEV, Q | c | etc... and the remaining workspace. | c | Also update pointer to be used on output. | c | Memory is laid out as follows: | c | workl(1:ncv*ncv) := generated Hessenberg matrix | c | workl(ncv*ncv+1:ncv*ncv+ncv) := ritz values | c | workl(ncv*ncv+ncv+1:ncv*ncv+2*ncv) := error bounds | c %--------------------------------------------------------% c c %-----------------------------------------------------------% c | The following is used and set by CNEUPD. | c | workl(ncv*ncv+2*ncv+1:ncv*ncv+3*ncv) := The untransformed | c | Ritz values. | c | workl(ncv*ncv+3*ncv+1:ncv*ncv+4*ncv) := The untransformed | c | error bounds of | c | the Ritz values | c | workl(ncv*ncv+4*ncv+1:2*ncv*ncv+4*ncv) := Holds the upper | c | triangular matrix | c | for H. | c | workl(2*ncv*ncv+4*ncv+1: 3*ncv*ncv+4*ncv) := Holds the | c | associated matrix | c | representation of | c | the invariant | c | subspace for H. | c | GRAND total of NCV * ( 3 * NCV + 4 ) locations. | c %-----------------------------------------------------------% c ih = ipntr(5) ritz = ipntr(6) iq = ipntr(7) bounds = ipntr(8) ldh = ncv ldq = ncv iheig = bounds + ldh ihbds = iheig + ldh iuptri = ihbds + ldh invsub = iuptri + ldh*ncv ipntr(9) = iheig ipntr(11) = ihbds ipntr(12) = iuptri ipntr(13) = invsub wr = 1 iwev = wr + ncv c c %-----------------------------------------% c | irz points to the Ritz values computed | c | by _neigh before exiting _naup2. | c | ibd points to the Ritz estimates | c | computed by _neigh before exiting | c | _naup2. | c %-----------------------------------------% c irz = ipntr(14) + ncv*ncv ibd = irz + ncv c c %------------------------------------% c | RNORM is B-norm of the RESID(1:N). | c %------------------------------------% c rnorm = workl(ih+2) workl(ih+2) = zero c if (msglvl .gt. 2) then call cvout(logfil, ncv, workl(irz), ndigit, & '_neupd: Ritz values passed in from _NAUPD.') call cvout(logfil, ncv, workl(ibd), ndigit, & '_neupd: Ritz estimates passed in from _NAUPD.') end if c if (rvec) then c reord = .false. c c %---------------------------------------------------% c | Use the temporary bounds array to store indices | c | These will be used to mark the select array later | c %---------------------------------------------------% c do 10 j = 1,ncv workl(bounds+j-1) = j select(j) = .false. 10 continue c c %-------------------------------------% c | Select the wanted Ritz values. | c | Sort the Ritz values so that the | c | wanted ones appear at the tailing | c | NEV positions of workl(irr) and | c | workl(iri). Move the corresponding | c | error estimates in workl(ibd) | c | accordingly. | c %-------------------------------------% c np = ncv - nev ishift = 0 call cngets(ishift, which , nev , & np , workl(irz), workl(bounds)) c if (msglvl .gt. 2) then call cvout (logfil, ncv, workl(irz), ndigit, & '_neupd: Ritz values after calling _NGETS.') call cvout (logfil, ncv, workl(bounds), ndigit, & '_neupd: Ritz value indices after calling _NGETS.') end if c c %-----------------------------------------------------% c | Record indices of the converged wanted Ritz values | c | Mark the select array for possible reordering | c %-----------------------------------------------------% c numcnv = 0 do 11 j = 1,ncv rtemp = max(eps23, & slapy2 ( real(workl(irz+ncv-j)), & aimag(workl(irz+ncv-j)) )) jj = workl(bounds + ncv - j) if (numcnv .lt. nconv .and. & slapy2( real(workl(ibd+jj-1)), & aimag(workl(ibd+jj-1)) ) & .le. tol*rtemp) then select(jj) = .true. numcnv = numcnv + 1 if (jj .gt. nev) reord = .true. endif 11 continue c c %-----------------------------------------------------------% c | Check the count (numcnv) of converged Ritz values with | c | the number (nconv) reported by dnaupd. If these two | c | are different then there has probably been an error | c | caused by incorrect passing of the dnaupd data. | c %-----------------------------------------------------------% c if (msglvl .gt. 2) then call ivout(logfil, 1, numcnv, ndigit, & '_neupd: Number of specified eigenvalues') call ivout(logfil, 1, nconv, ndigit, & '_neupd: Number of "converged" eigenvalues') end if c if (numcnv .ne. nconv) then info = -15 go to 9000 end if c c %-------------------------------------------------------% c | Call LAPACK routine clahqr to compute the Schur form | c | of the upper Hessenberg matrix returned by CNAUPD. | c | Make a copy of the upper Hessenberg matrix. | c | Initialize the Schur vector matrix Q to the identity. | c %-------------------------------------------------------% c call ccopy(ldh*ncv, workl(ih), 1, workl(iuptri), 1) call claset('All', ncv, ncv , & zero , one, workl(invsub), & ldq) call clahqr(.true., .true. , ncv , & 1 , ncv , workl(iuptri), & ldh , workl(iheig) , 1 , & ncv , workl(invsub), ldq , & ierr) call ccopy(ncv , workl(invsub+ncv-1), ldq, & workl(ihbds), 1) c if (ierr .ne. 0) then info = -8 go to 9000 end if c if (msglvl .gt. 1) then call cvout (logfil, ncv, workl(iheig), ndigit, & '_neupd: Eigenvalues of H') call cvout (logfil, ncv, workl(ihbds), ndigit, & '_neupd: Last row of the Schur vector matrix') if (msglvl .gt. 3) then call cmout (logfil , ncv, ncv , & workl(iuptri), ldh, ndigit, & '_neupd: The upper triangular matrix ') end if end if c if (reord) then c c %-----------------------------------------------% c | Reorder the computed upper triangular matrix. | c %-----------------------------------------------% c call ctrsen('None' , 'V' , select , & ncv , workl(iuptri), ldh , & workl(invsub), ldq , workl(iheig), & nconv , conds , sep , & workev , ncv , ierr) c if (ierr .eq. 1) then info = 1 go to 9000 end if c if (msglvl .gt. 2) then call cvout (logfil, ncv, workl(iheig), ndigit, & '_neupd: Eigenvalues of H--reordered') if (msglvl .gt. 3) then call cmout(logfil , ncv, ncv , & workl(iuptri), ldq, ndigit, & '_neupd: Triangular matrix after re-ordering') end if end if c end if c c %---------------------------------------------% c | Copy the last row of the Schur basis matrix | c | to workl(ihbds). This vector will be used | c | to compute the Ritz estimates of converged | c | Ritz values. | c %---------------------------------------------% c call ccopy(ncv , workl(invsub+ncv-1), ldq, & workl(ihbds), 1) c c %--------------------------------------------% c | Place the computed eigenvalues of H into D | c | if a spectral transformation was not used. | c %--------------------------------------------% c if (type .eq. 'REGULR') then call ccopy(nconv, workl(iheig), 1, d, 1) end if c c %----------------------------------------------------------% c | Compute the QR factorization of the matrix representing | c | the wanted invariant subspace located in the first NCONV | c | columns of workl(invsub,ldq). | c %----------------------------------------------------------% c call cgeqr2(ncv , nconv , workl(invsub), & ldq , workev, workev(ncv+1), & ierr) c c %--------------------------------------------------------% c | * Postmultiply V by Q using cunm2r. | c | * Copy the first NCONV columns of VQ into Z. | c | * Postmultiply Z by R. | c | The N by NCONV matrix Z is now a matrix representation | c | of the approximate invariant subspace associated with | c | the Ritz values in workl(iheig). The first NCONV | c | columns of V are now approximate Schur vectors | c | associated with the upper triangular matrix of order | c | NCONV in workl(iuptri). | c %--------------------------------------------------------% c call cunm2r('Right', 'Notranspose', n , & ncv , nconv , workl(invsub), & ldq , workev , v , & ldv , workd(n+1) , ierr) call clacpy('All', n, nconv, v, ldv, z, ldz) c do 20 j=1, nconv c c %---------------------------------------------------% c | Perform both a column and row scaling if the | c | diagonal element of workl(invsub,ldq) is negative | c | I'm lazy and don't take advantage of the upper | c | triangular form of workl(iuptri,ldq). | c | Note that since Q is orthogonal, R is a diagonal | c | matrix consisting of plus or minus ones. | c %---------------------------------------------------% c if ( real( workl(invsub+(j-1)*ldq+j-1) ) .lt. & real(zero) ) then call cscal(nconv, -one, workl(iuptri+j-1), ldq) call cscal(nconv, -one, workl(iuptri+(j-1)*ldq), 1) end if c 20 continue c if (howmny .eq. 'A') then c c %--------------------------------------------% c | Compute the NCONV wanted eigenvectors of T | c | located in workl(iuptri,ldq). | c %--------------------------------------------% c do 30 j=1, ncv if (j .le. nconv) then select(j) = .true. else select(j) = .false. end if 30 continue c call ctrevc('Right', 'Select' , select , & ncv , workl(iuptri), ldq , & vl , 1 , workl(invsub), & ldq , ncv , outncv , & workev , rwork , ierr) c if (ierr .ne. 0) then info = -9 go to 9000 end if c c %------------------------------------------------% c | Scale the returning eigenvectors so that their | c | Euclidean norms are all one. LAPACK subroutine | c | ctrevc returns each eigenvector normalized so | c | that the element of largest magnitude has | c | magnitude 1. | c %------------------------------------------------% c do 40 j=1, nconv rtemp = scnrm2(ncv, workl(invsub+(j-1)*ldq), 1) rtemp = real(one) / rtemp call csscal ( ncv, rtemp, & workl(invsub+(j-1)*ldq), 1 ) c c %------------------------------------------% c | Ritz estimates can be obtained by taking | c | the inner product of the last row of the | c | Schur basis of H with eigenvectors of T. | c | Note that the eigenvector matrix of T is | c | upper triangular, thus the length of the | c | inner product can be set to j. | c %------------------------------------------% c workev(j) = cdotc(j, workl(ihbds), 1, & workl(invsub+(j-1)*ldq), 1) 40 continue c if (msglvl .gt. 2) then call ccopy(nconv, workl(invsub+ncv-1), ldq, & workl(ihbds), 1) call cvout (logfil, nconv, workl(ihbds), ndigit, & '_neupd: Last row of the eigenvector matrix for T') if (msglvl .gt. 3) then call cmout(logfil , ncv, ncv , & workl(invsub), ldq, ndigit, & '_neupd: The eigenvector matrix for T') end if end if c c %---------------------------------------% c | Copy Ritz estimates into workl(ihbds) | c %---------------------------------------% c call ccopy(nconv, workev, 1, workl(ihbds), 1) c c %----------------------------------------------% c | The eigenvector matrix Q of T is triangular. | c | Form Z*Q. | c %----------------------------------------------% c call ctrmm('Right' , 'Upper' , 'No transpose', & 'Non-unit', n , nconv , & one , workl(invsub), ldq , & z , ldz) end if c else c c %--------------------------------------------------% c | An approximate invariant subspace is not needed. | c | Place the Ritz values computed CNAUPD into D. | c %--------------------------------------------------% c call ccopy(nconv, workl(ritz), 1, d, 1) call ccopy(nconv, workl(ritz), 1, workl(iheig), 1) call ccopy(nconv, workl(bounds), 1, workl(ihbds), 1) c end if c c %------------------------------------------------% c | Transform the Ritz values and possibly vectors | c | and corresponding error bounds of OP to those | c | of A*x = lambda*B*x. | c %------------------------------------------------% c if (type .eq. 'REGULR') then c if (rvec) & call cscal(ncv, rnorm, workl(ihbds), 1) c else c c %---------------------------------------% c | A spectral transformation was used. | c | * Determine the Ritz estimates of the | c | Ritz values in the original system. | c %---------------------------------------% c if (rvec) & call cscal(ncv, rnorm, workl(ihbds), 1) c do 50 k=1, ncv temp = workl(iheig+k-1) workl(ihbds+k-1) = workl(ihbds+k-1) / temp / temp 50 continue c end if c c %-----------------------------------------------------------% c | * Transform the Ritz values back to the original system. | c | For TYPE = 'SHIFTI' the transformation is | c | lambda = 1/theta + sigma | c | NOTES: | c | *The Ritz vectors are not affected by the transformation. | c %-----------------------------------------------------------% c if (type .eq. 'SHIFTI') then do 60 k=1, nconv d(k) = one / workl(iheig+k-1) + sigma 60 continue end if c if (type .ne. 'REGULR' .and. msglvl .gt. 1) then call cvout (logfil, nconv, d, ndigit, & '_neupd: Untransformed Ritz values.') call cvout (logfil, nconv, workl(ihbds), ndigit, & '_neupd: Ritz estimates of the untransformed Ritz values.') else if ( msglvl .gt. 1) then call cvout (logfil, nconv, d, ndigit, & '_neupd: Converged Ritz values.') call cvout (logfil, nconv, workl(ihbds), ndigit, & '_neupd: Associated Ritz estimates.') end if c c %-------------------------------------------------% c | Eigenvector Purification step. Formally perform | c | one of inverse subspace iteration. Only used | c | for MODE = 3. See reference 3. | c %-------------------------------------------------% c if (rvec .and. howmny .eq. 'A' .and. type .eq. 'SHIFTI') then c c %------------------------------------------------% c | Purify the computed Ritz vectors by adding a | c | little bit of the residual vector: | c | T | c | resid(:)*( e s ) / theta | c | NCV | c | where H s = s theta. | c %------------------------------------------------% c do 100 j=1, nconv if (workl(iheig+j-1) .ne. zero) then workev(j) = workl(invsub+(j-1)*ldq+ncv-1) / & workl(iheig+j-1) endif 100 continue c %---------------------------------------% c | Perform a rank one update to Z and | c | purify all the Ritz vectors together. | c %---------------------------------------% c call cgeru (n, nconv, one, resid, 1, workev, 1, z, ldz) c end if c 9000 continue c return c c %---------------% c | End of cneupd| c %---------------% c end arpack-0.92.1/SRC/sstats.f0000644000175000017500000000221610776001577012117 00000000000000c c\SCCS Information: @(#) c FILE: stats.F SID: 2.1 DATE OF SID: 4/19/96 RELEASE: 2 c %---------------------------------------------% c | Initialize statistic and timing information | c | for symmetric Arnoldi code. | c %---------------------------------------------% subroutine sstats c %--------------------------------% c | See stat.doc for documentation | c %--------------------------------% include 'stat.h' c %-----------------------% c | Executable Statements | c %-----------------------% nopx = 0 nbx = 0 nrorth = 0 nitref = 0 nrstrt = 0 tsaupd = 0.0E+0 tsaup2 = 0.0E+0 tsaitr = 0.0E+0 tseigt = 0.0E+0 tsgets = 0.0E+0 tsapps = 0.0E+0 tsconv = 0.0E+0 titref = 0.0E+0 tgetv0 = 0.0E+0 trvec = 0.0E+0 c %----------------------------------------------------% c | User time including reverse communication overhead | c %----------------------------------------------------% tmvopx = 0.0E+0 tmvbx = 0.0E+0 return c c End of sstats c end arpack-0.92.1/SRC/dsortr.f0000644000175000017500000001235410776001577012117 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: dsortr c c\Description: c Sort the array X1 in the order specified by WHICH and optionally c applies the permutation to the array X2. c c\Usage: c call dsortr c ( WHICH, APPLY, N, X1, X2 ) c c\Arguments c WHICH Character*2. (Input) c 'LM' -> X1 is sorted into increasing order of magnitude. c 'SM' -> X1 is sorted into decreasing order of magnitude. c 'LA' -> X1 is sorted into increasing order of algebraic. c 'SA' -> X1 is sorted into decreasing order of algebraic. c c APPLY Logical. (Input) c APPLY = .TRUE. -> apply the sorted order to X2. c APPLY = .FALSE. -> do not apply the sorted order to X2. c c N Integer. (INPUT) c Size of the arrays. c c X1 Double precision array of length N. (INPUT/OUTPUT) c The array to be sorted. c c X2 Double precision array of length N. (INPUT/OUTPUT) c Only referenced if APPLY = .TRUE. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c 12/16/93: Version ' 2.1'. c Adapted from the sort routine in LANSO. c c\SCCS Information: @(#) c FILE: sortr.F SID: 2.3 DATE OF SID: 4/19/96 RELEASE: 2 c c\EndLib c c----------------------------------------------------------------------- c subroutine dsortr (which, apply, n, x1, x2) c c %------------------% c | Scalar Arguments | c %------------------% c character*2 which logical apply integer n c c %-----------------% c | Array Arguments | c %-----------------% c Double precision & x1(0:n-1), x2(0:n-1) c c %---------------% c | Local Scalars | c %---------------% c integer i, igap, j Double precision & temp c c %-----------------------% c | Executable Statements | c %-----------------------% c igap = n / 2 c if (which .eq. 'SA') then c c X1 is sorted into decreasing order of algebraic. c 10 continue if (igap .eq. 0) go to 9000 do 30 i = igap, n-1 j = i-igap 20 continue c if (j.lt.0) go to 30 c if (x1(j).lt.x1(j+igap)) then temp = x1(j) x1(j) = x1(j+igap) x1(j+igap) = temp if (apply) then temp = x2(j) x2(j) = x2(j+igap) x2(j+igap) = temp end if else go to 30 endif j = j-igap go to 20 30 continue igap = igap / 2 go to 10 c else if (which .eq. 'SM') then c c X1 is sorted into decreasing order of magnitude. c 40 continue if (igap .eq. 0) go to 9000 do 60 i = igap, n-1 j = i-igap 50 continue c if (j.lt.0) go to 60 c if (abs(x1(j)).lt.abs(x1(j+igap))) then temp = x1(j) x1(j) = x1(j+igap) x1(j+igap) = temp if (apply) then temp = x2(j) x2(j) = x2(j+igap) x2(j+igap) = temp end if else go to 60 endif j = j-igap go to 50 60 continue igap = igap / 2 go to 40 c else if (which .eq. 'LA') then c c X1 is sorted into increasing order of algebraic. c 70 continue if (igap .eq. 0) go to 9000 do 90 i = igap, n-1 j = i-igap 80 continue c if (j.lt.0) go to 90 c if (x1(j).gt.x1(j+igap)) then temp = x1(j) x1(j) = x1(j+igap) x1(j+igap) = temp if (apply) then temp = x2(j) x2(j) = x2(j+igap) x2(j+igap) = temp end if else go to 90 endif j = j-igap go to 80 90 continue igap = igap / 2 go to 70 c else if (which .eq. 'LM') then c c X1 is sorted into increasing order of magnitude. c 100 continue if (igap .eq. 0) go to 9000 do 120 i = igap, n-1 j = i-igap 110 continue c if (j.lt.0) go to 120 c if (abs(x1(j)).gt.abs(x1(j+igap))) then temp = x1(j) x1(j) = x1(j+igap) x1(j+igap) = temp if (apply) then temp = x2(j) x2(j) = x2(j+igap) x2(j+igap) = temp end if else go to 120 endif j = j-igap go to 110 120 continue igap = igap / 2 go to 100 end if c 9000 continue return c c %---------------% c | End of dsortr | c %---------------% c end arpack-0.92.1/SRC/ssgets.f0000644000175000017500000001634110776001577012112 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: ssgets c c\Description: c Given the eigenvalues of the symmetric tridiagonal matrix H, c computes the NP shifts AMU that are zeros of the polynomial of c degree NP which filters out components of the unwanted eigenvectors c corresponding to the AMU's based on some given criteria. c c NOTE: This is called even in the case of user specified shifts in c order to sort the eigenvalues, and error bounds of H for later use. c c\Usage: c call ssgets c ( ISHIFT, WHICH, KEV, NP, RITZ, BOUNDS, SHIFTS ) c c\Arguments c ISHIFT Integer. (INPUT) c Method for selecting the implicit shifts at each iteration. c ISHIFT = 0: user specified shifts c ISHIFT = 1: exact shift with respect to the matrix H. c c WHICH Character*2. (INPUT) c Shift selection criteria. c 'LM' -> KEV eigenvalues of largest magnitude are retained. c 'SM' -> KEV eigenvalues of smallest magnitude are retained. c 'LA' -> KEV eigenvalues of largest value are retained. c 'SA' -> KEV eigenvalues of smallest value are retained. c 'BE' -> KEV eigenvalues, half from each end of the spectrum. c If KEV is odd, compute one more from the high end. c c KEV Integer. (INPUT) c KEV+NP is the size of the matrix H. c c NP Integer. (INPUT) c Number of implicit shifts to be computed. c c RITZ Real array of length KEV+NP. (INPUT/OUTPUT) c On INPUT, RITZ contains the eigenvalues of H. c On OUTPUT, RITZ are sorted so that the unwanted eigenvalues c are in the first NP locations and the wanted part is in c the last KEV locations. When exact shifts are selected, the c unwanted part corresponds to the shifts to be applied. c c BOUNDS Real array of length KEV+NP. (INPUT/OUTPUT) c Error bounds corresponding to the ordering in RITZ. c c SHIFTS Real array of length NP. (INPUT/OUTPUT) c On INPUT: contains the user specified shifts if ISHIFT = 0. c On OUTPUT: contains the shifts sorted into decreasing order c of magnitude with respect to the Ritz estimates contained in c BOUNDS. If ISHIFT = 0, SHIFTS is not modified on exit. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx real c c\Routines called: c ssortr ARPACK utility sorting routine. c ivout ARPACK utility routine that prints integers. c arscnd ARPACK utility routine for timing. c svout ARPACK utility routine that prints vectors. c scopy Level 1 BLAS that copies one vector to another. c sswap Level 1 BLAS that swaps the contents of two vectors. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c xx/xx/93: Version ' 2.1' c c\SCCS Information: @(#) c FILE: sgets.F SID: 2.4 DATE OF SID: 4/19/96 RELEASE: 2 c c\Remarks c c\EndLib c c----------------------------------------------------------------------- c subroutine ssgets ( ishift, which, kev, np, ritz, bounds, shifts ) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character*2 which integer ishift, kev, np c c %-----------------% c | Array Arguments | c %-----------------% c Real & bounds(kev+np), ritz(kev+np), shifts(np) c c %------------% c | Parameters | c %------------% c Real & one, zero parameter (one = 1.0E+0, zero = 0.0E+0) c c %---------------% c | Local Scalars | c %---------------% c integer kevd2, msglvl c c %----------------------% c | External Subroutines | c %----------------------% c external sswap, scopy, ssortr, arscnd c c %---------------------% c | Intrinsic Functions | c %---------------------% c intrinsic max, min c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call arscnd (t0) msglvl = msgets c if (which .eq. 'BE') then c c %-----------------------------------------------------% c | Both ends of the spectrum are requested. | c | Sort the eigenvalues into algebraically increasing | c | order first then swap high end of the spectrum next | c | to low end in appropriate locations. | c | NOTE: when np < floor(kev/2) be careful not to swap | c | overlapping locations. | c %-----------------------------------------------------% c call ssortr ('LA', .true., kev+np, ritz, bounds) kevd2 = kev / 2 if ( kev .gt. 1 ) then call sswap ( min(kevd2,np), ritz, 1, & ritz( max(kevd2,np)+1 ), 1) call sswap ( min(kevd2,np), bounds, 1, & bounds( max(kevd2,np)+1 ), 1) end if c else c c %----------------------------------------------------% c | LM, SM, LA, SA case. | c | Sort the eigenvalues of H into the desired order | c | and apply the resulting order to BOUNDS. | c | The eigenvalues are sorted so that the wanted part | c | are always in the last KEV locations. | c %----------------------------------------------------% c call ssortr (which, .true., kev+np, ritz, bounds) end if c if (ishift .eq. 1 .and. np .gt. 0) then c c %-------------------------------------------------------% c | Sort the unwanted Ritz values used as shifts so that | c | the ones with largest Ritz estimates are first. | c | This will tend to minimize the effects of the | c | forward instability of the iteration when the shifts | c | are applied in subroutine ssapps. | c %-------------------------------------------------------% c call ssortr ('SM', .true., np, bounds, ritz) call scopy (np, ritz, 1, shifts, 1) end if c call arscnd (t1) tsgets = tsgets + (t1 - t0) c if (msglvl .gt. 0) then call ivout (logfil, 1, kev, ndigit, '_sgets: KEV is') call ivout (logfil, 1, np, ndigit, '_sgets: NP is') call svout (logfil, kev+np, ritz, ndigit, & '_sgets: Eigenvalues of current H matrix') call svout (logfil, kev+np, bounds, ndigit, & '_sgets: Associated Ritz estimates') end if c return c c %---------------% c | End of ssgets | c %---------------% c end arpack-0.92.1/SRC/sgetv0.f0000644000175000017500000003146610776001577012017 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: sgetv0 c c\Description: c Generate a random initial residual vector for the Arnoldi process. c Force the residual vector to be in the range of the operator OP. c c\Usage: c call sgetv0 c ( IDO, BMAT, ITRY, INITV, N, J, V, LDV, RESID, RNORM, c IPNTR, WORKD, IERR ) c c\Arguments c IDO Integer. (INPUT/OUTPUT) c Reverse communication flag. IDO must be zero on the first c call to sgetv0. c ------------------------------------------------------------- c IDO = 0: first call to the reverse communication interface c IDO = -1: compute Y = OP * X where c IPNTR(1) is the pointer into WORKD for X, c IPNTR(2) is the pointer into WORKD for Y. c This is for the initialization phase to force the c starting vector into the range of OP. c IDO = 2: compute Y = B * X where c IPNTR(1) is the pointer into WORKD for X, c IPNTR(2) is the pointer into WORKD for Y. c IDO = 99: done c ------------------------------------------------------------- c c BMAT Character*1. (INPUT) c BMAT specifies the type of the matrix B in the (generalized) c eigenvalue problem A*x = lambda*B*x. c B = 'I' -> standard eigenvalue problem A*x = lambda*x c B = 'G' -> generalized eigenvalue problem A*x = lambda*B*x c c ITRY Integer. (INPUT) c ITRY counts the number of times that sgetv0 is called. c It should be set to 1 on the initial call to sgetv0. c c INITV Logical variable. (INPUT) c .TRUE. => the initial residual vector is given in RESID. c .FALSE. => generate a random initial residual vector. c c N Integer. (INPUT) c Dimension of the problem. c c J Integer. (INPUT) c Index of the residual vector to be generated, with respect to c the Arnoldi process. J > 1 in case of a "restart". c c V Real N by J array. (INPUT) c The first J-1 columns of V contain the current Arnoldi basis c if this is a "restart". c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling c program. c c RESID Real array of length N. (INPUT/OUTPUT) c Initial residual vector to be generated. If RESID is c provided, force RESID into the range of the operator OP. c c RNORM Real scalar. (OUTPUT) c B-norm of the generated residual. c c IPNTR Integer array of length 3. (OUTPUT) c c WORKD Real work array of length 2*N. (REVERSE COMMUNICATION). c On exit, WORK(1:N) = B*RESID to be used in SSAITR. c c IERR Integer. (OUTPUT) c = 0: Normal exit. c = -1: Cannot generate a nontrivial restarted residual vector c in the range of the operator OP. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx real c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly c Restarted Arnoldi Iteration", Rice University Technical Report c TR95-13, Department of Computational and Applied Mathematics. c c\Routines called: c arscnd ARPACK utility routine for timing. c svout ARPACK utility routine for vector output. c slarnv LAPACK routine for generating a random vector. c sgemv Level 2 BLAS routine for matrix vector multiplication. c scopy Level 1 BLAS that copies one vector to another. c sdot Level 1 BLAS that computes the scalar product of two vectors. c snrm2 Level 1 BLAS that computes the norm of a vector. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: getv0.F SID: 2.7 DATE OF SID: 04/07/99 RELEASE: 2 c c\EndLib c c----------------------------------------------------------------------- c subroutine sgetv0 & ( ido, bmat, itry, initv, n, j, v, ldv, resid, rnorm, & ipntr, workd, ierr ) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character bmat*1 logical initv integer ido, ierr, itry, j, ldv, n Real & rnorm c c %-----------------% c | Array Arguments | c %-----------------% c integer ipntr(3) Real & resid(n), v(ldv,j), workd(2*n) c c %------------% c | Parameters | c %------------% c Real & one, zero parameter (one = 1.0E+0, zero = 0.0E+0) c c %------------------------% c | Local Scalars & Arrays | c %------------------------% c logical first, inits, orth integer idist, iseed(4), iter, msglvl, jj Real & rnorm0 save first, iseed, inits, iter, msglvl, orth, rnorm0 c c %----------------------% c | External Subroutines | c %----------------------% c external slarnv, svout, scopy, sgemv, arscnd c c %--------------------% c | External Functions | c %--------------------% c Real & sdot, snrm2 external sdot, snrm2 c c %---------------------% c | Intrinsic Functions | c %---------------------% c intrinsic abs, sqrt c c %-----------------% c | Data Statements | c %-----------------% c data inits /.true./ c c %-----------------------% c | Executable Statements | c %-----------------------% c c c %-----------------------------------% c | Initialize the seed of the LAPACK | c | random number generator | c %-----------------------------------% c if (inits) then iseed(1) = 1 iseed(2) = 3 iseed(3) = 5 iseed(4) = 7 inits = .false. end if c if (ido .eq. 0) then c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call arscnd (t0) msglvl = mgetv0 c ierr = 0 iter = 0 first = .FALSE. orth = .FALSE. c c %-----------------------------------------------------% c | Possibly generate a random starting vector in RESID | c | Use a LAPACK random number generator used by the | c | matrix generation routines. | c | idist = 1: uniform (0,1) distribution; | c | idist = 2: uniform (-1,1) distribution; | c | idist = 3: normal (0,1) distribution; | c %-----------------------------------------------------% c if (.not.initv) then idist = 2 call slarnv (idist, iseed, n, resid) end if c c %----------------------------------------------------------% c | Force the starting vector into the range of OP to handle | c | the generalized problem when B is possibly (singular). | c %----------------------------------------------------------% c call arscnd (t2) if (bmat .eq. 'G') then nopx = nopx + 1 ipntr(1) = 1 ipntr(2) = n + 1 call scopy (n, resid, 1, workd, 1) ido = -1 go to 9000 end if end if c c %-----------------------------------------% c | Back from computing OP*(initial-vector) | c %-----------------------------------------% c if (first) go to 20 c c %-----------------------------------------------% c | Back from computing B*(orthogonalized-vector) | c %-----------------------------------------------% c if (orth) go to 40 c if (bmat .eq. 'G') then call arscnd (t3) tmvopx = tmvopx + (t3 - t2) end if c c %------------------------------------------------------% c | Starting vector is now in the range of OP; r = OP*r; | c | Compute B-norm of starting vector. | c %------------------------------------------------------% c call arscnd (t2) first = .TRUE. if (bmat .eq. 'G') then nbx = nbx + 1 call scopy (n, workd(n+1), 1, resid, 1) ipntr(1) = n + 1 ipntr(2) = 1 ido = 2 go to 9000 else if (bmat .eq. 'I') then call scopy (n, resid, 1, workd, 1) end if c 20 continue c if (bmat .eq. 'G') then call arscnd (t3) tmvbx = tmvbx + (t3 - t2) end if c first = .FALSE. if (bmat .eq. 'G') then rnorm0 = sdot (n, resid, 1, workd, 1) rnorm0 = sqrt(abs(rnorm0)) else if (bmat .eq. 'I') then rnorm0 = snrm2(n, resid, 1) end if rnorm = rnorm0 c c %---------------------------------------------% c | Exit if this is the very first Arnoldi step | c %---------------------------------------------% c if (j .eq. 1) go to 50 c c %---------------------------------------------------------------- c | Otherwise need to B-orthogonalize the starting vector against | c | the current Arnoldi basis using Gram-Schmidt with iter. ref. | c | This is the case where an invariant subspace is encountered | c | in the middle of the Arnoldi factorization. | c | | c | s = V^{T}*B*r; r = r - V*s; | c | | c | Stopping criteria used for iter. ref. is discussed in | c | Parlett's book, page 107 and in Gragg & Reichel TOMS paper. | c %---------------------------------------------------------------% c orth = .TRUE. 30 continue c call sgemv ('T', n, j-1, one, v, ldv, workd, 1, & zero, workd(n+1), 1) call sgemv ('N', n, j-1, -one, v, ldv, workd(n+1), 1, & one, resid, 1) c c %----------------------------------------------------------% c | Compute the B-norm of the orthogonalized starting vector | c %----------------------------------------------------------% c call arscnd (t2) if (bmat .eq. 'G') then nbx = nbx + 1 call scopy (n, resid, 1, workd(n+1), 1) ipntr(1) = n + 1 ipntr(2) = 1 ido = 2 go to 9000 else if (bmat .eq. 'I') then call scopy (n, resid, 1, workd, 1) end if c 40 continue c if (bmat .eq. 'G') then call arscnd (t3) tmvbx = tmvbx + (t3 - t2) end if c if (bmat .eq. 'G') then rnorm = sdot (n, resid, 1, workd, 1) rnorm = sqrt(abs(rnorm)) else if (bmat .eq. 'I') then rnorm = snrm2(n, resid, 1) end if c c %--------------------------------------% c | Check for further orthogonalization. | c %--------------------------------------% c if (msglvl .gt. 2) then call svout (logfil, 1, rnorm0, ndigit, & '_getv0: re-orthonalization ; rnorm0 is') call svout (logfil, 1, rnorm, ndigit, & '_getv0: re-orthonalization ; rnorm is') end if c if (rnorm .gt. 0.717*rnorm0) go to 50 c iter = iter + 1 if (iter .le. 5) then c c %-----------------------------------% c | Perform iterative refinement step | c %-----------------------------------% c rnorm0 = rnorm go to 30 else c c %------------------------------------% c | Iterative refinement step "failed" | c %------------------------------------% c do 45 jj = 1, n resid(jj) = zero 45 continue rnorm = zero ierr = -1 end if c 50 continue c if (msglvl .gt. 0) then call svout (logfil, 1, rnorm, ndigit, & '_getv0: B-norm of initial / restarted starting vector') end if if (msglvl .gt. 3) then call svout (logfil, n, resid, ndigit, & '_getv0: initial / restarted starting vector') end if ido = 99 c call arscnd (t1) tgetv0 = tgetv0 + (t1 - t0) c 9000 continue return c c %---------------% c | End of sgetv0 | c %---------------% c end arpack-0.92.1/SRC/dnapps.f0000644000175000017500000005572110776001577012074 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: dnapps c c\Description: c Given the Arnoldi factorization c c A*V_{k} - V_{k}*H_{k} = r_{k+p}*e_{k+p}^T, c c apply NP implicit shifts resulting in c c A*(V_{k}*Q) - (V_{k}*Q)*(Q^T* H_{k}*Q) = r_{k+p}*e_{k+p}^T * Q c c where Q is an orthogonal matrix which is the product of rotations c and reflections resulting from the NP bulge chage sweeps. c The updated Arnoldi factorization becomes: c c A*VNEW_{k} - VNEW_{k}*HNEW_{k} = rnew_{k}*e_{k}^T. c c\Usage: c call dnapps c ( N, KEV, NP, SHIFTR, SHIFTI, V, LDV, H, LDH, RESID, Q, LDQ, c WORKL, WORKD ) c c\Arguments c N Integer. (INPUT) c Problem size, i.e. size of matrix A. c c KEV Integer. (INPUT/OUTPUT) c KEV+NP is the size of the input matrix H. c KEV is the size of the updated matrix HNEW. KEV is only c updated on ouput when fewer than NP shifts are applied in c order to keep the conjugate pair together. c c NP Integer. (INPUT) c Number of implicit shifts to be applied. c c SHIFTR, Double precision array of length NP. (INPUT) c SHIFTI Real and imaginary part of the shifts to be applied. c Upon, entry to dnapps, the shifts must be sorted so that the c conjugate pairs are in consecutive locations. c c V Double precision N by (KEV+NP) array. (INPUT/OUTPUT) c On INPUT, V contains the current KEV+NP Arnoldi vectors. c On OUTPUT, V contains the updated KEV Arnoldi vectors c in the first KEV columns of V. c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling c program. c c H Double precision (KEV+NP) by (KEV+NP) array. (INPUT/OUTPUT) c On INPUT, H contains the current KEV+NP by KEV+NP upper c Hessenber matrix of the Arnoldi factorization. c On OUTPUT, H contains the updated KEV by KEV upper Hessenberg c matrix in the KEV leading submatrix. c c LDH Integer. (INPUT) c Leading dimension of H exactly as declared in the calling c program. c c RESID Double precision array of length N. (INPUT/OUTPUT) c On INPUT, RESID contains the the residual vector r_{k+p}. c On OUTPUT, RESID is the update residual vector rnew_{k} c in the first KEV locations. c c Q Double precision KEV+NP by KEV+NP work array. (WORKSPACE) c Work array used to accumulate the rotations and reflections c during the bulge chase sweep. c c LDQ Integer. (INPUT) c Leading dimension of Q exactly as declared in the calling c program. c c WORKL Double precision work array of length (KEV+NP). (WORKSPACE) c Private (replicated) array on each PE or array allocated on c the front end. c c WORKD Double precision work array of length 2*N. (WORKSPACE) c Distributed array used in the application of the accumulated c orthogonal matrix Q. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx real c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c c\Routines called: c ivout ARPACK utility routine that prints integers. c arscnd ARPACK utility routine for timing. c dmout ARPACK utility routine that prints matrices. c dvout ARPACK utility routine that prints vectors. c dlabad LAPACK routine that computes machine constants. c dlacpy LAPACK matrix copy routine. c dlamch LAPACK routine that determines machine constants. c dlanhs LAPACK routine that computes various norms of a matrix. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c dlarf LAPACK routine that applies Householder reflection to c a matrix. c dlarfg LAPACK Householder reflection construction routine. c dlartg LAPACK Givens rotation construction routine. c dlaset LAPACK matrix initialization routine. c dgemv Level 2 BLAS routine for matrix vector multiplication. c daxpy Level 1 BLAS that computes a vector triad. c dcopy Level 1 BLAS that copies one vector to another . c dscal Level 1 BLAS that scales a vector. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c xx/xx/92: Version ' 2.4' c c\SCCS Information: @(#) c FILE: napps.F SID: 2.4 DATE OF SID: 3/28/97 RELEASE: 2 c c\Remarks c 1. In this version, each shift is applied to all the sublocks of c the Hessenberg matrix H and not just to the submatrix that it c comes from. Deflation as in LAPACK routine dlahqr (QR algorithm c for upper Hessenberg matrices ) is used. c The subdiagonals of H are enforced to be non-negative. c c\EndLib c c----------------------------------------------------------------------- c subroutine dnapps & ( n, kev, np, shiftr, shifti, v, ldv, h, ldh, resid, q, ldq, & workl, workd ) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c integer kev, ldh, ldq, ldv, n, np c c %-----------------% c | Array Arguments | c %-----------------% c Double precision & h(ldh,kev+np), resid(n), shifti(np), shiftr(np), & v(ldv,kev+np), q(ldq,kev+np), workd(2*n), workl(kev+np) c c %------------% c | Parameters | c %------------% c Double precision & one, zero parameter (one = 1.0D+0, zero = 0.0D+0) c c %------------------------% c | Local Scalars & Arrays | c %------------------------% c integer i, iend, ir, istart, j, jj, kplusp, msglvl, nr logical cconj, first Double precision & c, f, g, h11, h12, h21, h22, h32, ovfl, r, s, sigmai, & sigmar, smlnum, ulp, unfl, u(3), t, tau, tst1 save first, ovfl, smlnum, ulp, unfl c c %----------------------% c | External Subroutines | c %----------------------% c external daxpy, dcopy, dscal, dlacpy, dlarfg, dlarf, & dlaset, dlabad, arscnd, dlartg c c %--------------------% c | External Functions | c %--------------------% c Double precision & dlamch, dlanhs, dlapy2 external dlamch, dlanhs, dlapy2 c c %----------------------% c | Intrinsics Functions | c %----------------------% c intrinsic abs, max, min c c %----------------% c | Data statments | c %----------------% c data first / .true. / c c %-----------------------% c | Executable Statements | c %-----------------------% c if (first) then c c %-----------------------------------------------% c | Set machine-dependent constants for the | c | stopping criterion. If norm(H) <= sqrt(OVFL), | c | overflow should not occur. | c | REFERENCE: LAPACK subroutine dlahqr | c %-----------------------------------------------% c unfl = dlamch( 'safe minimum' ) ovfl = one / unfl call dlabad( unfl, ovfl ) ulp = dlamch( 'precision' ) smlnum = unfl*( n / ulp ) first = .false. end if c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call arscnd (t0) msglvl = mnapps kplusp = kev + np c c %--------------------------------------------% c | Initialize Q to the identity to accumulate | c | the rotations and reflections | c %--------------------------------------------% c call dlaset ('All', kplusp, kplusp, zero, one, q, ldq) c c %----------------------------------------------% c | Quick return if there are no shifts to apply | c %----------------------------------------------% c if (np .eq. 0) go to 9000 c c %----------------------------------------------% c | Chase the bulge with the application of each | c | implicit shift. Each shift is applied to the | c | whole matrix including each block. | c %----------------------------------------------% c cconj = .false. do 110 jj = 1, np sigmar = shiftr(jj) sigmai = shifti(jj) c if (msglvl .gt. 2 ) then call ivout (logfil, 1, jj, ndigit, & '_napps: shift number.') call dvout (logfil, 1, sigmar, ndigit, & '_napps: The real part of the shift ') call dvout (logfil, 1, sigmai, ndigit, & '_napps: The imaginary part of the shift ') end if c c %-------------------------------------------------% c | The following set of conditionals is necessary | c | in order that complex conjugate pairs of shifts | c | are applied together or not at all. | c %-------------------------------------------------% c if ( cconj ) then c c %-----------------------------------------% c | cconj = .true. means the previous shift | c | had non-zero imaginary part. | c %-----------------------------------------% c cconj = .false. go to 110 else if ( jj .lt. np .and. abs( sigmai ) .gt. zero ) then c c %------------------------------------% c | Start of a complex conjugate pair. | c %------------------------------------% c cconj = .true. else if ( jj .eq. np .and. abs( sigmai ) .gt. zero ) then c c %----------------------------------------------% c | The last shift has a nonzero imaginary part. | c | Don't apply it; thus the order of the | c | compressed H is order KEV+1 since only np-1 | c | were applied. | c %----------------------------------------------% c kev = kev + 1 go to 110 end if istart = 1 20 continue c c %--------------------------------------------------% c | if sigmai = 0 then | c | Apply the jj-th shift ... | c | else | c | Apply the jj-th and (jj+1)-th together ... | c | (Note that jj < np at this point in the code) | c | end | c | to the current block of H. The next do loop | c | determines the current block ; | c %--------------------------------------------------% c do 30 i = istart, kplusp-1 c c %----------------------------------------% c | Check for splitting and deflation. Use | c | a standard test as in the QR algorithm | c | REFERENCE: LAPACK subroutine dlahqr | c %----------------------------------------% c tst1 = abs( h( i, i ) ) + abs( h( i+1, i+1 ) ) if( tst1.eq.zero ) & tst1 = dlanhs( '1', kplusp-jj+1, h, ldh, workl ) if( abs( h( i+1,i ) ).le.max( ulp*tst1, smlnum ) ) then if (msglvl .gt. 0) then call ivout (logfil, 1, i, ndigit, & '_napps: matrix splitting at row/column no.') call ivout (logfil, 1, jj, ndigit, & '_napps: matrix splitting with shift number.') call dvout (logfil, 1, h(i+1,i), ndigit, & '_napps: off diagonal element.') end if iend = i h(i+1,i) = zero go to 40 end if 30 continue iend = kplusp 40 continue c if (msglvl .gt. 2) then call ivout (logfil, 1, istart, ndigit, & '_napps: Start of current block ') call ivout (logfil, 1, iend, ndigit, & '_napps: End of current block ') end if c c %------------------------------------------------% c | No reason to apply a shift to block of order 1 | c %------------------------------------------------% c if ( istart .eq. iend ) go to 100 c c %------------------------------------------------------% c | If istart + 1 = iend then no reason to apply a | c | complex conjugate pair of shifts on a 2 by 2 matrix. | c %------------------------------------------------------% c if ( istart + 1 .eq. iend .and. abs( sigmai ) .gt. zero ) & go to 100 c h11 = h(istart,istart) h21 = h(istart+1,istart) if ( abs( sigmai ) .le. zero ) then c c %---------------------------------------------% c | Real-valued shift ==> apply single shift QR | c %---------------------------------------------% c f = h11 - sigmar g = h21 c do 80 i = istart, iend-1 c c %-----------------------------------------------------% c | Contruct the plane rotation G to zero out the bulge | c %-----------------------------------------------------% c call dlartg (f, g, c, s, r) if (i .gt. istart) then c c %-------------------------------------------% c | The following ensures that h(1:iend-1,1), | c | the first iend-2 off diagonal of elements | c | H, remain non negative. | c %-------------------------------------------% c if (r .lt. zero) then r = -r c = -c s = -s end if h(i,i-1) = r h(i+1,i-1) = zero end if c c %---------------------------------------------% c | Apply rotation to the left of H; H <- G'*H | c %---------------------------------------------% c do 50 j = i, kplusp t = c*h(i,j) + s*h(i+1,j) h(i+1,j) = -s*h(i,j) + c*h(i+1,j) h(i,j) = t 50 continue c c %---------------------------------------------% c | Apply rotation to the right of H; H <- H*G | c %---------------------------------------------% c do 60 j = 1, min(i+2,iend) t = c*h(j,i) + s*h(j,i+1) h(j,i+1) = -s*h(j,i) + c*h(j,i+1) h(j,i) = t 60 continue c c %----------------------------------------------------% c | Accumulate the rotation in the matrix Q; Q <- Q*G | c %----------------------------------------------------% c do 70 j = 1, min( i+jj, kplusp ) t = c*q(j,i) + s*q(j,i+1) q(j,i+1) = - s*q(j,i) + c*q(j,i+1) q(j,i) = t 70 continue c c %---------------------------% c | Prepare for next rotation | c %---------------------------% c if (i .lt. iend-1) then f = h(i+1,i) g = h(i+2,i) end if 80 continue c c %-----------------------------------% c | Finished applying the real shift. | c %-----------------------------------% c else c c %----------------------------------------------------% c | Complex conjugate shifts ==> apply double shift QR | c %----------------------------------------------------% c h12 = h(istart,istart+1) h22 = h(istart+1,istart+1) h32 = h(istart+2,istart+1) c c %---------------------------------------------------------% c | Compute 1st column of (H - shift*I)*(H - conj(shift)*I) | c %---------------------------------------------------------% c s = 2.0*sigmar t = dlapy2 ( sigmar, sigmai ) u(1) = ( h11 * (h11 - s) + t * t ) / h21 + h12 u(2) = h11 + h22 - s u(3) = h32 c do 90 i = istart, iend-1 c nr = min ( 3, iend-i+1 ) c c %-----------------------------------------------------% c | Construct Householder reflector G to zero out u(1). | c | G is of the form I - tau*( 1 u )' * ( 1 u' ). | c %-----------------------------------------------------% c call dlarfg ( nr, u(1), u(2), 1, tau ) c if (i .gt. istart) then h(i,i-1) = u(1) h(i+1,i-1) = zero if (i .lt. iend-1) h(i+2,i-1) = zero end if u(1) = one c c %--------------------------------------% c | Apply the reflector to the left of H | c %--------------------------------------% c call dlarf ('Left', nr, kplusp-i+1, u, 1, tau, & h(i,i), ldh, workl) c c %---------------------------------------% c | Apply the reflector to the right of H | c %---------------------------------------% c ir = min ( i+3, iend ) call dlarf ('Right', ir, nr, u, 1, tau, & h(1,i), ldh, workl) c c %-----------------------------------------------------% c | Accumulate the reflector in the matrix Q; Q <- Q*G | c %-----------------------------------------------------% c call dlarf ('Right', kplusp, nr, u, 1, tau, & q(1,i), ldq, workl) c c %----------------------------% c | Prepare for next reflector | c %----------------------------% c if (i .lt. iend-1) then u(1) = h(i+1,i) u(2) = h(i+2,i) if (i .lt. iend-2) u(3) = h(i+3,i) end if c 90 continue c c %--------------------------------------------% c | Finished applying a complex pair of shifts | c | to the current block | c %--------------------------------------------% c end if c 100 continue c c %---------------------------------------------------------% c | Apply the same shift to the next block if there is any. | c %---------------------------------------------------------% c istart = iend + 1 if (iend .lt. kplusp) go to 20 c c %---------------------------------------------% c | Loop back to the top to get the next shift. | c %---------------------------------------------% c 110 continue c c %--------------------------------------------------% c | Perform a similarity transformation that makes | c | sure that H will have non negative sub diagonals | c %--------------------------------------------------% c do 120 j=1,kev if ( h(j+1,j) .lt. zero ) then call dscal( kplusp-j+1, -one, h(j+1,j), ldh ) call dscal( min(j+2, kplusp), -one, h(1,j+1), 1 ) call dscal( min(j+np+1,kplusp), -one, q(1,j+1), 1 ) end if 120 continue c do 130 i = 1, kev c c %--------------------------------------------% c | Final check for splitting and deflation. | c | Use a standard test as in the QR algorithm | c | REFERENCE: LAPACK subroutine dlahqr | c %--------------------------------------------% c tst1 = abs( h( i, i ) ) + abs( h( i+1, i+1 ) ) if( tst1.eq.zero ) & tst1 = dlanhs( '1', kev, h, ldh, workl ) if( h( i+1,i ) .le. max( ulp*tst1, smlnum ) ) & h(i+1,i) = zero 130 continue c c %-------------------------------------------------% c | Compute the (kev+1)-st column of (V*Q) and | c | temporarily store the result in WORKD(N+1:2*N). | c | This is needed in the residual update since we | c | cannot GUARANTEE that the corresponding entry | c | of H would be zero as in exact arithmetic. | c %-------------------------------------------------% c if (h(kev+1,kev) .gt. zero) & call dgemv ('N', n, kplusp, one, v, ldv, q(1,kev+1), 1, zero, & workd(n+1), 1) c c %----------------------------------------------------------% c | Compute column 1 to kev of (V*Q) in backward order | c | taking advantage of the upper Hessenberg structure of Q. | c %----------------------------------------------------------% c do 140 i = 1, kev call dgemv ('N', n, kplusp-i+1, one, v, ldv, & q(1,kev-i+1), 1, zero, workd, 1) call dcopy (n, workd, 1, v(1,kplusp-i+1), 1) 140 continue c c %-------------------------------------------------% c | Move v(:,kplusp-kev+1:kplusp) into v(:,1:kev). | c %-------------------------------------------------% c call dlacpy ('A', n, kev, v(1,kplusp-kev+1), ldv, v, ldv) c c %--------------------------------------------------------------% c | Copy the (kev+1)-st column of (V*Q) in the appropriate place | c %--------------------------------------------------------------% c if (h(kev+1,kev) .gt. zero) & call dcopy (n, workd(n+1), 1, v(1,kev+1), 1) c c %-------------------------------------% c | Update the residual vector: | c | r <- sigmak*r + betak*v(:,kev+1) | c | where | c | sigmak = (e_{kplusp}'*Q)*e_{kev} | c | betak = e_{kev+1}'*H*e_{kev} | c %-------------------------------------% c call dscal (n, q(kplusp,kev), resid, 1) if (h(kev+1,kev) .gt. zero) & call daxpy (n, h(kev+1,kev), v(1,kev+1), 1, resid, 1) c if (msglvl .gt. 1) then call dvout (logfil, 1, q(kplusp,kev), ndigit, & '_napps: sigmak = (e_{kev+p}^T*Q)*e_{kev}') call dvout (logfil, 1, h(kev+1,kev), ndigit, & '_napps: betak = e_{kev+1}^T*H*e_{kev}') call ivout (logfil, 1, kev, ndigit, & '_napps: Order of the final Hessenberg matrix ') if (msglvl .gt. 2) then call dmout (logfil, kev, kev, h, ldh, ndigit, & '_napps: updated Hessenberg matrix H for next iteration') end if c end if c 9000 continue call arscnd (t1) tnapps = tnapps + (t1 - t0) c return c c %---------------% c | End of dnapps | c %---------------% c end arpack-0.92.1/SRC/dsaupd.f0000644000175000017500000007060710776001577012067 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: dsaupd c c\Description: c c Reverse communication interface for the Implicitly Restarted Arnoldi c Iteration. For symmetric problems this reduces to a variant of the Lanczos c method. This method has been designed to compute approximations to a c few eigenpairs of a linear operator OP that is real and symmetric c with respect to a real positive semi-definite symmetric matrix B, c i.e. c c B*OP = (OP`)*B. c c Another way to express this condition is c c < x,OPy > = < OPx,y > where < z,w > = z`Bw . c c In the standard eigenproblem B is the identity matrix. c ( A` denotes transpose of A) c c The computed approximate eigenvalues are called Ritz values and c the corresponding approximate eigenvectors are called Ritz vectors. c c dsaupd is usually called iteratively to solve one of the c following problems: c c Mode 1: A*x = lambda*x, A symmetric c ===> OP = A and B = I. c c Mode 2: A*x = lambda*M*x, A symmetric, M symmetric positive definite c ===> OP = inv[M]*A and B = M. c ===> (If M can be factored see remark 3 below) c c Mode 3: K*x = lambda*M*x, K symmetric, M symmetric positive semi-definite c ===> OP = (inv[K - sigma*M])*M and B = M. c ===> Shift-and-Invert mode c c Mode 4: K*x = lambda*KG*x, K symmetric positive semi-definite, c KG symmetric indefinite c ===> OP = (inv[K - sigma*KG])*K and B = K. c ===> Buckling mode c c Mode 5: A*x = lambda*M*x, A symmetric, M symmetric positive semi-definite c ===> OP = inv[A - sigma*M]*[A + sigma*M] and B = M. c ===> Cayley transformed mode c c NOTE: The action of w <- inv[A - sigma*M]*v or w <- inv[M]*v c should be accomplished either by a direct method c using a sparse matrix factorization and solving c c [A - sigma*M]*w = v or M*w = v, c c or through an iterative method for solving these c systems. If an iterative method is used, the c convergence test must be more stringent than c the accuracy requirements for the eigenvalue c approximations. c c\Usage: c call dsaupd c ( IDO, BMAT, N, WHICH, NEV, TOL, RESID, NCV, V, LDV, IPARAM, c IPNTR, WORKD, WORKL, LWORKL, INFO ) c c\Arguments c IDO Integer. (INPUT/OUTPUT) c Reverse communication flag. IDO must be zero on the first c call to dsaupd . IDO will be set internally to c indicate the type of operation to be performed. Control is c then given back to the calling routine which has the c responsibility to carry out the requested operation and call c dsaupd with the result. The operand is given in c WORKD(IPNTR(1)), the result must be put in WORKD(IPNTR(2)). c (If Mode = 2 see remark 5 below) c ------------------------------------------------------------- c IDO = 0: first call to the reverse communication interface c IDO = -1: compute Y = OP * X where c IPNTR(1) is the pointer into WORKD for X, c IPNTR(2) is the pointer into WORKD for Y. c This is for the initialization phase to force the c starting vector into the range of OP. c IDO = 1: compute Y = OP * X where c IPNTR(1) is the pointer into WORKD for X, c IPNTR(2) is the pointer into WORKD for Y. c In mode 3,4 and 5, the vector B * X is already c available in WORKD(ipntr(3)). It does not c need to be recomputed in forming OP * X. c IDO = 2: compute Y = B * X where c IPNTR(1) is the pointer into WORKD for X, c IPNTR(2) is the pointer into WORKD for Y. c IDO = 3: compute the IPARAM(8) shifts where c IPNTR(11) is the pointer into WORKL for c placing the shifts. See remark 6 below. c IDO = 99: done c ------------------------------------------------------------- c c BMAT Character*1. (INPUT) c BMAT specifies the type of the matrix B that defines the c semi-inner product for the operator OP. c B = 'I' -> standard eigenvalue problem A*x = lambda*x c B = 'G' -> generalized eigenvalue problem A*x = lambda*B*x c c N Integer. (INPUT) c Dimension of the eigenproblem. c c WHICH Character*2. (INPUT) c Specify which of the Ritz values of OP to compute. c c 'LA' - compute the NEV largest (algebraic) eigenvalues. c 'SA' - compute the NEV smallest (algebraic) eigenvalues. c 'LM' - compute the NEV largest (in magnitude) eigenvalues. c 'SM' - compute the NEV smallest (in magnitude) eigenvalues. c 'BE' - compute NEV eigenvalues, half from each end of the c spectrum. When NEV is odd, compute one more from the c high end than from the low end. c (see remark 1 below) c c NEV Integer. (INPUT) c Number of eigenvalues of OP to be computed. 0 < NEV < N. c c TOL Double precision scalar. (INPUT) c Stopping criterion: the relative accuracy of the Ritz value c is considered acceptable if BOUNDS(I) .LE. TOL*ABS(RITZ(I)). c If TOL .LE. 0. is passed a default is set: c DEFAULT = DLAMCH ('EPS') (machine precision as computed c by the LAPACK auxiliary subroutine DLAMCH ). c c RESID Double precision array of length N. (INPUT/OUTPUT) c On INPUT: c If INFO .EQ. 0, a random initial residual vector is used. c If INFO .NE. 0, RESID contains the initial residual vector, c possibly from a previous run. c On OUTPUT: c RESID contains the final residual vector. c c NCV Integer. (INPUT) c Number of columns of the matrix V (less than or equal to N). c This will indicate how many Lanczos vectors are generated c at each iteration. After the startup phase in which NEV c Lanczos vectors are generated, the algorithm generates c NCV-NEV Lanczos vectors at each subsequent update iteration. c Most of the cost in generating each Lanczos vector is in the c matrix-vector product OP*x. (See remark 4 below). c c V Double precision N by NCV array. (OUTPUT) c The NCV columns of V contain the Lanczos basis vectors. c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling c program. c c IPARAM Integer array of length 11. (INPUT/OUTPUT) c IPARAM(1) = ISHIFT: method for selecting the implicit shifts. c The shifts selected at each iteration are used to restart c the Arnoldi iteration in an implicit fashion. c ------------------------------------------------------------- c ISHIFT = 0: the shifts are provided by the user via c reverse communication. The NCV eigenvalues of c the current tridiagonal matrix T are returned in c the part of WORKL array corresponding to RITZ. c See remark 6 below. c ISHIFT = 1: exact shifts with respect to the reduced c tridiagonal matrix T. This is equivalent to c restarting the iteration with a starting vector c that is a linear combination of Ritz vectors c associated with the "wanted" Ritz values. c ------------------------------------------------------------- c c IPARAM(2) = LEVEC c No longer referenced. See remark 2 below. c c IPARAM(3) = MXITER c On INPUT: maximum number of Arnoldi update iterations allowed. c On OUTPUT: actual number of Arnoldi update iterations taken. c c IPARAM(4) = NB: blocksize to be used in the recurrence. c The code currently works only for NB = 1. c c IPARAM(5) = NCONV: number of "converged" Ritz values. c This represents the number of Ritz values that satisfy c the convergence criterion. c c IPARAM(6) = IUPD c No longer referenced. Implicit restarting is ALWAYS used. c c IPARAM(7) = MODE c On INPUT determines what type of eigenproblem is being solved. c Must be 1,2,3,4,5; See under \Description of dsaupd for the c five modes available. c c IPARAM(8) = NP c When ido = 3 and the user provides shifts through reverse c communication (IPARAM(1)=0), dsaupd returns NP, the number c of shifts the user is to provide. 0 < NP <=NCV-NEV. See Remark c 6 below. c c IPARAM(9) = NUMOP, IPARAM(10) = NUMOPB, IPARAM(11) = NUMREO, c OUTPUT: NUMOP = total number of OP*x operations, c NUMOPB = total number of B*x operations if BMAT='G', c NUMREO = total number of steps of re-orthogonalization. c c IPNTR Integer array of length 11. (OUTPUT) c Pointer to mark the starting locations in the WORKD and WORKL c arrays for matrices/vectors used by the Lanczos iteration. c ------------------------------------------------------------- c IPNTR(1): pointer to the current operand vector X in WORKD. c IPNTR(2): pointer to the current result vector Y in WORKD. c IPNTR(3): pointer to the vector B * X in WORKD when used in c the shift-and-invert mode. c IPNTR(4): pointer to the next available location in WORKL c that is untouched by the program. c IPNTR(5): pointer to the NCV by 2 tridiagonal matrix T in WORKL. c IPNTR(6): pointer to the NCV RITZ values array in WORKL. c IPNTR(7): pointer to the Ritz estimates in array WORKL associated c with the Ritz values located in RITZ in WORKL. c IPNTR(11): pointer to the NP shifts in WORKL. See Remark 6 below. c c Note: IPNTR(8:10) is only referenced by dseupd . See Remark 2. c IPNTR(8): pointer to the NCV RITZ values of the original system. c IPNTR(9): pointer to the NCV corresponding error bounds. c IPNTR(10): pointer to the NCV by NCV matrix of eigenvectors c of the tridiagonal matrix T. Only referenced by c dseupd if RVEC = .TRUE. See Remarks. c ------------------------------------------------------------- c c WORKD Double precision work array of length 3*N. (REVERSE COMMUNICATION) c Distributed array to be used in the basic Arnoldi iteration c for reverse communication. The user should not use WORKD c as temporary workspace during the iteration. Upon termination c WORKD(1:N) contains B*RESID(1:N). If the Ritz vectors are desired c subroutine dseupd uses this output. c See Data Distribution Note below. c c WORKL Double precision work array of length LWORKL. (OUTPUT/WORKSPACE) c Private (replicated) array on each PE or array allocated on c the front end. See Data Distribution Note below. c c LWORKL Integer. (INPUT) c LWORKL must be at least NCV**2 + 8*NCV . c c INFO Integer. (INPUT/OUTPUT) c If INFO .EQ. 0, a randomly initial residual vector is used. c If INFO .NE. 0, RESID contains the initial residual vector, c possibly from a previous run. c Error flag on output. c = 0: Normal exit. c = 1: Maximum number of iterations taken. c All possible eigenvalues of OP has been found. IPARAM(5) c returns the number of wanted converged Ritz values. c = 2: No longer an informational error. Deprecated starting c with release 2 of ARPACK. c = 3: No shifts could be applied during a cycle of the c Implicitly restarted Arnoldi iteration. One possibility c is to increase the size of NCV relative to NEV. c See remark 4 below. c = -1: N must be positive. c = -2: NEV must be positive. c = -3: NCV must be greater than NEV and less than or equal to N. c = -4: The maximum number of Arnoldi update iterations allowed c must be greater than zero. c = -5: WHICH must be one of 'LM', 'SM', 'LA', 'SA' or 'BE'. c = -6: BMAT must be one of 'I' or 'G'. c = -7: Length of private work array WORKL is not sufficient. c = -8: Error return from trid. eigenvalue calculation; c Informatinal error from LAPACK routine dsteqr . c = -9: Starting vector is zero. c = -10: IPARAM(7) must be 1,2,3,4,5. c = -11: IPARAM(7) = 1 and BMAT = 'G' are incompatable. c = -12: IPARAM(1) must be equal to 0 or 1. c = -13: NEV and WHICH = 'BE' are incompatable. c = -9999: Could not build an Arnoldi factorization. c IPARAM(5) returns the size of the current Arnoldi c factorization. The user is advised to check that c enough workspace and array storage has been allocated. c c c\Remarks c 1. The converged Ritz values are always returned in ascending c algebraic order. The computed Ritz values are approximate c eigenvalues of OP. The selection of WHICH should be made c with this in mind when Mode = 3,4,5. After convergence, c approximate eigenvalues of the original problem may be obtained c with the ARPACK subroutine dseupd . c c 2. If the Ritz vectors corresponding to the converged Ritz values c are needed, the user must call dseupd immediately following completion c of dsaupd . This is new starting with version 2.1 of ARPACK. c c 3. If M can be factored into a Cholesky factorization M = LL` c then Mode = 2 should not be selected. Instead one should use c Mode = 1 with OP = inv(L)*A*inv(L`). Appropriate triangular c linear systems should be solved with L and L` rather c than computing inverses. After convergence, an approximate c eigenvector z of the original problem is recovered by solving c L`z = x where x is a Ritz vector of OP. c c 4. At present there is no a-priori analysis to guide the selection c of NCV relative to NEV. The only formal requrement is that NCV > NEV. c However, it is recommended that NCV .ge. 2*NEV. If many problems of c the same type are to be solved, one should experiment with increasing c NCV while keeping NEV fixed for a given test problem. This will c usually decrease the required number of OP*x operations but it c also increases the work and storage required to maintain the orthogonal c basis vectors. The optimal "cross-over" with respect to CPU time c is problem dependent and must be determined empirically. c c 5. If IPARAM(7) = 2 then in the Reverse commuication interface the user c must do the following. When IDO = 1, Y = OP * X is to be computed. c When IPARAM(7) = 2 OP = inv(B)*A. After computing A*X the user c must overwrite X with A*X. Y is then the solution to the linear set c of equations B*Y = A*X. c c 6. When IPARAM(1) = 0, and IDO = 3, the user needs to provide the c NP = IPARAM(8) shifts in locations: c 1 WORKL(IPNTR(11)) c 2 WORKL(IPNTR(11)+1) c . c . c . c NP WORKL(IPNTR(11)+NP-1). c c The eigenvalues of the current tridiagonal matrix are located in c WORKL(IPNTR(6)) through WORKL(IPNTR(6)+NCV-1). They are in the c order defined by WHICH. The associated Ritz estimates are located in c WORKL(IPNTR(8)), WORKL(IPNTR(8)+1), ... , WORKL(IPNTR(8)+NCV-1). c c----------------------------------------------------------------------- c c\Data Distribution Note: c c Fortran-D syntax: c ================ c REAL RESID(N), V(LDV,NCV), WORKD(3*N), WORKL(LWORKL) c DECOMPOSE D1(N), D2(N,NCV) c ALIGN RESID(I) with D1(I) c ALIGN V(I,J) with D2(I,J) c ALIGN WORKD(I) with D1(I) range (1:N) c ALIGN WORKD(I) with D1(I-N) range (N+1:2*N) c ALIGN WORKD(I) with D1(I-2*N) range (2*N+1:3*N) c DISTRIBUTE D1(BLOCK), D2(BLOCK,:) c REPLICATED WORKL(LWORKL) c c Cray MPP syntax: c =============== c REAL RESID(N), V(LDV,NCV), WORKD(N,3), WORKL(LWORKL) c SHARED RESID(BLOCK), V(BLOCK,:), WORKD(BLOCK,:) c REPLICATED WORKL(LWORKL) c c c\BeginLib c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly c Restarted Arnoldi Iteration", Rice University Technical Report c TR95-13, Department of Computational and Applied Mathematics. c 3. B.N. Parlett, "The Symmetric Eigenvalue Problem". Prentice-Hall, c 1980. c 4. B.N. Parlett, B. Nour-Omid, "Towards a Black Box Lanczos Program", c Computer Physics Communications, 53 (1989), pp 169-179. c 5. B. Nour-Omid, B.N. Parlett, T. Ericson, P.S. Jensen, "How to c Implement the Spectral Transformation", Math. Comp., 48 (1987), c pp 663-673. c 6. R.G. Grimes, J.G. Lewis and H.D. Simon, "A Shifted Block Lanczos c Algorithm for Solving Sparse Symmetric Generalized Eigenproblems", c SIAM J. Matr. Anal. Apps., January (1993). c 7. L. Reichel, W.B. Gragg, "Algorithm 686: FORTRAN Subroutines c for Updating the QR decomposition", ACM TOMS, December 1990, c Volume 16 Number 4, pp 369-377. c 8. R.B. Lehoucq, D.C. Sorensen, "Implementation of Some Spectral c Transformations in a k-Step Arnoldi Method". In Preparation. c c\Routines called: c dsaup2 ARPACK routine that implements the Implicitly Restarted c Arnoldi Iteration. c dstats ARPACK routine that initialize timing and other statistics c variables. c ivout ARPACK utility routine that prints integers. c arscnd ARPACK utility routine for timing. c dvout ARPACK utility routine that prints vectors. c dlamch LAPACK routine that determines machine constants. c c\Authors c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c 12/15/93: Version ' 2.4' c c\SCCS Information: @(#) c FILE: saupd.F SID: 2.8 DATE OF SID: 04/10/01 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c----------------------------------------------------------------------- c subroutine dsaupd & ( ido, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam, & ipntr, workd, workl, lworkl, info ) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character bmat*1, which*2 integer ido, info, ldv, lworkl, n, ncv, nev Double precision & tol c c %-----------------% c | Array Arguments | c %-----------------% c integer iparam(11), ipntr(11) Double precision & resid(n), v(ldv,ncv), workd(3*n), workl(lworkl) c c %------------% c | Parameters | c %------------% c Double precision & one, zero parameter (one = 1.0D+0 , zero = 0.0D+0 ) c c %---------------% c | Local Scalars | c %---------------% c integer bounds, ierr, ih, iq, ishift, iupd, iw, & ldh, ldq, msglvl, mxiter, mode, nb, & nev0, next, np, ritz, j save bounds, ierr, ih, iq, ishift, iupd, iw, & ldh, ldq, msglvl, mxiter, mode, nb, & nev0, next, np, ritz c c %----------------------% c | External Subroutines | c %----------------------% c external dsaup2 , dvout , ivout, arscnd, dstats c c %--------------------% c | External Functions | c %--------------------% c Double precision & dlamch external dlamch c c %-----------------------% c | Executable Statements | c %-----------------------% c if (ido .eq. 0) then c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call dstats call arscnd (t0) msglvl = msaupd c ierr = 0 ishift = iparam(1) mxiter = iparam(3) c nb = iparam(4) nb = 1 c c %--------------------------------------------% c | Revision 2 performs only implicit restart. | c %--------------------------------------------% c iupd = 1 mode = iparam(7) c c %----------------% c | Error checking | c %----------------% c if (n .le. 0) then ierr = -1 else if (nev .le. 0) then ierr = -2 else if (ncv .le. nev .or. ncv .gt. n) then ierr = -3 end if c c %----------------------------------------------% c | NP is the number of additional steps to | c | extend the length NEV Lanczos factorization. | c %----------------------------------------------% c np = ncv - nev c if (mxiter .le. 0) ierr = -4 if (which .ne. 'LM' .and. & which .ne. 'SM' .and. & which .ne. 'LA' .and. & which .ne. 'SA' .and. & which .ne. 'BE') ierr = -5 if (bmat .ne. 'I' .and. bmat .ne. 'G') ierr = -6 c if (lworkl .lt. ncv**2 + 8*ncv) ierr = -7 if (mode .lt. 1 .or. mode .gt. 5) then ierr = -10 else if (mode .eq. 1 .and. bmat .eq. 'G') then ierr = -11 else if (ishift .lt. 0 .or. ishift .gt. 1) then ierr = -12 else if (nev .eq. 1 .and. which .eq. 'BE') then ierr = -13 end if c c %------------% c | Error Exit | c %------------% c if (ierr .ne. 0) then info = ierr ido = 99 go to 9000 end if c c %------------------------% c | Set default parameters | c %------------------------% c if (nb .le. 0) nb = 1 if (tol .le. zero) tol = dlamch ('EpsMach') c c %----------------------------------------------% c | NP is the number of additional steps to | c | extend the length NEV Lanczos factorization. | c | NEV0 is the local variable designating the | c | size of the invariant subspace desired. | c %----------------------------------------------% c np = ncv - nev nev0 = nev c c %-----------------------------% c | Zero out internal workspace | c %-----------------------------% c do 10 j = 1, ncv**2 + 8*ncv workl(j) = zero 10 continue c c %-------------------------------------------------------% c | Pointer into WORKL for address of H, RITZ, BOUNDS, Q | c | etc... and the remaining workspace. | c | Also update pointer to be used on output. | c | Memory is laid out as follows: | c | workl(1:2*ncv) := generated tridiagonal matrix | c | workl(2*ncv+1:2*ncv+ncv) := ritz values | c | workl(3*ncv+1:3*ncv+ncv) := computed error bounds | c | workl(4*ncv+1:4*ncv+ncv*ncv) := rotation matrix Q | c | workl(4*ncv+ncv*ncv+1:7*ncv+ncv*ncv) := workspace | c %-------------------------------------------------------% c ldh = ncv ldq = ncv ih = 1 ritz = ih + 2*ldh bounds = ritz + ncv iq = bounds + ncv iw = iq + ncv**2 next = iw + 3*ncv c ipntr(4) = next ipntr(5) = ih ipntr(6) = ritz ipntr(7) = bounds ipntr(11) = iw end if c c %-------------------------------------------------------% c | Carry out the Implicitly restarted Lanczos Iteration. | c %-------------------------------------------------------% c call dsaup2 & ( ido, bmat, n, which, nev0, np, tol, resid, mode, iupd, & ishift, mxiter, v, ldv, workl(ih), ldh, workl(ritz), & workl(bounds), workl(iq), ldq, workl(iw), ipntr, workd, & info ) c c %--------------------------------------------------% c | ido .ne. 99 implies use of reverse communication | c | to compute operations involving OP or shifts. | c %--------------------------------------------------% c if (ido .eq. 3) iparam(8) = np if (ido .ne. 99) go to 9000 c iparam(3) = mxiter iparam(5) = np iparam(9) = nopx iparam(10) = nbx iparam(11) = nrorth c c %------------------------------------% c | Exit if there was an informational | c | error within dsaup2 . | c %------------------------------------% c if (info .lt. 0) go to 9000 if (info .eq. 2) info = 3 c if (msglvl .gt. 0) then call ivout (logfil, 1, mxiter, ndigit, & '_saupd: number of update iterations taken') call ivout (logfil, 1, np, ndigit, & '_saupd: number of "converged" Ritz values') call dvout (logfil, np, workl(Ritz), ndigit, & '_saupd: final Ritz values') call dvout (logfil, np, workl(Bounds), ndigit, & '_saupd: corresponding error bounds') end if c call arscnd (t1) tsaupd = t1 - t0 c if (msglvl .gt. 0) then c c %--------------------------------------------------------% c | Version Number & Version Date are defined in version.h | c %--------------------------------------------------------% c write (6,1000) write (6,1100) mxiter, nopx, nbx, nrorth, nitref, nrstrt, & tmvopx, tmvbx, tsaupd, tsaup2, tsaitr, titref, & tgetv0, tseigt, tsgets, tsapps, tsconv 1000 format (//, & 5x, '==========================================',/ & 5x, '= Symmetric implicit Arnoldi update code =',/ & 5x, '= Version Number:', ' 2.4' , 19x, ' =',/ & 5x, '= Version Date: ', ' 07/31/96' , 14x, ' =',/ & 5x, '==========================================',/ & 5x, '= Summary of timing statistics =',/ & 5x, '==========================================',//) 1100 format ( & 5x, 'Total number update iterations = ', i5,/ & 5x, 'Total number of OP*x operations = ', i5,/ & 5x, 'Total number of B*x operations = ', i5,/ & 5x, 'Total number of reorthogonalization steps = ', i5,/ & 5x, 'Total number of iterative refinement steps = ', i5,/ & 5x, 'Total number of restart steps = ', i5,/ & 5x, 'Total time in user OP*x operation = ', f12.6,/ & 5x, 'Total time in user B*x operation = ', f12.6,/ & 5x, 'Total time in Arnoldi update routine = ', f12.6,/ & 5x, 'Total time in saup2 routine = ', f12.6,/ & 5x, 'Total time in basic Arnoldi iteration loop = ', f12.6,/ & 5x, 'Total time in reorthogonalization phase = ', f12.6,/ & 5x, 'Total time in (re)start vector generation = ', f12.6,/ & 5x, 'Total time in trid eigenvalue subproblem = ', f12.6,/ & 5x, 'Total time in getting the shifts = ', f12.6,/ & 5x, 'Total time in applying the shifts = ', f12.6,/ & 5x, 'Total time in convergence testing = ', f12.6) end if c 9000 continue c return c c %---------------% c | End of dsaupd | c %---------------% c end arpack-0.92.1/SRC/snaup2.f0000644000175000017500000007514510776001577012021 00000000000000c\BeginDoc c c\Name: snaup2 c c\Description: c Intermediate level interface called by snaupd. c c\Usage: c call snaup2 c ( IDO, BMAT, N, WHICH, NEV, NP, TOL, RESID, MODE, IUPD, c ISHIFT, MXITER, V, LDV, H, LDH, RITZR, RITZI, BOUNDS, c Q, LDQ, WORKL, IPNTR, WORKD, INFO ) c c\Arguments c c IDO, BMAT, N, WHICH, NEV, TOL, RESID: same as defined in snaupd. c MODE, ISHIFT, MXITER: see the definition of IPARAM in snaupd. c c NP Integer. (INPUT/OUTPUT) c Contains the number of implicit shifts to apply during c each Arnoldi iteration. c If ISHIFT=1, NP is adjusted dynamically at each iteration c to accelerate convergence and prevent stagnation. c This is also roughly equal to the number of matrix-vector c products (involving the operator OP) per Arnoldi iteration. c The logic for adjusting is contained within the current c subroutine. c If ISHIFT=0, NP is the number of shifts the user needs c to provide via reverse comunication. 0 < NP < NCV-NEV. c NP may be less than NCV-NEV for two reasons. The first, is c to keep complex conjugate pairs of "wanted" Ritz values c together. The second, is that a leading block of the current c upper Hessenberg matrix has split off and contains "unwanted" c Ritz values. c Upon termination of the IRA iteration, NP contains the number c of "converged" wanted Ritz values. c c IUPD Integer. (INPUT) c IUPD .EQ. 0: use explicit restart instead implicit update. c IUPD .NE. 0: use implicit update. c c V Real N by (NEV+NP) array. (INPUT/OUTPUT) c The Arnoldi basis vectors are returned in the first NEV c columns of V. c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling c program. c c H Real (NEV+NP) by (NEV+NP) array. (OUTPUT) c H is used to store the generated upper Hessenberg matrix c c LDH Integer. (INPUT) c Leading dimension of H exactly as declared in the calling c program. c c RITZR, Real arrays of length NEV+NP. (OUTPUT) c RITZI RITZR(1:NEV) (resp. RITZI(1:NEV)) contains the real (resp. c imaginary) part of the computed Ritz values of OP. c c BOUNDS Real array of length NEV+NP. (OUTPUT) c BOUNDS(1:NEV) contain the error bounds corresponding to c the computed Ritz values. c c Q Real (NEV+NP) by (NEV+NP) array. (WORKSPACE) c Private (replicated) work array used to accumulate the c rotation in the shift application step. c c LDQ Integer. (INPUT) c Leading dimension of Q exactly as declared in the calling c program. c c WORKL Real work array of length at least c (NEV+NP)**2 + 3*(NEV+NP). (INPUT/WORKSPACE) c Private (replicated) array on each PE or array allocated on c the front end. It is used in shifts calculation, shifts c application and convergence checking. c c On exit, the last 3*(NEV+NP) locations of WORKL contain c the Ritz values (real,imaginary) and associated Ritz c estimates of the current Hessenberg matrix. They are c listed in the same order as returned from sneigh. c c If ISHIFT .EQ. O and IDO .EQ. 3, the first 2*NP locations c of WORKL are used in reverse communication to hold the user c supplied shifts. c c IPNTR Integer array of length 3. (OUTPUT) c Pointer to mark the starting locations in the WORKD for c vectors used by the Arnoldi iteration. c ------------------------------------------------------------- c IPNTR(1): pointer to the current operand vector X. c IPNTR(2): pointer to the current result vector Y. c IPNTR(3): pointer to the vector B * X when used in the c shift-and-invert mode. X is the current operand. c ------------------------------------------------------------- c c WORKD Real work array of length 3*N. (WORKSPACE) c Distributed array to be used in the basic Arnoldi iteration c for reverse communication. The user should not use WORKD c as temporary workspace during the iteration !!!!!!!!!! c See Data Distribution Note in DNAUPD. c c INFO Integer. (INPUT/OUTPUT) c If INFO .EQ. 0, a randomly initial residual vector is used. c If INFO .NE. 0, RESID contains the initial residual vector, c possibly from a previous run. c Error flag on output. c = 0: Normal return. c = 1: Maximum number of iterations taken. c All possible eigenvalues of OP has been found. c NP returns the number of converged Ritz values. c = 2: No shifts could be applied. c = -8: Error return from LAPACK eigenvalue calculation; c This should never happen. c = -9: Starting vector is zero. c = -9999: Could not build an Arnoldi factorization. c Size that was built in returned in NP. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx real c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly c Restarted Arnoldi Iteration", Rice University Technical Report c TR95-13, Department of Computational and Applied Mathematics. c c\Routines called: c sgetv0 ARPACK initial vector generation routine. c snaitr ARPACK Arnoldi factorization routine. c snapps ARPACK application of implicit shifts routine. c snconv ARPACK convergence of Ritz values routine. c sneigh ARPACK compute Ritz values and error bounds routine. c sngets ARPACK reorder Ritz values and error bounds routine. c ssortc ARPACK sorting routine. c ivout ARPACK utility routine that prints integers. c arscnd ARPACK utility routine for timing. c smout ARPACK utility routine that prints matrices c svout ARPACK utility routine that prints vectors. c slamch LAPACK routine that determines machine constants. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c scopy Level 1 BLAS that copies one vector to another . c sdot Level 1 BLAS that computes the scalar product of two vectors. c snrm2 Level 1 BLAS that computes the norm of a vector. c sswap Level 1 BLAS that swaps two vectors. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: naup2.F SID: 2.8 DATE OF SID: 10/17/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c----------------------------------------------------------------------- c subroutine snaup2 & ( ido, bmat, n, which, nev, np, tol, resid, mode, iupd, & ishift, mxiter, v, ldv, h, ldh, ritzr, ritzi, bounds, & q, ldq, workl, ipntr, workd, info ) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character bmat*1, which*2 integer ido, info, ishift, iupd, mode, ldh, ldq, ldv, mxiter, & n, nev, np Real & tol c c %-----------------% c | Array Arguments | c %-----------------% c integer ipntr(13) Real & bounds(nev+np), h(ldh,nev+np), q(ldq,nev+np), resid(n), & ritzi(nev+np), ritzr(nev+np), v(ldv,nev+np), & workd(3*n), workl( (nev+np)*(nev+np+3) ) c c %------------% c | Parameters | c %------------% c Real & one, zero parameter (one = 1.0E+0, zero = 0.0E+0) c c %---------------% c | Local Scalars | c %---------------% c character wprime*2 logical cnorm , getv0, initv, update, ushift integer ierr , iter , j , kplusp, msglvl, nconv, & nevbef, nev0 , np0 , nptemp, numcnv Real & rnorm , temp , eps23 save cnorm , getv0, initv, update, ushift, & rnorm , iter , eps23, kplusp, msglvl, nconv , & nevbef, nev0 , np0 , numcnv c c %-----------------------% c | Local array arguments | c %-----------------------% c integer kp(4) c c %----------------------% c | External Subroutines | c %----------------------% c external scopy , sgetv0, snaitr, snconv, sneigh, & sngets, snapps, svout , ivout , arscnd c c %--------------------% c | External Functions | c %--------------------% c Real & sdot, snrm2, slapy2, slamch external sdot, snrm2, slapy2, slamch c c %---------------------% c | Intrinsic Functions | c %---------------------% c intrinsic min, max, abs, sqrt c c %-----------------------% c | Executable Statements | c %-----------------------% c if (ido .eq. 0) then c call arscnd (t0) c msglvl = mnaup2 c c %-------------------------------------% c | Get the machine dependent constant. | c %-------------------------------------% c eps23 = slamch('Epsilon-Machine') eps23 = eps23**(2.0E+0 / 3.0E+0) c nev0 = nev np0 = np c c %-------------------------------------% c | kplusp is the bound on the largest | c | Lanczos factorization built. | c | nconv is the current number of | c | "converged" eigenvlues. | c | iter is the counter on the current | c | iteration step. | c %-------------------------------------% c kplusp = nev + np nconv = 0 iter = 0 c c %---------------------------------------% c | Set flags for computing the first NEV | c | steps of the Arnoldi factorization. | c %---------------------------------------% c getv0 = .true. update = .false. ushift = .false. cnorm = .false. c if (info .ne. 0) then c c %--------------------------------------------% c | User provides the initial residual vector. | c %--------------------------------------------% c initv = .true. info = 0 else initv = .false. end if end if c c %---------------------------------------------% c | Get a possibly random starting vector and | c | force it into the range of the operator OP. | c %---------------------------------------------% c 10 continue c if (getv0) then call sgetv0 (ido, bmat, 1, initv, n, 1, v, ldv, resid, rnorm, & ipntr, workd, info) c if (ido .ne. 99) go to 9000 c if (rnorm .eq. zero) then c c %-----------------------------------------% c | The initial vector is zero. Error exit. | c %-----------------------------------------% c info = -9 go to 1100 end if getv0 = .false. ido = 0 end if c c %-----------------------------------% c | Back from reverse communication : | c | continue with update step | c %-----------------------------------% c if (update) go to 20 c c %-------------------------------------------% c | Back from computing user specified shifts | c %-------------------------------------------% c if (ushift) go to 50 c c %-------------------------------------% c | Back from computing residual norm | c | at the end of the current iteration | c %-------------------------------------% c if (cnorm) go to 100 c c %----------------------------------------------------------% c | Compute the first NEV steps of the Arnoldi factorization | c %----------------------------------------------------------% c call snaitr (ido, bmat, n, 0, nev, mode, resid, rnorm, v, ldv, & h, ldh, ipntr, workd, info) c c %---------------------------------------------------% c | ido .ne. 99 implies use of reverse communication | c | to compute operations involving OP and possibly B | c %---------------------------------------------------% c if (ido .ne. 99) go to 9000 c if (info .gt. 0) then np = info mxiter = iter info = -9999 go to 1200 end if c c %--------------------------------------------------------------% c | | c | M A I N ARNOLDI I T E R A T I O N L O O P | c | Each iteration implicitly restarts the Arnoldi | c | factorization in place. | c | | c %--------------------------------------------------------------% c 1000 continue c iter = iter + 1 c if (msglvl .gt. 0) then call ivout (logfil, 1, iter, ndigit, & '_naup2: **** Start of major iteration number ****') end if c c %-----------------------------------------------------------% c | Compute NP additional steps of the Arnoldi factorization. | c | Adjust NP since NEV might have been updated by last call | c | to the shift application routine snapps. | c %-----------------------------------------------------------% c np = kplusp - nev c if (msglvl .gt. 1) then call ivout (logfil, 1, nev, ndigit, & '_naup2: The length of the current Arnoldi factorization') call ivout (logfil, 1, np, ndigit, & '_naup2: Extend the Arnoldi factorization by') end if c c %-----------------------------------------------------------% c | Compute NP additional steps of the Arnoldi factorization. | c %-----------------------------------------------------------% c ido = 0 20 continue update = .true. c call snaitr (ido , bmat, n , nev, np , mode , resid, & rnorm, v , ldv, h , ldh, ipntr, workd, & info) c c %---------------------------------------------------% c | ido .ne. 99 implies use of reverse communication | c | to compute operations involving OP and possibly B | c %---------------------------------------------------% c if (ido .ne. 99) go to 9000 c if (info .gt. 0) then np = info mxiter = iter info = -9999 go to 1200 end if update = .false. c if (msglvl .gt. 1) then call svout (logfil, 1, rnorm, ndigit, & '_naup2: Corresponding B-norm of the residual') end if c c %--------------------------------------------------------% c | Compute the eigenvalues and corresponding error bounds | c | of the current upper Hessenberg matrix. | c %--------------------------------------------------------% c call sneigh (rnorm, kplusp, h, ldh, ritzr, ritzi, bounds, & q, ldq, workl, ierr) c if (ierr .ne. 0) then info = -8 go to 1200 end if c c %----------------------------------------------------% c | Make a copy of eigenvalues and corresponding error | c | bounds obtained from sneigh. | c %----------------------------------------------------% c call scopy(kplusp, ritzr, 1, workl(kplusp**2+1), 1) call scopy(kplusp, ritzi, 1, workl(kplusp**2+kplusp+1), 1) call scopy(kplusp, bounds, 1, workl(kplusp**2+2*kplusp+1), 1) c c %---------------------------------------------------% c | Select the wanted Ritz values and their bounds | c | to be used in the convergence test. | c | The wanted part of the spectrum and corresponding | c | error bounds are in the last NEV loc. of RITZR, | c | RITZI and BOUNDS respectively. The variables NEV | c | and NP may be updated if the NEV-th wanted Ritz | c | value has a non zero imaginary part. In this case | c | NEV is increased by one and NP decreased by one. | c | NOTE: The last two arguments of sngets are no | c | longer used as of version 2.1. | c %---------------------------------------------------% c nev = nev0 np = np0 numcnv = nev call sngets (ishift, which, nev, np, ritzr, ritzi, & bounds, workl, workl(np+1)) if (nev .eq. nev0+1) numcnv = nev0+1 c c %-------------------% c | Convergence test. | c %-------------------% c call scopy (nev, bounds(np+1), 1, workl(2*np+1), 1) call snconv (nev, ritzr(np+1), ritzi(np+1), workl(2*np+1), & tol, nconv) c if (msglvl .gt. 2) then kp(1) = nev kp(2) = np kp(3) = numcnv kp(4) = nconv call ivout (logfil, 4, kp, ndigit, & '_naup2: NEV, NP, NUMCNV, NCONV are') call svout (logfil, kplusp, ritzr, ndigit, & '_naup2: Real part of the eigenvalues of H') call svout (logfil, kplusp, ritzi, ndigit, & '_naup2: Imaginary part of the eigenvalues of H') call svout (logfil, kplusp, bounds, ndigit, & '_naup2: Ritz estimates of the current NCV Ritz values') end if c c %---------------------------------------------------------% c | Count the number of unwanted Ritz values that have zero | c | Ritz estimates. If any Ritz estimates are equal to zero | c | then a leading block of H of order equal to at least | c | the number of Ritz values with zero Ritz estimates has | c | split off. None of these Ritz values may be removed by | c | shifting. Decrease NP the number of shifts to apply. If | c | no shifts may be applied, then prepare to exit | c %---------------------------------------------------------% c nptemp = np do 30 j=1, nptemp if (bounds(j) .eq. zero) then np = np - 1 nev = nev + 1 end if 30 continue c if ( (nconv .ge. numcnv) .or. & (iter .gt. mxiter) .or. & (np .eq. 0) ) then c if (msglvl .gt. 4) then call svout(logfil, kplusp, workl(kplusp**2+1), ndigit, & '_naup2: Real part of the eig computed by _neigh:') call svout(logfil, kplusp, workl(kplusp**2+kplusp+1), & ndigit, & '_naup2: Imag part of the eig computed by _neigh:') call svout(logfil, kplusp, workl(kplusp**2+kplusp*2+1), & ndigit, & '_naup2: Ritz eistmates computed by _neigh:') end if c c %------------------------------------------------% c | Prepare to exit. Put the converged Ritz values | c | and corresponding bounds in RITZ(1:NCONV) and | c | BOUNDS(1:NCONV) respectively. Then sort. Be | c | careful when NCONV > NP | c %------------------------------------------------% c c %------------------------------------------% c | Use h( 3,1 ) as storage to communicate | c | rnorm to _neupd if needed | c %------------------------------------------% h(3,1) = rnorm c c %----------------------------------------------% c | To be consistent with sngets, we first do a | c | pre-processing sort in order to keep complex | c | conjugate pairs together. This is similar | c | to the pre-processing sort used in sngets | c | except that the sort is done in the opposite | c | order. | c %----------------------------------------------% c if (which .eq. 'LM') wprime = 'SR' if (which .eq. 'SM') wprime = 'LR' if (which .eq. 'LR') wprime = 'SM' if (which .eq. 'SR') wprime = 'LM' if (which .eq. 'LI') wprime = 'SM' if (which .eq. 'SI') wprime = 'LM' c call ssortc (wprime, .true., kplusp, ritzr, ritzi, bounds) c c %----------------------------------------------% c | Now sort Ritz values so that converged Ritz | c | values appear within the first NEV locations | c | of ritzr, ritzi and bounds, and the most | c | desired one appears at the front. | c %----------------------------------------------% c if (which .eq. 'LM') wprime = 'SM' if (which .eq. 'SM') wprime = 'LM' if (which .eq. 'LR') wprime = 'SR' if (which .eq. 'SR') wprime = 'LR' if (which .eq. 'LI') wprime = 'SI' if (which .eq. 'SI') wprime = 'LI' c call ssortc(wprime, .true., kplusp, ritzr, ritzi, bounds) c c %--------------------------------------------------% c | Scale the Ritz estimate of each Ritz value | c | by 1 / max(eps23,magnitude of the Ritz value). | c %--------------------------------------------------% c do 35 j = 1, numcnv temp = max(eps23,slapy2(ritzr(j), & ritzi(j))) bounds(j) = bounds(j)/temp 35 continue c c %----------------------------------------------------% c | Sort the Ritz values according to the scaled Ritz | c | esitmates. This will push all the converged ones | c | towards the front of ritzr, ritzi, bounds | c | (in the case when NCONV < NEV.) | c %----------------------------------------------------% c wprime = 'LR' call ssortc(wprime, .true., numcnv, bounds, ritzr, ritzi) c c %----------------------------------------------% c | Scale the Ritz estimate back to its original | c | value. | c %----------------------------------------------% c do 40 j = 1, numcnv temp = max(eps23, slapy2(ritzr(j), & ritzi(j))) bounds(j) = bounds(j)*temp 40 continue c c %------------------------------------------------% c | Sort the converged Ritz values again so that | c | the "threshold" value appears at the front of | c | ritzr, ritzi and bound. | c %------------------------------------------------% c call ssortc(which, .true., nconv, ritzr, ritzi, bounds) c if (msglvl .gt. 1) then call svout (logfil, kplusp, ritzr, ndigit, & '_naup2: Sorted real part of the eigenvalues') call svout (logfil, kplusp, ritzi, ndigit, & '_naup2: Sorted imaginary part of the eigenvalues') call svout (logfil, kplusp, bounds, ndigit, & '_naup2: Sorted ritz estimates.') end if c c %------------------------------------% c | Max iterations have been exceeded. | c %------------------------------------% c if (iter .gt. mxiter .and. nconv .lt. numcnv) info = 1 c c %---------------------% c | No shifts to apply. | c %---------------------% c if (np .eq. 0 .and. nconv .lt. numcnv) info = 2 c np = nconv go to 1100 c else if ( (nconv .lt. numcnv) .and. (ishift .eq. 1) ) then c c %-------------------------------------------------% c | Do not have all the requested eigenvalues yet. | c | To prevent possible stagnation, adjust the size | c | of NEV. | c %-------------------------------------------------% c nevbef = nev nev = nev + min(nconv, np/2) if (nev .eq. 1 .and. kplusp .ge. 6) then nev = kplusp / 2 else if (nev .eq. 1 .and. kplusp .gt. 3) then nev = 2 end if np = kplusp - nev c c %---------------------------------------% c | If the size of NEV was just increased | c | resort the eigenvalues. | c %---------------------------------------% c if (nevbef .lt. nev) & call sngets (ishift, which, nev, np, ritzr, ritzi, & bounds, workl, workl(np+1)) c end if c if (msglvl .gt. 0) then call ivout (logfil, 1, nconv, ndigit, & '_naup2: no. of "converged" Ritz values at this iter.') if (msglvl .gt. 1) then kp(1) = nev kp(2) = np call ivout (logfil, 2, kp, ndigit, & '_naup2: NEV and NP are') call svout (logfil, nev, ritzr(np+1), ndigit, & '_naup2: "wanted" Ritz values -- real part') call svout (logfil, nev, ritzi(np+1), ndigit, & '_naup2: "wanted" Ritz values -- imag part') call svout (logfil, nev, bounds(np+1), ndigit, & '_naup2: Ritz estimates of the "wanted" values ') end if end if c if (ishift .eq. 0) then c c %-------------------------------------------------------% c | User specified shifts: reverse comminucation to | c | compute the shifts. They are returned in the first | c | 2*NP locations of WORKL. | c %-------------------------------------------------------% c ushift = .true. ido = 3 go to 9000 end if c 50 continue c c %------------------------------------% c | Back from reverse communication; | c | User specified shifts are returned | c | in WORKL(1:2*NP) | c %------------------------------------% c ushift = .false. c if ( ishift .eq. 0 ) then c c %----------------------------------% c | Move the NP shifts from WORKL to | c | RITZR, RITZI to free up WORKL | c | for non-exact shift case. | c %----------------------------------% c call scopy (np, workl, 1, ritzr, 1) call scopy (np, workl(np+1), 1, ritzi, 1) end if c if (msglvl .gt. 2) then call ivout (logfil, 1, np, ndigit, & '_naup2: The number of shifts to apply ') call svout (logfil, np, ritzr, ndigit, & '_naup2: Real part of the shifts') call svout (logfil, np, ritzi, ndigit, & '_naup2: Imaginary part of the shifts') if ( ishift .eq. 1 ) & call svout (logfil, np, bounds, ndigit, & '_naup2: Ritz estimates of the shifts') end if c c %---------------------------------------------------------% c | Apply the NP implicit shifts by QR bulge chasing. | c | Each shift is applied to the whole upper Hessenberg | c | matrix H. | c | The first 2*N locations of WORKD are used as workspace. | c %---------------------------------------------------------% c call snapps (n, nev, np, ritzr, ritzi, v, ldv, & h, ldh, resid, q, ldq, workl, workd) c c %---------------------------------------------% c | Compute the B-norm of the updated residual. | c | Keep B*RESID in WORKD(1:N) to be used in | c | the first step of the next call to snaitr. | c %---------------------------------------------% c cnorm = .true. call arscnd (t2) if (bmat .eq. 'G') then nbx = nbx + 1 call scopy (n, resid, 1, workd(n+1), 1) ipntr(1) = n + 1 ipntr(2) = 1 ido = 2 c c %----------------------------------% c | Exit in order to compute B*RESID | c %----------------------------------% c go to 9000 else if (bmat .eq. 'I') then call scopy (n, resid, 1, workd, 1) end if c 100 continue c c %----------------------------------% c | Back from reverse communication; | c | WORKD(1:N) := B*RESID | c %----------------------------------% c if (bmat .eq. 'G') then call arscnd (t3) tmvbx = tmvbx + (t3 - t2) end if c if (bmat .eq. 'G') then rnorm = sdot (n, resid, 1, workd, 1) rnorm = sqrt(abs(rnorm)) else if (bmat .eq. 'I') then rnorm = snrm2(n, resid, 1) end if cnorm = .false. c if (msglvl .gt. 2) then call svout (logfil, 1, rnorm, ndigit, & '_naup2: B-norm of residual for compressed factorization') call smout (logfil, nev, nev, h, ldh, ndigit, & '_naup2: Compressed upper Hessenberg matrix H') end if c go to 1000 c c %---------------------------------------------------------------% c | | c | E N D O F M A I N I T E R A T I O N L O O P | c | | c %---------------------------------------------------------------% c 1100 continue c mxiter = iter nev = numcnv c 1200 continue ido = 99 c c %------------% c | Error Exit | c %------------% c call arscnd (t1) tnaup2 = t1 - t0 c 9000 continue c c %---------------% c | End of snaup2 | c %---------------% c return end arpack-0.92.1/SRC/znapps.f0000644000175000017500000004233110776001577012113 00000000000000c\BeginDoc c c\Name: znapps c c\Description: c Given the Arnoldi factorization c c A*V_{k} - V_{k}*H_{k} = r_{k+p}*e_{k+p}^T, c c apply NP implicit shifts resulting in c c A*(V_{k}*Q) - (V_{k}*Q)*(Q^T* H_{k}*Q) = r_{k+p}*e_{k+p}^T * Q c c where Q is an orthogonal matrix which is the product of rotations c and reflections resulting from the NP bulge change sweeps. c The updated Arnoldi factorization becomes: c c A*VNEW_{k} - VNEW_{k}*HNEW_{k} = rnew_{k}*e_{k}^T. c c\Usage: c call znapps c ( N, KEV, NP, SHIFT, V, LDV, H, LDH, RESID, Q, LDQ, c WORKL, WORKD ) c c\Arguments c N Integer. (INPUT) c Problem size, i.e. size of matrix A. c c KEV Integer. (INPUT/OUTPUT) c KEV+NP is the size of the input matrix H. c KEV is the size of the updated matrix HNEW. c c NP Integer. (INPUT) c Number of implicit shifts to be applied. c c SHIFT Complex*16 array of length NP. (INPUT) c The shifts to be applied. c c V Complex*16 N by (KEV+NP) array. (INPUT/OUTPUT) c On INPUT, V contains the current KEV+NP Arnoldi vectors. c On OUTPUT, V contains the updated KEV Arnoldi vectors c in the first KEV columns of V. c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling c program. c c H Complex*16 (KEV+NP) by (KEV+NP) array. (INPUT/OUTPUT) c On INPUT, H contains the current KEV+NP by KEV+NP upper c Hessenberg matrix of the Arnoldi factorization. c On OUTPUT, H contains the updated KEV by KEV upper Hessenberg c matrix in the KEV leading submatrix. c c LDH Integer. (INPUT) c Leading dimension of H exactly as declared in the calling c program. c c RESID Complex*16 array of length N. (INPUT/OUTPUT) c On INPUT, RESID contains the the residual vector r_{k+p}. c On OUTPUT, RESID is the update residual vector rnew_{k} c in the first KEV locations. c c Q Complex*16 KEV+NP by KEV+NP work array. (WORKSPACE) c Work array used to accumulate the rotations and reflections c during the bulge chase sweep. c c LDQ Integer. (INPUT) c Leading dimension of Q exactly as declared in the calling c program. c c WORKL Complex*16 work array of length (KEV+NP). (WORKSPACE) c Private (replicated) array on each PE or array allocated on c the front end. c c WORKD Complex*16 work array of length 2*N. (WORKSPACE) c Distributed array used in the application of the accumulated c orthogonal matrix Q. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx Complex*16 c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c c\Routines called: c ivout ARPACK utility routine that prints integers. c arscnd ARPACK utility routine for timing. c zmout ARPACK utility routine that prints matrices c zvout ARPACK utility routine that prints vectors. c zlacpy LAPACK matrix copy routine. c zlanhs LAPACK routine that computes various norms of a matrix. c zlartg LAPACK Givens rotation construction routine. c zlaset LAPACK matrix initialization routine. c dlabad LAPACK routine for defining the underflow and overflow c limits. c dlamch LAPACK routine that determines machine constants. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c zgemv Level 2 BLAS routine for matrix vector multiplication. c zaxpy Level 1 BLAS that computes a vector triad. c zcopy Level 1 BLAS that copies one vector to another. c zscal Level 1 BLAS that scales a vector. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: napps.F SID: 2.3 DATE OF SID: 3/28/97 RELEASE: 2 c c\Remarks c 1. In this version, each shift is applied to all the sublocks of c the Hessenberg matrix H and not just to the submatrix that it c comes from. Deflation as in LAPACK routine zlahqr (QR algorithm c for upper Hessenberg matrices ) is used. c Upon output, the subdiagonals of H are enforced to be non-negative c real numbers. c c\EndLib c c----------------------------------------------------------------------- c subroutine znapps & ( n, kev, np, shift, v, ldv, h, ldh, resid, q, ldq, & workl, workd ) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c integer kev, ldh, ldq, ldv, n, np c c %-----------------% c | Array Arguments | c %-----------------% c Complex*16 & h(ldh,kev+np), resid(n), shift(np), & v(ldv,kev+np), q(ldq,kev+np), workd(2*n), workl(kev+np) c c %------------% c | Parameters | c %------------% c Complex*16 & one, zero Double precision & rzero parameter (one = (1.0D+0, 0.0D+0), zero = (0.0D+0, 0.0D+0), & rzero = 0.0D+0) c c %------------------------% c | Local Scalars & Arrays | c %------------------------% c integer i, iend, istart, j, jj, kplusp, msglvl logical first Complex*16 & cdum, f, g, h11, h21, r, s, sigma, t Double precision & c, ovfl, smlnum, ulp, unfl, tst1 save first, ovfl, smlnum, ulp, unfl c c %----------------------% c | External Subroutines | c %----------------------% c external zaxpy, zcopy, zgemv, zscal, zlacpy, zlartg, & zvout, zlaset, dlabad, zmout, arscnd, ivout c c %--------------------% c | External Functions | c %--------------------% c Double precision & zlanhs, dlamch, dlapy2 external zlanhs, dlamch, dlapy2 c c %----------------------% c | Intrinsics Functions | c %----------------------% c intrinsic abs, dimag, conjg, dcmplx, max, min, dble c c %---------------------% c | Statement Functions | c %---------------------% c Double precision & zabs1 zabs1( cdum ) = abs( dble( cdum ) ) + abs( dimag( cdum ) ) c c %----------------% c | Data statments | c %----------------% c data first / .true. / c c %-----------------------% c | Executable Statements | c %-----------------------% c if (first) then c c %-----------------------------------------------% c | Set machine-dependent constants for the | c | stopping criterion. If norm(H) <= sqrt(OVFL), | c | overflow should not occur. | c | REFERENCE: LAPACK subroutine zlahqr | c %-----------------------------------------------% c unfl = dlamch( 'safe minimum' ) ovfl = dble(one / unfl) call dlabad( unfl, ovfl ) ulp = dlamch( 'precision' ) smlnum = unfl*( n / ulp ) first = .false. end if c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call arscnd (t0) msglvl = mcapps c kplusp = kev + np c c %--------------------------------------------% c | Initialize Q to the identity to accumulate | c | the rotations and reflections | c %--------------------------------------------% c call zlaset ('All', kplusp, kplusp, zero, one, q, ldq) c c %----------------------------------------------% c | Quick return if there are no shifts to apply | c %----------------------------------------------% c if (np .eq. 0) go to 9000 c c %----------------------------------------------% c | Chase the bulge with the application of each | c | implicit shift. Each shift is applied to the | c | whole matrix including each block. | c %----------------------------------------------% c do 110 jj = 1, np sigma = shift(jj) c if (msglvl .gt. 2 ) then call ivout (logfil, 1, jj, ndigit, & '_napps: shift number.') call zvout (logfil, 1, sigma, ndigit, & '_napps: Value of the shift ') end if c istart = 1 20 continue c do 30 i = istart, kplusp-1 c c %----------------------------------------% c | Check for splitting and deflation. Use | c | a standard test as in the QR algorithm | c | REFERENCE: LAPACK subroutine zlahqr | c %----------------------------------------% c tst1 = zabs1( h( i, i ) ) + zabs1( h( i+1, i+1 ) ) if( tst1.eq.rzero ) & tst1 = zlanhs( '1', kplusp-jj+1, h, ldh, workl ) if ( abs(dble(h(i+1,i))) & .le. max(ulp*tst1, smlnum) ) then if (msglvl .gt. 0) then call ivout (logfil, 1, i, ndigit, & '_napps: matrix splitting at row/column no.') call ivout (logfil, 1, jj, ndigit, & '_napps: matrix splitting with shift number.') call zvout (logfil, 1, h(i+1,i), ndigit, & '_napps: off diagonal element.') end if iend = i h(i+1,i) = zero go to 40 end if 30 continue iend = kplusp 40 continue c if (msglvl .gt. 2) then call ivout (logfil, 1, istart, ndigit, & '_napps: Start of current block ') call ivout (logfil, 1, iend, ndigit, & '_napps: End of current block ') end if c c %------------------------------------------------% c | No reason to apply a shift to block of order 1 | c | or if the current block starts after the point | c | of compression since we'll discard this stuff | c %------------------------------------------------% c if ( istart .eq. iend .or. istart .gt. kev) go to 100 c h11 = h(istart,istart) h21 = h(istart+1,istart) f = h11 - sigma g = h21 c do 80 i = istart, iend-1 c c %------------------------------------------------------% c | Construct the plane rotation G to zero out the bulge | c %------------------------------------------------------% c call zlartg (f, g, c, s, r) if (i .gt. istart) then h(i,i-1) = r h(i+1,i-1) = zero end if c c %---------------------------------------------% c | Apply rotation to the left of H; H <- G'*H | c %---------------------------------------------% c do 50 j = i, kplusp t = c*h(i,j) + s*h(i+1,j) h(i+1,j) = -conjg(s)*h(i,j) + c*h(i+1,j) h(i,j) = t 50 continue c c %---------------------------------------------% c | Apply rotation to the right of H; H <- H*G | c %---------------------------------------------% c do 60 j = 1, min(i+2,iend) t = c*h(j,i) + conjg(s)*h(j,i+1) h(j,i+1) = -s*h(j,i) + c*h(j,i+1) h(j,i) = t 60 continue c c %-----------------------------------------------------% c | Accumulate the rotation in the matrix Q; Q <- Q*G' | c %-----------------------------------------------------% c do 70 j = 1, min(i+jj, kplusp) t = c*q(j,i) + conjg(s)*q(j,i+1) q(j,i+1) = - s*q(j,i) + c*q(j,i+1) q(j,i) = t 70 continue c c %---------------------------% c | Prepare for next rotation | c %---------------------------% c if (i .lt. iend-1) then f = h(i+1,i) g = h(i+2,i) end if 80 continue c c %-------------------------------% c | Finished applying the shift. | c %-------------------------------% c 100 continue c c %---------------------------------------------------------% c | Apply the same shift to the next block if there is any. | c %---------------------------------------------------------% c istart = iend + 1 if (iend .lt. kplusp) go to 20 c c %---------------------------------------------% c | Loop back to the top to get the next shift. | c %---------------------------------------------% c 110 continue c c %---------------------------------------------------% c | Perform a similarity transformation that makes | c | sure that the compressed H will have non-negative | c | real subdiagonal elements. | c %---------------------------------------------------% c do 120 j=1,kev if ( dble( h(j+1,j) ) .lt. rzero .or. & dimag( h(j+1,j) ) .ne. rzero ) then t = h(j+1,j) / dlapy2(dble(h(j+1,j)),dimag(h(j+1,j))) call zscal( kplusp-j+1, conjg(t), h(j+1,j), ldh ) call zscal( min(j+2, kplusp), t, h(1,j+1), 1 ) call zscal( min(j+np+1,kplusp), t, q(1,j+1), 1 ) h(j+1,j) = dcmplx( dble( h(j+1,j) ), rzero ) end if 120 continue c do 130 i = 1, kev c c %--------------------------------------------% c | Final check for splitting and deflation. | c | Use a standard test as in the QR algorithm | c | REFERENCE: LAPACK subroutine zlahqr. | c | Note: Since the subdiagonals of the | c | compressed H are nonnegative real numbers, | c | we take advantage of this. | c %--------------------------------------------% c tst1 = zabs1( h( i, i ) ) + zabs1( h( i+1, i+1 ) ) if( tst1 .eq. rzero ) & tst1 = zlanhs( '1', kev, h, ldh, workl ) if( dble( h( i+1,i ) ) .le. max( ulp*tst1, smlnum ) ) & h(i+1,i) = zero 130 continue c c %-------------------------------------------------% c | Compute the (kev+1)-st column of (V*Q) and | c | temporarily store the result in WORKD(N+1:2*N). | c | This is needed in the residual update since we | c | cannot GUARANTEE that the corresponding entry | c | of H would be zero as in exact arithmetic. | c %-------------------------------------------------% c if ( dble( h(kev+1,kev) ) .gt. rzero ) & call zgemv ('N', n, kplusp, one, v, ldv, q(1,kev+1), 1, zero, & workd(n+1), 1) c c %----------------------------------------------------------% c | Compute column 1 to kev of (V*Q) in backward order | c | taking advantage of the upper Hessenberg structure of Q. | c %----------------------------------------------------------% c do 140 i = 1, kev call zgemv ('N', n, kplusp-i+1, one, v, ldv, & q(1,kev-i+1), 1, zero, workd, 1) call zcopy (n, workd, 1, v(1,kplusp-i+1), 1) 140 continue c c %-------------------------------------------------% c | Move v(:,kplusp-kev+1:kplusp) into v(:,1:kev). | c %-------------------------------------------------% c call zlacpy ('A', n, kev, v(1,kplusp-kev+1), ldv, v, ldv) c c %--------------------------------------------------------------% c | Copy the (kev+1)-st column of (V*Q) in the appropriate place | c %--------------------------------------------------------------% c if ( dble( h(kev+1,kev) ) .gt. rzero ) & call zcopy (n, workd(n+1), 1, v(1,kev+1), 1) c c %-------------------------------------% c | Update the residual vector: | c | r <- sigmak*r + betak*v(:,kev+1) | c | where | c | sigmak = (e_{kev+p}'*Q)*e_{kev} | c | betak = e_{kev+1}'*H*e_{kev} | c %-------------------------------------% c call zscal (n, q(kplusp,kev), resid, 1) if ( dble( h(kev+1,kev) ) .gt. rzero ) & call zaxpy (n, h(kev+1,kev), v(1,kev+1), 1, resid, 1) c if (msglvl .gt. 1) then call zvout (logfil, 1, q(kplusp,kev), ndigit, & '_napps: sigmak = (e_{kev+p}^T*Q)*e_{kev}') call zvout (logfil, 1, h(kev+1,kev), ndigit, & '_napps: betak = e_{kev+1}^T*H*e_{kev}') call ivout (logfil, 1, kev, ndigit, & '_napps: Order of the final Hessenberg matrix ') if (msglvl .gt. 2) then call zmout (logfil, kev, kev, h, ldh, ndigit, & '_napps: updated Hessenberg matrix H for next iteration') end if c end if c 9000 continue call arscnd (t1) tcapps = tcapps + (t1 - t0) c return c c %---------------% c | End of znapps | c %---------------% c end arpack-0.92.1/SRC/dseigt.f0000644000175000017500000001211510776001577012054 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: dseigt c c\Description: c Compute the eigenvalues of the current symmetric tridiagonal matrix c and the corresponding error bounds given the current residual norm. c c\Usage: c call dseigt c ( RNORM, N, H, LDH, EIG, BOUNDS, WORKL, IERR ) c c\Arguments c RNORM Double precision scalar. (INPUT) c RNORM contains the residual norm corresponding to the current c symmetric tridiagonal matrix H. c c N Integer. (INPUT) c Size of the symmetric tridiagonal matrix H. c c H Double precision N by 2 array. (INPUT) c H contains the symmetric tridiagonal matrix with the c subdiagonal in the first column starting at H(2,1) and the c main diagonal in second column. c c LDH Integer. (INPUT) c Leading dimension of H exactly as declared in the calling c program. c c EIG Double precision array of length N. (OUTPUT) c On output, EIG contains the N eigenvalues of H possibly c unsorted. The BOUNDS arrays are returned in the c same sorted order as EIG. c c BOUNDS Double precision array of length N. (OUTPUT) c On output, BOUNDS contains the error estimates corresponding c to the eigenvalues EIG. This is equal to RNORM times the c last components of the eigenvectors corresponding to the c eigenvalues in EIG. c c WORKL Double precision work array of length 3*N. (WORKSPACE) c Private (replicated) array on each PE or array allocated on c the front end. c c IERR Integer. (OUTPUT) c Error exit flag from dstqrb. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx real c c\Routines called: c dstqrb ARPACK routine that computes the eigenvalues and the c last components of the eigenvectors of a symmetric c and tridiagonal matrix. c arscnd ARPACK utility routine for timing. c dvout ARPACK utility routine that prints vectors. c dcopy Level 1 BLAS that copies one vector to another. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c xx/xx/92: Version ' 2.4' c c\SCCS Information: @(#) c FILE: seigt.F SID: 2.4 DATE OF SID: 8/27/96 RELEASE: 2 c c\Remarks c None c c\EndLib c c----------------------------------------------------------------------- c subroutine dseigt & ( rnorm, n, h, ldh, eig, bounds, workl, ierr ) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c integer ierr, ldh, n Double precision & rnorm c c %-----------------% c | Array Arguments | c %-----------------% c Double precision & eig(n), bounds(n), h(ldh,2), workl(3*n) c c %------------% c | Parameters | c %------------% c Double precision & zero parameter (zero = 0.0D+0) c c %---------------% c | Local Scalars | c %---------------% c integer i, k, msglvl c c %----------------------% c | External Subroutines | c %----------------------% c external dcopy, dstqrb, dvout, arscnd c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call arscnd (t0) msglvl = mseigt c if (msglvl .gt. 0) then call dvout (logfil, n, h(1,2), ndigit, & '_seigt: main diagonal of matrix H') if (n .gt. 1) then call dvout (logfil, n-1, h(2,1), ndigit, & '_seigt: sub diagonal of matrix H') end if end if c call dcopy (n, h(1,2), 1, eig, 1) call dcopy (n-1, h(2,1), 1, workl, 1) call dstqrb (n, eig, workl, bounds, workl(n+1), ierr) if (ierr .ne. 0) go to 9000 if (msglvl .gt. 1) then call dvout (logfil, n, bounds, ndigit, & '_seigt: last row of the eigenvector matrix for H') end if c c %-----------------------------------------------% c | Finally determine the error bounds associated | c | with the n Ritz values of H. | c %-----------------------------------------------% c do 30 k = 1, n bounds(k) = rnorm*abs(bounds(k)) 30 continue c call arscnd (t1) tseigt = tseigt + (t1 - t0) c 9000 continue return c c %---------------% c | End of dseigt | c %---------------% c end arpack-0.92.1/SRC/cnaup2.f0000644000175000017500000007103510776001577011773 00000000000000c\BeginDoc c c\Name: cnaup2 c c\Description: c Intermediate level interface called by cnaupd. c c\Usage: c call cnaup2 c ( IDO, BMAT, N, WHICH, NEV, NP, TOL, RESID, MODE, IUPD, c ISHIFT, MXITER, V, LDV, H, LDH, RITZ, BOUNDS, c Q, LDQ, WORKL, IPNTR, WORKD, RWORK, INFO ) c c\Arguments c c IDO, BMAT, N, WHICH, NEV, TOL, RESID: same as defined in cnaupd. c MODE, ISHIFT, MXITER: see the definition of IPARAM in cnaupd. c c NP Integer. (INPUT/OUTPUT) c Contains the number of implicit shifts to apply during c each Arnoldi iteration. c If ISHIFT=1, NP is adjusted dynamically at each iteration c to accelerate convergence and prevent stagnation. c This is also roughly equal to the number of matrix-vector c products (involving the operator OP) per Arnoldi iteration. c The logic for adjusting is contained within the current c subroutine. c If ISHIFT=0, NP is the number of shifts the user needs c to provide via reverse comunication. 0 < NP < NCV-NEV. c NP may be less than NCV-NEV since a leading block of the current c upper Hessenberg matrix has split off and contains "unwanted" c Ritz values. c Upon termination of the IRA iteration, NP contains the number c of "converged" wanted Ritz values. c c IUPD Integer. (INPUT) c IUPD .EQ. 0: use explicit restart instead implicit update. c IUPD .NE. 0: use implicit update. c c V Complex N by (NEV+NP) array. (INPUT/OUTPUT) c The Arnoldi basis vectors are returned in the first NEV c columns of V. c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling c program. c c H Complex (NEV+NP) by (NEV+NP) array. (OUTPUT) c H is used to store the generated upper Hessenberg matrix c c LDH Integer. (INPUT) c Leading dimension of H exactly as declared in the calling c program. c c RITZ Complex array of length NEV+NP. (OUTPUT) c RITZ(1:NEV) contains the computed Ritz values of OP. c c BOUNDS Complex array of length NEV+NP. (OUTPUT) c BOUNDS(1:NEV) contain the error bounds corresponding to c the computed Ritz values. c c Q Complex (NEV+NP) by (NEV+NP) array. (WORKSPACE) c Private (replicated) work array used to accumulate the c rotation in the shift application step. c c LDQ Integer. (INPUT) c Leading dimension of Q exactly as declared in the calling c program. c c WORKL Complex work array of length at least c (NEV+NP)**2 + 3*(NEV+NP). (WORKSPACE) c Private (replicated) array on each PE or array allocated on c the front end. It is used in shifts calculation, shifts c application and convergence checking. c c c IPNTR Integer array of length 3. (OUTPUT) c Pointer to mark the starting locations in the WORKD for c vectors used by the Arnoldi iteration. c ------------------------------------------------------------- c IPNTR(1): pointer to the current operand vector X. c IPNTR(2): pointer to the current result vector Y. c IPNTR(3): pointer to the vector B * X when used in the c shift-and-invert mode. X is the current operand. c ------------------------------------------------------------- c c WORKD Complex work array of length 3*N. (WORKSPACE) c Distributed array to be used in the basic Arnoldi iteration c for reverse communication. The user should not use WORKD c as temporary workspace during the iteration !!!!!!!!!! c See Data Distribution Note in CNAUPD. c c RWORK Real work array of length NEV+NP ( WORKSPACE) c Private (replicated) array on each PE or array allocated on c the front end. c c INFO Integer. (INPUT/OUTPUT) c If INFO .EQ. 0, a randomly initial residual vector is used. c If INFO .NE. 0, RESID contains the initial residual vector, c possibly from a previous run. c Error flag on output. c = 0: Normal return. c = 1: Maximum number of iterations taken. c All possible eigenvalues of OP has been found. c NP returns the number of converged Ritz values. c = 2: No shifts could be applied. c = -8: Error return from LAPACK eigenvalue calculation; c This should never happen. c = -9: Starting vector is zero. c = -9999: Could not build an Arnoldi factorization. c Size that was built in returned in NP. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx Complex c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly c Restarted Arnoldi Iteration", Rice University Technical Report c TR95-13, Department of Computational and Applied Mathematics. c c\Routines called: c cgetv0 ARPACK initial vector generation routine. c cnaitr ARPACK Arnoldi factorization routine. c cnapps ARPACK application of implicit shifts routine. c cneigh ARPACK compute Ritz values and error bounds routine. c cngets ARPACK reorder Ritz values and error bounds routine. c csortc ARPACK sorting routine. c ivout ARPACK utility routine that prints integers. c arscnd ARPACK utility routine for timing. c cmout ARPACK utility routine that prints matrices c cvout ARPACK utility routine that prints vectors. c svout ARPACK utility routine that prints vectors. c slamch LAPACK routine that determines machine constants. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c ccopy Level 1 BLAS that copies one vector to another . c cdotc Level 1 BLAS that computes the scalar product of two vectors. c cswap Level 1 BLAS that swaps two vectors. c scnrm2 Level 1 BLAS that computes the norm of a vector. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice Universitya c Chao Yang Houston, Texas c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: naup2.F SID: 2.6 DATE OF SID: 06/01/00 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c----------------------------------------------------------------------- c subroutine cnaup2 & ( ido, bmat, n, which, nev, np, tol, resid, mode, iupd, & ishift, mxiter, v, ldv, h, ldh, ritz, bounds, & q, ldq, workl, ipntr, workd, rwork, info ) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character bmat*1, which*2 integer ido, info, ishift, iupd, mode, ldh, ldq, ldv, mxiter, & n, nev, np Real & tol c c %-----------------% c | Array Arguments | c %-----------------% c integer ipntr(13) Complex & bounds(nev+np), h(ldh,nev+np), q(ldq,nev+np), & resid(n), ritz(nev+np), v(ldv,nev+np), & workd(3*n), workl( (nev+np)*(nev+np+3) ) Real & rwork(nev+np) c c %------------% c | Parameters | c %------------% c Complex & one, zero Real & rzero parameter (one = (1.0E+0, 0.0E+0) , zero = (0.0E+0, 0.0E+0) , & rzero = 0.0E+0 ) c c %---------------% c | Local Scalars | c %---------------% c logical cnorm , getv0, initv , update, ushift integer ierr , iter , kplusp, msglvl, nconv, & nevbef, nev0 , np0 , nptemp, i , & j Complex & cmpnorm Real & rnorm , eps23, rtemp character wprime*2 c save cnorm, getv0, initv , update, ushift, & rnorm, iter , kplusp, msglvl, nconv , & nevbef, nev0 , np0 , eps23 c c c %-----------------------% c | Local array arguments | c %-----------------------% c integer kp(3) c c %----------------------% c | External Subroutines | c %----------------------% c external ccopy, cgetv0, cnaitr, cneigh, cngets, cnapps, & csortc, cswap, cmout, cvout, ivout, arscnd c c %--------------------% c | External functions | c %--------------------% c Complex & cdotc Real & scnrm2, slamch, slapy2 external cdotc, scnrm2, slamch, slapy2 c c %---------------------% c | Intrinsic Functions | c %---------------------% c intrinsic aimag, real , min, max c c %-----------------------% c | Executable Statements | c %-----------------------% c if (ido .eq. 0) then c call arscnd (t0) c msglvl = mcaup2 c nev0 = nev np0 = np c c %-------------------------------------% c | kplusp is the bound on the largest | c | Lanczos factorization built. | c | nconv is the current number of | c | "converged" eigenvalues. | c | iter is the counter on the current | c | iteration step. | c %-------------------------------------% c kplusp = nev + np nconv = 0 iter = 0 c c %---------------------------------% c | Get machine dependent constant. | c %---------------------------------% c eps23 = slamch('Epsilon-Machine') eps23 = eps23**(2.0E+0 / 3.0E+0 ) c c %---------------------------------------% c | Set flags for computing the first NEV | c | steps of the Arnoldi factorization. | c %---------------------------------------% c getv0 = .true. update = .false. ushift = .false. cnorm = .false. c if (info .ne. 0) then c c %--------------------------------------------% c | User provides the initial residual vector. | c %--------------------------------------------% c initv = .true. info = 0 else initv = .false. end if end if c c %---------------------------------------------% c | Get a possibly random starting vector and | c | force it into the range of the operator OP. | c %---------------------------------------------% c 10 continue c if (getv0) then call cgetv0 (ido, bmat, 1, initv, n, 1, v, ldv, resid, rnorm, & ipntr, workd, info) c if (ido .ne. 99) go to 9000 c if (rnorm .eq. rzero) then c c %-----------------------------------------% c | The initial vector is zero. Error exit. | c %-----------------------------------------% c info = -9 go to 1100 end if getv0 = .false. ido = 0 end if c c %-----------------------------------% c | Back from reverse communication : | c | continue with update step | c %-----------------------------------% c if (update) go to 20 c c %-------------------------------------------% c | Back from computing user specified shifts | c %-------------------------------------------% c if (ushift) go to 50 c c %-------------------------------------% c | Back from computing residual norm | c | at the end of the current iteration | c %-------------------------------------% c if (cnorm) go to 100 c c %----------------------------------------------------------% c | Compute the first NEV steps of the Arnoldi factorization | c %----------------------------------------------------------% c call cnaitr (ido, bmat, n, 0, nev, mode, resid, rnorm, v, ldv, & h, ldh, ipntr, workd, info) c if (ido .ne. 99) go to 9000 c if (info .gt. 0) then np = info mxiter = iter info = -9999 go to 1200 end if c c %--------------------------------------------------------------% c | | c | M A I N ARNOLDI I T E R A T I O N L O O P | c | Each iteration implicitly restarts the Arnoldi | c | factorization in place. | c | | c %--------------------------------------------------------------% c 1000 continue c iter = iter + 1 c if (msglvl .gt. 0) then call ivout (logfil, 1, iter, ndigit, & '_naup2: **** Start of major iteration number ****') end if c c %-----------------------------------------------------------% c | Compute NP additional steps of the Arnoldi factorization. | c | Adjust NP since NEV might have been updated by last call | c | to the shift application routine cnapps. | c %-----------------------------------------------------------% c np = kplusp - nev c if (msglvl .gt. 1) then call ivout (logfil, 1, nev, ndigit, & '_naup2: The length of the current Arnoldi factorization') call ivout (logfil, 1, np, ndigit, & '_naup2: Extend the Arnoldi factorization by') end if c c %-----------------------------------------------------------% c | Compute NP additional steps of the Arnoldi factorization. | c %-----------------------------------------------------------% c ido = 0 20 continue update = .true. c call cnaitr(ido, bmat, n, nev, np, mode, resid, rnorm, & v , ldv , h, ldh, ipntr, workd, info) c if (ido .ne. 99) go to 9000 c if (info .gt. 0) then np = info mxiter = iter info = -9999 go to 1200 end if update = .false. c if (msglvl .gt. 1) then call svout (logfil, 1, rnorm, ndigit, & '_naup2: Corresponding B-norm of the residual') end if c c %--------------------------------------------------------% c | Compute the eigenvalues and corresponding error bounds | c | of the current upper Hessenberg matrix. | c %--------------------------------------------------------% c call cneigh (rnorm, kplusp, h, ldh, ritz, bounds, & q, ldq, workl, rwork, ierr) c if (ierr .ne. 0) then info = -8 go to 1200 end if c c %---------------------------------------------------% c | Select the wanted Ritz values and their bounds | c | to be used in the convergence test. | c | The wanted part of the spectrum and corresponding | c | error bounds are in the last NEV loc. of RITZ, | c | and BOUNDS respectively. | c %---------------------------------------------------% c nev = nev0 np = np0 c c %--------------------------------------------------% c | Make a copy of Ritz values and the corresponding | c | Ritz estimates obtained from cneigh. | c %--------------------------------------------------% c call ccopy(kplusp,ritz,1,workl(kplusp**2+1),1) call ccopy(kplusp,bounds,1,workl(kplusp**2+kplusp+1),1) c c %---------------------------------------------------% c | Select the wanted Ritz values and their bounds | c | to be used in the convergence test. | c | The wanted part of the spectrum and corresponding | c | bounds are in the last NEV loc. of RITZ | c | BOUNDS respectively. | c %---------------------------------------------------% c call cngets (ishift, which, nev, np, ritz, bounds) c c %------------------------------------------------------------% c | Convergence test: currently we use the following criteria. | c | The relative accuracy of a Ritz value is considered | c | acceptable if: | c | | c | error_bounds(i) .le. tol*max(eps23, magnitude_of_ritz(i)). | c | | c %------------------------------------------------------------% c nconv = 0 c do 25 i = 1, nev rtemp = max( eps23, slapy2( real (ritz(np+i)), & aimag(ritz(np+i)) ) ) if ( slapy2(real (bounds(np+i)),aimag(bounds(np+i))) & .le. tol*rtemp ) then nconv = nconv + 1 end if 25 continue c if (msglvl .gt. 2) then kp(1) = nev kp(2) = np kp(3) = nconv call ivout (logfil, 3, kp, ndigit, & '_naup2: NEV, NP, NCONV are') call cvout (logfil, kplusp, ritz, ndigit, & '_naup2: The eigenvalues of H') call cvout (logfil, kplusp, bounds, ndigit, & '_naup2: Ritz estimates of the current NCV Ritz values') end if c c %---------------------------------------------------------% c | Count the number of unwanted Ritz values that have zero | c | Ritz estimates. If any Ritz estimates are equal to zero | c | then a leading block of H of order equal to at least | c | the number of Ritz values with zero Ritz estimates has | c | split off. None of these Ritz values may be removed by | c | shifting. Decrease NP the number of shifts to apply. If | c | no shifts may be applied, then prepare to exit | c %---------------------------------------------------------% c nptemp = np do 30 j=1, nptemp if (bounds(j) .eq. zero) then np = np - 1 nev = nev + 1 end if 30 continue c if ( (nconv .ge. nev0) .or. & (iter .gt. mxiter) .or. & (np .eq. 0) ) then c if (msglvl .gt. 4) then call cvout(logfil, kplusp, workl(kplusp**2+1), ndigit, & '_naup2: Eigenvalues computed by _neigh:') call cvout(logfil, kplusp, workl(kplusp**2+kplusp+1), & ndigit, & '_naup2: Ritz estimates computed by _neigh:') end if c c %------------------------------------------------% c | Prepare to exit. Put the converged Ritz values | c | and corresponding bounds in RITZ(1:NCONV) and | c | BOUNDS(1:NCONV) respectively. Then sort. Be | c | careful when NCONV > NP | c %------------------------------------------------% c c %------------------------------------------% c | Use h( 3,1 ) as storage to communicate | c | rnorm to cneupd if needed | c %------------------------------------------% h(3,1) = cmplx(rnorm,rzero) c c %----------------------------------------------% c | Sort Ritz values so that converged Ritz | c | values appear within the first NEV locations | c | of ritz and bounds, and the most desired one | c | appears at the front. | c %----------------------------------------------% c if (which .eq. 'LM') wprime = 'SM' if (which .eq. 'SM') wprime = 'LM' if (which .eq. 'LR') wprime = 'SR' if (which .eq. 'SR') wprime = 'LR' if (which .eq. 'LI') wprime = 'SI' if (which .eq. 'SI') wprime = 'LI' c call csortc(wprime, .true., kplusp, ritz, bounds) c c %--------------------------------------------------% c | Scale the Ritz estimate of each Ritz value | c | by 1 / max(eps23, magnitude of the Ritz value). | c %--------------------------------------------------% c do 35 j = 1, nev0 rtemp = max( eps23, slapy2( real (ritz(j)), & aimag(ritz(j)) ) ) bounds(j) = bounds(j)/rtemp 35 continue c c %---------------------------------------------------% c | Sort the Ritz values according to the scaled Ritz | c | estimates. This will push all the converged ones | c | towards the front of ritz, bounds (in the case | c | when NCONV < NEV.) | c %---------------------------------------------------% c wprime = 'LM' call csortc(wprime, .true., nev0, bounds, ritz) c c %----------------------------------------------% c | Scale the Ritz estimate back to its original | c | value. | c %----------------------------------------------% c do 40 j = 1, nev0 rtemp = max( eps23, slapy2( real (ritz(j)), & aimag(ritz(j)) ) ) bounds(j) = bounds(j)*rtemp 40 continue c c %-----------------------------------------------% c | Sort the converged Ritz values again so that | c | the "threshold" value appears at the front of | c | ritz and bound. | c %-----------------------------------------------% c call csortc(which, .true., nconv, ritz, bounds) c if (msglvl .gt. 1) then call cvout (logfil, kplusp, ritz, ndigit, & '_naup2: Sorted eigenvalues') call cvout (logfil, kplusp, bounds, ndigit, & '_naup2: Sorted ritz estimates.') end if c c %------------------------------------% c | Max iterations have been exceeded. | c %------------------------------------% c if (iter .gt. mxiter .and. nconv .lt. nev0) info = 1 c c %---------------------% c | No shifts to apply. | c %---------------------% c if (np .eq. 0 .and. nconv .lt. nev0) info = 2 c np = nconv go to 1100 c else if ( (nconv .lt. nev0) .and. (ishift .eq. 1) ) then c c %-------------------------------------------------% c | Do not have all the requested eigenvalues yet. | c | To prevent possible stagnation, adjust the size | c | of NEV. | c %-------------------------------------------------% c nevbef = nev nev = nev + min(nconv, np/2) if (nev .eq. 1 .and. kplusp .ge. 6) then nev = kplusp / 2 else if (nev .eq. 1 .and. kplusp .gt. 3) then nev = 2 end if np = kplusp - nev c c %---------------------------------------% c | If the size of NEV was just increased | c | resort the eigenvalues. | c %---------------------------------------% c if (nevbef .lt. nev) & call cngets (ishift, which, nev, np, ritz, bounds) c end if c if (msglvl .gt. 0) then call ivout (logfil, 1, nconv, ndigit, & '_naup2: no. of "converged" Ritz values at this iter.') if (msglvl .gt. 1) then kp(1) = nev kp(2) = np call ivout (logfil, 2, kp, ndigit, & '_naup2: NEV and NP are') call cvout (logfil, nev, ritz(np+1), ndigit, & '_naup2: "wanted" Ritz values ') call cvout (logfil, nev, bounds(np+1), ndigit, & '_naup2: Ritz estimates of the "wanted" values ') end if end if c if (ishift .eq. 0) then c c %-------------------------------------------------------% c | User specified shifts: pop back out to get the shifts | c | and return them in the first 2*NP locations of WORKL. | c %-------------------------------------------------------% c ushift = .true. ido = 3 go to 9000 end if 50 continue ushift = .false. c if ( ishift .ne. 1 ) then c c %----------------------------------% c | Move the NP shifts from WORKL to | c | RITZ, to free up WORKL | c | for non-exact shift case. | c %----------------------------------% c call ccopy (np, workl, 1, ritz, 1) end if c if (msglvl .gt. 2) then call ivout (logfil, 1, np, ndigit, & '_naup2: The number of shifts to apply ') call cvout (logfil, np, ritz, ndigit, & '_naup2: values of the shifts') if ( ishift .eq. 1 ) & call cvout (logfil, np, bounds, ndigit, & '_naup2: Ritz estimates of the shifts') end if c c %---------------------------------------------------------% c | Apply the NP implicit shifts by QR bulge chasing. | c | Each shift is applied to the whole upper Hessenberg | c | matrix H. | c | The first 2*N locations of WORKD are used as workspace. | c %---------------------------------------------------------% c call cnapps (n, nev, np, ritz, v, ldv, & h, ldh, resid, q, ldq, workl, workd) c c %---------------------------------------------% c | Compute the B-norm of the updated residual. | c | Keep B*RESID in WORKD(1:N) to be used in | c | the first step of the next call to cnaitr. | c %---------------------------------------------% c cnorm = .true. call arscnd (t2) if (bmat .eq. 'G') then nbx = nbx + 1 call ccopy (n, resid, 1, workd(n+1), 1) ipntr(1) = n + 1 ipntr(2) = 1 ido = 2 c c %----------------------------------% c | Exit in order to compute B*RESID | c %----------------------------------% c go to 9000 else if (bmat .eq. 'I') then call ccopy (n, resid, 1, workd, 1) end if c 100 continue c c %----------------------------------% c | Back from reverse communication; | c | WORKD(1:N) := B*RESID | c %----------------------------------% c if (bmat .eq. 'G') then call arscnd (t3) tmvbx = tmvbx + (t3 - t2) end if c if (bmat .eq. 'G') then cmpnorm = cdotc (n, resid, 1, workd, 1) rnorm = sqrt(slapy2(real (cmpnorm),aimag(cmpnorm))) else if (bmat .eq. 'I') then rnorm = scnrm2(n, resid, 1) end if cnorm = .false. c if (msglvl .gt. 2) then call svout (logfil, 1, rnorm, ndigit, & '_naup2: B-norm of residual for compressed factorization') call cmout (logfil, nev, nev, h, ldh, ndigit, & '_naup2: Compressed upper Hessenberg matrix H') end if c go to 1000 c c %---------------------------------------------------------------% c | | c | E N D O F M A I N I T E R A T I O N L O O P | c | | c %---------------------------------------------------------------% c 1100 continue c mxiter = iter nev = nconv c 1200 continue ido = 99 c c %------------% c | Error Exit | c %------------% c call arscnd (t1) tcaup2 = t1 - t0 c 9000 continue c c %---------------% c | End of cnaup2 | c %---------------% c return end arpack-0.92.1/SRC/snaitr.f0000644000175000017500000007346710776001577012116 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: snaitr c c\Description: c Reverse communication interface for applying NP additional steps to c a K step nonsymmetric Arnoldi factorization. c c Input: OP*V_{k} - V_{k}*H = r_{k}*e_{k}^T c c with (V_{k}^T)*B*V_{k} = I, (V_{k}^T)*B*r_{k} = 0. c c Output: OP*V_{k+p} - V_{k+p}*H = r_{k+p}*e_{k+p}^T c c with (V_{k+p}^T)*B*V_{k+p} = I, (V_{k+p}^T)*B*r_{k+p} = 0. c c where OP and B are as in snaupd. The B-norm of r_{k+p} is also c computed and returned. c c\Usage: c call snaitr c ( IDO, BMAT, N, K, NP, NB, RESID, RNORM, V, LDV, H, LDH, c IPNTR, WORKD, INFO ) c c\Arguments c IDO Integer. (INPUT/OUTPUT) c Reverse communication flag. c ------------------------------------------------------------- c IDO = 0: first call to the reverse communication interface c IDO = -1: compute Y = OP * X where c IPNTR(1) is the pointer into WORK for X, c IPNTR(2) is the pointer into WORK for Y. c This is for the restart phase to force the new c starting vector into the range of OP. c IDO = 1: compute Y = OP * X where c IPNTR(1) is the pointer into WORK for X, c IPNTR(2) is the pointer into WORK for Y, c IPNTR(3) is the pointer into WORK for B * X. c IDO = 2: compute Y = B * X where c IPNTR(1) is the pointer into WORK for X, c IPNTR(2) is the pointer into WORK for Y. c IDO = 99: done c ------------------------------------------------------------- c When the routine is used in the "shift-and-invert" mode, the c vector B * Q is already available and do not need to be c recompute in forming OP * Q. c c BMAT Character*1. (INPUT) c BMAT specifies the type of the matrix B that defines the c semi-inner product for the operator OP. See snaupd. c B = 'I' -> standard eigenvalue problem A*x = lambda*x c B = 'G' -> generalized eigenvalue problem A*x = lambda*M**x c c N Integer. (INPUT) c Dimension of the eigenproblem. c c K Integer. (INPUT) c Current size of V and H. c c NP Integer. (INPUT) c Number of additional Arnoldi steps to take. c c NB Integer. (INPUT) c Blocksize to be used in the recurrence. c Only work for NB = 1 right now. The goal is to have a c program that implement both the block and non-block method. c c RESID Real array of length N. (INPUT/OUTPUT) c On INPUT: RESID contains the residual vector r_{k}. c On OUTPUT: RESID contains the residual vector r_{k+p}. c c RNORM Real scalar. (INPUT/OUTPUT) c B-norm of the starting residual on input. c B-norm of the updated residual r_{k+p} on output. c c V Real N by K+NP array. (INPUT/OUTPUT) c On INPUT: V contains the Arnoldi vectors in the first K c columns. c On OUTPUT: V contains the new NP Arnoldi vectors in the next c NP columns. The first K columns are unchanged. c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling c program. c c H Real (K+NP) by (K+NP) array. (INPUT/OUTPUT) c H is used to store the generated upper Hessenberg matrix. c c LDH Integer. (INPUT) c Leading dimension of H exactly as declared in the calling c program. c c IPNTR Integer array of length 3. (OUTPUT) c Pointer to mark the starting locations in the WORK for c vectors used by the Arnoldi iteration. c ------------------------------------------------------------- c IPNTR(1): pointer to the current operand vector X. c IPNTR(2): pointer to the current result vector Y. c IPNTR(3): pointer to the vector B * X when used in the c shift-and-invert mode. X is the current operand. c ------------------------------------------------------------- c c WORKD Real work array of length 3*N. (REVERSE COMMUNICATION) c Distributed array to be used in the basic Arnoldi iteration c for reverse communication. The calling program should not c use WORKD as temporary workspace during the iteration !!!!!! c On input, WORKD(1:N) = B*RESID and is used to save some c computation at the first step. c c INFO Integer. (OUTPUT) c = 0: Normal exit. c > 0: Size of the spanning invariant subspace of OP found. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx real c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly c Restarted Arnoldi Iteration", Rice University Technical Report c TR95-13, Department of Computational and Applied Mathematics. c c\Routines called: c sgetv0 ARPACK routine to generate the initial vector. c ivout ARPACK utility routine that prints integers. c arscnd ARPACK utility routine for timing. c smout ARPACK utility routine that prints matrices c svout ARPACK utility routine that prints vectors. c slabad LAPACK routine that computes machine constants. c slamch LAPACK routine that determines machine constants. c slascl LAPACK routine for careful scaling of a matrix. c slanhs LAPACK routine that computes various norms of a matrix. c sgemv Level 2 BLAS routine for matrix vector multiplication. c saxpy Level 1 BLAS that computes a vector triad. c sscal Level 1 BLAS that scales a vector. c scopy Level 1 BLAS that copies one vector to another . c sdot Level 1 BLAS that computes the scalar product of two vectors. c snrm2 Level 1 BLAS that computes the norm of a vector. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c xx/xx/92: Version ' 2.4' c c\SCCS Information: @(#) c FILE: naitr.F SID: 2.4 DATE OF SID: 8/27/96 RELEASE: 2 c c\Remarks c The algorithm implemented is: c c restart = .false. c Given V_{k} = [v_{1}, ..., v_{k}], r_{k}; c r_{k} contains the initial residual vector even for k = 0; c Also assume that rnorm = || B*r_{k} || and B*r_{k} are already c computed by the calling program. c c betaj = rnorm ; p_{k+1} = B*r_{k} ; c For j = k+1, ..., k+np Do c 1) if ( betaj < tol ) stop or restart depending on j. c ( At present tol is zero ) c if ( restart ) generate a new starting vector. c 2) v_{j} = r(j-1)/betaj; V_{j} = [V_{j-1}, v_{j}]; c p_{j} = p_{j}/betaj c 3) r_{j} = OP*v_{j} where OP is defined as in snaupd c For shift-invert mode p_{j} = B*v_{j} is already available. c wnorm = || OP*v_{j} || c 4) Compute the j-th step residual vector. c w_{j} = V_{j}^T * B * OP * v_{j} c r_{j} = OP*v_{j} - V_{j} * w_{j} c H(:,j) = w_{j}; c H(j,j-1) = rnorm c rnorm = || r_(j) || c If (rnorm > 0.717*wnorm) accept step and go back to 1) c 5) Re-orthogonalization step: c s = V_{j}'*B*r_{j} c r_{j} = r_{j} - V_{j}*s; rnorm1 = || r_{j} || c alphaj = alphaj + s_{j}; c 6) Iterative refinement step: c If (rnorm1 > 0.717*rnorm) then c rnorm = rnorm1 c accept step and go back to 1) c Else c rnorm = rnorm1 c If this is the first time in step 6), go to 5) c Else r_{j} lies in the span of V_{j} numerically. c Set r_{j} = 0 and rnorm = 0; go to 1) c EndIf c End Do c c\EndLib c c----------------------------------------------------------------------- c subroutine snaitr & (ido, bmat, n, k, np, nb, resid, rnorm, v, ldv, h, ldh, & ipntr, workd, info) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character bmat*1 integer ido, info, k, ldh, ldv, n, nb, np Real & rnorm c c %-----------------% c | Array Arguments | c %-----------------% c integer ipntr(3) Real & h(ldh,k+np), resid(n), v(ldv,k+np), workd(3*n) c c %------------% c | Parameters | c %------------% c Real & one, zero parameter (one = 1.0E+0, zero = 0.0E+0) c c %---------------% c | Local Scalars | c %---------------% c logical first, orth1, orth2, rstart, step3, step4 integer ierr, i, infol, ipj, irj, ivj, iter, itry, j, msglvl, & jj Real & betaj, ovfl, temp1, rnorm1, smlnum, tst1, ulp, unfl, & wnorm save first, orth1, orth2, rstart, step3, step4, & ierr, ipj, irj, ivj, iter, itry, j, msglvl, ovfl, & betaj, rnorm1, smlnum, ulp, unfl, wnorm c c %-----------------------% c | Local Array Arguments | c %-----------------------% c Real & xtemp(2) c c %----------------------% c | External Subroutines | c %----------------------% c external saxpy, scopy, sscal, sgemv, sgetv0, slabad, & svout, smout, ivout, arscnd c c %--------------------% c | External Functions | c %--------------------% c Real & sdot, snrm2, slanhs, slamch external sdot, snrm2, slanhs, slamch c c %---------------------% c | Intrinsic Functions | c %---------------------% c intrinsic abs, sqrt c c %-----------------% c | Data statements | c %-----------------% c data first / .true. / c c %-----------------------% c | Executable Statements | c %-----------------------% c if (first) then c c %-----------------------------------------% c | Set machine-dependent constants for the | c | the splitting and deflation criterion. | c | If norm(H) <= sqrt(OVFL), | c | overflow should not occur. | c | REFERENCE: LAPACK subroutine slahqr | c %-----------------------------------------% c unfl = slamch( 'safe minimum' ) ovfl = one / unfl call slabad( unfl, ovfl ) ulp = slamch( 'precision' ) smlnum = unfl*( n / ulp ) first = .false. end if c if (ido .eq. 0) then c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call arscnd (t0) msglvl = mnaitr c c %------------------------------% c | Initial call to this routine | c %------------------------------% c info = 0 step3 = .false. step4 = .false. rstart = .false. orth1 = .false. orth2 = .false. j = k + 1 ipj = 1 irj = ipj + n ivj = irj + n end if c c %-------------------------------------------------% c | When in reverse communication mode one of: | c | STEP3, STEP4, ORTH1, ORTH2, RSTART | c | will be .true. when .... | c | STEP3: return from computing OP*v_{j}. | c | STEP4: return from computing B-norm of OP*v_{j} | c | ORTH1: return from computing B-norm of r_{j+1} | c | ORTH2: return from computing B-norm of | c | correction to the residual vector. | c | RSTART: return from OP computations needed by | c | sgetv0. | c %-------------------------------------------------% c if (step3) go to 50 if (step4) go to 60 if (orth1) go to 70 if (orth2) go to 90 if (rstart) go to 30 c c %-----------------------------% c | Else this is the first step | c %-----------------------------% c c %--------------------------------------------------------------% c | | c | A R N O L D I I T E R A T I O N L O O P | c | | c | Note: B*r_{j-1} is already in WORKD(1:N)=WORKD(IPJ:IPJ+N-1) | c %--------------------------------------------------------------% 1000 continue c if (msglvl .gt. 1) then call ivout (logfil, 1, j, ndigit, & '_naitr: generating Arnoldi vector number') call svout (logfil, 1, rnorm, ndigit, & '_naitr: B-norm of the current residual is') end if c c %---------------------------------------------------% c | STEP 1: Check if the B norm of j-th residual | c | vector is zero. Equivalent to determing whether | c | an exact j-step Arnoldi factorization is present. | c %---------------------------------------------------% c betaj = rnorm if (rnorm .gt. zero) go to 40 c c %---------------------------------------------------% c | Invariant subspace found, generate a new starting | c | vector which is orthogonal to the current Arnoldi | c | basis and continue the iteration. | c %---------------------------------------------------% c if (msglvl .gt. 0) then call ivout (logfil, 1, j, ndigit, & '_naitr: ****** RESTART AT STEP ******') end if c c %---------------------------------------------% c | ITRY is the loop variable that controls the | c | maximum amount of times that a restart is | c | attempted. NRSTRT is used by stat.h | c %---------------------------------------------% c betaj = zero nrstrt = nrstrt + 1 itry = 1 20 continue rstart = .true. ido = 0 30 continue c c %--------------------------------------% c | If in reverse communication mode and | c | RSTART = .true. flow returns here. | c %--------------------------------------% c call sgetv0 (ido, bmat, itry, .false., n, j, v, ldv, & resid, rnorm, ipntr, workd, ierr) if (ido .ne. 99) go to 9000 if (ierr .lt. 0) then itry = itry + 1 if (itry .le. 3) go to 20 c c %------------------------------------------------% c | Give up after several restart attempts. | c | Set INFO to the size of the invariant subspace | c | which spans OP and exit. | c %------------------------------------------------% c info = j - 1 call arscnd (t1) tnaitr = tnaitr + (t1 - t0) ido = 99 go to 9000 end if c 40 continue c c %---------------------------------------------------------% c | STEP 2: v_{j} = r_{j-1}/rnorm and p_{j} = p_{j}/rnorm | c | Note that p_{j} = B*r_{j-1}. In order to avoid overflow | c | when reciprocating a small RNORM, test against lower | c | machine bound. | c %---------------------------------------------------------% c call scopy (n, resid, 1, v(1,j), 1) if (rnorm .ge. unfl) then temp1 = one / rnorm call sscal (n, temp1, v(1,j), 1) call sscal (n, temp1, workd(ipj), 1) else c c %-----------------------------------------% c | To scale both v_{j} and p_{j} carefully | c | use LAPACK routine SLASCL | c %-----------------------------------------% c call slascl ('General', i, i, rnorm, one, n, 1, & v(1,j), n, infol) call slascl ('General', i, i, rnorm, one, n, 1, & workd(ipj), n, infol) end if c c %------------------------------------------------------% c | STEP 3: r_{j} = OP*v_{j}; Note that p_{j} = B*v_{j} | c | Note that this is not quite yet r_{j}. See STEP 4 | c %------------------------------------------------------% c step3 = .true. nopx = nopx + 1 call arscnd (t2) call scopy (n, v(1,j), 1, workd(ivj), 1) ipntr(1) = ivj ipntr(2) = irj ipntr(3) = ipj ido = 1 c c %-----------------------------------% c | Exit in order to compute OP*v_{j} | c %-----------------------------------% c go to 9000 50 continue c c %----------------------------------% c | Back from reverse communication; | c | WORKD(IRJ:IRJ+N-1) := OP*v_{j} | c | if step3 = .true. | c %----------------------------------% c call arscnd (t3) tmvopx = tmvopx + (t3 - t2) step3 = .false. c c %------------------------------------------% c | Put another copy of OP*v_{j} into RESID. | c %------------------------------------------% c call scopy (n, workd(irj), 1, resid, 1) c c %---------------------------------------% c | STEP 4: Finish extending the Arnoldi | c | factorization to length j. | c %---------------------------------------% c call arscnd (t2) if (bmat .eq. 'G') then nbx = nbx + 1 step4 = .true. ipntr(1) = irj ipntr(2) = ipj ido = 2 c c %-------------------------------------% c | Exit in order to compute B*OP*v_{j} | c %-------------------------------------% c go to 9000 else if (bmat .eq. 'I') then call scopy (n, resid, 1, workd(ipj), 1) end if 60 continue c c %----------------------------------% c | Back from reverse communication; | c | WORKD(IPJ:IPJ+N-1) := B*OP*v_{j} | c | if step4 = .true. | c %----------------------------------% c if (bmat .eq. 'G') then call arscnd (t3) tmvbx = tmvbx + (t3 - t2) end if c step4 = .false. c c %-------------------------------------% c | The following is needed for STEP 5. | c | Compute the B-norm of OP*v_{j}. | c %-------------------------------------% c if (bmat .eq. 'G') then wnorm = sdot (n, resid, 1, workd(ipj), 1) wnorm = sqrt(abs(wnorm)) else if (bmat .eq. 'I') then wnorm = snrm2(n, resid, 1) end if c c %-----------------------------------------% c | Compute the j-th residual corresponding | c | to the j step factorization. | c | Use Classical Gram Schmidt and compute: | c | w_{j} <- V_{j}^T * B * OP * v_{j} | c | r_{j} <- OP*v_{j} - V_{j} * w_{j} | c %-----------------------------------------% c c c %------------------------------------------% c | Compute the j Fourier coefficients w_{j} | c | WORKD(IPJ:IPJ+N-1) contains B*OP*v_{j}. | c %------------------------------------------% c call sgemv ('T', n, j, one, v, ldv, workd(ipj), 1, & zero, h(1,j), 1) c c %--------------------------------------% c | Orthogonalize r_{j} against V_{j}. | c | RESID contains OP*v_{j}. See STEP 3. | c %--------------------------------------% c call sgemv ('N', n, j, -one, v, ldv, h(1,j), 1, & one, resid, 1) c if (j .gt. 1) h(j,j-1) = betaj c call arscnd (t4) c orth1 = .true. c call arscnd (t2) if (bmat .eq. 'G') then nbx = nbx + 1 call scopy (n, resid, 1, workd(irj), 1) ipntr(1) = irj ipntr(2) = ipj ido = 2 c c %----------------------------------% c | Exit in order to compute B*r_{j} | c %----------------------------------% c go to 9000 else if (bmat .eq. 'I') then call scopy (n, resid, 1, workd(ipj), 1) end if 70 continue c c %---------------------------------------------------% c | Back from reverse communication if ORTH1 = .true. | c | WORKD(IPJ:IPJ+N-1) := B*r_{j}. | c %---------------------------------------------------% c if (bmat .eq. 'G') then call arscnd (t3) tmvbx = tmvbx + (t3 - t2) end if c orth1 = .false. c c %------------------------------% c | Compute the B-norm of r_{j}. | c %------------------------------% c if (bmat .eq. 'G') then rnorm = sdot (n, resid, 1, workd(ipj), 1) rnorm = sqrt(abs(rnorm)) else if (bmat .eq. 'I') then rnorm = snrm2(n, resid, 1) end if c c %-----------------------------------------------------------% c | STEP 5: Re-orthogonalization / Iterative refinement phase | c | Maximum NITER_ITREF tries. | c | | c | s = V_{j}^T * B * r_{j} | c | r_{j} = r_{j} - V_{j}*s | c | alphaj = alphaj + s_{j} | c | | c | The stopping criteria used for iterative refinement is | c | discussed in Parlett's book SEP, page 107 and in Gragg & | c | Reichel ACM TOMS paper; Algorithm 686, Dec. 1990. | c | Determine if we need to correct the residual. The goal is | c | to enforce ||v(:,1:j)^T * r_{j}|| .le. eps * || r_{j} || | c | The following test determines whether the sine of the | c | angle between OP*x and the computed residual is less | c | than or equal to 0.717. | c %-----------------------------------------------------------% c if (rnorm .gt. 0.717*wnorm) go to 100 iter = 0 nrorth = nrorth + 1 c c %---------------------------------------------------% c | Enter the Iterative refinement phase. If further | c | refinement is necessary, loop back here. The loop | c | variable is ITER. Perform a step of Classical | c | Gram-Schmidt using all the Arnoldi vectors V_{j} | c %---------------------------------------------------% c 80 continue c if (msglvl .gt. 2) then xtemp(1) = wnorm xtemp(2) = rnorm call svout (logfil, 2, xtemp, ndigit, & '_naitr: re-orthonalization; wnorm and rnorm are') call svout (logfil, j, h(1,j), ndigit, & '_naitr: j-th column of H') end if c c %----------------------------------------------------% c | Compute V_{j}^T * B * r_{j}. | c | WORKD(IRJ:IRJ+J-1) = v(:,1:J)'*WORKD(IPJ:IPJ+N-1). | c %----------------------------------------------------% c call sgemv ('T', n, j, one, v, ldv, workd(ipj), 1, & zero, workd(irj), 1) c c %---------------------------------------------% c | Compute the correction to the residual: | c | r_{j} = r_{j} - V_{j} * WORKD(IRJ:IRJ+J-1). | c | The correction to H is v(:,1:J)*H(1:J,1:J) | c | + v(:,1:J)*WORKD(IRJ:IRJ+J-1)*e'_j. | c %---------------------------------------------% c call sgemv ('N', n, j, -one, v, ldv, workd(irj), 1, & one, resid, 1) call saxpy (j, one, workd(irj), 1, h(1,j), 1) c orth2 = .true. call arscnd (t2) if (bmat .eq. 'G') then nbx = nbx + 1 call scopy (n, resid, 1, workd(irj), 1) ipntr(1) = irj ipntr(2) = ipj ido = 2 c c %-----------------------------------% c | Exit in order to compute B*r_{j}. | c | r_{j} is the corrected residual. | c %-----------------------------------% c go to 9000 else if (bmat .eq. 'I') then call scopy (n, resid, 1, workd(ipj), 1) end if 90 continue c c %---------------------------------------------------% c | Back from reverse communication if ORTH2 = .true. | c %---------------------------------------------------% c if (bmat .eq. 'G') then call arscnd (t3) tmvbx = tmvbx + (t3 - t2) end if c c %-----------------------------------------------------% c | Compute the B-norm of the corrected residual r_{j}. | c %-----------------------------------------------------% c if (bmat .eq. 'G') then rnorm1 = sdot (n, resid, 1, workd(ipj), 1) rnorm1 = sqrt(abs(rnorm1)) else if (bmat .eq. 'I') then rnorm1 = snrm2(n, resid, 1) end if c if (msglvl .gt. 0 .and. iter .gt. 0) then call ivout (logfil, 1, j, ndigit, & '_naitr: Iterative refinement for Arnoldi residual') if (msglvl .gt. 2) then xtemp(1) = rnorm xtemp(2) = rnorm1 call svout (logfil, 2, xtemp, ndigit, & '_naitr: iterative refinement ; rnorm and rnorm1 are') end if end if c c %-----------------------------------------% c | Determine if we need to perform another | c | step of re-orthogonalization. | c %-----------------------------------------% c if (rnorm1 .gt. 0.717*rnorm) then c c %---------------------------------------% c | No need for further refinement. | c | The cosine of the angle between the | c | corrected residual vector and the old | c | residual vector is greater than 0.717 | c | In other words the corrected residual | c | and the old residual vector share an | c | angle of less than arcCOS(0.717) | c %---------------------------------------% c rnorm = rnorm1 c else c c %-------------------------------------------% c | Another step of iterative refinement step | c | is required. NITREF is used by stat.h | c %-------------------------------------------% c nitref = nitref + 1 rnorm = rnorm1 iter = iter + 1 if (iter .le. 1) go to 80 c c %-------------------------------------------------% c | Otherwise RESID is numerically in the span of V | c %-------------------------------------------------% c do 95 jj = 1, n resid(jj) = zero 95 continue rnorm = zero end if c c %----------------------------------------------% c | Branch here directly if iterative refinement | c | wasn't necessary or after at most NITER_REF | c | steps of iterative refinement. | c %----------------------------------------------% c 100 continue c rstart = .false. orth2 = .false. c call arscnd (t5) titref = titref + (t5 - t4) c c %------------------------------------% c | STEP 6: Update j = j+1; Continue | c %------------------------------------% c j = j + 1 if (j .gt. k+np) then call arscnd (t1) tnaitr = tnaitr + (t1 - t0) ido = 99 do 110 i = max(1,k), k+np-1 c c %--------------------------------------------% c | Check for splitting and deflation. | c | Use a standard test as in the QR algorithm | c | REFERENCE: LAPACK subroutine slahqr | c %--------------------------------------------% c tst1 = abs( h( i, i ) ) + abs( h( i+1, i+1 ) ) if( tst1.eq.zero ) & tst1 = slanhs( '1', k+np, h, ldh, workd(n+1) ) if( abs( h( i+1,i ) ).le.max( ulp*tst1, smlnum ) ) & h(i+1,i) = zero 110 continue c if (msglvl .gt. 2) then call smout (logfil, k+np, k+np, h, ldh, ndigit, & '_naitr: Final upper Hessenberg matrix H of order K+NP') end if c go to 9000 end if c c %--------------------------------------------------------% c | Loop back to extend the factorization by another step. | c %--------------------------------------------------------% c go to 1000 c c %---------------------------------------------------------------% c | | c | E N D O F M A I N I T E R A T I O N L O O P | c | | c %---------------------------------------------------------------% c 9000 continue return c c %---------------% c | End of snaitr | c %---------------% c end arpack-0.92.1/SRC/dstats.f0000644000175000017500000000221610776001577012100 00000000000000c c\SCCS Information: @(#) c FILE: stats.F SID: 2.1 DATE OF SID: 4/19/96 RELEASE: 2 c %---------------------------------------------% c | Initialize statistic and timing information | c | for symmetric Arnoldi code. | c %---------------------------------------------% subroutine dstats c %--------------------------------% c | See stat.doc for documentation | c %--------------------------------% include 'stat.h' c %-----------------------% c | Executable Statements | c %-----------------------% nopx = 0 nbx = 0 nrorth = 0 nitref = 0 nrstrt = 0 tsaupd = 0.0D+0 tsaup2 = 0.0D+0 tsaitr = 0.0D+0 tseigt = 0.0D+0 tsgets = 0.0D+0 tsapps = 0.0D+0 tsconv = 0.0D+0 titref = 0.0D+0 tgetv0 = 0.0D+0 trvec = 0.0D+0 c %----------------------------------------------------% c | User time including reverse communication overhead | c %----------------------------------------------------% tmvopx = 0.0D+0 tmvbx = 0.0D+0 return c c End of dstats c end arpack-0.92.1/SRC/dsapps.f0000644000175000017500000004412210776001577012072 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: dsapps c c\Description: c Given the Arnoldi factorization c c A*V_{k} - V_{k}*H_{k} = r_{k+p}*e_{k+p}^T, c c apply NP shifts implicitly resulting in c c A*(V_{k}*Q) - (V_{k}*Q)*(Q^T* H_{k}*Q) = r_{k+p}*e_{k+p}^T * Q c c where Q is an orthogonal matrix of order KEV+NP. Q is the product of c rotations resulting from the NP bulge chasing sweeps. The updated Arnoldi c factorization becomes: c c A*VNEW_{k} - VNEW_{k}*HNEW_{k} = rnew_{k}*e_{k}^T. c c\Usage: c call dsapps c ( N, KEV, NP, SHIFT, V, LDV, H, LDH, RESID, Q, LDQ, WORKD ) c c\Arguments c N Integer. (INPUT) c Problem size, i.e. dimension of matrix A. c c KEV Integer. (INPUT) c INPUT: KEV+NP is the size of the input matrix H. c OUTPUT: KEV is the size of the updated matrix HNEW. c c NP Integer. (INPUT) c Number of implicit shifts to be applied. c c SHIFT Double precision array of length NP. (INPUT) c The shifts to be applied. c c V Double precision N by (KEV+NP) array. (INPUT/OUTPUT) c INPUT: V contains the current KEV+NP Arnoldi vectors. c OUTPUT: VNEW = V(1:n,1:KEV); the updated Arnoldi vectors c are in the first KEV columns of V. c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling c program. c c H Double precision (KEV+NP) by 2 array. (INPUT/OUTPUT) c INPUT: H contains the symmetric tridiagonal matrix of the c Arnoldi factorization with the subdiagonal in the 1st column c starting at H(2,1) and the main diagonal in the 2nd column. c OUTPUT: H contains the updated tridiagonal matrix in the c KEV leading submatrix. c c LDH Integer. (INPUT) c Leading dimension of H exactly as declared in the calling c program. c c RESID Double precision array of length (N). (INPUT/OUTPUT) c INPUT: RESID contains the the residual vector r_{k+p}. c OUTPUT: RESID is the updated residual vector rnew_{k}. c c Q Double precision KEV+NP by KEV+NP work array. (WORKSPACE) c Work array used to accumulate the rotations during the bulge c chase sweep. c c LDQ Integer. (INPUT) c Leading dimension of Q exactly as declared in the calling c program. c c WORKD Double precision work array of length 2*N. (WORKSPACE) c Distributed array used in the application of the accumulated c orthogonal matrix Q. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx real c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly c Restarted Arnoldi Iteration", Rice University Technical Report c TR95-13, Department of Computational and Applied Mathematics. c c\Routines called: c ivout ARPACK utility routine that prints integers. c arscnd ARPACK utility routine for timing. c dvout ARPACK utility routine that prints vectors. c dlamch LAPACK routine that determines machine constants. c dlartg LAPACK Givens rotation construction routine. c dlacpy LAPACK matrix copy routine. c dlaset LAPACK matrix initialization routine. c dgemv Level 2 BLAS routine for matrix vector multiplication. c daxpy Level 1 BLAS that computes a vector triad. c dcopy Level 1 BLAS that copies one vector to another. c dscal Level 1 BLAS that scales a vector. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c 12/16/93: Version ' 2.4' c c\SCCS Information: @(#) c FILE: sapps.F SID: 2.6 DATE OF SID: 3/28/97 RELEASE: 2 c c\Remarks c 1. In this version, each shift is applied to all the subblocks of c the tridiagonal matrix H and not just to the submatrix that it c comes from. This routine assumes that the subdiagonal elements c of H that are stored in h(1:kev+np,1) are nonegative upon input c and enforce this condition upon output. This version incorporates c deflation. See code for documentation. c c\EndLib c c----------------------------------------------------------------------- c subroutine dsapps & ( n, kev, np, shift, v, ldv, h, ldh, resid, q, ldq, workd ) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c integer kev, ldh, ldq, ldv, n, np c c %-----------------% c | Array Arguments | c %-----------------% c Double precision & h(ldh,2), q(ldq,kev+np), resid(n), shift(np), & v(ldv,kev+np), workd(2*n) c c %------------% c | Parameters | c %------------% c Double precision & one, zero parameter (one = 1.0D+0, zero = 0.0D+0) c c %---------------% c | Local Scalars | c %---------------% c integer i, iend, istart, itop, j, jj, kplusp, msglvl logical first Double precision & a1, a2, a3, a4, big, c, epsmch, f, g, r, s save epsmch, first c c c %----------------------% c | External Subroutines | c %----------------------% c external daxpy, dcopy, dscal, dlacpy, dlartg, dlaset, dvout, & ivout, arscnd, dgemv c c %--------------------% c | External Functions | c %--------------------% c Double precision & dlamch external dlamch c c %----------------------% c | Intrinsics Functions | c %----------------------% c intrinsic abs c c %----------------% c | Data statments | c %----------------% c data first / .true. / c c %-----------------------% c | Executable Statements | c %-----------------------% c if (first) then epsmch = dlamch('Epsilon-Machine') first = .false. end if itop = 1 c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call arscnd (t0) msglvl = msapps c kplusp = kev + np c c %----------------------------------------------% c | Initialize Q to the identity matrix of order | c | kplusp used to accumulate the rotations. | c %----------------------------------------------% c call dlaset ('All', kplusp, kplusp, zero, one, q, ldq) c c %----------------------------------------------% c | Quick return if there are no shifts to apply | c %----------------------------------------------% c if (np .eq. 0) go to 9000 c c %----------------------------------------------------------% c | Apply the np shifts implicitly. Apply each shift to the | c | whole matrix and not just to the submatrix from which it | c | comes. | c %----------------------------------------------------------% c do 90 jj = 1, np c istart = itop c c %----------------------------------------------------------% c | Check for splitting and deflation. Currently we consider | c | an off-diagonal element h(i+1,1) negligible if | c | h(i+1,1) .le. epsmch*( |h(i,2)| + |h(i+1,2)| ) | c | for i=1:KEV+NP-1. | c | If above condition tests true then we set h(i+1,1) = 0. | c | Note that h(1:KEV+NP,1) are assumed to be non negative. | c %----------------------------------------------------------% c 20 continue c c %------------------------------------------------% c | The following loop exits early if we encounter | c | a negligible off diagonal element. | c %------------------------------------------------% c do 30 i = istart, kplusp-1 big = abs(h(i,2)) + abs(h(i+1,2)) if (h(i+1,1) .le. epsmch*big) then if (msglvl .gt. 0) then call ivout (logfil, 1, i, ndigit, & '_sapps: deflation at row/column no.') call ivout (logfil, 1, jj, ndigit, & '_sapps: occured before shift number.') call dvout (logfil, 1, h(i+1,1), ndigit, & '_sapps: the corresponding off diagonal element') end if h(i+1,1) = zero iend = i go to 40 end if 30 continue iend = kplusp 40 continue c if (istart .lt. iend) then c c %--------------------------------------------------------% c | Construct the plane rotation G'(istart,istart+1,theta) | c | that attempts to drive h(istart+1,1) to zero. | c %--------------------------------------------------------% c f = h(istart,2) - shift(jj) g = h(istart+1,1) call dlartg (f, g, c, s, r) c c %-------------------------------------------------------% c | Apply rotation to the left and right of H; | c | H <- G' * H * G, where G = G(istart,istart+1,theta). | c | This will create a "bulge". | c %-------------------------------------------------------% c a1 = c*h(istart,2) + s*h(istart+1,1) a2 = c*h(istart+1,1) + s*h(istart+1,2) a4 = c*h(istart+1,2) - s*h(istart+1,1) a3 = c*h(istart+1,1) - s*h(istart,2) h(istart,2) = c*a1 + s*a2 h(istart+1,2) = c*a4 - s*a3 h(istart+1,1) = c*a3 + s*a4 c c %----------------------------------------------------% c | Accumulate the rotation in the matrix Q; Q <- Q*G | c %----------------------------------------------------% c do 60 j = 1, min(istart+jj,kplusp) a1 = c*q(j,istart) + s*q(j,istart+1) q(j,istart+1) = - s*q(j,istart) + c*q(j,istart+1) q(j,istart) = a1 60 continue c c c %----------------------------------------------% c | The following loop chases the bulge created. | c | Note that the previous rotation may also be | c | done within the following loop. But it is | c | kept separate to make the distinction among | c | the bulge chasing sweeps and the first plane | c | rotation designed to drive h(istart+1,1) to | c | zero. | c %----------------------------------------------% c do 70 i = istart+1, iend-1 c c %----------------------------------------------% c | Construct the plane rotation G'(i,i+1,theta) | c | that zeros the i-th bulge that was created | c | by G(i-1,i,theta). g represents the bulge. | c %----------------------------------------------% c f = h(i,1) g = s*h(i+1,1) c c %----------------------------------% c | Final update with G(i-1,i,theta) | c %----------------------------------% c h(i+1,1) = c*h(i+1,1) call dlartg (f, g, c, s, r) c c %-------------------------------------------% c | The following ensures that h(1:iend-1,1), | c | the first iend-2 off diagonal of elements | c | H, remain non negative. | c %-------------------------------------------% c if (r .lt. zero) then r = -r c = -c s = -s end if c c %--------------------------------------------% c | Apply rotation to the left and right of H; | c | H <- G * H * G', where G = G(i,i+1,theta) | c %--------------------------------------------% c h(i,1) = r c a1 = c*h(i,2) + s*h(i+1,1) a2 = c*h(i+1,1) + s*h(i+1,2) a3 = c*h(i+1,1) - s*h(i,2) a4 = c*h(i+1,2) - s*h(i+1,1) c h(i,2) = c*a1 + s*a2 h(i+1,2) = c*a4 - s*a3 h(i+1,1) = c*a3 + s*a4 c c %----------------------------------------------------% c | Accumulate the rotation in the matrix Q; Q <- Q*G | c %----------------------------------------------------% c do 50 j = 1, min( i+jj, kplusp ) a1 = c*q(j,i) + s*q(j,i+1) q(j,i+1) = - s*q(j,i) + c*q(j,i+1) q(j,i) = a1 50 continue c 70 continue c end if c c %--------------------------% c | Update the block pointer | c %--------------------------% c istart = iend + 1 c c %------------------------------------------% c | Make sure that h(iend,1) is non-negative | c | If not then set h(iend,1) <-- -h(iend,1) | c | and negate the last column of Q. | c | We have effectively carried out a | c | similarity on transformation H | c %------------------------------------------% c if (h(iend,1) .lt. zero) then h(iend,1) = -h(iend,1) call dscal(kplusp, -one, q(1,iend), 1) end if c c %--------------------------------------------------------% c | Apply the same shift to the next block if there is any | c %--------------------------------------------------------% c if (iend .lt. kplusp) go to 20 c c %-----------------------------------------------------% c | Check if we can increase the the start of the block | c %-----------------------------------------------------% c do 80 i = itop, kplusp-1 if (h(i+1,1) .gt. zero) go to 90 itop = itop + 1 80 continue c c %-----------------------------------% c | Finished applying the jj-th shift | c %-----------------------------------% c 90 continue c c %------------------------------------------% c | All shifts have been applied. Check for | c | more possible deflation that might occur | c | after the last shift is applied. | c %------------------------------------------% c do 100 i = itop, kplusp-1 big = abs(h(i,2)) + abs(h(i+1,2)) if (h(i+1,1) .le. epsmch*big) then if (msglvl .gt. 0) then call ivout (logfil, 1, i, ndigit, & '_sapps: deflation at row/column no.') call dvout (logfil, 1, h(i+1,1), ndigit, & '_sapps: the corresponding off diagonal element') end if h(i+1,1) = zero end if 100 continue c c %-------------------------------------------------% c | Compute the (kev+1)-st column of (V*Q) and | c | temporarily store the result in WORKD(N+1:2*N). | c | This is not necessary if h(kev+1,1) = 0. | c %-------------------------------------------------% c if ( h(kev+1,1) .gt. zero ) & call dgemv ('N', n, kplusp, one, v, ldv, & q(1,kev+1), 1, zero, workd(n+1), 1) c c %-------------------------------------------------------% c | Compute column 1 to kev of (V*Q) in backward order | c | taking advantage that Q is an upper triangular matrix | c | with lower bandwidth np. | c | Place results in v(:,kplusp-kev:kplusp) temporarily. | c %-------------------------------------------------------% c do 130 i = 1, kev call dgemv ('N', n, kplusp-i+1, one, v, ldv, & q(1,kev-i+1), 1, zero, workd, 1) call dcopy (n, workd, 1, v(1,kplusp-i+1), 1) 130 continue c c %-------------------------------------------------% c | Move v(:,kplusp-kev+1:kplusp) into v(:,1:kev). | c %-------------------------------------------------% c call dlacpy ('All', n, kev, v(1,np+1), ldv, v, ldv) c c %--------------------------------------------% c | Copy the (kev+1)-st column of (V*Q) in the | c | appropriate place if h(kev+1,1) .ne. zero. | c %--------------------------------------------% c if ( h(kev+1,1) .gt. zero ) & call dcopy (n, workd(n+1), 1, v(1,kev+1), 1) c c %-------------------------------------% c | Update the residual vector: | c | r <- sigmak*r + betak*v(:,kev+1) | c | where | c | sigmak = (e_{kev+p}'*Q)*e_{kev} | c | betak = e_{kev+1}'*H*e_{kev} | c %-------------------------------------% c call dscal (n, q(kplusp,kev), resid, 1) if (h(kev+1,1) .gt. zero) & call daxpy (n, h(kev+1,1), v(1,kev+1), 1, resid, 1) c if (msglvl .gt. 1) then call dvout (logfil, 1, q(kplusp,kev), ndigit, & '_sapps: sigmak of the updated residual vector') call dvout (logfil, 1, h(kev+1,1), ndigit, & '_sapps: betak of the updated residual vector') call dvout (logfil, kev, h(1,2), ndigit, & '_sapps: updated main diagonal of H for next iteration') if (kev .gt. 1) then call dvout (logfil, kev-1, h(2,1), ndigit, & '_sapps: updated sub diagonal of H for next iteration') end if end if c call arscnd (t1) tsapps = tsapps + (t1 - t0) c 9000 continue return c c %---------------% c | End of dsapps | c %---------------% c end arpack-0.92.1/SRC/sseigt.f0000644000175000017500000001175510776001577012104 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: sseigt c c\Description: c Compute the eigenvalues of the current symmetric tridiagonal matrix c and the corresponding error bounds given the current residual norm. c c\Usage: c call sseigt c ( RNORM, N, H, LDH, EIG, BOUNDS, WORKL, IERR ) c c\Arguments c RNORM Real scalar. (INPUT) c RNORM contains the residual norm corresponding to the current c symmetric tridiagonal matrix H. c c N Integer. (INPUT) c Size of the symmetric tridiagonal matrix H. c c H Real N by 2 array. (INPUT) c H contains the symmetric tridiagonal matrix with the c subdiagonal in the first column starting at H(2,1) and the c main diagonal in second column. c c LDH Integer. (INPUT) c Leading dimension of H exactly as declared in the calling c program. c c EIG Real array of length N. (OUTPUT) c On output, EIG contains the N eigenvalues of H possibly c unsorted. The BOUNDS arrays are returned in the c same sorted order as EIG. c c BOUNDS Real array of length N. (OUTPUT) c On output, BOUNDS contains the error estimates corresponding c to the eigenvalues EIG. This is equal to RNORM times the c last components of the eigenvectors corresponding to the c eigenvalues in EIG. c c WORKL Real work array of length 3*N. (WORKSPACE) c Private (replicated) array on each PE or array allocated on c the front end. c c IERR Integer. (OUTPUT) c Error exit flag from sstqrb. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx real c c\Routines called: c sstqrb ARPACK routine that computes the eigenvalues and the c last components of the eigenvectors of a symmetric c and tridiagonal matrix. c arscnd ARPACK utility routine for timing. c svout ARPACK utility routine that prints vectors. c scopy Level 1 BLAS that copies one vector to another. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c xx/xx/92: Version ' 2.4' c c\SCCS Information: @(#) c FILE: seigt.F SID: 2.4 DATE OF SID: 8/27/96 RELEASE: 2 c c\Remarks c None c c\EndLib c c----------------------------------------------------------------------- c subroutine sseigt & ( rnorm, n, h, ldh, eig, bounds, workl, ierr ) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c integer ierr, ldh, n Real & rnorm c c %-----------------% c | Array Arguments | c %-----------------% c Real & eig(n), bounds(n), h(ldh,2), workl(3*n) c c %------------% c | Parameters | c %------------% c Real & zero parameter (zero = 0.0E+0) c c %---------------% c | Local Scalars | c %---------------% c integer i, k, msglvl c c %----------------------% c | External Subroutines | c %----------------------% c external scopy, sstqrb, svout, arscnd c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call arscnd (t0) msglvl = mseigt c if (msglvl .gt. 0) then call svout (logfil, n, h(1,2), ndigit, & '_seigt: main diagonal of matrix H') if (n .gt. 1) then call svout (logfil, n-1, h(2,1), ndigit, & '_seigt: sub diagonal of matrix H') end if end if c call scopy (n, h(1,2), 1, eig, 1) call scopy (n-1, h(2,1), 1, workl, 1) call sstqrb (n, eig, workl, bounds, workl(n+1), ierr) if (ierr .ne. 0) go to 9000 if (msglvl .gt. 1) then call svout (logfil, n, bounds, ndigit, & '_seigt: last row of the eigenvector matrix for H') end if c c %-----------------------------------------------% c | Finally determine the error bounds associated | c | with the n Ritz values of H. | c %-----------------------------------------------% c do 30 k = 1, n bounds(k) = rnorm*abs(bounds(k)) 30 continue c call arscnd (t1) tseigt = tseigt + (t1 - t0) c 9000 continue return c c %---------------% c | End of sseigt | c %---------------% c end arpack-0.92.1/SRC/sngets.f0000644000175000017500000001745410776001577012113 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: sngets c c\Description: c Given the eigenvalues of the upper Hessenberg matrix H, c computes the NP shifts AMU that are zeros of the polynomial of c degree NP which filters out components of the unwanted eigenvectors c corresponding to the AMU's based on some given criteria. c c NOTE: call this even in the case of user specified shifts in order c to sort the eigenvalues, and error bounds of H for later use. c c\Usage: c call sngets c ( ISHIFT, WHICH, KEV, NP, RITZR, RITZI, BOUNDS, SHIFTR, SHIFTI ) c c\Arguments c ISHIFT Integer. (INPUT) c Method for selecting the implicit shifts at each iteration. c ISHIFT = 0: user specified shifts c ISHIFT = 1: exact shift with respect to the matrix H. c c WHICH Character*2. (INPUT) c Shift selection criteria. c 'LM' -> want the KEV eigenvalues of largest magnitude. c 'SM' -> want the KEV eigenvalues of smallest magnitude. c 'LR' -> want the KEV eigenvalues of largest real part. c 'SR' -> want the KEV eigenvalues of smallest real part. c 'LI' -> want the KEV eigenvalues of largest imaginary part. c 'SI' -> want the KEV eigenvalues of smallest imaginary part. c c KEV Integer. (INPUT/OUTPUT) c INPUT: KEV+NP is the size of the matrix H. c OUTPUT: Possibly increases KEV by one to keep complex conjugate c pairs together. c c NP Integer. (INPUT/OUTPUT) c Number of implicit shifts to be computed. c OUTPUT: Possibly decreases NP by one to keep complex conjugate c pairs together. c c RITZR, Real array of length KEV+NP. (INPUT/OUTPUT) c RITZI On INPUT, RITZR and RITZI contain the real and imaginary c parts of the eigenvalues of H. c On OUTPUT, RITZR and RITZI are sorted so that the unwanted c eigenvalues are in the first NP locations and the wanted c portion is in the last KEV locations. When exact shifts are c selected, the unwanted part corresponds to the shifts to c be applied. Also, if ISHIFT .eq. 1, the unwanted eigenvalues c are further sorted so that the ones with largest Ritz values c are first. c c BOUNDS Real array of length KEV+NP. (INPUT/OUTPUT) c Error bounds corresponding to the ordering in RITZ. c c SHIFTR, SHIFTI *** USE deprecated as of version 2.1. *** c c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx real c c\Routines called: c ssortc ARPACK sorting routine. c scopy Level 1 BLAS that copies one vector to another . c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c xx/xx/92: Version ' 2.1' c c\SCCS Information: @(#) c FILE: ngets.F SID: 2.3 DATE OF SID: 4/20/96 RELEASE: 2 c c\Remarks c 1. xxxx c c\EndLib c c----------------------------------------------------------------------- c subroutine sngets ( ishift, which, kev, np, ritzr, ritzi, bounds, & shiftr, shifti ) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character*2 which integer ishift, kev, np c c %-----------------% c | Array Arguments | c %-----------------% c Real & bounds(kev+np), ritzr(kev+np), ritzi(kev+np), & shiftr(1), shifti(1) c c %------------% c | Parameters | c %------------% c Real & one, zero parameter (one = 1.0, zero = 0.0) c c %---------------% c | Local Scalars | c %---------------% c integer msglvl c c %----------------------% c | External Subroutines | c %----------------------% c external scopy, ssortc, arscnd c c %----------------------% c | Intrinsics Functions | c %----------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call arscnd (t0) msglvl = mngets c c %----------------------------------------------------% c | LM, SM, LR, SR, LI, SI case. | c | Sort the eigenvalues of H into the desired order | c | and apply the resulting order to BOUNDS. | c | The eigenvalues are sorted so that the wanted part | c | are always in the last KEV locations. | c | We first do a pre-processing sort in order to keep | c | complex conjugate pairs together | c %----------------------------------------------------% c if (which .eq. 'LM') then call ssortc ('LR', .true., kev+np, ritzr, ritzi, bounds) else if (which .eq. 'SM') then call ssortc ('SR', .true., kev+np, ritzr, ritzi, bounds) else if (which .eq. 'LR') then call ssortc ('LM', .true., kev+np, ritzr, ritzi, bounds) else if (which .eq. 'SR') then call ssortc ('SM', .true., kev+np, ritzr, ritzi, bounds) else if (which .eq. 'LI') then call ssortc ('LM', .true., kev+np, ritzr, ritzi, bounds) else if (which .eq. 'SI') then call ssortc ('SM', .true., kev+np, ritzr, ritzi, bounds) end if c call ssortc (which, .true., kev+np, ritzr, ritzi, bounds) c c %-------------------------------------------------------% c | Increase KEV by one if the ( ritzr(np),ritzi(np) ) | c | = ( ritzr(np+1),-ritzi(np+1) ) and ritz(np) .ne. zero | c | Accordingly decrease NP by one. In other words keep | c | complex conjugate pairs together. | c %-------------------------------------------------------% c if ( ( ritzr(np+1) - ritzr(np) ) .eq. zero & .and. ( ritzi(np+1) + ritzi(np) ) .eq. zero ) then np = np - 1 kev = kev + 1 end if c if ( ishift .eq. 1 ) then c c %-------------------------------------------------------% c | Sort the unwanted Ritz values used as shifts so that | c | the ones with largest Ritz estimates are first | c | This will tend to minimize the effects of the | c | forward instability of the iteration when they shifts | c | are applied in subroutine snapps. | c | Be careful and use 'SR' since we want to sort BOUNDS! | c %-------------------------------------------------------% c call ssortc ( 'SR', .true., np, bounds, ritzr, ritzi ) end if c call arscnd (t1) tngets = tngets + (t1 - t0) c if (msglvl .gt. 0) then call ivout (logfil, 1, kev, ndigit, '_ngets: KEV is') call ivout (logfil, 1, np, ndigit, '_ngets: NP is') call svout (logfil, kev+np, ritzr, ndigit, & '_ngets: Eigenvalues of current H matrix -- real part') call svout (logfil, kev+np, ritzi, ndigit, & '_ngets: Eigenvalues of current H matrix -- imag part') call svout (logfil, kev+np, bounds, ndigit, & '_ngets: Ritz estimates of the current KEV+NP Ritz values') end if c return c c %---------------% c | End of sngets | c %---------------% c end arpack-0.92.1/SRC/dgetv0.f0000644000175000017500000003164210776001577011774 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: dgetv0 c c\Description: c Generate a random initial residual vector for the Arnoldi process. c Force the residual vector to be in the range of the operator OP. c c\Usage: c call dgetv0 c ( IDO, BMAT, ITRY, INITV, N, J, V, LDV, RESID, RNORM, c IPNTR, WORKD, IERR ) c c\Arguments c IDO Integer. (INPUT/OUTPUT) c Reverse communication flag. IDO must be zero on the first c call to dgetv0. c ------------------------------------------------------------- c IDO = 0: first call to the reverse communication interface c IDO = -1: compute Y = OP * X where c IPNTR(1) is the pointer into WORKD for X, c IPNTR(2) is the pointer into WORKD for Y. c This is for the initialization phase to force the c starting vector into the range of OP. c IDO = 2: compute Y = B * X where c IPNTR(1) is the pointer into WORKD for X, c IPNTR(2) is the pointer into WORKD for Y. c IDO = 99: done c ------------------------------------------------------------- c c BMAT Character*1. (INPUT) c BMAT specifies the type of the matrix B in the (generalized) c eigenvalue problem A*x = lambda*B*x. c B = 'I' -> standard eigenvalue problem A*x = lambda*x c B = 'G' -> generalized eigenvalue problem A*x = lambda*B*x c c ITRY Integer. (INPUT) c ITRY counts the number of times that dgetv0 is called. c It should be set to 1 on the initial call to dgetv0. c c INITV Logical variable. (INPUT) c .TRUE. => the initial residual vector is given in RESID. c .FALSE. => generate a random initial residual vector. c c N Integer. (INPUT) c Dimension of the problem. c c J Integer. (INPUT) c Index of the residual vector to be generated, with respect to c the Arnoldi process. J > 1 in case of a "restart". c c V Double precision N by J array. (INPUT) c The first J-1 columns of V contain the current Arnoldi basis c if this is a "restart". c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling c program. c c RESID Double precision array of length N. (INPUT/OUTPUT) c Initial residual vector to be generated. If RESID is c provided, force RESID into the range of the operator OP. c c RNORM Double precision scalar. (OUTPUT) c B-norm of the generated residual. c c IPNTR Integer array of length 3. (OUTPUT) c c WORKD Double precision work array of length 2*N. (REVERSE COMMUNICATION). c On exit, WORK(1:N) = B*RESID to be used in SSAITR. c c IERR Integer. (OUTPUT) c = 0: Normal exit. c = -1: Cannot generate a nontrivial restarted residual vector c in the range of the operator OP. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx real c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly c Restarted Arnoldi Iteration", Rice University Technical Report c TR95-13, Department of Computational and Applied Mathematics. c c\Routines called: c arscnd ARPACK utility routine for timing. c dvout ARPACK utility routine for vector output. c dlarnv LAPACK routine for generating a random vector. c dgemv Level 2 BLAS routine for matrix vector multiplication. c dcopy Level 1 BLAS that copies one vector to another. c ddot Level 1 BLAS that computes the scalar product of two vectors. c dnrm2 Level 1 BLAS that computes the norm of a vector. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: getv0.F SID: 2.7 DATE OF SID: 04/07/99 RELEASE: 2 c c\EndLib c c----------------------------------------------------------------------- c subroutine dgetv0 & ( ido, bmat, itry, initv, n, j, v, ldv, resid, rnorm, & ipntr, workd, ierr ) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character bmat*1 logical initv integer ido, ierr, itry, j, ldv, n Double precision & rnorm c c %-----------------% c | Array Arguments | c %-----------------% c integer ipntr(3) Double precision & resid(n), v(ldv,j), workd(2*n) c c %------------% c | Parameters | c %------------% c Double precision & one, zero parameter (one = 1.0D+0, zero = 0.0D+0) c c %------------------------% c | Local Scalars & Arrays | c %------------------------% c logical first, inits, orth integer idist, iseed(4), iter, msglvl, jj Double precision & rnorm0 save first, iseed, inits, iter, msglvl, orth, rnorm0 c c %----------------------% c | External Subroutines | c %----------------------% c external dlarnv, dvout, dcopy, dgemv, arscnd c c %--------------------% c | External Functions | c %--------------------% c Double precision & ddot, dnrm2 external ddot, dnrm2 c c %---------------------% c | Intrinsic Functions | c %---------------------% c intrinsic abs, sqrt c c %-----------------% c | Data Statements | c %-----------------% c data inits /.true./ c c %-----------------------% c | Executable Statements | c %-----------------------% c c c %-----------------------------------% c | Initialize the seed of the LAPACK | c | random number generator | c %-----------------------------------% c if (inits) then iseed(1) = 1 iseed(2) = 3 iseed(3) = 5 iseed(4) = 7 inits = .false. end if c if (ido .eq. 0) then c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call arscnd (t0) msglvl = mgetv0 c ierr = 0 iter = 0 first = .FALSE. orth = .FALSE. c c %-----------------------------------------------------% c | Possibly generate a random starting vector in RESID | c | Use a LAPACK random number generator used by the | c | matrix generation routines. | c | idist = 1: uniform (0,1) distribution; | c | idist = 2: uniform (-1,1) distribution; | c | idist = 3: normal (0,1) distribution; | c %-----------------------------------------------------% c if (.not.initv) then idist = 2 call dlarnv (idist, iseed, n, resid) end if c c %----------------------------------------------------------% c | Force the starting vector into the range of OP to handle | c | the generalized problem when B is possibly (singular). | c %----------------------------------------------------------% c call arscnd (t2) if (bmat .eq. 'G') then nopx = nopx + 1 ipntr(1) = 1 ipntr(2) = n + 1 call dcopy (n, resid, 1, workd, 1) ido = -1 go to 9000 end if end if c c %-----------------------------------------% c | Back from computing OP*(initial-vector) | c %-----------------------------------------% c if (first) go to 20 c c %-----------------------------------------------% c | Back from computing B*(orthogonalized-vector) | c %-----------------------------------------------% c if (orth) go to 40 c if (bmat .eq. 'G') then call arscnd (t3) tmvopx = tmvopx + (t3 - t2) end if c c %------------------------------------------------------% c | Starting vector is now in the range of OP; r = OP*r; | c | Compute B-norm of starting vector. | c %------------------------------------------------------% c call arscnd (t2) first = .TRUE. if (bmat .eq. 'G') then nbx = nbx + 1 call dcopy (n, workd(n+1), 1, resid, 1) ipntr(1) = n + 1 ipntr(2) = 1 ido = 2 go to 9000 else if (bmat .eq. 'I') then call dcopy (n, resid, 1, workd, 1) end if c 20 continue c if (bmat .eq. 'G') then call arscnd (t3) tmvbx = tmvbx + (t3 - t2) end if c first = .FALSE. if (bmat .eq. 'G') then rnorm0 = ddot (n, resid, 1, workd, 1) rnorm0 = sqrt(abs(rnorm0)) else if (bmat .eq. 'I') then rnorm0 = dnrm2(n, resid, 1) end if rnorm = rnorm0 c c %---------------------------------------------% c | Exit if this is the very first Arnoldi step | c %---------------------------------------------% c if (j .eq. 1) go to 50 c c %---------------------------------------------------------------- c | Otherwise need to B-orthogonalize the starting vector against | c | the current Arnoldi basis using Gram-Schmidt with iter. ref. | c | This is the case where an invariant subspace is encountered | c | in the middle of the Arnoldi factorization. | c | | c | s = V^{T}*B*r; r = r - V*s; | c | | c | Stopping criteria used for iter. ref. is discussed in | c | Parlett's book, page 107 and in Gragg & Reichel TOMS paper. | c %---------------------------------------------------------------% c orth = .TRUE. 30 continue c call dgemv ('T', n, j-1, one, v, ldv, workd, 1, & zero, workd(n+1), 1) call dgemv ('N', n, j-1, -one, v, ldv, workd(n+1), 1, & one, resid, 1) c c %----------------------------------------------------------% c | Compute the B-norm of the orthogonalized starting vector | c %----------------------------------------------------------% c call arscnd (t2) if (bmat .eq. 'G') then nbx = nbx + 1 call dcopy (n, resid, 1, workd(n+1), 1) ipntr(1) = n + 1 ipntr(2) = 1 ido = 2 go to 9000 else if (bmat .eq. 'I') then call dcopy (n, resid, 1, workd, 1) end if c 40 continue c if (bmat .eq. 'G') then call arscnd (t3) tmvbx = tmvbx + (t3 - t2) end if c if (bmat .eq. 'G') then rnorm = ddot (n, resid, 1, workd, 1) rnorm = sqrt(abs(rnorm)) else if (bmat .eq. 'I') then rnorm = dnrm2(n, resid, 1) end if c c %--------------------------------------% c | Check for further orthogonalization. | c %--------------------------------------% c if (msglvl .gt. 2) then call dvout (logfil, 1, rnorm0, ndigit, & '_getv0: re-orthonalization ; rnorm0 is') call dvout (logfil, 1, rnorm, ndigit, & '_getv0: re-orthonalization ; rnorm is') end if c if (rnorm .gt. 0.717*rnorm0) go to 50 c iter = iter + 1 if (iter .le. 5) then c c %-----------------------------------% c | Perform iterative refinement step | c %-----------------------------------% c rnorm0 = rnorm go to 30 else c c %------------------------------------% c | Iterative refinement step "failed" | c %------------------------------------% c do 45 jj = 1, n resid(jj) = zero 45 continue rnorm = zero ierr = -1 end if c 50 continue c if (msglvl .gt. 0) then call dvout (logfil, 1, rnorm, ndigit, & '_getv0: B-norm of initial / restarted starting vector') end if if (msglvl .gt. 3) then call dvout (logfil, n, resid, ndigit, & '_getv0: initial / restarted starting vector') end if ido = 99 c call arscnd (t1) tgetv0 = tgetv0 + (t1 - t0) c 9000 continue return c c %---------------% c | End of dgetv0 | c %---------------% c end arpack-0.92.1/SRC/version.h0000644000175000017500000000234610776001577012271 00000000000000/* In the current version, the parameter KAPPA in the Kahan's test for orthogonality is set to 0.717, the same as used by Gragg & Reichel. However computational experience indicates that this is a little too strict and will frequently force reorthogonalization when it is not necessary to do so. Also the "moving boundary" idea is not currently activated in the nonsymmetric code since it is not conclusive that it's the right thing to do all the time. Requires further investigation. As of 02/01/93 Richard Lehoucq assumes software control of the codes from Phuong Vu. On 03/01/93 all the *.F files were migrated SCCS. The 1.1 version of codes are those received from Phuong Vu. The frozen version of 07/08/92 is now considered version 1.1. Version 2.1 contains two new symmetric routines, sesrt and seupd. Changes as well as bug fixes for version 1.1 codes that were only corrected for programming bugs are version 1.2. These 1.2 versions will also be in version 2.1. Subroutine [d,s]saupd now requires slightly more workspace. See [d,s]saupd for the details. \SCCS Information: @(#) FILE: version.h SID: 2.3 DATE OF SID: 11/16/95 RELEASE: 2 */ #define VERSION_NUMBER ' 2.1' #define VERSION_DATE ' 11/15/95' arpack-0.92.1/SRC/slaqrb.f0000644000175000017500000004364410776001577012074 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: slaqrb c c\Description: c Compute the eigenvalues and the Schur decomposition of an upper c Hessenberg submatrix in rows and columns ILO to IHI. Only the c last component of the Schur vectors are computed. c c This is mostly a modification of the LAPACK routine slahqr. c c\Usage: c call slaqrb c ( WANTT, N, ILO, IHI, H, LDH, WR, WI, Z, INFO ) c c\Arguments c WANTT Logical variable. (INPUT) c = .TRUE. : the full Schur form T is required; c = .FALSE.: only eigenvalues are required. c c N Integer. (INPUT) c The order of the matrix H. N >= 0. c c ILO Integer. (INPUT) c IHI Integer. (INPUT) c It is assumed that H is already upper quasi-triangular in c rows and columns IHI+1:N, and that H(ILO,ILO-1) = 0 (unless c ILO = 1). SLAQRB works primarily with the Hessenberg c submatrix in rows and columns ILO to IHI, but applies c transformations to all of H if WANTT is .TRUE.. c 1 <= ILO <= max(1,IHI); IHI <= N. c c H Real array, dimension (LDH,N). (INPUT/OUTPUT) c On entry, the upper Hessenberg matrix H. c On exit, if WANTT is .TRUE., H is upper quasi-triangular in c rows and columns ILO:IHI, with any 2-by-2 diagonal blocks in c standard form. If WANTT is .FALSE., the contents of H are c unspecified on exit. c c LDH Integer. (INPUT) c The leading dimension of the array H. LDH >= max(1,N). c c WR Real array, dimension (N). (OUTPUT) c WI Real array, dimension (N). (OUTPUT) c The real and imaginary parts, respectively, of the computed c eigenvalues ILO to IHI are stored in the corresponding c elements of WR and WI. If two eigenvalues are computed as a c complex conjugate pair, they are stored in consecutive c elements of WR and WI, say the i-th and (i+1)th, with c WI(i) > 0 and WI(i+1) < 0. If WANTT is .TRUE., the c eigenvalues are stored in the same order as on the diagonal c of the Schur form returned in H, with WR(i) = H(i,i), and, if c H(i:i+1,i:i+1) is a 2-by-2 diagonal block, c WI(i) = sqrt(H(i+1,i)*H(i,i+1)) and WI(i+1) = -WI(i). c c Z Real array, dimension (N). (OUTPUT) c On exit Z contains the last components of the Schur vectors. c c INFO Integer. (OUPUT) c = 0: successful exit c > 0: SLAQRB failed to compute all the eigenvalues ILO to IHI c in a total of 30*(IHI-ILO+1) iterations; if INFO = i, c elements i+1:ihi of WR and WI contain those eigenvalues c which have been successfully computed. c c\Remarks c 1. None. c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx real c c\Routines called: c slabad LAPACK routine that computes machine constants. c slamch LAPACK routine that determines machine constants. c slanhs LAPACK routine that computes various norms of a matrix. c slanv2 LAPACK routine that computes the Schur factorization of c 2 by 2 nonsymmetric matrix in standard form. c slarfg LAPACK Householder reflection construction routine. c scopy Level 1 BLAS that copies one vector to another. c srot Level 1 BLAS that applies a rotation to a 2 by 2 matrix. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c xx/xx/92: Version ' 2.4' c Modified from the LAPACK routine slahqr so that only the c last component of the Schur vectors are computed. c c\SCCS Information: @(#) c FILE: laqrb.F SID: 2.2 DATE OF SID: 8/27/96 RELEASE: 2 c c\Remarks c 1. None c c\EndLib c c----------------------------------------------------------------------- c subroutine slaqrb ( wantt, n, ilo, ihi, h, ldh, wr, wi, & z, info ) c c %------------------% c | Scalar Arguments | c %------------------% c logical wantt integer ihi, ilo, info, ldh, n c c %-----------------% c | Array Arguments | c %-----------------% c Real & h( ldh, * ), wi( * ), wr( * ), z( * ) c c %------------% c | Parameters | c %------------% c Real & zero, one, dat1, dat2 parameter (zero = 0.0E+0, one = 1.0E+0, dat1 = 7.5E-1, & dat2 = -4.375E-1) c c %------------------------% c | Local Scalars & Arrays | c %------------------------% c integer i, i1, i2, itn, its, j, k, l, m, nh, nr Real & cs, h00, h10, h11, h12, h21, h22, h33, h33s, & h43h34, h44, h44s, ovfl, s, smlnum, sn, sum, & t1, t2, t3, tst1, ulp, unfl, v1, v2, v3 Real & v( 3 ), work( 1 ) c c %--------------------% c | External Functions | c %--------------------% c Real & slamch, slanhs external slamch, slanhs c c %----------------------% c | External Subroutines | c %----------------------% c external scopy, slabad, slanv2, slarfg, srot c c %-----------------------% c | Executable Statements | c %-----------------------% c info = 0 c c %--------------------------% c | Quick return if possible | c %--------------------------% c if( n.eq.0 ) & return if( ilo.eq.ihi ) then wr( ilo ) = h( ilo, ilo ) wi( ilo ) = zero return end if c c %---------------------------------------------% c | Initialize the vector of last components of | c | the Schur vectors for accumulation. | c %---------------------------------------------% c do 5 j = 1, n-1 z(j) = zero 5 continue z(n) = one c nh = ihi - ilo + 1 c c %-------------------------------------------------------------% c | Set machine-dependent constants for the stopping criterion. | c | If norm(H) <= sqrt(OVFL), overflow should not occur. | c %-------------------------------------------------------------% c unfl = slamch( 'safe minimum' ) ovfl = one / unfl call slabad( unfl, ovfl ) ulp = slamch( 'precision' ) smlnum = unfl*( nh / ulp ) c c %---------------------------------------------------------------% c | I1 and I2 are the indices of the first row and last column | c | of H to which transformations must be applied. If eigenvalues | c | only are computed, I1 and I2 are set inside the main loop. | c | Zero out H(J+2,J) = ZERO for J=1:N if WANTT = .TRUE. | c | else H(J+2,J) for J=ILO:IHI-ILO-1 if WANTT = .FALSE. | c %---------------------------------------------------------------% c if( wantt ) then i1 = 1 i2 = n do 8 i=1,i2-2 h(i1+i+1,i) = zero 8 continue else do 9 i=1, ihi-ilo-1 h(ilo+i+1,ilo+i-1) = zero 9 continue end if c c %---------------------------------------------------% c | ITN is the total number of QR iterations allowed. | c %---------------------------------------------------% c itn = 30*nh c c ------------------------------------------------------------------ c The main loop begins here. I is the loop index and decreases from c IHI to ILO in steps of 1 or 2. Each iteration of the loop works c with the active submatrix in rows and columns L to I. c Eigenvalues I+1 to IHI have already converged. Either L = ILO or c H(L,L-1) is negligible so that the matrix splits. c ------------------------------------------------------------------ c i = ihi 10 continue l = ilo if( i.lt.ilo ) & go to 150 c %--------------------------------------------------------------% c | Perform QR iterations on rows and columns ILO to I until a | c | submatrix of order 1 or 2 splits off at the bottom because a | c | subdiagonal element has become negligible. | c %--------------------------------------------------------------% do 130 its = 0, itn c c %----------------------------------------------% c | Look for a single small subdiagonal element. | c %----------------------------------------------% c do 20 k = i, l + 1, -1 tst1 = abs( h( k-1, k-1 ) ) + abs( h( k, k ) ) if( tst1.eq.zero ) & tst1 = slanhs( '1', i-l+1, h( l, l ), ldh, work ) if( abs( h( k, k-1 ) ).le.max( ulp*tst1, smlnum ) ) & go to 30 20 continue 30 continue l = k if( l.gt.ilo ) then c c %------------------------% c | H(L,L-1) is negligible | c %------------------------% c h( l, l-1 ) = zero end if c c %-------------------------------------------------------------% c | Exit from loop if a submatrix of order 1 or 2 has split off | c %-------------------------------------------------------------% c if( l.ge.i-1 ) & go to 140 c c %---------------------------------------------------------% c | Now the active submatrix is in rows and columns L to I. | c | If eigenvalues only are being computed, only the active | c | submatrix need be transformed. | c %---------------------------------------------------------% c if( .not.wantt ) then i1 = l i2 = i end if c if( its.eq.10 .or. its.eq.20 ) then c c %-------------------% c | Exceptional shift | c %-------------------% c s = abs( h( i, i-1 ) ) + abs( h( i-1, i-2 ) ) h44 = dat1*s h33 = h44 h43h34 = dat2*s*s c else c c %-----------------------------------------% c | Prepare to use Wilkinson's double shift | c %-----------------------------------------% c h44 = h( i, i ) h33 = h( i-1, i-1 ) h43h34 = h( i, i-1 )*h( i-1, i ) end if c c %-----------------------------------------------------% c | Look for two consecutive small subdiagonal elements | c %-----------------------------------------------------% c do 40 m = i - 2, l, -1 c c %---------------------------------------------------------% c | Determine the effect of starting the double-shift QR | c | iteration at row M, and see if this would make H(M,M-1) | c | negligible. | c %---------------------------------------------------------% c h11 = h( m, m ) h22 = h( m+1, m+1 ) h21 = h( m+1, m ) h12 = h( m, m+1 ) h44s = h44 - h11 h33s = h33 - h11 v1 = ( h33s*h44s-h43h34 ) / h21 + h12 v2 = h22 - h11 - h33s - h44s v3 = h( m+2, m+1 ) s = abs( v1 ) + abs( v2 ) + abs( v3 ) v1 = v1 / s v2 = v2 / s v3 = v3 / s v( 1 ) = v1 v( 2 ) = v2 v( 3 ) = v3 if( m.eq.l ) & go to 50 h00 = h( m-1, m-1 ) h10 = h( m, m-1 ) tst1 = abs( v1 )*( abs( h00 )+abs( h11 )+abs( h22 ) ) if( abs( h10 )*( abs( v2 )+abs( v3 ) ).le.ulp*tst1 ) & go to 50 40 continue 50 continue c c %----------------------% c | Double-shift QR step | c %----------------------% c do 120 k = m, i - 1 c c ------------------------------------------------------------ c The first iteration of this loop determines a reflection G c from the vector V and applies it from left and right to H, c thus creating a nonzero bulge below the subdiagonal. c c Each subsequent iteration determines a reflection G to c restore the Hessenberg form in the (K-1)th column, and thus c chases the bulge one step toward the bottom of the active c submatrix. NR is the order of G. c ------------------------------------------------------------ c nr = min( 3, i-k+1 ) if( k.gt.m ) & call scopy( nr, h( k, k-1 ), 1, v, 1 ) call slarfg( nr, v( 1 ), v( 2 ), 1, t1 ) if( k.gt.m ) then h( k, k-1 ) = v( 1 ) h( k+1, k-1 ) = zero if( k.lt.i-1 ) & h( k+2, k-1 ) = zero else if( m.gt.l ) then h( k, k-1 ) = -h( k, k-1 ) end if v2 = v( 2 ) t2 = t1*v2 if( nr.eq.3 ) then v3 = v( 3 ) t3 = t1*v3 c c %------------------------------------------------% c | Apply G from the left to transform the rows of | c | the matrix in columns K to I2. | c %------------------------------------------------% c do 60 j = k, i2 sum = h( k, j ) + v2*h( k+1, j ) + v3*h( k+2, j ) h( k, j ) = h( k, j ) - sum*t1 h( k+1, j ) = h( k+1, j ) - sum*t2 h( k+2, j ) = h( k+2, j ) - sum*t3 60 continue c c %----------------------------------------------------% c | Apply G from the right to transform the columns of | c | the matrix in rows I1 to min(K+3,I). | c %----------------------------------------------------% c do 70 j = i1, min( k+3, i ) sum = h( j, k ) + v2*h( j, k+1 ) + v3*h( j, k+2 ) h( j, k ) = h( j, k ) - sum*t1 h( j, k+1 ) = h( j, k+1 ) - sum*t2 h( j, k+2 ) = h( j, k+2 ) - sum*t3 70 continue c c %----------------------------------% c | Accumulate transformations for Z | c %----------------------------------% c sum = z( k ) + v2*z( k+1 ) + v3*z( k+2 ) z( k ) = z( k ) - sum*t1 z( k+1 ) = z( k+1 ) - sum*t2 z( k+2 ) = z( k+2 ) - sum*t3 else if( nr.eq.2 ) then c c %------------------------------------------------% c | Apply G from the left to transform the rows of | c | the matrix in columns K to I2. | c %------------------------------------------------% c do 90 j = k, i2 sum = h( k, j ) + v2*h( k+1, j ) h( k, j ) = h( k, j ) - sum*t1 h( k+1, j ) = h( k+1, j ) - sum*t2 90 continue c c %----------------------------------------------------% c | Apply G from the right to transform the columns of | c | the matrix in rows I1 to min(K+3,I). | c %----------------------------------------------------% c do 100 j = i1, i sum = h( j, k ) + v2*h( j, k+1 ) h( j, k ) = h( j, k ) - sum*t1 h( j, k+1 ) = h( j, k+1 ) - sum*t2 100 continue c c %----------------------------------% c | Accumulate transformations for Z | c %----------------------------------% c sum = z( k ) + v2*z( k+1 ) z( k ) = z( k ) - sum*t1 z( k+1 ) = z( k+1 ) - sum*t2 end if 120 continue 130 continue c c %-------------------------------------------------------% c | Failure to converge in remaining number of iterations | c %-------------------------------------------------------% c info = i return 140 continue if( l.eq.i ) then c c %------------------------------------------------------% c | H(I,I-1) is negligible: one eigenvalue has converged | c %------------------------------------------------------% c wr( i ) = h( i, i ) wi( i ) = zero else if( l.eq.i-1 ) then c c %--------------------------------------------------------% c | H(I-1,I-2) is negligible; | c | a pair of eigenvalues have converged. | c | | c | Transform the 2-by-2 submatrix to standard Schur form, | c | and compute and store the eigenvalues. | c %--------------------------------------------------------% c call slanv2( h( i-1, i-1 ), h( i-1, i ), h( i, i-1 ), & h( i, i ), wr( i-1 ), wi( i-1 ), wr( i ), wi( i ), & cs, sn ) if( wantt ) then c c %-----------------------------------------------------% c | Apply the transformation to the rest of H and to Z, | c | as required. | c %-----------------------------------------------------% c if( i2.gt.i ) & call srot( i2-i, h( i-1, i+1 ), ldh, h( i, i+1 ), ldh, & cs, sn ) call srot( i-i1-1, h( i1, i-1 ), 1, h( i1, i ), 1, cs, sn ) sum = cs*z( i-1 ) + sn*z( i ) z( i ) = cs*z( i ) - sn*z( i-1 ) z( i-1 ) = sum end if end if c c %---------------------------------------------------------% c | Decrement number of remaining iterations, and return to | c | start of the main loop with new value of I. | c %---------------------------------------------------------% c itn = itn - its i = l - 1 go to 10 150 continue return c c %---------------% c | End of slaqrb | c %---------------% c end arpack-0.92.1/SRC/ssconv.f0000644000175000017500000000645610776001577012123 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: ssconv c c\Description: c Convergence testing for the symmetric Arnoldi eigenvalue routine. c c\Usage: c call ssconv c ( N, RITZ, BOUNDS, TOL, NCONV ) c c\Arguments c N Integer. (INPUT) c Number of Ritz values to check for convergence. c c RITZ Real array of length N. (INPUT) c The Ritz values to be checked for convergence. c c BOUNDS Real array of length N. (INPUT) c Ritz estimates associated with the Ritz values in RITZ. c c TOL Real scalar. (INPUT) c Desired relative accuracy for a Ritz value to be considered c "converged". c c NCONV Integer scalar. (OUTPUT) c Number of "converged" Ritz values. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Routines called: c arscnd ARPACK utility routine for timing. c slamch LAPACK routine that determines machine constants. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: sconv.F SID: 2.4 DATE OF SID: 4/19/96 RELEASE: 2 c c\Remarks c 1. Starting with version 2.4, this routine no longer uses the c Parlett strategy using the gap conditions. c c\EndLib c c----------------------------------------------------------------------- c subroutine ssconv (n, ritz, bounds, tol, nconv) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c integer n, nconv Real & tol c c %-----------------% c | Array Arguments | c %-----------------% c Real & ritz(n), bounds(n) c c %---------------% c | Local Scalars | c %---------------% c integer i Real & temp, eps23 c c %-------------------% c | External routines | c %-------------------% c Real & slamch external slamch c %---------------------% c | Intrinsic Functions | c %---------------------% c intrinsic abs c c %-----------------------% c | Executable Statements | c %-----------------------% c call arscnd (t0) c eps23 = slamch('Epsilon-Machine') eps23 = eps23**(2.0E+0 / 3.0E+0) c nconv = 0 do 10 i = 1, n c c %-----------------------------------------------------% c | The i-th Ritz value is considered "converged" | c | when: bounds(i) .le. TOL*max(eps23, abs(ritz(i))) | c %-----------------------------------------------------% c temp = max( eps23, abs(ritz(i)) ) if ( bounds(i) .le. tol*temp ) then nconv = nconv + 1 end if c 10 continue c call arscnd (t1) tsconv = tsconv + (t1 - t0) c return c c %---------------% c | End of ssconv | c %---------------% c end arpack-0.92.1/SRC/sstatn.f0000644000175000017500000000271010776001577012111 00000000000000c c %---------------------------------------------% c | Initialize statistic and timing information | c | for nonsymmetric Arnoldi code. | c %---------------------------------------------% c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: statn.F SID: 2.4 DATE OF SID: 4/20/96 RELEASE: 2 c subroutine sstatn c c %--------------------------------% c | See stat.doc for documentation | c %--------------------------------% c include 'stat.h' c c %-----------------------% c | Executable Statements | c %-----------------------% c nopx = 0 nbx = 0 nrorth = 0 nitref = 0 nrstrt = 0 c tnaupd = 0.0E+0 tnaup2 = 0.0E+0 tnaitr = 0.0E+0 tneigh = 0.0E+0 tngets = 0.0E+0 tnapps = 0.0E+0 tnconv = 0.0E+0 titref = 0.0E+0 tgetv0 = 0.0E+0 trvec = 0.0E+0 c c %----------------------------------------------------% c | User time including reverse communication overhead | c %----------------------------------------------------% c tmvopx = 0.0E+0 tmvbx = 0.0E+0 c return c c c %---------------% c | End of sstatn | c %---------------% c end arpack-0.92.1/SRC/dneupd.f0000644000175000017500000012656311276620103012055 00000000000000c\BeginDoc c c\Name: dneupd c c\Description: c c This subroutine returns the converged approximations to eigenvalues c of A*z = lambda*B*z and (optionally): c c (1) The corresponding approximate eigenvectors; c c (2) An orthonormal basis for the associated approximate c invariant subspace; c c (3) Both. c c There is negligible additional cost to obtain eigenvectors. An orthonormal c basis is always computed. There is an additional storage cost of n*nev c if both are requested (in this case a separate array Z must be supplied). c c The approximate eigenvalues and eigenvectors of A*z = lambda*B*z c are derived from approximate eigenvalues and eigenvectors of c of the linear operator OP prescribed by the MODE selection in the c call to DNAUPD . DNAUPD must be called before this routine is called. c These approximate eigenvalues and vectors are commonly called Ritz c values and Ritz vectors respectively. They are referred to as such c in the comments that follow. The computed orthonormal basis for the c invariant subspace corresponding to these Ritz values is referred to as a c Schur basis. c c See documentation in the header of the subroutine DNAUPD for c definition of OP as well as other terms and the relation of computed c Ritz values and Ritz vectors of OP with respect to the given problem c A*z = lambda*B*z. For a brief description, see definitions of c IPARAM(7), MODE and WHICH in the documentation of DNAUPD . c c\Usage: c call dneupd c ( RVEC, HOWMNY, SELECT, DR, DI, Z, LDZ, SIGMAR, SIGMAI, WORKEV, BMAT, c N, WHICH, NEV, TOL, RESID, NCV, V, LDV, IPARAM, IPNTR, WORKD, WORKL, c LWORKL, INFO ) c c\Arguments: c RVEC LOGICAL (INPUT) c Specifies whether a basis for the invariant subspace corresponding c to the converged Ritz value approximations for the eigenproblem c A*z = lambda*B*z is computed. c c RVEC = .FALSE. Compute Ritz values only. c c RVEC = .TRUE. Compute the Ritz vectors or Schur vectors. c See Remarks below. c c HOWMNY Character*1 (INPUT) c Specifies the form of the basis for the invariant subspace c corresponding to the converged Ritz values that is to be computed. c c = 'A': Compute NEV Ritz vectors; c = 'P': Compute NEV Schur vectors; c = 'S': compute some of the Ritz vectors, specified c by the logical array SELECT. c c SELECT Logical array of dimension NCV. (INPUT) c If HOWMNY = 'S', SELECT specifies the Ritz vectors to be c computed. To select the Ritz vector corresponding to a c Ritz value (DR(j), DI(j)), SELECT(j) must be set to .TRUE.. c If HOWMNY = 'A' or 'P', SELECT is used as internal workspace. c c DR Double precision array of dimension NEV+1. (OUTPUT) c If IPARAM(7) = 1,2 or 3 and SIGMAI=0.0 then on exit: DR contains c the real part of the Ritz approximations to the eigenvalues of c A*z = lambda*B*z. c If IPARAM(7) = 3, 4 and SIGMAI is not equal to zero, then on exit: c DR contains the real part of the Ritz values of OP computed by c DNAUPD . A further computation must be performed by the user c to transform the Ritz values computed for OP by DNAUPD to those c of the original system A*z = lambda*B*z. See remark 3 below. c c DI Double precision array of dimension NEV+1. (OUTPUT) c On exit, DI contains the imaginary part of the Ritz value c approximations to the eigenvalues of A*z = lambda*B*z associated c with DR. c c NOTE: When Ritz values are complex, they will come in complex c conjugate pairs. If eigenvectors are requested, the c corresponding Ritz vectors will also come in conjugate c pairs and the real and imaginary parts of these are c represented in two consecutive columns of the array Z c (see below). c c Z Double precision N by NEV+1 array if RVEC = .TRUE. and HOWMNY = 'A'. (OUTPUT) c On exit, if RVEC = .TRUE. and HOWMNY = 'A', then the columns of c Z represent approximate eigenvectors (Ritz vectors) corresponding c to the NCONV=IPARAM(5) Ritz values for eigensystem c A*z = lambda*B*z. c c The complex Ritz vector associated with the Ritz value c with positive imaginary part is stored in two consecutive c columns. The first column holds the real part of the Ritz c vector and the second column holds the imaginary part. The c Ritz vector associated with the Ritz value with negative c imaginary part is simply the complex conjugate of the Ritz vector c associated with the positive imaginary part. c c If RVEC = .FALSE. or HOWMNY = 'P', then Z is not referenced. c c NOTE: If if RVEC = .TRUE. and a Schur basis is not required, c the array Z may be set equal to first NEV+1 columns of the Arnoldi c basis array V computed by DNAUPD . In this case the Arnoldi basis c will be destroyed and overwritten with the eigenvector basis. c c LDZ Integer. (INPUT) c The leading dimension of the array Z. If Ritz vectors are c desired, then LDZ >= max( 1, N ). In any case, LDZ >= 1. c c SIGMAR Double precision (INPUT) c If IPARAM(7) = 3 or 4, represents the real part of the shift. c Not referenced if IPARAM(7) = 1 or 2. c c SIGMAI Double precision (INPUT) c If IPARAM(7) = 3 or 4, represents the imaginary part of the shift. c Not referenced if IPARAM(7) = 1 or 2. See remark 3 below. c c WORKEV Double precision work array of dimension 3*NCV. (WORKSPACE) c c **** The remaining arguments MUST be the same as for the **** c **** call to DNAUPD that was just completed. **** c c NOTE: The remaining arguments c c BMAT, N, WHICH, NEV, TOL, RESID, NCV, V, LDV, IPARAM, IPNTR, c WORKD, WORKL, LWORKL, INFO c c must be passed directly to DNEUPD following the last call c to DNAUPD . These arguments MUST NOT BE MODIFIED between c the the last call to DNAUPD and the call to DNEUPD . c c Three of these parameters (V, WORKL, INFO) are also output parameters: c c V Double precision N by NCV array. (INPUT/OUTPUT) c c Upon INPUT: the NCV columns of V contain the Arnoldi basis c vectors for OP as constructed by DNAUPD . c c Upon OUTPUT: If RVEC = .TRUE. the first NCONV=IPARAM(5) columns c contain approximate Schur vectors that span the c desired invariant subspace. See Remark 2 below. c c NOTE: If the array Z has been set equal to first NEV+1 columns c of the array V and RVEC=.TRUE. and HOWMNY= 'A', then the c Arnoldi basis held by V has been overwritten by the desired c Ritz vectors. If a separate array Z has been passed then c the first NCONV=IPARAM(5) columns of V will contain approximate c Schur vectors that span the desired invariant subspace. c c WORKL Double precision work array of length LWORKL. (OUTPUT/WORKSPACE) c WORKL(1:ncv*ncv+3*ncv) contains information obtained in c dnaupd . They are not changed by dneupd . c WORKL(ncv*ncv+3*ncv+1:3*ncv*ncv+6*ncv) holds the c real and imaginary part of the untransformed Ritz values, c the upper quasi-triangular matrix for H, and the c associated matrix representation of the invariant subspace for H. c c Note: IPNTR(9:13) contains the pointer into WORKL for addresses c of the above information computed by dneupd . c ------------------------------------------------------------- c IPNTR(9): pointer to the real part of the NCV RITZ values of the c original system. c IPNTR(10): pointer to the imaginary part of the NCV RITZ values of c the original system. c IPNTR(11): pointer to the NCV corresponding error bounds. c IPNTR(12): pointer to the NCV by NCV upper quasi-triangular c Schur matrix for H. c IPNTR(13): pointer to the NCV by NCV matrix of eigenvectors c of the upper Hessenberg matrix H. Only referenced by c dneupd if RVEC = .TRUE. See Remark 2 below. c ------------------------------------------------------------- c c INFO Integer. (OUTPUT) c Error flag on output. c c = 0: Normal exit. c c = 1: The Schur form computed by LAPACK routine dlahqr c could not be reordered by LAPACK routine dtrsen . c Re-enter subroutine dneupd with IPARAM(5)=NCV and c increase the size of the arrays DR and DI to have c dimension at least dimension NCV and allocate at least NCV c columns for Z. NOTE: Not necessary if Z and V share c the same space. Please notify the authors if this error c occurs. c c = -1: N must be positive. c = -2: NEV must be positive. c = -3: NCV-NEV >= 2 and less than or equal to N. c = -5: WHICH must be one of 'LM', 'SM', 'LR', 'SR', 'LI', 'SI' c = -6: BMAT must be one of 'I' or 'G'. c = -7: Length of private work WORKL array is not sufficient. c = -8: Error return from calculation of a real Schur form. c Informational error from LAPACK routine dlahqr . c = -9: Error return from calculation of eigenvectors. c Informational error from LAPACK routine dtrevc . c = -10: IPARAM(7) must be 1,2,3,4. c = -11: IPARAM(7) = 1 and BMAT = 'G' are incompatible. c = -12: HOWMNY = 'S' not yet implemented c = -13: HOWMNY must be one of 'A' or 'P' if RVEC = .true. c = -14: DNAUPD did not find any eigenvalues to sufficient c accuracy. c = -15: DNEUPD got a different count of the number of converged c Ritz values than DNAUPD got. This indicates the user c probably made an error in passing data from DNAUPD to c DNEUPD or that the data was modified before entering c DNEUPD c c\BeginLib c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly c Restarted Arnoldi Iteration", Rice University Technical Report c TR95-13, Department of Computational and Applied Mathematics. c 3. B.N. Parlett & Y. Saad, "Complex Shift and Invert Strategies for c Real Matrices", Linear Algebra and its Applications, vol 88/89, c pp 575-595, (1987). c c\Routines called: c ivout ARPACK utility routine that prints integers. c dmout ARPACK utility routine that prints matrices c dvout ARPACK utility routine that prints vectors. c dgeqr2 LAPACK routine that computes the QR factorization of c a matrix. c dlacpy LAPACK matrix copy routine. c dlahqr LAPACK routine to compute the real Schur form of an c upper Hessenberg matrix. c dlamch LAPACK routine that determines machine constants. c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c dlaset LAPACK matrix initialization routine. c dorm2r LAPACK routine that applies an orthogonal matrix in c factored form. c dtrevc LAPACK routine to compute the eigenvectors of a matrix c in upper quasi-triangular form. c dtrsen LAPACK routine that re-orders the Schur form. c dtrmm Level 3 BLAS matrix times an upper triangular matrix. c dger Level 2 BLAS rank one update to a matrix. c dcopy Level 1 BLAS that copies one vector to another . c ddot Level 1 BLAS that computes the scalar product of two vectors. c dnrm2 Level 1 BLAS that computes the norm of a vector. c dscal Level 1 BLAS that scales a vector. c c\Remarks c c 1. Currently only HOWMNY = 'A' and 'P' are implemented. c c Let trans(X) denote the transpose of X. c c 2. Schur vectors are an orthogonal representation for the basis of c Ritz vectors. Thus, their numerical properties are often superior. c If RVEC = .TRUE. then the relationship c A * V(:,1:IPARAM(5)) = V(:,1:IPARAM(5)) * T, and c trans(V(:,1:IPARAM(5))) * V(:,1:IPARAM(5)) = I are approximately c satisfied. Here T is the leading submatrix of order IPARAM(5) of the c real upper quasi-triangular matrix stored workl(ipntr(12)). That is, c T is block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; c each 2-by-2 diagonal block has its diagonal elements equal and its c off-diagonal elements of opposite sign. Corresponding to each 2-by-2 c diagonal block is a complex conjugate pair of Ritz values. The real c Ritz values are stored on the diagonal of T. c c 3. If IPARAM(7) = 3 or 4 and SIGMAI is not equal zero, then the user must c form the IPARAM(5) Rayleigh quotients in order to transform the Ritz c values computed by DNAUPD for OP to those of A*z = lambda*B*z. c Set RVEC = .true. and HOWMNY = 'A', and c compute c trans(Z(:,I)) * A * Z(:,I) if DI(I) = 0. c If DI(I) is not equal to zero and DI(I+1) = - D(I), c then the desired real and imaginary parts of the Ritz value are c trans(Z(:,I)) * A * Z(:,I) + trans(Z(:,I+1)) * A * Z(:,I+1), c trans(Z(:,I)) * A * Z(:,I+1) - trans(Z(:,I+1)) * A * Z(:,I), c respectively. c Another possibility is to set RVEC = .true. and HOWMNY = 'P' and c compute trans(V(:,1:IPARAM(5))) * A * V(:,1:IPARAM(5)) and then an upper c quasi-triangular matrix of order IPARAM(5) is computed. See remark c 2 above. c c\Authors c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Chao Yang Houston, Texas c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: neupd.F SID: 2.7 DATE OF SID: 09/20/00 RELEASE: 2 c c\EndLib c c----------------------------------------------------------------------- subroutine dneupd (rvec , howmny, select, dr , di, & z , ldz , sigmar, sigmai, workev, & bmat , n , which , nev , tol, & resid, ncv , v , ldv , iparam, & ipntr, workd , workl , lworkl, info) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character bmat, howmny, which*2 logical rvec integer info, ldz, ldv, lworkl, n, ncv, nev Double precision & sigmar, sigmai, tol c c %-----------------% c | Array Arguments | c %-----------------% c integer iparam(11), ipntr(14) logical select(ncv) Double precision & dr(nev+1) , di(nev+1), resid(n) , & v(ldv,ncv) , z(ldz,*) , workd(3*n), & workl(lworkl), workev(3*ncv) c c %------------% c | Parameters | c %------------% c Double precision & one, zero parameter (one = 1.0D+0 , zero = 0.0D+0 ) c c %---------------% c | Local Scalars | c %---------------% c character type*6 integer bounds, ierr , ih , ihbds , & iheigr, iheigi, iconj , nconv , & invsub, iuptri, iwev , iwork(1), & j , k , ldh , ldq , & mode , msglvl, outncv, ritzr , & ritzi , wri , wrr , irr , & iri , ibd , ishift, numcnv , & np , jj logical reord Double precision & conds , rnorm, sep , temp, & vl(1,1), temp1, eps23 c c %----------------------% c | External Subroutines | c %----------------------% c external dcopy , dger , dgeqr2 , dlacpy , & dlahqr , dlaset , dmout , dorm2r , & dtrevc , dtrmm , dtrsen , dscal , & dvout , ivout c c %--------------------% c | External Functions | c %--------------------% c Double precision & dlapy2 , dnrm2 , dlamch , ddot external dlapy2 , dnrm2 , dlamch , ddot c c %---------------------% c | Intrinsic Functions | c %---------------------% c intrinsic abs, min, sqrt c c %-----------------------% c | Executable Statements | c %-----------------------% c c %------------------------% c | Set default parameters | c %------------------------% c msglvl = mneupd mode = iparam(7) nconv = iparam(5) info = 0 c c %---------------------------------% c | Get machine dependent constant. | c %---------------------------------% c eps23 = dlamch ('Epsilon-Machine') eps23 = eps23**(2.0D+0 / 3.0D+0 ) c c %--------------% c | Quick return | c %--------------% c ierr = 0 c if (nconv .le. 0) then ierr = -14 else if (n .le. 0) then ierr = -1 else if (nev .le. 0) then ierr = -2 else if (ncv .le. nev+1 .or. ncv .gt. n) then ierr = -3 else if (which .ne. 'LM' .and. & which .ne. 'SM' .and. & which .ne. 'LR' .and. & which .ne. 'SR' .and. & which .ne. 'LI' .and. & which .ne. 'SI') then ierr = -5 else if (bmat .ne. 'I' .and. bmat .ne. 'G') then ierr = -6 else if (lworkl .lt. 3*ncv**2 + 6*ncv) then ierr = -7 else if ( (howmny .ne. 'A' .and. & howmny .ne. 'P' .and. & howmny .ne. 'S') .and. rvec ) then ierr = -13 else if (howmny .eq. 'S' ) then ierr = -12 end if c if (mode .eq. 1 .or. mode .eq. 2) then type = 'REGULR' else if (mode .eq. 3 .and. sigmai .eq. zero) then type = 'SHIFTI' else if (mode .eq. 3 ) then type = 'REALPT' else if (mode .eq. 4 ) then type = 'IMAGPT' else ierr = -10 end if if (mode .eq. 1 .and. bmat .eq. 'G') ierr = -11 c c %------------% c | Error Exit | c %------------% c if (ierr .ne. 0) then info = ierr go to 9000 end if c c %--------------------------------------------------------% c | Pointer into WORKL for address of H, RITZ, BOUNDS, Q | c | etc... and the remaining workspace. | c | Also update pointer to be used on output. | c | Memory is laid out as follows: | c | workl(1:ncv*ncv) := generated Hessenberg matrix | c | workl(ncv*ncv+1:ncv*ncv+2*ncv) := real and imaginary | c | parts of ritz values | c | workl(ncv*ncv+2*ncv+1:ncv*ncv+3*ncv) := error bounds | c %--------------------------------------------------------% c c %-----------------------------------------------------------% c | The following is used and set by DNEUPD . | c | workl(ncv*ncv+3*ncv+1:ncv*ncv+4*ncv) := The untransformed | c | real part of the Ritz values. | c | workl(ncv*ncv+4*ncv+1:ncv*ncv+5*ncv) := The untransformed | c | imaginary part of the Ritz values. | c | workl(ncv*ncv+5*ncv+1:ncv*ncv+6*ncv) := The untransformed | c | error bounds of the Ritz values | c | workl(ncv*ncv+6*ncv+1:2*ncv*ncv+6*ncv) := Holds the upper | c | quasi-triangular matrix for H | c | workl(2*ncv*ncv+6*ncv+1: 3*ncv*ncv+6*ncv) := Holds the | c | associated matrix representation of the invariant | c | subspace for H. | c | GRAND total of NCV * ( 3 * NCV + 6 ) locations. | c %-----------------------------------------------------------% c ih = ipntr(5) ritzr = ipntr(6) ritzi = ipntr(7) bounds = ipntr(8) ldh = ncv ldq = ncv iheigr = bounds + ldh iheigi = iheigr + ldh ihbds = iheigi + ldh iuptri = ihbds + ldh invsub = iuptri + ldh*ncv ipntr(9) = iheigr ipntr(10) = iheigi ipntr(11) = ihbds ipntr(12) = iuptri ipntr(13) = invsub wrr = 1 wri = ncv + 1 iwev = wri + ncv c c %-----------------------------------------% c | irr points to the REAL part of the Ritz | c | values computed by _neigh before | c | exiting _naup2. | c | iri points to the IMAGINARY part of the | c | Ritz values computed by _neigh | c | before exiting _naup2. | c | ibd points to the Ritz estimates | c | computed by _neigh before exiting | c | _naup2. | c %-----------------------------------------% c irr = ipntr(14)+ncv*ncv iri = irr+ncv ibd = iri+ncv c c %------------------------------------% c | RNORM is B-norm of the RESID(1:N). | c %------------------------------------% c rnorm = workl(ih+2) workl(ih+2) = zero c if (msglvl .gt. 2) then call dvout (logfil, ncv, workl(irr), ndigit, & '_neupd: Real part of Ritz values passed in from _NAUPD.') call dvout (logfil, ncv, workl(iri), ndigit, & '_neupd: Imag part of Ritz values passed in from _NAUPD.') call dvout (logfil, ncv, workl(ibd), ndigit, & '_neupd: Ritz estimates passed in from _NAUPD.') end if c if (rvec) then c reord = .false. c c %---------------------------------------------------% c | Use the temporary bounds array to store indices | c | These will be used to mark the select array later | c %---------------------------------------------------% c do 10 j = 1,ncv workl(bounds+j-1) = j select(j) = .false. 10 continue c c %-------------------------------------% c | Select the wanted Ritz values. | c | Sort the Ritz values so that the | c | wanted ones appear at the tailing | c | NEV positions of workl(irr) and | c | workl(iri). Move the corresponding | c | error estimates in workl(bound) | c | accordingly. | c %-------------------------------------% c np = ncv - nev ishift = 0 call dngets (ishift , which , nev , & np , workl(irr), workl(iri), & workl(bounds), workl , workl(np+1)) c if (msglvl .gt. 2) then call dvout (logfil, ncv, workl(irr), ndigit, & '_neupd: Real part of Ritz values after calling _NGETS.') call dvout (logfil, ncv, workl(iri), ndigit, & '_neupd: Imag part of Ritz values after calling _NGETS.') call dvout (logfil, ncv, workl(bounds), ndigit, & '_neupd: Ritz value indices after calling _NGETS.') end if c c %-----------------------------------------------------% c | Record indices of the converged wanted Ritz values | c | Mark the select array for possible reordering | c %-----------------------------------------------------% c numcnv = 0 do 11 j = 1,ncv temp1 = max(eps23, & dlapy2 ( workl(irr+ncv-j), workl(iri+ncv-j) )) jj = workl(bounds + ncv - j) if (numcnv .lt. nconv .and. & workl(ibd+jj-1) .le. tol*temp1) then select(jj) = .true. numcnv = numcnv + 1 if (jj .gt. nev) reord = .true. endif 11 continue c c %-----------------------------------------------------------% c | Check the count (numcnv) of converged Ritz values with | c | the number (nconv) reported by dnaupd. If these two | c | are different then there has probably been an error | c | caused by incorrect passing of the dnaupd data. | c %-----------------------------------------------------------% c if (msglvl .gt. 2) then call ivout(logfil, 1, numcnv, ndigit, & '_neupd: Number of specified eigenvalues') call ivout(logfil, 1, nconv, ndigit, & '_neupd: Number of "converged" eigenvalues') end if c if (numcnv .ne. nconv) then info = -15 go to 9000 end if c c %-----------------------------------------------------------% c | Call LAPACK routine dlahqr to compute the real Schur form | c | of the upper Hessenberg matrix returned by DNAUPD . | c | Make a copy of the upper Hessenberg matrix. | c | Initialize the Schur vector matrix Q to the identity. | c %-----------------------------------------------------------% c call dcopy (ldh*ncv, workl(ih), 1, workl(iuptri), 1) call dlaset ('All', ncv, ncv, & zero , one, workl(invsub), & ldq) call dlahqr (.true., .true. , ncv, & 1 , ncv , workl(iuptri), & ldh , workl(iheigr), workl(iheigi), & 1 , ncv , workl(invsub), & ldq , ierr) call dcopy (ncv , workl(invsub+ncv-1), ldq, & workl(ihbds), 1) c if (ierr .ne. 0) then info = -8 go to 9000 end if c if (msglvl .gt. 1) then call dvout (logfil, ncv, workl(iheigr), ndigit, & '_neupd: Real part of the eigenvalues of H') call dvout (logfil, ncv, workl(iheigi), ndigit, & '_neupd: Imaginary part of the Eigenvalues of H') call dvout (logfil, ncv, workl(ihbds), ndigit, & '_neupd: Last row of the Schur vector matrix') if (msglvl .gt. 3) then call dmout (logfil , ncv, ncv , & workl(iuptri), ldh, ndigit, & '_neupd: The upper quasi-triangular matrix ') end if end if c if (reord) then c c %-----------------------------------------------------% c | Reorder the computed upper quasi-triangular matrix. | c %-----------------------------------------------------% c call dtrsen ('None' , 'V' , & select , ncv , & workl(iuptri), ldh , & workl(invsub), ldq , & workl(iheigr), workl(iheigi), & nconv , conds , & sep , workl(ihbds) , & ncv , iwork , & 1 , ierr) c if (ierr .eq. 1) then info = 1 go to 9000 end if c if (msglvl .gt. 2) then call dvout (logfil, ncv, workl(iheigr), ndigit, & '_neupd: Real part of the eigenvalues of H--reordered') call dvout (logfil, ncv, workl(iheigi), ndigit, & '_neupd: Imag part of the eigenvalues of H--reordered') if (msglvl .gt. 3) then call dmout (logfil , ncv, ncv , & workl(iuptri), ldq, ndigit, & '_neupd: Quasi-triangular matrix after re-ordering') end if end if c end if c c %---------------------------------------% c | Copy the last row of the Schur vector | c | into workl(ihbds). This will be used | c | to compute the Ritz estimates of | c | converged Ritz values. | c %---------------------------------------% c call dcopy (ncv, workl(invsub+ncv-1), ldq, workl(ihbds), 1) c c %----------------------------------------------------% c | Place the computed eigenvalues of H into DR and DI | c | if a spectral transformation was not used. | c %----------------------------------------------------% c if (nconv .ge. nev+1) then nconv = nev+1 end if if (type .eq. 'REGULR') then call dcopy (nconv, workl(iheigr), 1, dr, 1) call dcopy (nconv, workl(iheigi), 1, di, 1) end if c c %----------------------------------------------------------% c | Compute the QR factorization of the matrix representing | c | the wanted invariant subspace located in the first NCONV | c | columns of workl(invsub,ldq). | c %----------------------------------------------------------% c call dgeqr2 (ncv, nconv , workl(invsub), & ldq, workev, workev(ncv+1), & ierr) c c %---------------------------------------------------------% c | * Postmultiply V by Q using dorm2r . | c | * Copy the first NCONV columns of VQ into Z. | c | * Postmultiply Z by R. | c | The N by NCONV matrix Z is now a matrix representation | c | of the approximate invariant subspace associated with | c | the Ritz values in workl(iheigr) and workl(iheigi) | c | The first NCONV columns of V are now approximate Schur | c | vectors associated with the real upper quasi-triangular | c | matrix of order NCONV in workl(iuptri) | c %---------------------------------------------------------% c call dorm2r ('Right', 'Notranspose', n , & ncv , nconv , workl(invsub), & ldq , workev , v , & ldv , workd(n+1) , ierr) call dlacpy ('All', n, nconv, v, ldv, z, ldz) c do 20 j=1, nconv c c %---------------------------------------------------% c | Perform both a column and row scaling if the | c | diagonal element of workl(invsub,ldq) is negative | c | I'm lazy and don't take advantage of the upper | c | quasi-triangular form of workl(iuptri,ldq) | c | Note that since Q is orthogonal, R is a diagonal | c | matrix consisting of plus or minus ones | c %---------------------------------------------------% c if (workl(invsub+(j-1)*ldq+j-1) .lt. zero) then call dscal (nconv, -one, workl(iuptri+j-1), ldq) call dscal (nconv, -one, workl(iuptri+(j-1)*ldq), 1) end if c 20 continue c if (howmny .eq. 'A') then c c %--------------------------------------------% c | Compute the NCONV wanted eigenvectors of T | c | located in workl(iuptri,ldq). | c %--------------------------------------------% c do 30 j=1, ncv if (j .le. nconv) then select(j) = .true. else select(j) = .false. end if 30 continue c call dtrevc ('Right', 'Select' , select , & ncv , workl(iuptri), ldq , & vl , 1 , workl(invsub), & ldq , ncv , outncv , & workev , ierr) c if (ierr .ne. 0) then info = -9 go to 9000 end if c c %------------------------------------------------% c | Scale the returning eigenvectors so that their | c | Euclidean norms are all one. LAPACK subroutine | c | dtrevc returns each eigenvector normalized so | c | that the element of largest magnitude has | c | magnitude 1; | c %------------------------------------------------% c iconj = 0 do 40 j=1, nconv c if ( workl(iheigi+j-1) .eq. zero ) then c c %----------------------% c | real eigenvalue case | c %----------------------% c temp = dnrm2 ( ncv, workl(invsub+(j-1)*ldq), 1 ) call dscal ( ncv, one / temp, & workl(invsub+(j-1)*ldq), 1 ) c else c c %-------------------------------------------% c | Complex conjugate pair case. Note that | c | since the real and imaginary part of | c | the eigenvector are stored in consecutive | c | columns, we further normalize by the | c | square root of two. | c %-------------------------------------------% c if (iconj .eq. 0) then temp = dlapy2 (dnrm2 (ncv, & workl(invsub+(j-1)*ldq), & 1), & dnrm2 (ncv, & workl(invsub+j*ldq), & 1)) call dscal (ncv, one/temp, & workl(invsub+(j-1)*ldq), 1 ) call dscal (ncv, one/temp, & workl(invsub+j*ldq), 1 ) iconj = 1 else iconj = 0 end if c end if c 40 continue c call dgemv ('T', ncv, nconv, one, workl(invsub), & ldq, workl(ihbds), 1, zero, workev, 1) c iconj = 0 do 45 j=1, nconv if (workl(iheigi+j-1) .ne. zero) then c c %-------------------------------------------% c | Complex conjugate pair case. Note that | c | since the real and imaginary part of | c | the eigenvector are stored in consecutive | c %-------------------------------------------% c if (iconj .eq. 0) then workev(j) = dlapy2 (workev(j), workev(j+1)) workev(j+1) = workev(j) iconj = 1 else iconj = 0 end if end if 45 continue c if (msglvl .gt. 2) then call dcopy (ncv, workl(invsub+ncv-1), ldq, & workl(ihbds), 1) call dvout (logfil, ncv, workl(ihbds), ndigit, & '_neupd: Last row of the eigenvector matrix for T') if (msglvl .gt. 3) then call dmout (logfil, ncv, ncv, workl(invsub), ldq, & ndigit, '_neupd: The eigenvector matrix for T') end if end if c c %---------------------------------------% c | Copy Ritz estimates into workl(ihbds) | c %---------------------------------------% c call dcopy (nconv, workev, 1, workl(ihbds), 1) c c %---------------------------------------------------------% c | Compute the QR factorization of the eigenvector matrix | c | associated with leading portion of T in the first NCONV | c | columns of workl(invsub,ldq). | c %---------------------------------------------------------% c call dgeqr2 (ncv, nconv , workl(invsub), & ldq, workev, workev(ncv+1), & ierr) c c %----------------------------------------------% c | * Postmultiply Z by Q. | c | * Postmultiply Z by R. | c | The N by NCONV matrix Z is now contains the | c | Ritz vectors associated with the Ritz values | c | in workl(iheigr) and workl(iheigi). | c %----------------------------------------------% c call dorm2r ('Right', 'Notranspose', n , & ncv , nconv , workl(invsub), & ldq , workev , z , & ldz , workd(n+1) , ierr) c call dtrmm ('Right' , 'Upper' , 'No transpose', & 'Non-unit', n , nconv , & one , workl(invsub), ldq , & z , ldz) c end if c else c c %------------------------------------------------------% c | An approximate invariant subspace is not needed. | c | Place the Ritz values computed DNAUPD into DR and DI | c %------------------------------------------------------% c call dcopy (nconv, workl(ritzr), 1, dr, 1) call dcopy (nconv, workl(ritzi), 1, di, 1) call dcopy (nconv, workl(ritzr), 1, workl(iheigr), 1) call dcopy (nconv, workl(ritzi), 1, workl(iheigi), 1) call dcopy (nconv, workl(bounds), 1, workl(ihbds), 1) end if c c %------------------------------------------------% c | Transform the Ritz values and possibly vectors | c | and corresponding error bounds of OP to those | c | of A*x = lambda*B*x. | c %------------------------------------------------% c if (type .eq. 'REGULR') then c if (rvec) & call dscal (ncv, rnorm, workl(ihbds), 1) c else c c %---------------------------------------% c | A spectral transformation was used. | c | * Determine the Ritz estimates of the | c | Ritz values in the original system. | c %---------------------------------------% c if (type .eq. 'SHIFTI') then c if (rvec) & call dscal (ncv, rnorm, workl(ihbds), 1) c do 50 k=1, ncv temp = dlapy2 ( workl(iheigr+k-1), & workl(iheigi+k-1) ) workl(ihbds+k-1) = abs( workl(ihbds+k-1) ) & / temp / temp 50 continue c else if (type .eq. 'REALPT') then c do 60 k=1, ncv 60 continue c else if (type .eq. 'IMAGPT') then c do 70 k=1, ncv 70 continue c end if c c %-----------------------------------------------------------% c | * Transform the Ritz values back to the original system. | c | For TYPE = 'SHIFTI' the transformation is | c | lambda = 1/theta + sigma | c | For TYPE = 'REALPT' or 'IMAGPT' the user must from | c | Rayleigh quotients or a projection. See remark 3 above.| c | NOTES: | c | *The Ritz vectors are not affected by the transformation. | c %-----------------------------------------------------------% c if (type .eq. 'SHIFTI') then c do 80 k=1, ncv temp = dlapy2 ( workl(iheigr+k-1), & workl(iheigi+k-1) ) workl(iheigr+k-1) = workl(iheigr+k-1)/temp/temp & + sigmar workl(iheigi+k-1) = -workl(iheigi+k-1)/temp/temp & + sigmai 80 continue c call dcopy (nconv, workl(iheigr), 1, dr, 1) call dcopy (nconv, workl(iheigi), 1, di, 1) c else if (type .eq. 'REALPT' .or. type .eq. 'IMAGPT') then c call dcopy (nconv, workl(iheigr), 1, dr, 1) call dcopy (nconv, workl(iheigi), 1, di, 1) c end if c end if c if (type .eq. 'SHIFTI' .and. msglvl .gt. 1) then call dvout (logfil, nconv, dr, ndigit, & '_neupd: Untransformed real part of the Ritz valuess.') call dvout (logfil, nconv, di, ndigit, & '_neupd: Untransformed imag part of the Ritz valuess.') call dvout (logfil, nconv, workl(ihbds), ndigit, & '_neupd: Ritz estimates of untransformed Ritz values.') else if (type .eq. 'REGULR' .and. msglvl .gt. 1) then call dvout (logfil, nconv, dr, ndigit, & '_neupd: Real parts of converged Ritz values.') call dvout (logfil, nconv, di, ndigit, & '_neupd: Imag parts of converged Ritz values.') call dvout (logfil, nconv, workl(ihbds), ndigit, & '_neupd: Associated Ritz estimates.') end if c c %-------------------------------------------------% c | Eigenvector Purification step. Formally perform | c | one of inverse subspace iteration. Only used | c | for MODE = 2. | c %-------------------------------------------------% c if (rvec .and. howmny .eq. 'A' .and. type .eq. 'SHIFTI') then c c %------------------------------------------------% c | Purify the computed Ritz vectors by adding a | c | little bit of the residual vector: | c | T | c | resid(:)*( e s ) / theta | c | NCV | c | where H s = s theta. Remember that when theta | c | has nonzero imaginary part, the corresponding | c | Ritz vector is stored across two columns of Z. | c %------------------------------------------------% c iconj = 0 do 110 j=1, nconv if (workl(iheigi+j-1) .eq. zero) then workev(j) = workl(invsub+(j-1)*ldq+ncv-1) / & workl(iheigr+j-1) else if (iconj .eq. 0) then temp = dlapy2 ( workl(iheigr+j-1), workl(iheigi+j-1) ) workev(j) = ( workl(invsub+(j-1)*ldq+ncv-1) * & workl(iheigr+j-1) + & workl(invsub+j*ldq+ncv-1) * & workl(iheigi+j-1) ) / temp / temp workev(j+1) = ( workl(invsub+j*ldq+ncv-1) * & workl(iheigr+j-1) - & workl(invsub+(j-1)*ldq+ncv-1) * & workl(iheigi+j-1) ) / temp / temp iconj = 1 else iconj = 0 end if 110 continue c c %---------------------------------------% c | Perform a rank one update to Z and | c | purify all the Ritz vectors together. | c %---------------------------------------% c call dger (n, nconv, one, resid, 1, workev, 1, z, ldz) c end if c 9000 continue c return c c %---------------% c | End of DNEUPD | c %---------------% c end arpack-0.92.1/SRC/zgetv0.f0000644000175000017500000003127410776001577012023 00000000000000c\BeginDoc c c\Name: zgetv0 c c\Description: c Generate a random initial residual vector for the Arnoldi process. c Force the residual vector to be in the range of the operator OP. c c\Usage: c call zgetv0 c ( IDO, BMAT, ITRY, INITV, N, J, V, LDV, RESID, RNORM, c IPNTR, WORKD, IERR ) c c\Arguments c IDO Integer. (INPUT/OUTPUT) c Reverse communication flag. IDO must be zero on the first c call to zgetv0. c ------------------------------------------------------------- c IDO = 0: first call to the reverse communication interface c IDO = -1: compute Y = OP * X where c IPNTR(1) is the pointer into WORKD for X, c IPNTR(2) is the pointer into WORKD for Y. c This is for the initialization phase to force the c starting vector into the range of OP. c IDO = 2: compute Y = B * X where c IPNTR(1) is the pointer into WORKD for X, c IPNTR(2) is the pointer into WORKD for Y. c IDO = 99: done c ------------------------------------------------------------- c c BMAT Character*1. (INPUT) c BMAT specifies the type of the matrix B in the (generalized) c eigenvalue problem A*x = lambda*B*x. c B = 'I' -> standard eigenvalue problem A*x = lambda*x c B = 'G' -> generalized eigenvalue problem A*x = lambda*B*x c c ITRY Integer. (INPUT) c ITRY counts the number of times that zgetv0 is called. c It should be set to 1 on the initial call to zgetv0. c c INITV Logical variable. (INPUT) c .TRUE. => the initial residual vector is given in RESID. c .FALSE. => generate a random initial residual vector. c c N Integer. (INPUT) c Dimension of the problem. c c J Integer. (INPUT) c Index of the residual vector to be generated, with respect to c the Arnoldi process. J > 1 in case of a "restart". c c V Complex*16 N by J array. (INPUT) c The first J-1 columns of V contain the current Arnoldi basis c if this is a "restart". c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling c program. c c RESID Complex*16 array of length N. (INPUT/OUTPUT) c Initial residual vector to be generated. If RESID is c provided, force RESID into the range of the operator OP. c c RNORM Double precision scalar. (OUTPUT) c B-norm of the generated residual. c c IPNTR Integer array of length 3. (OUTPUT) c c WORKD Complex*16 work array of length 2*N. (REVERSE COMMUNICATION). c On exit, WORK(1:N) = B*RESID to be used in SSAITR. c c IERR Integer. (OUTPUT) c = 0: Normal exit. c = -1: Cannot generate a nontrivial restarted residual vector c in the range of the operator OP. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx Complex*16 c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c c\Routines called: c arscnd ARPACK utility routine for timing. c zvout ARPACK utility routine that prints vectors. c zlarnv LAPACK routine for generating a random vector. c zgemv Level 2 BLAS routine for matrix vector multiplication. c zcopy Level 1 BLAS that copies one vector to another. c zdotc Level 1 BLAS that computes the scalar product of two vectors. c dznrm2 Level 1 BLAS that computes the norm of a vector. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: getv0.F SID: 2.3 DATE OF SID: 08/27/96 RELEASE: 2 c c\EndLib c c----------------------------------------------------------------------- c subroutine zgetv0 & ( ido, bmat, itry, initv, n, j, v, ldv, resid, rnorm, & ipntr, workd, ierr ) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character bmat*1 logical initv integer ido, ierr, itry, j, ldv, n Double precision & rnorm c c %-----------------% c | Array Arguments | c %-----------------% c integer ipntr(3) Complex*16 & resid(n), v(ldv,j), workd(2*n) c c %------------% c | Parameters | c %------------% c Complex*16 & one, zero Double precision & rzero parameter (one = (1.0D+0, 0.0D+0), zero = (0.0D+0, 0.0D+0), & rzero = 0.0D+0) c c %------------------------% c | Local Scalars & Arrays | c %------------------------% c logical first, inits, orth integer idist, iseed(4), iter, msglvl, jj Double precision & rnorm0 Complex*16 & cnorm save first, iseed, inits, iter, msglvl, orth, rnorm0 c c %----------------------% c | External Subroutines | c %----------------------% c external zcopy, zgemv, zlarnv, zvout, arscnd c c %--------------------% c | External Functions | c %--------------------% c Double precision & dznrm2, dlapy2 Complex*16 & zdotc external zdotc, dznrm2, dlapy2 c c %-----------------% c | Data Statements | c %-----------------% c data inits /.true./ c c %-----------------------% c | Executable Statements | c %-----------------------% c c c %-----------------------------------% c | Initialize the seed of the LAPACK | c | random number generator | c %-----------------------------------% c if (inits) then iseed(1) = 1 iseed(2) = 3 iseed(3) = 5 iseed(4) = 7 inits = .false. end if c if (ido .eq. 0) then c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call arscnd (t0) msglvl = mgetv0 c ierr = 0 iter = 0 first = .FALSE. orth = .FALSE. c c %-----------------------------------------------------% c | Possibly generate a random starting vector in RESID | c | Use a LAPACK random number generator used by the | c | matrix generation routines. | c | idist = 1: uniform (0,1) distribution; | c | idist = 2: uniform (-1,1) distribution; | c | idist = 3: normal (0,1) distribution; | c %-----------------------------------------------------% c if (.not.initv) then idist = 2 call zlarnv (idist, iseed, n, resid) end if c c %----------------------------------------------------------% c | Force the starting vector into the range of OP to handle | c | the generalized problem when B is possibly (singular). | c %----------------------------------------------------------% c call arscnd (t2) if (bmat .eq. 'G') then nopx = nopx + 1 ipntr(1) = 1 ipntr(2) = n + 1 call zcopy (n, resid, 1, workd, 1) ido = -1 go to 9000 end if end if c c %----------------------------------------% c | Back from computing B*(initial-vector) | c %----------------------------------------% c if (first) go to 20 c c %-----------------------------------------------% c | Back from computing B*(orthogonalized-vector) | c %-----------------------------------------------% c if (orth) go to 40 c call arscnd (t3) tmvopx = tmvopx + (t3 - t2) c c %------------------------------------------------------% c | Starting vector is now in the range of OP; r = OP*r; | c | Compute B-norm of starting vector. | c %------------------------------------------------------% c call arscnd (t2) first = .TRUE. if (bmat .eq. 'G') then nbx = nbx + 1 call zcopy (n, workd(n+1), 1, resid, 1) ipntr(1) = n + 1 ipntr(2) = 1 ido = 2 go to 9000 else if (bmat .eq. 'I') then call zcopy (n, resid, 1, workd, 1) end if c 20 continue c if (bmat .eq. 'G') then call arscnd (t3) tmvbx = tmvbx + (t3 - t2) end if c first = .FALSE. if (bmat .eq. 'G') then cnorm = zdotc (n, resid, 1, workd, 1) rnorm0 = sqrt(dlapy2(dble(cnorm),dimag(cnorm))) else if (bmat .eq. 'I') then rnorm0 = dznrm2(n, resid, 1) end if rnorm = rnorm0 c c %---------------------------------------------% c | Exit if this is the very first Arnoldi step | c %---------------------------------------------% c if (j .eq. 1) go to 50 c c %---------------------------------------------------------------- c | Otherwise need to B-orthogonalize the starting vector against | c | the current Arnoldi basis using Gram-Schmidt with iter. ref. | c | This is the case where an invariant subspace is encountered | c | in the middle of the Arnoldi factorization. | c | | c | s = V^{T}*B*r; r = r - V*s; | c | | c | Stopping criteria used for iter. ref. is discussed in | c | Parlett's book, page 107 and in Gragg & Reichel TOMS paper. | c %---------------------------------------------------------------% c orth = .TRUE. 30 continue c call zgemv ('C', n, j-1, one, v, ldv, workd, 1, & zero, workd(n+1), 1) call zgemv ('N', n, j-1, -one, v, ldv, workd(n+1), 1, & one, resid, 1) c c %----------------------------------------------------------% c | Compute the B-norm of the orthogonalized starting vector | c %----------------------------------------------------------% c call arscnd (t2) if (bmat .eq. 'G') then nbx = nbx + 1 call zcopy (n, resid, 1, workd(n+1), 1) ipntr(1) = n + 1 ipntr(2) = 1 ido = 2 go to 9000 else if (bmat .eq. 'I') then call zcopy (n, resid, 1, workd, 1) end if c 40 continue c if (bmat .eq. 'G') then call arscnd (t3) tmvbx = tmvbx + (t3 - t2) end if c if (bmat .eq. 'G') then cnorm = zdotc (n, resid, 1, workd, 1) rnorm = sqrt(dlapy2(dble(cnorm),dimag(cnorm))) else if (bmat .eq. 'I') then rnorm = dznrm2(n, resid, 1) end if c c %--------------------------------------% c | Check for further orthogonalization. | c %--------------------------------------% c if (msglvl .gt. 2) then call dvout (logfil, 1, rnorm0, ndigit, & '_getv0: re-orthonalization ; rnorm0 is') call dvout (logfil, 1, rnorm, ndigit, & '_getv0: re-orthonalization ; rnorm is') end if c if (rnorm .gt. 0.717*rnorm0) go to 50 c iter = iter + 1 if (iter .le. 1) then c c %-----------------------------------% c | Perform iterative refinement step | c %-----------------------------------% c rnorm0 = rnorm go to 30 else c c %------------------------------------% c | Iterative refinement step "failed" | c %------------------------------------% c do 45 jj = 1, n resid(jj) = zero 45 continue rnorm = rzero ierr = -1 end if c 50 continue c if (msglvl .gt. 0) then call dvout (logfil, 1, rnorm, ndigit, & '_getv0: B-norm of initial / restarted starting vector') end if if (msglvl .gt. 2) then call zvout (logfil, n, resid, ndigit, & '_getv0: initial / restarted starting vector') end if ido = 99 c call arscnd (t1) tgetv0 = tgetv0 + (t1 - t0) c 9000 continue return c c %---------------% c | End of zgetv0 | c %---------------% c end arpack-0.92.1/SRC/zsortc.f0000644000175000017500000001766010776001577012133 00000000000000c\BeginDoc c c\Name: zsortc c c\Description: c Sorts the Complex*16 array in X into the order c specified by WHICH and optionally applies the permutation to the c Double precision array Y. c c\Usage: c call zsortc c ( WHICH, APPLY, N, X, Y ) c c\Arguments c WHICH Character*2. (Input) c 'LM' -> sort X into increasing order of magnitude. c 'SM' -> sort X into decreasing order of magnitude. c 'LR' -> sort X with real(X) in increasing algebraic order c 'SR' -> sort X with real(X) in decreasing algebraic order c 'LI' -> sort X with imag(X) in increasing algebraic order c 'SI' -> sort X with imag(X) in decreasing algebraic order c c APPLY Logical. (Input) c APPLY = .TRUE. -> apply the sorted order to array Y. c APPLY = .FALSE. -> do not apply the sorted order to array Y. c c N Integer. (INPUT) c Size of the arrays. c c X Complex*16 array of length N. (INPUT/OUTPUT) c This is the array to be sorted. c c Y Complex*16 array of length N. (INPUT/OUTPUT) c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Routines called: c dlapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c Adapted from the sort routine in LANSO. c c\SCCS Information: @(#) c FILE: sortc.F SID: 2.2 DATE OF SID: 4/20/96 RELEASE: 2 c c\EndLib c c----------------------------------------------------------------------- c subroutine zsortc (which, apply, n, x, y) c c %------------------% c | Scalar Arguments | c %------------------% c character*2 which logical apply integer n c c %-----------------% c | Array Arguments | c %-----------------% c Complex*16 & x(0:n-1), y(0:n-1) c c %---------------% c | Local Scalars | c %---------------% c integer i, igap, j Complex*16 & temp Double precision & temp1, temp2 c c %--------------------% c | External functions | c %--------------------% c Double precision & dlapy2 c c %--------------------% c | Intrinsic Functions | c %--------------------% Intrinsic & dble, dimag c c %-----------------------% c | Executable Statements | c %-----------------------% c igap = n / 2 c if (which .eq. 'LM') then c c %--------------------------------------------% c | Sort X into increasing order of magnitude. | c %--------------------------------------------% c 10 continue if (igap .eq. 0) go to 9000 c do 30 i = igap, n-1 j = i-igap 20 continue c if (j.lt.0) go to 30 c temp1 = dlapy2(dble(x(j)),dimag(x(j))) temp2 = dlapy2(dble(x(j+igap)),dimag(x(j+igap))) c if (temp1.gt.temp2) then temp = x(j) x(j) = x(j+igap) x(j+igap) = temp c if (apply) then temp = y(j) y(j) = y(j+igap) y(j+igap) = temp end if else go to 30 end if j = j-igap go to 20 30 continue igap = igap / 2 go to 10 c else if (which .eq. 'SM') then c c %--------------------------------------------% c | Sort X into decreasing order of magnitude. | c %--------------------------------------------% c 40 continue if (igap .eq. 0) go to 9000 c do 60 i = igap, n-1 j = i-igap 50 continue c if (j .lt. 0) go to 60 c temp1 = dlapy2(dble(x(j)),dimag(x(j))) temp2 = dlapy2(dble(x(j+igap)),dimag(x(j+igap))) c if (temp1.lt.temp2) then temp = x(j) x(j) = x(j+igap) x(j+igap) = temp c if (apply) then temp = y(j) y(j) = y(j+igap) y(j+igap) = temp end if else go to 60 endif j = j-igap go to 50 60 continue igap = igap / 2 go to 40 c else if (which .eq. 'LR') then c c %------------------------------------------------% c | Sort XREAL into increasing order of algebraic. | c %------------------------------------------------% c 70 continue if (igap .eq. 0) go to 9000 c do 90 i = igap, n-1 j = i-igap 80 continue c if (j.lt.0) go to 90 c if (dble(x(j)).gt.dble(x(j+igap))) then temp = x(j) x(j) = x(j+igap) x(j+igap) = temp c if (apply) then temp = y(j) y(j) = y(j+igap) y(j+igap) = temp end if else go to 90 endif j = j-igap go to 80 90 continue igap = igap / 2 go to 70 c else if (which .eq. 'SR') then c c %------------------------------------------------% c | Sort XREAL into decreasing order of algebraic. | c %------------------------------------------------% c 100 continue if (igap .eq. 0) go to 9000 do 120 i = igap, n-1 j = i-igap 110 continue c if (j.lt.0) go to 120 c if (dble(x(j)).lt.dble(x(j+igap))) then temp = x(j) x(j) = x(j+igap) x(j+igap) = temp c if (apply) then temp = y(j) y(j) = y(j+igap) y(j+igap) = temp end if else go to 120 endif j = j-igap go to 110 120 continue igap = igap / 2 go to 100 c else if (which .eq. 'LI') then c c %--------------------------------------------% c | Sort XIMAG into increasing algebraic order | c %--------------------------------------------% c 130 continue if (igap .eq. 0) go to 9000 do 150 i = igap, n-1 j = i-igap 140 continue c if (j.lt.0) go to 150 c if (dimag(x(j)).gt.dimag(x(j+igap))) then temp = x(j) x(j) = x(j+igap) x(j+igap) = temp c if (apply) then temp = y(j) y(j) = y(j+igap) y(j+igap) = temp end if else go to 150 endif j = j-igap go to 140 150 continue igap = igap / 2 go to 130 c else if (which .eq. 'SI') then c c %---------------------------------------------% c | Sort XIMAG into decreasing algebraic order | c %---------------------------------------------% c 160 continue if (igap .eq. 0) go to 9000 do 180 i = igap, n-1 j = i-igap 170 continue c if (j.lt.0) go to 180 c if (dimag(x(j)).lt.dimag(x(j+igap))) then temp = x(j) x(j) = x(j+igap) x(j+igap) = temp c if (apply) then temp = y(j) y(j) = y(j+igap) y(j+igap) = temp end if else go to 180 endif j = j-igap go to 170 180 continue igap = igap / 2 go to 160 end if c 9000 continue return c c %---------------% c | End of zsortc | c %---------------% c end arpack-0.92.1/SRC/sseupd.f0000644000175000017500000010314311453435054012074 00000000000000c\BeginDoc c c\Name: sseupd c c\Description: c c This subroutine returns the converged approximations to eigenvalues c of A*z = lambda*B*z and (optionally): c c (1) the corresponding approximate eigenvectors, c c (2) an orthonormal (Lanczos) basis for the associated approximate c invariant subspace, c c (3) Both. c c There is negligible additional cost to obtain eigenvectors. An orthonormal c (Lanczos) basis is always computed. There is an additional storage cost c of n*nev if both are requested (in this case a separate array Z must be c supplied). c c These quantities are obtained from the Lanczos factorization computed c by SSAUPD for the linear operator OP prescribed by the MODE selection c (see IPARAM(7) in SSAUPD documentation.) SSAUPD must be called before c this routine is called. These approximate eigenvalues and vectors are c commonly called Ritz values and Ritz vectors respectively. They are c referred to as such in the comments that follow. The computed orthonormal c basis for the invariant subspace corresponding to these Ritz values is c referred to as a Lanczos basis. c c See documentation in the header of the subroutine SSAUPD for a definition c of OP as well as other terms and the relation of computed Ritz values c and vectors of OP with respect to the given problem A*z = lambda*B*z. c c The approximate eigenvalues of the original problem are returned in c ascending algebraic order. The user may elect to call this routine c once for each desired Ritz vector and store it peripherally if desired. c There is also the option of computing a selected set of these vectors c with a single call. c c\Usage: c call sseupd c ( RVEC, HOWMNY, SELECT, D, Z, LDZ, SIGMA, BMAT, N, WHICH, NEV, TOL, c RESID, NCV, V, LDV, IPARAM, IPNTR, WORKD, WORKL, LWORKL, INFO ) c c RVEC LOGICAL (INPUT) c Specifies whether Ritz vectors corresponding to the Ritz value c approximations to the eigenproblem A*z = lambda*B*z are computed. c c RVEC = .FALSE. Compute Ritz values only. c c RVEC = .TRUE. Compute Ritz vectors. c c HOWMNY Character*1 (INPUT) c Specifies how many Ritz vectors are wanted and the form of Z c the matrix of Ritz vectors. See remark 1 below. c = 'A': compute NEV Ritz vectors; c = 'S': compute some of the Ritz vectors, specified c by the logical array SELECT. c c SELECT Logical array of dimension NCV. (INPUT/WORKSPACE) c If HOWMNY = 'S', SELECT specifies the Ritz vectors to be c computed. To select the Ritz vector corresponding to a c Ritz value D(j), SELECT(j) must be set to .TRUE.. c If HOWMNY = 'A' , SELECT is used as a workspace for c reordering the Ritz values. c c D Real array of dimension NEV. (OUTPUT) c On exit, D contains the Ritz value approximations to the c eigenvalues of A*z = lambda*B*z. The values are returned c in ascending order. If IPARAM(7) = 3,4,5 then D represents c the Ritz values of OP computed by ssaupd transformed to c those of the original eigensystem A*z = lambda*B*z. If c IPARAM(7) = 1,2 then the Ritz values of OP are the same c as the those of A*z = lambda*B*z. c c Z Real N by NEV array if HOWMNY = 'A'. (OUTPUT) c On exit, Z contains the B-orthonormal Ritz vectors of the c eigensystem A*z = lambda*B*z corresponding to the Ritz c value approximations. c If RVEC = .FALSE. then Z is not referenced. c NOTE: The array Z may be set equal to first NEV columns of the c Arnoldi/Lanczos basis array V computed by SSAUPD. c c LDZ Integer. (INPUT) c The leading dimension of the array Z. If Ritz vectors are c desired, then LDZ .ge. max( 1, N ). In any case, LDZ .ge. 1. c c SIGMA Real (INPUT) c If IPARAM(7) = 3,4,5 represents the shift. Not referenced if c IPARAM(7) = 1 or 2. c c c **** The remaining arguments MUST be the same as for the **** c **** call to SSAUPD that was just completed. **** c c NOTE: The remaining arguments c c BMAT, N, WHICH, NEV, TOL, RESID, NCV, V, LDV, IPARAM, IPNTR, c WORKD, WORKL, LWORKL, INFO c c must be passed directly to SSEUPD following the last call c to SSAUPD. These arguments MUST NOT BE MODIFIED between c the the last call to SSAUPD and the call to SSEUPD. c c Two of these parameters (WORKL, INFO) are also output parameters: c c WORKL Real work array of length LWORKL. (OUTPUT/WORKSPACE) c WORKL(1:4*ncv) contains information obtained in c ssaupd. They are not changed by sseupd. c WORKL(4*ncv+1:ncv*ncv+8*ncv) holds the c untransformed Ritz values, the computed error estimates, c and the associated eigenvector matrix of H. c c Note: IPNTR(8:10) contains the pointer into WORKL for addresses c of the above information computed by sseupd. c ------------------------------------------------------------- c IPNTR(8): pointer to the NCV RITZ values of the original system. c IPNTR(9): pointer to the NCV corresponding error bounds. c IPNTR(10): pointer to the NCV by NCV matrix of eigenvectors c of the tridiagonal matrix T. Only referenced by c sseupd if RVEC = .TRUE. See Remarks. c ------------------------------------------------------------- c c INFO Integer. (OUTPUT) c Error flag on output. c = 0: Normal exit. c = -1: N must be positive. c = -2: NEV must be positive. c = -3: NCV must be greater than NEV and less than or equal to N. c = -5: WHICH must be one of 'LM', 'SM', 'LA', 'SA' or 'BE'. c = -6: BMAT must be one of 'I' or 'G'. c = -7: Length of private work WORKL array is not sufficient. c = -8: Error return from trid. eigenvalue calculation; c Information error from LAPACK routine ssteqr. c = -9: Starting vector is zero. c = -10: IPARAM(7) must be 1,2,3,4,5. c = -11: IPARAM(7) = 1 and BMAT = 'G' are incompatible. c = -12: NEV and WHICH = 'BE' are incompatible. c = -14: SSAUPD did not find any eigenvalues to sufficient c accuracy. c = -15: HOWMNY must be one of 'A' or 'S' if RVEC = .true. c = -16: HOWMNY = 'S' not yet implemented c = -17: SSEUPD got a different count of the number of converged c Ritz values than SSAUPD got. This indicates the user c probably made an error in passing data from SSAUPD to c SSEUPD or that the data was modified before entering c SSEUPD. c c\BeginLib c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly c Restarted Arnoldi Iteration", Rice University Technical Report c TR95-13, Department of Computational and Applied Mathematics. c 3. B.N. Parlett, "The Symmetric Eigenvalue Problem". Prentice-Hall, c 1980. c 4. B.N. Parlett, B. Nour-Omid, "Towards a Black Box Lanczos Program", c Computer Physics Communications, 53 (1989), pp 169-179. c 5. B. Nour-Omid, B.N. Parlett, T. Ericson, P.S. Jensen, "How to c Implement the Spectral Transformation", Math. Comp., 48 (1987), c pp 663-673. c 6. R.G. Grimes, J.G. Lewis and H.D. Simon, "A Shifted Block Lanczos c Algorithm for Solving Sparse Symmetric Generalized Eigenproblems", c SIAM J. Matr. Anal. Apps., January (1993). c 7. L. Reichel, W.B. Gragg, "Algorithm 686: FORTRAN Subroutines c for Updating the QR decomposition", ACM TOMS, December 1990, c Volume 16 Number 4, pp 369-377. c c\Remarks c 1. The converged Ritz values are always returned in increasing c (algebraic) order. c c 2. Currently only HOWMNY = 'A' is implemented. It is included at this c stage for the user who wants to incorporate it. c c\Routines called: c ssesrt ARPACK routine that sorts an array X, and applies the c corresponding permutation to a matrix A. c ssortr ssortr ARPACK sorting routine. c ivout ARPACK utility routine that prints integers. c svout ARPACK utility routine that prints vectors. c sgeqr2 LAPACK routine that computes the QR factorization of c a matrix. c slacpy LAPACK matrix copy routine. c slamch LAPACK routine that determines machine constants. c sorm2r LAPACK routine that applies an orthogonal matrix in c factored form. c ssteqr LAPACK routine that computes eigenvalues and eigenvectors c of a tridiagonal matrix. c sger Level 2 BLAS rank one update to a matrix. c scopy Level 1 BLAS that copies one vector to another . c snrm2 Level 1 BLAS that computes the norm of a vector. c sscal Level 1 BLAS that scales a vector. c sswap Level 1 BLAS that swaps the contents of two vectors. c\Authors c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Chao Yang Houston, Texas c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c 12/15/93: Version ' 2.1' c c\SCCS Information: @(#) c FILE: seupd.F SID: 2.11 DATE OF SID: 04/10/01 RELEASE: 2 c c\EndLib c c----------------------------------------------------------------------- subroutine sseupd(rvec , howmny, select, d , & z , ldz , sigma , bmat , & n , which , nev , tol , & resid , ncv , v , ldv , & iparam, ipntr , workd , workl, & lworkl, info ) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character bmat, howmny, which*2 logical rvec integer info, ldz, ldv, lworkl, n, ncv, nev Real & sigma, tol c c %-----------------% c | Array Arguments | c %-----------------% c integer iparam(7), ipntr(11) logical select(ncv) Real & d(nev) , resid(n) , v(ldv,ncv), & z(ldz, nev), workd(2*n), workl(lworkl) c c %------------% c | Parameters | c %------------% c Real & one, zero parameter (one = 1.0E+0 , zero = 0.0E+0 ) c c %---------------% c | Local Scalars | c %---------------% c character type*6 integer bounds , ierr , ih , ihb , ihd , & iq , iw , j , k , ldh , & ldq , mode , msglvl, nconv , next , & ritz , irz , ibd , np , ishift, & leftptr, rghtptr, numcnv, jj Real & bnorm2 , rnorm, temp, temp1, eps23 logical reord c c %----------------------% c | External Subroutines | c %----------------------% c external scopy , sger , sgeqr2, slacpy, sorm2r, sscal, & ssesrt, ssteqr, sswap , svout , ivout , ssortr c c %--------------------% c | External Functions | c %--------------------% c Real & snrm2, slamch external snrm2, slamch c c %---------------------% c | Intrinsic Functions | c %---------------------% c intrinsic min c c %-----------------------% c | Executable Statements | c %-----------------------% c c %------------------------% c | Set default parameters | c %------------------------% c msglvl = mseupd mode = iparam(7) nconv = iparam(5) info = 0 c c %--------------% c | Quick return | c %--------------% c if (nconv .eq. 0) go to 9000 ierr = 0 c if (nconv .le. 0) ierr = -14 if (n .le. 0) ierr = -1 if (nev .le. 0) ierr = -2 if (ncv .le. nev .or. ncv .gt. n) ierr = -3 if (which .ne. 'LM' .and. & which .ne. 'SM' .and. & which .ne. 'LA' .and. & which .ne. 'SA' .and. & which .ne. 'BE') ierr = -5 if (bmat .ne. 'I' .and. bmat .ne. 'G') ierr = -6 if ( (howmny .ne. 'A' .and. & howmny .ne. 'P' .and. & howmny .ne. 'S') .and. rvec ) & ierr = -15 if (rvec .and. howmny .eq. 'S') ierr = -16 c if (rvec .and. lworkl .lt. ncv**2+8*ncv) ierr = -7 c if (mode .eq. 1 .or. mode .eq. 2) then type = 'REGULR' else if (mode .eq. 3 ) then type = 'SHIFTI' else if (mode .eq. 4 ) then type = 'BUCKLE' else if (mode .eq. 5 ) then type = 'CAYLEY' else ierr = -10 end if if (mode .eq. 1 .and. bmat .eq. 'G') ierr = -11 if (nev .eq. 1 .and. which .eq. 'BE') ierr = -12 c c %------------% c | Error Exit | c %------------% c if (ierr .ne. 0) then info = ierr go to 9000 end if c c %-------------------------------------------------------% c | Pointer into WORKL for address of H, RITZ, BOUNDS, Q | c | etc... and the remaining workspace. | c | Also update pointer to be used on output. | c | Memory is laid out as follows: | c | workl(1:2*ncv) := generated tridiagonal matrix H | c | The subdiagonal is stored in workl(2:ncv). | c | The dead spot is workl(1) but upon exiting | c | ssaupd stores the B-norm of the last residual | c | vector in workl(1). We use this !!! | c | workl(2*ncv+1:2*ncv+ncv) := ritz values | c | The wanted values are in the first NCONV spots. | c | workl(3*ncv+1:3*ncv+ncv) := computed Ritz estimates | c | The wanted values are in the first NCONV spots. | c | NOTE: workl(1:4*ncv) is set by ssaupd and is not | c | modified by sseupd. | c %-------------------------------------------------------% c c %-------------------------------------------------------% c | The following is used and set by sseupd. | c | workl(4*ncv+1:4*ncv+ncv) := used as workspace during | c | computation of the eigenvectors of H. Stores | c | the diagonal of H. Upon EXIT contains the NCV | c | Ritz values of the original system. The first | c | NCONV spots have the wanted values. If MODE = | c | 1 or 2 then will equal workl(2*ncv+1:3*ncv). | c | workl(5*ncv+1:5*ncv+ncv) := used as workspace during | c | computation of the eigenvectors of H. Stores | c | the subdiagonal of H. Upon EXIT contains the | c | NCV corresponding Ritz estimates of the | c | original system. The first NCONV spots have the | c | wanted values. If MODE = 1,2 then will equal | c | workl(3*ncv+1:4*ncv). | c | workl(6*ncv+1:6*ncv+ncv*ncv) := orthogonal Q that is | c | the eigenvector matrix for H as returned by | c | ssteqr. Not referenced if RVEC = .False. | c | Ordering follows that of workl(4*ncv+1:5*ncv) | c | workl(6*ncv+ncv*ncv+1:6*ncv+ncv*ncv+2*ncv) := | c | Workspace. Needed by ssteqr and by sseupd. | c | GRAND total of NCV*(NCV+8) locations. | c %-------------------------------------------------------% c c ih = ipntr(5) ritz = ipntr(6) bounds = ipntr(7) ldh = ncv ldq = ncv ihd = bounds + ldh ihb = ihd + ldh iq = ihb + ldh iw = iq + ldh*ncv next = iw + 2*ncv ipntr(4) = next ipntr(8) = ihd ipntr(9) = ihb ipntr(10) = iq c c %----------------------------------------% c | irz points to the Ritz values computed | c | by _seigt before exiting _saup2. | c | ibd points to the Ritz estimates | c | computed by _seigt before exiting | c | _saup2. | c %----------------------------------------% c irz = ipntr(11)+ncv ibd = irz+ncv c c c %---------------------------------% c | Set machine dependent constant. | c %---------------------------------% c eps23 = slamch('Epsilon-Machine') eps23 = eps23**(2.0E+0 / 3.0E+0 ) c c %---------------------------------------% c | RNORM is B-norm of the RESID(1:N). | c | BNORM2 is the 2 norm of B*RESID(1:N). | c | Upon exit of ssaupd WORKD(1:N) has | c | B*RESID(1:N). | c %---------------------------------------% c rnorm = workl(ih) if (bmat .eq. 'I') then bnorm2 = rnorm else if (bmat .eq. 'G') then bnorm2 = snrm2(n, workd, 1) end if c if (msglvl .gt. 2) then call svout(logfil, ncv, workl(irz), ndigit, & '_seupd: Ritz values passed in from _SAUPD.') call svout(logfil, ncv, workl(ibd), ndigit, & '_seupd: Ritz estimates passed in from _SAUPD.') end if c if (rvec) then c reord = .false. c c %---------------------------------------------------% c | Use the temporary bounds array to store indices | c | These will be used to mark the select array later | c %---------------------------------------------------% c do 10 j = 1,ncv workl(bounds+j-1) = j select(j) = .false. 10 continue c c %-------------------------------------% c | Select the wanted Ritz values. | c | Sort the Ritz values so that the | c | wanted ones appear at the tailing | c | NEV positions of workl(irr) and | c | workl(iri). Move the corresponding | c | error estimates in workl(bound) | c | accordingly. | c %-------------------------------------% c np = ncv - nev ishift = 0 call ssgets(ishift, which , nev , & np , workl(irz) , workl(bounds), & workl) c if (msglvl .gt. 2) then call svout(logfil, ncv, workl(irz), ndigit, & '_seupd: Ritz values after calling _SGETS.') call svout(logfil, ncv, workl(bounds), ndigit, & '_seupd: Ritz value indices after calling _SGETS.') end if c c %-----------------------------------------------------% c | Record indices of the converged wanted Ritz values | c | Mark the select array for possible reordering | c %-----------------------------------------------------% c numcnv = 0 do 11 j = 1,ncv temp1 = max(eps23, abs(workl(irz+ncv-j)) ) jj = workl(bounds + ncv - j) if (numcnv .lt. nconv .and. & workl(ibd+jj-1) .le. tol*temp1) then select(jj) = .true. numcnv = numcnv + 1 if (jj .gt. nev) reord = .true. endif 11 continue c c %-----------------------------------------------------------% c | Check the count (numcnv) of converged Ritz values with | c | the number (nconv) reported by _saupd. If these two | c | are different then there has probably been an error | c | caused by incorrect passing of the _saupd data. | c %-----------------------------------------------------------% c if (msglvl .gt. 2) then call ivout(logfil, 1, numcnv, ndigit, & '_seupd: Number of specified eigenvalues') call ivout(logfil, 1, nconv, ndigit, & '_seupd: Number of "converged" eigenvalues') end if c if (numcnv .ne. nconv) then info = -17 go to 9000 end if c c %-----------------------------------------------------------% c | Call LAPACK routine _steqr to compute the eigenvalues and | c | eigenvectors of the final symmetric tridiagonal matrix H. | c | Initialize the eigenvector matrix Q to the identity. | c %-----------------------------------------------------------% c call scopy(ncv-1, workl(ih+1), 1, workl(ihb), 1) call scopy(ncv, workl(ih+ldh), 1, workl(ihd), 1) c call ssteqr('Identity', ncv, workl(ihd), workl(ihb), & workl(iq) , ldq, workl(iw), ierr) c if (ierr .ne. 0) then info = -8 go to 9000 end if c if (msglvl .gt. 1) then call scopy(ncv, workl(iq+ncv-1), ldq, workl(iw), 1) call svout(logfil, ncv, workl(ihd), ndigit, & '_seupd: NCV Ritz values of the final H matrix') call svout(logfil, ncv, workl(iw), ndigit, & '_seupd: last row of the eigenvector matrix for H') end if c if (reord) then c c %---------------------------------------------% c | Reordered the eigenvalues and eigenvectors | c | computed by _steqr so that the "converged" | c | eigenvalues appear in the first NCONV | c | positions of workl(ihd), and the associated | c | eigenvectors appear in the first NCONV | c | columns. | c %---------------------------------------------% c leftptr = 1 rghtptr = ncv c if (.not. (ncv .eq. 1)) then c 20 if (select(leftptr)) then c c %-------------------------------------------% c | Search, from the left, for the first Ritz | c | value that has not converged. | c %-------------------------------------------% c leftptr = leftptr + 1 c else if ( .not. select(rghtptr)) then c c %----------------------------------------------% c | Search, from the right, the first Ritz value | c | that has converged. | c %----------------------------------------------% c rghtptr = rghtptr - 1 c else c c %----------------------------------------------% c | Swap the Ritz value on the left that has not | c | converged with the Ritz value on the right | c | that has converged. Swap the associated | c | eigenvector of the tridiagonal matrix H as | c | well. | c %----------------------------------------------% c temp = workl(ihd+leftptr-1) workl(ihd+leftptr-1) = workl(ihd+rghtptr-1) workl(ihd+rghtptr-1) = temp call scopy(ncv, workl(iq+ncv*(leftptr-1)), 1, & workl(iw), 1) call scopy(ncv, workl(iq+ncv*(rghtptr-1)), 1, & workl(iq+ncv*(leftptr-1)), 1) call scopy(ncv, workl(iw), 1, & workl(iq+ncv*(rghtptr-1)), 1) leftptr = leftptr + 1 rghtptr = rghtptr - 1 c end if c if (leftptr .lt. rghtptr) go to 20 c end if end if c if (msglvl .gt. 2) then call svout (logfil, ncv, workl(ihd), ndigit, & '_seupd: The eigenvalues of H--reordered') end if c c %----------------------------------------% c | Load the converged Ritz values into D. | c %----------------------------------------% c call scopy(nconv, workl(ihd), 1, d, 1) c else c c %-----------------------------------------------------% c | Ritz vectors not required. Load Ritz values into D. | c %-----------------------------------------------------% c call scopy(nconv, workl(ritz), 1, d, 1) call scopy(ncv, workl(ritz), 1, workl(ihd), 1) c end if c c %------------------------------------------------------------------% c | Transform the Ritz values and possibly vectors and corresponding | c | Ritz estimates of OP to those of A*x=lambda*B*x. The Ritz values | c | (and corresponding data) are returned in ascending order. | c %------------------------------------------------------------------% c if (type .eq. 'REGULR') then c c %---------------------------------------------------------% c | Ascending sort of wanted Ritz values, vectors and error | c | bounds. Not necessary if only Ritz values are desired. | c %---------------------------------------------------------% c if (rvec) then call ssesrt('LA', rvec , nconv, d, ncv, workl(iq), ldq) else call scopy(ncv, workl(bounds), 1, workl(ihb), 1) end if c else c c %-------------------------------------------------------------% c | * Make a copy of all the Ritz values. | c | * Transform the Ritz values back to the original system. | c | For TYPE = 'SHIFTI' the transformation is | c | lambda = 1/theta + sigma | c | For TYPE = 'BUCKLE' the transformation is | c | lambda = sigma * theta / ( theta - 1 ) | c | For TYPE = 'CAYLEY' the transformation is | c | lambda = sigma * (theta + 1) / (theta - 1 ) | c | where the theta are the Ritz values returned by ssaupd. | c | NOTES: | c | *The Ritz vectors are not affected by the transformation. | c | They are only reordered. | c %-------------------------------------------------------------% c call scopy (ncv, workl(ihd), 1, workl(iw), 1) if (type .eq. 'SHIFTI') then do 40 k=1, ncv workl(ihd+k-1) = one / workl(ihd+k-1) + sigma 40 continue else if (type .eq. 'BUCKLE') then do 50 k=1, ncv workl(ihd+k-1) = sigma * workl(ihd+k-1) / & (workl(ihd+k-1) - one) 50 continue else if (type .eq. 'CAYLEY') then do 60 k=1, ncv workl(ihd+k-1) = sigma * (workl(ihd+k-1) + one) / & (workl(ihd+k-1) - one) 60 continue end if c c %-------------------------------------------------------------% c | * Store the wanted NCONV lambda values into D. | c | * Sort the NCONV wanted lambda in WORKL(IHD:IHD+NCONV-1) | c | into ascending order and apply sort to the NCONV theta | c | values in the transformed system. We will need this to | c | compute Ritz estimates in the original system. | c | * Finally sort the lambda`s into ascending order and apply | c | to Ritz vectors if wanted. Else just sort lambda`s into | c | ascending order. | c | NOTES: | c | *workl(iw:iw+ncv-1) contain the theta ordered so that they | c | match the ordering of the lambda. We`ll use them again for | c | Ritz vector purification. | c %-------------------------------------------------------------% c call scopy(nconv, workl(ihd), 1, d, 1) call ssortr('LA', .true., nconv, workl(ihd), workl(iw)) if (rvec) then call ssesrt('LA', rvec , nconv, d, ncv, workl(iq), ldq) else call scopy(ncv, workl(bounds), 1, workl(ihb), 1) call sscal(ncv, bnorm2/rnorm, workl(ihb), 1) call ssortr('LA', .true., nconv, d, workl(ihb)) end if c end if c c %------------------------------------------------% c | Compute the Ritz vectors. Transform the wanted | c | eigenvectors of the symmetric tridiagonal H by | c | the Lanczos basis matrix V. | c %------------------------------------------------% c if (rvec .and. howmny .eq. 'A') then c c %----------------------------------------------------------% c | Compute the QR factorization of the matrix representing | c | the wanted invariant subspace located in the first NCONV | c | columns of workl(iq,ldq). | c %----------------------------------------------------------% c call sgeqr2(ncv, nconv , workl(iq) , & ldq, workl(iw+ncv), workl(ihb), & ierr) c c %--------------------------------------------------------% c | * Postmultiply V by Q. | c | * Copy the first NCONV columns of VQ into Z. | c | The N by NCONV matrix Z is now a matrix representation | c | of the approximate invariant subspace associated with | c | the Ritz values in workl(ihd). | c %--------------------------------------------------------% c call sorm2r('Right', 'Notranspose', n , & ncv , nconv , workl(iq), & ldq , workl(iw+ncv), v , & ldv , workd(n+1) , ierr) call slacpy('All', n, nconv, v, ldv, z, ldz) c c %-----------------------------------------------------% c | In order to compute the Ritz estimates for the Ritz | c | values in both systems, need the last row of the | c | eigenvector matrix. Remember, it`s in factored form | c %-----------------------------------------------------% c do 65 j = 1, ncv-1 workl(ihb+j-1) = zero 65 continue workl(ihb+ncv-1) = one call sorm2r('Left', 'Transpose' , ncv , & 1 , nconv , workl(iq) , & ldq , workl(iw+ncv), workl(ihb), & ncv , temp , ierr) c else if (rvec .and. howmny .eq. 'S') then c c Not yet implemented. See remark 2 above. c end if c if (type .eq. 'REGULR' .and. rvec) then c do 70 j=1, ncv workl(ihb+j-1) = rnorm * abs( workl(ihb+j-1) ) 70 continue c else if (type .ne. 'REGULR' .and. rvec) then c c %-------------------------------------------------% c | * Determine Ritz estimates of the theta. | c | If RVEC = .true. then compute Ritz estimates | c | of the theta. | c | If RVEC = .false. then copy Ritz estimates | c | as computed by ssaupd. | c | * Determine Ritz estimates of the lambda. | c %-------------------------------------------------% c call sscal (ncv, bnorm2, workl(ihb), 1) if (type .eq. 'SHIFTI') then c do 80 k=1, ncv workl(ihb+k-1) = abs( workl(ihb+k-1) ) & / workl(iw+k-1)**2 80 continue c else if (type .eq. 'BUCKLE') then c do 90 k=1, ncv workl(ihb+k-1) = sigma * abs( workl(ihb+k-1) ) & / (workl(iw+k-1)-one )**2 90 continue c else if (type .eq. 'CAYLEY') then c do 100 k=1, ncv workl(ihb+k-1) = abs( workl(ihb+k-1) & / workl(iw+k-1)*(workl(iw+k-1)-one) ) 100 continue c end if c end if c if (type .ne. 'REGULR' .and. msglvl .gt. 1) then call svout(logfil, nconv, d, ndigit, & '_seupd: Untransformed converged Ritz values') call svout(logfil, nconv, workl(ihb), ndigit, & '_seupd: Ritz estimates of the untransformed Ritz values') else if (msglvl .gt. 1) then call svout(logfil, nconv, d, ndigit, & '_seupd: Converged Ritz values') call svout(logfil, nconv, workl(ihb), ndigit, & '_seupd: Associated Ritz estimates') end if c c %-------------------------------------------------% c | Ritz vector purification step. Formally perform | c | one of inverse subspace iteration. Only used | c | for MODE = 3,4,5. See reference 7 | c %-------------------------------------------------% c if (rvec .and. (type .eq. 'SHIFTI' .or. type .eq. 'CAYLEY')) then c do 110 k=0, nconv-1 workl(iw+k) = workl(iq+k*ldq+ncv-1) & / workl(iw+k) 110 continue c else if (rvec .and. type .eq. 'BUCKLE') then c do 120 k=0, nconv-1 workl(iw+k) = workl(iq+k*ldq+ncv-1) & / (workl(iw+k)-one) 120 continue c end if c if (type .ne. 'REGULR') & call sger (n, nconv, one, resid, 1, workl(iw), 1, z, ldz) c 9000 continue c return c c %---------------% c | End of sseupd| c %---------------% c end arpack-0.92.1/SRC/ssortr.f0000644000175000017500000001227410776001577012137 00000000000000c----------------------------------------------------------------------- c\BeginDoc c c\Name: ssortr c c\Description: c Sort the array X1 in the order specified by WHICH and optionally c applies the permutation to the array X2. c c\Usage: c call ssortr c ( WHICH, APPLY, N, X1, X2 ) c c\Arguments c WHICH Character*2. (Input) c 'LM' -> X1 is sorted into increasing order of magnitude. c 'SM' -> X1 is sorted into decreasing order of magnitude. c 'LA' -> X1 is sorted into increasing order of algebraic. c 'SA' -> X1 is sorted into decreasing order of algebraic. c c APPLY Logical. (Input) c APPLY = .TRUE. -> apply the sorted order to X2. c APPLY = .FALSE. -> do not apply the sorted order to X2. c c N Integer. (INPUT) c Size of the arrays. c c X1 Real array of length N. (INPUT/OUTPUT) c The array to be sorted. c c X2 Real array of length N. (INPUT/OUTPUT) c Only referenced if APPLY = .TRUE. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c 12/16/93: Version ' 2.1'. c Adapted from the sort routine in LANSO. c c\SCCS Information: @(#) c FILE: sortr.F SID: 2.3 DATE OF SID: 4/19/96 RELEASE: 2 c c\EndLib c c----------------------------------------------------------------------- c subroutine ssortr (which, apply, n, x1, x2) c c %------------------% c | Scalar Arguments | c %------------------% c character*2 which logical apply integer n c c %-----------------% c | Array Arguments | c %-----------------% c Real & x1(0:n-1), x2(0:n-1) c c %---------------% c | Local Scalars | c %---------------% c integer i, igap, j Real & temp c c %-----------------------% c | Executable Statements | c %-----------------------% c igap = n / 2 c if (which .eq. 'SA') then c c X1 is sorted into decreasing order of algebraic. c 10 continue if (igap .eq. 0) go to 9000 do 30 i = igap, n-1 j = i-igap 20 continue c if (j.lt.0) go to 30 c if (x1(j).lt.x1(j+igap)) then temp = x1(j) x1(j) = x1(j+igap) x1(j+igap) = temp if (apply) then temp = x2(j) x2(j) = x2(j+igap) x2(j+igap) = temp end if else go to 30 endif j = j-igap go to 20 30 continue igap = igap / 2 go to 10 c else if (which .eq. 'SM') then c c X1 is sorted into decreasing order of magnitude. c 40 continue if (igap .eq. 0) go to 9000 do 60 i = igap, n-1 j = i-igap 50 continue c if (j.lt.0) go to 60 c if (abs(x1(j)).lt.abs(x1(j+igap))) then temp = x1(j) x1(j) = x1(j+igap) x1(j+igap) = temp if (apply) then temp = x2(j) x2(j) = x2(j+igap) x2(j+igap) = temp end if else go to 60 endif j = j-igap go to 50 60 continue igap = igap / 2 go to 40 c else if (which .eq. 'LA') then c c X1 is sorted into increasing order of algebraic. c 70 continue if (igap .eq. 0) go to 9000 do 90 i = igap, n-1 j = i-igap 80 continue c if (j.lt.0) go to 90 c if (x1(j).gt.x1(j+igap)) then temp = x1(j) x1(j) = x1(j+igap) x1(j+igap) = temp if (apply) then temp = x2(j) x2(j) = x2(j+igap) x2(j+igap) = temp end if else go to 90 endif j = j-igap go to 80 90 continue igap = igap / 2 go to 70 c else if (which .eq. 'LM') then c c X1 is sorted into increasing order of magnitude. c 100 continue if (igap .eq. 0) go to 9000 do 120 i = igap, n-1 j = i-igap 110 continue c if (j.lt.0) go to 120 c if (abs(x1(j)).gt.abs(x1(j+igap))) then temp = x1(j) x1(j) = x1(j+igap) x1(j+igap) = temp if (apply) then temp = x2(j) x2(j) = x2(j+igap) x2(j+igap) = temp end if else go to 120 endif j = j-igap go to 110 120 continue igap = igap / 2 go to 100 end if c 9000 continue return c c %---------------% c | End of ssortr | c %---------------% c end arpack-0.92.1/SRC/dseupd.f0000644000175000017500000010347111453435054012061 00000000000000c\BeginDoc c c\Name: dseupd c c\Description: c c This subroutine returns the converged approximations to eigenvalues c of A*z = lambda*B*z and (optionally): c c (1) the corresponding approximate eigenvectors, c c (2) an orthonormal (Lanczos) basis for the associated approximate c invariant subspace, c c (3) Both. c c There is negligible additional cost to obtain eigenvectors. An orthonormal c (Lanczos) basis is always computed. There is an additional storage cost c of n*nev if both are requested (in this case a separate array Z must be c supplied). c c These quantities are obtained from the Lanczos factorization computed c by DSAUPD for the linear operator OP prescribed by the MODE selection c (see IPARAM(7) in DSAUPD documentation.) DSAUPD must be called before c this routine is called. These approximate eigenvalues and vectors are c commonly called Ritz values and Ritz vectors respectively. They are c referred to as such in the comments that follow. The computed orthonormal c basis for the invariant subspace corresponding to these Ritz values is c referred to as a Lanczos basis. c c See documentation in the header of the subroutine DSAUPD for a definition c of OP as well as other terms and the relation of computed Ritz values c and vectors of OP with respect to the given problem A*z = lambda*B*z. c c The approximate eigenvalues of the original problem are returned in c ascending algebraic order. The user may elect to call this routine c once for each desired Ritz vector and store it peripherally if desired. c There is also the option of computing a selected set of these vectors c with a single call. c c\Usage: c call dseupd c ( RVEC, HOWMNY, SELECT, D, Z, LDZ, SIGMA, BMAT, N, WHICH, NEV, TOL, c RESID, NCV, V, LDV, IPARAM, IPNTR, WORKD, WORKL, LWORKL, INFO ) c c RVEC LOGICAL (INPUT) c Specifies whether Ritz vectors corresponding to the Ritz value c approximations to the eigenproblem A*z = lambda*B*z are computed. c c RVEC = .FALSE. Compute Ritz values only. c c RVEC = .TRUE. Compute Ritz vectors. c c HOWMNY Character*1 (INPUT) c Specifies how many Ritz vectors are wanted and the form of Z c the matrix of Ritz vectors. See remark 1 below. c = 'A': compute NEV Ritz vectors; c = 'S': compute some of the Ritz vectors, specified c by the logical array SELECT. c c SELECT Logical array of dimension NCV. (INPUT/WORKSPACE) c If HOWMNY = 'S', SELECT specifies the Ritz vectors to be c computed. To select the Ritz vector corresponding to a c Ritz value D(j), SELECT(j) must be set to .TRUE.. c If HOWMNY = 'A' , SELECT is used as a workspace for c reordering the Ritz values. c c D Double precision array of dimension NEV. (OUTPUT) c On exit, D contains the Ritz value approximations to the c eigenvalues of A*z = lambda*B*z. The values are returned c in ascending order. If IPARAM(7) = 3,4,5 then D represents c the Ritz values of OP computed by dsaupd transformed to c those of the original eigensystem A*z = lambda*B*z. If c IPARAM(7) = 1,2 then the Ritz values of OP are the same c as the those of A*z = lambda*B*z. c c Z Double precision N by NEV array if HOWMNY = 'A'. (OUTPUT) c On exit, Z contains the B-orthonormal Ritz vectors of the c eigensystem A*z = lambda*B*z corresponding to the Ritz c value approximations. c If RVEC = .FALSE. then Z is not referenced. c NOTE: The array Z may be set equal to first NEV columns of the c Arnoldi/Lanczos basis array V computed by DSAUPD . c c LDZ Integer. (INPUT) c The leading dimension of the array Z. If Ritz vectors are c desired, then LDZ .ge. max( 1, N ). In any case, LDZ .ge. 1. c c SIGMA Double precision (INPUT) c If IPARAM(7) = 3,4,5 represents the shift. Not referenced if c IPARAM(7) = 1 or 2. c c c **** The remaining arguments MUST be the same as for the **** c **** call to DSAUPD that was just completed. **** c c NOTE: The remaining arguments c c BMAT, N, WHICH, NEV, TOL, RESID, NCV, V, LDV, IPARAM, IPNTR, c WORKD, WORKL, LWORKL, INFO c c must be passed directly to DSEUPD following the last call c to DSAUPD . These arguments MUST NOT BE MODIFIED between c the the last call to DSAUPD and the call to DSEUPD . c c Two of these parameters (WORKL, INFO) are also output parameters: c c WORKL Double precision work array of length LWORKL. (OUTPUT/WORKSPACE) c WORKL(1:4*ncv) contains information obtained in c dsaupd . They are not changed by dseupd . c WORKL(4*ncv+1:ncv*ncv+8*ncv) holds the c untransformed Ritz values, the computed error estimates, c and the associated eigenvector matrix of H. c c Note: IPNTR(8:10) contains the pointer into WORKL for addresses c of the above information computed by dseupd . c ------------------------------------------------------------- c IPNTR(8): pointer to the NCV RITZ values of the original system. c IPNTR(9): pointer to the NCV corresponding error bounds. c IPNTR(10): pointer to the NCV by NCV matrix of eigenvectors c of the tridiagonal matrix T. Only referenced by c dseupd if RVEC = .TRUE. See Remarks. c ------------------------------------------------------------- c c INFO Integer. (OUTPUT) c Error flag on output. c = 0: Normal exit. c = -1: N must be positive. c = -2: NEV must be positive. c = -3: NCV must be greater than NEV and less than or equal to N. c = -5: WHICH must be one of 'LM', 'SM', 'LA', 'SA' or 'BE'. c = -6: BMAT must be one of 'I' or 'G'. c = -7: Length of private work WORKL array is not sufficient. c = -8: Error return from trid. eigenvalue calculation; c Information error from LAPACK routine dsteqr . c = -9: Starting vector is zero. c = -10: IPARAM(7) must be 1,2,3,4,5. c = -11: IPARAM(7) = 1 and BMAT = 'G' are incompatible. c = -12: NEV and WHICH = 'BE' are incompatible. c = -14: DSAUPD did not find any eigenvalues to sufficient c accuracy. c = -15: HOWMNY must be one of 'A' or 'S' if RVEC = .true. c = -16: HOWMNY = 'S' not yet implemented c = -17: DSEUPD got a different count of the number of converged c Ritz values than DSAUPD got. This indicates the user c probably made an error in passing data from DSAUPD to c DSEUPD or that the data was modified before entering c DSEUPD . c c\BeginLib c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c 2. R.B. Lehoucq, "Analysis and Implementation of an Implicitly c Restarted Arnoldi Iteration", Rice University Technical Report c TR95-13, Department of Computational and Applied Mathematics. c 3. B.N. Parlett, "The Symmetric Eigenvalue Problem". Prentice-Hall, c 1980. c 4. B.N. Parlett, B. Nour-Omid, "Towards a Black Box Lanczos Program", c Computer Physics Communications, 53 (1989), pp 169-179. c 5. B. Nour-Omid, B.N. Parlett, T. Ericson, P.S. Jensen, "How to c Implement the Spectral Transformation", Math. Comp., 48 (1987), c pp 663-673. c 6. R.G. Grimes, J.G. Lewis and H.D. Simon, "A Shifted Block Lanczos c Algorithm for Solving Sparse Symmetric Generalized Eigenproblems", c SIAM J. Matr. Anal. Apps., January (1993). c 7. L. Reichel, W.B. Gragg, "Algorithm 686: FORTRAN Subroutines c for Updating the QR decomposition", ACM TOMS, December 1990, c Volume 16 Number 4, pp 369-377. c c\Remarks c 1. The converged Ritz values are always returned in increasing c (algebraic) order. c c 2. Currently only HOWMNY = 'A' is implemented. It is included at this c stage for the user who wants to incorporate it. c c\Routines called: c dsesrt ARPACK routine that sorts an array X, and applies the c corresponding permutation to a matrix A. c dsortr dsortr ARPACK sorting routine. c ivout ARPACK utility routine that prints integers. c dvout ARPACK utility routine that prints vectors. c dgeqr2 LAPACK routine that computes the QR factorization of c a matrix. c dlacpy LAPACK matrix copy routine. c dlamch LAPACK routine that determines machine constants. c dorm2r LAPACK routine that applies an orthogonal matrix in c factored form. c dsteqr LAPACK routine that computes eigenvalues and eigenvectors c of a tridiagonal matrix. c dger Level 2 BLAS rank one update to a matrix. c dcopy Level 1 BLAS that copies one vector to another . c dnrm2 Level 1 BLAS that computes the norm of a vector. c dscal Level 1 BLAS that scales a vector. c dswap Level 1 BLAS that swaps the contents of two vectors. c\Authors c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Chao Yang Houston, Texas c Dept. of Computational & c Applied Mathematics c Rice University c Houston, Texas c c\Revision history: c 12/15/93: Version ' 2.1' c c\SCCS Information: @(#) c FILE: seupd.F SID: 2.11 DATE OF SID: 04/10/01 RELEASE: 2 c c\EndLib c c----------------------------------------------------------------------- subroutine dseupd (rvec , howmny, select, d , & z , ldz , sigma , bmat , & n , which , nev , tol , & resid , ncv , v , ldv , & iparam, ipntr , workd , workl, & lworkl, info ) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c character bmat, howmny, which*2 logical rvec integer info, ldz, ldv, lworkl, n, ncv, nev Double precision & sigma, tol c c %-----------------% c | Array Arguments | c %-----------------% c integer iparam(7), ipntr(11) logical select(ncv) Double precision & d(nev) , resid(n) , v(ldv,ncv), & z(ldz, nev), workd(2*n), workl(lworkl) c c %------------% c | Parameters | c %------------% c Double precision & one, zero parameter (one = 1.0D+0 , zero = 0.0D+0 ) c c %---------------% c | Local Scalars | c %---------------% c character type*6 integer bounds , ierr , ih , ihb , ihd , & iq , iw , j , k , ldh , & ldq , mode , msglvl, nconv , next , & ritz , irz , ibd , np , ishift, & leftptr, rghtptr, numcnv, jj Double precision & bnorm2 , rnorm, temp, temp1, eps23 logical reord c c %----------------------% c | External Subroutines | c %----------------------% c external dcopy , dger , dgeqr2 , dlacpy , dorm2r , dscal , & dsesrt , dsteqr , dswap , dvout , ivout , dsortr c c %--------------------% c | External Functions | c %--------------------% c Double precision & dnrm2 , dlamch external dnrm2 , dlamch c c %---------------------% c | Intrinsic Functions | c %---------------------% c intrinsic min c c %-----------------------% c | Executable Statements | c %-----------------------% c c %------------------------% c | Set default parameters | c %------------------------% c msglvl = mseupd mode = iparam(7) nconv = iparam(5) info = 0 c c %--------------% c | Quick return | c %--------------% c if (nconv .eq. 0) go to 9000 ierr = 0 c if (nconv .le. 0) ierr = -14 if (n .le. 0) ierr = -1 if (nev .le. 0) ierr = -2 if (ncv .le. nev .or. ncv .gt. n) ierr = -3 if (which .ne. 'LM' .and. & which .ne. 'SM' .and. & which .ne. 'LA' .and. & which .ne. 'SA' .and. & which .ne. 'BE') ierr = -5 if (bmat .ne. 'I' .and. bmat .ne. 'G') ierr = -6 if ( (howmny .ne. 'A' .and. & howmny .ne. 'P' .and. & howmny .ne. 'S') .and. rvec ) & ierr = -15 if (rvec .and. howmny .eq. 'S') ierr = -16 c if (rvec .and. lworkl .lt. ncv**2+8*ncv) ierr = -7 c if (mode .eq. 1 .or. mode .eq. 2) then type = 'REGULR' else if (mode .eq. 3 ) then type = 'SHIFTI' else if (mode .eq. 4 ) then type = 'BUCKLE' else if (mode .eq. 5 ) then type = 'CAYLEY' else ierr = -10 end if if (mode .eq. 1 .and. bmat .eq. 'G') ierr = -11 if (nev .eq. 1 .and. which .eq. 'BE') ierr = -12 c c %------------% c | Error Exit | c %------------% c if (ierr .ne. 0) then info = ierr go to 9000 end if c c %-------------------------------------------------------% c | Pointer into WORKL for address of H, RITZ, BOUNDS, Q | c | etc... and the remaining workspace. | c | Also update pointer to be used on output. | c | Memory is laid out as follows: | c | workl(1:2*ncv) := generated tridiagonal matrix H | c | The subdiagonal is stored in workl(2:ncv). | c | The dead spot is workl(1) but upon exiting | c | dsaupd stores the B-norm of the last residual | c | vector in workl(1). We use this !!! | c | workl(2*ncv+1:2*ncv+ncv) := ritz values | c | The wanted values are in the first NCONV spots. | c | workl(3*ncv+1:3*ncv+ncv) := computed Ritz estimates | c | The wanted values are in the first NCONV spots. | c | NOTE: workl(1:4*ncv) is set by dsaupd and is not | c | modified by dseupd . | c %-------------------------------------------------------% c c %-------------------------------------------------------% c | The following is used and set by dseupd . | c | workl(4*ncv+1:4*ncv+ncv) := used as workspace during | c | computation of the eigenvectors of H. Stores | c | the diagonal of H. Upon EXIT contains the NCV | c | Ritz values of the original system. The first | c | NCONV spots have the wanted values. If MODE = | c | 1 or 2 then will equal workl(2*ncv+1:3*ncv). | c | workl(5*ncv+1:5*ncv+ncv) := used as workspace during | c | computation of the eigenvectors of H. Stores | c | the subdiagonal of H. Upon EXIT contains the | c | NCV corresponding Ritz estimates of the | c | original system. The first NCONV spots have the | c | wanted values. If MODE = 1,2 then will equal | c | workl(3*ncv+1:4*ncv). | c | workl(6*ncv+1:6*ncv+ncv*ncv) := orthogonal Q that is | c | the eigenvector matrix for H as returned by | c | dsteqr . Not referenced if RVEC = .False. | c | Ordering follows that of workl(4*ncv+1:5*ncv) | c | workl(6*ncv+ncv*ncv+1:6*ncv+ncv*ncv+2*ncv) := | c | Workspace. Needed by dsteqr and by dseupd . | c | GRAND total of NCV*(NCV+8) locations. | c %-------------------------------------------------------% c c ih = ipntr(5) ritz = ipntr(6) bounds = ipntr(7) ldh = ncv ldq = ncv ihd = bounds + ldh ihb = ihd + ldh iq = ihb + ldh iw = iq + ldh*ncv next = iw + 2*ncv ipntr(4) = next ipntr(8) = ihd ipntr(9) = ihb ipntr(10) = iq c c %----------------------------------------% c | irz points to the Ritz values computed | c | by _seigt before exiting _saup2. | c | ibd points to the Ritz estimates | c | computed by _seigt before exiting | c | _saup2. | c %----------------------------------------% c irz = ipntr(11)+ncv ibd = irz+ncv c c c %---------------------------------% c | Set machine dependent constant. | c %---------------------------------% c eps23 = dlamch ('Epsilon-Machine') eps23 = eps23**(2.0D+0 / 3.0D+0 ) c c %---------------------------------------% c | RNORM is B-norm of the RESID(1:N). | c | BNORM2 is the 2 norm of B*RESID(1:N). | c | Upon exit of dsaupd WORKD(1:N) has | c | B*RESID(1:N). | c %---------------------------------------% c rnorm = workl(ih) if (bmat .eq. 'I') then bnorm2 = rnorm else if (bmat .eq. 'G') then bnorm2 = dnrm2 (n, workd, 1) end if c if (msglvl .gt. 2) then call dvout (logfil, ncv, workl(irz), ndigit, & '_seupd: Ritz values passed in from _SAUPD.') call dvout (logfil, ncv, workl(ibd), ndigit, & '_seupd: Ritz estimates passed in from _SAUPD.') end if c if (rvec) then c reord = .false. c c %---------------------------------------------------% c | Use the temporary bounds array to store indices | c | These will be used to mark the select array later | c %---------------------------------------------------% c do 10 j = 1,ncv workl(bounds+j-1) = j select(j) = .false. 10 continue c c %-------------------------------------% c | Select the wanted Ritz values. | c | Sort the Ritz values so that the | c | wanted ones appear at the tailing | c | NEV positions of workl(irr) and | c | workl(iri). Move the corresponding | c | error estimates in workl(bound) | c | accordingly. | c %-------------------------------------% c np = ncv - nev ishift = 0 call dsgets (ishift, which , nev , & np , workl(irz) , workl(bounds), & workl) c if (msglvl .gt. 2) then call dvout (logfil, ncv, workl(irz), ndigit, & '_seupd: Ritz values after calling _SGETS.') call dvout (logfil, ncv, workl(bounds), ndigit, & '_seupd: Ritz value indices after calling _SGETS.') end if c c %-----------------------------------------------------% c | Record indices of the converged wanted Ritz values | c | Mark the select array for possible reordering | c %-----------------------------------------------------% c numcnv = 0 do 11 j = 1,ncv temp1 = max(eps23, abs(workl(irz+ncv-j)) ) jj = workl(bounds + ncv - j) if (numcnv .lt. nconv .and. & workl(ibd+jj-1) .le. tol*temp1) then select(jj) = .true. numcnv = numcnv + 1 if (jj .gt. nev) reord = .true. endif 11 continue c c %-----------------------------------------------------------% c | Check the count (numcnv) of converged Ritz values with | c | the number (nconv) reported by _saupd. If these two | c | are different then there has probably been an error | c | caused by incorrect passing of the _saupd data. | c %-----------------------------------------------------------% c if (msglvl .gt. 2) then call ivout(logfil, 1, numcnv, ndigit, & '_seupd: Number of specified eigenvalues') call ivout(logfil, 1, nconv, ndigit, & '_seupd: Number of "converged" eigenvalues') end if c if (numcnv .ne. nconv) then info = -17 go to 9000 end if c c %-----------------------------------------------------------% c | Call LAPACK routine _steqr to compute the eigenvalues and | c | eigenvectors of the final symmetric tridiagonal matrix H. | c | Initialize the eigenvector matrix Q to the identity. | c %-----------------------------------------------------------% c call dcopy (ncv-1, workl(ih+1), 1, workl(ihb), 1) call dcopy (ncv, workl(ih+ldh), 1, workl(ihd), 1) c call dsteqr ('Identity', ncv, workl(ihd), workl(ihb), & workl(iq) , ldq, workl(iw), ierr) c if (ierr .ne. 0) then info = -8 go to 9000 end if c if (msglvl .gt. 1) then call dcopy (ncv, workl(iq+ncv-1), ldq, workl(iw), 1) call dvout (logfil, ncv, workl(ihd), ndigit, & '_seupd: NCV Ritz values of the final H matrix') call dvout (logfil, ncv, workl(iw), ndigit, & '_seupd: last row of the eigenvector matrix for H') end if c if (reord) then c c %---------------------------------------------% c | Reordered the eigenvalues and eigenvectors | c | computed by _steqr so that the "converged" | c | eigenvalues appear in the first NCONV | c | positions of workl(ihd), and the associated | c | eigenvectors appear in the first NCONV | c | columns. | c %---------------------------------------------% c leftptr = 1 rghtptr = ncv c if (.not. (ncv .eq. 1)) then c 20 if (select(leftptr)) then c c %-------------------------------------------% c | Search, from the left, for the first Ritz | c | value that has not converged. | c %-------------------------------------------% c leftptr = leftptr + 1 c else if ( .not. select(rghtptr)) then c c %----------------------------------------------% c | Search, from the right, the first Ritz value | c | that has converged. | c %----------------------------------------------% c rghtptr = rghtptr - 1 c else c c %----------------------------------------------% c | Swap the Ritz value on the left that has not | c | converged with the Ritz value on the right | c | that has converged. Swap the associated | c | eigenvector of the tridiagonal matrix H as | c | well. | c %----------------------------------------------% c temp = workl(ihd+leftptr-1) workl(ihd+leftptr-1) = workl(ihd+rghtptr-1) workl(ihd+rghtptr-1) = temp call dcopy (ncv, workl(iq+ncv*(leftptr-1)), 1, & workl(iw), 1) call dcopy (ncv, workl(iq+ncv*(rghtptr-1)), 1, & workl(iq+ncv*(leftptr-1)), 1) call dcopy (ncv, workl(iw), 1, & workl(iq+ncv*(rghtptr-1)), 1) leftptr = leftptr + 1 rghtptr = rghtptr - 1 c end if c if (leftptr .lt. rghtptr) go to 20 c end if end if c if (msglvl .gt. 2) then call dvout (logfil, ncv, workl(ihd), ndigit, & '_seupd: The eigenvalues of H--reordered') end if c c %----------------------------------------% c | Load the converged Ritz values into D. | c %----------------------------------------% c call dcopy (nconv, workl(ihd), 1, d, 1) c else c c %-----------------------------------------------------% c | Ritz vectors not required. Load Ritz values into D. | c %-----------------------------------------------------% c call dcopy (nconv, workl(ritz), 1, d, 1) call dcopy (ncv, workl(ritz), 1, workl(ihd), 1) c end if c c %------------------------------------------------------------------% c | Transform the Ritz values and possibly vectors and corresponding | c | Ritz estimates of OP to those of A*x=lambda*B*x. The Ritz values | c | (and corresponding data) are returned in ascending order. | c %------------------------------------------------------------------% c if (type .eq. 'REGULR') then c c %---------------------------------------------------------% c | Ascending sort of wanted Ritz values, vectors and error | c | bounds. Not necessary if only Ritz values are desired. | c %---------------------------------------------------------% c if (rvec) then call dsesrt ('LA', rvec , nconv, d, ncv, workl(iq), ldq) else call dcopy (ncv, workl(bounds), 1, workl(ihb), 1) end if c else c c %-------------------------------------------------------------% c | * Make a copy of all the Ritz values. | c | * Transform the Ritz values back to the original system. | c | For TYPE = 'SHIFTI' the transformation is | c | lambda = 1/theta + sigma | c | For TYPE = 'BUCKLE' the transformation is | c | lambda = sigma * theta / ( theta - 1 ) | c | For TYPE = 'CAYLEY' the transformation is | c | lambda = sigma * (theta + 1) / (theta - 1 ) | c | where the theta are the Ritz values returned by dsaupd . | c | NOTES: | c | *The Ritz vectors are not affected by the transformation. | c | They are only reordered. | c %-------------------------------------------------------------% c call dcopy (ncv, workl(ihd), 1, workl(iw), 1) if (type .eq. 'SHIFTI') then do 40 k=1, ncv workl(ihd+k-1) = one / workl(ihd+k-1) + sigma 40 continue else if (type .eq. 'BUCKLE') then do 50 k=1, ncv workl(ihd+k-1) = sigma * workl(ihd+k-1) / & (workl(ihd+k-1) - one) 50 continue else if (type .eq. 'CAYLEY') then do 60 k=1, ncv workl(ihd+k-1) = sigma * (workl(ihd+k-1) + one) / & (workl(ihd+k-1) - one) 60 continue end if c c %-------------------------------------------------------------% c | * Store the wanted NCONV lambda values into D. | c | * Sort the NCONV wanted lambda in WORKL(IHD:IHD+NCONV-1) | c | into ascending order and apply sort to the NCONV theta | c | values in the transformed system. We will need this to | c | compute Ritz estimates in the original system. | c | * Finally sort the lambda`s into ascending order and apply | c | to Ritz vectors if wanted. Else just sort lambda`s into | c | ascending order. | c | NOTES: | c | *workl(iw:iw+ncv-1) contain the theta ordered so that they | c | match the ordering of the lambda. We`ll use them again for | c | Ritz vector purification. | c %-------------------------------------------------------------% c call dcopy (nconv, workl(ihd), 1, d, 1) call dsortr ('LA', .true., nconv, workl(ihd), workl(iw)) if (rvec) then call dsesrt ('LA', rvec , nconv, d, ncv, workl(iq), ldq) else call dcopy (ncv, workl(bounds), 1, workl(ihb), 1) call dscal (ncv, bnorm2/rnorm, workl(ihb), 1) call dsortr ('LA', .true., nconv, d, workl(ihb)) end if c end if c c %------------------------------------------------% c | Compute the Ritz vectors. Transform the wanted | c | eigenvectors of the symmetric tridiagonal H by | c | the Lanczos basis matrix V. | c %------------------------------------------------% c if (rvec .and. howmny .eq. 'A') then c c %----------------------------------------------------------% c | Compute the QR factorization of the matrix representing | c | the wanted invariant subspace located in the first NCONV | c | columns of workl(iq,ldq). | c %----------------------------------------------------------% c call dgeqr2 (ncv, nconv , workl(iq) , & ldq, workl(iw+ncv), workl(ihb), & ierr) c c %--------------------------------------------------------% c | * Postmultiply V by Q. | c | * Copy the first NCONV columns of VQ into Z. | c | The N by NCONV matrix Z is now a matrix representation | c | of the approximate invariant subspace associated with | c | the Ritz values in workl(ihd). | c %--------------------------------------------------------% c call dorm2r ('Right', 'Notranspose', n , & ncv , nconv , workl(iq), & ldq , workl(iw+ncv), v , & ldv , workd(n+1) , ierr) call dlacpy ('All', n, nconv, v, ldv, z, ldz) c c %-----------------------------------------------------% c | In order to compute the Ritz estimates for the Ritz | c | values in both systems, need the last row of the | c | eigenvector matrix. Remember, it`s in factored form | c %-----------------------------------------------------% c do 65 j = 1, ncv-1 workl(ihb+j-1) = zero 65 continue workl(ihb+ncv-1) = one call dorm2r ('Left', 'Transpose' , ncv , & 1 , nconv , workl(iq) , & ldq , workl(iw+ncv), workl(ihb), & ncv , temp , ierr) c else if (rvec .and. howmny .eq. 'S') then c c Not yet implemented. See remark 2 above. c end if c if (type .eq. 'REGULR' .and. rvec) then c do 70 j=1, ncv workl(ihb+j-1) = rnorm * abs( workl(ihb+j-1) ) 70 continue c else if (type .ne. 'REGULR' .and. rvec) then c c %-------------------------------------------------% c | * Determine Ritz estimates of the theta. | c | If RVEC = .true. then compute Ritz estimates | c | of the theta. | c | If RVEC = .false. then copy Ritz estimates | c | as computed by dsaupd . | c | * Determine Ritz estimates of the lambda. | c %-------------------------------------------------% c call dscal (ncv, bnorm2, workl(ihb), 1) if (type .eq. 'SHIFTI') then c do 80 k=1, ncv workl(ihb+k-1) = abs( workl(ihb+k-1) ) & / workl(iw+k-1)**2 80 continue c else if (type .eq. 'BUCKLE') then c do 90 k=1, ncv workl(ihb+k-1) = sigma * abs( workl(ihb+k-1) ) & / (workl(iw+k-1)-one )**2 90 continue c else if (type .eq. 'CAYLEY') then c do 100 k=1, ncv workl(ihb+k-1) = abs( workl(ihb+k-1) & / workl(iw+k-1)*(workl(iw+k-1)-one) ) 100 continue c end if c end if c if (type .ne. 'REGULR' .and. msglvl .gt. 1) then call dvout (logfil, nconv, d, ndigit, & '_seupd: Untransformed converged Ritz values') call dvout (logfil, nconv, workl(ihb), ndigit, & '_seupd: Ritz estimates of the untransformed Ritz values') else if (msglvl .gt. 1) then call dvout (logfil, nconv, d, ndigit, & '_seupd: Converged Ritz values') call dvout (logfil, nconv, workl(ihb), ndigit, & '_seupd: Associated Ritz estimates') end if c c %-------------------------------------------------% c | Ritz vector purification step. Formally perform | c | one of inverse subspace iteration. Only used | c | for MODE = 3,4,5. See reference 7 | c %-------------------------------------------------% c if (rvec .and. (type .eq. 'SHIFTI' .or. type .eq. 'CAYLEY')) then c do 110 k=0, nconv-1 workl(iw+k) = workl(iq+k*ldq+ncv-1) & / workl(iw+k) 110 continue c else if (rvec .and. type .eq. 'BUCKLE') then c do 120 k=0, nconv-1 workl(iw+k) = workl(iq+k*ldq+ncv-1) & / (workl(iw+k)-one) 120 continue c end if c if (type .ne. 'REGULR') & call dger (n, nconv, one, resid, 1, workl(iw), 1, z, ldz) c 9000 continue c return c c %---------------% c | End of dseupd | c %---------------% c end arpack-0.92.1/SRC/cnapps.f0000644000175000017500000004220610776001577012065 00000000000000c\BeginDoc c c\Name: cnapps c c\Description: c Given the Arnoldi factorization c c A*V_{k} - V_{k}*H_{k} = r_{k+p}*e_{k+p}^T, c c apply NP implicit shifts resulting in c c A*(V_{k}*Q) - (V_{k}*Q)*(Q^T* H_{k}*Q) = r_{k+p}*e_{k+p}^T * Q c c where Q is an orthogonal matrix which is the product of rotations c and reflections resulting from the NP bulge change sweeps. c The updated Arnoldi factorization becomes: c c A*VNEW_{k} - VNEW_{k}*HNEW_{k} = rnew_{k}*e_{k}^T. c c\Usage: c call cnapps c ( N, KEV, NP, SHIFT, V, LDV, H, LDH, RESID, Q, LDQ, c WORKL, WORKD ) c c\Arguments c N Integer. (INPUT) c Problem size, i.e. size of matrix A. c c KEV Integer. (INPUT/OUTPUT) c KEV+NP is the size of the input matrix H. c KEV is the size of the updated matrix HNEW. c c NP Integer. (INPUT) c Number of implicit shifts to be applied. c c SHIFT Complex array of length NP. (INPUT) c The shifts to be applied. c c V Complex N by (KEV+NP) array. (INPUT/OUTPUT) c On INPUT, V contains the current KEV+NP Arnoldi vectors. c On OUTPUT, V contains the updated KEV Arnoldi vectors c in the first KEV columns of V. c c LDV Integer. (INPUT) c Leading dimension of V exactly as declared in the calling c program. c c H Complex (KEV+NP) by (KEV+NP) array. (INPUT/OUTPUT) c On INPUT, H contains the current KEV+NP by KEV+NP upper c Hessenberg matrix of the Arnoldi factorization. c On OUTPUT, H contains the updated KEV by KEV upper Hessenberg c matrix in the KEV leading submatrix. c c LDH Integer. (INPUT) c Leading dimension of H exactly as declared in the calling c program. c c RESID Complex array of length N. (INPUT/OUTPUT) c On INPUT, RESID contains the the residual vector r_{k+p}. c On OUTPUT, RESID is the update residual vector rnew_{k} c in the first KEV locations. c c Q Complex KEV+NP by KEV+NP work array. (WORKSPACE) c Work array used to accumulate the rotations and reflections c during the bulge chase sweep. c c LDQ Integer. (INPUT) c Leading dimension of Q exactly as declared in the calling c program. c c WORKL Complex work array of length (KEV+NP). (WORKSPACE) c Private (replicated) array on each PE or array allocated on c the front end. c c WORKD Complex work array of length 2*N. (WORKSPACE) c Distributed array used in the application of the accumulated c orthogonal matrix Q. c c\EndDoc c c----------------------------------------------------------------------- c c\BeginLib c c\Local variables: c xxxxxx Complex c c\References: c 1. D.C. Sorensen, "Implicit Application of Polynomial Filters in c a k-Step Arnoldi Method", SIAM J. Matr. Anal. Apps., 13 (1992), c pp 357-385. c c\Routines called: c ivout ARPACK utility routine that prints integers. c arscnd ARPACK utility routine for timing. c cmout ARPACK utility routine that prints matrices c cvout ARPACK utility routine that prints vectors. c clacpy LAPACK matrix copy routine. c clanhs LAPACK routine that computes various norms of a matrix. c clartg LAPACK Givens rotation construction routine. c claset LAPACK matrix initialization routine. c slabad LAPACK routine for defining the underflow and overflow c limits. c slamch LAPACK routine that determines machine constants. c slapy2 LAPACK routine to compute sqrt(x**2+y**2) carefully. c cgemv Level 2 BLAS routine for matrix vector multiplication. c caxpy Level 1 BLAS that computes a vector triad. c ccopy Level 1 BLAS that copies one vector to another. c cscal Level 1 BLAS that scales a vector. c c\Author c Danny Sorensen Phuong Vu c Richard Lehoucq CRPC / Rice University c Dept. of Computational & Houston, Texas c Applied Mathematics c Rice University c Houston, Texas c c\SCCS Information: @(#) c FILE: napps.F SID: 2.3 DATE OF SID: 3/28/97 RELEASE: 2 c c\Remarks c 1. In this version, each shift is applied to all the sublocks of c the Hessenberg matrix H and not just to the submatrix that it c comes from. Deflation as in LAPACK routine clahqr (QR algorithm c for upper Hessenberg matrices ) is used. c Upon output, the subdiagonals of H are enforced to be non-negative c real numbers. c c\EndLib c c----------------------------------------------------------------------- c subroutine cnapps & ( n, kev, np, shift, v, ldv, h, ldh, resid, q, ldq, & workl, workd ) c c %----------------------------------------------------% c | Include files for debugging and timing information | c %----------------------------------------------------% c include 'debug.h' include 'stat.h' c c %------------------% c | Scalar Arguments | c %------------------% c integer kev, ldh, ldq, ldv, n, np c c %-----------------% c | Array Arguments | c %-----------------% c Complex & h(ldh,kev+np), resid(n), shift(np), & v(ldv,kev+np), q(ldq,kev+np), workd(2*n), workl(kev+np) c c %------------% c | Parameters | c %------------% c Complex & one, zero Real & rzero parameter (one = (1.0E+0, 0.0E+0), zero = (0.0E+0, 0.0E+0), & rzero = 0.0E+0) c c %------------------------% c | Local Scalars & Arrays | c %------------------------% c integer i, iend, istart, j, jj, kplusp, msglvl logical first Complex & cdum, f, g, h11, h21, r, s, sigma, t Real & c, ovfl, smlnum, ulp, unfl, tst1 save first, ovfl, smlnum, ulp, unfl c c %----------------------% c | External Subroutines | c %----------------------% c external caxpy, ccopy, cgemv, cscal, clacpy, clartg, & cvout, claset, slabad, cmout, arscnd, ivout c c %--------------------% c | External Functions | c %--------------------% c Real & clanhs, slamch, slapy2 external clanhs, slamch, slapy2 c c %----------------------% c | Intrinsics Functions | c %----------------------% c intrinsic abs, aimag, conjg, cmplx, max, min, real c c %---------------------% c | Statement Functions | c %---------------------% c Real & cabs1 cabs1( cdum ) = abs( real( cdum ) ) + abs( aimag( cdum ) ) c c %----------------% c | Data statments | c %----------------% c data first / .true. / c c %-----------------------% c | Executable Statements | c %-----------------------% c if (first) then c c %-----------------------------------------------% c | Set machine-dependent constants for the | c | stopping criterion. If norm(H) <= sqrt(OVFL), | c | overflow should not occur. | c | REFERENCE: LAPACK subroutine clahqr | c %-----------------------------------------------% c unfl = slamch( 'safe minimum' ) ovfl = real(one / unfl) call slabad( unfl, ovfl ) ulp = slamch( 'precision' ) smlnum = unfl*( n / ulp ) first = .false. end if c c %-------------------------------% c | Initialize timing statistics | c | & message level for debugging | c %-------------------------------% c call arscnd (t0) msglvl = mcapps c kplusp = kev + np c c %--------------------------------------------% c | Initialize Q to the identity to accumulate | c | the rotations and reflections | c %--------------------------------------------% c call claset ('All', kplusp, kplusp, zero, one, q, ldq) c c %----------------------------------------------% c | Quick return if there are no shifts to apply | c %----------------------------------------------% c if (np .eq. 0) go to 9000 c c %----------------------------------------------% c | Chase the bulge with the application of each | c | implicit shift. Each shift is applied to the | c | whole matrix including each block. | c %----------------------------------------------% c do 110 jj = 1, np sigma = shift(jj) c if (msglvl .gt. 2 ) then call ivout (logfil, 1, jj, ndigit, & '_napps: shift number.') call cvout (logfil, 1, sigma, ndigit, & '_napps: Value of the shift ') end if c istart = 1 20 continue c do 30 i = istart, kplusp-1 c c %----------------------------------------% c | Check for splitting and deflation. Use | c | a standard test as in the QR algorithm | c | REFERENCE: LAPACK subroutine clahqr | c %----------------------------------------% c tst1 = cabs1( h( i, i ) ) + cabs1( h( i+1, i+1 ) ) if( tst1.eq.rzero ) & tst1 = clanhs( '1', kplusp-jj+1, h, ldh, workl ) if ( abs(real(h(i+1,i))) & .le. max(ulp*tst1, smlnum) ) then if (msglvl .gt. 0) then call ivout (logfil, 1, i, ndigit, & '_napps: matrix splitting at row/column no.') call ivout (logfil, 1, jj, ndigit, & '_napps: matrix splitting with shift number.') call cvout (logfil, 1, h(i+1,i), ndigit, & '_napps: off diagonal element.') end if iend = i h(i+1,i) = zero go to 40 end if 30 continue iend = kplusp 40 continue c if (msglvl .gt. 2) then call ivout (logfil, 1, istart, ndigit, & '_napps: Start of current block ') call ivout (logfil, 1, iend, ndigit, & '_napps: End of current block ') end if c c %------------------------------------------------% c | No reason to apply a shift to block of order 1 | c | or if the current block starts after the point | c | of compression since we'll discard this stuff | c %------------------------------------------------% c if ( istart .eq. iend .or. istart .gt. kev) go to 100 c h11 = h(istart,istart) h21 = h(istart+1,istart) f = h11 - sigma g = h21 c do 80 i = istart, iend-1 c c %------------------------------------------------------% c | Construct the plane rotation G to zero out the bulge | c %------------------------------------------------------% c call clartg (f, g, c, s, r) if (i .gt. istart) then h(i,i-1) = r h(i+1,i-1) = zero end if c c %---------------------------------------------% c | Apply rotation to the left of H; H <- G'*H | c %---------------------------------------------% c do 50 j = i, kplusp t = c*h(i,j) + s*h(i+1,j) h(i+1,j) = -conjg(s)*h(i,j) + c*h(i+1,j) h(i,j) = t 50 continue c c %---------------------------------------------% c | Apply rotation to the right of H; H <- H*G | c %---------------------------------------------% c do 60 j = 1, min(i+2,iend) t = c*h(j,i) + conjg(s)*h(j,i+1) h(j,i+1) = -s*h(j,i) + c*h(j,i+1) h(j,i) = t 60 continue c c %-----------------------------------------------------% c | Accumulate the rotation in the matrix Q; Q <- Q*G' | c %-----------------------------------------------------% c do 70 j = 1, min(i+jj, kplusp) t = c*q(j,i) + conjg(s)*q(j,i+1) q(j,i+1) = - s*q(j,i) + c*q(j,i+1) q(j,i) = t 70 continue c c %---------------------------% c | Prepare for next rotation | c %---------------------------% c if (i .lt. iend-1) then f = h(i+1,i) g = h(i+2,i) end if 80 continue c c %-------------------------------% c | Finished applying the shift. | c %-------------------------------% c 100 continue c c %---------------------------------------------------------% c | Apply the same shift to the next block if there is any. | c %---------------------------------------------------------% c istart = iend + 1 if (iend .lt. kplusp) go to 20 c c %---------------------------------------------% c | Loop back to the top to get the next shift. | c %---------------------------------------------% c 110 continue c c %---------------------------------------------------% c | Perform a similarity transformation that makes | c | sure that the compressed H will have non-negative | c | real subdiagonal elements. | c %---------------------------------------------------% c do 120 j=1,kev if ( real( h(j+1,j) ) .lt. rzero .or. & aimag( h(j+1,j) ) .ne. rzero ) then t = h(j+1,j) / slapy2(real(h(j+1,j)),aimag(h(j+1,j))) call cscal( kplusp-j+1, conjg(t), h(j+1,j), ldh ) call cscal( min(j+2, kplusp), t, h(1,j+1), 1 ) call cscal( min(j+np+1,kplusp), t, q(1,j+1), 1 ) h(j+1,j) = cmplx( real( h(j+1,j) ), rzero ) end if 120 continue c do 130 i = 1, kev c c %--------------------------------------------% c | Final check for splitting and deflation. | c | Use a standard test as in the QR algorithm | c | REFERENCE: LAPACK subroutine clahqr. | c | Note: Since the subdiagonals of the | c | compressed H are nonnegative real numbers, | c | we take advantage of this. | c %--------------------------------------------% c tst1 = cabs1( h( i, i ) ) + cabs1( h( i+1, i+1 ) ) if( tst1 .eq. rzero ) & tst1 = clanhs( '1', kev, h, ldh, workl ) if( real( h( i+1,i ) ) .le. max( ulp*tst1, smlnum ) ) & h(i+1,i) = zero 130 continue c c %-------------------------------------------------% c | Compute the (kev+1)-st column of (V*Q) and | c | temporarily store the result in WORKD(N+1:2*N). | c | This is needed in the residual update since we | c | cannot GUARANTEE that the corresponding entry | c | of H would be zero as in exact arithmetic. | c %-------------------------------------------------% c if ( real( h(kev+1,kev) ) .gt. rzero ) & call cgemv ('N', n, kplusp, one, v, ldv, q(1,kev+1), 1, zero, & workd(n+1), 1) c c %----------------------------------------------------------% c | Compute column 1 to kev of (V*Q) in backward order | c | taking advantage of the upper Hessenberg structure of Q. | c %----------------------------------------------------------% c do 140 i = 1, kev call cgemv ('N', n, kplusp-i+1, one, v, ldv, & q(1,kev-i+1), 1, zero, workd, 1) call ccopy (n, workd, 1, v(1,kplusp-i+1), 1) 140 continue c c %-------------------------------------------------% c | Move v(:,kplusp-kev+1:kplusp) into v(:,1:kev). | c %-------------------------------------------------% c call clacpy ('A', n, kev, v(1,kplusp-kev+1), ldv, v, ldv) c c %--------------------------------------------------------------% c | Copy the (kev+1)-st column of (V*Q) in the appropriate place | c %--------------------------------------------------------------% c if ( real( h(kev+1,kev) ) .gt. rzero ) & call ccopy (n, workd(n+1), 1, v(1,kev+1), 1) c c %-------------------------------------% c | Update the residual vector: | c | r <- sigmak*r + betak*v(:,kev+1) | c | where | c | sigmak = (e_{kev+p}'*Q)*e_{kev} | c | betak = e_{kev+1}'*H*e_{kev} | c %-------------------------------------% c call cscal (n, q(kplusp,kev), resid, 1) if ( real( h(kev+1,kev) ) .gt. rzero ) & call caxpy (n, h(kev+1,kev), v(1,kev+1), 1, resid, 1) c if (msglvl .gt. 1) then call cvout (logfil, 1, q(kplusp,kev), ndigit, & '_napps: sigmak = (e_{kev+p}^T*Q)*e_{kev}') call cvout (logfil, 1, h(kev+1,kev), ndigit, & '_napps: betak = e_{kev+1}^T*H*e_{kev}') call ivout (logfil, 1, kev, ndigit, & '_napps: Order of the final Hessenberg matrix ') if (msglvl .gt. 2) then call cmout (logfil, kev, kev, h, ldh, ndigit, & '_napps: updated Hessenberg matrix H for next iteration') end if c end if c 9000 continue call arscnd (t1) tcapps = tcapps + (t1 - 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then wl=$lt_prog_compiler_wl eval LDFLAGS=\"\$LDFLAGS $lt_prog_compiler_static\" AC_CACHE_CHECK([whether a statically linked program can dlopen itself], lt_cv_dlopen_self_static, [dnl _LT_TRY_DLOPEN_SELF( lt_cv_dlopen_self_static=yes, lt_cv_dlopen_self_static=yes, lt_cv_dlopen_self_static=no, lt_cv_dlopen_self_static=cross) ]) fi CPPFLAGS="$save_CPPFLAGS" LDFLAGS="$save_LDFLAGS" LIBS="$save_LIBS" ;; esac case $lt_cv_dlopen_self in yes|no) enable_dlopen_self=$lt_cv_dlopen_self ;; *) enable_dlopen_self=unknown ;; esac case $lt_cv_dlopen_self_static in yes|no) enable_dlopen_self_static=$lt_cv_dlopen_self_static ;; *) enable_dlopen_self_static=unknown ;; esac fi _LT_DECL([dlopen_support], [enable_dlopen], [0], [Whether dlopen is supported]) _LT_DECL([dlopen_self], [enable_dlopen_self], [0], [Whether dlopen of programs is supported]) _LT_DECL([dlopen_self_static], [enable_dlopen_self_static], [0], [Whether dlopen of statically linked programs is supported]) ])# LT_SYS_DLOPEN_SELF # Old name: AU_ALIAS([AC_LIBTOOL_DLOPEN_SELF], [LT_SYS_DLOPEN_SELF]) dnl aclocal-1.4 backwards compatibility: dnl AC_DEFUN([AC_LIBTOOL_DLOPEN_SELF], []) # _LT_COMPILER_C_O([TAGNAME]) # --------------------------- # Check to see if options -c and -o are simultaneously supported by compiler. # This macro does not hard code the compiler like AC_PROG_CC_C_O. m4_defun([_LT_COMPILER_C_O], [m4_require([_LT_DECL_SED])dnl m4_require([_LT_FILEUTILS_DEFAULTS])dnl m4_require([_LT_TAG_COMPILER])dnl AC_CACHE_CHECK([if $compiler supports -c -o file.$ac_objext], [_LT_TAGVAR(lt_cv_prog_compiler_c_o, $1)], [_LT_TAGVAR(lt_cv_prog_compiler_c_o, $1)=no $RM -r conftest 2>/dev/null mkdir conftest cd conftest mkdir out echo "$lt_simple_compile_test_code" > conftest.$ac_ext lt_compiler_flag="-o out/conftest2.$ac_objext" # Insert the option either (1) after the last *FLAGS variable, or # (2) before a word containing "conftest.", or (3) at the end. # Note that $ac_compile itself does not contain backslashes and begins # with a dollar sign (not a hyphen), so the echo should work correctly. lt_compile=`echo "$ac_compile" | $SED \ -e 's:.*FLAGS}\{0,1\} :&$lt_compiler_flag :; 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then lt_ld_extra=`awk '/^include / { system(sprintf("cd /etc; cat %s 2>/dev/null", \[$]2)); skip = 1; } { if (!skip) print \[$]0; skip = 0; }' < /etc/ld.so.conf | $SED -e 's/#.*//;/^[ ]*hwcap[ ]/d;s/[:, ]/ /g;s/=[^=]*$//;s/=[^= ]* / /g;/^$/d' | tr '\n' ' '` sys_lib_dlsearch_path_spec="/lib /usr/lib $lt_ld_extra" fi # We used to test for /lib/ld.so.1 and disable shared libraries on # powerpc, because MkLinux only supported shared libraries with the # GNU dynamic linker. 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newsos6) version_type=linux library_names_spec='${libname}${release}${shared_ext}$versuffix ${libname}${release}${shared_ext}$major $libname${shared_ext}' shlibpath_var=LD_LIBRARY_PATH shlibpath_overrides_runpath=yes ;; *nto* | *qnx*) version_type=qnx need_lib_prefix=no need_version=no library_names_spec='${libname}${release}${shared_ext}$versuffix ${libname}${release}${shared_ext}$major $libname${shared_ext}' soname_spec='${libname}${release}${shared_ext}$major' shlibpath_var=LD_LIBRARY_PATH shlibpath_overrides_runpath=no hardcode_into_libs=yes dynamic_linker='ldqnx.so' ;; openbsd*) version_type=sunos sys_lib_dlsearch_path_spec="/usr/lib" need_lib_prefix=no # Some older versions of OpenBSD (3.3 at least) *do* need versioned libs. case $host_os in openbsd3.3 | openbsd3.3.*) need_version=yes ;; *) need_version=no ;; esac library_names_spec='${libname}${release}${shared_ext}$versuffix ${libname}${shared_ext}$versuffix' finish_cmds='PATH="\$PATH:/sbin" ldconfig -m $libdir' shlibpath_var=LD_LIBRARY_PATH if test -z "`echo __ELF__ | $CC -E - | $GREP __ELF__`" || test "$host_os-$host_cpu" = "openbsd2.8-powerpc"; then case $host_os in openbsd2.[[89]] | openbsd2.[[89]].*) shlibpath_overrides_runpath=no ;; *) shlibpath_overrides_runpath=yes ;; esac else shlibpath_overrides_runpath=yes fi ;; os2*) libname_spec='$name' shrext_cmds=".dll" need_lib_prefix=no library_names_spec='$libname${shared_ext} $libname.a' dynamic_linker='OS/2 ld.exe' shlibpath_var=LIBPATH ;; osf3* | osf4* | osf5*) version_type=osf need_lib_prefix=no need_version=no soname_spec='${libname}${release}${shared_ext}$major' library_names_spec='${libname}${release}${shared_ext}$versuffix ${libname}${release}${shared_ext}$major $libname${shared_ext}' shlibpath_var=LD_LIBRARY_PATH sys_lib_search_path_spec="/usr/shlib /usr/ccs/lib /usr/lib/cmplrs/cc /usr/lib /usr/local/lib /var/shlib" sys_lib_dlsearch_path_spec="$sys_lib_search_path_spec" ;; rdos*) dynamic_linker=no ;; solaris*) version_type=linux need_lib_prefix=no need_version=no library_names_spec='${libname}${release}${shared_ext}$versuffix ${libname}${release}${shared_ext}$major $libname${shared_ext}' soname_spec='${libname}${release}${shared_ext}$major' shlibpath_var=LD_LIBRARY_PATH shlibpath_overrides_runpath=yes hardcode_into_libs=yes # ldd complains unless libraries are executable postinstall_cmds='chmod +x $lib' ;; sunos4*) version_type=sunos library_names_spec='${libname}${release}${shared_ext}$versuffix ${libname}${shared_ext}$versuffix' finish_cmds='PATH="\$PATH:/usr/etc" ldconfig $libdir' shlibpath_var=LD_LIBRARY_PATH shlibpath_overrides_runpath=yes if test "$with_gnu_ld" = yes; then need_lib_prefix=no fi need_version=yes ;; sysv4 | sysv4.3*) version_type=linux library_names_spec='${libname}${release}${shared_ext}$versuffix ${libname}${release}${shared_ext}$major $libname${shared_ext}' soname_spec='${libname}${release}${shared_ext}$major' shlibpath_var=LD_LIBRARY_PATH case $host_vendor in sni) shlibpath_overrides_runpath=no need_lib_prefix=no runpath_var=LD_RUN_PATH ;; siemens) need_lib_prefix=no ;; motorola) need_lib_prefix=no need_version=no shlibpath_overrides_runpath=no sys_lib_search_path_spec='/lib /usr/lib /usr/ccs/lib' ;; esac ;; sysv4*MP*) if test -d /usr/nec ;then version_type=linux library_names_spec='$libname${shared_ext}.$versuffix $libname${shared_ext}.$major $libname${shared_ext}' soname_spec='$libname${shared_ext}.$major' shlibpath_var=LD_LIBRARY_PATH fi ;; sysv5* | sco3.2v5* | sco5v6* | unixware* | OpenUNIX* | sysv4*uw2*) version_type=freebsd-elf need_lib_prefix=no need_version=no library_names_spec='${libname}${release}${shared_ext}$versuffix ${libname}${release}${shared_ext} $libname${shared_ext}' soname_spec='${libname}${release}${shared_ext}$major' shlibpath_var=LD_LIBRARY_PATH shlibpath_overrides_runpath=yes hardcode_into_libs=yes if test "$with_gnu_ld" = yes; then sys_lib_search_path_spec='/usr/local/lib /usr/gnu/lib /usr/ccs/lib /usr/lib /lib' else sys_lib_search_path_spec='/usr/ccs/lib /usr/lib' case $host_os in sco3.2v5*) sys_lib_search_path_spec="$sys_lib_search_path_spec /lib" ;; esac fi sys_lib_dlsearch_path_spec='/usr/lib' ;; tpf*) # TPF is a cross-target only. Preferred cross-host = GNU/Linux. version_type=linux need_lib_prefix=no need_version=no library_names_spec='${libname}${release}${shared_ext}$versuffix ${libname}${release}${shared_ext}$major $libname${shared_ext}' shlibpath_var=LD_LIBRARY_PATH shlibpath_overrides_runpath=no hardcode_into_libs=yes ;; uts4*) version_type=linux library_names_spec='${libname}${release}${shared_ext}$versuffix ${libname}${release}${shared_ext}$major $libname${shared_ext}' soname_spec='${libname}${release}${shared_ext}$major' shlibpath_var=LD_LIBRARY_PATH ;; *) dynamic_linker=no ;; esac AC_MSG_RESULT([$dynamic_linker]) test "$dynamic_linker" = no && can_build_shared=no variables_saved_for_relink="PATH $shlibpath_var $runpath_var" if test "$GCC" = yes; then variables_saved_for_relink="$variables_saved_for_relink GCC_EXEC_PREFIX COMPILER_PATH LIBRARY_PATH" fi if test "${lt_cv_sys_lib_search_path_spec+set}" = set; then sys_lib_search_path_spec="$lt_cv_sys_lib_search_path_spec" fi if test "${lt_cv_sys_lib_dlsearch_path_spec+set}" = set; then sys_lib_dlsearch_path_spec="$lt_cv_sys_lib_dlsearch_path_spec" fi _LT_DECL([], [variables_saved_for_relink], [1], [Variables whose values should be saved in libtool wrapper scripts and restored at link time]) _LT_DECL([], [need_lib_prefix], [0], [Do we need the "lib" prefix for modules?]) _LT_DECL([], [need_version], [0], [Do we need a version for libraries?]) _LT_DECL([], [version_type], [0], [Library versioning type]) _LT_DECL([], [runpath_var], [0], [Shared library runtime path variable]) _LT_DECL([], [shlibpath_var], [0],[Shared library path variable]) _LT_DECL([], [shlibpath_overrides_runpath], [0], [Is shlibpath searched before the hard-coded library search path?]) _LT_DECL([], [libname_spec], [1], [Format of library name prefix]) _LT_DECL([], [library_names_spec], [1], [[List of archive names. First name is the real one, the rest are links. The last name is the one that the linker finds with -lNAME]]) _LT_DECL([], [soname_spec], [1], [[The coded name of the library, if different from the real name]]) _LT_DECL([], [postinstall_cmds], [2], [Command to use after installation of a shared archive]) _LT_DECL([], [postuninstall_cmds], [2], [Command to use after uninstallation of a shared archive]) _LT_DECL([], [finish_cmds], [2], [Commands used to finish a libtool library installation in a directory]) _LT_DECL([], [finish_eval], [1], [[As "finish_cmds", except a single script fragment to be evaled but not shown]]) _LT_DECL([], [hardcode_into_libs], [0], [Whether we should hardcode library paths into libraries]) _LT_DECL([], [sys_lib_search_path_spec], [2], [Compile-time system search path for libraries]) _LT_DECL([], [sys_lib_dlsearch_path_spec], [2], [Run-time system search path for libraries]) ])# _LT_SYS_DYNAMIC_LINKER # _LT_PATH_TOOL_PREFIX(TOOL) # -------------------------- # find a file program which can recognize shared library AC_DEFUN([_LT_PATH_TOOL_PREFIX], [m4_require([_LT_DECL_EGREP])dnl AC_MSG_CHECKING([for $1]) AC_CACHE_VAL(lt_cv_path_MAGIC_CMD, [case $MAGIC_CMD in [[\\/*] | ?:[\\/]*]) lt_cv_path_MAGIC_CMD="$MAGIC_CMD" # Let the user override the test with a path. ;; *) lt_save_MAGIC_CMD="$MAGIC_CMD" lt_save_ifs="$IFS"; IFS=$PATH_SEPARATOR dnl $ac_dummy forces splitting on constant user-supplied paths. dnl POSIX.2 word splitting is done only on the output of word expansions, dnl not every word. This closes a longstanding sh security hole. ac_dummy="m4_if([$2], , $PATH, [$2])" for ac_dir in $ac_dummy; do IFS="$lt_save_ifs" test -z "$ac_dir" && ac_dir=. if test -f $ac_dir/$1; then lt_cv_path_MAGIC_CMD="$ac_dir/$1" if test -n "$file_magic_test_file"; then case $deplibs_check_method in "file_magic "*) file_magic_regex=`expr "$deplibs_check_method" : "file_magic \(.*\)"` MAGIC_CMD="$lt_cv_path_MAGIC_CMD" if eval $file_magic_cmd \$file_magic_test_file 2> /dev/null | $EGREP "$file_magic_regex" > /dev/null; then : else cat <<_LT_EOF 1>&2 *** Warning: the command libtool uses to detect shared libraries, *** $file_magic_cmd, produces output that libtool cannot recognize. *** The result is that libtool may fail to recognize shared libraries *** as such. This will affect the creation of libtool libraries that *** depend on shared libraries, but programs linked with such libtool *** libraries will work regardless of this problem. Nevertheless, you *** may want to report the problem to your system manager and/or to *** bug-libtool@gnu.org _LT_EOF fi ;; esac fi break fi done IFS="$lt_save_ifs" MAGIC_CMD="$lt_save_MAGIC_CMD" ;; esac]) MAGIC_CMD="$lt_cv_path_MAGIC_CMD" if test -n "$MAGIC_CMD"; then AC_MSG_RESULT($MAGIC_CMD) else AC_MSG_RESULT(no) fi _LT_DECL([], [MAGIC_CMD], [0], [Used to examine libraries when file_magic_cmd begins with "file"])dnl ])# _LT_PATH_TOOL_PREFIX # Old name: AU_ALIAS([AC_PATH_TOOL_PREFIX], [_LT_PATH_TOOL_PREFIX]) dnl aclocal-1.4 backwards compatibility: dnl AC_DEFUN([AC_PATH_TOOL_PREFIX], []) # _LT_PATH_MAGIC # -------------- # find a file program which can recognize a shared library m4_defun([_LT_PATH_MAGIC], [_LT_PATH_TOOL_PREFIX(${ac_tool_prefix}file, /usr/bin$PATH_SEPARATOR$PATH) if test -z "$lt_cv_path_MAGIC_CMD"; then if test -n "$ac_tool_prefix"; then _LT_PATH_TOOL_PREFIX(file, /usr/bin$PATH_SEPARATOR$PATH) else MAGIC_CMD=: fi fi ])# _LT_PATH_MAGIC # LT_PATH_LD # ---------- # find the pathname to the GNU or non-GNU linker AC_DEFUN([LT_PATH_LD], [AC_REQUIRE([AC_PROG_CC])dnl AC_REQUIRE([AC_CANONICAL_HOST])dnl AC_REQUIRE([AC_CANONICAL_BUILD])dnl m4_require([_LT_DECL_SED])dnl m4_require([_LT_DECL_EGREP])dnl AC_ARG_WITH([gnu-ld], [AS_HELP_STRING([--with-gnu-ld], [assume the C compiler uses GNU ld @<:@default=no@:>@])], [test "$withval" = no || with_gnu_ld=yes], [with_gnu_ld=no])dnl ac_prog=ld if test "$GCC" = yes; then # Check if gcc -print-prog-name=ld gives a path. AC_MSG_CHECKING([for ld used by $CC]) case $host in *-*-mingw*) # gcc leaves a trailing carriage return which upsets mingw ac_prog=`($CC -print-prog-name=ld) 2>&5 | tr -d '\015'` ;; *) ac_prog=`($CC -print-prog-name=ld) 2>&5` ;; esac case $ac_prog in # Accept absolute paths. [[\\/]]* | ?:[[\\/]]*) re_direlt='/[[^/]][[^/]]*/\.\./' # Canonicalize the pathname of ld ac_prog=`$ECHO "$ac_prog"| $SED 's%\\\\%/%g'` while $ECHO "$ac_prog" | $GREP "$re_direlt" > /dev/null 2>&1; do ac_prog=`$ECHO $ac_prog| $SED "s%$re_direlt%/%"` done test -z "$LD" && LD="$ac_prog" ;; "") # If it fails, then pretend we aren't using GCC. ac_prog=ld ;; *) # If it is relative, then search for the first ld in PATH. with_gnu_ld=unknown ;; esac elif test "$with_gnu_ld" = yes; then AC_MSG_CHECKING([for GNU ld]) else AC_MSG_CHECKING([for non-GNU ld]) fi AC_CACHE_VAL(lt_cv_path_LD, [if test -z "$LD"; then lt_save_ifs="$IFS"; IFS=$PATH_SEPARATOR for ac_dir in $PATH; do IFS="$lt_save_ifs" test -z "$ac_dir" && ac_dir=. if test -f "$ac_dir/$ac_prog" || test -f "$ac_dir/$ac_prog$ac_exeext"; then lt_cv_path_LD="$ac_dir/$ac_prog" # Check to see if the program is GNU ld. 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See mingw*. lt_cv_deplibs_check_method='file_magic file format pe-arm-.*little(.*architecture: arm)?' lt_cv_file_magic_cmd='$OBJDUMP -f' ;; darwin* | rhapsody*) lt_cv_deplibs_check_method=pass_all ;; freebsd* | dragonfly*) if echo __ELF__ | $CC -E - | $GREP __ELF__ > /dev/null; then case $host_cpu in i*86 ) # Not sure whether the presence of OpenBSD here was a mistake. # Let's accept both of them until this is cleared up. lt_cv_deplibs_check_method='file_magic (FreeBSD|OpenBSD|DragonFly)/i[[3-9]]86 (compact )?demand paged shared library' lt_cv_file_magic_cmd=/usr/bin/file lt_cv_file_magic_test_file=`echo /usr/lib/libc.so.*` ;; esac else lt_cv_deplibs_check_method=pass_all fi ;; gnu*) lt_cv_deplibs_check_method=pass_all ;; hpux10.20* | hpux11*) lt_cv_file_magic_cmd=/usr/bin/file case $host_cpu in ia64*) lt_cv_deplibs_check_method='file_magic (s[[0-9]][[0-9]][[0-9]]|ELF-[[0-9]][[0-9]]) shared object file - IA64' lt_cv_file_magic_test_file=/usr/lib/hpux32/libc.so ;; hppa*64*) [lt_cv_deplibs_check_method='file_magic (s[0-9][0-9][0-9]|ELF-[0-9][0-9]) shared object file - PA-RISC [0-9].[0-9]'] lt_cv_file_magic_test_file=/usr/lib/pa20_64/libc.sl ;; *) lt_cv_deplibs_check_method='file_magic (s[[0-9]][[0-9]][[0-9]]|PA-RISC[[0-9]].[[0-9]]) shared library' lt_cv_file_magic_test_file=/usr/lib/libc.sl ;; esac ;; interix[[3-9]]*) # PIC code is broken on Interix 3.x, that's why |\.a not |_pic\.a here lt_cv_deplibs_check_method='match_pattern /lib[[^/]]+(\.so|\.a)$' ;; irix5* | irix6* | nonstopux*) case $LD in *-32|*"-32 ") libmagic=32-bit;; *-n32|*"-n32 ") libmagic=N32;; *-64|*"-64 ") libmagic=64-bit;; *) libmagic=never-match;; esac lt_cv_deplibs_check_method=pass_all ;; # This must be Linux ELF. linux* | k*bsd*-gnu | kopensolaris*-gnu) lt_cv_deplibs_check_method=pass_all ;; netbsd* | netbsdelf*-gnu) if echo __ELF__ | $CC -E - | $GREP __ELF__ > /dev/null; then lt_cv_deplibs_check_method='match_pattern /lib[[^/]]+(\.so\.[[0-9]]+\.[[0-9]]+|_pic\.a)$' else lt_cv_deplibs_check_method='match_pattern /lib[[^/]]+(\.so|_pic\.a)$' fi ;; newos6*) lt_cv_deplibs_check_method='file_magic ELF [[0-9]][[0-9]]*-bit [[ML]]SB (executable|dynamic lib)' lt_cv_file_magic_cmd=/usr/bin/file lt_cv_file_magic_test_file=/usr/lib/libnls.so ;; *nto* | *qnx*) lt_cv_deplibs_check_method=pass_all ;; openbsd*) if test -z "`echo __ELF__ | $CC -E - | $GREP __ELF__`" || test "$host_os-$host_cpu" = "openbsd2.8-powerpc"; then lt_cv_deplibs_check_method='match_pattern /lib[[^/]]+(\.so\.[[0-9]]+\.[[0-9]]+|\.so|_pic\.a)$' else lt_cv_deplibs_check_method='match_pattern /lib[[^/]]+(\.so\.[[0-9]]+\.[[0-9]]+|_pic\.a)$' fi ;; osf3* | osf4* | osf5*) lt_cv_deplibs_check_method=pass_all ;; rdos*) lt_cv_deplibs_check_method=pass_all ;; solaris*) lt_cv_deplibs_check_method=pass_all ;; sysv5* | sco3.2v5* | sco5v6* | unixware* | OpenUNIX* | sysv4*uw2*) lt_cv_deplibs_check_method=pass_all ;; sysv4 | sysv4.3*) case $host_vendor in motorola) lt_cv_deplibs_check_method='file_magic ELF [[0-9]][[0-9]]*-bit [[ML]]SB (shared object|dynamic lib) M[[0-9]][[0-9]]* Version [[0-9]]' lt_cv_file_magic_test_file=`echo /usr/lib/libc.so*` ;; ncr) lt_cv_deplibs_check_method=pass_all ;; sequent) lt_cv_file_magic_cmd='/bin/file' lt_cv_deplibs_check_method='file_magic ELF [[0-9]][[0-9]]*-bit [[LM]]SB (shared object|dynamic lib )' ;; sni) lt_cv_file_magic_cmd='/bin/file' lt_cv_deplibs_check_method="file_magic ELF [[0-9]][[0-9]]*-bit [[LM]]SB dynamic lib" lt_cv_file_magic_test_file=/lib/libc.so ;; siemens) lt_cv_deplibs_check_method=pass_all ;; pc) lt_cv_deplibs_check_method=pass_all ;; esac ;; tpf*) lt_cv_deplibs_check_method=pass_all ;; esac ]) file_magic_cmd=$lt_cv_file_magic_cmd deplibs_check_method=$lt_cv_deplibs_check_method test -z "$deplibs_check_method" && deplibs_check_method=unknown _LT_DECL([], [deplibs_check_method], [1], [Method to check whether dependent libraries are shared objects]) _LT_DECL([], [file_magic_cmd], [1], [Command to use when deplibs_check_method == "file_magic"]) ])# _LT_CHECK_MAGIC_METHOD # LT_PATH_NM # ---------- # find the pathname to a BSD- or MS-compatible name lister AC_DEFUN([LT_PATH_NM], [AC_REQUIRE([AC_PROG_CC])dnl AC_CACHE_CHECK([for BSD- or MS-compatible name lister (nm)], lt_cv_path_NM, [if test -n "$NM"; then # Let the user override the test. lt_cv_path_NM="$NM" else lt_nm_to_check="${ac_tool_prefix}nm" if test -n "$ac_tool_prefix" && test "$build" = "$host"; then lt_nm_to_check="$lt_nm_to_check nm" fi for lt_tmp_nm in $lt_nm_to_check; do lt_save_ifs="$IFS"; IFS=$PATH_SEPARATOR for ac_dir in $PATH /usr/ccs/bin/elf /usr/ccs/bin /usr/ucb /bin; do IFS="$lt_save_ifs" test -z "$ac_dir" && ac_dir=. tmp_nm="$ac_dir/$lt_tmp_nm" if test -f "$tmp_nm" || test -f "$tmp_nm$ac_exeext" ; then # Check to see if the nm accepts a BSD-compat flag. # Adding the `sed 1q' prevents false positives on HP-UX, which says: # nm: unknown option "B" ignored # Tru64's nm complains that /dev/null is an invalid object file case `"$tmp_nm" -B /dev/null 2>&1 | sed '1q'` in */dev/null* | *'Invalid file or object type'*) lt_cv_path_NM="$tmp_nm -B" break ;; *) case `"$tmp_nm" -p /dev/null 2>&1 | sed '1q'` in */dev/null*) lt_cv_path_NM="$tmp_nm -p" break ;; *) lt_cv_path_NM=${lt_cv_path_NM="$tmp_nm"} # keep the first match, but continue # so that we can try to find one that supports BSD flags ;; esac ;; esac fi done IFS="$lt_save_ifs" done : ${lt_cv_path_NM=no} fi]) if test "$lt_cv_path_NM" != "no"; then NM="$lt_cv_path_NM" else # Didn't find any BSD compatible name lister, look for dumpbin. AC_CHECK_TOOLS(DUMPBIN, ["dumpbin -symbols" "link -dump -symbols"], :) AC_SUBST([DUMPBIN]) if test "$DUMPBIN" != ":"; then NM="$DUMPBIN" fi fi test -z "$NM" && NM=nm AC_SUBST([NM]) _LT_DECL([], [NM], [1], [A BSD- or MS-compatible name lister])dnl AC_CACHE_CHECK([the name lister ($NM) interface], [lt_cv_nm_interface], [lt_cv_nm_interface="BSD nm" echo "int some_variable = 0;" > conftest.$ac_ext (eval echo "\"\$as_me:__oline__: $ac_compile\"" >&AS_MESSAGE_LOG_FD) (eval "$ac_compile" 2>conftest.err) cat conftest.err >&AS_MESSAGE_LOG_FD (eval echo "\"\$as_me:__oline__: $NM \\\"conftest.$ac_objext\\\"\"" >&AS_MESSAGE_LOG_FD) (eval "$NM \"conftest.$ac_objext\"" 2>conftest.err > conftest.out) cat conftest.err >&AS_MESSAGE_LOG_FD (eval echo "\"\$as_me:__oline__: output\"" >&AS_MESSAGE_LOG_FD) cat conftest.out >&AS_MESSAGE_LOG_FD if $GREP 'External.*some_variable' conftest.out > /dev/null; then lt_cv_nm_interface="MS dumpbin" fi rm -f conftest*]) ])# LT_PATH_NM # Old names: AU_ALIAS([AM_PROG_NM], [LT_PATH_NM]) AU_ALIAS([AC_PROG_NM], [LT_PATH_NM]) dnl aclocal-1.4 backwards compatibility: dnl AC_DEFUN([AM_PROG_NM], []) dnl AC_DEFUN([AC_PROG_NM], []) # LT_LIB_M # -------- # check for math library AC_DEFUN([LT_LIB_M], [AC_REQUIRE([AC_CANONICAL_HOST])dnl LIBM= case $host in *-*-beos* | *-*-cygwin* | *-*-pw32* | *-*-darwin*) # These system don't have libm, or don't need it ;; *-ncr-sysv4.3*) AC_CHECK_LIB(mw, _mwvalidcheckl, LIBM="-lmw") AC_CHECK_LIB(m, cos, LIBM="$LIBM -lm") ;; *) AC_CHECK_LIB(m, cos, LIBM="-lm") ;; esac AC_SUBST([LIBM]) ])# LT_LIB_M # Old name: AU_ALIAS([AC_CHECK_LIBM], [LT_LIB_M]) dnl aclocal-1.4 backwards compatibility: dnl AC_DEFUN([AC_CHECK_LIBM], []) # _LT_COMPILER_NO_RTTI([TAGNAME]) # ------------------------------- m4_defun([_LT_COMPILER_NO_RTTI], [m4_require([_LT_TAG_COMPILER])dnl _LT_TAGVAR(lt_prog_compiler_no_builtin_flag, $1)= if test "$GCC" = yes; then _LT_TAGVAR(lt_prog_compiler_no_builtin_flag, $1)=' -fno-builtin' _LT_COMPILER_OPTION([if $compiler supports -fno-rtti -fno-exceptions], lt_cv_prog_compiler_rtti_exceptions, [-fno-rtti -fno-exceptions], [], [_LT_TAGVAR(lt_prog_compiler_no_builtin_flag, $1)="$_LT_TAGVAR(lt_prog_compiler_no_builtin_flag, $1) -fno-rtti -fno-exceptions"]) fi _LT_TAGDECL([no_builtin_flag], [lt_prog_compiler_no_builtin_flag], [1], [Compiler flag to turn off builtin functions]) ])# _LT_COMPILER_NO_RTTI # _LT_CMD_GLOBAL_SYMBOLS # ---------------------- m4_defun([_LT_CMD_GLOBAL_SYMBOLS], [AC_REQUIRE([AC_CANONICAL_HOST])dnl AC_REQUIRE([AC_PROG_CC])dnl AC_REQUIRE([LT_PATH_NM])dnl AC_REQUIRE([LT_PATH_LD])dnl m4_require([_LT_DECL_SED])dnl m4_require([_LT_DECL_EGREP])dnl m4_require([_LT_TAG_COMPILER])dnl # Check for command to grab the raw symbol name followed by C symbol from nm. AC_MSG_CHECKING([command to parse $NM output from $compiler object]) AC_CACHE_VAL([lt_cv_sys_global_symbol_pipe], [ # These are sane defaults that work on at least a few old systems. # [They come from Ultrix. What could be older than Ultrix?!! ;)] # Character class describing NM global symbol codes. symcode='[[BCDEGRST]]' # Regexp to match symbols that can be accessed directly from C. sympat='\([[_A-Za-z]][[_A-Za-z0-9]]*\)' # Define system-specific variables. case $host_os in aix*) symcode='[[BCDT]]' ;; cygwin* | mingw* | pw32* | cegcc*) symcode='[[ABCDGISTW]]' ;; hpux*) if test "$host_cpu" = ia64; then symcode='[[ABCDEGRST]]' fi ;; irix* | nonstopux*) symcode='[[BCDEGRST]]' ;; osf*) symcode='[[BCDEGQRST]]' ;; solaris*) symcode='[[BDRT]]' ;; sco3.2v5*) symcode='[[DT]]' ;; sysv4.2uw2*) symcode='[[DT]]' ;; sysv5* | sco5v6* | unixware* | OpenUNIX*) symcode='[[ABDT]]' ;; sysv4) symcode='[[DFNSTU]]' ;; esac # If we're using GNU nm, then use its standard symbol codes. case `$NM -V 2>&1` in *GNU* | *'with BFD'*) symcode='[[ABCDGIRSTW]]' ;; esac # Transform an extracted symbol line into a proper C declaration. # Some systems (esp. on ia64) link data and code symbols differently, # so use this general approach. lt_cv_sys_global_symbol_to_cdecl="sed -n -e 's/^T .* \(.*\)$/extern int \1();/p' -e 's/^$symcode* .* \(.*\)$/extern char \1;/p'" # Transform an extracted symbol line into symbol name and symbol address lt_cv_sys_global_symbol_to_c_name_address="sed -n -e 's/^: \([[^ ]]*\) $/ {\\\"\1\\\", (void *) 0},/p' -e 's/^$symcode* \([[^ ]]*\) \([[^ ]]*\)$/ {\"\2\", (void *) \&\2},/p'" lt_cv_sys_global_symbol_to_c_name_address_lib_prefix="sed -n -e 's/^: \([[^ ]]*\) $/ {\\\"\1\\\", (void *) 0},/p' -e 's/^$symcode* \([[^ ]]*\) \(lib[[^ ]]*\)$/ {\"\2\", (void *) \&\2},/p' -e 's/^$symcode* \([[^ ]]*\) \([[^ ]]*\)$/ {\"lib\2\", (void *) \&\2},/p'" # Handle CRLF in mingw tool chain opt_cr= case $build_os in mingw*) opt_cr=`$ECHO 'x\{0,1\}' | tr x '\015'` # option cr in regexp ;; esac # Try without a prefix underscore, then with it. for ac_symprfx in "" "_"; do # Transform symcode, sympat, and symprfx into a raw symbol and a C symbol. symxfrm="\\1 $ac_symprfx\\2 \\2" # Write the raw and C identifiers. if test "$lt_cv_nm_interface" = "MS dumpbin"; then # Fake it for dumpbin and say T for any non-static function # and D for any global variable. # Also find C++ and __fastcall symbols from MSVC++, # which start with @ or ?. lt_cv_sys_global_symbol_pipe="$AWK ['"\ " {last_section=section; section=\$ 3};"\ " /Section length .*#relocs.*(pick any)/{hide[last_section]=1};"\ " \$ 0!~/External *\|/{next};"\ " / 0+ UNDEF /{next}; / UNDEF \([^|]\)*()/{next};"\ " {if(hide[section]) next};"\ " {f=0}; \$ 0~/\(\).*\|/{f=1}; {printf f ? \"T \" : \"D \"};"\ " {split(\$ 0, a, /\||\r/); split(a[2], s)};"\ " s[1]~/^[@?]/{print s[1], s[1]; next};"\ " s[1]~prfx {split(s[1],t,\"@\"); print t[1], substr(t[1],length(prfx))}"\ " ' prfx=^$ac_symprfx]" else lt_cv_sys_global_symbol_pipe="sed -n -e 's/^.*[[ ]]\($symcode$symcode*\)[[ ]][[ ]]*$ac_symprfx$sympat$opt_cr$/$symxfrm/p'" fi # Check to see that the pipe works correctly. pipe_works=no rm -f conftest* cat > conftest.$ac_ext <<_LT_EOF #ifdef __cplusplus extern "C" { #endif char nm_test_var; void nm_test_func(void); void nm_test_func(void){} #ifdef __cplusplus } #endif int main(){nm_test_var='a';nm_test_func();return(0);} _LT_EOF if AC_TRY_EVAL(ac_compile); then # Now try to grab the symbols. nlist=conftest.nm if AC_TRY_EVAL(NM conftest.$ac_objext \| $lt_cv_sys_global_symbol_pipe \> $nlist) && test -s "$nlist"; then # Try sorting and uniquifying the output. if sort "$nlist" | uniq > "$nlist"T; then mv -f "$nlist"T "$nlist" else rm -f "$nlist"T fi # Make sure that we snagged all the symbols we need. if $GREP ' nm_test_var$' "$nlist" >/dev/null; then if $GREP ' nm_test_func$' "$nlist" >/dev/null; then cat <<_LT_EOF > conftest.$ac_ext #ifdef __cplusplus extern "C" { #endif _LT_EOF # Now generate the symbol file. eval "$lt_cv_sys_global_symbol_to_cdecl"' < "$nlist" | $GREP -v main >> conftest.$ac_ext' cat <<_LT_EOF >> conftest.$ac_ext /* The mapping between symbol names and symbols. */ const struct { const char *name; void *address; } lt__PROGRAM__LTX_preloaded_symbols[[]] = { { "@PROGRAM@", (void *) 0 }, _LT_EOF $SED "s/^$symcode$symcode* \(.*\) \(.*\)$/ {\"\2\", (void *) \&\2},/" < "$nlist" | $GREP -v main >> conftest.$ac_ext cat <<\_LT_EOF >> conftest.$ac_ext {0, (void *) 0} }; /* This works around a problem in FreeBSD linker */ #ifdef FREEBSD_WORKAROUND static const void *lt_preloaded_setup() { return lt__PROGRAM__LTX_preloaded_symbols; } #endif #ifdef __cplusplus } #endif _LT_EOF # Now try linking the two files. mv conftest.$ac_objext conftstm.$ac_objext lt_save_LIBS="$LIBS" lt_save_CFLAGS="$CFLAGS" LIBS="conftstm.$ac_objext" CFLAGS="$CFLAGS$_LT_TAGVAR(lt_prog_compiler_no_builtin_flag, $1)" if AC_TRY_EVAL(ac_link) && test -s conftest${ac_exeext}; then pipe_works=yes fi LIBS="$lt_save_LIBS" CFLAGS="$lt_save_CFLAGS" else echo "cannot find nm_test_func in $nlist" >&AS_MESSAGE_LOG_FD fi else echo "cannot find nm_test_var in $nlist" >&AS_MESSAGE_LOG_FD fi else echo "cannot run $lt_cv_sys_global_symbol_pipe" >&AS_MESSAGE_LOG_FD fi else echo "$progname: failed program was:" >&AS_MESSAGE_LOG_FD cat conftest.$ac_ext >&5 fi rm -rf conftest* conftst* # Do not use the global_symbol_pipe unless it works. if test "$pipe_works" = yes; then break else lt_cv_sys_global_symbol_pipe= fi done ]) if test -z "$lt_cv_sys_global_symbol_pipe"; then lt_cv_sys_global_symbol_to_cdecl= fi if test -z "$lt_cv_sys_global_symbol_pipe$lt_cv_sys_global_symbol_to_cdecl"; then AC_MSG_RESULT(failed) else AC_MSG_RESULT(ok) fi _LT_DECL([global_symbol_pipe], [lt_cv_sys_global_symbol_pipe], [1], [Take the output of nm and produce a listing of raw symbols and C names]) _LT_DECL([global_symbol_to_cdecl], [lt_cv_sys_global_symbol_to_cdecl], [1], [Transform the output of nm in a proper C declaration]) _LT_DECL([global_symbol_to_c_name_address], [lt_cv_sys_global_symbol_to_c_name_address], [1], [Transform the output of nm in a C name address pair]) _LT_DECL([global_symbol_to_c_name_address_lib_prefix], [lt_cv_sys_global_symbol_to_c_name_address_lib_prefix], [1], [Transform the output of nm in a C name address pair when lib prefix is needed]) ]) # _LT_CMD_GLOBAL_SYMBOLS # _LT_COMPILER_PIC([TAGNAME]) # --------------------------- m4_defun([_LT_COMPILER_PIC], [m4_require([_LT_TAG_COMPILER])dnl _LT_TAGVAR(lt_prog_compiler_wl, $1)= _LT_TAGVAR(lt_prog_compiler_pic, $1)= _LT_TAGVAR(lt_prog_compiler_static, $1)= AC_MSG_CHECKING([for $compiler option to produce PIC]) m4_if([$1], [CXX], [ # C++ specific cases for pic, static, wl, etc. if test "$GXX" = yes; then _LT_TAGVAR(lt_prog_compiler_wl, $1)='-Wl,' _LT_TAGVAR(lt_prog_compiler_static, $1)='-static' case $host_os in aix*) # All AIX code is PIC. if test "$host_cpu" = ia64; then # AIX 5 now supports IA64 processor _LT_TAGVAR(lt_prog_compiler_static, $1)='-Bstatic' fi ;; amigaos*) case $host_cpu in powerpc) # see comment about AmigaOS4 .so support _LT_TAGVAR(lt_prog_compiler_pic, $1)='-fPIC' ;; m68k) # FIXME: we need at least 68020 code to build shared libraries, but # adding the `-m68020' flag to GCC prevents building anything better, # like `-m68040'. _LT_TAGVAR(lt_prog_compiler_pic, $1)='-m68020 -resident32 -malways-restore-a4' ;; esac ;; beos* | irix5* | irix6* | nonstopux* | osf3* | osf4* | osf5*) # PIC is the default for these OSes. ;; mingw* | cygwin* | os2* | pw32* | cegcc*) # This hack is so that the source file can tell whether it is being # built for inclusion in a dll (and should export symbols for example). # Although the cygwin gcc ignores -fPIC, still need this for old-style # (--disable-auto-import) libraries m4_if([$1], [GCJ], [], [_LT_TAGVAR(lt_prog_compiler_pic, $1)='-DDLL_EXPORT']) ;; darwin* | rhapsody*) # PIC is the default on this platform # Common symbols not allowed in MH_DYLIB files _LT_TAGVAR(lt_prog_compiler_pic, $1)='-fno-common' ;; *djgpp*) # DJGPP does not support shared libraries at all _LT_TAGVAR(lt_prog_compiler_pic, $1)= ;; interix[[3-9]]*) # Interix 3.x gcc -fpic/-fPIC options generate broken code. # Instead, we relocate shared libraries at runtime. ;; sysv4*MP*) if test -d /usr/nec; then _LT_TAGVAR(lt_prog_compiler_pic, $1)=-Kconform_pic fi ;; hpux*) # PIC is the default for 64-bit PA HP-UX, but not for 32-bit # PA HP-UX. On IA64 HP-UX, PIC is the default but the pic flag # sets the default TLS model and affects inlining. case $host_cpu in hppa*64*) ;; *) _LT_TAGVAR(lt_prog_compiler_pic, $1)='-fPIC' ;; esac ;; *qnx* | *nto*) # QNX uses GNU C++, but need to define -shared option too, otherwise # it will coredump. _LT_TAGVAR(lt_prog_compiler_pic, $1)='-fPIC -shared' ;; *) _LT_TAGVAR(lt_prog_compiler_pic, $1)='-fPIC' ;; esac else case $host_os in aix[[4-9]]*) # All AIX code is PIC. if test "$host_cpu" = ia64; then # AIX 5 now supports IA64 processor _LT_TAGVAR(lt_prog_compiler_static, $1)='-Bstatic' else _LT_TAGVAR(lt_prog_compiler_static, $1)='-bnso -bI:/lib/syscalls.exp' fi ;; chorus*) case $cc_basename in cxch68*) # Green Hills C++ Compiler # _LT_TAGVAR(lt_prog_compiler_static, $1)="--no_auto_instantiation -u __main -u __premain -u _abort -r $COOL_DIR/lib/libOrb.a $MVME_DIR/lib/CC/libC.a $MVME_DIR/lib/classix/libcx.s.a" ;; esac ;; dgux*) case $cc_basename in ec++*) _LT_TAGVAR(lt_prog_compiler_pic, $1)='-KPIC' ;; ghcx*) # Green Hills C++ Compiler _LT_TAGVAR(lt_prog_compiler_pic, $1)='-pic' ;; *) ;; esac ;; freebsd* | dragonfly*) # FreeBSD uses GNU C++ ;; hpux9* | hpux10* | hpux11*) case $cc_basename in CC*) _LT_TAGVAR(lt_prog_compiler_wl, $1)='-Wl,' _LT_TAGVAR(lt_prog_compiler_static, $1)='${wl}-a ${wl}archive' if test "$host_cpu" != ia64; then _LT_TAGVAR(lt_prog_compiler_pic, $1)='+Z' fi ;; aCC*) _LT_TAGVAR(lt_prog_compiler_wl, $1)='-Wl,' _LT_TAGVAR(lt_prog_compiler_static, $1)='${wl}-a ${wl}archive' case $host_cpu in hppa*64*|ia64*) # +Z the default ;; *) _LT_TAGVAR(lt_prog_compiler_pic, $1)='+Z' ;; esac ;; *) ;; esac ;; interix*) # This is c89, which is MS Visual C++ (no shared libs) # Anyone wants to do a port? ;; irix5* | irix6* | nonstopux*) case $cc_basename in CC*) _LT_TAGVAR(lt_prog_compiler_wl, $1)='-Wl,' _LT_TAGVAR(lt_prog_compiler_static, $1)='-non_shared' # CC pic flag -KPIC is the default. ;; *) ;; esac ;; linux* | k*bsd*-gnu | kopensolaris*-gnu) case $cc_basename in KCC*) # KAI C++ Compiler _LT_TAGVAR(lt_prog_compiler_wl, $1)='--backend -Wl,' _LT_TAGVAR(lt_prog_compiler_pic, $1)='-fPIC' ;; ecpc* ) # old Intel C++ for x86_64 which still supported -KPIC. _LT_TAGVAR(lt_prog_compiler_wl, $1)='-Wl,' _LT_TAGVAR(lt_prog_compiler_pic, $1)='-KPIC' _LT_TAGVAR(lt_prog_compiler_static, $1)='-static' ;; icpc* ) # Intel C++, used to be incompatible with GCC. # ICC 10 doesn't accept -KPIC any more. _LT_TAGVAR(lt_prog_compiler_wl, $1)='-Wl,' _LT_TAGVAR(lt_prog_compiler_pic, $1)='-fPIC' _LT_TAGVAR(lt_prog_compiler_static, $1)='-static' ;; pgCC* | pgcpp*) # Portland Group C++ compiler _LT_TAGVAR(lt_prog_compiler_wl, $1)='-Wl,' _LT_TAGVAR(lt_prog_compiler_pic, $1)='-fpic' _LT_TAGVAR(lt_prog_compiler_static, $1)='-Bstatic' ;; cxx*) # Compaq C++ # Make sure the PIC flag is empty. It appears that all Alpha # Linux and Compaq Tru64 Unix objects are PIC. _LT_TAGVAR(lt_prog_compiler_pic, $1)= _LT_TAGVAR(lt_prog_compiler_static, $1)='-non_shared' ;; xlc* | xlC*) # IBM XL 8.0 on PPC _LT_TAGVAR(lt_prog_compiler_wl, $1)='-Wl,' _LT_TAGVAR(lt_prog_compiler_pic, $1)='-qpic' _LT_TAGVAR(lt_prog_compiler_static, $1)='-qstaticlink' ;; *) case `$CC -V 2>&1 | sed 5q` in *Sun\ C*) # Sun C++ 5.9 _LT_TAGVAR(lt_prog_compiler_pic, $1)='-KPIC' _LT_TAGVAR(lt_prog_compiler_static, $1)='-Bstatic' _LT_TAGVAR(lt_prog_compiler_wl, $1)='-Qoption ld ' ;; esac ;; esac ;; lynxos*) ;; m88k*) ;; mvs*) case $cc_basename in cxx*) _LT_TAGVAR(lt_prog_compiler_pic, $1)='-W c,exportall' ;; *) ;; esac ;; netbsd* | netbsdelf*-gnu) ;; *qnx* | *nto*) # QNX uses GNU C++, but need to define -shared option too, otherwise # it will coredump. _LT_TAGVAR(lt_prog_compiler_pic, $1)='-fPIC -shared' ;; osf3* | osf4* | osf5*) case $cc_basename in KCC*) _LT_TAGVAR(lt_prog_compiler_wl, $1)='--backend -Wl,' ;; RCC*) # Rational C++ 2.4.1 _LT_TAGVAR(lt_prog_compiler_pic, $1)='-pic' ;; cxx*) # Digital/Compaq C++ _LT_TAGVAR(lt_prog_compiler_wl, $1)='-Wl,' # Make sure the PIC flag is empty. It appears that all Alpha # Linux and Compaq Tru64 Unix objects are PIC. _LT_TAGVAR(lt_prog_compiler_pic, $1)= _LT_TAGVAR(lt_prog_compiler_static, $1)='-non_shared' ;; *) ;; esac ;; psos*) ;; solaris*) case $cc_basename in CC*) # Sun C++ 4.2, 5.x and Centerline C++ _LT_TAGVAR(lt_prog_compiler_pic, $1)='-KPIC' _LT_TAGVAR(lt_prog_compiler_static, $1)='-Bstatic' _LT_TAGVAR(lt_prog_compiler_wl, $1)='-Qoption ld ' ;; gcx*) # Green Hills C++ Compiler _LT_TAGVAR(lt_prog_compiler_pic, $1)='-PIC' ;; *) ;; esac ;; sunos4*) case $cc_basename in CC*) # Sun C++ 4.x _LT_TAGVAR(lt_prog_compiler_pic, $1)='-pic' _LT_TAGVAR(lt_prog_compiler_static, $1)='-Bstatic' ;; lcc*) # Lucid _LT_TAGVAR(lt_prog_compiler_pic, $1)='-pic' ;; *) ;; esac ;; sysv5* | unixware* | sco3.2v5* | sco5v6* | OpenUNIX*) case $cc_basename in CC*) _LT_TAGVAR(lt_prog_compiler_wl, $1)='-Wl,' _LT_TAGVAR(lt_prog_compiler_pic, $1)='-KPIC' _LT_TAGVAR(lt_prog_compiler_static, $1)='-Bstatic' ;; esac ;; tandem*) case $cc_basename in NCC*) # NonStop-UX NCC 3.20 _LT_TAGVAR(lt_prog_compiler_pic, $1)='-KPIC' ;; *) ;; esac ;; vxworks*) ;; *) _LT_TAGVAR(lt_prog_compiler_can_build_shared, $1)=no ;; esac fi ], [ if test "$GCC" = yes; then _LT_TAGVAR(lt_prog_compiler_wl, $1)='-Wl,' _LT_TAGVAR(lt_prog_compiler_static, $1)='-static' case $host_os in aix*) # All AIX code is PIC. if test "$host_cpu" = ia64; then # AIX 5 now supports IA64 processor _LT_TAGVAR(lt_prog_compiler_static, $1)='-Bstatic' fi ;; amigaos*) case $host_cpu in powerpc) # see comment about AmigaOS4 .so support _LT_TAGVAR(lt_prog_compiler_pic, $1)='-fPIC' ;; m68k) # FIXME: we need at least 68020 code to build shared libraries, but # adding the `-m68020' flag to GCC prevents building anything better, # like `-m68040'. _LT_TAGVAR(lt_prog_compiler_pic, $1)='-m68020 -resident32 -malways-restore-a4' ;; esac ;; beos* | irix5* | irix6* | nonstopux* | osf3* | osf4* | osf5*) # PIC is the default for these OSes. ;; mingw* | cygwin* | pw32* | os2* | cegcc*) # This hack is so that the source file can tell whether it is being # built for inclusion in a dll (and should export symbols for example). # Although the cygwin gcc ignores -fPIC, still need this for old-style # (--disable-auto-import) libraries m4_if([$1], [GCJ], [], [_LT_TAGVAR(lt_prog_compiler_pic, $1)='-DDLL_EXPORT']) ;; darwin* | rhapsody*) # PIC is the default on this platform # Common symbols not allowed in MH_DYLIB files _LT_TAGVAR(lt_prog_compiler_pic, $1)='-fno-common' ;; hpux*) # PIC is the default for 64-bit PA HP-UX, but not for 32-bit # PA HP-UX. On IA64 HP-UX, PIC is the default but the pic flag # sets the default TLS model and affects inlining. case $host_cpu in hppa*64*) # +Z the default ;; *) _LT_TAGVAR(lt_prog_compiler_pic, $1)='-fPIC' ;; esac ;; interix[[3-9]]*) # Interix 3.x gcc -fpic/-fPIC options generate broken code. # Instead, we relocate shared libraries at runtime. ;; msdosdjgpp*) # Just because we use GCC doesn't mean we suddenly get shared libraries # on systems that don't support them. _LT_TAGVAR(lt_prog_compiler_can_build_shared, $1)=no enable_shared=no ;; *nto* | *qnx*) # QNX uses GNU C++, but need to define -shared option too, otherwise # it will coredump. _LT_TAGVAR(lt_prog_compiler_pic, $1)='-fPIC -shared' ;; sysv4*MP*) if test -d /usr/nec; then _LT_TAGVAR(lt_prog_compiler_pic, $1)=-Kconform_pic fi ;; *) _LT_TAGVAR(lt_prog_compiler_pic, $1)='-fPIC' ;; esac else # PORTME Check for flag to pass linker flags through the system compiler. case $host_os in aix*) _LT_TAGVAR(lt_prog_compiler_wl, $1)='-Wl,' if test "$host_cpu" = ia64; then # AIX 5 now supports IA64 processor _LT_TAGVAR(lt_prog_compiler_static, $1)='-Bstatic' else _LT_TAGVAR(lt_prog_compiler_static, $1)='-bnso -bI:/lib/syscalls.exp' fi ;; mingw* | cygwin* | pw32* | os2* | cegcc*) # This hack is so that the source file can tell whether it is being # built for inclusion in a dll (and should export symbols for example). m4_if([$1], [GCJ], [], [_LT_TAGVAR(lt_prog_compiler_pic, $1)='-DDLL_EXPORT']) ;; hpux9* | hpux10* | hpux11*) _LT_TAGVAR(lt_prog_compiler_wl, $1)='-Wl,' # PIC is the default for IA64 HP-UX and 64-bit HP-UX, but # not for PA HP-UX. case $host_cpu in hppa*64*|ia64*) # +Z the default ;; *) _LT_TAGVAR(lt_prog_compiler_pic, $1)='+Z' ;; esac # Is there a better lt_prog_compiler_static that works with the bundled CC? _LT_TAGVAR(lt_prog_compiler_static, $1)='${wl}-a ${wl}archive' ;; irix5* | irix6* | nonstopux*) _LT_TAGVAR(lt_prog_compiler_wl, $1)='-Wl,' # PIC (with -KPIC) is the default. _LT_TAGVAR(lt_prog_compiler_static, $1)='-non_shared' ;; linux* | k*bsd*-gnu | kopensolaris*-gnu) case $cc_basename in # old Intel for x86_64 which still supported -KPIC. ecc*) _LT_TAGVAR(lt_prog_compiler_wl, $1)='-Wl,' _LT_TAGVAR(lt_prog_compiler_pic, $1)='-KPIC' _LT_TAGVAR(lt_prog_compiler_static, $1)='-static' ;; 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netbsd* | netbsdelf*-gnu) if echo __ELF__ | $CC -E - | $GREP __ELF__ >/dev/null; then _LT_TAGVAR(archive_cmds, $1)='$LD -Bshareable -o $lib $libobjs $deplibs $linker_flags' # a.out else _LT_TAGVAR(archive_cmds, $1)='$LD -shared -o $lib $libobjs $deplibs $linker_flags' # ELF fi _LT_TAGVAR(hardcode_libdir_flag_spec, $1)='-R$libdir' _LT_TAGVAR(hardcode_direct, $1)=yes _LT_TAGVAR(hardcode_shlibpath_var, $1)=no ;; newsos6) _LT_TAGVAR(archive_cmds, $1)='$LD -G -h $soname -o $lib $libobjs $deplibs $linker_flags' _LT_TAGVAR(hardcode_direct, $1)=yes _LT_TAGVAR(hardcode_libdir_flag_spec, $1)='${wl}-rpath ${wl}$libdir' _LT_TAGVAR(hardcode_libdir_separator, $1)=: _LT_TAGVAR(hardcode_shlibpath_var, $1)=no ;; *nto* | *qnx*) ;; openbsd*) if test -f /usr/libexec/ld.so; then _LT_TAGVAR(hardcode_direct, $1)=yes _LT_TAGVAR(hardcode_shlibpath_var, $1)=no _LT_TAGVAR(hardcode_direct_absolute, $1)=yes if test -z "`echo __ELF__ | $CC -E - | $GREP __ELF__`" || test "$host_os-$host_cpu" = "openbsd2.8-powerpc"; then _LT_TAGVAR(archive_cmds, $1)='$CC -shared $pic_flag -o $lib $libobjs $deplibs $compiler_flags' _LT_TAGVAR(archive_expsym_cmds, $1)='$CC -shared $pic_flag -o $lib $libobjs $deplibs $compiler_flags ${wl}-retain-symbols-file,$export_symbols' _LT_TAGVAR(hardcode_libdir_flag_spec, $1)='${wl}-rpath,$libdir' _LT_TAGVAR(export_dynamic_flag_spec, $1)='${wl}-E' else case $host_os in openbsd[[01]].* | openbsd2.[[0-7]] | openbsd2.[[0-7]].*) _LT_TAGVAR(archive_cmds, $1)='$LD -Bshareable -o $lib $libobjs $deplibs $linker_flags' _LT_TAGVAR(hardcode_libdir_flag_spec, $1)='-R$libdir' ;; *) _LT_TAGVAR(archive_cmds, $1)='$CC -shared $pic_flag -o $lib $libobjs $deplibs $compiler_flags' _LT_TAGVAR(hardcode_libdir_flag_spec, $1)='${wl}-rpath,$libdir' ;; esac fi else _LT_TAGVAR(ld_shlibs, $1)=no fi ;; os2*) _LT_TAGVAR(hardcode_libdir_flag_spec, $1)='-L$libdir' _LT_TAGVAR(hardcode_minus_L, $1)=yes _LT_TAGVAR(allow_undefined_flag, $1)=unsupported _LT_TAGVAR(archive_cmds, $1)='$ECHO "LIBRARY $libname INITINSTANCE" > $output_objdir/$libname.def~$ECHO "DESCRIPTION \"$libname\"" >> $output_objdir/$libname.def~$ECHO DATA >> $output_objdir/$libname.def~$ECHO " SINGLE NONSHARED" >> $output_objdir/$libname.def~$ECHO EXPORTS >> $output_objdir/$libname.def~emxexp $libobjs >> $output_objdir/$libname.def~$CC -Zdll -Zcrtdll -o $lib $libobjs $deplibs $compiler_flags $output_objdir/$libname.def' _LT_TAGVAR(old_archive_from_new_cmds, $1)='emximp -o $output_objdir/$libname.a $output_objdir/$libname.def' ;; 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do printf "%s %s\\n" -exported_symbol "\$i" >> $lib.exp; done; printf "%s\\n" "-hidden">> $lib.exp~ $CC -shared${allow_undefined_flag} ${wl}-input ${wl}$lib.exp $compiler_flags $libobjs $deplibs -soname $soname `test -n "$verstring" && $ECHO "X-set_version $verstring" | $Xsed` -update_registry ${output_objdir}/so_locations -o $lib~$RM $lib.exp' # Both c and cxx compiler support -rpath directly _LT_TAGVAR(hardcode_libdir_flag_spec, $1)='-rpath $libdir' fi _LT_TAGVAR(archive_cmds_need_lc, $1)='no' _LT_TAGVAR(hardcode_libdir_separator, $1)=: ;; solaris*) _LT_TAGVAR(no_undefined_flag, $1)=' -z defs' if test "$GCC" = yes; then wlarc='${wl}' _LT_TAGVAR(archive_cmds, $1)='$CC -shared ${wl}-z ${wl}text ${wl}-h ${wl}$soname -o $lib $libobjs $deplibs $compiler_flags' _LT_TAGVAR(archive_expsym_cmds, $1)='echo "{ global:" > $lib.exp~cat $export_symbols | $SED -e "s/\(.*\)/\1;/" >> $lib.exp~echo "local: *; };" >> $lib.exp~ $CC -shared ${wl}-z ${wl}text ${wl}-M ${wl}$lib.exp ${wl}-h ${wl}$soname -o $lib $libobjs $deplibs $compiler_flags~$RM $lib.exp' else case `$CC -V 2>&1` in *"Compilers 5.0"*) wlarc='' _LT_TAGVAR(archive_cmds, $1)='$LD -G${allow_undefined_flag} -h $soname -o $lib $libobjs $deplibs $linker_flags' _LT_TAGVAR(archive_expsym_cmds, $1)='echo "{ global:" > $lib.exp~cat $export_symbols | $SED -e "s/\(.*\)/\1;/" >> $lib.exp~echo "local: *; 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AC_MSG_CHECKING([whether -lc should be explicitly linked in]) $RM conftest* echo "$lt_simple_compile_test_code" > conftest.$ac_ext if AC_TRY_EVAL(ac_compile) 2>conftest.err; then soname=conftest lib=conftest libobjs=conftest.$ac_objext deplibs= wl=$_LT_TAGVAR(lt_prog_compiler_wl, $1) pic_flag=$_LT_TAGVAR(lt_prog_compiler_pic, $1) compiler_flags=-v linker_flags=-v verstring= output_objdir=. libname=conftest lt_save_allow_undefined_flag=$_LT_TAGVAR(allow_undefined_flag, $1) _LT_TAGVAR(allow_undefined_flag, $1)= if AC_TRY_EVAL(_LT_TAGVAR(archive_cmds, $1) 2\>\&1 \| $GREP \" -lc \" \>/dev/null 2\>\&1) then _LT_TAGVAR(archive_cmds_need_lc, $1)=no else _LT_TAGVAR(archive_cmds_need_lc, $1)=yes fi _LT_TAGVAR(allow_undefined_flag, $1)=$lt_save_allow_undefined_flag else cat conftest.err 1>&5 fi $RM conftest* AC_MSG_RESULT([$_LT_TAGVAR(archive_cmds_need_lc, $1)]) ;; esac fi ;; esac _LT_TAGDECL([build_libtool_need_lc], [archive_cmds_need_lc], [0], [Whether or not to add -lc for building shared libraries]) _LT_TAGDECL([allow_libtool_libs_with_static_runtimes], [enable_shared_with_static_runtimes], [0], [Whether or not to disallow shared libs when runtime libs are static]) _LT_TAGDECL([], [export_dynamic_flag_spec], [1], [Compiler flag to allow reflexive dlopens]) _LT_TAGDECL([], [whole_archive_flag_spec], [1], [Compiler flag to generate shared objects directly from archives]) _LT_TAGDECL([], [compiler_needs_object], [1], [Whether the compiler copes with passing no objects directly]) _LT_TAGDECL([], [old_archive_from_new_cmds], [2], [Create an old-style archive from a shared archive]) _LT_TAGDECL([], [old_archive_from_expsyms_cmds], [2], [Create a temporary old-style archive to link instead of a shared archive]) _LT_TAGDECL([], [archive_cmds], [2], [Commands used to build a shared archive]) _LT_TAGDECL([], [archive_expsym_cmds], [2]) _LT_TAGDECL([], [module_cmds], [2], [Commands used to build a loadable module if different from building a shared archive.]) _LT_TAGDECL([], [module_expsym_cmds], [2]) _LT_TAGDECL([], [with_gnu_ld], [1], [Whether we are building with GNU ld or not]) _LT_TAGDECL([], [allow_undefined_flag], [1], [Flag that allows shared libraries with undefined symbols to be built]) _LT_TAGDECL([], [no_undefined_flag], [1], [Flag that enforces no undefined symbols]) _LT_TAGDECL([], [hardcode_libdir_flag_spec], [1], [Flag to hardcode $libdir into a binary during linking. 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" >&6; } if test "${ac_cv_prog_OBJDUMP+set}" = set; then : $as_echo_n "(cached) " >&6 else if test -n "$OBJDUMP"; then ac_cv_prog_OBJDUMP="$OBJDUMP" # Let the user override the test. else as_save_IFS=$IFS; IFS=$PATH_SEPARATOR for as_dir in $PATH do IFS=$as_save_IFS test -z "$as_dir" && as_dir=. for ac_exec_ext in '' $ac_executable_extensions; do if { test -f "$as_dir/$ac_word$ac_exec_ext" && $as_test_x "$as_dir/$ac_word$ac_exec_ext"; }; then ac_cv_prog_OBJDUMP="${ac_tool_prefix}objdump" $as_echo "$as_me:${as_lineno-$LINENO}: found $as_dir/$ac_word$ac_exec_ext" >&5 break 2 fi done done IFS=$as_save_IFS fi fi OBJDUMP=$ac_cv_prog_OBJDUMP if test -n "$OBJDUMP"; then { $as_echo "$as_me:${as_lineno-$LINENO}: result: $OBJDUMP" >&5 $as_echo "$OBJDUMP" >&6; } else { $as_echo "$as_me:${as_lineno-$LINENO}: result: no" >&5 $as_echo "no" >&6; } fi fi if test -z "$ac_cv_prog_OBJDUMP"; then ac_ct_OBJDUMP=$OBJDUMP # Extract the first word of "objdump", so it can be a program name with args. set dummy objdump; ac_word=$2 { $as_echo "$as_me:${as_lineno-$LINENO}: checking for $ac_word" >&5 $as_echo_n "checking for $ac_word... " >&6; } if test "${ac_cv_prog_ac_ct_OBJDUMP+set}" = set; then : $as_echo_n "(cached) " >&6 else if test -n "$ac_ct_OBJDUMP"; then ac_cv_prog_ac_ct_OBJDUMP="$ac_ct_OBJDUMP" # Let the user override the test. else as_save_IFS=$IFS; IFS=$PATH_SEPARATOR for as_dir in $PATH do IFS=$as_save_IFS test -z "$as_dir" && as_dir=. for ac_exec_ext in '' $ac_executable_extensions; do if { test -f "$as_dir/$ac_word$ac_exec_ext" && $as_test_x "$as_dir/$ac_word$ac_exec_ext"; }; then ac_cv_prog_ac_ct_OBJDUMP="objdump" $as_echo "$as_me:${as_lineno-$LINENO}: found $as_dir/$ac_word$ac_exec_ext" >&5 break 2 fi done done IFS=$as_save_IFS fi fi ac_ct_OBJDUMP=$ac_cv_prog_ac_ct_OBJDUMP if test -n "$ac_ct_OBJDUMP"; then { $as_echo "$as_me:${as_lineno-$LINENO}: result: $ac_ct_OBJDUMP" >&5 $as_echo "$ac_ct_OBJDUMP" >&6; } else { $as_echo "$as_me:${as_lineno-$LINENO}: result: no" >&5 $as_echo "no" >&6; } fi if test "x$ac_ct_OBJDUMP" = x; then OBJDUMP="false" else case $cross_compiling:$ac_tool_warned in yes:) { $as_echo "$as_me:${as_lineno-$LINENO}: WARNING: using cross tools not prefixed with host triplet" >&5 $as_echo "$as_me: WARNING: using cross tools not prefixed with host triplet" >&2;} ac_tool_warned=yes ;; esac OBJDUMP=$ac_ct_OBJDUMP fi else OBJDUMP="$ac_cv_prog_OBJDUMP" fi test -z "$OBJDUMP" && OBJDUMP=objdump { $as_echo "$as_me:${as_lineno-$LINENO}: checking how to recognize dependent libraries" >&5 $as_echo_n "checking how to recognize dependent libraries... " >&6; } if test "${lt_cv_deplibs_check_method+set}" = set; then : $as_echo_n "(cached) " >&6 else lt_cv_file_magic_cmd='$MAGIC_CMD' lt_cv_file_magic_test_file= lt_cv_deplibs_check_method='unknown' # Need to set the preceding variable on all platforms that support # interlibrary dependencies. # 'none' -- dependencies not supported. # `unknown' -- same as none, but documents that we really don't know. # 'pass_all' -- all dependencies passed with no checks. # 'test_compile' -- check by making test program. # 'file_magic [[regex]]' -- check by looking for files in library path # which responds to the $file_magic_cmd with a given extended regex. # If you have `file' or equivalent on your system and you're not sure # whether `pass_all' will *always* work, you probably want this one. case $host_os in aix[4-9]*) lt_cv_deplibs_check_method=pass_all ;; beos*) lt_cv_deplibs_check_method=pass_all ;; bsdi[45]*) lt_cv_deplibs_check_method='file_magic ELF [0-9][0-9]*-bit [ML]SB (shared object|dynamic lib)' lt_cv_file_magic_cmd='/usr/bin/file -L' lt_cv_file_magic_test_file=/shlib/libc.so ;; cygwin*) # func_win32_libid is a shell function defined in ltmain.sh lt_cv_deplibs_check_method='file_magic ^x86 archive import|^x86 DLL' lt_cv_file_magic_cmd='func_win32_libid' ;; mingw* | pw32*) # Base MSYS/MinGW do not provide the 'file' command needed by # func_win32_libid shell function, so use a weaker test based on 'objdump', # unless we find 'file', for example because we are cross-compiling. if ( file / ) >/dev/null 2>&1; then lt_cv_deplibs_check_method='file_magic ^x86 archive import|^x86 DLL' lt_cv_file_magic_cmd='func_win32_libid' else lt_cv_deplibs_check_method='file_magic file format pei*-i386(.*architecture: i386)?' lt_cv_file_magic_cmd='$OBJDUMP -f' fi ;; cegcc) # use the weaker test based on 'objdump'. See mingw*. lt_cv_deplibs_check_method='file_magic file format pe-arm-.*little(.*architecture: arm)?' lt_cv_file_magic_cmd='$OBJDUMP -f' ;; darwin* | rhapsody*) lt_cv_deplibs_check_method=pass_all ;; freebsd* | dragonfly*) if echo __ELF__ | $CC -E - | $GREP __ELF__ > /dev/null; then case $host_cpu in i*86 ) # Not sure whether the presence of OpenBSD here was a mistake. # Let's accept both of them until this is cleared up. lt_cv_deplibs_check_method='file_magic (FreeBSD|OpenBSD|DragonFly)/i[3-9]86 (compact )?demand paged shared library' lt_cv_file_magic_cmd=/usr/bin/file lt_cv_file_magic_test_file=`echo /usr/lib/libc.so.*` ;; esac else lt_cv_deplibs_check_method=pass_all fi ;; gnu*) lt_cv_deplibs_check_method=pass_all ;; hpux10.20* | hpux11*) lt_cv_file_magic_cmd=/usr/bin/file case $host_cpu in ia64*) lt_cv_deplibs_check_method='file_magic (s[0-9][0-9][0-9]|ELF-[0-9][0-9]) shared object file - IA64' lt_cv_file_magic_test_file=/usr/lib/hpux32/libc.so ;; hppa*64*) lt_cv_deplibs_check_method='file_magic (s[0-9][0-9][0-9]|ELF-[0-9][0-9]) shared object file - PA-RISC [0-9].[0-9]' lt_cv_file_magic_test_file=/usr/lib/pa20_64/libc.sl ;; *) lt_cv_deplibs_check_method='file_magic (s[0-9][0-9][0-9]|PA-RISC[0-9].[0-9]) shared library' lt_cv_file_magic_test_file=/usr/lib/libc.sl ;; esac ;; interix[3-9]*) # PIC code is broken on Interix 3.x, that's why |\.a not |_pic\.a here lt_cv_deplibs_check_method='match_pattern /lib[^/]+(\.so|\.a)$' ;; irix5* | irix6* | nonstopux*) case $LD in *-32|*"-32 ") libmagic=32-bit;; *-n32|*"-n32 ") libmagic=N32;; *-64|*"-64 ") libmagic=64-bit;; *) libmagic=never-match;; esac lt_cv_deplibs_check_method=pass_all ;; # This must be Linux ELF. linux* | k*bsd*-gnu | kopensolaris*-gnu) lt_cv_deplibs_check_method=pass_all ;; netbsd* | netbsdelf*-gnu) if echo __ELF__ | $CC -E - | $GREP __ELF__ > /dev/null; then lt_cv_deplibs_check_method='match_pattern /lib[^/]+(\.so\.[0-9]+\.[0-9]+|_pic\.a)$' else lt_cv_deplibs_check_method='match_pattern /lib[^/]+(\.so|_pic\.a)$' fi ;; newos6*) lt_cv_deplibs_check_method='file_magic ELF [0-9][0-9]*-bit [ML]SB (executable|dynamic lib)' lt_cv_file_magic_cmd=/usr/bin/file lt_cv_file_magic_test_file=/usr/lib/libnls.so ;; *nto* | *qnx*) lt_cv_deplibs_check_method=pass_all ;; openbsd*) if test -z "`echo __ELF__ | $CC -E - | $GREP __ELF__`" || test "$host_os-$host_cpu" = "openbsd2.8-powerpc"; then lt_cv_deplibs_check_method='match_pattern /lib[^/]+(\.so\.[0-9]+\.[0-9]+|\.so|_pic\.a)$' else lt_cv_deplibs_check_method='match_pattern /lib[^/]+(\.so\.[0-9]+\.[0-9]+|_pic\.a)$' fi ;; osf3* | osf4* | osf5*) lt_cv_deplibs_check_method=pass_all ;; rdos*) lt_cv_deplibs_check_method=pass_all ;; solaris*) lt_cv_deplibs_check_method=pass_all ;; sysv5* | sco3.2v5* | sco5v6* | unixware* | OpenUNIX* | sysv4*uw2*) lt_cv_deplibs_check_method=pass_all ;; sysv4 | sysv4.3*) case $host_vendor in motorola) lt_cv_deplibs_check_method='file_magic ELF [0-9][0-9]*-bit [ML]SB (shared object|dynamic lib) M[0-9][0-9]* Version [0-9]' lt_cv_file_magic_test_file=`echo /usr/lib/libc.so*` ;; ncr) lt_cv_deplibs_check_method=pass_all ;; sequent) lt_cv_file_magic_cmd='/bin/file' lt_cv_deplibs_check_method='file_magic ELF [0-9][0-9]*-bit [LM]SB (shared object|dynamic lib )' ;; sni) lt_cv_file_magic_cmd='/bin/file' lt_cv_deplibs_check_method="file_magic ELF [0-9][0-9]*-bit [LM]SB dynamic lib" lt_cv_file_magic_test_file=/lib/libc.so ;; siemens) lt_cv_deplibs_check_method=pass_all ;; pc) lt_cv_deplibs_check_method=pass_all ;; esac ;; tpf*) lt_cv_deplibs_check_method=pass_all ;; esac fi { $as_echo "$as_me:${as_lineno-$LINENO}: result: $lt_cv_deplibs_check_method" >&5 $as_echo "$lt_cv_deplibs_check_method" >&6; } file_magic_cmd=$lt_cv_file_magic_cmd deplibs_check_method=$lt_cv_deplibs_check_method test -z "$deplibs_check_method" && deplibs_check_method=unknown if test -n "$ac_tool_prefix"; then # Extract the first word of "${ac_tool_prefix}ar", so it can be a program name with args. set dummy ${ac_tool_prefix}ar; ac_word=$2 { $as_echo "$as_me:${as_lineno-$LINENO}: checking for $ac_word" >&5 $as_echo_n "checking for $ac_word... " >&6; } if test "${ac_cv_prog_AR+set}" = set; then : $as_echo_n "(cached) " >&6 else if test -n "$AR"; then ac_cv_prog_AR="$AR" # Let the user override the test. else as_save_IFS=$IFS; IFS=$PATH_SEPARATOR for as_dir in $PATH do IFS=$as_save_IFS test -z "$as_dir" && as_dir=. for ac_exec_ext in '' $ac_executable_extensions; do if { test -f "$as_dir/$ac_word$ac_exec_ext" && $as_test_x "$as_dir/$ac_word$ac_exec_ext"; }; then ac_cv_prog_AR="${ac_tool_prefix}ar" $as_echo "$as_me:${as_lineno-$LINENO}: found $as_dir/$ac_word$ac_exec_ext" >&5 break 2 fi done done IFS=$as_save_IFS fi fi AR=$ac_cv_prog_AR if test -n "$AR"; then { $as_echo "$as_me:${as_lineno-$LINENO}: result: $AR" >&5 $as_echo "$AR" >&6; } else { $as_echo "$as_me:${as_lineno-$LINENO}: result: no" >&5 $as_echo "no" >&6; } fi fi if test -z "$ac_cv_prog_AR"; then ac_ct_AR=$AR # Extract the first word of "ar", so it can be a program name with args. set dummy ar; ac_word=$2 { $as_echo "$as_me:${as_lineno-$LINENO}: checking for $ac_word" >&5 $as_echo_n "checking for $ac_word... " >&6; } if test "${ac_cv_prog_ac_ct_AR+set}" = set; then : $as_echo_n "(cached) " >&6 else if test -n "$ac_ct_AR"; then ac_cv_prog_ac_ct_AR="$ac_ct_AR" # Let the user override the test. else as_save_IFS=$IFS; IFS=$PATH_SEPARATOR for as_dir in $PATH do IFS=$as_save_IFS test -z "$as_dir" && as_dir=. for ac_exec_ext in '' $ac_executable_extensions; do if { test -f "$as_dir/$ac_word$ac_exec_ext" && $as_test_x "$as_dir/$ac_word$ac_exec_ext"; }; then ac_cv_prog_ac_ct_AR="ar" $as_echo "$as_me:${as_lineno-$LINENO}: found $as_dir/$ac_word$ac_exec_ext" >&5 break 2 fi done done IFS=$as_save_IFS fi fi ac_ct_AR=$ac_cv_prog_ac_ct_AR if test -n "$ac_ct_AR"; then { $as_echo "$as_me:${as_lineno-$LINENO}: result: $ac_ct_AR" >&5 $as_echo "$ac_ct_AR" >&6; } else { $as_echo "$as_me:${as_lineno-$LINENO}: result: no" >&5 $as_echo "no" >&6; } fi if test "x$ac_ct_AR" = x; then AR="false" else case $cross_compiling:$ac_tool_warned in yes:) { $as_echo "$as_me:${as_lineno-$LINENO}: WARNING: using cross tools not prefixed with host triplet" >&5 $as_echo "$as_me: WARNING: using cross tools not prefixed with host triplet" >&2;} ac_tool_warned=yes ;; esac AR=$ac_ct_AR fi else AR="$ac_cv_prog_AR" fi test -z "$AR" && AR=ar test -z "$AR_FLAGS" && AR_FLAGS=cru if test -n "$ac_tool_prefix"; then # Extract the first word of "${ac_tool_prefix}strip", so it can be a program name with args. set dummy ${ac_tool_prefix}strip; ac_word=$2 { $as_echo "$as_me:${as_lineno-$LINENO}: checking for $ac_word" >&5 $as_echo_n "checking for $ac_word... " >&6; } if test "${ac_cv_prog_STRIP+set}" = set; then : $as_echo_n "(cached) " >&6 else if test -n "$STRIP"; then ac_cv_prog_STRIP="$STRIP" # Let the user override the test. else as_save_IFS=$IFS; IFS=$PATH_SEPARATOR for as_dir in $PATH do IFS=$as_save_IFS test -z "$as_dir" && as_dir=. for ac_exec_ext in '' $ac_executable_extensions; do if { test -f "$as_dir/$ac_word$ac_exec_ext" && $as_test_x "$as_dir/$ac_word$ac_exec_ext"; }; then ac_cv_prog_STRIP="${ac_tool_prefix}strip" $as_echo "$as_me:${as_lineno-$LINENO}: found $as_dir/$ac_word$ac_exec_ext" >&5 break 2 fi done done IFS=$as_save_IFS fi fi STRIP=$ac_cv_prog_STRIP if test -n "$STRIP"; then { $as_echo "$as_me:${as_lineno-$LINENO}: result: $STRIP" >&5 $as_echo "$STRIP" >&6; } else { $as_echo "$as_me:${as_lineno-$LINENO}: result: no" >&5 $as_echo "no" >&6; } fi fi if test -z "$ac_cv_prog_STRIP"; then ac_ct_STRIP=$STRIP # Extract the first word of "strip", so it can be a program name with args. set dummy strip; ac_word=$2 { $as_echo "$as_me:${as_lineno-$LINENO}: checking for $ac_word" >&5 $as_echo_n "checking for $ac_word... " >&6; } if test "${ac_cv_prog_ac_ct_STRIP+set}" = set; then : $as_echo_n "(cached) " >&6 else if test -n "$ac_ct_STRIP"; then ac_cv_prog_ac_ct_STRIP="$ac_ct_STRIP" # Let the user override the test. else as_save_IFS=$IFS; IFS=$PATH_SEPARATOR for as_dir in $PATH do IFS=$as_save_IFS test -z "$as_dir" && as_dir=. for ac_exec_ext in '' $ac_executable_extensions; do if { test -f "$as_dir/$ac_word$ac_exec_ext" && $as_test_x "$as_dir/$ac_word$ac_exec_ext"; }; then ac_cv_prog_ac_ct_STRIP="strip" $as_echo "$as_me:${as_lineno-$LINENO}: found $as_dir/$ac_word$ac_exec_ext" >&5 break 2 fi done done IFS=$as_save_IFS fi fi ac_ct_STRIP=$ac_cv_prog_ac_ct_STRIP if test -n "$ac_ct_STRIP"; then { $as_echo "$as_me:${as_lineno-$LINENO}: result: $ac_ct_STRIP" >&5 $as_echo "$ac_ct_STRIP" >&6; } else { $as_echo "$as_me:${as_lineno-$LINENO}: result: no" >&5 $as_echo "no" >&6; } fi if test "x$ac_ct_STRIP" = x; then STRIP=":" else case $cross_compiling:$ac_tool_warned in yes:) { $as_echo "$as_me:${as_lineno-$LINENO}: WARNING: using cross tools not prefixed with host triplet" >&5 $as_echo "$as_me: WARNING: using cross tools not prefixed with host triplet" >&2;} ac_tool_warned=yes ;; esac STRIP=$ac_ct_STRIP fi else STRIP="$ac_cv_prog_STRIP" fi test -z "$STRIP" && STRIP=: if test -n "$ac_tool_prefix"; then # Extract the first word of "${ac_tool_prefix}ranlib", so it can be a program name with args. set dummy ${ac_tool_prefix}ranlib; ac_word=$2 { $as_echo "$as_me:${as_lineno-$LINENO}: checking for $ac_word" >&5 $as_echo_n "checking for $ac_word... " >&6; } if test "${ac_cv_prog_RANLIB+set}" = set; then : $as_echo_n "(cached) " >&6 else if test -n "$RANLIB"; then ac_cv_prog_RANLIB="$RANLIB" # Let the user override the test. else as_save_IFS=$IFS; IFS=$PATH_SEPARATOR for as_dir in $PATH do IFS=$as_save_IFS test -z "$as_dir" && as_dir=. for ac_exec_ext in '' $ac_executable_extensions; do if { test -f "$as_dir/$ac_word$ac_exec_ext" && $as_test_x "$as_dir/$ac_word$ac_exec_ext"; }; then ac_cv_prog_RANLIB="${ac_tool_prefix}ranlib" $as_echo "$as_me:${as_lineno-$LINENO}: found $as_dir/$ac_word$ac_exec_ext" >&5 break 2 fi done done IFS=$as_save_IFS fi fi RANLIB=$ac_cv_prog_RANLIB if test -n "$RANLIB"; then { $as_echo "$as_me:${as_lineno-$LINENO}: result: $RANLIB" >&5 $as_echo "$RANLIB" >&6; } else { $as_echo "$as_me:${as_lineno-$LINENO}: result: no" >&5 $as_echo "no" >&6; } fi fi if test -z "$ac_cv_prog_RANLIB"; then ac_ct_RANLIB=$RANLIB # Extract the first word of "ranlib", so it can be a program name with args. set dummy ranlib; ac_word=$2 { $as_echo "$as_me:${as_lineno-$LINENO}: checking for $ac_word" >&5 $as_echo_n "checking for $ac_word... " >&6; } if test "${ac_cv_prog_ac_ct_RANLIB+set}" = set; then : $as_echo_n "(cached) " >&6 else if test -n "$ac_ct_RANLIB"; then ac_cv_prog_ac_ct_RANLIB="$ac_ct_RANLIB" # Let the user override the test. else as_save_IFS=$IFS; IFS=$PATH_SEPARATOR for as_dir in $PATH do IFS=$as_save_IFS test -z "$as_dir" && as_dir=. for ac_exec_ext in '' $ac_executable_extensions; do if { test -f "$as_dir/$ac_word$ac_exec_ext" && $as_test_x "$as_dir/$ac_word$ac_exec_ext"; }; then ac_cv_prog_ac_ct_RANLIB="ranlib" $as_echo "$as_me:${as_lineno-$LINENO}: found $as_dir/$ac_word$ac_exec_ext" >&5 break 2 fi done done IFS=$as_save_IFS fi fi ac_ct_RANLIB=$ac_cv_prog_ac_ct_RANLIB if test -n "$ac_ct_RANLIB"; then { $as_echo "$as_me:${as_lineno-$LINENO}: result: $ac_ct_RANLIB" >&5 $as_echo "$ac_ct_RANLIB" >&6; } else { $as_echo "$as_me:${as_lineno-$LINENO}: result: no" >&5 $as_echo "no" >&6; } fi if test "x$ac_ct_RANLIB" = x; then RANLIB=":" else case $cross_compiling:$ac_tool_warned in yes:) { $as_echo "$as_me:${as_lineno-$LINENO}: WARNING: using cross tools not prefixed with host triplet" >&5 $as_echo "$as_me: WARNING: using cross tools not prefixed with host triplet" >&2;} ac_tool_warned=yes ;; esac RANLIB=$ac_ct_RANLIB fi else RANLIB="$ac_cv_prog_RANLIB" fi test -z "$RANLIB" && RANLIB=: # Determine commands to create old-style static archives. old_archive_cmds='$AR $AR_FLAGS $oldlib$oldobjs' old_postinstall_cmds='chmod 644 $oldlib' old_postuninstall_cmds= if test -n "$RANLIB"; then case $host_os in openbsd*) old_postinstall_cmds="$old_postinstall_cmds~\$RANLIB -t \$oldlib" ;; *) old_postinstall_cmds="$old_postinstall_cmds~\$RANLIB \$oldlib" ;; esac old_archive_cmds="$old_archive_cmds~\$RANLIB \$oldlib" fi # If no C compiler was specified, use CC. LTCC=${LTCC-"$CC"} # If no C compiler flags were specified, use CFLAGS. LTCFLAGS=${LTCFLAGS-"$CFLAGS"} # Allow CC to be a program name with arguments. compiler=$CC # Check for command to grab the raw symbol name followed by C symbol from nm. { $as_echo "$as_me:${as_lineno-$LINENO}: checking command to parse $NM output from $compiler object" >&5 $as_echo_n "checking command to parse $NM output from $compiler object... " >&6; } if test "${lt_cv_sys_global_symbol_pipe+set}" = set; then : $as_echo_n "(cached) " >&6 else # These are sane defaults that work on at least a few old systems. # [They come from Ultrix. What could be older than Ultrix?!! ;)] # Character class describing NM global symbol codes. symcode='[BCDEGRST]' # Regexp to match symbols that can be accessed directly from C. sympat='\([_A-Za-z][_A-Za-z0-9]*\)' # Define system-specific variables. case $host_os in aix*) symcode='[BCDT]' ;; cygwin* | mingw* | pw32* | cegcc*) symcode='[ABCDGISTW]' ;; hpux*) if test "$host_cpu" = ia64; then symcode='[ABCDEGRST]' fi ;; irix* | nonstopux*) symcode='[BCDEGRST]' ;; osf*) symcode='[BCDEGQRST]' ;; solaris*) symcode='[BDRT]' ;; sco3.2v5*) symcode='[DT]' ;; sysv4.2uw2*) symcode='[DT]' ;; sysv5* | sco5v6* | unixware* | OpenUNIX*) symcode='[ABDT]' ;; sysv4) symcode='[DFNSTU]' ;; esac # If we're using GNU nm, then use its standard symbol codes. case `$NM -V 2>&1` in *GNU* | *'with BFD'*) symcode='[ABCDGIRSTW]' ;; esac # Transform an extracted symbol line into a proper C declaration. # Some systems (esp. on ia64) link data and code symbols differently, # so use this general approach. lt_cv_sys_global_symbol_to_cdecl="sed -n -e 's/^T .* \(.*\)$/extern int \1();/p' -e 's/^$symcode* .* \(.*\)$/extern char \1;/p'" # Transform an extracted symbol line into symbol name and symbol address lt_cv_sys_global_symbol_to_c_name_address="sed -n -e 's/^: \([^ ]*\) $/ {\\\"\1\\\", (void *) 0},/p' -e 's/^$symcode* \([^ ]*\) \([^ ]*\)$/ {\"\2\", (void *) \&\2},/p'" lt_cv_sys_global_symbol_to_c_name_address_lib_prefix="sed -n -e 's/^: \([^ ]*\) $/ {\\\"\1\\\", (void *) 0},/p' -e 's/^$symcode* \([^ ]*\) \(lib[^ ]*\)$/ {\"\2\", (void *) \&\2},/p' -e 's/^$symcode* \([^ ]*\) \([^ ]*\)$/ {\"lib\2\", (void *) \&\2},/p'" # Handle CRLF in mingw tool chain opt_cr= case $build_os in mingw*) opt_cr=`$ECHO 'x\{0,1\}' | tr x '\015'` # option cr in regexp ;; esac # Try without a prefix underscore, then with it. for ac_symprfx in "" "_"; do # Transform symcode, sympat, and symprfx into a raw symbol and a C symbol. symxfrm="\\1 $ac_symprfx\\2 \\2" # Write the raw and C identifiers. if test "$lt_cv_nm_interface" = "MS dumpbin"; then # Fake it for dumpbin and say T for any non-static function # and D for any global variable. # Also find C++ and __fastcall symbols from MSVC++, # which start with @ or ?. lt_cv_sys_global_symbol_pipe="$AWK '"\ " {last_section=section; section=\$ 3};"\ " /Section length .*#relocs.*(pick any)/{hide[last_section]=1};"\ " \$ 0!~/External *\|/{next};"\ " / 0+ UNDEF /{next}; / UNDEF \([^|]\)*()/{next};"\ " {if(hide[section]) next};"\ " {f=0}; \$ 0~/\(\).*\|/{f=1}; {printf f ? \"T \" : \"D \"};"\ " {split(\$ 0, a, /\||\r/); split(a[2], s)};"\ " s[1]~/^[@?]/{print s[1], s[1]; next};"\ " s[1]~prfx {split(s[1],t,\"@\"); print t[1], substr(t[1],length(prfx))}"\ " ' prfx=^$ac_symprfx" else lt_cv_sys_global_symbol_pipe="sed -n -e 's/^.*[ ]\($symcode$symcode*\)[ ][ ]*$ac_symprfx$sympat$opt_cr$/$symxfrm/p'" fi # Check to see that the pipe works correctly. pipe_works=no rm -f conftest* cat > conftest.$ac_ext <<_LT_EOF #ifdef __cplusplus extern "C" { #endif char nm_test_var; void nm_test_func(void); void nm_test_func(void){} #ifdef __cplusplus } #endif int main(){nm_test_var='a';nm_test_func();return(0);} _LT_EOF if { { eval echo "\"\$as_me\":${as_lineno-$LINENO}: \"$ac_compile\""; } >&5 (eval $ac_compile) 2>&5 ac_status=$? $as_echo "$as_me:${as_lineno-$LINENO}: \$? = $ac_status" >&5 test $ac_status = 0; }; then # Now try to grab the symbols. nlist=conftest.nm if { { eval echo "\"\$as_me\":${as_lineno-$LINENO}: \"$NM conftest.$ac_objext \| $lt_cv_sys_global_symbol_pipe \> $nlist\""; } >&5 (eval $NM conftest.$ac_objext \| $lt_cv_sys_global_symbol_pipe \> $nlist) 2>&5 ac_status=$? $as_echo "$as_me:${as_lineno-$LINENO}: \$? = $ac_status" >&5 test $ac_status = 0; } && test -s "$nlist"; then # Try sorting and uniquifying the output. if sort "$nlist" | uniq > "$nlist"T; then mv -f "$nlist"T "$nlist" else rm -f "$nlist"T fi # Make sure that we snagged all the symbols we need. if $GREP ' nm_test_var$' "$nlist" >/dev/null; then if $GREP ' nm_test_func$' "$nlist" >/dev/null; then cat <<_LT_EOF > conftest.$ac_ext #ifdef __cplusplus extern "C" { #endif _LT_EOF # Now generate the symbol file. eval "$lt_cv_sys_global_symbol_to_cdecl"' < "$nlist" | $GREP -v main >> conftest.$ac_ext' cat <<_LT_EOF >> conftest.$ac_ext /* The mapping between symbol names and symbols. */ const struct { const char *name; void *address; } lt__PROGRAM__LTX_preloaded_symbols[] = { { "@PROGRAM@", (void *) 0 }, _LT_EOF $SED "s/^$symcode$symcode* \(.*\) \(.*\)$/ {\"\2\", (void *) \&\2},/" < "$nlist" | $GREP -v main >> conftest.$ac_ext cat <<\_LT_EOF >> conftest.$ac_ext {0, (void *) 0} }; /* This works around a problem in FreeBSD linker */ #ifdef FREEBSD_WORKAROUND static const void *lt_preloaded_setup() { return lt__PROGRAM__LTX_preloaded_symbols; } #endif #ifdef __cplusplus } #endif _LT_EOF # Now try linking the two files. mv conftest.$ac_objext conftstm.$ac_objext lt_save_LIBS="$LIBS" lt_save_CFLAGS="$CFLAGS" LIBS="conftstm.$ac_objext" CFLAGS="$CFLAGS$lt_prog_compiler_no_builtin_flag" if { { eval echo "\"\$as_me\":${as_lineno-$LINENO}: \"$ac_link\""; } >&5 (eval $ac_link) 2>&5 ac_status=$? $as_echo "$as_me:${as_lineno-$LINENO}: \$? = $ac_status" >&5 test $ac_status = 0; } && test -s conftest${ac_exeext}; then pipe_works=yes fi LIBS="$lt_save_LIBS" CFLAGS="$lt_save_CFLAGS" else echo "cannot find nm_test_func in $nlist" >&5 fi else echo "cannot find nm_test_var in $nlist" >&5 fi else echo "cannot run $lt_cv_sys_global_symbol_pipe" >&5 fi else echo "$progname: failed program was:" >&5 cat conftest.$ac_ext >&5 fi rm -rf conftest* conftst* # Do not use the global_symbol_pipe unless it works. if test "$pipe_works" = yes; then break else lt_cv_sys_global_symbol_pipe= fi done fi if test -z "$lt_cv_sys_global_symbol_pipe"; then lt_cv_sys_global_symbol_to_cdecl= fi if test -z "$lt_cv_sys_global_symbol_pipe$lt_cv_sys_global_symbol_to_cdecl"; then { $as_echo "$as_me:${as_lineno-$LINENO}: result: failed" >&5 $as_echo "failed" >&6; } else { $as_echo "$as_me:${as_lineno-$LINENO}: result: ok" >&5 $as_echo "ok" >&6; } fi # Check whether --enable-libtool-lock was given. if test "${enable_libtool_lock+set}" = set; then : enableval=$enable_libtool_lock; fi test "x$enable_libtool_lock" != xno && enable_libtool_lock=yes # Some flags need to be propagated to the compiler or linker for good # libtool support. case $host in ia64-*-hpux*) # Find out which ABI we are using. echo 'int i;' > conftest.$ac_ext if { { eval echo "\"\$as_me\":${as_lineno-$LINENO}: \"$ac_compile\""; } >&5 (eval $ac_compile) 2>&5 ac_status=$? $as_echo "$as_me:${as_lineno-$LINENO}: \$? = $ac_status" >&5 test $ac_status = 0; }; then case `/usr/bin/file conftest.$ac_objext` in *ELF-32*) HPUX_IA64_MODE="32" ;; *ELF-64*) HPUX_IA64_MODE="64" ;; esac fi rm -rf conftest* ;; *-*-irix6*) # Find out which ABI we are using. echo '#line 6173 "configure"' > conftest.$ac_ext if { { eval echo "\"\$as_me\":${as_lineno-$LINENO}: \"$ac_compile\""; } >&5 (eval $ac_compile) 2>&5 ac_status=$? $as_echo "$as_me:${as_lineno-$LINENO}: \$? = $ac_status" >&5 test $ac_status = 0; }; then if test "$lt_cv_prog_gnu_ld" = yes; then case `/usr/bin/file conftest.$ac_objext` in *32-bit*) LD="${LD-ld} -melf32bsmip" ;; *N32*) LD="${LD-ld} -melf32bmipn32" ;; *64-bit*) LD="${LD-ld} -melf64bmip" ;; esac else case `/usr/bin/file conftest.$ac_objext` in *32-bit*) LD="${LD-ld} -32" ;; *N32*) LD="${LD-ld} -n32" ;; *64-bit*) LD="${LD-ld} -64" ;; esac fi fi rm -rf conftest* ;; x86_64-*kfreebsd*-gnu|x86_64-*linux*|ppc*-*linux*|powerpc*-*linux*| \ s390*-*linux*|s390*-*tpf*|sparc*-*linux*) # Find out which ABI we are using. echo 'int i;' > conftest.$ac_ext if { { eval echo "\"\$as_me\":${as_lineno-$LINENO}: \"$ac_compile\""; } >&5 (eval $ac_compile) 2>&5 ac_status=$? $as_echo "$as_me:${as_lineno-$LINENO}: \$? = $ac_status" >&5 test $ac_status = 0; }; then case `/usr/bin/file conftest.o` in *32-bit*) case $host in x86_64-*kfreebsd*-gnu) LD="${LD-ld} -m elf_i386_fbsd" ;; x86_64-*linux*) LD="${LD-ld} -m elf_i386" ;; ppc64-*linux*|powerpc64-*linux*) LD="${LD-ld} -m elf32ppclinux" ;; s390x-*linux*) LD="${LD-ld} -m elf_s390" ;; sparc64-*linux*) LD="${LD-ld} -m elf32_sparc" ;; esac ;; *64-bit*) case $host in x86_64-*kfreebsd*-gnu) LD="${LD-ld} -m elf_x86_64_fbsd" ;; x86_64-*linux*) LD="${LD-ld} -m elf_x86_64" ;; ppc*-*linux*|powerpc*-*linux*) LD="${LD-ld} -m elf64ppc" ;; s390*-*linux*|s390*-*tpf*) LD="${LD-ld} -m elf64_s390" ;; sparc*-*linux*) LD="${LD-ld} -m elf64_sparc" ;; esac ;; esac fi rm -rf conftest* ;; *-*-sco3.2v5*) # On SCO OpenServer 5, we need -belf to get full-featured binaries. SAVE_CFLAGS="$CFLAGS" CFLAGS="$CFLAGS -belf" { $as_echo "$as_me:${as_lineno-$LINENO}: checking whether the C compiler needs -belf" >&5 $as_echo_n "checking whether the C compiler needs -belf... " >&6; } if test "${lt_cv_cc_needs_belf+set}" = set; then : $as_echo_n "(cached) " >&6 else ac_ext=c ac_cpp='$CPP $CPPFLAGS' ac_compile='$CC -c $CFLAGS $CPPFLAGS conftest.$ac_ext >&5' ac_link='$CC -o conftest$ac_exeext $CFLAGS $CPPFLAGS $LDFLAGS conftest.$ac_ext $LIBS >&5' ac_compiler_gnu=$ac_cv_c_compiler_gnu cat confdefs.h - <<_ACEOF >conftest.$ac_ext /* end confdefs.h. */ int main () { ; return 0; } _ACEOF if ac_fn_c_try_link "$LINENO"; then : lt_cv_cc_needs_belf=yes else lt_cv_cc_needs_belf=no fi rm -f core conftest.err conftest.$ac_objext \ conftest$ac_exeext conftest.$ac_ext ac_ext=c ac_cpp='$CPP $CPPFLAGS' ac_compile='$CC -c $CFLAGS $CPPFLAGS conftest.$ac_ext >&5' ac_link='$CC -o conftest$ac_exeext $CFLAGS $CPPFLAGS $LDFLAGS conftest.$ac_ext $LIBS >&5' ac_compiler_gnu=$ac_cv_c_compiler_gnu fi { $as_echo "$as_me:${as_lineno-$LINENO}: result: $lt_cv_cc_needs_belf" >&5 $as_echo "$lt_cv_cc_needs_belf" >&6; } if test x"$lt_cv_cc_needs_belf" != x"yes"; then # this is probably gcc 2.8.0, egcs 1.0 or newer; no need for -belf CFLAGS="$SAVE_CFLAGS" fi ;; sparc*-*solaris*) # Find out which ABI we are using. echo 'int i;' > conftest.$ac_ext if { { eval echo "\"\$as_me\":${as_lineno-$LINENO}: \"$ac_compile\""; } >&5 (eval $ac_compile) 2>&5 ac_status=$? $as_echo "$as_me:${as_lineno-$LINENO}: \$? = $ac_status" >&5 test $ac_status = 0; }; then case `/usr/bin/file conftest.o` in *64-bit*) case $lt_cv_prog_gnu_ld in yes*) LD="${LD-ld} -m elf64_sparc" ;; *) if ${LD-ld} -64 -r -o conftest2.o conftest.o >/dev/null 2>&1; then LD="${LD-ld} -64" fi ;; esac ;; esac fi rm -rf conftest* ;; esac need_locks="$enable_libtool_lock" case $host_os in rhapsody* | darwin*) if test -n "$ac_tool_prefix"; then # Extract the first word of "${ac_tool_prefix}dsymutil", so it can be a program name with args. set dummy ${ac_tool_prefix}dsymutil; ac_word=$2 { $as_echo "$as_me:${as_lineno-$LINENO}: checking for $ac_word" >&5 $as_echo_n "checking for $ac_word... " >&6; } if test "${ac_cv_prog_DSYMUTIL+set}" = set; then : $as_echo_n "(cached) " >&6 else if test -n "$DSYMUTIL"; then ac_cv_prog_DSYMUTIL="$DSYMUTIL" # Let the user override the test. else as_save_IFS=$IFS; IFS=$PATH_SEPARATOR for as_dir in $PATH do IFS=$as_save_IFS test -z "$as_dir" && as_dir=. for ac_exec_ext in '' $ac_executable_extensions; do if { test -f "$as_dir/$ac_word$ac_exec_ext" && $as_test_x "$as_dir/$ac_word$ac_exec_ext"; }; then ac_cv_prog_DSYMUTIL="${ac_tool_prefix}dsymutil" $as_echo "$as_me:${as_lineno-$LINENO}: found $as_dir/$ac_word$ac_exec_ext" >&5 break 2 fi done done IFS=$as_save_IFS fi fi DSYMUTIL=$ac_cv_prog_DSYMUTIL if test -n "$DSYMUTIL"; then { $as_echo "$as_me:${as_lineno-$LINENO}: result: $DSYMUTIL" >&5 $as_echo "$DSYMUTIL" >&6; } else { $as_echo "$as_me:${as_lineno-$LINENO}: result: no" >&5 $as_echo "no" >&6; } fi fi if test -z "$ac_cv_prog_DSYMUTIL"; then ac_ct_DSYMUTIL=$DSYMUTIL # Extract the first word of "dsymutil", so it can be a program name with args. set dummy dsymutil; ac_word=$2 { $as_echo "$as_me:${as_lineno-$LINENO}: checking for $ac_word" >&5 $as_echo_n "checking for $ac_word... " >&6; } if test "${ac_cv_prog_ac_ct_DSYMUTIL+set}" = set; then : $as_echo_n "(cached) " >&6 else if test -n "$ac_ct_DSYMUTIL"; then ac_cv_prog_ac_ct_DSYMUTIL="$ac_ct_DSYMUTIL" # Let the user override the test. else as_save_IFS=$IFS; IFS=$PATH_SEPARATOR for as_dir in $PATH do IFS=$as_save_IFS test -z "$as_dir" && as_dir=. for ac_exec_ext in '' $ac_executable_extensions; do if { test -f "$as_dir/$ac_word$ac_exec_ext" && $as_test_x "$as_dir/$ac_word$ac_exec_ext"; }; then ac_cv_prog_ac_ct_DSYMUTIL="dsymutil" $as_echo "$as_me:${as_lineno-$LINENO}: found $as_dir/$ac_word$ac_exec_ext" >&5 break 2 fi done done IFS=$as_save_IFS fi fi ac_ct_DSYMUTIL=$ac_cv_prog_ac_ct_DSYMUTIL if test -n "$ac_ct_DSYMUTIL"; then { $as_echo "$as_me:${as_lineno-$LINENO}: result: $ac_ct_DSYMUTIL" >&5 $as_echo "$ac_ct_DSYMUTIL" >&6; } else { $as_echo "$as_me:${as_lineno-$LINENO}: result: no" >&5 $as_echo "no" >&6; } fi if test "x$ac_ct_DSYMUTIL" = x; then DSYMUTIL=":" else case $cross_compiling:$ac_tool_warned in yes:) { $as_echo "$as_me:${as_lineno-$LINENO}: WARNING: using cross tools not prefixed with host triplet" >&5 $as_echo "$as_me: WARNING: using cross tools not prefixed with host triplet" >&2;} ac_tool_warned=yes ;; esac DSYMUTIL=$ac_ct_DSYMUTIL fi else DSYMUTIL="$ac_cv_prog_DSYMUTIL" fi if test -n "$ac_tool_prefix"; then # Extract the first word of "${ac_tool_prefix}nmedit", so it can be a program name with args. set dummy ${ac_tool_prefix}nmedit; ac_word=$2 { $as_echo "$as_me:${as_lineno-$LINENO}: checking for $ac_word" >&5 $as_echo_n "checking for $ac_word... " >&6; } if test "${ac_cv_prog_NMEDIT+set}" = set; then : $as_echo_n "(cached) " >&6 else if test -n "$NMEDIT"; then ac_cv_prog_NMEDIT="$NMEDIT" # Let the user override the test. else as_save_IFS=$IFS; IFS=$PATH_SEPARATOR for as_dir in $PATH do IFS=$as_save_IFS test -z "$as_dir" && as_dir=. for ac_exec_ext in '' $ac_executable_extensions; do if { test -f "$as_dir/$ac_word$ac_exec_ext" && $as_test_x "$as_dir/$ac_word$ac_exec_ext"; }; then ac_cv_prog_NMEDIT="${ac_tool_prefix}nmedit" $as_echo "$as_me:${as_lineno-$LINENO}: found $as_dir/$ac_word$ac_exec_ext" >&5 break 2 fi done done IFS=$as_save_IFS fi fi NMEDIT=$ac_cv_prog_NMEDIT if test -n "$NMEDIT"; then { $as_echo "$as_me:${as_lineno-$LINENO}: result: $NMEDIT" >&5 $as_echo "$NMEDIT" >&6; } else { $as_echo "$as_me:${as_lineno-$LINENO}: result: no" >&5 $as_echo "no" >&6; } fi fi if test -z "$ac_cv_prog_NMEDIT"; then ac_ct_NMEDIT=$NMEDIT # Extract the first word of "nmedit", so it can be a program name with args. set dummy nmedit; ac_word=$2 { $as_echo "$as_me:${as_lineno-$LINENO}: checking for $ac_word" >&5 $as_echo_n "checking for $ac_word... " >&6; } if test "${ac_cv_prog_ac_ct_NMEDIT+set}" = set; then : $as_echo_n "(cached) " >&6 else if test -n "$ac_ct_NMEDIT"; then ac_cv_prog_ac_ct_NMEDIT="$ac_ct_NMEDIT" # Let the user override the test. else as_save_IFS=$IFS; IFS=$PATH_SEPARATOR for as_dir in $PATH do IFS=$as_save_IFS test -z "$as_dir" && as_dir=. for ac_exec_ext in '' $ac_executable_extensions; do if { test -f "$as_dir/$ac_word$ac_exec_ext" && $as_test_x "$as_dir/$ac_word$ac_exec_ext"; }; then ac_cv_prog_ac_ct_NMEDIT="nmedit" $as_echo "$as_me:${as_lineno-$LINENO}: found $as_dir/$ac_word$ac_exec_ext" >&5 break 2 fi done done IFS=$as_save_IFS fi fi ac_ct_NMEDIT=$ac_cv_prog_ac_ct_NMEDIT if test -n "$ac_ct_NMEDIT"; then { $as_echo "$as_me:${as_lineno-$LINENO}: result: $ac_ct_NMEDIT" >&5 $as_echo "$ac_ct_NMEDIT" >&6; } else { $as_echo "$as_me:${as_lineno-$LINENO}: result: no" >&5 $as_echo "no" >&6; } fi if test "x$ac_ct_NMEDIT" = x; then NMEDIT=":" else case $cross_compiling:$ac_tool_warned in yes:) { $as_echo "$as_me:${as_lineno-$LINENO}: WARNING: using cross tools not prefixed with host triplet" >&5 $as_echo "$as_me: WARNING: using cross tools not prefixed with host triplet" >&2;} ac_tool_warned=yes ;; esac NMEDIT=$ac_ct_NMEDIT fi else NMEDIT="$ac_cv_prog_NMEDIT" fi if test -n "$ac_tool_prefix"; then # Extract the first word of "${ac_tool_prefix}lipo", so it can be a program name with args. set dummy ${ac_tool_prefix}lipo; ac_word=$2 { $as_echo "$as_me:${as_lineno-$LINENO}: checking for $ac_word" >&5 $as_echo_n "checking for $ac_word... " >&6; } if test "${ac_cv_prog_LIPO+set}" = set; then : $as_echo_n "(cached) " >&6 else if test -n "$LIPO"; then ac_cv_prog_LIPO="$LIPO" # Let the user override the test. else as_save_IFS=$IFS; IFS=$PATH_SEPARATOR for as_dir in $PATH do IFS=$as_save_IFS test -z "$as_dir" && as_dir=. for ac_exec_ext in '' $ac_executable_extensions; do if { test -f "$as_dir/$ac_word$ac_exec_ext" && $as_test_x "$as_dir/$ac_word$ac_exec_ext"; }; then ac_cv_prog_LIPO="${ac_tool_prefix}lipo" $as_echo "$as_me:${as_lineno-$LINENO}: found $as_dir/$ac_word$ac_exec_ext" >&5 break 2 fi done done IFS=$as_save_IFS fi fi LIPO=$ac_cv_prog_LIPO if test -n "$LIPO"; then { $as_echo "$as_me:${as_lineno-$LINENO}: result: $LIPO" >&5 $as_echo "$LIPO" >&6; } else { $as_echo "$as_me:${as_lineno-$LINENO}: result: no" >&5 $as_echo "no" >&6; } fi fi if test -z "$ac_cv_prog_LIPO"; then ac_ct_LIPO=$LIPO # Extract the first word of "lipo", so it can be a program name with args. set dummy lipo; ac_word=$2 { $as_echo "$as_me:${as_lineno-$LINENO}: checking for $ac_word" >&5 $as_echo_n "checking for $ac_word... " >&6; } if test "${ac_cv_prog_ac_ct_LIPO+set}" = set; then : $as_echo_n "(cached) " >&6 else if test -n "$ac_ct_LIPO"; then ac_cv_prog_ac_ct_LIPO="$ac_ct_LIPO" # Let the user override the test. else as_save_IFS=$IFS; IFS=$PATH_SEPARATOR for as_dir in $PATH do IFS=$as_save_IFS test -z "$as_dir" && as_dir=. for ac_exec_ext in '' $ac_executable_extensions; do if { test -f "$as_dir/$ac_word$ac_exec_ext" && $as_test_x "$as_dir/$ac_word$ac_exec_ext"; }; then ac_cv_prog_ac_ct_LIPO="lipo" $as_echo "$as_me:${as_lineno-$LINENO}: found $as_dir/$ac_word$ac_exec_ext" >&5 break 2 fi done done IFS=$as_save_IFS fi fi ac_ct_LIPO=$ac_cv_prog_ac_ct_LIPO if test -n "$ac_ct_LIPO"; then { $as_echo "$as_me:${as_lineno-$LINENO}: result: $ac_ct_LIPO" >&5 $as_echo "$ac_ct_LIPO" >&6; } else { $as_echo "$as_me:${as_lineno-$LINENO}: result: no" >&5 $as_echo "no" >&6; } fi if test "x$ac_ct_LIPO" = x; then LIPO=":" else case $cross_compiling:$ac_tool_warned in yes:) { $as_echo "$as_me:${as_lineno-$LINENO}: WARNING: using cross tools not prefixed with host triplet" >&5 $as_echo "$as_me: WARNING: using cross tools not prefixed with host triplet" >&2;} ac_tool_warned=yes ;; esac LIPO=$ac_ct_LIPO fi else LIPO="$ac_cv_prog_LIPO" fi if test -n "$ac_tool_prefix"; then # Extract the first word of "${ac_tool_prefix}otool", so it can be a program name with args. set dummy ${ac_tool_prefix}otool; ac_word=$2 { $as_echo "$as_me:${as_lineno-$LINENO}: checking for $ac_word" >&5 $as_echo_n "checking for $ac_word... " >&6; } if test "${ac_cv_prog_OTOOL+set}" = set; then : $as_echo_n "(cached) " >&6 else if test -n "$OTOOL"; then ac_cv_prog_OTOOL="$OTOOL" # Let the user override the test. else as_save_IFS=$IFS; IFS=$PATH_SEPARATOR for as_dir in $PATH do IFS=$as_save_IFS test -z "$as_dir" && as_dir=. for ac_exec_ext in '' $ac_executable_extensions; do if { test -f "$as_dir/$ac_word$ac_exec_ext" && $as_test_x "$as_dir/$ac_word$ac_exec_ext"; }; then ac_cv_prog_OTOOL="${ac_tool_prefix}otool" $as_echo "$as_me:${as_lineno-$LINENO}: found $as_dir/$ac_word$ac_exec_ext" >&5 break 2 fi done done IFS=$as_save_IFS fi fi OTOOL=$ac_cv_prog_OTOOL if test -n "$OTOOL"; then { $as_echo "$as_me:${as_lineno-$LINENO}: result: $OTOOL" >&5 $as_echo "$OTOOL" >&6; } else { $as_echo "$as_me:${as_lineno-$LINENO}: result: no" >&5 $as_echo "no" >&6; } fi fi if test -z "$ac_cv_prog_OTOOL"; then ac_ct_OTOOL=$OTOOL # Extract the first word of "otool", so it can be a program name with args. set dummy otool; ac_word=$2 { $as_echo "$as_me:${as_lineno-$LINENO}: checking for $ac_word" >&5 $as_echo_n "checking for $ac_word... " >&6; } if test "${ac_cv_prog_ac_ct_OTOOL+set}" = set; then : $as_echo_n "(cached) " >&6 else if test -n "$ac_ct_OTOOL"; then ac_cv_prog_ac_ct_OTOOL="$ac_ct_OTOOL" # Let the user override the test. else as_save_IFS=$IFS; IFS=$PATH_SEPARATOR for as_dir in $PATH do IFS=$as_save_IFS test -z "$as_dir" && as_dir=. for ac_exec_ext in '' $ac_executable_extensions; do if { test -f "$as_dir/$ac_word$ac_exec_ext" && $as_test_x "$as_dir/$ac_word$ac_exec_ext"; }; then ac_cv_prog_ac_ct_OTOOL="otool" $as_echo "$as_me:${as_lineno-$LINENO}: found $as_dir/$ac_word$ac_exec_ext" >&5 break 2 fi done done IFS=$as_save_IFS fi fi ac_ct_OTOOL=$ac_cv_prog_ac_ct_OTOOL if test -n "$ac_ct_OTOOL"; then { $as_echo "$as_me:${as_lineno-$LINENO}: result: $ac_ct_OTOOL" >&5 $as_echo "$ac_ct_OTOOL" >&6; } else { $as_echo "$as_me:${as_lineno-$LINENO}: result: no" >&5 $as_echo "no" >&6; } fi if test "x$ac_ct_OTOOL" = x; then OTOOL=":" else case $cross_compiling:$ac_tool_warned in yes:) { $as_echo "$as_me:${as_lineno-$LINENO}: WARNING: using cross tools not prefixed with host triplet" >&5 $as_echo "$as_me: WARNING: using cross tools not prefixed with host triplet" >&2;} ac_tool_warned=yes ;; esac OTOOL=$ac_ct_OTOOL fi else OTOOL="$ac_cv_prog_OTOOL" fi if test -n "$ac_tool_prefix"; then # Extract the first word of "${ac_tool_prefix}otool64", so it can be a program name with args. set dummy ${ac_tool_prefix}otool64; ac_word=$2 { $as_echo "$as_me:${as_lineno-$LINENO}: checking for $ac_word" >&5 $as_echo_n "checking for $ac_word... " >&6; } if test "${ac_cv_prog_OTOOL64+set}" = set; then : $as_echo_n "(cached) " >&6 else if test -n "$OTOOL64"; then ac_cv_prog_OTOOL64="$OTOOL64" # Let the user override the test. else as_save_IFS=$IFS; IFS=$PATH_SEPARATOR for as_dir in $PATH do IFS=$as_save_IFS test -z "$as_dir" && as_dir=. for ac_exec_ext in '' $ac_executable_extensions; do if { test -f "$as_dir/$ac_word$ac_exec_ext" && $as_test_x "$as_dir/$ac_word$ac_exec_ext"; }; then ac_cv_prog_OTOOL64="${ac_tool_prefix}otool64" $as_echo "$as_me:${as_lineno-$LINENO}: found $as_dir/$ac_word$ac_exec_ext" >&5 break 2 fi done done IFS=$as_save_IFS fi fi OTOOL64=$ac_cv_prog_OTOOL64 if test -n "$OTOOL64"; then { $as_echo "$as_me:${as_lineno-$LINENO}: result: $OTOOL64" >&5 $as_echo "$OTOOL64" >&6; } else { $as_echo "$as_me:${as_lineno-$LINENO}: result: no" >&5 $as_echo "no" >&6; } fi fi if test -z "$ac_cv_prog_OTOOL64"; then ac_ct_OTOOL64=$OTOOL64 # Extract the first word of "otool64", so it can be a program name with args. set dummy otool64; ac_word=$2 { $as_echo "$as_me:${as_lineno-$LINENO}: checking for $ac_word" >&5 $as_echo_n "checking for $ac_word... " >&6; } if test "${ac_cv_prog_ac_ct_OTOOL64+set}" = set; then : $as_echo_n "(cached) " >&6 else if test -n "$ac_ct_OTOOL64"; then ac_cv_prog_ac_ct_OTOOL64="$ac_ct_OTOOL64" # Let the user override the test. else as_save_IFS=$IFS; IFS=$PATH_SEPARATOR for as_dir in $PATH do IFS=$as_save_IFS test -z "$as_dir" && as_dir=. for ac_exec_ext in '' $ac_executable_extensions; do if { test -f "$as_dir/$ac_word$ac_exec_ext" && $as_test_x "$as_dir/$ac_word$ac_exec_ext"; }; then ac_cv_prog_ac_ct_OTOOL64="otool64" $as_echo "$as_me:${as_lineno-$LINENO}: found $as_dir/$ac_word$ac_exec_ext" >&5 break 2 fi done done IFS=$as_save_IFS fi fi ac_ct_OTOOL64=$ac_cv_prog_ac_ct_OTOOL64 if test -n "$ac_ct_OTOOL64"; then { $as_echo "$as_me:${as_lineno-$LINENO}: result: $ac_ct_OTOOL64" >&5 $as_echo "$ac_ct_OTOOL64" >&6; } else { $as_echo "$as_me:${as_lineno-$LINENO}: result: no" >&5 $as_echo "no" >&6; } fi if test "x$ac_ct_OTOOL64" = x; then OTOOL64=":" else case $cross_compiling:$ac_tool_warned in yes:) { $as_echo "$as_me:${as_lineno-$LINENO}: WARNING: using cross tools not prefixed with host triplet" >&5 $as_echo "$as_me: WARNING: using cross tools not prefixed with host triplet" >&2;} ac_tool_warned=yes ;; esac OTOOL64=$ac_ct_OTOOL64 fi else OTOOL64="$ac_cv_prog_OTOOL64" fi { $as_echo "$as_me:${as_lineno-$LINENO}: checking for -single_module linker flag" >&5 $as_echo_n "checking for -single_module linker flag... " >&6; } if test "${lt_cv_apple_cc_single_mod+set}" = set; then : $as_echo_n "(cached) " >&6 else lt_cv_apple_cc_single_mod=no if test -z "${LT_MULTI_MODULE}"; then # By default we will add the -single_module flag. You can override # by either setting the environment variable LT_MULTI_MODULE # non-empty at configure time, or by adding -multi_module to the # link flags. rm -rf libconftest.dylib* echo "int foo(void){return 1;}" > conftest.c echo "$LTCC $LTCFLAGS $LDFLAGS -o libconftest.dylib \ -dynamiclib -Wl,-single_module conftest.c" >&5 $LTCC $LTCFLAGS $LDFLAGS -o libconftest.dylib \ -dynamiclib -Wl,-single_module conftest.c 2>conftest.err _lt_result=$? if test -f libconftest.dylib && test ! -s conftest.err && test $_lt_result = 0; then lt_cv_apple_cc_single_mod=yes else cat conftest.err >&5 fi rm -rf libconftest.dylib* rm -f conftest.* fi fi { $as_echo "$as_me:${as_lineno-$LINENO}: result: $lt_cv_apple_cc_single_mod" >&5 $as_echo "$lt_cv_apple_cc_single_mod" >&6; } { $as_echo "$as_me:${as_lineno-$LINENO}: checking for -exported_symbols_list linker flag" >&5 $as_echo_n "checking for -exported_symbols_list linker flag... " >&6; } if test "${lt_cv_ld_exported_symbols_list+set}" = set; then : $as_echo_n "(cached) " >&6 else lt_cv_ld_exported_symbols_list=no save_LDFLAGS=$LDFLAGS echo "_main" > conftest.sym LDFLAGS="$LDFLAGS -Wl,-exported_symbols_list,conftest.sym" cat confdefs.h - <<_ACEOF >conftest.$ac_ext /* end confdefs.h. */ int main () { ; return 0; } _ACEOF if ac_fn_c_try_link "$LINENO"; then : lt_cv_ld_exported_symbols_list=yes else lt_cv_ld_exported_symbols_list=no fi rm -f core conftest.err conftest.$ac_objext \ conftest$ac_exeext conftest.$ac_ext LDFLAGS="$save_LDFLAGS" fi { $as_echo "$as_me:${as_lineno-$LINENO}: result: $lt_cv_ld_exported_symbols_list" >&5 $as_echo "$lt_cv_ld_exported_symbols_list" >&6; } case $host_os in rhapsody* | darwin1.[012]) _lt_dar_allow_undefined='${wl}-undefined ${wl}suppress' ;; darwin1.*) _lt_dar_allow_undefined='${wl}-flat_namespace ${wl}-undefined ${wl}suppress' ;; darwin*) # darwin 5.x on # if running on 10.5 or later, the deployment target defaults # to the OS version, if on x86, and 10.4, the deployment # target defaults to 10.4. Don't you love it? case ${MACOSX_DEPLOYMENT_TARGET-10.0},$host in 10.0,*86*-darwin8*|10.0,*-darwin[91]*) _lt_dar_allow_undefined='${wl}-undefined ${wl}dynamic_lookup' ;; 10.[012]*) _lt_dar_allow_undefined='${wl}-flat_namespace ${wl}-undefined ${wl}suppress' ;; 10.*) _lt_dar_allow_undefined='${wl}-undefined ${wl}dynamic_lookup' ;; esac ;; esac if test "$lt_cv_apple_cc_single_mod" = "yes"; then _lt_dar_single_mod='$single_module' fi if test "$lt_cv_ld_exported_symbols_list" = "yes"; then _lt_dar_export_syms=' ${wl}-exported_symbols_list,$output_objdir/${libname}-symbols.expsym' else _lt_dar_export_syms='~$NMEDIT -s $output_objdir/${libname}-symbols.expsym ${lib}' fi if test "$DSYMUTIL" != ":"; then _lt_dsymutil='~$DSYMUTIL $lib || :' else _lt_dsymutil= fi ;; esac ac_ext=c ac_cpp='$CPP $CPPFLAGS' ac_compile='$CC -c $CFLAGS $CPPFLAGS conftest.$ac_ext >&5' ac_link='$CC -o conftest$ac_exeext $CFLAGS $CPPFLAGS $LDFLAGS conftest.$ac_ext $LIBS >&5' ac_compiler_gnu=$ac_cv_c_compiler_gnu { $as_echo "$as_me:${as_lineno-$LINENO}: checking how to run the C preprocessor" >&5 $as_echo_n "checking how to run the C preprocessor... " >&6; } # On Suns, sometimes $CPP names a directory. if test -n "$CPP" && test -d "$CPP"; then CPP= fi if test -z "$CPP"; then if test "${ac_cv_prog_CPP+set}" = set; then : $as_echo_n "(cached) " >&6 else # Double quotes because CPP needs to be expanded for CPP in "$CC -E" "$CC -E -traditional-cpp" "/lib/cpp" do ac_preproc_ok=false for ac_c_preproc_warn_flag in '' yes do # Use a header file that comes with gcc, so configuring glibc # with a fresh cross-compiler works. # Prefer to if __STDC__ is defined, since # exists even on freestanding compilers. # On the NeXT, cc -E runs the code through the compiler's parser, # not just through cpp. "Syntax error" is here to catch this case. cat confdefs.h - <<_ACEOF >conftest.$ac_ext /* end confdefs.h. */ #ifdef __STDC__ # include #else # include #endif Syntax error _ACEOF if ac_fn_c_try_cpp "$LINENO"; then : else # Broken: fails on valid input. continue fi rm -f conftest.err conftest.i conftest.$ac_ext # OK, works on sane cases. Now check whether nonexistent headers # can be detected and how. cat confdefs.h - <<_ACEOF >conftest.$ac_ext /* end confdefs.h. */ #include _ACEOF if ac_fn_c_try_cpp "$LINENO"; then : # Broken: success on invalid input. continue else # Passes both tests. ac_preproc_ok=: break fi rm -f conftest.err conftest.i conftest.$ac_ext done # Because of `break', _AC_PREPROC_IFELSE's cleaning code was skipped. rm -f conftest.i conftest.err conftest.$ac_ext if $ac_preproc_ok; then : break fi done ac_cv_prog_CPP=$CPP fi CPP=$ac_cv_prog_CPP else ac_cv_prog_CPP=$CPP fi { $as_echo "$as_me:${as_lineno-$LINENO}: result: $CPP" >&5 $as_echo "$CPP" >&6; } ac_preproc_ok=false for ac_c_preproc_warn_flag in '' yes do # Use a header file that comes with gcc, so configuring glibc # with a fresh cross-compiler works. # Prefer to if __STDC__ is defined, since # exists even on freestanding compilers. # On the NeXT, cc -E runs the code through the compiler's parser, # not just through cpp. "Syntax error" is here to catch this case. cat confdefs.h - <<_ACEOF >conftest.$ac_ext /* end confdefs.h. */ #ifdef __STDC__ # include #else # include #endif Syntax error _ACEOF if ac_fn_c_try_cpp "$LINENO"; then : else # Broken: fails on valid input. continue fi rm -f conftest.err conftest.i conftest.$ac_ext # OK, works on sane cases. Now check whether nonexistent headers # can be detected and how. cat confdefs.h - <<_ACEOF >conftest.$ac_ext /* end confdefs.h. */ #include _ACEOF if ac_fn_c_try_cpp "$LINENO"; then : # Broken: success on invalid input. continue else # Passes both tests. ac_preproc_ok=: break fi rm -f conftest.err conftest.i conftest.$ac_ext done # Because of `break', _AC_PREPROC_IFELSE's cleaning code was skipped. rm -f conftest.i conftest.err conftest.$ac_ext if $ac_preproc_ok; then : else { { $as_echo "$as_me:${as_lineno-$LINENO}: error: in \`$ac_pwd':" >&5 $as_echo "$as_me: error: in \`$ac_pwd':" >&2;} as_fn_error $? "C preprocessor \"$CPP\" fails sanity check See \`config.log' for more details" "$LINENO" 5 ; } fi ac_ext=c ac_cpp='$CPP $CPPFLAGS' ac_compile='$CC -c $CFLAGS $CPPFLAGS conftest.$ac_ext >&5' ac_link='$CC -o conftest$ac_exeext $CFLAGS $CPPFLAGS $LDFLAGS conftest.$ac_ext $LIBS >&5' ac_compiler_gnu=$ac_cv_c_compiler_gnu { $as_echo "$as_me:${as_lineno-$LINENO}: checking for ANSI C header files" >&5 $as_echo_n "checking for ANSI C header files... " >&6; } if test "${ac_cv_header_stdc+set}" = set; then : $as_echo_n "(cached) " >&6 else cat confdefs.h - <<_ACEOF >conftest.$ac_ext /* end confdefs.h. */ #include #include #include #include int main () { ; return 0; } _ACEOF if ac_fn_c_try_compile "$LINENO"; then : ac_cv_header_stdc=yes else ac_cv_header_stdc=no fi rm -f core conftest.err conftest.$ac_objext conftest.$ac_ext if test $ac_cv_header_stdc = yes; then # SunOS 4.x string.h does not declare mem*, contrary to ANSI. cat confdefs.h - <<_ACEOF >conftest.$ac_ext /* end confdefs.h. */ #include _ACEOF if (eval "$ac_cpp conftest.$ac_ext") 2>&5 | $EGREP "memchr" >/dev/null 2>&1; then : else ac_cv_header_stdc=no fi rm -f conftest* fi if test $ac_cv_header_stdc = yes; then # ISC 2.0.2 stdlib.h does not declare free, contrary to ANSI. cat confdefs.h - <<_ACEOF >conftest.$ac_ext /* end confdefs.h. */ #include _ACEOF if (eval "$ac_cpp conftest.$ac_ext") 2>&5 | $EGREP "free" >/dev/null 2>&1; then : else ac_cv_header_stdc=no fi rm -f conftest* fi if test $ac_cv_header_stdc = yes; then # /bin/cc in Irix-4.0.5 gets non-ANSI ctype macros unless using -ansi. if test "$cross_compiling" = yes; then : : else cat confdefs.h - <<_ACEOF >conftest.$ac_ext /* end confdefs.h. */ #include #include #if ((' ' & 0x0FF) == 0x020) # define ISLOWER(c) ('a' <= (c) && (c) <= 'z') # define TOUPPER(c) (ISLOWER(c) ? 'A' + ((c) - 'a') : (c)) #else # define ISLOWER(c) \ (('a' <= (c) && (c) <= 'i') \ || ('j' <= (c) && (c) <= 'r') \ || ('s' <= (c) && (c) <= 'z')) # define TOUPPER(c) (ISLOWER(c) ? ((c) | 0x40) : (c)) #endif #define XOR(e, f) (((e) && !(f)) || (!(e) && (f))) int main () { int i; for (i = 0; i < 256; i++) if (XOR (islower (i), ISLOWER (i)) || toupper (i) != TOUPPER (i)) return 2; return 0; } _ACEOF if ac_fn_c_try_run "$LINENO"; then : else ac_cv_header_stdc=no fi rm -f core *.core core.conftest.* gmon.out bb.out conftest$ac_exeext \ conftest.$ac_objext conftest.beam conftest.$ac_ext fi fi fi { $as_echo "$as_me:${as_lineno-$LINENO}: result: $ac_cv_header_stdc" >&5 $as_echo "$ac_cv_header_stdc" >&6; } if test $ac_cv_header_stdc = yes; then $as_echo "#define STDC_HEADERS 1" >>confdefs.h fi # On IRIX 5.3, sys/types and inttypes.h are conflicting. for ac_header in sys/types.h sys/stat.h stdlib.h string.h memory.h strings.h \ inttypes.h stdint.h unistd.h do : as_ac_Header=`$as_echo "ac_cv_header_$ac_header" | $as_tr_sh` ac_fn_c_check_header_compile "$LINENO" "$ac_header" "$as_ac_Header" "$ac_includes_default " if eval test \"x\$"$as_ac_Header"\" = x"yes"; then : cat >>confdefs.h <<_ACEOF #define `$as_echo "HAVE_$ac_header" | $as_tr_cpp` 1 _ACEOF fi done for ac_header in dlfcn.h do : ac_fn_c_check_header_compile "$LINENO" "dlfcn.h" "ac_cv_header_dlfcn_h" "$ac_includes_default " if test "x$ac_cv_header_dlfcn_h" = x""yes; then : cat >>confdefs.h <<_ACEOF #define HAVE_DLFCN_H 1 _ACEOF fi done ac_ext=f ac_compile='$F77 -c $FFLAGS conftest.$ac_ext >&5' ac_link='$F77 -o conftest$ac_exeext $FFLAGS $LDFLAGS conftest.$ac_ext $LIBS >&5' ac_compiler_gnu=$ac_cv_f77_compiler_gnu if test -n "$ac_tool_prefix"; then for ac_prog in g77 xlf f77 frt pgf77 cf77 fort77 fl32 af77 xlf90 f90 pgf90 pghpf epcf90 gfortran g95 xlf95 f95 fort ifort ifc efc pgfortran pgf95 lf95 ftn do # Extract the first word of "$ac_tool_prefix$ac_prog", so it can be a program name with args. set dummy $ac_tool_prefix$ac_prog; ac_word=$2 { $as_echo "$as_me:${as_lineno-$LINENO}: checking for $ac_word" >&5 $as_echo_n "checking for $ac_word... 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This will affect the creation of libtool libraries that *** depend on shared libraries, but programs linked with such libtool *** libraries will work regardless of this problem. Nevertheless, you *** may want to report the problem to your system manager and/or to *** bug-libtool@gnu.org _LT_EOF fi ;; esac fi break fi done IFS="$lt_save_ifs" MAGIC_CMD="$lt_save_MAGIC_CMD" ;; esac fi MAGIC_CMD="$lt_cv_path_MAGIC_CMD" if test -n "$MAGIC_CMD"; then { $as_echo "$as_me:${as_lineno-$LINENO}: result: $MAGIC_CMD" >&5 $as_echo "$MAGIC_CMD" >&6; } else { $as_echo "$as_me:${as_lineno-$LINENO}: result: no" >&5 $as_echo "no" >&6; } fi if test -z "$lt_cv_path_MAGIC_CMD"; then if test -n "$ac_tool_prefix"; then { $as_echo "$as_me:${as_lineno-$LINENO}: checking for file" >&5 $as_echo_n "checking for file... 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This will affect the creation of libtool libraries that *** depend on shared libraries, but programs linked with such libtool *** libraries will work regardless of this problem. 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If you *** really care for shared libraries, you may want to modify your PATH *** so that a non-GNU linker is found, and then restart. _LT_EOF fi ;; amigaos*) case $host_cpu in powerpc) # see comment about AmigaOS4 .so support archive_cmds='$CC -shared $libobjs $deplibs $compiler_flags ${wl}-soname $wl$soname -o $lib' archive_expsym_cmds='' ;; m68k) archive_cmds='$RM $output_objdir/a2ixlibrary.data~$ECHO "#define NAME $libname" > $output_objdir/a2ixlibrary.data~$ECHO "#define LIBRARY_ID 1" >> $output_objdir/a2ixlibrary.data~$ECHO "#define VERSION $major" >> $output_objdir/a2ixlibrary.data~$ECHO "#define REVISION $revision" >> $output_objdir/a2ixlibrary.data~$AR $AR_FLAGS $lib $libobjs~$RANLIB $lib~(cd $output_objdir && a2ixlibrary -32)' hardcode_libdir_flag_spec='-L$libdir' hardcode_minus_L=yes ;; esac ;; beos*) if $LD --help 2>&1 | $GREP ': supported targets:.* elf' > /dev/null; then allow_undefined_flag=unsupported # Joseph Beckenbach says some releases of gcc # support --undefined. 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Therefore, libtool *** is disabling shared libraries support. We urge you to upgrade GNU *** binutils to release 2.9.1 or newer. Another option is to modify *** your PATH or compiler configuration so that the native linker is *** used, and then restart. _LT_EOF elif $LD --help 2>&1 | $GREP ': supported targets:.* elf' > /dev/null; then archive_cmds='$CC -shared $libobjs $deplibs $compiler_flags ${wl}-soname $wl$soname -o $lib' archive_expsym_cmds='$CC -shared $libobjs $deplibs $compiler_flags ${wl}-soname $wl$soname ${wl}-retain-symbols-file $wl$export_symbols -o $lib' else ld_shlibs=no fi ;; sysv5* | sco3.2v5* | sco5v6* | unixware* | OpenUNIX*) case `$LD -v 2>&1` in *\ [01].* | *\ 2.[0-9].* | *\ 2.1[0-5].*) ld_shlibs=no cat <<_LT_EOF 1>&2 *** Warning: Releases of the GNU linker prior to 2.16.91.0.3 can not *** reliably create shared libraries on SCO systems. Therefore, libtool *** is disabling shared libraries support. 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If -brtl is somewhere in LDFLAGS, we # need to do runtime linking. case $host_os in aix4.[23]|aix4.[23].*|aix[5-9]*) for ld_flag in $LDFLAGS; do if (test $ld_flag = "-brtl" || test $ld_flag = "-Wl,-brtl"); then aix_use_runtimelinking=yes break fi done ;; esac exp_sym_flag='-bexport' no_entry_flag='-bnoentry' fi # When large executables or shared objects are built, AIX ld can # have problems creating the table of contents. If linking a library # or program results in "error TOC overflow" add -mminimal-toc to # CXXFLAGS/CFLAGS for g++/gcc. In the cases where that is not # enough to fix the problem, add -Wl,-bbigtoc to LDFLAGS. archive_cmds='' hardcode_direct=yes hardcode_direct_absolute=yes hardcode_libdir_separator=':' link_all_deplibs=yes file_list_spec='${wl}-f,' if test "$GCC" = yes; then case $host_os in aix4.[012]|aix4.[012].*) # We only want to do this on AIX 4.2 and lower, the check # below for broken collect2 doesn't work under 4.3+ collect2name=`${CC} -print-prog-name=collect2` if test -f "$collect2name" && strings "$collect2name" | $GREP resolve_lib_name >/dev/null then # We have reworked collect2 : else # We have old collect2 hardcode_direct=unsupported # It fails to find uninstalled libraries when the uninstalled # path is not listed in the libpath. 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then aix_libpath=`dump -HX64 conftest$ac_exeext 2>/dev/null | $SED -n -e "$lt_aix_libpath_sed"` fi fi rm -f core conftest.err conftest.$ac_objext \ conftest$ac_exeext conftest.$ac_ext if test -z "$aix_libpath"; then aix_libpath="/usr/lib:/lib"; fi hardcode_libdir_flag_spec='${wl}-blibpath:$libdir:'"$aix_libpath" archive_expsym_cmds='$CC -o $output_objdir/$soname $libobjs $deplibs '"\${wl}$no_entry_flag"' $compiler_flags `if test "x${allow_undefined_flag}" != "x"; then $ECHO "X${wl}${allow_undefined_flag}" | $Xsed; else :; fi` '"\${wl}$exp_sym_flag:\$export_symbols $shared_flag" else if test "$host_cpu" = ia64; then hardcode_libdir_flag_spec='${wl}-R $libdir:/usr/lib:/lib' allow_undefined_flag="-z nodefs" archive_expsym_cmds="\$CC $shared_flag"' -o $output_objdir/$soname $libobjs $deplibs '"\${wl}$no_entry_flag"' $compiler_flags ${wl}${allow_undefined_flag} '"\${wl}$exp_sym_flag:\$export_symbols" else # Determine the default libpath from the value encoded in an # empty executable. cat confdefs.h - <<_ACEOF >conftest.$ac_ext /* end confdefs.h. */ int main () { ; return 0; } _ACEOF if ac_fn_c_try_link "$LINENO"; then : lt_aix_libpath_sed=' /Import File Strings/,/^$/ { /^0/ { s/^0 *\(.*\)$/\1/ p } }' aix_libpath=`dump -H conftest$ac_exeext 2>/dev/null | $SED -n -e "$lt_aix_libpath_sed"` # Check for a 64-bit object if we didn't find anything. if test -z "$aix_libpath"; then aix_libpath=`dump -HX64 conftest$ac_exeext 2>/dev/null | $SED -n -e "$lt_aix_libpath_sed"` fi fi rm -f core conftest.err conftest.$ac_objext \ conftest$ac_exeext conftest.$ac_ext if test -z "$aix_libpath"; then aix_libpath="/usr/lib:/lib"; fi hardcode_libdir_flag_spec='${wl}-blibpath:$libdir:'"$aix_libpath" # Warning - without using the other run time loading flags, # -berok will link without error, but may produce a broken library. no_undefined_flag=' ${wl}-bernotok' allow_undefined_flag=' ${wl}-berok' # Exported symbols can be pulled into shared objects from archives whole_archive_flag_spec='$convenience' archive_cmds_need_lc=yes # This is similar to how AIX traditionally builds its shared libraries. archive_expsym_cmds="\$CC $shared_flag"' -o $output_objdir/$soname $libobjs $deplibs ${wl}-bnoentry $compiler_flags ${wl}-bE:$export_symbols${allow_undefined_flag}~$AR $AR_FLAGS $output_objdir/$libname$release.a $output_objdir/$soname' fi fi ;; amigaos*) case $host_cpu in powerpc) # see comment about AmigaOS4 .so support archive_cmds='$CC -shared $libobjs $deplibs $compiler_flags ${wl}-soname $wl$soname -o $lib' archive_expsym_cmds='' ;; m68k) archive_cmds='$RM $output_objdir/a2ixlibrary.data~$ECHO "#define NAME $libname" > $output_objdir/a2ixlibrary.data~$ECHO "#define LIBRARY_ID 1" >> $output_objdir/a2ixlibrary.data~$ECHO "#define VERSION $major" >> $output_objdir/a2ixlibrary.data~$ECHO "#define REVISION $revision" >> $output_objdir/a2ixlibrary.data~$AR $AR_FLAGS $lib $libobjs~$RANLIB $lib~(cd $output_objdir && a2ixlibrary -32)' hardcode_libdir_flag_spec='-L$libdir' hardcode_minus_L=yes ;; esac ;; bsdi[45]*) export_dynamic_flag_spec=-rdynamic ;; cygwin* | mingw* | pw32* | cegcc*) # When not using gcc, we currently assume that we are using # Microsoft Visual C++. # hardcode_libdir_flag_spec is actually meaningless, as there is # no search path for DLLs. hardcode_libdir_flag_spec=' ' allow_undefined_flag=unsupported # Tell ltmain to make .lib files, not .a files. libext=lib # Tell ltmain to make .dll files, not .so files. shrext_cmds=".dll" # FIXME: Setting linknames here is a bad hack. archive_cmds='$CC -o $lib $libobjs $compiler_flags `$ECHO "X$deplibs" | $Xsed -e '\''s/ -lc$//'\''` -link -dll~linknames=' # The linker will automatically build a .lib file if we build a DLL. old_archive_from_new_cmds='true' # FIXME: Should let the user specify the lib program. old_archive_cmds='lib -OUT:$oldlib$oldobjs$old_deplibs' fix_srcfile_path='`cygpath -w "$srcfile"`' enable_shared_with_static_runtimes=yes ;; 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dgux*) archive_cmds='$LD -G -h $soname -o $lib $libobjs $deplibs $linker_flags' hardcode_libdir_flag_spec='-L$libdir' hardcode_shlibpath_var=no ;; freebsd1*) ld_shlibs=no ;; # FreeBSD 2.2.[012] allows us to include c++rt0.o to get C++ constructor # support. Future versions do this automatically, but an explicit c++rt0.o # does not break anything, and helps significantly (at the cost of a little # extra space). freebsd2.2*) archive_cmds='$LD -Bshareable -o $lib $libobjs $deplibs $linker_flags /usr/lib/c++rt0.o' hardcode_libdir_flag_spec='-R$libdir' hardcode_direct=yes hardcode_shlibpath_var=no ;; # Unfortunately, older versions of FreeBSD 2 do not have this feature. freebsd2*) archive_cmds='$LD -Bshareable -o $lib $libobjs $deplibs $linker_flags' hardcode_direct=yes hardcode_minus_L=yes hardcode_shlibpath_var=no ;; # FreeBSD 3 and greater uses gcc -shared to do shared libraries. freebsd* | dragonfly*) archive_cmds='$CC -shared -o $lib $libobjs $deplibs $compiler_flags' hardcode_libdir_flag_spec='-R$libdir' hardcode_direct=yes hardcode_shlibpath_var=no ;; hpux9*) if test "$GCC" = yes; then archive_cmds='$RM $output_objdir/$soname~$CC -shared -fPIC ${wl}+b ${wl}$install_libdir -o $output_objdir/$soname $libobjs $deplibs $compiler_flags~test $output_objdir/$soname = $lib || mv $output_objdir/$soname $lib' else archive_cmds='$RM $output_objdir/$soname~$LD -b +b $install_libdir -o $output_objdir/$soname $libobjs $deplibs $linker_flags~test $output_objdir/$soname = $lib || mv $output_objdir/$soname $lib' fi hardcode_libdir_flag_spec='${wl}+b ${wl}$libdir' hardcode_libdir_separator=: hardcode_direct=yes # hardcode_minus_L: Not really in the search PATH, # but as the default location of the library. hardcode_minus_L=yes export_dynamic_flag_spec='${wl}-E' ;; hpux10*) if test "$GCC" = yes -a "$with_gnu_ld" = no; then archive_cmds='$CC -shared -fPIC ${wl}+h ${wl}$soname ${wl}+b ${wl}$install_libdir -o $lib $libobjs $deplibs $compiler_flags' else archive_cmds='$LD -b +h $soname +b $install_libdir -o $lib $libobjs $deplibs $linker_flags' fi if test "$with_gnu_ld" = no; then hardcode_libdir_flag_spec='${wl}+b ${wl}$libdir' hardcode_libdir_flag_spec_ld='+b $libdir' hardcode_libdir_separator=: hardcode_direct=yes hardcode_direct_absolute=yes export_dynamic_flag_spec='${wl}-E' # hardcode_minus_L: Not really in the search PATH, # but as the default location of the library. hardcode_minus_L=yes fi ;; hpux11*) if test "$GCC" = yes -a "$with_gnu_ld" = no; then case $host_cpu in hppa*64*) archive_cmds='$CC -shared ${wl}+h ${wl}$soname -o $lib $libobjs $deplibs $compiler_flags' ;; ia64*) archive_cmds='$CC -shared -fPIC ${wl}+h ${wl}$soname ${wl}+nodefaultrpath -o $lib $libobjs $deplibs $compiler_flags' ;; *) archive_cmds='$CC -shared -fPIC ${wl}+h ${wl}$soname ${wl}+b ${wl}$install_libdir -o $lib $libobjs $deplibs $compiler_flags' ;; esac else case $host_cpu in hppa*64*) archive_cmds='$CC -b ${wl}+h ${wl}$soname -o $lib $libobjs $deplibs $compiler_flags' ;; ia64*) archive_cmds='$CC -b ${wl}+h ${wl}$soname ${wl}+nodefaultrpath -o $lib $libobjs $deplibs $compiler_flags' ;; *) archive_cmds='$CC -b ${wl}+h ${wl}$soname ${wl}+b ${wl}$install_libdir -o $lib $libobjs $deplibs $compiler_flags' ;; esac fi if test "$with_gnu_ld" = no; then hardcode_libdir_flag_spec='${wl}+b ${wl}$libdir' hardcode_libdir_separator=: case $host_cpu in hppa*64*|ia64*) hardcode_direct=no hardcode_shlibpath_var=no ;; *) hardcode_direct=yes hardcode_direct_absolute=yes export_dynamic_flag_spec='${wl}-E' # hardcode_minus_L: Not really in the search PATH, # but as the default location of the library. hardcode_minus_L=yes ;; esac fi ;; irix5* | irix6* | nonstopux*) if test "$GCC" = yes; then archive_cmds='$CC -shared $libobjs $deplibs $compiler_flags ${wl}-soname ${wl}$soname `test -n "$verstring" && $ECHO "X${wl}-set_version ${wl}$verstring" | $Xsed` ${wl}-update_registry ${wl}${output_objdir}/so_locations -o $lib' # Try to use the -exported_symbol ld option, if it does not # work, assume that -exports_file does not work either and # implicitly export all symbols. save_LDFLAGS="$LDFLAGS" LDFLAGS="$LDFLAGS -shared ${wl}-exported_symbol ${wl}foo ${wl}-update_registry ${wl}/dev/null" cat confdefs.h - <<_ACEOF >conftest.$ac_ext /* end confdefs.h. */ int foo(void) {} _ACEOF if ac_fn_c_try_link "$LINENO"; then : archive_expsym_cmds='$CC -shared $libobjs $deplibs $compiler_flags ${wl}-soname ${wl}$soname `test -n "$verstring" && $ECHO "X${wl}-set_version ${wl}$verstring" | $Xsed` ${wl}-update_registry ${wl}${output_objdir}/so_locations ${wl}-exports_file ${wl}$export_symbols -o $lib' fi rm -f core conftest.err conftest.$ac_objext \ conftest$ac_exeext conftest.$ac_ext LDFLAGS="$save_LDFLAGS" else archive_cmds='$CC -shared $libobjs $deplibs $compiler_flags -soname $soname `test -n "$verstring" && $ECHO "X-set_version $verstring" | $Xsed` -update_registry ${output_objdir}/so_locations -o $lib' archive_expsym_cmds='$CC -shared $libobjs $deplibs $compiler_flags -soname $soname `test -n "$verstring" && $ECHO "X-set_version $verstring" | $Xsed` -update_registry ${output_objdir}/so_locations -exports_file $export_symbols -o $lib' fi archive_cmds_need_lc='no' hardcode_libdir_flag_spec='${wl}-rpath ${wl}$libdir' hardcode_libdir_separator=: inherit_rpath=yes link_all_deplibs=yes ;; netbsd* | netbsdelf*-gnu) if echo __ELF__ | $CC -E - | $GREP __ELF__ >/dev/null; then archive_cmds='$LD -Bshareable -o $lib $libobjs $deplibs $linker_flags' # a.out else archive_cmds='$LD -shared -o $lib $libobjs $deplibs $linker_flags' # ELF fi hardcode_libdir_flag_spec='-R$libdir' hardcode_direct=yes hardcode_shlibpath_var=no ;; newsos6) archive_cmds='$LD -G -h $soname -o $lib $libobjs $deplibs $linker_flags' hardcode_direct=yes hardcode_libdir_flag_spec='${wl}-rpath ${wl}$libdir' hardcode_libdir_separator=: hardcode_shlibpath_var=no ;; *nto* | *qnx*) ;; openbsd*) if test -f /usr/libexec/ld.so; then hardcode_direct=yes hardcode_shlibpath_var=no hardcode_direct_absolute=yes if test -z "`echo __ELF__ | $CC -E - | $GREP __ELF__`" || test "$host_os-$host_cpu" = "openbsd2.8-powerpc"; then archive_cmds='$CC -shared $pic_flag -o $lib $libobjs $deplibs $compiler_flags' archive_expsym_cmds='$CC -shared $pic_flag -o $lib $libobjs $deplibs $compiler_flags ${wl}-retain-symbols-file,$export_symbols' hardcode_libdir_flag_spec='${wl}-rpath,$libdir' export_dynamic_flag_spec='${wl}-E' else case $host_os in openbsd[01].* | openbsd2.[0-7] | openbsd2.[0-7].*) archive_cmds='$LD -Bshareable -o $lib $libobjs $deplibs $linker_flags' hardcode_libdir_flag_spec='-R$libdir' ;; *) archive_cmds='$CC -shared $pic_flag -o $lib $libobjs $deplibs $compiler_flags' hardcode_libdir_flag_spec='${wl}-rpath,$libdir' ;; esac fi else ld_shlibs=no fi ;; os2*) hardcode_libdir_flag_spec='-L$libdir' hardcode_minus_L=yes allow_undefined_flag=unsupported archive_cmds='$ECHO "LIBRARY $libname INITINSTANCE" > $output_objdir/$libname.def~$ECHO "DESCRIPTION \"$libname\"" >> $output_objdir/$libname.def~$ECHO DATA >> $output_objdir/$libname.def~$ECHO " SINGLE NONSHARED" >> $output_objdir/$libname.def~$ECHO EXPORTS >> $output_objdir/$libname.def~emxexp $libobjs >> $output_objdir/$libname.def~$CC -Zdll -Zcrtdll -o $lib $libobjs $deplibs $compiler_flags $output_objdir/$libname.def' old_archive_from_new_cmds='emximp -o $output_objdir/$libname.a $output_objdir/$libname.def' ;; osf3*) if test "$GCC" = yes; then allow_undefined_flag=' ${wl}-expect_unresolved ${wl}\*' archive_cmds='$CC -shared${allow_undefined_flag} $libobjs $deplibs $compiler_flags ${wl}-soname ${wl}$soname `test -n "$verstring" && $ECHO "X${wl}-set_version ${wl}$verstring" | $Xsed` ${wl}-update_registry ${wl}${output_objdir}/so_locations -o $lib' else allow_undefined_flag=' -expect_unresolved \*' archive_cmds='$CC -shared${allow_undefined_flag} $libobjs $deplibs $compiler_flags -soname $soname `test -n "$verstring" && $ECHO "X-set_version $verstring" | $Xsed` -update_registry ${output_objdir}/so_locations -o $lib' fi archive_cmds_need_lc='no' hardcode_libdir_flag_spec='${wl}-rpath ${wl}$libdir' hardcode_libdir_separator=: ;; osf4* | osf5*) # as osf3* with the addition of -msym flag if test "$GCC" = yes; then allow_undefined_flag=' ${wl}-expect_unresolved ${wl}\*' archive_cmds='$CC -shared${allow_undefined_flag} $libobjs $deplibs $compiler_flags ${wl}-msym ${wl}-soname ${wl}$soname `test -n "$verstring" && $ECHO "X${wl}-set_version ${wl}$verstring" | $Xsed` ${wl}-update_registry ${wl}${output_objdir}/so_locations -o $lib' hardcode_libdir_flag_spec='${wl}-rpath ${wl}$libdir' else allow_undefined_flag=' -expect_unresolved \*' archive_cmds='$CC -shared${allow_undefined_flag} $libobjs $deplibs $compiler_flags -msym -soname $soname `test -n "$verstring" && $ECHO "X-set_version $verstring" | $Xsed` -update_registry ${output_objdir}/so_locations -o $lib' archive_expsym_cmds='for i in `cat $export_symbols`; do printf "%s %s\\n" -exported_symbol "\$i" >> $lib.exp; done; printf "%s\\n" "-hidden">> $lib.exp~ $CC -shared${allow_undefined_flag} ${wl}-input ${wl}$lib.exp $compiler_flags $libobjs $deplibs -soname $soname `test -n "$verstring" && $ECHO "X-set_version $verstring" | $Xsed` -update_registry ${output_objdir}/so_locations -o $lib~$RM $lib.exp' # Both c and cxx compiler support -rpath directly hardcode_libdir_flag_spec='-rpath $libdir' fi archive_cmds_need_lc='no' hardcode_libdir_separator=: ;; solaris*) no_undefined_flag=' -z defs' if test "$GCC" = yes; then wlarc='${wl}' archive_cmds='$CC -shared ${wl}-z ${wl}text ${wl}-h ${wl}$soname -o $lib $libobjs $deplibs $compiler_flags' archive_expsym_cmds='echo "{ global:" > $lib.exp~cat $export_symbols | $SED -e "s/\(.*\)/\1;/" >> $lib.exp~echo "local: *; };" >> $lib.exp~ $CC -shared ${wl}-z ${wl}text ${wl}-M ${wl}$lib.exp ${wl}-h ${wl}$soname -o $lib $libobjs $deplibs $compiler_flags~$RM $lib.exp' else case `$CC -V 2>&1` in *"Compilers 5.0"*) wlarc='' archive_cmds='$LD -G${allow_undefined_flag} -h $soname -o $lib $libobjs $deplibs $linker_flags' archive_expsym_cmds='echo "{ global:" > $lib.exp~cat $export_symbols | $SED -e "s/\(.*\)/\1;/" >> $lib.exp~echo "local: *; };" >> $lib.exp~ $LD -G${allow_undefined_flag} -M $lib.exp -h $soname -o $lib $libobjs $deplibs $linker_flags~$RM $lib.exp' ;; *) wlarc='${wl}' archive_cmds='$CC -G${allow_undefined_flag} -h $soname -o $lib $libobjs $deplibs $compiler_flags' archive_expsym_cmds='echo "{ global:" > $lib.exp~cat $export_symbols | $SED -e "s/\(.*\)/\1;/" >> $lib.exp~echo "local: *; };" >> $lib.exp~ $CC -G${allow_undefined_flag} -M $lib.exp -h $soname -o $lib $libobjs $deplibs $compiler_flags~$RM $lib.exp' ;; esac fi hardcode_libdir_flag_spec='-R$libdir' hardcode_shlibpath_var=no case $host_os in solaris2.[0-5] | solaris2.[0-5].*) ;; *) # The compiler driver will combine and reorder linker options, # but understands `-z linker_flag'. GCC discards it without `$wl', # but is careful enough not to reorder. # Supported since Solaris 2.6 (maybe 2.5.1?) if test "$GCC" = yes; then whole_archive_flag_spec='${wl}-z ${wl}allextract$convenience ${wl}-z ${wl}defaultextract' else whole_archive_flag_spec='-z allextract$convenience -z defaultextract' fi ;; esac link_all_deplibs=yes ;; sunos4*) if test "x$host_vendor" = xsequent; then # Use $CC to link under sequent, because it throws in some extra .o # files that make .init and .fini sections work. archive_cmds='$CC -G ${wl}-h $soname -o $lib $libobjs $deplibs $compiler_flags' else archive_cmds='$LD -assert pure-text -Bstatic -o $lib $libobjs $deplibs $linker_flags' fi hardcode_libdir_flag_spec='-L$libdir' hardcode_direct=yes hardcode_minus_L=yes hardcode_shlibpath_var=no ;; sysv4) case $host_vendor in sni) archive_cmds='$LD -G -h $soname -o $lib $libobjs $deplibs $linker_flags' hardcode_direct=yes # is this really true??? ;; siemens) ## LD is ld it makes a PLAMLIB ## CC just makes a GrossModule. archive_cmds='$LD -G -o $lib $libobjs $deplibs $linker_flags' reload_cmds='$CC -r -o $output$reload_objs' hardcode_direct=no ;; motorola) archive_cmds='$LD -G -h $soname -o $lib $libobjs $deplibs $linker_flags' hardcode_direct=no #Motorola manual says yes, but my tests say they lie ;; esac runpath_var='LD_RUN_PATH' hardcode_shlibpath_var=no ;; sysv4.3*) archive_cmds='$LD -G -h $soname -o $lib $libobjs $deplibs $linker_flags' hardcode_shlibpath_var=no export_dynamic_flag_spec='-Bexport' ;; sysv4*MP*) if test -d /usr/nec; then archive_cmds='$LD -G -h $soname -o $lib $libobjs $deplibs $linker_flags' hardcode_shlibpath_var=no runpath_var=LD_RUN_PATH hardcode_runpath_var=yes ld_shlibs=yes fi ;; sysv4*uw2* | sysv5OpenUNIX* | sysv5UnixWare7.[01].[10]* | unixware7* | sco3.2v5.0.[024]*) no_undefined_flag='${wl}-z,text' archive_cmds_need_lc=no hardcode_shlibpath_var=no runpath_var='LD_RUN_PATH' if test "$GCC" = yes; then archive_cmds='$CC -shared ${wl}-h,$soname -o $lib $libobjs $deplibs $compiler_flags' archive_expsym_cmds='$CC -shared ${wl}-Bexport:$export_symbols ${wl}-h,$soname -o $lib $libobjs $deplibs $compiler_flags' else archive_cmds='$CC -G ${wl}-h,$soname -o $lib $libobjs $deplibs $compiler_flags' archive_expsym_cmds='$CC -G ${wl}-Bexport:$export_symbols ${wl}-h,$soname -o $lib $libobjs $deplibs $compiler_flags' fi ;; sysv5* | sco3.2v5* | sco5v6*) # Note: We can NOT use -z defs as we might desire, because we do not # link with -lc, and that would cause any symbols used from libc to # always be unresolved, which means just about no library would # ever link correctly. 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" >&6; } if test "${ac_cv_lib_svld_dlopen+set}" = set; then : $as_echo_n "(cached) " >&6 else ac_check_lib_save_LIBS=$LIBS LIBS="-lsvld $LIBS" cat confdefs.h - <<_ACEOF >conftest.$ac_ext /* end confdefs.h. */ /* Override any GCC internal prototype to avoid an error. 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If you *** really care for shared libraries, you may want to modify your PATH *** so that a non-GNU linker is found, and then restart. _LT_EOF fi ;; amigaos*) case $host_cpu in powerpc) # see comment about AmigaOS4 .so support archive_cmds_F77='$CC -shared $libobjs $deplibs $compiler_flags ${wl}-soname $wl$soname -o $lib' archive_expsym_cmds_F77='' ;; m68k) archive_cmds_F77='$RM $output_objdir/a2ixlibrary.data~$ECHO "#define NAME $libname" > $output_objdir/a2ixlibrary.data~$ECHO "#define LIBRARY_ID 1" >> $output_objdir/a2ixlibrary.data~$ECHO "#define VERSION $major" >> $output_objdir/a2ixlibrary.data~$ECHO "#define REVISION $revision" >> $output_objdir/a2ixlibrary.data~$AR $AR_FLAGS $lib $libobjs~$RANLIB $lib~(cd $output_objdir && a2ixlibrary -32)' hardcode_libdir_flag_spec_F77='-L$libdir' hardcode_minus_L_F77=yes ;; esac ;; beos*) if $LD --help 2>&1 | $GREP ': supported targets:.* elf' > /dev/null; then allow_undefined_flag_F77=unsupported # Joseph Beckenbach says some releases of gcc # support --undefined. This deserves some investigation. FIXME archive_cmds_F77='$CC -nostart $libobjs $deplibs $compiler_flags ${wl}-soname $wl$soname -o $lib' else ld_shlibs_F77=no fi ;; cygwin* | mingw* | pw32* | cegcc*) # _LT_TAGVAR(hardcode_libdir_flag_spec, F77) is actually meaningless, # as there is no search path for DLLs. hardcode_libdir_flag_spec_F77='-L$libdir' allow_undefined_flag_F77=unsupported always_export_symbols_F77=no enable_shared_with_static_runtimes_F77=yes export_symbols_cmds_F77='$NM $libobjs $convenience | $global_symbol_pipe | $SED -e '\''/^[BCDGRS][ ]/s/.*[ ]\([^ ]*\)/\1 DATA/'\'' | $SED -e '\''/^[AITW][ ]/s/.*[ ]//'\'' | sort | uniq > $export_symbols' if $LD --help 2>&1 | $GREP 'auto-import' > /dev/null; then archive_cmds_F77='$CC -shared $libobjs $deplibs $compiler_flags -o $output_objdir/$soname ${wl}--enable-auto-image-base -Xlinker --out-implib -Xlinker $lib' # If the export-symbols file already is a .def file (1st line # is EXPORTS), use it as is; otherwise, prepend... archive_expsym_cmds_F77='if test "x`$SED 1q $export_symbols`" = xEXPORTS; then cp $export_symbols $output_objdir/$soname.def; else echo EXPORTS > $output_objdir/$soname.def; cat $export_symbols >> $output_objdir/$soname.def; fi~ $CC -shared $output_objdir/$soname.def $libobjs $deplibs $compiler_flags -o $output_objdir/$soname ${wl}--enable-auto-image-base -Xlinker --out-implib -Xlinker $lib' else ld_shlibs_F77=no fi ;; interix[3-9]*) hardcode_direct_F77=no hardcode_shlibpath_var_F77=no hardcode_libdir_flag_spec_F77='${wl}-rpath,$libdir' export_dynamic_flag_spec_F77='${wl}-E' # Hack: On Interix 3.x, we cannot compile PIC because of a broken gcc. # Instead, shared libraries are loaded at an image base (0x10000000 by # default) and relocated if they conflict, which is a slow very memory # consuming and fragmenting process. To avoid this, we pick a random, # 256 KiB-aligned image base between 0x50000000 and 0x6FFC0000 at link # time. Moving up from 0x10000000 also allows more sbrk(2) space. archive_cmds_F77='$CC -shared $pic_flag $libobjs $deplibs $compiler_flags ${wl}-h,$soname ${wl}--image-base,`expr ${RANDOM-$$} % 4096 / 2 \* 262144 + 1342177280` -o $lib' archive_expsym_cmds_F77='sed "s,^,_," $export_symbols >$output_objdir/$soname.expsym~$CC -shared $pic_flag $libobjs $deplibs $compiler_flags ${wl}-h,$soname ${wl}--retain-symbols-file,$output_objdir/$soname.expsym ${wl}--image-base,`expr ${RANDOM-$$} % 4096 / 2 \* 262144 + 1342177280` -o $lib' ;; gnu* | linux* | tpf* | k*bsd*-gnu | kopensolaris*-gnu) tmp_diet=no if test "$host_os" = linux-dietlibc; then case $cc_basename in diet\ *) tmp_diet=yes;; # linux-dietlibc with static linking (!diet-dyn) esac fi if $LD --help 2>&1 | $EGREP ': supported targets:.* elf' > /dev/null \ && test "$tmp_diet" = no then tmp_addflag= tmp_sharedflag='-shared' case $cc_basename,$host_cpu in pgcc*) # Portland Group C compiler whole_archive_flag_spec_F77='${wl}--whole-archive`for conv in $convenience\"\"; do test -n \"$conv\" && new_convenience=\"$new_convenience,$conv\"; done; $ECHO \"$new_convenience\"` ${wl}--no-whole-archive' tmp_addflag=' $pic_flag' ;; pgf77* | pgf90* | pgf95*) # Portland Group f77 and f90 compilers whole_archive_flag_spec_F77='${wl}--whole-archive`for conv in $convenience\"\"; do test -n \"$conv\" && new_convenience=\"$new_convenience,$conv\"; done; $ECHO \"$new_convenience\"` ${wl}--no-whole-archive' tmp_addflag=' $pic_flag -Mnomain' ;; ecc*,ia64* | icc*,ia64*) # Intel C compiler on ia64 tmp_addflag=' -i_dynamic' ;; efc*,ia64* | ifort*,ia64*) # Intel Fortran compiler on ia64 tmp_addflag=' -i_dynamic -nofor_main' ;; ifc* | ifort*) # Intel Fortran compiler tmp_addflag=' -nofor_main' ;; lf95*) # Lahey Fortran 8.1 whole_archive_flag_spec_F77= tmp_sharedflag='--shared' ;; xl[cC]*) # IBM XL C 8.0 on PPC (deal with xlf below) tmp_sharedflag='-qmkshrobj' tmp_addflag= ;; esac case `$CC -V 2>&1 | sed 5q` in *Sun\ C*) # Sun C 5.9 whole_archive_flag_spec_F77='${wl}--whole-archive`new_convenience=; for conv in $convenience\"\"; do test -z \"$conv\" || new_convenience=\"$new_convenience,$conv\"; done; $ECHO \"$new_convenience\"` ${wl}--no-whole-archive' compiler_needs_object_F77=yes tmp_sharedflag='-G' ;; *Sun\ F*) # Sun Fortran 8.3 tmp_sharedflag='-G' ;; esac archive_cmds_F77='$CC '"$tmp_sharedflag""$tmp_addflag"' $libobjs $deplibs $compiler_flags ${wl}-soname $wl$soname -o $lib' if test "x$supports_anon_versioning" = xyes; then archive_expsym_cmds_F77='echo "{ global:" > $output_objdir/$libname.ver~ cat $export_symbols | sed -e "s/\(.*\)/\1;/" >> $output_objdir/$libname.ver~ echo "local: *; };" >> $output_objdir/$libname.ver~ $CC '"$tmp_sharedflag""$tmp_addflag"' $libobjs $deplibs $compiler_flags ${wl}-soname $wl$soname ${wl}-version-script ${wl}$output_objdir/$libname.ver -o $lib' fi case $cc_basename in xlf*) # IBM XL Fortran 10.1 on PPC cannot create shared libs itself whole_archive_flag_spec_F77='--whole-archive$convenience --no-whole-archive' hardcode_libdir_flag_spec_F77= hardcode_libdir_flag_spec_ld_F77='-rpath $libdir' archive_cmds_F77='$LD -shared $libobjs $deplibs $compiler_flags -soname $soname -o $lib' if test "x$supports_anon_versioning" = xyes; then archive_expsym_cmds_F77='echo "{ global:" > $output_objdir/$libname.ver~ cat $export_symbols | sed -e "s/\(.*\)/\1;/" >> $output_objdir/$libname.ver~ echo "local: *; };" >> $output_objdir/$libname.ver~ $LD -shared $libobjs $deplibs $compiler_flags -soname $soname -version-script $output_objdir/$libname.ver -o $lib' fi ;; esac else ld_shlibs_F77=no fi ;; netbsd* | netbsdelf*-gnu) if echo __ELF__ | $CC -E - | $GREP __ELF__ >/dev/null; then archive_cmds_F77='$LD -Bshareable $libobjs $deplibs $linker_flags -o $lib' wlarc= else archive_cmds_F77='$CC -shared $libobjs $deplibs $compiler_flags ${wl}-soname $wl$soname -o $lib' archive_expsym_cmds_F77='$CC -shared $libobjs $deplibs $compiler_flags ${wl}-soname $wl$soname ${wl}-retain-symbols-file $wl$export_symbols -o $lib' fi ;; solaris*) if $LD -v 2>&1 | $GREP 'BFD 2\.8' > /dev/null; then ld_shlibs_F77=no cat <<_LT_EOF 1>&2 *** Warning: The releases 2.8.* of the GNU linker cannot reliably *** create shared libraries on Solaris systems. Therefore, libtool *** is disabling shared libraries support. We urge you to upgrade GNU *** binutils to release 2.9.1 or newer. Another option is to modify *** your PATH or compiler configuration so that the native linker is *** used, and then restart. _LT_EOF elif $LD --help 2>&1 | $GREP ': supported targets:.* elf' > /dev/null; then archive_cmds_F77='$CC -shared $libobjs $deplibs $compiler_flags ${wl}-soname $wl$soname -o $lib' archive_expsym_cmds_F77='$CC -shared $libobjs $deplibs $compiler_flags ${wl}-soname $wl$soname ${wl}-retain-symbols-file $wl$export_symbols -o $lib' else ld_shlibs_F77=no fi ;; sysv5* | sco3.2v5* | sco5v6* | unixware* | OpenUNIX*) case `$LD -v 2>&1` in *\ [01].* | *\ 2.[0-9].* | *\ 2.1[0-5].*) ld_shlibs_F77=no cat <<_LT_EOF 1>&2 *** Warning: Releases of the GNU linker prior to 2.16.91.0.3 can not *** reliably create shared libraries on SCO systems. Therefore, libtool *** is disabling shared libraries support. We urge you to upgrade GNU *** binutils to release 2.16.91.0.3 or newer. Another option is to modify *** your PATH or compiler configuration so that the native linker is *** used, and then restart. _LT_EOF ;; *) # For security reasons, it is highly recommended that you always # use absolute paths for naming shared libraries, and exclude the # DT_RUNPATH tag from executables and libraries. But doing so # requires that you compile everything twice, which is a pain. if $LD --help 2>&1 | $GREP ': supported targets:.* elf' > /dev/null; then hardcode_libdir_flag_spec_F77='${wl}-rpath ${wl}$libdir' archive_cmds_F77='$CC -shared $libobjs $deplibs $compiler_flags ${wl}-soname $wl$soname -o $lib' archive_expsym_cmds_F77='$CC -shared $libobjs $deplibs $compiler_flags ${wl}-soname $wl$soname ${wl}-retain-symbols-file $wl$export_symbols -o $lib' else ld_shlibs_F77=no fi ;; esac ;; sunos4*) archive_cmds_F77='$LD -assert pure-text -Bshareable -o $lib $libobjs $deplibs $linker_flags' wlarc= hardcode_direct_F77=yes hardcode_shlibpath_var_F77=no ;; *) if $LD --help 2>&1 | $GREP ': supported targets:.* elf' > /dev/null; then archive_cmds_F77='$CC -shared $libobjs $deplibs $compiler_flags ${wl}-soname $wl$soname -o $lib' archive_expsym_cmds_F77='$CC -shared $libobjs $deplibs $compiler_flags ${wl}-soname $wl$soname ${wl}-retain-symbols-file $wl$export_symbols -o $lib' else ld_shlibs_F77=no fi ;; esac if test "$ld_shlibs_F77" = no; then runpath_var= hardcode_libdir_flag_spec_F77= export_dynamic_flag_spec_F77= whole_archive_flag_spec_F77= fi else # PORTME fill in a description of your system's linker (not GNU ld) case $host_os in aix3*) allow_undefined_flag_F77=unsupported always_export_symbols_F77=yes archive_expsym_cmds_F77='$LD -o $output_objdir/$soname $libobjs $deplibs $linker_flags -bE:$export_symbols -T512 -H512 -bM:SRE~$AR $AR_FLAGS $lib $output_objdir/$soname' # Note: this linker hardcodes the directories in LIBPATH if there # are no directories specified by -L. hardcode_minus_L_F77=yes if test "$GCC" = yes && test -z "$lt_prog_compiler_static"; then # Neither direct hardcoding nor static linking is supported with a # broken collect2. hardcode_direct_F77=unsupported fi ;; aix[4-9]*) if test "$host_cpu" = ia64; then # On IA64, the linker does run time linking by default, so we don't # have to do anything special. aix_use_runtimelinking=no exp_sym_flag='-Bexport' no_entry_flag="" else # If we're using GNU nm, then we don't want the "-C" option. # -C means demangle to AIX nm, but means don't demangle with GNU nm if $NM -V 2>&1 | $GREP 'GNU' > /dev/null; then export_symbols_cmds_F77='$NM -Bpg $libobjs $convenience | awk '\''{ if (((\$ 2 == "T") || (\$ 2 == "D") || (\$ 2 == "B")) && (substr(\$ 3,1,1) != ".")) { print \$ 3 } }'\'' | sort -u > $export_symbols' else export_symbols_cmds_F77='$NM -BCpg $libobjs $convenience | awk '\''{ if (((\$ 2 == "T") || (\$ 2 == "D") || (\$ 2 == "B")) && (substr(\$ 3,1,1) != ".")) { print \$ 3 } }'\'' | sort -u > $export_symbols' fi aix_use_runtimelinking=no # Test if we are trying to use run time linking or normal # AIX style linking. If -brtl is somewhere in LDFLAGS, we # need to do runtime linking. case $host_os in aix4.[23]|aix4.[23].*|aix[5-9]*) for ld_flag in $LDFLAGS; do if (test $ld_flag = "-brtl" || test $ld_flag = "-Wl,-brtl"); then aix_use_runtimelinking=yes break fi done ;; esac exp_sym_flag='-bexport' no_entry_flag='-bnoentry' fi # When large executables or shared objects are built, AIX ld can # have problems creating the table of contents. If linking a library # or program results in "error TOC overflow" add -mminimal-toc to # CXXFLAGS/CFLAGS for g++/gcc. In the cases where that is not # enough to fix the problem, add -Wl,-bbigtoc to LDFLAGS. archive_cmds_F77='' hardcode_direct_F77=yes hardcode_direct_absolute_F77=yes hardcode_libdir_separator_F77=':' link_all_deplibs_F77=yes file_list_spec_F77='${wl}-f,' if test "$GCC" = yes; then case $host_os in aix4.[012]|aix4.[012].*) # We only want to do this on AIX 4.2 and lower, the check # below for broken collect2 doesn't work under 4.3+ collect2name=`${CC} -print-prog-name=collect2` if test -f "$collect2name" && strings "$collect2name" | $GREP resolve_lib_name >/dev/null then # We have reworked collect2 : else # We have old collect2 hardcode_direct_F77=unsupported # It fails to find uninstalled libraries when the uninstalled # path is not listed in the libpath. Setting hardcode_minus_L # to unsupported forces relinking hardcode_minus_L_F77=yes hardcode_libdir_flag_spec_F77='-L$libdir' hardcode_libdir_separator_F77= fi ;; esac shared_flag='-shared' if test "$aix_use_runtimelinking" = yes; then shared_flag="$shared_flag "'${wl}-G' fi link_all_deplibs_F77=no else # not using gcc if test "$host_cpu" = ia64; then # VisualAge C++, Version 5.5 for AIX 5L for IA-64, Beta 3 Release # chokes on -Wl,-G. The following line is correct: shared_flag='-G' else if test "$aix_use_runtimelinking" = yes; then shared_flag='${wl}-G' else shared_flag='${wl}-bM:SRE' fi fi fi export_dynamic_flag_spec_F77='${wl}-bexpall' # It seems that -bexpall does not export symbols beginning with # underscore (_), so it is better to generate a list of symbols to export. always_export_symbols_F77=yes if test "$aix_use_runtimelinking" = yes; then # Warning - without using the other runtime loading flags (-brtl), # -berok will link without error, but may produce a broken library. allow_undefined_flag_F77='-berok' # Determine the default libpath from the value encoded in an # empty executable. cat > conftest.$ac_ext <<_ACEOF program main end _ACEOF if ac_fn_f77_try_link "$LINENO"; then : lt_aix_libpath_sed=' /Import File Strings/,/^$/ { /^0/ { s/^0 *\(.*\)$/\1/ p } }' aix_libpath=`dump -H conftest$ac_exeext 2>/dev/null | $SED -n -e "$lt_aix_libpath_sed"` # Check for a 64-bit object if we didn't find anything. if test -z "$aix_libpath"; then aix_libpath=`dump -HX64 conftest$ac_exeext 2>/dev/null | $SED -n -e "$lt_aix_libpath_sed"` fi fi rm -f core conftest.err conftest.$ac_objext \ conftest$ac_exeext conftest.$ac_ext if test -z "$aix_libpath"; then aix_libpath="/usr/lib:/lib"; fi hardcode_libdir_flag_spec_F77='${wl}-blibpath:$libdir:'"$aix_libpath" archive_expsym_cmds_F77='$CC -o $output_objdir/$soname $libobjs $deplibs '"\${wl}$no_entry_flag"' $compiler_flags `if test "x${allow_undefined_flag}" != "x"; then $ECHO "X${wl}${allow_undefined_flag}" | $Xsed; else :; fi` '"\${wl}$exp_sym_flag:\$export_symbols $shared_flag" else if test "$host_cpu" = ia64; then hardcode_libdir_flag_spec_F77='${wl}-R $libdir:/usr/lib:/lib' allow_undefined_flag_F77="-z nodefs" archive_expsym_cmds_F77="\$CC $shared_flag"' -o $output_objdir/$soname $libobjs $deplibs '"\${wl}$no_entry_flag"' $compiler_flags ${wl}${allow_undefined_flag} '"\${wl}$exp_sym_flag:\$export_symbols" else # Determine the default libpath from the value encoded in an # empty executable. cat > conftest.$ac_ext <<_ACEOF program main end _ACEOF if ac_fn_f77_try_link "$LINENO"; then : lt_aix_libpath_sed=' /Import File Strings/,/^$/ { /^0/ { s/^0 *\(.*\)$/\1/ p } }' aix_libpath=`dump -H conftest$ac_exeext 2>/dev/null | $SED -n -e "$lt_aix_libpath_sed"` # Check for a 64-bit object if we didn't find anything. if test -z "$aix_libpath"; then aix_libpath=`dump -HX64 conftest$ac_exeext 2>/dev/null | $SED -n -e "$lt_aix_libpath_sed"` fi fi rm -f core conftest.err conftest.$ac_objext \ conftest$ac_exeext conftest.$ac_ext if test -z "$aix_libpath"; then aix_libpath="/usr/lib:/lib"; fi hardcode_libdir_flag_spec_F77='${wl}-blibpath:$libdir:'"$aix_libpath" # Warning - without using the other run time loading flags, # -berok will link without error, but may produce a broken library. no_undefined_flag_F77=' ${wl}-bernotok' allow_undefined_flag_F77=' ${wl}-berok' # Exported symbols can be pulled into shared objects from archives whole_archive_flag_spec_F77='$convenience' archive_cmds_need_lc_F77=yes # This is similar to how AIX traditionally builds its shared libraries. archive_expsym_cmds_F77="\$CC $shared_flag"' -o $output_objdir/$soname $libobjs $deplibs ${wl}-bnoentry $compiler_flags ${wl}-bE:$export_symbols${allow_undefined_flag}~$AR $AR_FLAGS $output_objdir/$libname$release.a $output_objdir/$soname' fi fi ;; amigaos*) case $host_cpu in powerpc) # see comment about AmigaOS4 .so support archive_cmds_F77='$CC -shared $libobjs $deplibs $compiler_flags ${wl}-soname $wl$soname -o $lib' archive_expsym_cmds_F77='' ;; m68k) archive_cmds_F77='$RM $output_objdir/a2ixlibrary.data~$ECHO "#define NAME $libname" > $output_objdir/a2ixlibrary.data~$ECHO "#define LIBRARY_ID 1" >> $output_objdir/a2ixlibrary.data~$ECHO "#define VERSION $major" >> $output_objdir/a2ixlibrary.data~$ECHO "#define REVISION $revision" >> $output_objdir/a2ixlibrary.data~$AR $AR_FLAGS $lib $libobjs~$RANLIB $lib~(cd $output_objdir && a2ixlibrary -32)' hardcode_libdir_flag_spec_F77='-L$libdir' hardcode_minus_L_F77=yes ;; esac ;; bsdi[45]*) export_dynamic_flag_spec_F77=-rdynamic ;; cygwin* | mingw* | pw32* | cegcc*) # When not using gcc, we currently assume that we are using # Microsoft Visual C++. # hardcode_libdir_flag_spec is actually meaningless, as there is # no search path for DLLs. hardcode_libdir_flag_spec_F77=' ' allow_undefined_flag_F77=unsupported # Tell ltmain to make .lib files, not .a files. libext=lib # Tell ltmain to make .dll files, not .so files. shrext_cmds=".dll" # FIXME: Setting linknames here is a bad hack. archive_cmds_F77='$CC -o $lib $libobjs $compiler_flags `$ECHO "X$deplibs" | $Xsed -e '\''s/ -lc$//'\''` -link -dll~linknames=' # The linker will automatically build a .lib file if we build a DLL. old_archive_from_new_cmds_F77='true' # FIXME: Should let the user specify the lib program. old_archive_cmds_F77='lib -OUT:$oldlib$oldobjs$old_deplibs' fix_srcfile_path_F77='`cygpath -w "$srcfile"`' enable_shared_with_static_runtimes_F77=yes ;; darwin* | rhapsody*) archive_cmds_need_lc_F77=no hardcode_direct_F77=no hardcode_automatic_F77=yes hardcode_shlibpath_var_F77=unsupported whole_archive_flag_spec_F77='' link_all_deplibs_F77=yes allow_undefined_flag_F77="$_lt_dar_allow_undefined" case $cc_basename in ifort*) _lt_dar_can_shared=yes ;; *) _lt_dar_can_shared=$GCC ;; esac if test "$_lt_dar_can_shared" = "yes"; then output_verbose_link_cmd=echo archive_cmds_F77="\$CC -dynamiclib \$allow_undefined_flag -o \$lib \$libobjs \$deplibs \$compiler_flags -install_name \$rpath/\$soname \$verstring $_lt_dar_single_mod${_lt_dsymutil}" module_cmds_F77="\$CC \$allow_undefined_flag -o \$lib -bundle \$libobjs \$deplibs \$compiler_flags${_lt_dsymutil}" archive_expsym_cmds_F77="sed 's,^,_,' < \$export_symbols > \$output_objdir/\${libname}-symbols.expsym~\$CC -dynamiclib \$allow_undefined_flag -o \$lib \$libobjs \$deplibs \$compiler_flags -install_name \$rpath/\$soname \$verstring ${_lt_dar_single_mod}${_lt_dar_export_syms}${_lt_dsymutil}" module_expsym_cmds_F77="sed -e 's,^,_,' < \$export_symbols > \$output_objdir/\${libname}-symbols.expsym~\$CC \$allow_undefined_flag -o \$lib -bundle \$libobjs \$deplibs \$compiler_flags${_lt_dar_export_syms}${_lt_dsymutil}" else ld_shlibs_F77=no fi ;; dgux*) archive_cmds_F77='$LD -G -h $soname -o $lib $libobjs $deplibs $linker_flags' hardcode_libdir_flag_spec_F77='-L$libdir' hardcode_shlibpath_var_F77=no ;; freebsd1*) ld_shlibs_F77=no ;; # FreeBSD 2.2.[012] allows us to include c++rt0.o to get C++ constructor # support. Future versions do this automatically, but an explicit c++rt0.o # does not break anything, and helps significantly (at the cost of a little # extra space). freebsd2.2*) archive_cmds_F77='$LD -Bshareable -o $lib $libobjs $deplibs $linker_flags /usr/lib/c++rt0.o' hardcode_libdir_flag_spec_F77='-R$libdir' hardcode_direct_F77=yes hardcode_shlibpath_var_F77=no ;; # Unfortunately, older versions of FreeBSD 2 do not have this feature. freebsd2*) archive_cmds_F77='$LD -Bshareable -o $lib $libobjs $deplibs $linker_flags' hardcode_direct_F77=yes hardcode_minus_L_F77=yes hardcode_shlibpath_var_F77=no ;; # FreeBSD 3 and greater uses gcc -shared to do shared libraries. freebsd* | dragonfly*) archive_cmds_F77='$CC -shared -o $lib $libobjs $deplibs $compiler_flags' hardcode_libdir_flag_spec_F77='-R$libdir' hardcode_direct_F77=yes hardcode_shlibpath_var_F77=no ;; hpux9*) if test "$GCC" = yes; then archive_cmds_F77='$RM $output_objdir/$soname~$CC -shared -fPIC ${wl}+b ${wl}$install_libdir -o $output_objdir/$soname $libobjs $deplibs $compiler_flags~test $output_objdir/$soname = $lib || mv $output_objdir/$soname $lib' else archive_cmds_F77='$RM $output_objdir/$soname~$LD -b +b $install_libdir -o $output_objdir/$soname $libobjs $deplibs $linker_flags~test $output_objdir/$soname = $lib || mv $output_objdir/$soname $lib' fi hardcode_libdir_flag_spec_F77='${wl}+b ${wl}$libdir' hardcode_libdir_separator_F77=: hardcode_direct_F77=yes # hardcode_minus_L: Not really in the search PATH, # but as the default location of the library. hardcode_minus_L_F77=yes export_dynamic_flag_spec_F77='${wl}-E' ;; hpux10*) if test "$GCC" = yes -a "$with_gnu_ld" = no; then archive_cmds_F77='$CC -shared -fPIC ${wl}+h ${wl}$soname ${wl}+b ${wl}$install_libdir -o $lib $libobjs $deplibs $compiler_flags' else archive_cmds_F77='$LD -b +h $soname +b $install_libdir -o $lib $libobjs $deplibs $linker_flags' fi if test "$with_gnu_ld" = no; then hardcode_libdir_flag_spec_F77='${wl}+b ${wl}$libdir' hardcode_libdir_flag_spec_ld_F77='+b $libdir' hardcode_libdir_separator_F77=: hardcode_direct_F77=yes hardcode_direct_absolute_F77=yes export_dynamic_flag_spec_F77='${wl}-E' # hardcode_minus_L: Not really in the search PATH, # but as the default location of the library. hardcode_minus_L_F77=yes fi ;; hpux11*) if test "$GCC" = yes -a "$with_gnu_ld" = no; then case $host_cpu in hppa*64*) archive_cmds_F77='$CC -shared ${wl}+h ${wl}$soname -o $lib $libobjs $deplibs $compiler_flags' ;; ia64*) archive_cmds_F77='$CC -shared -fPIC ${wl}+h ${wl}$soname ${wl}+nodefaultrpath -o $lib $libobjs $deplibs $compiler_flags' ;; *) archive_cmds_F77='$CC -shared -fPIC ${wl}+h ${wl}$soname ${wl}+b ${wl}$install_libdir -o $lib $libobjs $deplibs $compiler_flags' ;; esac else case $host_cpu in hppa*64*) archive_cmds_F77='$CC -b ${wl}+h ${wl}$soname -o $lib $libobjs $deplibs $compiler_flags' ;; ia64*) archive_cmds_F77='$CC -b ${wl}+h ${wl}$soname ${wl}+nodefaultrpath -o $lib $libobjs $deplibs $compiler_flags' ;; *) archive_cmds_F77='$CC -b ${wl}+h ${wl}$soname ${wl}+b ${wl}$install_libdir -o $lib $libobjs $deplibs $compiler_flags' ;; esac fi if test "$with_gnu_ld" = no; then hardcode_libdir_flag_spec_F77='${wl}+b ${wl}$libdir' hardcode_libdir_separator_F77=: case $host_cpu in hppa*64*|ia64*) hardcode_direct_F77=no hardcode_shlibpath_var_F77=no ;; *) hardcode_direct_F77=yes hardcode_direct_absolute_F77=yes export_dynamic_flag_spec_F77='${wl}-E' # hardcode_minus_L: Not really in the search PATH, # but as the default location of the library. hardcode_minus_L_F77=yes ;; esac fi ;; irix5* | irix6* | nonstopux*) if test "$GCC" = yes; then archive_cmds_F77='$CC -shared $libobjs $deplibs $compiler_flags ${wl}-soname ${wl}$soname `test -n "$verstring" && $ECHO "X${wl}-set_version ${wl}$verstring" | $Xsed` ${wl}-update_registry ${wl}${output_objdir}/so_locations -o $lib' # Try to use the -exported_symbol ld option, if it does not # work, assume that -exports_file does not work either and # implicitly export all symbols. save_LDFLAGS="$LDFLAGS" LDFLAGS="$LDFLAGS -shared ${wl}-exported_symbol ${wl}foo ${wl}-update_registry ${wl}/dev/null" cat > conftest.$ac_ext <<_ACEOF int foo(void) {} _ACEOF if ac_fn_f77_try_link "$LINENO"; then : archive_expsym_cmds_F77='$CC -shared $libobjs $deplibs $compiler_flags ${wl}-soname ${wl}$soname `test -n "$verstring" && $ECHO "X${wl}-set_version ${wl}$verstring" | $Xsed` ${wl}-update_registry ${wl}${output_objdir}/so_locations ${wl}-exports_file ${wl}$export_symbols -o $lib' fi rm -f core conftest.err conftest.$ac_objext \ conftest$ac_exeext conftest.$ac_ext LDFLAGS="$save_LDFLAGS" else archive_cmds_F77='$CC -shared $libobjs $deplibs $compiler_flags -soname $soname `test -n "$verstring" && $ECHO "X-set_version $verstring" | $Xsed` -update_registry ${output_objdir}/so_locations -o $lib' archive_expsym_cmds_F77='$CC -shared $libobjs $deplibs $compiler_flags -soname $soname `test -n "$verstring" && $ECHO "X-set_version $verstring" | $Xsed` -update_registry ${output_objdir}/so_locations -exports_file $export_symbols -o $lib' fi archive_cmds_need_lc_F77='no' hardcode_libdir_flag_spec_F77='${wl}-rpath ${wl}$libdir' hardcode_libdir_separator_F77=: inherit_rpath_F77=yes link_all_deplibs_F77=yes ;; netbsd* | netbsdelf*-gnu) if echo __ELF__ | $CC -E - | $GREP __ELF__ >/dev/null; then archive_cmds_F77='$LD -Bshareable -o $lib $libobjs $deplibs $linker_flags' # a.out else archive_cmds_F77='$LD -shared -o $lib $libobjs $deplibs $linker_flags' # ELF fi hardcode_libdir_flag_spec_F77='-R$libdir' hardcode_direct_F77=yes hardcode_shlibpath_var_F77=no ;; newsos6) archive_cmds_F77='$LD -G -h $soname -o $lib $libobjs $deplibs $linker_flags' hardcode_direct_F77=yes hardcode_libdir_flag_spec_F77='${wl}-rpath ${wl}$libdir' hardcode_libdir_separator_F77=: hardcode_shlibpath_var_F77=no ;; *nto* | *qnx*) ;; openbsd*) if test -f /usr/libexec/ld.so; then hardcode_direct_F77=yes hardcode_shlibpath_var_F77=no hardcode_direct_absolute_F77=yes if test -z "`echo __ELF__ | $CC -E - | $GREP __ELF__`" || test "$host_os-$host_cpu" = "openbsd2.8-powerpc"; then archive_cmds_F77='$CC -shared $pic_flag -o $lib $libobjs $deplibs $compiler_flags' archive_expsym_cmds_F77='$CC -shared $pic_flag -o $lib $libobjs $deplibs $compiler_flags ${wl}-retain-symbols-file,$export_symbols' hardcode_libdir_flag_spec_F77='${wl}-rpath,$libdir' export_dynamic_flag_spec_F77='${wl}-E' else case $host_os in openbsd[01].* | openbsd2.[0-7] | openbsd2.[0-7].*) archive_cmds_F77='$LD -Bshareable -o $lib $libobjs $deplibs $linker_flags' hardcode_libdir_flag_spec_F77='-R$libdir' ;; *) archive_cmds_F77='$CC -shared $pic_flag -o $lib $libobjs $deplibs $compiler_flags' hardcode_libdir_flag_spec_F77='${wl}-rpath,$libdir' ;; esac fi else ld_shlibs_F77=no fi ;; os2*) hardcode_libdir_flag_spec_F77='-L$libdir' hardcode_minus_L_F77=yes allow_undefined_flag_F77=unsupported archive_cmds_F77='$ECHO "LIBRARY $libname INITINSTANCE" > $output_objdir/$libname.def~$ECHO "DESCRIPTION \"$libname\"" >> $output_objdir/$libname.def~$ECHO DATA >> $output_objdir/$libname.def~$ECHO " SINGLE NONSHARED" >> $output_objdir/$libname.def~$ECHO EXPORTS >> $output_objdir/$libname.def~emxexp $libobjs >> $output_objdir/$libname.def~$CC -Zdll -Zcrtdll -o $lib $libobjs $deplibs $compiler_flags $output_objdir/$libname.def' old_archive_from_new_cmds_F77='emximp -o $output_objdir/$libname.a $output_objdir/$libname.def' ;; osf3*) if test "$GCC" = yes; then allow_undefined_flag_F77=' ${wl}-expect_unresolved ${wl}\*' archive_cmds_F77='$CC -shared${allow_undefined_flag} $libobjs $deplibs $compiler_flags ${wl}-soname ${wl}$soname `test -n "$verstring" && $ECHO "X${wl}-set_version ${wl}$verstring" | $Xsed` ${wl}-update_registry ${wl}${output_objdir}/so_locations -o $lib' else allow_undefined_flag_F77=' -expect_unresolved \*' archive_cmds_F77='$CC -shared${allow_undefined_flag} $libobjs $deplibs $compiler_flags -soname $soname `test -n "$verstring" && $ECHO "X-set_version $verstring" | $Xsed` -update_registry ${output_objdir}/so_locations -o $lib' fi archive_cmds_need_lc_F77='no' hardcode_libdir_flag_spec_F77='${wl}-rpath ${wl}$libdir' hardcode_libdir_separator_F77=: ;; osf4* | osf5*) # as osf3* with the addition of -msym flag if test "$GCC" = yes; then allow_undefined_flag_F77=' ${wl}-expect_unresolved ${wl}\*' archive_cmds_F77='$CC -shared${allow_undefined_flag} $libobjs $deplibs $compiler_flags ${wl}-msym ${wl}-soname ${wl}$soname `test -n "$verstring" && $ECHO "X${wl}-set_version ${wl}$verstring" | $Xsed` ${wl}-update_registry ${wl}${output_objdir}/so_locations -o $lib' hardcode_libdir_flag_spec_F77='${wl}-rpath ${wl}$libdir' else allow_undefined_flag_F77=' -expect_unresolved \*' archive_cmds_F77='$CC -shared${allow_undefined_flag} $libobjs $deplibs $compiler_flags -msym -soname $soname `test -n "$verstring" && $ECHO "X-set_version $verstring" | $Xsed` -update_registry ${output_objdir}/so_locations -o $lib' archive_expsym_cmds_F77='for i in `cat $export_symbols`; do printf "%s %s\\n" -exported_symbol "\$i" >> $lib.exp; done; printf "%s\\n" "-hidden">> $lib.exp~ $CC -shared${allow_undefined_flag} ${wl}-input ${wl}$lib.exp $compiler_flags $libobjs $deplibs -soname $soname `test -n "$verstring" && $ECHO "X-set_version $verstring" | $Xsed` -update_registry ${output_objdir}/so_locations -o $lib~$RM $lib.exp' # Both c and cxx compiler support -rpath directly hardcode_libdir_flag_spec_F77='-rpath $libdir' fi archive_cmds_need_lc_F77='no' hardcode_libdir_separator_F77=: ;; solaris*) no_undefined_flag_F77=' -z defs' if test "$GCC" = yes; then wlarc='${wl}' archive_cmds_F77='$CC -shared ${wl}-z ${wl}text ${wl}-h ${wl}$soname -o $lib $libobjs $deplibs $compiler_flags' archive_expsym_cmds_F77='echo "{ global:" > $lib.exp~cat $export_symbols | $SED -e "s/\(.*\)/\1;/" >> $lib.exp~echo "local: *; };" >> $lib.exp~ $CC -shared ${wl}-z ${wl}text ${wl}-M ${wl}$lib.exp ${wl}-h ${wl}$soname -o $lib $libobjs $deplibs $compiler_flags~$RM $lib.exp' else case `$CC -V 2>&1` in *"Compilers 5.0"*) wlarc='' archive_cmds_F77='$LD -G${allow_undefined_flag} -h $soname -o $lib $libobjs $deplibs $linker_flags' archive_expsym_cmds_F77='echo "{ global:" > $lib.exp~cat $export_symbols | $SED -e "s/\(.*\)/\1;/" >> $lib.exp~echo "local: *; };" >> $lib.exp~ $LD -G${allow_undefined_flag} -M $lib.exp -h $soname -o $lib $libobjs $deplibs $linker_flags~$RM $lib.exp' ;; *) wlarc='${wl}' archive_cmds_F77='$CC -G${allow_undefined_flag} -h $soname -o $lib $libobjs $deplibs $compiler_flags' archive_expsym_cmds_F77='echo "{ global:" > $lib.exp~cat $export_symbols | $SED -e "s/\(.*\)/\1;/" >> $lib.exp~echo "local: *; };" >> $lib.exp~ $CC -G${allow_undefined_flag} -M $lib.exp -h $soname -o $lib $libobjs $deplibs $compiler_flags~$RM $lib.exp' ;; esac fi hardcode_libdir_flag_spec_F77='-R$libdir' hardcode_shlibpath_var_F77=no case $host_os in solaris2.[0-5] | solaris2.[0-5].*) ;; *) # The compiler driver will combine and reorder linker options, # but understands `-z linker_flag'. GCC discards it without `$wl', # but is careful enough not to reorder. # Supported since Solaris 2.6 (maybe 2.5.1?) if test "$GCC" = yes; then whole_archive_flag_spec_F77='${wl}-z ${wl}allextract$convenience ${wl}-z ${wl}defaultextract' else whole_archive_flag_spec_F77='-z allextract$convenience -z defaultextract' fi ;; esac link_all_deplibs_F77=yes ;; sunos4*) if test "x$host_vendor" = xsequent; then # Use $CC to link under sequent, because it throws in some extra .o # files that make .init and .fini sections work. archive_cmds_F77='$CC -G ${wl}-h $soname -o $lib $libobjs $deplibs $compiler_flags' else archive_cmds_F77='$LD -assert pure-text -Bstatic -o $lib $libobjs $deplibs $linker_flags' fi hardcode_libdir_flag_spec_F77='-L$libdir' hardcode_direct_F77=yes hardcode_minus_L_F77=yes hardcode_shlibpath_var_F77=no ;; sysv4) case $host_vendor in sni) archive_cmds_F77='$LD -G -h $soname -o $lib $libobjs $deplibs $linker_flags' hardcode_direct_F77=yes # is this really true??? ;; siemens) ## LD is ld it makes a PLAMLIB ## CC just makes a GrossModule. archive_cmds_F77='$LD -G -o $lib $libobjs $deplibs $linker_flags' reload_cmds_F77='$CC -r -o $output$reload_objs' hardcode_direct_F77=no ;; motorola) archive_cmds_F77='$LD -G -h $soname -o $lib $libobjs $deplibs $linker_flags' hardcode_direct_F77=no #Motorola manual says yes, but my tests say they lie ;; esac runpath_var='LD_RUN_PATH' hardcode_shlibpath_var_F77=no ;; sysv4.3*) archive_cmds_F77='$LD -G -h $soname -o $lib $libobjs $deplibs $linker_flags' hardcode_shlibpath_var_F77=no export_dynamic_flag_spec_F77='-Bexport' ;; sysv4*MP*) if test -d /usr/nec; then archive_cmds_F77='$LD -G -h $soname -o $lib $libobjs $deplibs $linker_flags' hardcode_shlibpath_var_F77=no runpath_var=LD_RUN_PATH hardcode_runpath_var=yes ld_shlibs_F77=yes fi ;; sysv4*uw2* | sysv5OpenUNIX* | sysv5UnixWare7.[01].[10]* | unixware7* | sco3.2v5.0.[024]*) no_undefined_flag_F77='${wl}-z,text' archive_cmds_need_lc_F77=no hardcode_shlibpath_var_F77=no runpath_var='LD_RUN_PATH' if test "$GCC" = yes; then archive_cmds_F77='$CC -shared ${wl}-h,$soname -o $lib $libobjs $deplibs $compiler_flags' archive_expsym_cmds_F77='$CC -shared ${wl}-Bexport:$export_symbols ${wl}-h,$soname -o $lib $libobjs $deplibs $compiler_flags' else archive_cmds_F77='$CC -G ${wl}-h,$soname -o $lib $libobjs $deplibs $compiler_flags' archive_expsym_cmds_F77='$CC -G ${wl}-Bexport:$export_symbols ${wl}-h,$soname -o $lib $libobjs $deplibs $compiler_flags' fi ;; sysv5* | sco3.2v5* | sco5v6*) # Note: We can NOT use -z defs as we might desire, because we do not # link with -lc, and that would cause any symbols used from libc to # always be unresolved, which means just about no library would # ever link correctly. If we're not using GNU ld we use -z text # though, which does catch some bad symbols but isn't as heavy-handed # as -z defs. no_undefined_flag_F77='${wl}-z,text' allow_undefined_flag_F77='${wl}-z,nodefs' archive_cmds_need_lc_F77=no hardcode_shlibpath_var_F77=no hardcode_libdir_flag_spec_F77='${wl}-R,$libdir' hardcode_libdir_separator_F77=':' link_all_deplibs_F77=yes export_dynamic_flag_spec_F77='${wl}-Bexport' runpath_var='LD_RUN_PATH' if test "$GCC" = yes; then archive_cmds_F77='$CC -shared ${wl}-h,$soname -o $lib $libobjs $deplibs $compiler_flags' archive_expsym_cmds_F77='$CC -shared ${wl}-Bexport:$export_symbols ${wl}-h,$soname -o $lib $libobjs $deplibs $compiler_flags' else archive_cmds_F77='$CC -G ${wl}-h,$soname -o $lib $libobjs $deplibs $compiler_flags' archive_expsym_cmds_F77='$CC -G ${wl}-Bexport:$export_symbols ${wl}-h,$soname -o $lib $libobjs $deplibs $compiler_flags' fi ;; uts4*) archive_cmds_F77='$LD -G -h $soname -o $lib $libobjs $deplibs $linker_flags' hardcode_libdir_flag_spec_F77='-L$libdir' hardcode_shlibpath_var_F77=no ;; *) ld_shlibs_F77=no ;; esac if test x$host_vendor = xsni; then case $host in sysv4 | sysv4.2uw2* | sysv4.3* | sysv5*) export_dynamic_flag_spec_F77='${wl}-Blargedynsym' ;; esac fi fi { $as_echo "$as_me:${as_lineno-$LINENO}: result: $ld_shlibs_F77" >&5 $as_echo "$ld_shlibs_F77" >&6; } test "$ld_shlibs_F77" = no && can_build_shared=no with_gnu_ld_F77=$with_gnu_ld # # Do we need to explicitly link libc? # case "x$archive_cmds_need_lc_F77" in x|xyes) # Assume -lc should be added archive_cmds_need_lc_F77=yes if test "$enable_shared" = yes && test "$GCC" = yes; then case $archive_cmds_F77 in *'~'*) # FIXME: we may have to deal with multi-command sequences. ;; '$CC '*) # Test whether the compiler implicitly links with -lc since on some # systems, -lgcc has to come before -lc. If gcc already passes -lc # to ld, don't add -lc before -lgcc. { $as_echo "$as_me:${as_lineno-$LINENO}: checking whether -lc should be explicitly linked in" >&5 $as_echo_n "checking whether -lc should be explicitly linked in... 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" >&6; } library_names_spec= libname_spec='lib$name' soname_spec= shrext_cmds=".so" postinstall_cmds= postuninstall_cmds= finish_cmds= finish_eval= shlibpath_var= shlibpath_overrides_runpath=unknown version_type=none dynamic_linker="$host_os ld.so" sys_lib_dlsearch_path_spec="/lib /usr/lib" need_lib_prefix=unknown hardcode_into_libs=no # when you set need_version to no, make sure it does not cause -set_version # flags to be left without arguments need_version=unknown case $host_os in aix3*) version_type=linux library_names_spec='${libname}${release}${shared_ext}$versuffix $libname.a' shlibpath_var=LIBPATH # AIX 3 has no versioning support, so we append a major version to the name. soname_spec='${libname}${release}${shared_ext}$major' ;; aix[4-9]*) version_type=linux need_lib_prefix=no need_version=no hardcode_into_libs=yes if test "$host_cpu" = ia64; then # AIX 5 supports IA64 library_names_spec='${libname}${release}${shared_ext}$major ${libname}${release}${shared_ext}$versuffix $libname${shared_ext}' shlibpath_var=LD_LIBRARY_PATH else # With GCC up to 2.95.x, collect2 would create an import file # for dependence libraries. 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The following line is correct: shared_flag='-G' else if test "$aix_use_runtimelinking" = yes; then shared_flag='${wl}-G' else shared_flag='${wl}-bM:SRE' fi fi fi export_dynamic_flag_spec_FC='${wl}-bexpall' # It seems that -bexpall does not export symbols beginning with # underscore (_), so it is better to generate a list of symbols to export. always_export_symbols_FC=yes if test "$aix_use_runtimelinking" = yes; then # Warning - without using the other runtime loading flags (-brtl), # -berok will link without error, but may produce a broken library. allow_undefined_flag_FC='-berok' # Determine the default libpath from the value encoded in an # empty executable. cat > conftest.$ac_ext <<_ACEOF program main end _ACEOF if ac_fn_fc_try_link "$LINENO"; then : lt_aix_libpath_sed=' /Import File Strings/,/^$/ { /^0/ { s/^0 *\(.*\)$/\1/ p } }' aix_libpath=`dump -H conftest$ac_exeext 2>/dev/null | $SED -n -e "$lt_aix_libpath_sed"` # Check for a 64-bit object if we didn't find anything. if test -z "$aix_libpath"; then aix_libpath=`dump -HX64 conftest$ac_exeext 2>/dev/null | $SED -n -e "$lt_aix_libpath_sed"` fi fi rm -f core conftest.err conftest.$ac_objext \ conftest$ac_exeext conftest.$ac_ext if test -z "$aix_libpath"; then aix_libpath="/usr/lib:/lib"; fi hardcode_libdir_flag_spec_FC='${wl}-blibpath:$libdir:'"$aix_libpath" archive_expsym_cmds_FC='$CC -o $output_objdir/$soname $libobjs $deplibs '"\${wl}$no_entry_flag"' $compiler_flags `if test "x${allow_undefined_flag}" != "x"; then $ECHO "X${wl}${allow_undefined_flag}" | $Xsed; else :; fi` '"\${wl}$exp_sym_flag:\$export_symbols $shared_flag" else if test "$host_cpu" = ia64; then hardcode_libdir_flag_spec_FC='${wl}-R $libdir:/usr/lib:/lib' allow_undefined_flag_FC="-z nodefs" archive_expsym_cmds_FC="\$CC $shared_flag"' -o $output_objdir/$soname $libobjs $deplibs '"\${wl}$no_entry_flag"' $compiler_flags ${wl}${allow_undefined_flag} '"\${wl}$exp_sym_flag:\$export_symbols" else # Determine the default libpath from the value encoded in an # empty executable. cat > conftest.$ac_ext <<_ACEOF program main end _ACEOF if ac_fn_fc_try_link "$LINENO"; then : lt_aix_libpath_sed=' /Import File Strings/,/^$/ { /^0/ { s/^0 *\(.*\)$/\1/ p } }' aix_libpath=`dump -H conftest$ac_exeext 2>/dev/null | $SED -n -e "$lt_aix_libpath_sed"` # Check for a 64-bit object if we didn't find anything. if test -z "$aix_libpath"; then aix_libpath=`dump -HX64 conftest$ac_exeext 2>/dev/null | $SED -n -e "$lt_aix_libpath_sed"` fi fi rm -f core conftest.err conftest.$ac_objext \ conftest$ac_exeext conftest.$ac_ext if test -z "$aix_libpath"; then aix_libpath="/usr/lib:/lib"; fi hardcode_libdir_flag_spec_FC='${wl}-blibpath:$libdir:'"$aix_libpath" # Warning - without using the other run time loading flags, # -berok will link without error, but may produce a broken library. no_undefined_flag_FC=' ${wl}-bernotok' allow_undefined_flag_FC=' ${wl}-berok' # Exported symbols can be pulled into shared objects from archives whole_archive_flag_spec_FC='$convenience' archive_cmds_need_lc_FC=yes # This is similar to how AIX traditionally builds its shared libraries. archive_expsym_cmds_FC="\$CC $shared_flag"' -o $output_objdir/$soname $libobjs $deplibs ${wl}-bnoentry $compiler_flags ${wl}-bE:$export_symbols${allow_undefined_flag}~$AR $AR_FLAGS $output_objdir/$libname$release.a $output_objdir/$soname' fi fi ;; amigaos*) case $host_cpu in powerpc) # see comment about AmigaOS4 .so support archive_cmds_FC='$CC -shared $libobjs $deplibs $compiler_flags ${wl}-soname $wl$soname -o $lib' archive_expsym_cmds_FC='' ;; m68k) archive_cmds_FC='$RM $output_objdir/a2ixlibrary.data~$ECHO "#define NAME $libname" > $output_objdir/a2ixlibrary.data~$ECHO "#define LIBRARY_ID 1" >> $output_objdir/a2ixlibrary.data~$ECHO "#define VERSION $major" >> $output_objdir/a2ixlibrary.data~$ECHO "#define REVISION $revision" >> $output_objdir/a2ixlibrary.data~$AR $AR_FLAGS $lib $libobjs~$RANLIB $lib~(cd $output_objdir && a2ixlibrary -32)' hardcode_libdir_flag_spec_FC='-L$libdir' hardcode_minus_L_FC=yes ;; esac ;; bsdi[45]*) export_dynamic_flag_spec_FC=-rdynamic ;; cygwin* | mingw* | pw32* | cegcc*) # When not using gcc, we currently assume that we are using # Microsoft Visual C++. # hardcode_libdir_flag_spec is actually meaningless, as there is # no search path for DLLs. hardcode_libdir_flag_spec_FC=' ' allow_undefined_flag_FC=unsupported # Tell ltmain to make .lib files, not .a files. libext=lib # Tell ltmain to make .dll files, not .so files. shrext_cmds=".dll" # FIXME: Setting linknames here is a bad hack. archive_cmds_FC='$CC -o $lib $libobjs $compiler_flags `$ECHO "X$deplibs" | $Xsed -e '\''s/ -lc$//'\''` -link -dll~linknames=' # The linker will automatically build a .lib file if we build a DLL. old_archive_from_new_cmds_FC='true' # FIXME: Should let the user specify the lib program. old_archive_cmds_FC='lib -OUT:$oldlib$oldobjs$old_deplibs' fix_srcfile_path_FC='`cygpath -w "$srcfile"`' enable_shared_with_static_runtimes_FC=yes ;; darwin* | rhapsody*) archive_cmds_need_lc_FC=no hardcode_direct_FC=no hardcode_automatic_FC=yes hardcode_shlibpath_var_FC=unsupported whole_archive_flag_spec_FC='' link_all_deplibs_FC=yes allow_undefined_flag_FC="$_lt_dar_allow_undefined" case $cc_basename in ifort*) _lt_dar_can_shared=yes ;; *) _lt_dar_can_shared=$GCC ;; esac if test "$_lt_dar_can_shared" = "yes"; then output_verbose_link_cmd=echo archive_cmds_FC="\$CC -dynamiclib \$allow_undefined_flag -o \$lib \$libobjs \$deplibs \$compiler_flags -install_name \$rpath/\$soname \$verstring $_lt_dar_single_mod${_lt_dsymutil}" module_cmds_FC="\$CC \$allow_undefined_flag -o \$lib -bundle \$libobjs \$deplibs \$compiler_flags${_lt_dsymutil}" archive_expsym_cmds_FC="sed 's,^,_,' < \$export_symbols > \$output_objdir/\${libname}-symbols.expsym~\$CC -dynamiclib \$allow_undefined_flag -o \$lib \$libobjs \$deplibs \$compiler_flags -install_name \$rpath/\$soname \$verstring ${_lt_dar_single_mod}${_lt_dar_export_syms}${_lt_dsymutil}" module_expsym_cmds_FC="sed -e 's,^,_,' < \$export_symbols > \$output_objdir/\${libname}-symbols.expsym~\$CC \$allow_undefined_flag -o \$lib -bundle \$libobjs \$deplibs \$compiler_flags${_lt_dar_export_syms}${_lt_dsymutil}" else ld_shlibs_FC=no fi ;; dgux*) archive_cmds_FC='$LD -G -h $soname -o $lib $libobjs $deplibs $linker_flags' hardcode_libdir_flag_spec_FC='-L$libdir' hardcode_shlibpath_var_FC=no ;; freebsd1*) ld_shlibs_FC=no ;; # FreeBSD 2.2.[012] allows us to include c++rt0.o to get C++ constructor # support. Future versions do this automatically, but an explicit c++rt0.o # does not break anything, and helps significantly (at the cost of a little # extra space). freebsd2.2*) archive_cmds_FC='$LD -Bshareable -o $lib $libobjs $deplibs $linker_flags /usr/lib/c++rt0.o' hardcode_libdir_flag_spec_FC='-R$libdir' hardcode_direct_FC=yes hardcode_shlibpath_var_FC=no ;; # Unfortunately, older versions of FreeBSD 2 do not have this feature. freebsd2*) archive_cmds_FC='$LD -Bshareable -o $lib $libobjs $deplibs $linker_flags' hardcode_direct_FC=yes hardcode_minus_L_FC=yes hardcode_shlibpath_var_FC=no ;; # FreeBSD 3 and greater uses gcc -shared to do shared libraries. freebsd* | dragonfly*) archive_cmds_FC='$CC -shared -o $lib $libobjs $deplibs $compiler_flags' hardcode_libdir_flag_spec_FC='-R$libdir' hardcode_direct_FC=yes hardcode_shlibpath_var_FC=no ;; hpux9*) if test "$GCC" = yes; then archive_cmds_FC='$RM $output_objdir/$soname~$CC -shared -fPIC ${wl}+b ${wl}$install_libdir -o $output_objdir/$soname $libobjs $deplibs $compiler_flags~test $output_objdir/$soname = $lib || mv $output_objdir/$soname $lib' else archive_cmds_FC='$RM $output_objdir/$soname~$LD -b +b $install_libdir -o $output_objdir/$soname $libobjs $deplibs $linker_flags~test $output_objdir/$soname = $lib || mv $output_objdir/$soname $lib' fi hardcode_libdir_flag_spec_FC='${wl}+b ${wl}$libdir' hardcode_libdir_separator_FC=: hardcode_direct_FC=yes # hardcode_minus_L: Not really in the search PATH, # but as the default location of the library. hardcode_minus_L_FC=yes export_dynamic_flag_spec_FC='${wl}-E' ;; hpux10*) if test "$GCC" = yes -a "$with_gnu_ld" = no; then archive_cmds_FC='$CC -shared -fPIC ${wl}+h ${wl}$soname ${wl}+b ${wl}$install_libdir -o $lib $libobjs $deplibs $compiler_flags' else archive_cmds_FC='$LD -b +h $soname +b $install_libdir -o $lib $libobjs $deplibs $linker_flags' fi if test "$with_gnu_ld" = no; then hardcode_libdir_flag_spec_FC='${wl}+b ${wl}$libdir' hardcode_libdir_flag_spec_ld_FC='+b $libdir' hardcode_libdir_separator_FC=: hardcode_direct_FC=yes hardcode_direct_absolute_FC=yes export_dynamic_flag_spec_FC='${wl}-E' # hardcode_minus_L: Not really in the search PATH, # but as the default location of the library. hardcode_minus_L_FC=yes fi ;; hpux11*) if test "$GCC" = yes -a "$with_gnu_ld" = no; then case $host_cpu in hppa*64*) archive_cmds_FC='$CC -shared ${wl}+h ${wl}$soname -o $lib $libobjs $deplibs $compiler_flags' ;; ia64*) archive_cmds_FC='$CC -shared -fPIC ${wl}+h ${wl}$soname ${wl}+nodefaultrpath -o $lib $libobjs $deplibs $compiler_flags' ;; *) archive_cmds_FC='$CC -shared -fPIC ${wl}+h ${wl}$soname ${wl}+b ${wl}$install_libdir -o $lib $libobjs $deplibs $compiler_flags' ;; esac else case $host_cpu in hppa*64*) archive_cmds_FC='$CC -b ${wl}+h ${wl}$soname -o $lib $libobjs $deplibs $compiler_flags' ;; ia64*) archive_cmds_FC='$CC -b ${wl}+h ${wl}$soname ${wl}+nodefaultrpath -o $lib $libobjs $deplibs $compiler_flags' ;; *) archive_cmds_FC='$CC -b ${wl}+h ${wl}$soname ${wl}+b ${wl}$install_libdir -o $lib $libobjs $deplibs $compiler_flags' ;; esac fi if test "$with_gnu_ld" = no; then hardcode_libdir_flag_spec_FC='${wl}+b ${wl}$libdir' hardcode_libdir_separator_FC=: case $host_cpu in hppa*64*|ia64*) hardcode_direct_FC=no hardcode_shlibpath_var_FC=no ;; *) hardcode_direct_FC=yes hardcode_direct_absolute_FC=yes export_dynamic_flag_spec_FC='${wl}-E' # hardcode_minus_L: Not really in the search PATH, # but as the default location of the library. hardcode_minus_L_FC=yes ;; esac fi ;; irix5* | irix6* | nonstopux*) if test "$GCC" = yes; then archive_cmds_FC='$CC -shared $libobjs $deplibs $compiler_flags ${wl}-soname ${wl}$soname `test -n "$verstring" && $ECHO "X${wl}-set_version ${wl}$verstring" | $Xsed` ${wl}-update_registry ${wl}${output_objdir}/so_locations -o $lib' # Try to use the -exported_symbol ld option, if it does not # work, assume that -exports_file does not work either and # implicitly export all symbols. save_LDFLAGS="$LDFLAGS" LDFLAGS="$LDFLAGS -shared ${wl}-exported_symbol ${wl}foo ${wl}-update_registry ${wl}/dev/null" cat > conftest.$ac_ext <<_ACEOF int foo(void) {} _ACEOF if ac_fn_fc_try_link "$LINENO"; then : archive_expsym_cmds_FC='$CC -shared $libobjs $deplibs $compiler_flags ${wl}-soname ${wl}$soname `test -n "$verstring" && $ECHO "X${wl}-set_version ${wl}$verstring" | $Xsed` ${wl}-update_registry ${wl}${output_objdir}/so_locations ${wl}-exports_file ${wl}$export_symbols -o $lib' fi rm -f core conftest.err conftest.$ac_objext \ conftest$ac_exeext conftest.$ac_ext LDFLAGS="$save_LDFLAGS" else archive_cmds_FC='$CC -shared $libobjs $deplibs $compiler_flags -soname $soname `test -n "$verstring" && $ECHO "X-set_version $verstring" | $Xsed` -update_registry ${output_objdir}/so_locations -o $lib' archive_expsym_cmds_FC='$CC -shared $libobjs $deplibs $compiler_flags -soname $soname `test -n "$verstring" && $ECHO "X-set_version $verstring" | $Xsed` -update_registry ${output_objdir}/so_locations -exports_file $export_symbols -o $lib' fi archive_cmds_need_lc_FC='no' hardcode_libdir_flag_spec_FC='${wl}-rpath ${wl}$libdir' hardcode_libdir_separator_FC=: inherit_rpath_FC=yes link_all_deplibs_FC=yes ;; netbsd* | netbsdelf*-gnu) if echo __ELF__ | $CC -E - | $GREP __ELF__ >/dev/null; then archive_cmds_FC='$LD -Bshareable -o $lib $libobjs $deplibs $linker_flags' # a.out else archive_cmds_FC='$LD -shared -o $lib $libobjs $deplibs $linker_flags' # ELF fi hardcode_libdir_flag_spec_FC='-R$libdir' hardcode_direct_FC=yes hardcode_shlibpath_var_FC=no ;; newsos6) archive_cmds_FC='$LD -G -h $soname -o $lib $libobjs $deplibs $linker_flags' hardcode_direct_FC=yes hardcode_libdir_flag_spec_FC='${wl}-rpath ${wl}$libdir' hardcode_libdir_separator_FC=: hardcode_shlibpath_var_FC=no ;; *nto* | *qnx*) ;; openbsd*) if test -f /usr/libexec/ld.so; then hardcode_direct_FC=yes hardcode_shlibpath_var_FC=no hardcode_direct_absolute_FC=yes if test -z "`echo __ELF__ | $CC -E - | $GREP __ELF__`" || test "$host_os-$host_cpu" = "openbsd2.8-powerpc"; then archive_cmds_FC='$CC -shared $pic_flag -o $lib $libobjs $deplibs $compiler_flags' archive_expsym_cmds_FC='$CC -shared $pic_flag -o $lib $libobjs $deplibs $compiler_flags ${wl}-retain-symbols-file,$export_symbols' hardcode_libdir_flag_spec_FC='${wl}-rpath,$libdir' export_dynamic_flag_spec_FC='${wl}-E' else case $host_os in openbsd[01].* | openbsd2.[0-7] | openbsd2.[0-7].*) archive_cmds_FC='$LD -Bshareable -o $lib $libobjs $deplibs $linker_flags' hardcode_libdir_flag_spec_FC='-R$libdir' ;; *) archive_cmds_FC='$CC -shared $pic_flag -o $lib $libobjs $deplibs $compiler_flags' hardcode_libdir_flag_spec_FC='${wl}-rpath,$libdir' ;; esac fi else ld_shlibs_FC=no fi ;; os2*) hardcode_libdir_flag_spec_FC='-L$libdir' hardcode_minus_L_FC=yes allow_undefined_flag_FC=unsupported archive_cmds_FC='$ECHO "LIBRARY $libname INITINSTANCE" > $output_objdir/$libname.def~$ECHO "DESCRIPTION \"$libname\"" >> $output_objdir/$libname.def~$ECHO DATA >> $output_objdir/$libname.def~$ECHO " SINGLE NONSHARED" >> $output_objdir/$libname.def~$ECHO EXPORTS >> $output_objdir/$libname.def~emxexp $libobjs >> $output_objdir/$libname.def~$CC -Zdll -Zcrtdll -o $lib $libobjs $deplibs $compiler_flags $output_objdir/$libname.def' old_archive_from_new_cmds_FC='emximp -o $output_objdir/$libname.a $output_objdir/$libname.def' ;; osf3*) if test "$GCC" = yes; then allow_undefined_flag_FC=' ${wl}-expect_unresolved ${wl}\*' archive_cmds_FC='$CC -shared${allow_undefined_flag} $libobjs $deplibs $compiler_flags ${wl}-soname ${wl}$soname `test -n "$verstring" && $ECHO "X${wl}-set_version ${wl}$verstring" | $Xsed` ${wl}-update_registry ${wl}${output_objdir}/so_locations -o $lib' else allow_undefined_flag_FC=' -expect_unresolved \*' archive_cmds_FC='$CC -shared${allow_undefined_flag} $libobjs $deplibs $compiler_flags -soname $soname `test -n "$verstring" && $ECHO "X-set_version $verstring" | $Xsed` -update_registry ${output_objdir}/so_locations -o $lib' fi archive_cmds_need_lc_FC='no' hardcode_libdir_flag_spec_FC='${wl}-rpath ${wl}$libdir' hardcode_libdir_separator_FC=: ;; osf4* | osf5*) # as osf3* with the addition of -msym flag if test "$GCC" = yes; then allow_undefined_flag_FC=' ${wl}-expect_unresolved ${wl}\*' archive_cmds_FC='$CC -shared${allow_undefined_flag} $libobjs $deplibs $compiler_flags ${wl}-msym ${wl}-soname ${wl}$soname `test -n "$verstring" && $ECHO "X${wl}-set_version ${wl}$verstring" | $Xsed` ${wl}-update_registry ${wl}${output_objdir}/so_locations -o $lib' hardcode_libdir_flag_spec_FC='${wl}-rpath ${wl}$libdir' else allow_undefined_flag_FC=' -expect_unresolved \*' archive_cmds_FC='$CC -shared${allow_undefined_flag} $libobjs $deplibs $compiler_flags -msym -soname $soname `test -n "$verstring" && $ECHO "X-set_version $verstring" | $Xsed` -update_registry ${output_objdir}/so_locations -o $lib' archive_expsym_cmds_FC='for i in `cat $export_symbols`; do printf "%s %s\\n" -exported_symbol "\$i" >> $lib.exp; done; printf "%s\\n" "-hidden">> $lib.exp~ $CC -shared${allow_undefined_flag} ${wl}-input ${wl}$lib.exp $compiler_flags $libobjs $deplibs -soname $soname `test -n "$verstring" && $ECHO "X-set_version $verstring" | $Xsed` -update_registry ${output_objdir}/so_locations -o $lib~$RM $lib.exp' # Both c and cxx compiler support -rpath directly hardcode_libdir_flag_spec_FC='-rpath $libdir' fi archive_cmds_need_lc_FC='no' hardcode_libdir_separator_FC=: ;; solaris*) no_undefined_flag_FC=' -z defs' if test "$GCC" = yes; then wlarc='${wl}' archive_cmds_FC='$CC -shared ${wl}-z ${wl}text ${wl}-h ${wl}$soname -o $lib $libobjs $deplibs $compiler_flags' archive_expsym_cmds_FC='echo "{ global:" > $lib.exp~cat $export_symbols | $SED -e "s/\(.*\)/\1;/" >> $lib.exp~echo "local: *; };" >> $lib.exp~ $CC -shared ${wl}-z ${wl}text ${wl}-M ${wl}$lib.exp ${wl}-h ${wl}$soname -o $lib $libobjs $deplibs $compiler_flags~$RM $lib.exp' else case `$CC -V 2>&1` in *"Compilers 5.0"*) wlarc='' archive_cmds_FC='$LD -G${allow_undefined_flag} -h $soname -o $lib $libobjs $deplibs $linker_flags' archive_expsym_cmds_FC='echo "{ global:" > $lib.exp~cat $export_symbols | $SED -e "s/\(.*\)/\1;/" >> $lib.exp~echo "local: *; };" >> $lib.exp~ $LD -G${allow_undefined_flag} -M $lib.exp -h $soname -o $lib $libobjs $deplibs $linker_flags~$RM $lib.exp' ;; *) wlarc='${wl}' archive_cmds_FC='$CC -G${allow_undefined_flag} -h $soname -o $lib $libobjs $deplibs $compiler_flags' archive_expsym_cmds_FC='echo "{ global:" > $lib.exp~cat $export_symbols | $SED -e "s/\(.*\)/\1;/" >> $lib.exp~echo "local: *; };" >> $lib.exp~ $CC -G${allow_undefined_flag} -M $lib.exp -h $soname -o $lib $libobjs $deplibs $compiler_flags~$RM $lib.exp' ;; esac fi hardcode_libdir_flag_spec_FC='-R$libdir' hardcode_shlibpath_var_FC=no case $host_os in solaris2.[0-5] | solaris2.[0-5].*) ;; *) # The compiler driver will combine and reorder linker options, # but understands `-z linker_flag'. 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compiler_F77='`$ECHO "X$compiler_F77" | $Xsed -e "$delay_single_quote_subst"`' compiler_FC='`$ECHO "X$compiler_FC" | $Xsed -e "$delay_single_quote_subst"`' GCC_F77='`$ECHO "X$GCC_F77" | $Xsed -e "$delay_single_quote_subst"`' GCC_FC='`$ECHO "X$GCC_FC" | $Xsed -e "$delay_single_quote_subst"`' lt_prog_compiler_no_builtin_flag_F77='`$ECHO "X$lt_prog_compiler_no_builtin_flag_F77" | $Xsed -e "$delay_single_quote_subst"`' lt_prog_compiler_no_builtin_flag_FC='`$ECHO "X$lt_prog_compiler_no_builtin_flag_FC" | $Xsed -e "$delay_single_quote_subst"`' lt_prog_compiler_wl_F77='`$ECHO "X$lt_prog_compiler_wl_F77" | $Xsed -e "$delay_single_quote_subst"`' lt_prog_compiler_wl_FC='`$ECHO "X$lt_prog_compiler_wl_FC" | $Xsed -e "$delay_single_quote_subst"`' lt_prog_compiler_pic_F77='`$ECHO "X$lt_prog_compiler_pic_F77" | $Xsed -e "$delay_single_quote_subst"`' lt_prog_compiler_pic_FC='`$ECHO "X$lt_prog_compiler_pic_FC" | $Xsed -e "$delay_single_quote_subst"`' lt_prog_compiler_static_F77='`$ECHO "X$lt_prog_compiler_static_F77" | $Xsed -e "$delay_single_quote_subst"`' lt_prog_compiler_static_FC='`$ECHO "X$lt_prog_compiler_static_FC" | $Xsed -e "$delay_single_quote_subst"`' lt_cv_prog_compiler_c_o_F77='`$ECHO "X$lt_cv_prog_compiler_c_o_F77" | $Xsed -e "$delay_single_quote_subst"`' lt_cv_prog_compiler_c_o_FC='`$ECHO "X$lt_cv_prog_compiler_c_o_FC" | $Xsed -e "$delay_single_quote_subst"`' archive_cmds_need_lc_F77='`$ECHO "X$archive_cmds_need_lc_F77" | $Xsed -e "$delay_single_quote_subst"`' archive_cmds_need_lc_FC='`$ECHO "X$archive_cmds_need_lc_FC" | $Xsed -e "$delay_single_quote_subst"`' enable_shared_with_static_runtimes_F77='`$ECHO "X$enable_shared_with_static_runtimes_F77" | $Xsed -e "$delay_single_quote_subst"`' enable_shared_with_static_runtimes_FC='`$ECHO "X$enable_shared_with_static_runtimes_FC" | $Xsed -e "$delay_single_quote_subst"`' export_dynamic_flag_spec_F77='`$ECHO "X$export_dynamic_flag_spec_F77" | $Xsed -e "$delay_single_quote_subst"`' export_dynamic_flag_spec_FC='`$ECHO "X$export_dynamic_flag_spec_FC" | $Xsed -e "$delay_single_quote_subst"`' whole_archive_flag_spec_F77='`$ECHO "X$whole_archive_flag_spec_F77" | $Xsed -e "$delay_single_quote_subst"`' whole_archive_flag_spec_FC='`$ECHO "X$whole_archive_flag_spec_FC" | $Xsed -e "$delay_single_quote_subst"`' compiler_needs_object_F77='`$ECHO "X$compiler_needs_object_F77" | $Xsed -e "$delay_single_quote_subst"`' compiler_needs_object_FC='`$ECHO "X$compiler_needs_object_FC" | $Xsed -e "$delay_single_quote_subst"`' old_archive_from_new_cmds_F77='`$ECHO "X$old_archive_from_new_cmds_F77" | $Xsed -e "$delay_single_quote_subst"`' old_archive_from_new_cmds_FC='`$ECHO "X$old_archive_from_new_cmds_FC" | $Xsed -e "$delay_single_quote_subst"`' old_archive_from_expsyms_cmds_F77='`$ECHO "X$old_archive_from_expsyms_cmds_F77" | $Xsed -e "$delay_single_quote_subst"`' old_archive_from_expsyms_cmds_FC='`$ECHO "X$old_archive_from_expsyms_cmds_FC" | $Xsed -e "$delay_single_quote_subst"`' archive_cmds_F77='`$ECHO "X$archive_cmds_F77" | $Xsed -e "$delay_single_quote_subst"`' archive_cmds_FC='`$ECHO "X$archive_cmds_FC" | $Xsed -e "$delay_single_quote_subst"`' archive_expsym_cmds_F77='`$ECHO "X$archive_expsym_cmds_F77" | $Xsed -e "$delay_single_quote_subst"`' archive_expsym_cmds_FC='`$ECHO "X$archive_expsym_cmds_FC" | $Xsed -e "$delay_single_quote_subst"`' module_cmds_F77='`$ECHO "X$module_cmds_F77" | $Xsed -e "$delay_single_quote_subst"`' module_cmds_FC='`$ECHO "X$module_cmds_FC" | $Xsed -e "$delay_single_quote_subst"`' module_expsym_cmds_F77='`$ECHO "X$module_expsym_cmds_F77" | $Xsed -e "$delay_single_quote_subst"`' module_expsym_cmds_FC='`$ECHO "X$module_expsym_cmds_FC" | $Xsed -e "$delay_single_quote_subst"`' with_gnu_ld_F77='`$ECHO "X$with_gnu_ld_F77" | $Xsed -e "$delay_single_quote_subst"`' with_gnu_ld_FC='`$ECHO "X$with_gnu_ld_FC" | $Xsed -e "$delay_single_quote_subst"`' allow_undefined_flag_F77='`$ECHO "X$allow_undefined_flag_F77" | $Xsed -e "$delay_single_quote_subst"`' allow_undefined_flag_FC='`$ECHO "X$allow_undefined_flag_FC" | $Xsed -e "$delay_single_quote_subst"`' no_undefined_flag_F77='`$ECHO "X$no_undefined_flag_F77" | $Xsed -e "$delay_single_quote_subst"`' no_undefined_flag_FC='`$ECHO "X$no_undefined_flag_FC" | $Xsed -e "$delay_single_quote_subst"`' hardcode_libdir_flag_spec_F77='`$ECHO "X$hardcode_libdir_flag_spec_F77" | $Xsed -e "$delay_single_quote_subst"`' hardcode_libdir_flag_spec_FC='`$ECHO "X$hardcode_libdir_flag_spec_FC" | $Xsed -e "$delay_single_quote_subst"`' hardcode_libdir_flag_spec_ld_F77='`$ECHO "X$hardcode_libdir_flag_spec_ld_F77" | $Xsed -e "$delay_single_quote_subst"`' hardcode_libdir_flag_spec_ld_FC='`$ECHO "X$hardcode_libdir_flag_spec_ld_FC" | $Xsed -e "$delay_single_quote_subst"`' hardcode_libdir_separator_F77='`$ECHO "X$hardcode_libdir_separator_F77" | $Xsed -e "$delay_single_quote_subst"`' hardcode_libdir_separator_FC='`$ECHO "X$hardcode_libdir_separator_FC" | $Xsed -e "$delay_single_quote_subst"`' hardcode_direct_F77='`$ECHO "X$hardcode_direct_F77" | $Xsed -e "$delay_single_quote_subst"`' hardcode_direct_FC='`$ECHO "X$hardcode_direct_FC" | $Xsed -e "$delay_single_quote_subst"`' hardcode_direct_absolute_F77='`$ECHO "X$hardcode_direct_absolute_F77" | $Xsed -e "$delay_single_quote_subst"`' hardcode_direct_absolute_FC='`$ECHO "X$hardcode_direct_absolute_FC" | $Xsed -e "$delay_single_quote_subst"`' hardcode_minus_L_F77='`$ECHO "X$hardcode_minus_L_F77" | $Xsed -e "$delay_single_quote_subst"`' hardcode_minus_L_FC='`$ECHO "X$hardcode_minus_L_FC" | $Xsed -e "$delay_single_quote_subst"`' hardcode_shlibpath_var_F77='`$ECHO "X$hardcode_shlibpath_var_F77" | $Xsed -e "$delay_single_quote_subst"`' hardcode_shlibpath_var_FC='`$ECHO "X$hardcode_shlibpath_var_FC" | $Xsed -e "$delay_single_quote_subst"`' hardcode_automatic_F77='`$ECHO "X$hardcode_automatic_F77" | $Xsed -e "$delay_single_quote_subst"`' hardcode_automatic_FC='`$ECHO "X$hardcode_automatic_FC" | $Xsed -e "$delay_single_quote_subst"`' inherit_rpath_F77='`$ECHO "X$inherit_rpath_F77" | $Xsed -e "$delay_single_quote_subst"`' inherit_rpath_FC='`$ECHO "X$inherit_rpath_FC" | $Xsed -e "$delay_single_quote_subst"`' link_all_deplibs_F77='`$ECHO "X$link_all_deplibs_F77" | $Xsed -e "$delay_single_quote_subst"`' link_all_deplibs_FC='`$ECHO "X$link_all_deplibs_FC" | $Xsed -e "$delay_single_quote_subst"`' fix_srcfile_path_F77='`$ECHO "X$fix_srcfile_path_F77" | $Xsed -e "$delay_single_quote_subst"`' fix_srcfile_path_FC='`$ECHO "X$fix_srcfile_path_FC" | $Xsed -e "$delay_single_quote_subst"`' always_export_symbols_F77='`$ECHO "X$always_export_symbols_F77" | $Xsed -e "$delay_single_quote_subst"`' always_export_symbols_FC='`$ECHO "X$always_export_symbols_FC" | $Xsed -e "$delay_single_quote_subst"`' export_symbols_cmds_F77='`$ECHO "X$export_symbols_cmds_F77" | $Xsed -e "$delay_single_quote_subst"`' export_symbols_cmds_FC='`$ECHO "X$export_symbols_cmds_FC" | $Xsed -e "$delay_single_quote_subst"`' exclude_expsyms_F77='`$ECHO "X$exclude_expsyms_F77" | $Xsed -e "$delay_single_quote_subst"`' exclude_expsyms_FC='`$ECHO "X$exclude_expsyms_FC" | $Xsed -e "$delay_single_quote_subst"`' include_expsyms_F77='`$ECHO "X$include_expsyms_F77" | $Xsed -e "$delay_single_quote_subst"`' include_expsyms_FC='`$ECHO "X$include_expsyms_FC" | $Xsed -e "$delay_single_quote_subst"`' prelink_cmds_F77='`$ECHO "X$prelink_cmds_F77" | $Xsed -e "$delay_single_quote_subst"`' prelink_cmds_FC='`$ECHO "X$prelink_cmds_FC" | $Xsed -e "$delay_single_quote_subst"`' file_list_spec_F77='`$ECHO "X$file_list_spec_F77" | $Xsed -e "$delay_single_quote_subst"`' file_list_spec_FC='`$ECHO "X$file_list_spec_FC" | $Xsed -e "$delay_single_quote_subst"`' hardcode_action_F77='`$ECHO "X$hardcode_action_F77" | $Xsed -e "$delay_single_quote_subst"`' hardcode_action_FC='`$ECHO "X$hardcode_action_FC" | $Xsed -e "$delay_single_quote_subst"`' compiler_lib_search_dirs_F77='`$ECHO "X$compiler_lib_search_dirs_F77" | $Xsed -e "$delay_single_quote_subst"`' compiler_lib_search_dirs_FC='`$ECHO "X$compiler_lib_search_dirs_FC" | $Xsed -e "$delay_single_quote_subst"`' predep_objects_F77='`$ECHO "X$predep_objects_F77" | $Xsed -e "$delay_single_quote_subst"`' predep_objects_FC='`$ECHO "X$predep_objects_FC" | $Xsed -e "$delay_single_quote_subst"`' postdep_objects_F77='`$ECHO "X$postdep_objects_F77" | $Xsed -e "$delay_single_quote_subst"`' postdep_objects_FC='`$ECHO "X$postdep_objects_FC" | $Xsed -e "$delay_single_quote_subst"`' predeps_F77='`$ECHO "X$predeps_F77" | $Xsed -e "$delay_single_quote_subst"`' predeps_FC='`$ECHO "X$predeps_FC" | $Xsed -e "$delay_single_quote_subst"`' postdeps_F77='`$ECHO "X$postdeps_F77" | $Xsed -e "$delay_single_quote_subst"`' postdeps_FC='`$ECHO "X$postdeps_FC" | $Xsed -e "$delay_single_quote_subst"`' compiler_lib_search_path_F77='`$ECHO "X$compiler_lib_search_path_F77" | $Xsed -e "$delay_single_quote_subst"`' compiler_lib_search_path_FC='`$ECHO "X$compiler_lib_search_path_FC" | $Xsed -e "$delay_single_quote_subst"`' LTCC='$LTCC' LTCFLAGS='$LTCFLAGS' compiler='$compiler_DEFAULT' # Quote evaled strings. for var in SED \ GREP \ EGREP \ FGREP \ LD \ NM \ LN_S \ lt_SP2NL \ lt_NL2SP \ reload_flag \ OBJDUMP \ deplibs_check_method \ file_magic_cmd \ AR \ AR_FLAGS \ STRIP \ RANLIB \ CC \ CFLAGS \ compiler \ lt_cv_sys_global_symbol_pipe \ lt_cv_sys_global_symbol_to_cdecl \ lt_cv_sys_global_symbol_to_c_name_address \ lt_cv_sys_global_symbol_to_c_name_address_lib_prefix \ SHELL \ ECHO \ lt_prog_compiler_no_builtin_flag \ lt_prog_compiler_wl \ lt_prog_compiler_pic \ lt_prog_compiler_static \ lt_cv_prog_compiler_c_o \ need_locks \ DSYMUTIL \ NMEDIT \ LIPO \ OTOOL \ OTOOL64 \ shrext_cmds \ export_dynamic_flag_spec \ whole_archive_flag_spec \ compiler_needs_object \ with_gnu_ld \ allow_undefined_flag \ no_undefined_flag \ hardcode_libdir_flag_spec \ hardcode_libdir_flag_spec_ld \ hardcode_libdir_separator \ fix_srcfile_path \ exclude_expsyms \ include_expsyms \ file_list_spec \ variables_saved_for_relink \ libname_spec \ library_names_spec \ soname_spec \ finish_eval \ old_striplib \ striplib \ compiler_lib_search_dirs \ predep_objects \ postdep_objects \ predeps \ postdeps \ compiler_lib_search_path \ LD_F77 \ LD_FC \ compiler_F77 \ compiler_FC \ lt_prog_compiler_no_builtin_flag_F77 \ lt_prog_compiler_no_builtin_flag_FC \ lt_prog_compiler_wl_F77 \ lt_prog_compiler_wl_FC \ lt_prog_compiler_pic_F77 \ lt_prog_compiler_pic_FC \ lt_prog_compiler_static_F77 \ lt_prog_compiler_static_FC \ lt_cv_prog_compiler_c_o_F77 \ lt_cv_prog_compiler_c_o_FC \ export_dynamic_flag_spec_F77 \ export_dynamic_flag_spec_FC \ whole_archive_flag_spec_F77 \ whole_archive_flag_spec_FC \ compiler_needs_object_F77 \ compiler_needs_object_FC \ with_gnu_ld_F77 \ with_gnu_ld_FC \ allow_undefined_flag_F77 \ allow_undefined_flag_FC \ no_undefined_flag_F77 \ no_undefined_flag_FC \ hardcode_libdir_flag_spec_F77 \ hardcode_libdir_flag_spec_FC \ hardcode_libdir_flag_spec_ld_F77 \ hardcode_libdir_flag_spec_ld_FC \ hardcode_libdir_separator_F77 \ hardcode_libdir_separator_FC \ fix_srcfile_path_F77 \ fix_srcfile_path_FC \ exclude_expsyms_F77 \ exclude_expsyms_FC \ include_expsyms_F77 \ include_expsyms_FC \ file_list_spec_F77 \ file_list_spec_FC \ compiler_lib_search_dirs_F77 \ compiler_lib_search_dirs_FC \ predep_objects_F77 \ predep_objects_FC \ postdep_objects_F77 \ postdep_objects_FC \ predeps_F77 \ predeps_FC \ postdeps_F77 \ postdeps_FC \ compiler_lib_search_path_F77 \ compiler_lib_search_path_FC; do case \`eval \\\\\$ECHO "X\\\\\$\$var"\` in *[\\\\\\\`\\"\\\$]*) eval "lt_\$var=\\\\\\"\\\`\\\$ECHO \\"X\\\$\$var\\" | \\\$Xsed -e \\"\\\$sed_quote_subst\\"\\\`\\\\\\"" ;; *) eval "lt_\$var=\\\\\\"\\\$\$var\\\\\\"" ;; esac done # Double-quote double-evaled strings. for var in reload_cmds \ old_postinstall_cmds \ old_postuninstall_cmds \ old_archive_cmds \ extract_expsyms_cmds \ old_archive_from_new_cmds \ old_archive_from_expsyms_cmds \ archive_cmds \ archive_expsym_cmds \ module_cmds \ module_expsym_cmds \ export_symbols_cmds \ prelink_cmds \ postinstall_cmds \ postuninstall_cmds \ finish_cmds \ sys_lib_search_path_spec \ sys_lib_dlsearch_path_spec \ old_archive_cmds_F77 \ old_archive_cmds_FC \ old_archive_from_new_cmds_F77 \ old_archive_from_new_cmds_FC \ old_archive_from_expsyms_cmds_F77 \ old_archive_from_expsyms_cmds_FC \ archive_cmds_F77 \ archive_cmds_FC \ archive_expsym_cmds_F77 \ archive_expsym_cmds_FC \ module_cmds_F77 \ module_cmds_FC \ module_expsym_cmds_F77 \ module_expsym_cmds_FC \ export_symbols_cmds_F77 \ export_symbols_cmds_FC \ prelink_cmds_F77 \ prelink_cmds_FC; do case \`eval \\\\\$ECHO "X\\\\\$\$var"\` in *[\\\\\\\`\\"\\\$]*) eval "lt_\$var=\\\\\\"\\\`\\\$ECHO \\"X\\\$\$var\\" | \\\$Xsed -e \\"\\\$double_quote_subst\\" -e \\"\\\$sed_quote_subst\\" -e \\"\\\$delay_variable_subst\\"\\\`\\\\\\"" ;; *) eval "lt_\$var=\\\\\\"\\\$\$var\\\\\\"" ;; esac done # Fix-up fallback echo if it was mangled by the above quoting rules. case \$lt_ECHO in *'\\\$0 --fallback-echo"') lt_ECHO=\`\$ECHO "X\$lt_ECHO" | \$Xsed -e 's/\\\\\\\\\\\\\\\$0 --fallback-echo"\$/\$0 --fallback-echo"/'\` ;; esac ac_aux_dir='$ac_aux_dir' xsi_shell='$xsi_shell' lt_shell_append='$lt_shell_append' # See if we are running on zsh, and set the options which allow our # commands through without removal of \ escapes INIT. if test -n "\${ZSH_VERSION+set}" ; then setopt NO_GLOB_SUBST fi PACKAGE='$PACKAGE' VERSION='$VERSION' TIMESTAMP='$TIMESTAMP' RM='$RM' ofile='$ofile' _ACEOF cat >>$CONFIG_STATUS <<\_ACEOF || ac_write_fail=1 # Handling of arguments. for ac_config_target in $ac_config_targets do case $ac_config_target in "depfiles") CONFIG_COMMANDS="$CONFIG_COMMANDS depfiles" ;; "libtool") CONFIG_COMMANDS="$CONFIG_COMMANDS libtool" ;; "Makefile") CONFIG_FILES="$CONFIG_FILES Makefile" ;; "SRC/Makefile") CONFIG_FILES="$CONFIG_FILES SRC/Makefile" ;; *) as_fn_error $? "invalid argument: \`$ac_config_target'" "$LINENO" 5 ;; esac done # If the user did not use the arguments to specify the items to instantiate, # then the envvar interface is used. Set only those that are not. # We use the long form for the default assignment because of an extremely # bizarre bug on SunOS 4.1.3. if $ac_need_defaults; then test "${CONFIG_FILES+set}" = set || CONFIG_FILES=$config_files test "${CONFIG_COMMANDS+set}" = set || CONFIG_COMMANDS=$config_commands fi # Have a temporary directory for convenience. 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"$LINENO" 5 # Set up the scripts for CONFIG_FILES section. # No need to generate them if there are no CONFIG_FILES. # This happens for instance with `./config.status config.h'. if test -n "$CONFIG_FILES"; then ac_cr=`echo X | tr X '\015'` # On cygwin, bash can eat \r inside `` if the user requested igncr. # But we know of no other shell where ac_cr would be empty at this # point, so we can use a bashism as a fallback. if test "x$ac_cr" = x; then eval ac_cr=\$\'\\r\' fi ac_cs_awk_cr=`$AWK 'BEGIN { print "a\rb" }' /dev/null` if test "$ac_cs_awk_cr" = "a${ac_cr}b"; then ac_cs_awk_cr='\\r' else ac_cs_awk_cr=$ac_cr fi echo 'BEGIN {' >"$tmp/subs1.awk" && _ACEOF { echo "cat >conf$$subs.awk <<_ACEOF" && echo "$ac_subst_vars" | sed 's/.*/&!$&$ac_delim/' && echo "_ACEOF" } >conf$$subs.sh || as_fn_error $? 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For efficiency, we do not delegate to # those functions but instead duplicate the functionality here. func_dirname_and_basename () { # Extract subdirectory from the argument. func_dirname_result=`$ECHO "X${1}" | $Xsed -e "$dirname"` if test "X$func_dirname_result" = "X${1}"; then func_dirname_result="${3}" else func_dirname_result="$func_dirname_result${2}" fi func_basename_result=`$ECHO "X${1}" | $Xsed -e "$basename"` } # Generated shell functions inserted here. # Work around backward compatibility issue on IRIX 6.5. On IRIX 6.4+, sh # is ksh but when the shell is invoked as "sh" and the current value of # the _XPG environment variable is not equal to 1 (one), the special # positional parameter $0, within a function call, is the name of the # function. progpath="$0" # The name of this program: # In the unlikely event $progname began with a '-', it would play havoc with # func_echo (imagine progname=-n), so we prepend ./ in that case: func_dirname_and_basename "$progpath" progname=$func_basename_result case $progname in -*) progname=./$progname ;; esac # Make sure we have an absolute path for reexecution: case $progpath in [\\/]*|[A-Za-z]:\\*) ;; *[\\/]*) progdir=$func_dirname_result progdir=`cd "$progdir" && pwd` progpath="$progdir/$progname" ;; *) save_IFS="$IFS" IFS=: for progdir in $PATH; do IFS="$save_IFS" test -x "$progdir/$progname" && break done IFS="$save_IFS" test -n "$progdir" || progdir=`pwd` progpath="$progdir/$progname" ;; esac # Sed substitution that helps us do robust quoting. It backslashifies # metacharacters that are still active within double-quoted strings. Xsed="${SED}"' -e 1s/^X//' sed_quote_subst='s/\([`"$\\]\)/\\\1/g' # Same as above, but do not quote variable references. double_quote_subst='s/\(["`\\]\)/\\\1/g' # Re-`\' parameter expansions in output of double_quote_subst that were # `\'-ed in input to the same. If an odd number of `\' preceded a '$' # in input to double_quote_subst, that '$' was protected from expansion. # Since each input `\' is now two `\'s, look for any number of runs of # four `\'s followed by two `\'s and then a '$'. `\' that '$'. bs='\\' bs2='\\\\' bs4='\\\\\\\\' dollar='\$' sed_double_backslash="\ s/$bs4/&\\ /g s/^$bs2$dollar/$bs&/ s/\\([^$bs]\\)$bs2$dollar/\\1$bs2$bs$dollar/g s/\n//g" # Standard options: opt_dry_run=false opt_help=false opt_quiet=false opt_verbose=false opt_warning=: # func_echo arg... # Echo program name prefixed message, along with the current mode # name if it has been set yet. func_echo () { $ECHO "$progname${mode+: }$mode: $*" } # func_verbose arg... # Echo program name prefixed message in verbose mode only. func_verbose () { $opt_verbose && func_echo ${1+"$@"} # A bug in bash halts the script if the last line of a function # fails when set -e is in force, so we need another command to # work around that: : } # func_error arg... # Echo program name prefixed message to standard error. func_error () { $ECHO "$progname${mode+: }$mode: "${1+"$@"} 1>&2 } # func_warning arg... # Echo program name prefixed warning message to standard error. func_warning () { $opt_warning && $ECHO "$progname${mode+: }$mode: warning: "${1+"$@"} 1>&2 # bash bug again: : } # func_fatal_error arg... # Echo program name prefixed message to standard error, and exit. func_fatal_error () { func_error ${1+"$@"} exit $EXIT_FAILURE } # func_fatal_help arg... # Echo program name prefixed message to standard error, followed by # a help hint, and exit. func_fatal_help () { func_error ${1+"$@"} func_fatal_error "$help" } help="Try \`$progname --help' for more information." ## default # func_grep expression filename # Check whether EXPRESSION matches any line of FILENAME, without output. func_grep () { $GREP "$1" "$2" >/dev/null 2>&1 } # func_mkdir_p directory-path # Make sure the entire path to DIRECTORY-PATH is available. func_mkdir_p () { my_directory_path="$1" my_dir_list= if test -n "$my_directory_path" && test "$opt_dry_run" != ":"; then # Protect directory names starting with `-' case $my_directory_path in -*) my_directory_path="./$my_directory_path" ;; esac # While some portion of DIR does not yet exist... while test ! -d "$my_directory_path"; do # ...make a list in topmost first order. Use a colon delimited # list incase some portion of path contains whitespace. my_dir_list="$my_directory_path:$my_dir_list" # If the last portion added has no slash in it, the list is done case $my_directory_path in */*) ;; *) break ;; esac # ...otherwise throw away the child directory and loop my_directory_path=`$ECHO "X$my_directory_path" | $Xsed -e "$dirname"` done my_dir_list=`$ECHO "X$my_dir_list" | $Xsed -e 's,:*$,,'` save_mkdir_p_IFS="$IFS"; IFS=':' for my_dir in $my_dir_list; do IFS="$save_mkdir_p_IFS" # mkdir can fail with a `File exist' error if two processes # try to create one of the directories concurrently. Don't # stop in that case! $MKDIR "$my_dir" 2>/dev/null || : done IFS="$save_mkdir_p_IFS" # Bail out if we (or some other process) failed to create a directory. test -d "$my_directory_path" || \ func_fatal_error "Failed to create \`$1'" fi } # func_mktempdir [string] # Make a temporary directory that won't clash with other running # libtool processes, and avoids race conditions if possible. If # given, STRING is the basename for that directory. func_mktempdir () { my_template="${TMPDIR-/tmp}/${1-$progname}" if test "$opt_dry_run" = ":"; then # Return a directory name, but don't create it in dry-run mode my_tmpdir="${my_template}-$$" else # If mktemp works, use that first and foremost my_tmpdir=`mktemp -d "${my_template}-XXXXXXXX" 2>/dev/null` if test ! -d "$my_tmpdir"; then # Failing that, at least try and use $RANDOM to avoid a race my_tmpdir="${my_template}-${RANDOM-0}$$" save_mktempdir_umask=`umask` umask 0077 $MKDIR "$my_tmpdir" umask $save_mktempdir_umask fi # If we're not in dry-run mode, bomb out on failure test -d "$my_tmpdir" || \ func_fatal_error "cannot create temporary directory \`$my_tmpdir'" fi $ECHO "X$my_tmpdir" | $Xsed } # func_quote_for_eval arg # Aesthetically quote ARG to be evaled later. # This function returns two values: FUNC_QUOTE_FOR_EVAL_RESULT # is double-quoted, suitable for a subsequent eval, whereas # FUNC_QUOTE_FOR_EVAL_UNQUOTED_RESULT has merely all characters # which are still active within double quotes backslashified. func_quote_for_eval () { case $1 in *[\\\`\"\$]*) func_quote_for_eval_unquoted_result=`$ECHO "X$1" | $Xsed -e "$sed_quote_subst"` ;; *) func_quote_for_eval_unquoted_result="$1" ;; esac case $func_quote_for_eval_unquoted_result in # Double-quote args containing shell metacharacters to delay # word splitting, command substitution and and variable # expansion for a subsequent eval. # Many Bourne shells cannot handle close brackets correctly # in scan sets, so we specify it separately. *[\[\~\#\^\&\*\(\)\{\}\|\;\<\>\?\'\ \ ]*|*]*|"") func_quote_for_eval_result="\"$func_quote_for_eval_unquoted_result\"" ;; *) func_quote_for_eval_result="$func_quote_for_eval_unquoted_result" esac } # func_quote_for_expand arg # Aesthetically quote ARG to be evaled later; same as above, # but do not quote variable references. func_quote_for_expand () { case $1 in *[\\\`\"]*) my_arg=`$ECHO "X$1" | $Xsed \ -e "$double_quote_subst" -e "$sed_double_backslash"` ;; *) my_arg="$1" ;; esac case $my_arg in # Double-quote args containing shell metacharacters to delay # word splitting and command substitution for a subsequent eval. # Many Bourne shells cannot handle close brackets correctly # in scan sets, so we specify it separately. *[\[\~\#\^\&\*\(\)\{\}\|\;\<\>\?\'\ \ ]*|*]*|"") my_arg="\"$my_arg\"" ;; esac func_quote_for_expand_result="$my_arg" } # func_show_eval cmd [fail_exp] # Unless opt_silent is true, then output CMD. Then, if opt_dryrun is # not true, evaluate CMD. If the evaluation of CMD fails, and FAIL_EXP # is given, then evaluate it. func_show_eval () { my_cmd="$1" my_fail_exp="${2-:}" ${opt_silent-false} || { func_quote_for_expand "$my_cmd" eval "func_echo $func_quote_for_expand_result" } if ${opt_dry_run-false}; then :; else eval "$my_cmd" my_status=$? if test "$my_status" -eq 0; then :; else eval "(exit $my_status); $my_fail_exp" fi fi } # func_show_eval_locale cmd [fail_exp] # Unless opt_silent is true, then output CMD. Then, if opt_dryrun is # not true, evaluate CMD. If the evaluation of CMD fails, and FAIL_EXP # is given, then evaluate it. Use the saved locale for evaluation. func_show_eval_locale () { my_cmd="$1" my_fail_exp="${2-:}" ${opt_silent-false} || { func_quote_for_expand "$my_cmd" eval "func_echo $func_quote_for_expand_result" } if ${opt_dry_run-false}; then :; else eval "$lt_user_locale $my_cmd" my_status=$? eval "$lt_safe_locale" if test "$my_status" -eq 0; then :; else eval "(exit $my_status); $my_fail_exp" fi fi } # func_version # Echo version message to standard output and exit. func_version () { $SED -n '/^# '$PROGRAM' (GNU /,/# warranty; / { s/^# // s/^# *$// s/\((C)\)[ 0-9,-]*\( [1-9][0-9]*\)/\1\2/ p }' < "$progpath" exit $? } # func_usage # Echo short help message to standard output and exit. func_usage () { $SED -n '/^# Usage:/,/# -h/ { s/^# // s/^# *$// s/\$progname/'$progname'/ p }' < "$progpath" $ECHO $ECHO "run \`$progname --help | more' for full usage" exit $? } # func_help # Echo long help message to standard output and exit. func_help () { $SED -n '/^# Usage:/,/# Report bugs to/ { s/^# // s/^# *$// s*\$progname*'$progname'* s*\$host*'"$host"'* s*\$SHELL*'"$SHELL"'* s*\$LTCC*'"$LTCC"'* s*\$LTCFLAGS*'"$LTCFLAGS"'* s*\$LD*'"$LD"'* s/\$with_gnu_ld/'"$with_gnu_ld"'/ s/\$automake_version/'"`(automake --version) 2>/dev/null |$SED 1q`"'/ s/\$autoconf_version/'"`(autoconf --version) 2>/dev/null |$SED 1q`"'/ p }' < "$progpath" exit $? } # func_missing_arg argname # Echo program name prefixed message to standard error and set global # exit_cmd. func_missing_arg () { func_error "missing argument for $1" exit_cmd=exit } exit_cmd=: # Check that we have a working $ECHO. if test "X$1" = X--no-reexec; then # Discard the --no-reexec flag, and continue. shift elif test "X$1" = X--fallback-echo; then # Avoid inline document here, it may be left over : elif test "X`{ $ECHO '\t'; } 2>/dev/null`" = 'X\t'; then # Yippee, $ECHO works! : else # Restart under the correct shell, and then maybe $ECHO will work. exec $SHELL "$progpath" --no-reexec ${1+"$@"} fi if test "X$1" = X--fallback-echo; then # used as fallback echo shift cat </dev/null 2>&1; then taglist="$taglist $tagname" # Evaluate the configuration. Be careful to quote the path # and the sed script, to avoid splitting on whitespace, but # also don't use non-portable quotes within backquotes within # quotes we have to do it in 2 steps: extractedcf=`$SED -n -e "$sed_extractcf" < "$progpath"` eval "$extractedcf" else func_error "ignoring unknown tag $tagname" fi ;; esac } # Parse options once, thoroughly. This comes as soon as possible in # the script to make things like `libtool --version' happen quickly. { # Shorthand for --mode=foo, only valid as the first argument case $1 in clean|clea|cle|cl) shift; set dummy --mode clean ${1+"$@"}; shift ;; compile|compil|compi|comp|com|co|c) shift; set dummy --mode compile ${1+"$@"}; shift ;; execute|execut|execu|exec|exe|ex|e) shift; set dummy --mode execute ${1+"$@"}; shift ;; finish|finis|fini|fin|fi|f) shift; set dummy --mode finish ${1+"$@"}; shift ;; install|instal|insta|inst|ins|in|i) shift; set dummy --mode install ${1+"$@"}; shift ;; link|lin|li|l) shift; set dummy --mode link ${1+"$@"}; shift ;; uninstall|uninstal|uninsta|uninst|unins|unin|uni|un|u) shift; set dummy --mode uninstall ${1+"$@"}; shift ;; esac # Parse non-mode specific arguments: while test "$#" -gt 0; do opt="$1" shift case $opt in --config) func_config ;; --debug) preserve_args="$preserve_args $opt" func_echo "enabling shell trace mode" opt_debug='set -x' $opt_debug ;; -dlopen) test "$#" -eq 0 && func_missing_arg "$opt" && break execute_dlfiles="$execute_dlfiles $1" shift ;; --dry-run | -n) opt_dry_run=: ;; --features) func_features ;; --finish) mode="finish" ;; --mode) test "$#" -eq 0 && func_missing_arg "$opt" && break case $1 in # Valid mode arguments: clean) ;; compile) ;; execute) ;; finish) ;; install) ;; link) ;; relink) ;; uninstall) ;; # Catch anything else as an error *) func_error "invalid argument for $opt" exit_cmd=exit break ;; esac mode="$1" shift ;; --preserve-dup-deps) opt_duplicate_deps=: ;; --quiet|--silent) preserve_args="$preserve_args $opt" opt_silent=: ;; --verbose| -v) preserve_args="$preserve_args $opt" opt_silent=false ;; --tag) test "$#" -eq 0 && func_missing_arg "$opt" && break preserve_args="$preserve_args $opt $1" func_enable_tag "$1" # tagname is set here shift ;; # Separate optargs to long options: -dlopen=*|--mode=*|--tag=*) func_opt_split "$opt" set dummy "$func_opt_split_opt" "$func_opt_split_arg" ${1+"$@"} shift ;; -\?|-h) func_usage ;; --help) opt_help=: ;; --version) func_version ;; -*) func_fatal_help "unrecognized option \`$opt'" ;; *) nonopt="$opt" break ;; esac done case $host in *cygwin* | *mingw* | *pw32* | *cegcc*) # don't eliminate duplications in $postdeps and $predeps opt_duplicate_compiler_generated_deps=: ;; *) opt_duplicate_compiler_generated_deps=$opt_duplicate_deps ;; esac # Having warned about all mis-specified options, bail out if # anything was wrong. $exit_cmd $EXIT_FAILURE } # func_check_version_match # Ensure that we are using m4 macros, and libtool script from the same # release of libtool. func_check_version_match () { if test "$package_revision" != "$macro_revision"; then if test "$VERSION" != "$macro_version"; then if test -z "$macro_version"; then cat >&2 <<_LT_EOF $progname: Version mismatch error. This is $PACKAGE $VERSION, but the $progname: definition of this LT_INIT comes from an older release. $progname: You should recreate aclocal.m4 with macros from $PACKAGE $VERSION $progname: and run autoconf again. _LT_EOF else cat >&2 <<_LT_EOF $progname: Version mismatch error. This is $PACKAGE $VERSION, but the $progname: definition of this LT_INIT comes from $PACKAGE $macro_version. $progname: You should recreate aclocal.m4 with macros from $PACKAGE $VERSION $progname: and run autoconf again. _LT_EOF fi else cat >&2 <<_LT_EOF $progname: Version mismatch error. This is $PACKAGE $VERSION, revision $package_revision, $progname: but the definition of this LT_INIT comes from revision $macro_revision. $progname: You should recreate aclocal.m4 with macros from revision $package_revision $progname: of $PACKAGE $VERSION and run autoconf again. _LT_EOF fi exit $EXIT_MISMATCH fi } ## ----------- ## ## Main. ## ## ----------- ## $opt_help || { # Sanity checks first: func_check_version_match if test "$build_libtool_libs" != yes && test "$build_old_libs" != yes; then func_fatal_configuration "not configured to build any kind of library" fi test -z "$mode" && func_fatal_error "error: you must specify a MODE." # Darwin sucks eval std_shrext=\"$shrext_cmds\" # Only execute mode is allowed to have -dlopen flags. if test -n "$execute_dlfiles" && test "$mode" != execute; then func_error "unrecognized option \`-dlopen'" $ECHO "$help" 1>&2 exit $EXIT_FAILURE fi # Change the help message to a mode-specific one. generic_help="$help" help="Try \`$progname --help --mode=$mode' for more information." } # func_lalib_p file # True iff FILE is a libtool `.la' library or `.lo' object file. # This function is only a basic sanity check; it will hardly flush out # determined imposters. func_lalib_p () { test -f "$1" && $SED -e 4q "$1" 2>/dev/null \ | $GREP "^# Generated by .*$PACKAGE" > /dev/null 2>&1 } # func_lalib_unsafe_p file # True iff FILE is a libtool `.la' library or `.lo' object file. # This function implements the same check as func_lalib_p without # resorting to external programs. To this end, it redirects stdin and # closes it afterwards, without saving the original file descriptor. # As a safety measure, use it only where a negative result would be # fatal anyway. Works if `file' does not exist. func_lalib_unsafe_p () { lalib_p=no if test -f "$1" && test -r "$1" && exec 5<&0 <"$1"; then for lalib_p_l in 1 2 3 4 do read lalib_p_line case "$lalib_p_line" in \#\ Generated\ by\ *$PACKAGE* ) lalib_p=yes; break;; esac done exec 0<&5 5<&- fi test "$lalib_p" = yes } # func_ltwrapper_script_p file # True iff FILE is a libtool wrapper script # This function is only a basic sanity check; it will hardly flush out # determined imposters. func_ltwrapper_script_p () { func_lalib_p "$1" } # func_ltwrapper_executable_p file # True iff FILE is a libtool wrapper executable # This function is only a basic sanity check; it will hardly flush out # determined imposters. func_ltwrapper_executable_p () { func_ltwrapper_exec_suffix= case $1 in *.exe) ;; *) func_ltwrapper_exec_suffix=.exe ;; esac $GREP "$magic_exe" "$1$func_ltwrapper_exec_suffix" >/dev/null 2>&1 } # func_ltwrapper_scriptname file # Assumes file is an ltwrapper_executable # uses $file to determine the appropriate filename for a # temporary ltwrapper_script. func_ltwrapper_scriptname () { func_ltwrapper_scriptname_result="" if func_ltwrapper_executable_p "$1"; then func_dirname_and_basename "$1" "" "." func_stripname '' '.exe' "$func_basename_result" func_ltwrapper_scriptname_result="$func_dirname_result/$objdir/${func_stripname_result}_ltshwrapper" fi } # func_ltwrapper_p file # True iff FILE is a libtool wrapper script or wrapper executable # This function is only a basic sanity check; it will hardly flush out # determined imposters. func_ltwrapper_p () { func_ltwrapper_script_p "$1" || func_ltwrapper_executable_p "$1" } # func_execute_cmds commands fail_cmd # Execute tilde-delimited COMMANDS. # If FAIL_CMD is given, eval that upon failure. # FAIL_CMD may read-access the current command in variable CMD! func_execute_cmds () { $opt_debug save_ifs=$IFS; IFS='~' for cmd in $1; do IFS=$save_ifs eval cmd=\"$cmd\" func_show_eval "$cmd" "${2-:}" done IFS=$save_ifs } # func_source file # Source FILE, adding directory component if necessary. # Note that it is not necessary on cygwin/mingw to append a dot to # FILE even if both FILE and FILE.exe exist: automatic-append-.exe # behavior happens only for exec(3), not for open(2)! Also, sourcing # `FILE.' does not work on cygwin managed mounts. func_source () { $opt_debug case $1 in */* | *\\*) . "$1" ;; *) . "./$1" ;; esac } # func_infer_tag arg # Infer tagged configuration to use if any are available and # if one wasn't chosen via the "--tag" command line option. # Only attempt this if the compiler in the base compile # command doesn't match the default compiler. # arg is usually of the form 'gcc ...' func_infer_tag () { $opt_debug if test -n "$available_tags" && test -z "$tagname"; then CC_quoted= for arg in $CC; do func_quote_for_eval "$arg" CC_quoted="$CC_quoted $func_quote_for_eval_result" done case $@ in # Blanks in the command may have been stripped by the calling shell, # but not from the CC environment variable when configure was run. " $CC "* | "$CC "* | " `$ECHO $CC` "* | "`$ECHO $CC` "* | " $CC_quoted"* | "$CC_quoted "* | " `$ECHO $CC_quoted` "* | "`$ECHO $CC_quoted` "*) ;; # Blanks at the start of $base_compile will cause this to fail # if we don't check for them as well. *) for z in $available_tags; do if $GREP "^# ### BEGIN LIBTOOL TAG CONFIG: $z$" < "$progpath" > /dev/null; then # Evaluate the configuration. eval "`${SED} -n -e '/^# ### BEGIN LIBTOOL TAG CONFIG: '$z'$/,/^# ### END LIBTOOL TAG CONFIG: '$z'$/p' < $progpath`" CC_quoted= for arg in $CC; do # Double-quote args containing other shell metacharacters. func_quote_for_eval "$arg" CC_quoted="$CC_quoted $func_quote_for_eval_result" done case "$@ " in " $CC "* | "$CC "* | " `$ECHO $CC` "* | "`$ECHO $CC` "* | " $CC_quoted"* | "$CC_quoted "* | " `$ECHO $CC_quoted` "* | "`$ECHO $CC_quoted` "*) # The compiler in the base compile command matches # the one in the tagged configuration. # Assume this is the tagged configuration we want. tagname=$z break ;; esac fi done # If $tagname still isn't set, then no tagged configuration # was found and let the user know that the "--tag" command # line option must be used. if test -z "$tagname"; then func_echo "unable to infer tagged configuration" func_fatal_error "specify a tag with \`--tag'" # else # func_verbose "using $tagname tagged configuration" fi ;; esac fi } # func_write_libtool_object output_name pic_name nonpic_name # Create a libtool object file (analogous to a ".la" file), # but don't create it if we're doing a dry run. func_write_libtool_object () { write_libobj=${1} if test "$build_libtool_libs" = yes; then write_lobj=\'${2}\' else write_lobj=none fi if test "$build_old_libs" = yes; then write_oldobj=\'${3}\' else write_oldobj=none fi $opt_dry_run || { cat >${write_libobj}T <?"'"'"' &()|`$[]' \ && func_warning "libobj name \`$libobj' may not contain shell special characters." func_dirname_and_basename "$obj" "/" "" objname="$func_basename_result" xdir="$func_dirname_result" lobj=${xdir}$objdir/$objname test -z "$base_compile" && \ func_fatal_help "you must specify a compilation command" # Delete any leftover library objects. if test "$build_old_libs" = yes; then removelist="$obj $lobj $libobj ${libobj}T" else removelist="$lobj $libobj ${libobj}T" fi # On Cygwin there's no "real" PIC flag so we must build both object types case $host_os in cygwin* | mingw* | pw32* | os2* | cegcc*) pic_mode=default ;; esac if test "$pic_mode" = no && test "$deplibs_check_method" != pass_all; then # non-PIC code in shared libraries is not supported pic_mode=default fi # Calculate the filename of the output object if compiler does # not support -o with -c if test "$compiler_c_o" = no; then output_obj=`$ECHO "X$srcfile" | $Xsed -e 's%^.*/%%' -e 's%\.[^.]*$%%'`.${objext} lockfile="$output_obj.lock" else output_obj= need_locks=no lockfile= fi # Lock this critical section if it is needed # We use this script file to make the link, it avoids creating a new file if test "$need_locks" = yes; then until $opt_dry_run || ln "$progpath" "$lockfile" 2>/dev/null; do func_echo "Waiting for $lockfile to be removed" sleep 2 done elif test "$need_locks" = warn; then if test -f "$lockfile"; then $ECHO "\ *** ERROR, $lockfile exists and contains: `cat $lockfile 2>/dev/null` This indicates that another process is trying to use the same temporary object file, and libtool could not work around it because your compiler does not support \`-c' and \`-o' together. If you repeat this compilation, it may succeed, by chance, but you had better avoid parallel builds (make -j) in this platform, or get a better compiler." $opt_dry_run || $RM $removelist exit $EXIT_FAILURE fi removelist="$removelist $output_obj" $ECHO "$srcfile" > "$lockfile" fi $opt_dry_run || $RM $removelist removelist="$removelist $lockfile" trap '$opt_dry_run || $RM $removelist; exit $EXIT_FAILURE' 1 2 15 if test -n "$fix_srcfile_path"; then eval srcfile=\"$fix_srcfile_path\" fi func_quote_for_eval "$srcfile" qsrcfile=$func_quote_for_eval_result # Only build a PIC object if we are building libtool libraries. if test "$build_libtool_libs" = yes; then # Without this assignment, base_compile gets emptied. fbsd_hideous_sh_bug=$base_compile if test "$pic_mode" != no; then command="$base_compile $qsrcfile $pic_flag" else # Don't build PIC code command="$base_compile $qsrcfile" fi func_mkdir_p "$xdir$objdir" if test -z "$output_obj"; then # Place PIC objects in $objdir command="$command -o $lobj" fi func_show_eval_locale "$command" \ 'test -n "$output_obj" && $RM $removelist; exit $EXIT_FAILURE' if test "$need_locks" = warn && test "X`cat $lockfile 2>/dev/null`" != "X$srcfile"; then $ECHO "\ *** ERROR, $lockfile contains: `cat $lockfile 2>/dev/null` but it should contain: $srcfile This indicates that another process is trying to use the same temporary object file, and libtool could not work around it because your compiler does not support \`-c' and \`-o' together. If you repeat this compilation, it may succeed, by chance, but you had better avoid parallel builds (make -j) in this platform, or get a better compiler." $opt_dry_run || $RM $removelist exit $EXIT_FAILURE fi # Just move the object if needed, then go on to compile the next one if test -n "$output_obj" && test "X$output_obj" != "X$lobj"; then func_show_eval '$MV "$output_obj" "$lobj"' \ 'error=$?; $opt_dry_run || $RM $removelist; exit $error' fi # Allow error messages only from the first compilation. if test "$suppress_opt" = yes; then suppress_output=' >/dev/null 2>&1' fi fi # Only build a position-dependent object if we build old libraries. if test "$build_old_libs" = yes; then if test "$pic_mode" != yes; then # Don't build PIC code command="$base_compile $qsrcfile$pie_flag" else command="$base_compile $qsrcfile $pic_flag" fi if test "$compiler_c_o" = yes; then command="$command -o $obj" fi # Suppress compiler output if we already did a PIC compilation. command="$command$suppress_output" func_show_eval_locale "$command" \ '$opt_dry_run || $RM $removelist; exit $EXIT_FAILURE' if test "$need_locks" = warn && test "X`cat $lockfile 2>/dev/null`" != "X$srcfile"; then $ECHO "\ *** ERROR, $lockfile contains: `cat $lockfile 2>/dev/null` but it should contain: $srcfile This indicates that another process is trying to use the same temporary object file, and libtool could not work around it because your compiler does not support \`-c' and \`-o' together. If you repeat this compilation, it may succeed, by chance, but you had better avoid parallel builds (make -j) in this platform, or get a better compiler." $opt_dry_run || $RM $removelist exit $EXIT_FAILURE fi # Just move the object if needed if test -n "$output_obj" && test "X$output_obj" != "X$obj"; then func_show_eval '$MV "$output_obj" "$obj"' \ 'error=$?; $opt_dry_run || $RM $removelist; exit $error' fi fi $opt_dry_run || { func_write_libtool_object "$libobj" "$objdir/$objname" "$objname" # Unlock the critical section if it was locked if test "$need_locks" != no; then removelist=$lockfile $RM "$lockfile" fi } exit $EXIT_SUCCESS } $opt_help || { test "$mode" = compile && func_mode_compile ${1+"$@"} } func_mode_help () { # We need to display help for each of the modes. case $mode in "") # Generic help is extracted from the usage comments # at the start of this file. func_help ;; clean) $ECHO \ "Usage: $progname [OPTION]... --mode=clean RM [RM-OPTION]... FILE... Remove files from the build directory. RM is the name of the program to use to delete files associated with each FILE (typically \`/bin/rm'). RM-OPTIONS are options (such as \`-f') to be passed to RM. If FILE is a libtool library, object or program, all the files associated with it are deleted. Otherwise, only FILE itself is deleted using RM." ;; compile) $ECHO \ "Usage: $progname [OPTION]... --mode=compile COMPILE-COMMAND... SOURCEFILE Compile a source file into a libtool library object. This mode accepts the following additional options: -o OUTPUT-FILE set the output file name to OUTPUT-FILE -no-suppress do not suppress compiler output for multiple passes -prefer-pic try to building PIC objects only -prefer-non-pic try to building non-PIC objects only -shared do not build a \`.o' file suitable for static linking -static only build a \`.o' file suitable for static linking COMPILE-COMMAND is a command to be used in creating a \`standard' object file from the given SOURCEFILE. The output file name is determined by removing the directory component from SOURCEFILE, then substituting the C source code suffix \`.c' with the library object suffix, \`.lo'." ;; execute) $ECHO \ "Usage: $progname [OPTION]... --mode=execute COMMAND [ARGS]... Automatically set library path, then run a program. This mode accepts the following additional options: -dlopen FILE add the directory containing FILE to the library path This mode sets the library path environment variable according to \`-dlopen' flags. If any of the ARGS are libtool executable wrappers, then they are translated into their corresponding uninstalled binary, and any of their required library directories are added to the library path. Then, COMMAND is executed, with ARGS as arguments." ;; finish) $ECHO \ "Usage: $progname [OPTION]... --mode=finish [LIBDIR]... Complete the installation of libtool libraries. Each LIBDIR is a directory that contains libtool libraries. The commands that this mode executes may require superuser privileges. Use the \`--dry-run' option if you just want to see what would be executed." ;; install) $ECHO \ "Usage: $progname [OPTION]... --mode=install INSTALL-COMMAND... Install executables or libraries. INSTALL-COMMAND is the installation command. The first component should be either the \`install' or \`cp' program. The following components of INSTALL-COMMAND are treated specially: -inst-prefix PREFIX-DIR Use PREFIX-DIR as a staging area for installation The rest of the components are interpreted as arguments to that command (only BSD-compatible install options are recognized)." ;; link) $ECHO \ "Usage: $progname [OPTION]... --mode=link LINK-COMMAND... Link object files or libraries together to form another library, or to create an executable program. LINK-COMMAND is a command using the C compiler that you would use to create a program from several object files. The following components of LINK-COMMAND are treated specially: -all-static do not do any dynamic linking at all -avoid-version do not add a version suffix if possible -dlopen FILE \`-dlpreopen' FILE if it cannot be dlopened at runtime -dlpreopen FILE link in FILE and add its symbols to lt_preloaded_symbols -export-dynamic allow symbols from OUTPUT-FILE to be resolved with dlsym(3) -export-symbols SYMFILE try to export only the symbols listed in SYMFILE -export-symbols-regex REGEX try to export only the symbols matching REGEX -LLIBDIR search LIBDIR for required installed libraries -lNAME OUTPUT-FILE requires the installed library libNAME -module build a library that can dlopened -no-fast-install disable the fast-install mode -no-install link a not-installable executable -no-undefined declare that a library does not refer to external symbols -o OUTPUT-FILE create OUTPUT-FILE from the specified objects -objectlist FILE Use a list of object files found in FILE to specify objects -precious-files-regex REGEX don't remove output files matching REGEX -release RELEASE specify package release information -rpath LIBDIR the created library will eventually be installed in LIBDIR -R[ ]LIBDIR add LIBDIR to the runtime path of programs and libraries -shared only do dynamic linking of libtool libraries -shrext SUFFIX override the standard shared library file extension -static do not do any dynamic linking of uninstalled libtool libraries -static-libtool-libs do not do any dynamic linking of libtool libraries -version-info CURRENT[:REVISION[:AGE]] specify library version info [each variable defaults to 0] -weak LIBNAME declare that the target provides the LIBNAME interface All other options (arguments beginning with \`-') are ignored. Every other argument is treated as a filename. Files ending in \`.la' are treated as uninstalled libtool libraries, other files are standard or library object files. If the OUTPUT-FILE ends in \`.la', then a libtool library is created, only library objects (\`.lo' files) may be specified, and \`-rpath' is required, except when creating a convenience library. If OUTPUT-FILE ends in \`.a' or \`.lib', then a standard library is created using \`ar' and \`ranlib', or on Windows using \`lib'. If OUTPUT-FILE ends in \`.lo' or \`.${objext}', then a reloadable object file is created, otherwise an executable program is created." ;; uninstall) $ECHO \ "Usage: $progname [OPTION]... --mode=uninstall RM [RM-OPTION]... FILE... Remove libraries from an installation directory. RM is the name of the program to use to delete files associated with each FILE (typically \`/bin/rm'). RM-OPTIONS are options (such as \`-f') to be passed to RM. If FILE is a libtool library, all the files associated with it are deleted. Otherwise, only FILE itself is deleted using RM." ;; *) func_fatal_help "invalid operation mode \`$mode'" ;; esac $ECHO $ECHO "Try \`$progname --help' for more information about other modes." exit $? } # Now that we've collected a possible --mode arg, show help if necessary $opt_help && func_mode_help # func_mode_execute arg... func_mode_execute () { $opt_debug # The first argument is the command name. cmd="$nonopt" test -z "$cmd" && \ func_fatal_help "you must specify a COMMAND" # Handle -dlopen flags immediately. for file in $execute_dlfiles; do test -f "$file" \ || func_fatal_help "\`$file' is not a file" dir= case $file in *.la) # Check to see that this really is a libtool archive. func_lalib_unsafe_p "$file" \ || func_fatal_help "\`$lib' is not a valid libtool archive" # Read the libtool library. dlname= library_names= func_source "$file" # Skip this library if it cannot be dlopened. if test -z "$dlname"; then # Warn if it was a shared library. test -n "$library_names" && \ func_warning "\`$file' was not linked with \`-export-dynamic'" continue fi func_dirname "$file" "" "." dir="$func_dirname_result" if test -f "$dir/$objdir/$dlname"; then dir="$dir/$objdir" else if test ! -f "$dir/$dlname"; then func_fatal_error "cannot find \`$dlname' in \`$dir' or \`$dir/$objdir'" fi fi ;; *.lo) # Just add the directory containing the .lo file. func_dirname "$file" "" "." dir="$func_dirname_result" ;; *) func_warning "\`-dlopen' is ignored for non-libtool libraries and objects" continue ;; esac # Get the absolute pathname. absdir=`cd "$dir" && pwd` test -n "$absdir" && dir="$absdir" # Now add the directory to shlibpath_var. if eval "test -z \"\$$shlibpath_var\""; then eval "$shlibpath_var=\"\$dir\"" else eval "$shlibpath_var=\"\$dir:\$$shlibpath_var\"" fi done # This variable tells wrapper scripts just to set shlibpath_var # rather than running their programs. libtool_execute_magic="$magic" # Check if any of the arguments is a wrapper script. args= for file do case $file in -*) ;; *) # Do a test to see if this is really a libtool program. if func_ltwrapper_script_p "$file"; then func_source "$file" # Transform arg to wrapped name. file="$progdir/$program" elif func_ltwrapper_executable_p "$file"; then func_ltwrapper_scriptname "$file" func_source "$func_ltwrapper_scriptname_result" # Transform arg to wrapped name. file="$progdir/$program" fi ;; esac # Quote arguments (to preserve shell metacharacters). func_quote_for_eval "$file" args="$args $func_quote_for_eval_result" done if test "X$opt_dry_run" = Xfalse; then if test -n "$shlibpath_var"; then # Export the shlibpath_var. eval "export $shlibpath_var" fi # Restore saved environment variables for lt_var in LANG LANGUAGE LC_ALL LC_CTYPE LC_COLLATE LC_MESSAGES do eval "if test \"\${save_$lt_var+set}\" = set; then $lt_var=\$save_$lt_var; export $lt_var else $lt_unset $lt_var fi" done # Now prepare to actually exec the command. exec_cmd="\$cmd$args" else # Display what would be done. if test -n "$shlibpath_var"; then eval "\$ECHO \"\$shlibpath_var=\$$shlibpath_var\"" $ECHO "export $shlibpath_var" fi $ECHO "$cmd$args" exit $EXIT_SUCCESS fi } test "$mode" = execute && func_mode_execute ${1+"$@"} # func_mode_finish arg... func_mode_finish () { $opt_debug libdirs="$nonopt" admincmds= if test -n "$finish_cmds$finish_eval" && test -n "$libdirs"; then for dir do libdirs="$libdirs $dir" done for libdir in $libdirs; do if test -n "$finish_cmds"; then # Do each command in the finish commands. func_execute_cmds "$finish_cmds" 'admincmds="$admincmds '"$cmd"'"' fi if test -n "$finish_eval"; then # Do the single finish_eval. eval cmds=\"$finish_eval\" $opt_dry_run || eval "$cmds" || admincmds="$admincmds $cmds" fi done fi # Exit here if they wanted silent mode. $opt_silent && exit $EXIT_SUCCESS $ECHO "X----------------------------------------------------------------------" | $Xsed $ECHO "Libraries have been installed in:" for libdir in $libdirs; do $ECHO " $libdir" done $ECHO $ECHO "If you ever happen to want to link against installed libraries" $ECHO "in a given directory, LIBDIR, you must either use libtool, and" $ECHO "specify the full pathname of the library, or use the \`-LLIBDIR'" $ECHO "flag during linking and do at least one of the following:" if test -n "$shlibpath_var"; then $ECHO " - add LIBDIR to the \`$shlibpath_var' environment variable" $ECHO " during execution" fi if test -n "$runpath_var"; then $ECHO " - add LIBDIR to the \`$runpath_var' environment variable" $ECHO " during linking" fi if test -n "$hardcode_libdir_flag_spec"; then libdir=LIBDIR eval flag=\"$hardcode_libdir_flag_spec\" $ECHO " - use the \`$flag' linker flag" fi if test -n "$admincmds"; then $ECHO " - have your system administrator run these commands:$admincmds" fi if test -f /etc/ld.so.conf; then $ECHO " - have your system administrator add LIBDIR to \`/etc/ld.so.conf'" fi $ECHO $ECHO "See any operating system documentation about shared libraries for" case $host in solaris2.[6789]|solaris2.1[0-9]) $ECHO "more information, such as the ld(1), crle(1) and ld.so(8) manual" $ECHO "pages." ;; *) $ECHO "more information, such as the ld(1) and ld.so(8) manual pages." ;; esac $ECHO "X----------------------------------------------------------------------" | $Xsed exit $EXIT_SUCCESS } test "$mode" = finish && func_mode_finish ${1+"$@"} # func_mode_install arg... func_mode_install () { $opt_debug # There may be an optional sh(1) argument at the beginning of # install_prog (especially on Windows NT). if test "$nonopt" = "$SHELL" || test "$nonopt" = /bin/sh || # Allow the use of GNU shtool's install command. $ECHO "X$nonopt" | $GREP shtool >/dev/null; then # Aesthetically quote it. func_quote_for_eval "$nonopt" install_prog="$func_quote_for_eval_result " arg=$1 shift else install_prog= arg=$nonopt fi # The real first argument should be the name of the installation program. # Aesthetically quote it. func_quote_for_eval "$arg" install_prog="$install_prog$func_quote_for_eval_result" # We need to accept at least all the BSD install flags. dest= files= opts= prev= install_type= isdir=no stripme= for arg do if test -n "$dest"; then files="$files $dest" dest=$arg continue fi case $arg in -d) isdir=yes ;; -f) case " $install_prog " in *[\\\ /]cp\ *) ;; *) prev=$arg ;; esac ;; -g | -m | -o) prev=$arg ;; -s) stripme=" -s" continue ;; -*) ;; *) # If the previous option needed an argument, then skip it. if test -n "$prev"; then prev= else dest=$arg continue fi ;; esac # Aesthetically quote the argument. func_quote_for_eval "$arg" install_prog="$install_prog $func_quote_for_eval_result" done test -z "$install_prog" && \ func_fatal_help "you must specify an install program" test -n "$prev" && \ func_fatal_help "the \`$prev' option requires an argument" if test -z "$files"; then if test -z "$dest"; then func_fatal_help "no file or destination specified" else func_fatal_help "you must specify a destination" fi fi # Strip any trailing slash from the destination. func_stripname '' '/' "$dest" dest=$func_stripname_result # Check to see that the destination is a directory. test -d "$dest" && isdir=yes if test "$isdir" = yes; then destdir="$dest" destname= else func_dirname_and_basename "$dest" "" "." destdir="$func_dirname_result" destname="$func_basename_result" # Not a directory, so check to see that there is only one file specified. set dummy $files; shift test "$#" -gt 1 && \ func_fatal_help "\`$dest' is not a directory" fi case $destdir in [\\/]* | [A-Za-z]:[\\/]*) ;; *) for file in $files; do case $file in *.lo) ;; *) func_fatal_help "\`$destdir' must be an absolute directory name" ;; esac done ;; esac # This variable tells wrapper scripts just to set variables rather # than running their programs. libtool_install_magic="$magic" staticlibs= future_libdirs= current_libdirs= for file in $files; do # Do each installation. case $file in *.$libext) # Do the static libraries later. staticlibs="$staticlibs $file" ;; *.la) # Check to see that this really is a libtool archive. func_lalib_unsafe_p "$file" \ || func_fatal_help "\`$file' is not a valid libtool archive" library_names= old_library= relink_command= func_source "$file" # Add the libdir to current_libdirs if it is the destination. if test "X$destdir" = "X$libdir"; then case "$current_libdirs " in *" $libdir "*) ;; *) current_libdirs="$current_libdirs $libdir" ;; esac else # Note the libdir as a future libdir. case "$future_libdirs " in *" $libdir "*) ;; *) future_libdirs="$future_libdirs $libdir" ;; esac fi func_dirname "$file" "/" "" dir="$func_dirname_result" dir="$dir$objdir" if test -n "$relink_command"; then # Determine the prefix the user has applied to our future dir. inst_prefix_dir=`$ECHO "X$destdir" | $Xsed -e "s%$libdir\$%%"` # Don't allow the user to place us outside of our expected # location b/c this prevents finding dependent libraries that # are installed to the same prefix. # At present, this check doesn't affect windows .dll's that # are installed into $libdir/../bin (currently, that works fine) # but it's something to keep an eye on. test "$inst_prefix_dir" = "$destdir" && \ func_fatal_error "error: cannot install \`$file' to a directory not ending in $libdir" if test -n "$inst_prefix_dir"; then # Stick the inst_prefix_dir data into the link command. relink_command=`$ECHO "X$relink_command" | $Xsed -e "s%@inst_prefix_dir@%-inst-prefix-dir $inst_prefix_dir%"` else relink_command=`$ECHO "X$relink_command" | $Xsed -e "s%@inst_prefix_dir@%%"` fi func_warning "relinking \`$file'" func_show_eval "$relink_command" \ 'func_fatal_error "error: relink \`$file'\'' with the above command before installing it"' fi # See the names of the shared library. set dummy $library_names; shift if test -n "$1"; then realname="$1" shift srcname="$realname" test -n "$relink_command" && srcname="$realname"T # Install the shared library and build the symlinks. func_show_eval "$install_prog $dir/$srcname $destdir/$realname" \ 'exit $?' tstripme="$stripme" case $host_os in cygwin* | mingw* | pw32* | cegcc*) case $realname in *.dll.a) tstripme="" ;; esac ;; esac if test -n "$tstripme" && test -n "$striplib"; then func_show_eval "$striplib $destdir/$realname" 'exit $?' fi if test "$#" -gt 0; then # Delete the old symlinks, and create new ones. # Try `ln -sf' first, because the `ln' binary might depend on # the symlink we replace! Solaris /bin/ln does not understand -f, # so we also need to try rm && ln -s. for linkname do test "$linkname" != "$realname" \ && func_show_eval "(cd $destdir && { $LN_S -f $realname $linkname || { $RM $linkname && $LN_S $realname $linkname; }; })" done fi # Do each command in the postinstall commands. lib="$destdir/$realname" func_execute_cmds "$postinstall_cmds" 'exit $?' fi # Install the pseudo-library for information purposes. func_basename "$file" name="$func_basename_result" instname="$dir/$name"i func_show_eval "$install_prog $instname $destdir/$name" 'exit $?' # Maybe install the static library, too. test -n "$old_library" && staticlibs="$staticlibs $dir/$old_library" ;; *.lo) # Install (i.e. copy) a libtool object. # Figure out destination file name, if it wasn't already specified. if test -n "$destname"; then destfile="$destdir/$destname" else func_basename "$file" destfile="$func_basename_result" destfile="$destdir/$destfile" fi # Deduce the name of the destination old-style object file. case $destfile in *.lo) func_lo2o "$destfile" staticdest=$func_lo2o_result ;; *.$objext) staticdest="$destfile" destfile= ;; *) func_fatal_help "cannot copy a libtool object to \`$destfile'" ;; esac # Install the libtool object if requested. test -n "$destfile" && \ func_show_eval "$install_prog $file $destfile" 'exit $?' # Install the old object if enabled. if test "$build_old_libs" = yes; then # Deduce the name of the old-style object file. func_lo2o "$file" staticobj=$func_lo2o_result func_show_eval "$install_prog \$staticobj \$staticdest" 'exit $?' fi exit $EXIT_SUCCESS ;; *) # Figure out destination file name, if it wasn't already specified. if test -n "$destname"; then destfile="$destdir/$destname" else func_basename "$file" destfile="$func_basename_result" destfile="$destdir/$destfile" fi # If the file is missing, and there is a .exe on the end, strip it # because it is most likely a libtool script we actually want to # install stripped_ext="" case $file in *.exe) if test ! -f "$file"; then func_stripname '' '.exe' "$file" file=$func_stripname_result stripped_ext=".exe" fi ;; esac # Do a test to see if this is really a libtool program. case $host in *cygwin* | *mingw*) if func_ltwrapper_executable_p "$file"; then func_ltwrapper_scriptname "$file" wrapper=$func_ltwrapper_scriptname_result else func_stripname '' '.exe' "$file" wrapper=$func_stripname_result fi ;; *) wrapper=$file ;; esac if func_ltwrapper_script_p "$wrapper"; then notinst_deplibs= relink_command= func_source "$wrapper" # Check the variables that should have been set. test -z "$generated_by_libtool_version" && \ func_fatal_error "invalid libtool wrapper script \`$wrapper'" finalize=yes for lib in $notinst_deplibs; do # Check to see that each library is installed. libdir= if test -f "$lib"; then func_source "$lib" fi libfile="$libdir/"`$ECHO "X$lib" | $Xsed -e 's%^.*/%%g'` ### testsuite: skip nested quoting test if test -n "$libdir" && test ! -f "$libfile"; then func_warning "\`$lib' has not been installed in \`$libdir'" finalize=no fi done relink_command= func_source "$wrapper" outputname= if test "$fast_install" = no && test -n "$relink_command"; then $opt_dry_run || { if test "$finalize" = yes; then tmpdir=`func_mktempdir` func_basename "$file$stripped_ext" file="$func_basename_result" outputname="$tmpdir/$file" # Replace the output file specification. relink_command=`$ECHO "X$relink_command" | $Xsed -e 's%@OUTPUT@%'"$outputname"'%g'` $opt_silent || { func_quote_for_expand "$relink_command" eval "func_echo $func_quote_for_expand_result" } if eval "$relink_command"; then : else func_error "error: relink \`$file' with the above command before installing it" $opt_dry_run || ${RM}r "$tmpdir" continue fi file="$outputname" else func_warning "cannot relink \`$file'" fi } else # Install the binary that we compiled earlier. file=`$ECHO "X$file$stripped_ext" | $Xsed -e "s%\([^/]*\)$%$objdir/\1%"` fi fi # remove .exe since cygwin /usr/bin/install will append another # one anyway case $install_prog,$host in */usr/bin/install*,*cygwin*) case $file:$destfile in *.exe:*.exe) # this is ok ;; *.exe:*) destfile=$destfile.exe ;; *:*.exe) func_stripname '' '.exe' "$destfile" destfile=$func_stripname_result ;; esac ;; esac func_show_eval "$install_prog\$stripme \$file \$destfile" 'exit $?' $opt_dry_run || if test -n "$outputname"; then ${RM}r "$tmpdir" fi ;; esac done for file in $staticlibs; do func_basename "$file" name="$func_basename_result" # Set up the ranlib parameters. oldlib="$destdir/$name" func_show_eval "$install_prog \$file \$oldlib" 'exit $?' if test -n "$stripme" && test -n "$old_striplib"; then func_show_eval "$old_striplib $oldlib" 'exit $?' fi # Do each command in the postinstall commands. func_execute_cmds "$old_postinstall_cmds" 'exit $?' done test -n "$future_libdirs" && \ func_warning "remember to run \`$progname --finish$future_libdirs'" if test -n "$current_libdirs"; then # Maybe just do a dry run. $opt_dry_run && current_libdirs=" -n$current_libdirs" exec_cmd='$SHELL $progpath $preserve_args --finish$current_libdirs' else exit $EXIT_SUCCESS fi } test "$mode" = install && func_mode_install ${1+"$@"} # func_generate_dlsyms outputname originator pic_p # Extract symbols from dlprefiles and create ${outputname}S.o with # a dlpreopen symbol table. func_generate_dlsyms () { $opt_debug my_outputname="$1" my_originator="$2" my_pic_p="${3-no}" my_prefix=`$ECHO "$my_originator" | sed 's%[^a-zA-Z0-9]%_%g'` my_dlsyms= if test -n "$dlfiles$dlprefiles" || test "$dlself" != no; then if test -n "$NM" && test -n "$global_symbol_pipe"; then my_dlsyms="${my_outputname}S.c" else func_error "not configured to extract global symbols from dlpreopened files" fi fi if test -n "$my_dlsyms"; then case $my_dlsyms in "") ;; *.c) # Discover the nlist of each of the dlfiles. nlist="$output_objdir/${my_outputname}.nm" func_show_eval "$RM $nlist ${nlist}S ${nlist}T" # Parse the name list into a source file. func_verbose "creating $output_objdir/$my_dlsyms" $opt_dry_run || $ECHO > "$output_objdir/$my_dlsyms" "\ /* $my_dlsyms - symbol resolution table for \`$my_outputname' dlsym emulation. */ /* Generated by $PROGRAM (GNU $PACKAGE$TIMESTAMP) $VERSION */ #ifdef __cplusplus extern \"C\" { #endif /* External symbol declarations for the compiler. */\ " if test "$dlself" = yes; then func_verbose "generating symbol list for \`$output'" $opt_dry_run || echo ': @PROGRAM@ ' > "$nlist" # Add our own program objects to the symbol list. progfiles=`$ECHO "X$objs$old_deplibs" | $SP2NL | $Xsed -e "$lo2o" | $NL2SP` for progfile in $progfiles; do func_verbose "extracting global C symbols from \`$progfile'" $opt_dry_run || eval "$NM $progfile | $global_symbol_pipe >> '$nlist'" done if test -n "$exclude_expsyms"; then $opt_dry_run || { eval '$EGREP -v " ($exclude_expsyms)$" "$nlist" > "$nlist"T' eval '$MV "$nlist"T "$nlist"' } fi if test -n "$export_symbols_regex"; then $opt_dry_run || { eval '$EGREP -e "$export_symbols_regex" "$nlist" > "$nlist"T' eval '$MV "$nlist"T "$nlist"' } fi # Prepare the list of exported symbols if test -z "$export_symbols"; then export_symbols="$output_objdir/$outputname.exp" $opt_dry_run || { $RM $export_symbols eval "${SED} -n -e '/^: @PROGRAM@ $/d' -e 's/^.* \(.*\)$/\1/p' "'< "$nlist" > "$export_symbols"' case $host in *cygwin* | *mingw* | *cegcc* ) eval "echo EXPORTS "'> "$output_objdir/$outputname.def"' eval 'cat "$export_symbols" >> "$output_objdir/$outputname.def"' ;; esac } else $opt_dry_run || { eval "${SED} -e 's/\([].[*^$]\)/\\\\\1/g' -e 's/^/ /' -e 's/$/$/'"' < "$export_symbols" > "$output_objdir/$outputname.exp"' eval '$GREP -f "$output_objdir/$outputname.exp" < "$nlist" > "$nlist"T' eval '$MV "$nlist"T "$nlist"' case $host in *cygwin | *mingw* | *cegcc* ) eval "echo EXPORTS "'> "$output_objdir/$outputname.def"' eval 'cat "$nlist" >> "$output_objdir/$outputname.def"' ;; esac } fi fi for dlprefile in $dlprefiles; do func_verbose "extracting global C symbols from \`$dlprefile'" func_basename "$dlprefile" name="$func_basename_result" $opt_dry_run || { eval '$ECHO ": $name " >> "$nlist"' eval "$NM $dlprefile 2>/dev/null | $global_symbol_pipe >> '$nlist'" } done $opt_dry_run || { # Make sure we have at least an empty file. test -f "$nlist" || : > "$nlist" if test -n "$exclude_expsyms"; then $EGREP -v " ($exclude_expsyms)$" "$nlist" > "$nlist"T $MV "$nlist"T "$nlist" fi # Try sorting and uniquifying the output. if $GREP -v "^: " < "$nlist" | if sort -k 3 /dev/null 2>&1; then sort -k 3 else sort +2 fi | uniq > "$nlist"S; then : else $GREP -v "^: " < "$nlist" > "$nlist"S fi if test -f "$nlist"S; then eval "$global_symbol_to_cdecl"' < "$nlist"S >> "$output_objdir/$my_dlsyms"' else $ECHO '/* NONE */' >> "$output_objdir/$my_dlsyms" fi $ECHO >> "$output_objdir/$my_dlsyms" "\ /* The mapping between symbol names and symbols. */ typedef struct { const char *name; void *address; } lt_dlsymlist; " case $host in *cygwin* | *mingw* | *cegcc* ) $ECHO >> "$output_objdir/$my_dlsyms" "\ /* DATA imports from DLLs on WIN32 con't be const, because runtime relocations are performed -- see ld's documentation on pseudo-relocs. */" lt_dlsym_const= ;; *osf5*) echo >> "$output_objdir/$my_dlsyms" "\ /* This system does not cope well with relocations in const data */" lt_dlsym_const= ;; *) lt_dlsym_const=const ;; esac $ECHO >> "$output_objdir/$my_dlsyms" "\ extern $lt_dlsym_const lt_dlsymlist lt_${my_prefix}_LTX_preloaded_symbols[]; $lt_dlsym_const lt_dlsymlist lt_${my_prefix}_LTX_preloaded_symbols[] = {\ { \"$my_originator\", (void *) 0 }," case $need_lib_prefix in no) eval "$global_symbol_to_c_name_address" < "$nlist" >> "$output_objdir/$my_dlsyms" ;; *) eval "$global_symbol_to_c_name_address_lib_prefix" < "$nlist" >> "$output_objdir/$my_dlsyms" ;; esac $ECHO >> "$output_objdir/$my_dlsyms" "\ {0, (void *) 0} }; /* This works around a problem in FreeBSD linker */ #ifdef FREEBSD_WORKAROUND static const void *lt_preloaded_setup() { return lt_${my_prefix}_LTX_preloaded_symbols; } #endif #ifdef __cplusplus } #endif\ " } # !$opt_dry_run pic_flag_for_symtable= case "$compile_command " in *" -static "*) ;; *) case $host in # compiling the symbol table file with pic_flag works around # a FreeBSD bug that causes programs to crash when -lm is # linked before any other PIC object. But we must not use # pic_flag when linking with -static. The problem exists in # FreeBSD 2.2.6 and is fixed in FreeBSD 3.1. *-*-freebsd2*|*-*-freebsd3.0*|*-*-freebsdelf3.0*) pic_flag_for_symtable=" $pic_flag -DFREEBSD_WORKAROUND" ;; *-*-hpux*) pic_flag_for_symtable=" $pic_flag" ;; *) if test "X$my_pic_p" != Xno; then pic_flag_for_symtable=" $pic_flag" fi ;; esac ;; esac symtab_cflags= for arg in $LTCFLAGS; do case $arg in -pie | -fpie | -fPIE) ;; *) symtab_cflags="$symtab_cflags $arg" ;; esac done # Now compile the dynamic symbol file. func_show_eval '(cd $output_objdir && $LTCC$symtab_cflags -c$no_builtin_flag$pic_flag_for_symtable "$my_dlsyms")' 'exit $?' # Clean up the generated files. func_show_eval '$RM "$output_objdir/$my_dlsyms" "$nlist" "${nlist}S" "${nlist}T"' # Transform the symbol file into the correct name. symfileobj="$output_objdir/${my_outputname}S.$objext" case $host in *cygwin* | *mingw* | *cegcc* ) if test -f "$output_objdir/$my_outputname.def"; then compile_command=`$ECHO "X$compile_command" | $Xsed -e "s%@SYMFILE@%$output_objdir/$my_outputname.def $symfileobj%"` finalize_command=`$ECHO "X$finalize_command" | $Xsed -e "s%@SYMFILE@%$output_objdir/$my_outputname.def $symfileobj%"` else compile_command=`$ECHO "X$compile_command" | $Xsed -e "s%@SYMFILE@%$symfileobj%"` finalize_command=`$ECHO "X$finalize_command" | $Xsed -e "s%@SYMFILE@%$symfileobj%"` fi ;; *) compile_command=`$ECHO "X$compile_command" | $Xsed -e "s%@SYMFILE@%$symfileobj%"` finalize_command=`$ECHO "X$finalize_command" | $Xsed -e "s%@SYMFILE@%$symfileobj%"` ;; esac ;; *) func_fatal_error "unknown suffix for \`$my_dlsyms'" ;; esac else # We keep going just in case the user didn't refer to # lt_preloaded_symbols. The linker will fail if global_symbol_pipe # really was required. # Nullify the symbol file. compile_command=`$ECHO "X$compile_command" | $Xsed -e "s% @SYMFILE@%%"` finalize_command=`$ECHO "X$finalize_command" | $Xsed -e "s% @SYMFILE@%%"` fi } # func_win32_libid arg # return the library type of file 'arg' # # Need a lot of goo to handle *both* DLLs and import libs # Has to be a shell function in order to 'eat' the argument # that is supplied when $file_magic_command is called. func_win32_libid () { $opt_debug win32_libid_type="unknown" win32_fileres=`file -L $1 2>/dev/null` case $win32_fileres in *ar\ archive\ import\ library*) # definitely import win32_libid_type="x86 archive import" ;; *ar\ archive*) # could be an import, or static if eval $OBJDUMP -f $1 | $SED -e '10q' 2>/dev/null | $EGREP 'file format pe-i386(.*architecture: i386)?' >/dev/null ; then win32_nmres=`eval $NM -f posix -A $1 | $SED -n -e ' 1,100{ / I /{ s,.*,import, p q } }'` case $win32_nmres in import*) win32_libid_type="x86 archive import";; *) win32_libid_type="x86 archive static";; esac fi ;; *DLL*) win32_libid_type="x86 DLL" ;; *executable*) # but shell scripts are "executable" too... case $win32_fileres in *MS\ Windows\ PE\ Intel*) win32_libid_type="x86 DLL" ;; esac ;; esac $ECHO "$win32_libid_type" } # func_extract_an_archive dir oldlib func_extract_an_archive () { $opt_debug f_ex_an_ar_dir="$1"; shift f_ex_an_ar_oldlib="$1" func_show_eval "(cd \$f_ex_an_ar_dir && $AR x \"\$f_ex_an_ar_oldlib\")" 'exit $?' if ($AR t "$f_ex_an_ar_oldlib" | sort | sort -uc >/dev/null 2>&1); then : else func_fatal_error "object name conflicts in archive: $f_ex_an_ar_dir/$f_ex_an_ar_oldlib" fi } # func_extract_archives gentop oldlib ... func_extract_archives () { $opt_debug my_gentop="$1"; shift my_oldlibs=${1+"$@"} my_oldobjs="" my_xlib="" my_xabs="" my_xdir="" for my_xlib in $my_oldlibs; do # Extract the objects. case $my_xlib in [\\/]* | [A-Za-z]:[\\/]*) my_xabs="$my_xlib" ;; *) my_xabs=`pwd`"/$my_xlib" ;; esac func_basename "$my_xlib" my_xlib="$func_basename_result" my_xlib_u=$my_xlib while :; do case " $extracted_archives " in *" $my_xlib_u "*) func_arith $extracted_serial + 1 extracted_serial=$func_arith_result my_xlib_u=lt$extracted_serial-$my_xlib ;; *) break ;; esac done extracted_archives="$extracted_archives $my_xlib_u" my_xdir="$my_gentop/$my_xlib_u" func_mkdir_p "$my_xdir" case $host in *-darwin*) func_verbose "Extracting $my_xabs" # Do not bother doing anything if just a dry run $opt_dry_run || { darwin_orig_dir=`pwd` cd $my_xdir || exit $? darwin_archive=$my_xabs darwin_curdir=`pwd` darwin_base_archive=`basename "$darwin_archive"` darwin_arches=`$LIPO -info "$darwin_archive" 2>/dev/null | $GREP Architectures 2>/dev/null || true` if test -n "$darwin_arches"; then darwin_arches=`$ECHO "$darwin_arches" | $SED -e 's/.*are://'` darwin_arch= func_verbose "$darwin_base_archive has multiple architectures $darwin_arches" for darwin_arch in $darwin_arches ; do func_mkdir_p "unfat-$$/${darwin_base_archive}-${darwin_arch}" $LIPO -thin $darwin_arch -output "unfat-$$/${darwin_base_archive}-${darwin_arch}/${darwin_base_archive}" "${darwin_archive}" cd "unfat-$$/${darwin_base_archive}-${darwin_arch}" func_extract_an_archive "`pwd`" "${darwin_base_archive}" cd "$darwin_curdir" $RM "unfat-$$/${darwin_base_archive}-${darwin_arch}/${darwin_base_archive}" done # $darwin_arches ## Okay now we've a bunch of thin objects, gotta fatten them up :) darwin_filelist=`find unfat-$$ -type f -name \*.o -print -o -name \*.lo -print | $SED -e "$basename" | sort -u` darwin_file= darwin_files= for darwin_file in $darwin_filelist; do darwin_files=`find unfat-$$ -name $darwin_file -print | $NL2SP` $LIPO -create -output "$darwin_file" $darwin_files done # $darwin_filelist $RM -rf unfat-$$ cd "$darwin_orig_dir" else cd $darwin_orig_dir func_extract_an_archive "$my_xdir" "$my_xabs" fi # $darwin_arches } # !$opt_dry_run ;; *) func_extract_an_archive "$my_xdir" "$my_xabs" ;; esac my_oldobjs="$my_oldobjs "`find $my_xdir -name \*.$objext -print -o -name \*.lo -print | $NL2SP` done func_extract_archives_result="$my_oldobjs" } # func_emit_wrapper_part1 [arg=no] # # Emit the first part of a libtool wrapper script on stdout. # For more information, see the description associated with # func_emit_wrapper(), below. func_emit_wrapper_part1 () { func_emit_wrapper_part1_arg1=no if test -n "$1" ; then func_emit_wrapper_part1_arg1=$1 fi $ECHO "\ #! $SHELL # $output - temporary wrapper script for $objdir/$outputname # Generated by $PROGRAM (GNU $PACKAGE$TIMESTAMP) $VERSION # # The $output program cannot be directly executed until all the libtool # libraries that it depends on are installed. # # This wrapper script should never be moved out of the build directory. # If it is, it will not operate correctly. # Sed substitution that helps us do robust quoting. It backslashifies # metacharacters that are still active within double-quoted strings. Xsed='${SED} -e 1s/^X//' sed_quote_subst='$sed_quote_subst' # Be Bourne compatible if test -n \"\${ZSH_VERSION+set}\" && (emulate sh) >/dev/null 2>&1; then emulate sh NULLCMD=: # Zsh 3.x and 4.x performs word splitting on \${1+\"\$@\"}, which # is contrary to our usage. Disable this feature. alias -g '\${1+\"\$@\"}'='\"\$@\"' setopt NO_GLOB_SUBST else case \`(set -o) 2>/dev/null\` in *posix*) set -o posix;; esac fi BIN_SH=xpg4; export BIN_SH # for Tru64 DUALCASE=1; export DUALCASE # for MKS sh # The HP-UX ksh and POSIX shell print the target directory to stdout # if CDPATH is set. (unset CDPATH) >/dev/null 2>&1 && unset CDPATH relink_command=\"$relink_command\" # This environment variable determines our operation mode. if test \"\$libtool_install_magic\" = \"$magic\"; then # install mode needs the following variables: generated_by_libtool_version='$macro_version' notinst_deplibs='$notinst_deplibs' else # When we are sourced in execute mode, \$file and \$ECHO are already set. if test \"\$libtool_execute_magic\" != \"$magic\"; then ECHO=\"$qecho\" file=\"\$0\" # Make sure echo works. if test \"X\$1\" = X--no-reexec; then # Discard the --no-reexec flag, and continue. shift elif test \"X\`{ \$ECHO '\t'; } 2>/dev/null\`\" = 'X\t'; then # Yippee, \$ECHO works! : else # Restart under the correct shell, and then maybe \$ECHO will work. exec $SHELL \"\$0\" --no-reexec \${1+\"\$@\"} fi fi\ " $ECHO "\ # Find the directory that this script lives in. thisdir=\`\$ECHO \"X\$file\" | \$Xsed -e 's%/[^/]*$%%'\` test \"x\$thisdir\" = \"x\$file\" && thisdir=. # Follow symbolic links until we get to the real thisdir. file=\`ls -ld \"\$file\" | ${SED} -n 's/.*-> //p'\` while test -n \"\$file\"; do destdir=\`\$ECHO \"X\$file\" | \$Xsed -e 's%/[^/]*\$%%'\` # If there was a directory component, then change thisdir. if test \"x\$destdir\" != \"x\$file\"; then case \"\$destdir\" in [\\\\/]* | [A-Za-z]:[\\\\/]*) thisdir=\"\$destdir\" ;; *) thisdir=\"\$thisdir/\$destdir\" ;; esac fi file=\`\$ECHO \"X\$file\" | \$Xsed -e 's%^.*/%%'\` file=\`ls -ld \"\$thisdir/\$file\" | ${SED} -n 's/.*-> //p'\` done " } # end: func_emit_wrapper_part1 # func_emit_wrapper_part2 [arg=no] # # Emit the second part of a libtool wrapper script on stdout. # For more information, see the description associated with # func_emit_wrapper(), below. func_emit_wrapper_part2 () { func_emit_wrapper_part2_arg1=no if test -n "$1" ; then func_emit_wrapper_part2_arg1=$1 fi $ECHO "\ # Usually 'no', except on cygwin/mingw when embedded into # the cwrapper. WRAPPER_SCRIPT_BELONGS_IN_OBJDIR=$func_emit_wrapper_part2_arg1 if test \"\$WRAPPER_SCRIPT_BELONGS_IN_OBJDIR\" = \"yes\"; then # special case for '.' if test \"\$thisdir\" = \".\"; then thisdir=\`pwd\` fi # remove .libs from thisdir case \"\$thisdir\" in *[\\\\/]$objdir ) thisdir=\`\$ECHO \"X\$thisdir\" | \$Xsed -e 's%[\\\\/][^\\\\/]*$%%'\` ;; $objdir ) thisdir=. ;; esac fi # Try to get the absolute directory name. absdir=\`cd \"\$thisdir\" && pwd\` test -n \"\$absdir\" && thisdir=\"\$absdir\" " if test "$fast_install" = yes; then $ECHO "\ program=lt-'$outputname'$exeext progdir=\"\$thisdir/$objdir\" if test ! -f \"\$progdir/\$program\" || { file=\`ls -1dt \"\$progdir/\$program\" \"\$progdir/../\$program\" 2>/dev/null | ${SED} 1q\`; \\ test \"X\$file\" != \"X\$progdir/\$program\"; }; then file=\"\$\$-\$program\" if test ! -d \"\$progdir\"; then $MKDIR \"\$progdir\" else $RM \"\$progdir/\$file\" fi" $ECHO "\ # relink executable if necessary if test -n \"\$relink_command\"; then if relink_command_output=\`eval \$relink_command 2>&1\`; then : else $ECHO \"\$relink_command_output\" >&2 $RM \"\$progdir/\$file\" exit 1 fi fi $MV \"\$progdir/\$file\" \"\$progdir/\$program\" 2>/dev/null || { $RM \"\$progdir/\$program\"; $MV \"\$progdir/\$file\" \"\$progdir/\$program\"; } $RM \"\$progdir/\$file\" fi" else $ECHO "\ program='$outputname' progdir=\"\$thisdir/$objdir\" " fi $ECHO "\ if test -f \"\$progdir/\$program\"; then" # Export our shlibpath_var if we have one. if test "$shlibpath_overrides_runpath" = yes && test -n "$shlibpath_var" && test -n "$temp_rpath"; then $ECHO "\ # Add our own library path to $shlibpath_var $shlibpath_var=\"$temp_rpath\$$shlibpath_var\" # Some systems cannot cope with colon-terminated $shlibpath_var # The second colon is a workaround for a bug in BeOS R4 sed $shlibpath_var=\`\$ECHO \"X\$$shlibpath_var\" | \$Xsed -e 's/::*\$//'\` export $shlibpath_var " fi # fixup the dll searchpath if we need to. if test -n "$dllsearchpath"; then $ECHO "\ # Add the dll search path components to the executable PATH PATH=$dllsearchpath:\$PATH " fi $ECHO "\ if test \"\$libtool_execute_magic\" != \"$magic\"; then # Run the actual program with our arguments. " case $host in # Backslashes separate directories on plain windows *-*-mingw | *-*-os2* | *-cegcc*) $ECHO "\ exec \"\$progdir\\\\\$program\" \${1+\"\$@\"} " ;; *) $ECHO "\ exec \"\$progdir/\$program\" \${1+\"\$@\"} " ;; esac $ECHO "\ \$ECHO \"\$0: cannot exec \$program \$*\" 1>&2 exit 1 fi else # The program doesn't exist. \$ECHO \"\$0: error: \\\`\$progdir/\$program' does not exist\" 1>&2 \$ECHO \"This script is just a wrapper for \$program.\" 1>&2 $ECHO \"See the $PACKAGE documentation for more information.\" 1>&2 exit 1 fi fi\ " } # end: func_emit_wrapper_part2 # func_emit_wrapper [arg=no] # # Emit a libtool wrapper script on stdout. # Don't directly open a file because we may want to # incorporate the script contents within a cygwin/mingw # wrapper executable. Must ONLY be called from within # func_mode_link because it depends on a number of variables # set therein. # # ARG is the value that the WRAPPER_SCRIPT_BELONGS_IN_OBJDIR # variable will take. If 'yes', then the emitted script # will assume that the directory in which it is stored is # the $objdir directory. This is a cygwin/mingw-specific # behavior. func_emit_wrapper () { func_emit_wrapper_arg1=no if test -n "$1" ; then func_emit_wrapper_arg1=$1 fi # split this up so that func_emit_cwrapperexe_src # can call each part independently. func_emit_wrapper_part1 "${func_emit_wrapper_arg1}" func_emit_wrapper_part2 "${func_emit_wrapper_arg1}" } # func_to_host_path arg # # Convert paths to host format when used with build tools. # Intended for use with "native" mingw (where libtool itself # is running under the msys shell), or in the following cross- # build environments: # $build $host # mingw (msys) mingw [e.g. native] # cygwin mingw # *nix + wine mingw # where wine is equipped with the `winepath' executable. # In the native mingw case, the (msys) shell automatically # converts paths for any non-msys applications it launches, # but that facility isn't available from inside the cwrapper. # Similar accommodations are necessary for $host mingw and # $build cygwin. Calling this function does no harm for other # $host/$build combinations not listed above. # # ARG is the path (on $build) that should be converted to # the proper representation for $host. The result is stored # in $func_to_host_path_result. func_to_host_path () { func_to_host_path_result="$1" if test -n "$1" ; then case $host in *mingw* ) lt_sed_naive_backslashify='s|\\\\*|\\|g;s|/|\\|g;s|\\|\\\\|g' case $build in *mingw* ) # actually, msys # awkward: cmd appends spaces to result lt_sed_strip_trailing_spaces="s/[ ]*\$//" func_to_host_path_tmp1=`( cmd //c echo "$1" |\ $SED -e "$lt_sed_strip_trailing_spaces" ) 2>/dev/null || echo ""` func_to_host_path_result=`echo "$func_to_host_path_tmp1" |\ $SED -e "$lt_sed_naive_backslashify"` ;; *cygwin* ) func_to_host_path_tmp1=`cygpath -w "$1"` func_to_host_path_result=`echo "$func_to_host_path_tmp1" |\ $SED -e "$lt_sed_naive_backslashify"` ;; * ) # Unfortunately, winepath does not exit with a non-zero # error code, so we are forced to check the contents of # stdout. On the other hand, if the command is not # found, the shell will set an exit code of 127 and print # *an error message* to stdout. So we must check for both # error code of zero AND non-empty stdout, which explains # the odd construction: func_to_host_path_tmp1=`winepath -w "$1" 2>/dev/null` if test "$?" -eq 0 && test -n "${func_to_host_path_tmp1}"; then func_to_host_path_result=`echo "$func_to_host_path_tmp1" |\ $SED -e "$lt_sed_naive_backslashify"` else # Allow warning below. func_to_host_path_result="" fi ;; esac if test -z "$func_to_host_path_result" ; then func_error "Could not determine host path corresponding to" func_error " '$1'" func_error "Continuing, but uninstalled executables may not work." # Fallback: func_to_host_path_result="$1" fi ;; esac fi } # end: func_to_host_path # func_to_host_pathlist arg # # Convert pathlists to host format when used with build tools. # See func_to_host_path(), above. This function supports the # following $build/$host combinations (but does no harm for # combinations not listed here): # $build $host # mingw (msys) mingw [e.g. native] # cygwin mingw # *nix + wine mingw # # Path separators are also converted from $build format to # $host format. If ARG begins or ends with a path separator # character, it is preserved (but converted to $host format) # on output. # # ARG is a pathlist (on $build) that should be converted to # the proper representation on $host. The result is stored # in $func_to_host_pathlist_result. func_to_host_pathlist () { func_to_host_pathlist_result="$1" if test -n "$1" ; then case $host in *mingw* ) lt_sed_naive_backslashify='s|\\\\*|\\|g;s|/|\\|g;s|\\|\\\\|g' # Remove leading and trailing path separator characters from # ARG. msys behavior is inconsistent here, cygpath turns them # into '.;' and ';.', and winepath ignores them completely. func_to_host_pathlist_tmp2="$1" # Once set for this call, this variable should not be # reassigned. It is used in tha fallback case. func_to_host_pathlist_tmp1=`echo "$func_to_host_pathlist_tmp2" |\ $SED -e 's|^:*||' -e 's|:*$||'` case $build in *mingw* ) # Actually, msys. # Awkward: cmd appends spaces to result. lt_sed_strip_trailing_spaces="s/[ ]*\$//" func_to_host_pathlist_tmp2=`( cmd //c echo "$func_to_host_pathlist_tmp1" |\ $SED -e "$lt_sed_strip_trailing_spaces" ) 2>/dev/null || echo ""` func_to_host_pathlist_result=`echo "$func_to_host_pathlist_tmp2" |\ $SED -e "$lt_sed_naive_backslashify"` ;; *cygwin* ) func_to_host_pathlist_tmp2=`cygpath -w -p "$func_to_host_pathlist_tmp1"` func_to_host_pathlist_result=`echo "$func_to_host_pathlist_tmp2" |\ $SED -e "$lt_sed_naive_backslashify"` ;; * ) # unfortunately, winepath doesn't convert pathlists func_to_host_pathlist_result="" func_to_host_pathlist_oldIFS=$IFS IFS=: for func_to_host_pathlist_f in $func_to_host_pathlist_tmp1 ; do IFS=$func_to_host_pathlist_oldIFS if test -n "$func_to_host_pathlist_f" ; then func_to_host_path "$func_to_host_pathlist_f" if test -n "$func_to_host_path_result" ; then if test -z "$func_to_host_pathlist_result" ; then func_to_host_pathlist_result="$func_to_host_path_result" else func_to_host_pathlist_result="$func_to_host_pathlist_result;$func_to_host_path_result" fi fi fi IFS=: done IFS=$func_to_host_pathlist_oldIFS ;; esac if test -z "$func_to_host_pathlist_result" ; then func_error "Could not determine the host path(s) corresponding to" func_error " '$1'" func_error "Continuing, but uninstalled executables may not work." # Fallback. This may break if $1 contains DOS-style drive # specifications. The fix is not to complicate the expression # below, but for the user to provide a working wine installation # with winepath so that path translation in the cross-to-mingw # case works properly. lt_replace_pathsep_nix_to_dos="s|:|;|g" func_to_host_pathlist_result=`echo "$func_to_host_pathlist_tmp1" |\ $SED -e "$lt_replace_pathsep_nix_to_dos"` fi # Now, add the leading and trailing path separators back case "$1" in :* ) func_to_host_pathlist_result=";$func_to_host_pathlist_result" ;; esac case "$1" in *: ) func_to_host_pathlist_result="$func_to_host_pathlist_result;" ;; esac ;; esac fi } # end: func_to_host_pathlist # func_emit_cwrapperexe_src # emit the source code for a wrapper executable on stdout # Must ONLY be called from within func_mode_link because # it depends on a number of variable set therein. func_emit_cwrapperexe_src () { cat < #include #ifdef _MSC_VER # include # include # include # define setmode _setmode #else # include # include # ifdef __CYGWIN__ # include # define HAVE_SETENV # ifdef __STRICT_ANSI__ char *realpath (const char *, char *); int putenv (char *); int setenv (const char *, const char *, int); # endif # endif #endif #include #include #include #include #include #include #include #include #if defined(PATH_MAX) # define LT_PATHMAX PATH_MAX #elif defined(MAXPATHLEN) # define LT_PATHMAX MAXPATHLEN #else # define LT_PATHMAX 1024 #endif #ifndef S_IXOTH # define S_IXOTH 0 #endif #ifndef S_IXGRP # define S_IXGRP 0 #endif #ifdef _MSC_VER # define S_IXUSR _S_IEXEC # define stat _stat # ifndef _INTPTR_T_DEFINED # define intptr_t int # endif #endif #ifndef DIR_SEPARATOR # define DIR_SEPARATOR '/' # define PATH_SEPARATOR ':' #endif #if defined (_WIN32) || defined (__MSDOS__) || defined (__DJGPP__) || \ defined (__OS2__) # define HAVE_DOS_BASED_FILE_SYSTEM # define FOPEN_WB "wb" # ifndef DIR_SEPARATOR_2 # define DIR_SEPARATOR_2 '\\' # endif # ifndef PATH_SEPARATOR_2 # define PATH_SEPARATOR_2 ';' # endif #endif #ifndef DIR_SEPARATOR_2 # define IS_DIR_SEPARATOR(ch) ((ch) == DIR_SEPARATOR) #else /* DIR_SEPARATOR_2 */ # define IS_DIR_SEPARATOR(ch) \ (((ch) == DIR_SEPARATOR) || ((ch) == DIR_SEPARATOR_2)) #endif /* DIR_SEPARATOR_2 */ #ifndef PATH_SEPARATOR_2 # define IS_PATH_SEPARATOR(ch) ((ch) == PATH_SEPARATOR) #else /* PATH_SEPARATOR_2 */ # define IS_PATH_SEPARATOR(ch) ((ch) == PATH_SEPARATOR_2) #endif /* PATH_SEPARATOR_2 */ #ifdef __CYGWIN__ # define FOPEN_WB "wb" #endif #ifndef FOPEN_WB # define FOPEN_WB "w" #endif #ifndef _O_BINARY # define _O_BINARY 0 #endif #define XMALLOC(type, num) ((type *) xmalloc ((num) * sizeof(type))) #define XFREE(stale) do { \ if (stale) { free ((void *) stale); stale = 0; } \ } while (0) #undef LTWRAPPER_DEBUGPRINTF #if defined DEBUGWRAPPER # define LTWRAPPER_DEBUGPRINTF(args) ltwrapper_debugprintf args static void ltwrapper_debugprintf (const char *fmt, ...) { va_list args; va_start (args, fmt); (void) vfprintf (stderr, fmt, args); va_end (args); } #else # define LTWRAPPER_DEBUGPRINTF(args) #endif const char *program_name = NULL; void *xmalloc (size_t num); char *xstrdup (const char *string); const char *base_name (const char *name); char *find_executable (const char *wrapper); char *chase_symlinks (const char *pathspec); int make_executable (const char *path); int check_executable (const char *path); char *strendzap (char *str, const char *pat); void lt_fatal (const char *message, ...); void lt_setenv (const char *name, const char *value); char *lt_extend_str (const char *orig_value, const char *add, int to_end); void lt_opt_process_env_set (const char *arg); void lt_opt_process_env_prepend (const char *arg); void lt_opt_process_env_append (const char *arg); int lt_split_name_value (const char *arg, char** name, char** value); void lt_update_exe_path (const char *name, const char *value); void lt_update_lib_path (const char *name, const char *value); static const char *script_text_part1 = EOF func_emit_wrapper_part1 yes | $SED -e 's/\([\\"]\)/\\\1/g' \ -e 's/^/ "/' -e 's/$/\\n"/' echo ";" cat <"))); for (i = 0; i < newargc; i++) { LTWRAPPER_DEBUGPRINTF (("(main) newargz[%d] : %s\n", i, (newargz[i] ? newargz[i] : ""))); } EOF case $host_os in mingw*) cat <<"EOF" /* execv doesn't actually work on mingw as expected on unix */ rval = _spawnv (_P_WAIT, lt_argv_zero, (const char * const *) newargz); if (rval == -1) { /* failed to start process */ LTWRAPPER_DEBUGPRINTF (("(main) failed to launch target \"%s\": errno = %d\n", lt_argv_zero, errno)); return 127; } return rval; EOF ;; *) cat <<"EOF" execv (lt_argv_zero, newargz); return rval; /* =127, but avoids unused variable warning */ EOF ;; esac cat <<"EOF" } void * xmalloc (size_t num) { void *p = (void *) malloc (num); if (!p) lt_fatal ("Memory exhausted"); return p; } char * xstrdup (const char *string) { return string ? strcpy ((char *) xmalloc (strlen (string) + 1), string) : NULL; } const char * base_name (const char *name) { const char *base; #if defined (HAVE_DOS_BASED_FILE_SYSTEM) /* Skip over the disk name in MSDOS pathnames. */ if (isalpha ((unsigned char) name[0]) && name[1] == ':') name += 2; #endif for (base = name; *name; name++) if (IS_DIR_SEPARATOR (*name)) base = name + 1; return base; } int check_executable (const char *path) { struct stat st; LTWRAPPER_DEBUGPRINTF (("(check_executable) : %s\n", path ? (*path ? path : "EMPTY!") : "NULL!")); if ((!path) || (!*path)) return 0; if ((stat (path, &st) >= 0) && (st.st_mode & (S_IXUSR | S_IXGRP | S_IXOTH))) return 1; else return 0; } int make_executable (const char *path) { int rval = 0; struct stat st; LTWRAPPER_DEBUGPRINTF (("(make_executable) : %s\n", path ? (*path ? path : "EMPTY!") : "NULL!")); if ((!path) || (!*path)) return 0; if (stat (path, &st) >= 0) { rval = chmod (path, st.st_mode | S_IXOTH | S_IXGRP | S_IXUSR); } return rval; } /* Searches for the full path of the wrapper. Returns newly allocated full path name if found, NULL otherwise Does not chase symlinks, even on platforms that support them. */ char * find_executable (const char *wrapper) { int has_slash = 0; const char *p; const char *p_next; /* static buffer for getcwd */ char tmp[LT_PATHMAX + 1]; int tmp_len; char *concat_name; LTWRAPPER_DEBUGPRINTF (("(find_executable) : %s\n", wrapper ? (*wrapper ? wrapper : "EMPTY!") : "NULL!")); if ((wrapper == NULL) || (*wrapper == '\0')) return NULL; /* Absolute path? */ #if defined (HAVE_DOS_BASED_FILE_SYSTEM) if (isalpha ((unsigned char) wrapper[0]) && wrapper[1] == ':') { concat_name = xstrdup (wrapper); if (check_executable (concat_name)) return concat_name; XFREE (concat_name); } else { #endif if (IS_DIR_SEPARATOR (wrapper[0])) { concat_name = xstrdup (wrapper); if (check_executable (concat_name)) return concat_name; XFREE (concat_name); } #if defined (HAVE_DOS_BASED_FILE_SYSTEM) } #endif for (p = wrapper; *p; p++) if (*p == '/') { has_slash = 1; break; } if (!has_slash) { /* no slashes; search PATH */ const char *path = getenv ("PATH"); if (path != NULL) { for (p = path; *p; p = p_next) { const char *q; size_t p_len; for (q = p; *q; q++) if (IS_PATH_SEPARATOR (*q)) break; p_len = q - p; p_next = (*q == '\0' ? q : q + 1); if (p_len == 0) { /* empty path: current directory */ if (getcwd (tmp, LT_PATHMAX) == NULL) lt_fatal ("getcwd failed"); tmp_len = strlen (tmp); concat_name = XMALLOC (char, tmp_len + 1 + strlen (wrapper) + 1); memcpy (concat_name, tmp, tmp_len); concat_name[tmp_len] = '/'; strcpy (concat_name + tmp_len + 1, wrapper); } else { concat_name = XMALLOC (char, p_len + 1 + strlen (wrapper) + 1); memcpy (concat_name, p, p_len); concat_name[p_len] = '/'; strcpy (concat_name + p_len + 1, wrapper); } if (check_executable (concat_name)) return concat_name; XFREE (concat_name); } } /* not found in PATH; assume curdir */ } /* Relative path | not found in path: prepend cwd */ if (getcwd (tmp, LT_PATHMAX) == NULL) lt_fatal ("getcwd failed"); tmp_len = strlen (tmp); concat_name = XMALLOC (char, tmp_len + 1 + strlen (wrapper) + 1); memcpy (concat_name, tmp, tmp_len); concat_name[tmp_len] = '/'; strcpy (concat_name + tmp_len + 1, wrapper); if (check_executable (concat_name)) return concat_name; XFREE (concat_name); return NULL; } char * chase_symlinks (const char *pathspec) { #ifndef S_ISLNK return xstrdup (pathspec); #else char buf[LT_PATHMAX]; struct stat s; char *tmp_pathspec = xstrdup (pathspec); char *p; int has_symlinks = 0; while (strlen (tmp_pathspec) && !has_symlinks) { LTWRAPPER_DEBUGPRINTF (("checking path component for symlinks: %s\n", tmp_pathspec)); if (lstat (tmp_pathspec, &s) == 0) { if (S_ISLNK (s.st_mode) != 0) { has_symlinks = 1; break; } /* search backwards for last DIR_SEPARATOR */ p = tmp_pathspec + strlen (tmp_pathspec) - 1; while ((p > tmp_pathspec) && (!IS_DIR_SEPARATOR (*p))) p--; if ((p == tmp_pathspec) && (!IS_DIR_SEPARATOR (*p))) { /* no more DIR_SEPARATORS left */ break; } *p = '\0'; } else { char *errstr = strerror (errno); lt_fatal ("Error accessing file %s (%s)", tmp_pathspec, errstr); } } XFREE (tmp_pathspec); if (!has_symlinks) { return xstrdup (pathspec); } tmp_pathspec = realpath (pathspec, buf); if (tmp_pathspec == 0) { lt_fatal ("Could not follow symlinks for %s", pathspec); } return xstrdup (tmp_pathspec); #endif } char * strendzap (char *str, const char *pat) { size_t len, patlen; assert (str != NULL); assert (pat != NULL); len = strlen (str); patlen = strlen (pat); if (patlen <= len) { str += len - patlen; if (strcmp (str, pat) == 0) *str = '\0'; } return str; } static void lt_error_core (int exit_status, const char *mode, const char *message, va_list ap) { fprintf (stderr, "%s: %s: ", program_name, mode); vfprintf (stderr, message, ap); fprintf (stderr, ".\n"); if (exit_status >= 0) exit (exit_status); } void lt_fatal (const char *message, ...) { va_list ap; va_start (ap, message); lt_error_core (EXIT_FAILURE, "FATAL", message, ap); va_end (ap); } void lt_setenv (const char *name, const char *value) { LTWRAPPER_DEBUGPRINTF (("(lt_setenv) setting '%s' to '%s'\n", (name ? name : ""), (value ? value : ""))); { #ifdef HAVE_SETENV /* always make a copy, for consistency with !HAVE_SETENV */ char *str = xstrdup (value); setenv (name, str, 1); #else int len = strlen (name) + 1 + strlen (value) + 1; char *str = XMALLOC (char, len); sprintf (str, "%s=%s", name, value); if (putenv (str) != EXIT_SUCCESS) { XFREE (str); } #endif } } char * lt_extend_str (const char *orig_value, const char *add, int to_end) { char *new_value; if (orig_value && *orig_value) { int orig_value_len = strlen (orig_value); int add_len = strlen (add); new_value = XMALLOC (char, add_len + orig_value_len + 1); if (to_end) { strcpy (new_value, orig_value); strcpy (new_value + orig_value_len, add); } else { strcpy (new_value, add); strcpy (new_value + add_len, orig_value); } } else { new_value = xstrdup (add); } return new_value; } int lt_split_name_value (const char *arg, char** name, char** value) { const char *p; int len; if (!arg || !*arg) return 1; p = strchr (arg, (int)'='); if (!p) return 1; *value = xstrdup (++p); len = strlen (arg) - strlen (*value); *name = XMALLOC (char, len); strncpy (*name, arg, len-1); (*name)[len - 1] = '\0'; return 0; } void lt_opt_process_env_set (const char *arg) { char *name = NULL; char *value = NULL; if (lt_split_name_value (arg, &name, &value) != 0) { XFREE (name); XFREE (value); lt_fatal ("bad argument for %s: '%s'", env_set_opt, arg); } lt_setenv (name, value); XFREE (name); XFREE (value); } void lt_opt_process_env_prepend (const char *arg) { char *name = NULL; char *value = NULL; char *new_value = NULL; if (lt_split_name_value (arg, &name, &value) != 0) { XFREE (name); XFREE (value); lt_fatal ("bad argument for %s: '%s'", env_prepend_opt, arg); } new_value = lt_extend_str (getenv (name), value, 0); lt_setenv (name, new_value); XFREE (new_value); XFREE (name); XFREE (value); } void lt_opt_process_env_append (const char *arg) { char *name = NULL; char *value = NULL; char *new_value = NULL; if (lt_split_name_value (arg, &name, &value) != 0) { XFREE (name); XFREE (value); lt_fatal ("bad argument for %s: '%s'", env_append_opt, arg); } new_value = lt_extend_str (getenv (name), value, 1); lt_setenv (name, new_value); XFREE (new_value); XFREE (name); XFREE (value); } void lt_update_exe_path (const char *name, const char *value) { LTWRAPPER_DEBUGPRINTF (("(lt_update_exe_path) modifying '%s' by prepending '%s'\n", (name ? name : ""), (value ? value : ""))); if (name && *name && value && *value) { char *new_value = lt_extend_str (getenv (name), value, 0); /* some systems can't cope with a ':'-terminated path #' */ int len = strlen (new_value); while (((len = strlen (new_value)) > 0) && IS_PATH_SEPARATOR (new_value[len-1])) { new_value[len-1] = '\0'; } lt_setenv (name, new_value); XFREE (new_value); } } void lt_update_lib_path (const char *name, const char *value) { LTWRAPPER_DEBUGPRINTF (("(lt_update_lib_path) modifying '%s' by prepending '%s'\n", (name ? name : ""), (value ? value : ""))); if (name && *name && value && *value) { char *new_value = lt_extend_str (getenv (name), value, 0); lt_setenv (name, new_value); XFREE (new_value); } } EOF } # end: func_emit_cwrapperexe_src # func_mode_link arg... func_mode_link () { $opt_debug case $host in *-*-cygwin* | *-*-mingw* | *-*-pw32* | *-*-os2* | *-cegcc*) # It is impossible to link a dll without this setting, and # we shouldn't force the makefile maintainer to figure out # which system we are compiling for in order to pass an extra # flag for every libtool invocation. # allow_undefined=no # FIXME: Unfortunately, there are problems with the above when trying # to make a dll which has undefined symbols, in which case not # even a static library is built. For now, we need to specify # -no-undefined on the libtool link line when we can be certain # that all symbols are satisfied, otherwise we get a static library. allow_undefined=yes ;; *) allow_undefined=yes ;; esac libtool_args=$nonopt base_compile="$nonopt $@" compile_command=$nonopt finalize_command=$nonopt compile_rpath= finalize_rpath= compile_shlibpath= finalize_shlibpath= convenience= old_convenience= deplibs= old_deplibs= compiler_flags= linker_flags= dllsearchpath= lib_search_path=`pwd` inst_prefix_dir= new_inherited_linker_flags= avoid_version=no dlfiles= dlprefiles= dlself=no export_dynamic=no export_symbols= export_symbols_regex= generated= libobjs= ltlibs= module=no no_install=no objs= non_pic_objects= precious_files_regex= prefer_static_libs=no preload=no prev= prevarg= release= rpath= xrpath= perm_rpath= temp_rpath= thread_safe=no vinfo= vinfo_number=no weak_libs= single_module="${wl}-single_module" func_infer_tag $base_compile # We need to know -static, to get the right output filenames. for arg do case $arg in -shared) test "$build_libtool_libs" != yes && \ func_fatal_configuration "can not build a shared library" build_old_libs=no break ;; -all-static | -static | -static-libtool-libs) case $arg in -all-static) if test "$build_libtool_libs" = yes && test -z "$link_static_flag"; then func_warning "complete static linking is impossible in this configuration" fi if test -n "$link_static_flag"; then dlopen_self=$dlopen_self_static fi prefer_static_libs=yes ;; -static) if test -z "$pic_flag" && test -n "$link_static_flag"; then dlopen_self=$dlopen_self_static fi prefer_static_libs=built ;; -static-libtool-libs) if test -z "$pic_flag" && test -n "$link_static_flag"; then dlopen_self=$dlopen_self_static fi prefer_static_libs=yes ;; esac build_libtool_libs=no build_old_libs=yes break ;; esac done # See if our shared archives depend on static archives. test -n "$old_archive_from_new_cmds" && build_old_libs=yes # Go through the arguments, transforming them on the way. while test "$#" -gt 0; do arg="$1" shift func_quote_for_eval "$arg" qarg=$func_quote_for_eval_unquoted_result func_append libtool_args " $func_quote_for_eval_result" # If the previous option needs an argument, assign it. if test -n "$prev"; then case $prev in output) func_append compile_command " @OUTPUT@" func_append finalize_command " @OUTPUT@" ;; esac case $prev in dlfiles|dlprefiles) if test "$preload" = no; then # Add the symbol object into the linking commands. func_append compile_command " @SYMFILE@" func_append finalize_command " @SYMFILE@" preload=yes fi case $arg in *.la | *.lo) ;; # We handle these cases below. force) if test "$dlself" = no; then dlself=needless export_dynamic=yes fi prev= continue ;; self) if test "$prev" = dlprefiles; then dlself=yes elif test "$prev" = dlfiles && test "$dlopen_self" != yes; then dlself=yes else dlself=needless export_dynamic=yes fi prev= continue ;; *) if test "$prev" = dlfiles; then dlfiles="$dlfiles $arg" else dlprefiles="$dlprefiles $arg" fi prev= continue ;; esac ;; expsyms) export_symbols="$arg" test -f "$arg" \ || func_fatal_error "symbol file \`$arg' does not exist" prev= continue ;; expsyms_regex) export_symbols_regex="$arg" prev= continue ;; framework) case $host in *-*-darwin*) case "$deplibs " in *" $qarg.ltframework "*) ;; *) deplibs="$deplibs $qarg.ltframework" # this is fixed later ;; esac ;; esac prev= continue ;; inst_prefix) inst_prefix_dir="$arg" prev= continue ;; objectlist) if test -f "$arg"; then save_arg=$arg moreargs= for fil in `cat "$save_arg"` do # moreargs="$moreargs $fil" arg=$fil # A libtool-controlled object. # Check to see that this really is a libtool object. if func_lalib_unsafe_p "$arg"; then pic_object= non_pic_object= # Read the .lo file func_source "$arg" if test -z "$pic_object" || test -z "$non_pic_object" || test "$pic_object" = none && test "$non_pic_object" = none; then func_fatal_error "cannot find name of object for \`$arg'" fi # Extract subdirectory from the argument. func_dirname "$arg" "/" "" xdir="$func_dirname_result" if test "$pic_object" != none; then # Prepend the subdirectory the object is found in. pic_object="$xdir$pic_object" if test "$prev" = dlfiles; then if test "$build_libtool_libs" = yes && test "$dlopen_support" = yes; then dlfiles="$dlfiles $pic_object" prev= continue else # If libtool objects are unsupported, then we need to preload. prev=dlprefiles fi fi # CHECK ME: I think I busted this. -Ossama if test "$prev" = dlprefiles; then # Preload the old-style object. dlprefiles="$dlprefiles $pic_object" prev= fi # A PIC object. func_append libobjs " $pic_object" arg="$pic_object" fi # Non-PIC object. if test "$non_pic_object" != none; then # Prepend the subdirectory the object is found in. non_pic_object="$xdir$non_pic_object" # A standard non-PIC object func_append non_pic_objects " $non_pic_object" if test -z "$pic_object" || test "$pic_object" = none ; then arg="$non_pic_object" fi else # If the PIC object exists, use it instead. # $xdir was prepended to $pic_object above. non_pic_object="$pic_object" func_append non_pic_objects " $non_pic_object" fi else # Only an error if not doing a dry-run. if $opt_dry_run; then # Extract subdirectory from the argument. func_dirname "$arg" "/" "" xdir="$func_dirname_result" func_lo2o "$arg" pic_object=$xdir$objdir/$func_lo2o_result non_pic_object=$xdir$func_lo2o_result func_append libobjs " $pic_object" func_append non_pic_objects " $non_pic_object" else func_fatal_error "\`$arg' is not a valid libtool object" fi fi done else func_fatal_error "link input file \`$arg' does not exist" fi arg=$save_arg prev= continue ;; precious_regex) precious_files_regex="$arg" prev= continue ;; release) release="-$arg" prev= continue ;; rpath | xrpath) # We need an absolute path. case $arg in [\\/]* | [A-Za-z]:[\\/]*) ;; *) func_fatal_error "only absolute run-paths are allowed" ;; esac if test "$prev" = rpath; then case "$rpath " in *" $arg "*) ;; *) rpath="$rpath $arg" ;; esac else case "$xrpath " in *" $arg "*) ;; *) xrpath="$xrpath $arg" ;; esac fi prev= continue ;; shrext) shrext_cmds="$arg" prev= continue ;; weak) weak_libs="$weak_libs $arg" prev= continue ;; xcclinker) linker_flags="$linker_flags $qarg" compiler_flags="$compiler_flags $qarg" prev= func_append compile_command " $qarg" func_append finalize_command " $qarg" continue ;; xcompiler) compiler_flags="$compiler_flags $qarg" prev= func_append compile_command " $qarg" func_append finalize_command " $qarg" continue ;; xlinker) linker_flags="$linker_flags $qarg" compiler_flags="$compiler_flags $wl$qarg" prev= func_append compile_command " $wl$qarg" func_append finalize_command " $wl$qarg" continue ;; *) eval "$prev=\"\$arg\"" prev= continue ;; esac fi # test -n "$prev" prevarg="$arg" case $arg in -all-static) if test -n "$link_static_flag"; then # See comment for -static flag below, for more details. func_append compile_command " $link_static_flag" func_append finalize_command " $link_static_flag" fi continue ;; -allow-undefined) # FIXME: remove this flag sometime in the future. func_fatal_error "\`-allow-undefined' must not be used because it is the default" ;; -avoid-version) avoid_version=yes continue ;; -dlopen) prev=dlfiles continue ;; -dlpreopen) prev=dlprefiles continue ;; -export-dynamic) export_dynamic=yes continue ;; -export-symbols | -export-symbols-regex) if test -n "$export_symbols" || test -n "$export_symbols_regex"; then func_fatal_error "more than one -exported-symbols argument is not allowed" fi if test "X$arg" = "X-export-symbols"; then prev=expsyms else prev=expsyms_regex fi continue ;; -framework) prev=framework continue ;; -inst-prefix-dir) prev=inst_prefix continue ;; # The native IRIX linker understands -LANG:*, -LIST:* and -LNO:* # so, if we see these flags be careful not to treat them like -L -L[A-Z][A-Z]*:*) case $with_gcc/$host in no/*-*-irix* | /*-*-irix*) func_append compile_command " $arg" func_append finalize_command " $arg" ;; esac continue ;; -L*) func_stripname '-L' '' "$arg" dir=$func_stripname_result if test -z "$dir"; then if test "$#" -gt 0; then func_fatal_error "require no space between \`-L' and \`$1'" else func_fatal_error "need path for \`-L' option" fi fi # We need an absolute path. case $dir in [\\/]* | [A-Za-z]:[\\/]*) ;; *) absdir=`cd "$dir" && pwd` test -z "$absdir" && \ func_fatal_error "cannot determine absolute directory name of \`$dir'" dir="$absdir" ;; esac case "$deplibs " in *" -L$dir "*) ;; *) deplibs="$deplibs -L$dir" lib_search_path="$lib_search_path $dir" ;; esac case $host in *-*-cygwin* | *-*-mingw* | *-*-pw32* | *-*-os2* | *-cegcc*) testbindir=`$ECHO "X$dir" | $Xsed -e 's*/lib$*/bin*'` case :$dllsearchpath: in *":$dir:"*) ;; ::) dllsearchpath=$dir;; *) dllsearchpath="$dllsearchpath:$dir";; esac case :$dllsearchpath: in *":$testbindir:"*) ;; ::) dllsearchpath=$testbindir;; *) dllsearchpath="$dllsearchpath:$testbindir";; esac ;; esac continue ;; -l*) if test "X$arg" = "X-lc" || test "X$arg" = "X-lm"; then case $host in *-*-cygwin* | *-*-mingw* | *-*-pw32* | *-*-beos* | *-cegcc*) # These systems don't actually have a C or math library (as such) continue ;; *-*-os2*) # These systems don't actually have a C library (as such) test "X$arg" = "X-lc" && continue ;; *-*-openbsd* | *-*-freebsd* | *-*-dragonfly*) # Do not include libc due to us having libc/libc_r. test "X$arg" = "X-lc" && continue ;; *-*-rhapsody* | *-*-darwin1.[012]) # Rhapsody C and math libraries are in the System framework deplibs="$deplibs System.ltframework" continue ;; *-*-sco3.2v5* | *-*-sco5v6*) # Causes problems with __ctype test "X$arg" = "X-lc" && continue ;; *-*-sysv4.2uw2* | *-*-sysv5* | *-*-unixware* | *-*-OpenUNIX*) # Compiler inserts libc in the correct place for threads to work test "X$arg" = "X-lc" && continue ;; esac elif test "X$arg" = "X-lc_r"; then case $host in *-*-openbsd* | *-*-freebsd* | *-*-dragonfly*) # Do not include libc_r directly, use -pthread flag. continue ;; esac fi deplibs="$deplibs $arg" continue ;; -module) module=yes continue ;; # Tru64 UNIX uses -model [arg] to determine the layout of C++ # classes, name mangling, and exception handling. # Darwin uses the -arch flag to determine output architecture. -model|-arch|-isysroot) compiler_flags="$compiler_flags $arg" func_append compile_command " $arg" func_append finalize_command " $arg" prev=xcompiler continue ;; -mt|-mthreads|-kthread|-Kthread|-pthread|-pthreads|--thread-safe|-threads) compiler_flags="$compiler_flags $arg" func_append compile_command " $arg" func_append finalize_command " $arg" case "$new_inherited_linker_flags " in *" $arg "*) ;; * ) new_inherited_linker_flags="$new_inherited_linker_flags $arg" ;; esac continue ;; -multi_module) single_module="${wl}-multi_module" continue ;; -no-fast-install) fast_install=no continue ;; -no-install) case $host in *-*-cygwin* | *-*-mingw* | *-*-pw32* | *-*-os2* | *-*-darwin* | *-cegcc*) # The PATH hackery in wrapper scripts is required on Windows # and Darwin in order for the loader to find any dlls it needs. func_warning "\`-no-install' is ignored for $host" func_warning "assuming \`-no-fast-install' instead" fast_install=no ;; *) no_install=yes ;; esac continue ;; -no-undefined) allow_undefined=no continue ;; -objectlist) prev=objectlist continue ;; -o) prev=output ;; -precious-files-regex) prev=precious_regex continue ;; -release) prev=release continue ;; -rpath) prev=rpath continue ;; -R) prev=xrpath continue ;; -R*) func_stripname '-R' '' "$arg" dir=$func_stripname_result # We need an absolute path. case $dir in [\\/]* | [A-Za-z]:[\\/]*) ;; *) func_fatal_error "only absolute run-paths are allowed" ;; esac case "$xrpath " in *" $dir "*) ;; *) xrpath="$xrpath $dir" ;; esac continue ;; -shared) # The effects of -shared are defined in a previous loop. continue ;; -shrext) prev=shrext continue ;; -static | -static-libtool-libs) # The effects of -static are defined in a previous loop. # We used to do the same as -all-static on platforms that # didn't have a PIC flag, but the assumption that the effects # would be equivalent was wrong. It would break on at least # Digital Unix and AIX. continue ;; -thread-safe) thread_safe=yes continue ;; -version-info) prev=vinfo continue ;; -version-number) prev=vinfo vinfo_number=yes continue ;; -weak) prev=weak continue ;; -Wc,*) func_stripname '-Wc,' '' "$arg" args=$func_stripname_result arg= save_ifs="$IFS"; IFS=',' for flag in $args; do IFS="$save_ifs" func_quote_for_eval "$flag" arg="$arg $wl$func_quote_for_eval_result" compiler_flags="$compiler_flags $func_quote_for_eval_result" done IFS="$save_ifs" func_stripname ' ' '' "$arg" arg=$func_stripname_result ;; -Wl,*) func_stripname '-Wl,' '' "$arg" args=$func_stripname_result arg= save_ifs="$IFS"; IFS=',' for flag in $args; do IFS="$save_ifs" func_quote_for_eval "$flag" arg="$arg $wl$func_quote_for_eval_result" compiler_flags="$compiler_flags $wl$func_quote_for_eval_result" linker_flags="$linker_flags $func_quote_for_eval_result" done IFS="$save_ifs" func_stripname ' ' '' "$arg" arg=$func_stripname_result ;; -Xcompiler) prev=xcompiler continue ;; -Xlinker) prev=xlinker continue ;; -XCClinker) prev=xcclinker continue ;; # -msg_* for osf cc -msg_*) func_quote_for_eval "$arg" arg="$func_quote_for_eval_result" ;; # -64, -mips[0-9] enable 64-bit mode on the SGI compiler # -r[0-9][0-9]* specifies the processor on the SGI compiler # -xarch=*, -xtarget=* enable 64-bit mode on the Sun compiler # +DA*, +DD* enable 64-bit mode on the HP compiler # -q* pass through compiler args for the IBM compiler # -m*, -t[45]*, -txscale* pass through architecture-specific # compiler args for GCC # -F/path gives path to uninstalled frameworks, gcc on darwin # -p, -pg, --coverage, -fprofile-* pass through profiling flag for GCC # @file GCC response files -64|-mips[0-9]|-r[0-9][0-9]*|-xarch=*|-xtarget=*|+DA*|+DD*|-q*|-m*| \ -t[45]*|-txscale*|-p|-pg|--coverage|-fprofile-*|-F*|@*) func_quote_for_eval "$arg" arg="$func_quote_for_eval_result" func_append compile_command " $arg" func_append finalize_command " $arg" compiler_flags="$compiler_flags $arg" continue ;; # Some other compiler flag. -* | +*) func_quote_for_eval "$arg" arg="$func_quote_for_eval_result" ;; *.$objext) # A standard object. objs="$objs $arg" ;; *.lo) # A libtool-controlled object. # Check to see that this really is a libtool object. if func_lalib_unsafe_p "$arg"; then pic_object= non_pic_object= # Read the .lo file func_source "$arg" if test -z "$pic_object" || test -z "$non_pic_object" || test "$pic_object" = none && test "$non_pic_object" = none; then func_fatal_error "cannot find name of object for \`$arg'" fi # Extract subdirectory from the argument. func_dirname "$arg" "/" "" xdir="$func_dirname_result" if test "$pic_object" != none; then # Prepend the subdirectory the object is found in. pic_object="$xdir$pic_object" if test "$prev" = dlfiles; then if test "$build_libtool_libs" = yes && test "$dlopen_support" = yes; then dlfiles="$dlfiles $pic_object" prev= continue else # If libtool objects are unsupported, then we need to preload. prev=dlprefiles fi fi # CHECK ME: I think I busted this. -Ossama if test "$prev" = dlprefiles; then # Preload the old-style object. dlprefiles="$dlprefiles $pic_object" prev= fi # A PIC object. func_append libobjs " $pic_object" arg="$pic_object" fi # Non-PIC object. if test "$non_pic_object" != none; then # Prepend the subdirectory the object is found in. non_pic_object="$xdir$non_pic_object" # A standard non-PIC object func_append non_pic_objects " $non_pic_object" if test -z "$pic_object" || test "$pic_object" = none ; then arg="$non_pic_object" fi else # If the PIC object exists, use it instead. # $xdir was prepended to $pic_object above. non_pic_object="$pic_object" func_append non_pic_objects " $non_pic_object" fi else # Only an error if not doing a dry-run. if $opt_dry_run; then # Extract subdirectory from the argument. func_dirname "$arg" "/" "" xdir="$func_dirname_result" func_lo2o "$arg" pic_object=$xdir$objdir/$func_lo2o_result non_pic_object=$xdir$func_lo2o_result func_append libobjs " $pic_object" func_append non_pic_objects " $non_pic_object" else func_fatal_error "\`$arg' is not a valid libtool object" fi fi ;; *.$libext) # An archive. deplibs="$deplibs $arg" old_deplibs="$old_deplibs $arg" continue ;; *.la) # A libtool-controlled library. if test "$prev" = dlfiles; then # This library was specified with -dlopen. dlfiles="$dlfiles $arg" prev= elif test "$prev" = dlprefiles; then # The library was specified with -dlpreopen. dlprefiles="$dlprefiles $arg" prev= else deplibs="$deplibs $arg" fi continue ;; # Some other compiler argument. *) # Unknown arguments in both finalize_command and compile_command need # to be aesthetically quoted because they are evaled later. func_quote_for_eval "$arg" arg="$func_quote_for_eval_result" ;; esac # arg # Now actually substitute the argument into the commands. if test -n "$arg"; then func_append compile_command " $arg" func_append finalize_command " $arg" fi done # argument parsing loop test -n "$prev" && \ func_fatal_help "the \`$prevarg' option requires an argument" if test "$export_dynamic" = yes && test -n "$export_dynamic_flag_spec"; then eval arg=\"$export_dynamic_flag_spec\" func_append compile_command " $arg" func_append finalize_command " $arg" fi oldlibs= # calculate the name of the file, without its directory func_basename "$output" outputname="$func_basename_result" libobjs_save="$libobjs" if test -n "$shlibpath_var"; then # get the directories listed in $shlibpath_var eval shlib_search_path=\`\$ECHO \"X\${$shlibpath_var}\" \| \$Xsed -e \'s/:/ /g\'\` else shlib_search_path= fi eval sys_lib_search_path=\"$sys_lib_search_path_spec\" eval sys_lib_dlsearch_path=\"$sys_lib_dlsearch_path_spec\" func_dirname "$output" "/" "" output_objdir="$func_dirname_result$objdir" # Create the object directory. func_mkdir_p "$output_objdir" # Determine the type of output case $output in "") func_fatal_help "you must specify an output file" ;; *.$libext) linkmode=oldlib ;; *.lo | *.$objext) linkmode=obj ;; *.la) linkmode=lib ;; *) linkmode=prog ;; # Anything else should be a program. esac specialdeplibs= libs= # Find all interdependent deplibs by searching for libraries # that are linked more than once (e.g. -la -lb -la) for deplib in $deplibs; do if $opt_duplicate_deps ; then case "$libs " in *" $deplib "*) specialdeplibs="$specialdeplibs $deplib" ;; esac fi libs="$libs $deplib" done if test "$linkmode" = lib; then libs="$predeps $libs $compiler_lib_search_path $postdeps" # Compute libraries that are listed more than once in $predeps # $postdeps and mark them as special (i.e., whose duplicates are # not to be eliminated). pre_post_deps= if $opt_duplicate_compiler_generated_deps; then for pre_post_dep in $predeps $postdeps; do case "$pre_post_deps " in *" $pre_post_dep "*) specialdeplibs="$specialdeplibs $pre_post_deps" ;; esac pre_post_deps="$pre_post_deps $pre_post_dep" done fi pre_post_deps= fi deplibs= newdependency_libs= newlib_search_path= need_relink=no # whether we're linking any uninstalled libtool libraries notinst_deplibs= # not-installed libtool libraries notinst_path= # paths that contain not-installed libtool libraries case $linkmode in lib) passes="conv dlpreopen link" for file in $dlfiles $dlprefiles; do case $file in *.la) ;; *) func_fatal_help "libraries can \`-dlopen' only libtool libraries: $file" ;; esac done ;; prog) compile_deplibs= finalize_deplibs= alldeplibs=no newdlfiles= newdlprefiles= passes="conv scan dlopen dlpreopen link" ;; *) passes="conv" ;; esac for pass in $passes; do # The preopen pass in lib mode reverses $deplibs; put it back here # so that -L comes before libs that need it for instance... if test "$linkmode,$pass" = "lib,link"; then ## FIXME: Find the place where the list is rebuilt in the wrong ## order, and fix it there properly tmp_deplibs= for deplib in $deplibs; do tmp_deplibs="$deplib $tmp_deplibs" done deplibs="$tmp_deplibs" fi if test "$linkmode,$pass" = "lib,link" || test "$linkmode,$pass" = "prog,scan"; then libs="$deplibs" deplibs= fi if test "$linkmode" = prog; then case $pass in dlopen) libs="$dlfiles" ;; dlpreopen) libs="$dlprefiles" ;; link) libs="$deplibs %DEPLIBS%" test "X$link_all_deplibs" != Xno && libs="$libs $dependency_libs" ;; esac fi if test "$linkmode,$pass" = "lib,dlpreopen"; then # Collect and forward deplibs of preopened libtool libs for lib in $dlprefiles; do # Ignore non-libtool-libs dependency_libs= case $lib in *.la) func_source "$lib" ;; esac # Collect preopened libtool deplibs, except any this library # has declared as weak libs for deplib in $dependency_libs; do deplib_base=`$ECHO "X$deplib" | $Xsed -e "$basename"` case " $weak_libs " in *" $deplib_base "*) ;; *) deplibs="$deplibs $deplib" ;; esac done done libs="$dlprefiles" fi if test "$pass" = dlopen; then # Collect dlpreopened libraries save_deplibs="$deplibs" deplibs= fi for deplib in $libs; do lib= found=no case $deplib in -mt|-mthreads|-kthread|-Kthread|-pthread|-pthreads|--thread-safe|-threads) if test "$linkmode,$pass" = "prog,link"; then compile_deplibs="$deplib $compile_deplibs" finalize_deplibs="$deplib $finalize_deplibs" else compiler_flags="$compiler_flags $deplib" if test "$linkmode" = lib ; then case "$new_inherited_linker_flags " in *" $deplib "*) ;; * ) new_inherited_linker_flags="$new_inherited_linker_flags $deplib" ;; esac fi fi continue ;; -l*) if test "$linkmode" != lib && test "$linkmode" != prog; then func_warning "\`-l' is ignored for archives/objects" continue fi func_stripname '-l' '' "$deplib" name=$func_stripname_result if test "$linkmode" = lib; then searchdirs="$newlib_search_path $lib_search_path $compiler_lib_search_dirs $sys_lib_search_path $shlib_search_path" else searchdirs="$newlib_search_path $lib_search_path $sys_lib_search_path $shlib_search_path" fi for searchdir in $searchdirs; do for search_ext in .la $std_shrext .so .a; do # Search the libtool library lib="$searchdir/lib${name}${search_ext}" if test -f "$lib"; then if test "$search_ext" = ".la"; then found=yes else found=no fi break 2 fi done done if test "$found" != yes; then # deplib doesn't seem to be a libtool library if test "$linkmode,$pass" = "prog,link"; then compile_deplibs="$deplib $compile_deplibs" finalize_deplibs="$deplib $finalize_deplibs" else deplibs="$deplib $deplibs" test "$linkmode" = lib && newdependency_libs="$deplib $newdependency_libs" fi continue else # deplib is a libtool library # If $allow_libtool_libs_with_static_runtimes && $deplib is a stdlib, # We need to do some special things here, and not later. if test "X$allow_libtool_libs_with_static_runtimes" = "Xyes" ; then case " $predeps $postdeps " in *" $deplib "*) if func_lalib_p "$lib"; then library_names= old_library= func_source "$lib" for l in $old_library $library_names; do ll="$l" done if test "X$ll" = "X$old_library" ; then # only static version available found=no func_dirname "$lib" "" "." ladir="$func_dirname_result" lib=$ladir/$old_library if test "$linkmode,$pass" = "prog,link"; then compile_deplibs="$deplib $compile_deplibs" finalize_deplibs="$deplib $finalize_deplibs" else deplibs="$deplib $deplibs" test "$linkmode" = lib && newdependency_libs="$deplib $newdependency_libs" fi continue fi fi ;; *) ;; esac fi fi ;; # -l *.ltframework) if test "$linkmode,$pass" = "prog,link"; then compile_deplibs="$deplib $compile_deplibs" finalize_deplibs="$deplib $finalize_deplibs" else deplibs="$deplib $deplibs" if test "$linkmode" = lib ; then case "$new_inherited_linker_flags " in *" $deplib "*) ;; * ) new_inherited_linker_flags="$new_inherited_linker_flags $deplib" ;; esac fi fi continue ;; -L*) case $linkmode in lib) deplibs="$deplib $deplibs" test "$pass" = conv && continue newdependency_libs="$deplib $newdependency_libs" func_stripname '-L' '' "$deplib" newlib_search_path="$newlib_search_path $func_stripname_result" ;; prog) if test "$pass" = conv; then deplibs="$deplib $deplibs" continue fi if test "$pass" = scan; then deplibs="$deplib $deplibs" else compile_deplibs="$deplib $compile_deplibs" finalize_deplibs="$deplib $finalize_deplibs" fi func_stripname '-L' '' "$deplib" newlib_search_path="$newlib_search_path $func_stripname_result" ;; *) func_warning "\`-L' is ignored for archives/objects" ;; esac # linkmode continue ;; # -L -R*) if test "$pass" = link; then func_stripname '-R' '' "$deplib" dir=$func_stripname_result # Make sure the xrpath contains only unique directories. case "$xrpath " in *" $dir "*) ;; *) xrpath="$xrpath $dir" ;; esac fi deplibs="$deplib $deplibs" continue ;; *.la) lib="$deplib" ;; *.$libext) if test "$pass" = conv; then deplibs="$deplib $deplibs" continue fi case $linkmode in lib) # Linking convenience modules into shared libraries is allowed, # but linking other static libraries is non-portable. case " $dlpreconveniencelibs " in *" $deplib "*) ;; *) valid_a_lib=no case $deplibs_check_method in match_pattern*) set dummy $deplibs_check_method; shift match_pattern_regex=`expr "$deplibs_check_method" : "$1 \(.*\)"` if eval "\$ECHO \"X$deplib\"" 2>/dev/null | $Xsed -e 10q \ | $EGREP "$match_pattern_regex" > /dev/null; then valid_a_lib=yes fi ;; pass_all) valid_a_lib=yes ;; esac if test "$valid_a_lib" != yes; then $ECHO $ECHO "*** Warning: Trying to link with static lib archive $deplib." $ECHO "*** I have the capability to make that library automatically link in when" $ECHO "*** you link to this library. But I can only do this if you have a" $ECHO "*** shared version of the library, which you do not appear to have" $ECHO "*** because the file extensions .$libext of this argument makes me believe" $ECHO "*** that it is just a static archive that I should not use here." else $ECHO $ECHO "*** Warning: Linking the shared library $output against the" $ECHO "*** static library $deplib is not portable!" deplibs="$deplib $deplibs" fi ;; esac continue ;; prog) if test "$pass" != link; then deplibs="$deplib $deplibs" else compile_deplibs="$deplib $compile_deplibs" finalize_deplibs="$deplib $finalize_deplibs" fi continue ;; esac # linkmode ;; # *.$libext *.lo | *.$objext) if test "$pass" = conv; then deplibs="$deplib $deplibs" elif test "$linkmode" = prog; then if test "$pass" = dlpreopen || test "$dlopen_support" != yes || test "$build_libtool_libs" = no; then # If there is no dlopen support or we're linking statically, # we need to preload. newdlprefiles="$newdlprefiles $deplib" compile_deplibs="$deplib $compile_deplibs" finalize_deplibs="$deplib $finalize_deplibs" else newdlfiles="$newdlfiles $deplib" fi fi continue ;; %DEPLIBS%) alldeplibs=yes continue ;; esac # case $deplib if test "$found" = yes || test -f "$lib"; then : else func_fatal_error "cannot find the library \`$lib' or unhandled argument \`$deplib'" fi # Check to see that this really is a libtool archive. func_lalib_unsafe_p "$lib" \ || func_fatal_error "\`$lib' is not a valid libtool archive" func_dirname "$lib" "" "." ladir="$func_dirname_result" dlname= dlopen= dlpreopen= libdir= library_names= old_library= inherited_linker_flags= # If the library was installed with an old release of libtool, # it will not redefine variables installed, or shouldnotlink installed=yes shouldnotlink=no avoidtemprpath= # Read the .la file func_source "$lib" # Convert "-framework foo" to "foo.ltframework" if test -n "$inherited_linker_flags"; then tmp_inherited_linker_flags=`$ECHO "X$inherited_linker_flags" | $Xsed -e 's/-framework \([^ $]*\)/\1.ltframework/g'` for tmp_inherited_linker_flag in $tmp_inherited_linker_flags; do case " $new_inherited_linker_flags " in *" $tmp_inherited_linker_flag "*) ;; *) new_inherited_linker_flags="$new_inherited_linker_flags $tmp_inherited_linker_flag";; esac done fi dependency_libs=`$ECHO "X $dependency_libs" | $Xsed -e 's% \([^ $]*\).ltframework% -framework \1%g'` if test "$linkmode,$pass" = "lib,link" || test "$linkmode,$pass" = "prog,scan" || { test "$linkmode" != prog && test "$linkmode" != lib; }; then test -n "$dlopen" && dlfiles="$dlfiles $dlopen" test -n "$dlpreopen" && dlprefiles="$dlprefiles $dlpreopen" fi if test "$pass" = conv; then # Only check for convenience libraries deplibs="$lib $deplibs" if test -z "$libdir"; then if test -z "$old_library"; then func_fatal_error "cannot find name of link library for \`$lib'" fi # It is a libtool convenience library, so add in its objects. convenience="$convenience $ladir/$objdir/$old_library" old_convenience="$old_convenience $ladir/$objdir/$old_library" tmp_libs= for deplib in $dependency_libs; do deplibs="$deplib $deplibs" if $opt_duplicate_deps ; then case "$tmp_libs " in *" $deplib "*) specialdeplibs="$specialdeplibs $deplib" ;; esac fi tmp_libs="$tmp_libs $deplib" done elif test "$linkmode" != prog && test "$linkmode" != lib; then func_fatal_error "\`$lib' is not a convenience library" fi continue fi # $pass = conv # Get the name of the library we link against. linklib= for l in $old_library $library_names; do linklib="$l" done if test -z "$linklib"; then func_fatal_error "cannot find name of link library for \`$lib'" fi # This library was specified with -dlopen. if test "$pass" = dlopen; then if test -z "$libdir"; then func_fatal_error "cannot -dlopen a convenience library: \`$lib'" fi if test -z "$dlname" || test "$dlopen_support" != yes || test "$build_libtool_libs" = no; then # If there is no dlname, no dlopen support or we're linking # statically, we need to preload. We also need to preload any # dependent libraries so libltdl's deplib preloader doesn't # bomb out in the load deplibs phase. dlprefiles="$dlprefiles $lib $dependency_libs" else newdlfiles="$newdlfiles $lib" fi continue fi # $pass = dlopen # We need an absolute path. case $ladir in [\\/]* | [A-Za-z]:[\\/]*) abs_ladir="$ladir" ;; *) abs_ladir=`cd "$ladir" && pwd` if test -z "$abs_ladir"; then func_warning "cannot determine absolute directory name of \`$ladir'" func_warning "passing it literally to the linker, although it might fail" abs_ladir="$ladir" fi ;; esac func_basename "$lib" laname="$func_basename_result" # Find the relevant object directory and library name. if test "X$installed" = Xyes; then if test ! -f "$libdir/$linklib" && test -f "$abs_ladir/$linklib"; then func_warning "library \`$lib' was moved." dir="$ladir" absdir="$abs_ladir" libdir="$abs_ladir" else dir="$libdir" absdir="$libdir" fi test "X$hardcode_automatic" = Xyes && avoidtemprpath=yes else if test ! -f "$ladir/$objdir/$linklib" && test -f "$abs_ladir/$linklib"; then dir="$ladir" absdir="$abs_ladir" # Remove this search path later notinst_path="$notinst_path $abs_ladir" else dir="$ladir/$objdir" absdir="$abs_ladir/$objdir" # Remove this search path later notinst_path="$notinst_path $abs_ladir" fi fi # $installed = yes func_stripname 'lib' '.la' "$laname" name=$func_stripname_result # This library was specified with -dlpreopen. if test "$pass" = dlpreopen; then if test -z "$libdir" && test "$linkmode" = prog; then func_fatal_error "only libraries may -dlpreopen a convenience library: \`$lib'" fi # Prefer using a static library (so that no silly _DYNAMIC symbols # are required to link). if test -n "$old_library"; then newdlprefiles="$newdlprefiles $dir/$old_library" # Keep a list of preopened convenience libraries to check # that they are being used correctly in the link pass. test -z "$libdir" && \ dlpreconveniencelibs="$dlpreconveniencelibs $dir/$old_library" # Otherwise, use the dlname, so that lt_dlopen finds it. elif test -n "$dlname"; then newdlprefiles="$newdlprefiles $dir/$dlname" else newdlprefiles="$newdlprefiles $dir/$linklib" fi fi # $pass = dlpreopen if test -z "$libdir"; then # Link the convenience library if test "$linkmode" = lib; then deplibs="$dir/$old_library $deplibs" elif test "$linkmode,$pass" = "prog,link"; then compile_deplibs="$dir/$old_library $compile_deplibs" finalize_deplibs="$dir/$old_library $finalize_deplibs" else deplibs="$lib $deplibs" # used for prog,scan pass fi continue fi if test "$linkmode" = prog && test "$pass" != link; then newlib_search_path="$newlib_search_path $ladir" deplibs="$lib $deplibs" linkalldeplibs=no if test "$link_all_deplibs" != no || test -z "$library_names" || test "$build_libtool_libs" = no; then linkalldeplibs=yes fi tmp_libs= for deplib in $dependency_libs; do case $deplib in -L*) func_stripname '-L' '' "$deplib" newlib_search_path="$newlib_search_path $func_stripname_result" ;; esac # Need to link against all dependency_libs? if test "$linkalldeplibs" = yes; then deplibs="$deplib $deplibs" else # Need to hardcode shared library paths # or/and link against static libraries newdependency_libs="$deplib $newdependency_libs" fi if $opt_duplicate_deps ; then case "$tmp_libs " in *" $deplib "*) specialdeplibs="$specialdeplibs $deplib" ;; esac fi tmp_libs="$tmp_libs $deplib" done # for deplib continue fi # $linkmode = prog... if test "$linkmode,$pass" = "prog,link"; then if test -n "$library_names" && { { test "$prefer_static_libs" = no || test "$prefer_static_libs,$installed" = "built,yes"; } || test -z "$old_library"; }; then # We need to hardcode the library path if test -n "$shlibpath_var" && test -z "$avoidtemprpath" ; then # Make sure the rpath contains only unique directories. case "$temp_rpath:" in *"$absdir:"*) ;; *) temp_rpath="$temp_rpath$absdir:" ;; esac fi # Hardcode the library path. # Skip directories that are in the system default run-time # search path. case " $sys_lib_dlsearch_path " in *" $absdir "*) ;; *) case "$compile_rpath " in *" $absdir "*) ;; *) compile_rpath="$compile_rpath $absdir" esac ;; esac case " $sys_lib_dlsearch_path " in *" $libdir "*) ;; *) case "$finalize_rpath " in *" $libdir "*) ;; *) finalize_rpath="$finalize_rpath $libdir" esac ;; esac fi # $linkmode,$pass = prog,link... if test "$alldeplibs" = yes && { test "$deplibs_check_method" = pass_all || { test "$build_libtool_libs" = yes && test -n "$library_names"; }; }; then # We only need to search for static libraries continue fi fi link_static=no # Whether the deplib will be linked statically use_static_libs=$prefer_static_libs if test "$use_static_libs" = built && test "$installed" = yes; then use_static_libs=no fi if test -n "$library_names" && { test "$use_static_libs" = no || test -z "$old_library"; }; then case $host in *cygwin* | *mingw* | *cegcc*) # No point in relinking DLLs because paths are not encoded notinst_deplibs="$notinst_deplibs $lib" need_relink=no ;; *) if test "$installed" = no; then notinst_deplibs="$notinst_deplibs $lib" need_relink=yes fi ;; esac # This is a shared library # Warn about portability, can't link against -module's on some # systems (darwin). Don't bleat about dlopened modules though! dlopenmodule="" for dlpremoduletest in $dlprefiles; do if test "X$dlpremoduletest" = "X$lib"; then dlopenmodule="$dlpremoduletest" break fi done if test -z "$dlopenmodule" && test "$shouldnotlink" = yes && test "$pass" = link; then $ECHO if test "$linkmode" = prog; then $ECHO "*** Warning: Linking the executable $output against the loadable module" else $ECHO "*** Warning: Linking the shared library $output against the loadable module" fi $ECHO "*** $linklib is not portable!" fi if test "$linkmode" = lib && test "$hardcode_into_libs" = yes; then # Hardcode the library path. # Skip directories that are in the system default run-time # search path. case " $sys_lib_dlsearch_path " in *" $absdir "*) ;; *) case "$compile_rpath " in *" $absdir "*) ;; *) compile_rpath="$compile_rpath $absdir" esac ;; esac case " $sys_lib_dlsearch_path " in *" $libdir "*) ;; *) case "$finalize_rpath " in *" $libdir "*) ;; *) finalize_rpath="$finalize_rpath $libdir" esac ;; esac fi if test -n "$old_archive_from_expsyms_cmds"; then # figure out the soname set dummy $library_names shift realname="$1" shift libname=`eval "\\$ECHO \"$libname_spec\""` # use dlname if we got it. it's perfectly good, no? if test -n "$dlname"; then soname="$dlname" elif test -n "$soname_spec"; then # bleh windows case $host in *cygwin* | mingw* | *cegcc*) func_arith $current - $age major=$func_arith_result versuffix="-$major" ;; esac eval soname=\"$soname_spec\" else soname="$realname" fi # Make a new name for the extract_expsyms_cmds to use soroot="$soname" func_basename "$soroot" soname="$func_basename_result" func_stripname 'lib' '.dll' "$soname" newlib=libimp-$func_stripname_result.a # If the library has no export list, then create one now if test -f "$output_objdir/$soname-def"; then : else func_verbose "extracting exported symbol list from \`$soname'" func_execute_cmds "$extract_expsyms_cmds" 'exit $?' fi # Create $newlib if test -f "$output_objdir/$newlib"; then :; else func_verbose "generating import library for \`$soname'" func_execute_cmds "$old_archive_from_expsyms_cmds" 'exit $?' fi # make sure the library variables are pointing to the new library dir=$output_objdir linklib=$newlib fi # test -n "$old_archive_from_expsyms_cmds" if test "$linkmode" = prog || test "$mode" != relink; then add_shlibpath= add_dir= add= lib_linked=yes case $hardcode_action in immediate | unsupported) if test "$hardcode_direct" = no; then add="$dir/$linklib" case $host in *-*-sco3.2v5.0.[024]*) add_dir="-L$dir" ;; *-*-sysv4*uw2*) add_dir="-L$dir" ;; *-*-sysv5OpenUNIX* | *-*-sysv5UnixWare7.[01].[10]* | \ *-*-unixware7*) add_dir="-L$dir" ;; *-*-darwin* ) # if the lib is a (non-dlopened) module then we can not # link against it, someone is ignoring the earlier warnings if /usr/bin/file -L $add 2> /dev/null | $GREP ": [^:]* bundle" >/dev/null ; then if test "X$dlopenmodule" != "X$lib"; then $ECHO "*** Warning: lib $linklib is a module, not a shared library" if test -z "$old_library" ; then $ECHO $ECHO "*** And there doesn't seem to be a static archive available" $ECHO "*** The link will probably fail, sorry" else add="$dir/$old_library" fi elif test -n "$old_library"; then add="$dir/$old_library" fi fi esac elif test "$hardcode_minus_L" = no; then case $host in *-*-sunos*) add_shlibpath="$dir" ;; esac add_dir="-L$dir" add="-l$name" elif test "$hardcode_shlibpath_var" = no; then add_shlibpath="$dir" add="-l$name" else lib_linked=no fi ;; relink) if test "$hardcode_direct" = yes && test "$hardcode_direct_absolute" = no; then add="$dir/$linklib" elif test "$hardcode_minus_L" = yes; then add_dir="-L$dir" # Try looking first in the location we're being installed to. if test -n "$inst_prefix_dir"; then case $libdir in [\\/]*) add_dir="$add_dir -L$inst_prefix_dir$libdir" ;; esac fi add="-l$name" elif test "$hardcode_shlibpath_var" = yes; then add_shlibpath="$dir" add="-l$name" else lib_linked=no fi ;; *) lib_linked=no ;; esac if test "$lib_linked" != yes; then func_fatal_configuration "unsupported hardcode properties" fi if test -n "$add_shlibpath"; then case :$compile_shlibpath: in *":$add_shlibpath:"*) ;; *) compile_shlibpath="$compile_shlibpath$add_shlibpath:" ;; esac fi if test "$linkmode" = prog; then test -n "$add_dir" && compile_deplibs="$add_dir $compile_deplibs" test -n "$add" && compile_deplibs="$add $compile_deplibs" else test -n "$add_dir" && deplibs="$add_dir $deplibs" test -n "$add" && deplibs="$add $deplibs" if test "$hardcode_direct" != yes && test "$hardcode_minus_L" != yes && test "$hardcode_shlibpath_var" = yes; then case :$finalize_shlibpath: in *":$libdir:"*) ;; *) finalize_shlibpath="$finalize_shlibpath$libdir:" ;; esac fi fi fi if test "$linkmode" = prog || test "$mode" = relink; then add_shlibpath= add_dir= add= # Finalize command for both is simple: just hardcode it. if test "$hardcode_direct" = yes && test "$hardcode_direct_absolute" = no; then add="$libdir/$linklib" elif test "$hardcode_minus_L" = yes; then add_dir="-L$libdir" add="-l$name" elif test "$hardcode_shlibpath_var" = yes; then case :$finalize_shlibpath: in *":$libdir:"*) ;; *) finalize_shlibpath="$finalize_shlibpath$libdir:" ;; esac add="-l$name" elif test "$hardcode_automatic" = yes; then if test -n "$inst_prefix_dir" && test -f "$inst_prefix_dir$libdir/$linklib" ; then add="$inst_prefix_dir$libdir/$linklib" else add="$libdir/$linklib" fi else # We cannot seem to hardcode it, guess we'll fake it. add_dir="-L$libdir" # Try looking first in the location we're being installed to. if test -n "$inst_prefix_dir"; then case $libdir in [\\/]*) add_dir="$add_dir -L$inst_prefix_dir$libdir" ;; esac fi add="-l$name" fi if test "$linkmode" = prog; then test -n "$add_dir" && finalize_deplibs="$add_dir $finalize_deplibs" test -n "$add" && finalize_deplibs="$add $finalize_deplibs" else test -n "$add_dir" && deplibs="$add_dir $deplibs" test -n "$add" && deplibs="$add $deplibs" fi fi elif test "$linkmode" = prog; then # Here we assume that one of hardcode_direct or hardcode_minus_L # is not unsupported. This is valid on all known static and # shared platforms. if test "$hardcode_direct" != unsupported; then test -n "$old_library" && linklib="$old_library" compile_deplibs="$dir/$linklib $compile_deplibs" finalize_deplibs="$dir/$linklib $finalize_deplibs" else compile_deplibs="-l$name -L$dir $compile_deplibs" finalize_deplibs="-l$name -L$dir $finalize_deplibs" fi elif test "$build_libtool_libs" = yes; then # Not a shared library if test "$deplibs_check_method" != pass_all; then # We're trying link a shared library against a static one # but the system doesn't support it. # Just print a warning and add the library to dependency_libs so # that the program can be linked against the static library. $ECHO $ECHO "*** Warning: This system can not link to static lib archive $lib." $ECHO "*** I have the capability to make that library automatically link in when" $ECHO "*** you link to this library. But I can only do this if you have a" $ECHO "*** shared version of the library, which you do not appear to have." if test "$module" = yes; then $ECHO "*** But as you try to build a module library, libtool will still create " $ECHO "*** a static module, that should work as long as the dlopening application" $ECHO "*** is linked with the -dlopen flag to resolve symbols at runtime." if test -z "$global_symbol_pipe"; then $ECHO $ECHO "*** However, this would only work if libtool was able to extract symbol" $ECHO "*** lists from a program, using \`nm' or equivalent, but libtool could" $ECHO "*** not find such a program. So, this module is probably useless." $ECHO "*** \`nm' from GNU binutils and a full rebuild may help." fi if test "$build_old_libs" = no; then build_libtool_libs=module build_old_libs=yes else build_libtool_libs=no fi fi else deplibs="$dir/$old_library $deplibs" link_static=yes fi fi # link shared/static library? if test "$linkmode" = lib; then if test -n "$dependency_libs" && { test "$hardcode_into_libs" != yes || test "$build_old_libs" = yes || test "$link_static" = yes; }; then # Extract -R from dependency_libs temp_deplibs= for libdir in $dependency_libs; do case $libdir in -R*) func_stripname '-R' '' "$libdir" temp_xrpath=$func_stripname_result case " $xrpath " in *" $temp_xrpath "*) ;; *) xrpath="$xrpath $temp_xrpath";; esac;; *) temp_deplibs="$temp_deplibs $libdir";; esac done dependency_libs="$temp_deplibs" fi newlib_search_path="$newlib_search_path $absdir" # Link against this library test "$link_static" = no && newdependency_libs="$abs_ladir/$laname $newdependency_libs" # ... and its dependency_libs tmp_libs= for deplib in $dependency_libs; do newdependency_libs="$deplib $newdependency_libs" if $opt_duplicate_deps ; then case "$tmp_libs " in *" $deplib "*) specialdeplibs="$specialdeplibs $deplib" ;; esac fi tmp_libs="$tmp_libs $deplib" done if test "$link_all_deplibs" != no; then # Add the search paths of all dependency libraries for deplib in $dependency_libs; do path= case $deplib in -L*) path="$deplib" ;; *.la) func_dirname "$deplib" "" "." dir="$func_dirname_result" # We need an absolute path. case $dir in [\\/]* | [A-Za-z]:[\\/]*) absdir="$dir" ;; *) absdir=`cd "$dir" && pwd` if test -z "$absdir"; then func_warning "cannot determine absolute directory name of \`$dir'" absdir="$dir" fi ;; esac if $GREP "^installed=no" $deplib > /dev/null; then case $host in *-*-darwin*) depdepl= eval deplibrary_names=`${SED} -n -e 's/^library_names=\(.*\)$/\1/p' $deplib` if test -n "$deplibrary_names" ; then for tmp in $deplibrary_names ; do depdepl=$tmp done if test -f "$absdir/$objdir/$depdepl" ; then depdepl="$absdir/$objdir/$depdepl" darwin_install_name=`${OTOOL} -L $depdepl | awk '{if (NR == 2) {print $1;exit}}'` if test -z "$darwin_install_name"; then darwin_install_name=`${OTOOL64} -L $depdepl | awk '{if (NR == 2) {print $1;exit}}'` fi compiler_flags="$compiler_flags ${wl}-dylib_file ${wl}${darwin_install_name}:${depdepl}" linker_flags="$linker_flags -dylib_file ${darwin_install_name}:${depdepl}" path= fi fi ;; *) path="-L$absdir/$objdir" ;; esac else eval libdir=`${SED} -n -e 's/^libdir=\(.*\)$/\1/p' $deplib` test -z "$libdir" && \ func_fatal_error "\`$deplib' is not a valid libtool archive" test "$absdir" != "$libdir" && \ func_warning "\`$deplib' seems to be moved" path="-L$absdir" fi ;; esac case " $deplibs " in *" $path "*) ;; *) deplibs="$path $deplibs" ;; esac done fi # link_all_deplibs != no fi # linkmode = lib done # for deplib in $libs if test "$pass" = link; then if test "$linkmode" = "prog"; then compile_deplibs="$new_inherited_linker_flags $compile_deplibs" finalize_deplibs="$new_inherited_linker_flags $finalize_deplibs" else compiler_flags="$compiler_flags "`$ECHO "X $new_inherited_linker_flags" | $Xsed -e 's% \([^ $]*\).ltframework% -framework \1%g'` fi fi dependency_libs="$newdependency_libs" if test "$pass" = dlpreopen; then # Link the dlpreopened libraries before other libraries for deplib in $save_deplibs; do deplibs="$deplib $deplibs" done fi if test "$pass" != dlopen; then if test "$pass" != conv; then # Make sure lib_search_path contains only unique directories. lib_search_path= for dir in $newlib_search_path; do case "$lib_search_path " in *" $dir "*) ;; *) lib_search_path="$lib_search_path $dir" ;; esac done newlib_search_path= fi if test "$linkmode,$pass" != "prog,link"; then vars="deplibs" else vars="compile_deplibs finalize_deplibs" fi for var in $vars dependency_libs; do # Add libraries to $var in reverse order eval tmp_libs=\"\$$var\" new_libs= for deplib in $tmp_libs; do # FIXME: Pedantically, this is the right thing to do, so # that some nasty dependency loop isn't accidentally # broken: #new_libs="$deplib $new_libs" # Pragmatically, this seems to cause very few problems in # practice: case $deplib in -L*) new_libs="$deplib $new_libs" ;; -R*) ;; *) # And here is the reason: when a library appears more # than once as an explicit dependence of a library, or # is implicitly linked in more than once by the # compiler, it is considered special, and multiple # occurrences thereof are not removed. Compare this # with having the same library being listed as a # dependency of multiple other libraries: in this case, # we know (pedantically, we assume) the library does not # need to be listed more than once, so we keep only the # last copy. This is not always right, but it is rare # enough that we require users that really mean to play # such unportable linking tricks to link the library # using -Wl,-lname, so that libtool does not consider it # for duplicate removal. case " $specialdeplibs " in *" $deplib "*) new_libs="$deplib $new_libs" ;; *) case " $new_libs " in *" $deplib "*) ;; *) new_libs="$deplib $new_libs" ;; esac ;; esac ;; esac done tmp_libs= for deplib in $new_libs; do case $deplib in -L*) case " $tmp_libs " in *" $deplib "*) ;; *) tmp_libs="$tmp_libs $deplib" ;; esac ;; *) tmp_libs="$tmp_libs $deplib" ;; esac done eval $var=\"$tmp_libs\" done # for var fi # Last step: remove runtime libs from dependency_libs # (they stay in deplibs) tmp_libs= for i in $dependency_libs ; do case " $predeps $postdeps $compiler_lib_search_path " in *" $i "*) i="" ;; esac if test -n "$i" ; then tmp_libs="$tmp_libs $i" fi done dependency_libs=$tmp_libs done # for pass if test "$linkmode" = prog; then dlfiles="$newdlfiles" fi if test "$linkmode" = prog || test "$linkmode" = lib; then dlprefiles="$newdlprefiles" fi case $linkmode in oldlib) if test -n "$dlfiles$dlprefiles" || test "$dlself" != no; then func_warning "\`-dlopen' is ignored for archives" fi case " $deplibs" in *\ -l* | *\ -L*) func_warning "\`-l' and \`-L' are ignored for archives" ;; esac test -n "$rpath" && \ func_warning "\`-rpath' is ignored for archives" test -n "$xrpath" && \ func_warning "\`-R' is ignored for archives" test -n "$vinfo" && \ func_warning "\`-version-info/-version-number' is ignored for archives" test -n "$release" && \ func_warning "\`-release' is ignored for archives" test -n "$export_symbols$export_symbols_regex" && \ func_warning "\`-export-symbols' is ignored for archives" # Now set the variables for building old libraries. build_libtool_libs=no oldlibs="$output" objs="$objs$old_deplibs" ;; lib) # Make sure we only generate libraries of the form `libNAME.la'. case $outputname in lib*) func_stripname 'lib' '.la' "$outputname" name=$func_stripname_result eval shared_ext=\"$shrext_cmds\" eval libname=\"$libname_spec\" ;; *) test "$module" = no && \ func_fatal_help "libtool library \`$output' must begin with \`lib'" if test "$need_lib_prefix" != no; then # Add the "lib" prefix for modules if required func_stripname '' '.la' "$outputname" name=$func_stripname_result eval shared_ext=\"$shrext_cmds\" eval libname=\"$libname_spec\" else func_stripname '' '.la' "$outputname" libname=$func_stripname_result fi ;; esac if test -n "$objs"; then if test "$deplibs_check_method" != pass_all; then func_fatal_error "cannot build libtool library \`$output' from non-libtool objects on this host:$objs" else $ECHO $ECHO "*** Warning: Linking the shared library $output against the non-libtool" $ECHO "*** objects $objs is not portable!" libobjs="$libobjs $objs" fi fi test "$dlself" != no && \ func_warning "\`-dlopen self' is ignored for libtool libraries" set dummy $rpath shift test "$#" -gt 1 && \ func_warning "ignoring multiple \`-rpath's for a libtool library" install_libdir="$1" oldlibs= if test -z "$rpath"; then if test "$build_libtool_libs" = yes; then # Building a libtool convenience library. # Some compilers have problems with a `.al' extension so # convenience libraries should have the same extension an # archive normally would. oldlibs="$output_objdir/$libname.$libext $oldlibs" build_libtool_libs=convenience build_old_libs=yes fi test -n "$vinfo" && \ func_warning "\`-version-info/-version-number' is ignored for convenience libraries" test -n "$release" && \ func_warning "\`-release' is ignored for convenience libraries" else # Parse the version information argument. save_ifs="$IFS"; IFS=':' set dummy $vinfo 0 0 0 shift IFS="$save_ifs" test -n "$7" && \ func_fatal_help "too many parameters to \`-version-info'" # convert absolute version numbers to libtool ages # this retains compatibility with .la files and attempts # to make the code below a bit more comprehensible case $vinfo_number in yes) number_major="$1" number_minor="$2" number_revision="$3" # # There are really only two kinds -- those that # use the current revision as the major version # and those that subtract age and use age as # a minor version. But, then there is irix # which has an extra 1 added just for fun # case $version_type in darwin|linux|osf|windows|none) func_arith $number_major + $number_minor current=$func_arith_result age="$number_minor" revision="$number_revision" ;; freebsd-aout|freebsd-elf|sunos) current="$number_major" revision="$number_minor" age="0" ;; irix|nonstopux) func_arith $number_major + $number_minor current=$func_arith_result age="$number_minor" revision="$number_minor" lt_irix_increment=no ;; *) func_fatal_configuration "$modename: unknown library version type \`$version_type'" ;; esac ;; no) current="$1" revision="$2" age="$3" ;; esac # Check that each of the things are valid numbers. case $current in 0|[1-9]|[1-9][0-9]|[1-9][0-9][0-9]|[1-9][0-9][0-9][0-9]|[1-9][0-9][0-9][0-9][0-9]) ;; *) func_error "CURRENT \`$current' must be a nonnegative integer" func_fatal_error "\`$vinfo' is not valid version information" ;; esac case $revision in 0|[1-9]|[1-9][0-9]|[1-9][0-9][0-9]|[1-9][0-9][0-9][0-9]|[1-9][0-9][0-9][0-9][0-9]) ;; *) func_error "REVISION \`$revision' must be a nonnegative integer" func_fatal_error "\`$vinfo' is not valid version information" ;; esac case $age in 0|[1-9]|[1-9][0-9]|[1-9][0-9][0-9]|[1-9][0-9][0-9][0-9]|[1-9][0-9][0-9][0-9][0-9]) ;; *) func_error "AGE \`$age' must be a nonnegative integer" func_fatal_error "\`$vinfo' is not valid version information" ;; esac if test "$age" -gt "$current"; then func_error "AGE \`$age' is greater than the current interface number \`$current'" func_fatal_error "\`$vinfo' is not valid version information" fi # Calculate the version variables. major= versuffix= verstring= case $version_type in none) ;; darwin) # Like Linux, but with the current version available in # verstring for coding it into the library header func_arith $current - $age major=.$func_arith_result versuffix="$major.$age.$revision" # Darwin ld doesn't like 0 for these options... func_arith $current + 1 minor_current=$func_arith_result xlcverstring="${wl}-compatibility_version ${wl}$minor_current ${wl}-current_version ${wl}$minor_current.$revision" verstring="-compatibility_version $minor_current -current_version $minor_current.$revision" ;; freebsd-aout) major=".$current" versuffix=".$current.$revision"; ;; freebsd-elf) major=".$current" versuffix=".$current" ;; irix | nonstopux) if test "X$lt_irix_increment" = "Xno"; then func_arith $current - $age else func_arith $current - $age + 1 fi major=$func_arith_result case $version_type in nonstopux) verstring_prefix=nonstopux ;; *) verstring_prefix=sgi ;; esac verstring="$verstring_prefix$major.$revision" # Add in all the interfaces that we are compatible with. loop=$revision while test "$loop" -ne 0; do func_arith $revision - $loop iface=$func_arith_result func_arith $loop - 1 loop=$func_arith_result verstring="$verstring_prefix$major.$iface:$verstring" done # Before this point, $major must not contain `.'. major=.$major versuffix="$major.$revision" ;; linux) func_arith $current - $age major=.$func_arith_result versuffix="$major.$age.$revision" ;; osf) func_arith $current - $age major=.$func_arith_result versuffix=".$current.$age.$revision" verstring="$current.$age.$revision" # Add in all the interfaces that we are compatible with. loop=$age while test "$loop" -ne 0; do func_arith $current - $loop iface=$func_arith_result func_arith $loop - 1 loop=$func_arith_result verstring="$verstring:${iface}.0" done # Make executables depend on our current version. verstring="$verstring:${current}.0" ;; qnx) major=".$current" versuffix=".$current" ;; sunos) major=".$current" versuffix=".$current.$revision" ;; windows) # Use '-' rather than '.', since we only want one # extension on DOS 8.3 filesystems. func_arith $current - $age major=$func_arith_result versuffix="-$major" ;; *) func_fatal_configuration "unknown library version type \`$version_type'" ;; esac # Clear the version info if we defaulted, and they specified a release. if test -z "$vinfo" && test -n "$release"; then major= case $version_type in darwin) # we can't check for "0.0" in archive_cmds due to quoting # problems, so we reset it completely verstring= ;; *) verstring="0.0" ;; esac if test "$need_version" = no; then versuffix= else versuffix=".0.0" fi fi # Remove version info from name if versioning should be avoided if test "$avoid_version" = yes && test "$need_version" = no; then major= versuffix= verstring="" fi # Check to see if the archive will have undefined symbols. if test "$allow_undefined" = yes; then if test "$allow_undefined_flag" = unsupported; then func_warning "undefined symbols not allowed in $host shared libraries" build_libtool_libs=no build_old_libs=yes fi else # Don't allow undefined symbols. allow_undefined_flag="$no_undefined_flag" fi fi func_generate_dlsyms "$libname" "$libname" "yes" libobjs="$libobjs $symfileobj" test "X$libobjs" = "X " && libobjs= if test "$mode" != relink; then # Remove our outputs, but don't remove object files since they # may have been created when compiling PIC objects. removelist= tempremovelist=`$ECHO "$output_objdir/*"` for p in $tempremovelist; do case $p in *.$objext | *.gcno) ;; $output_objdir/$outputname | $output_objdir/$libname.* | $output_objdir/${libname}${release}.*) if test "X$precious_files_regex" != "X"; then if $ECHO "$p" | $EGREP -e "$precious_files_regex" >/dev/null 2>&1 then continue fi fi removelist="$removelist $p" ;; *) ;; esac done test -n "$removelist" && \ func_show_eval "${RM}r \$removelist" fi # Now set the variables for building old libraries. if test "$build_old_libs" = yes && test "$build_libtool_libs" != convenience ; then oldlibs="$oldlibs $output_objdir/$libname.$libext" # Transform .lo files to .o files. oldobjs="$objs "`$ECHO "X$libobjs" | $SP2NL | $Xsed -e '/\.'${libext}'$/d' -e "$lo2o" | $NL2SP` fi # Eliminate all temporary directories. #for path in $notinst_path; do # lib_search_path=`$ECHO "X$lib_search_path " | $Xsed -e "s% $path % %g"` # deplibs=`$ECHO "X$deplibs " | $Xsed -e "s% -L$path % %g"` # dependency_libs=`$ECHO "X$dependency_libs " | $Xsed -e "s% -L$path % %g"` #done if test -n "$xrpath"; then # If the user specified any rpath flags, then add them. temp_xrpath= for libdir in $xrpath; do temp_xrpath="$temp_xrpath -R$libdir" case "$finalize_rpath " in *" $libdir "*) ;; *) finalize_rpath="$finalize_rpath $libdir" ;; esac done if test "$hardcode_into_libs" != yes || test "$build_old_libs" = yes; then dependency_libs="$temp_xrpath $dependency_libs" fi fi # Make sure dlfiles contains only unique files that won't be dlpreopened old_dlfiles="$dlfiles" dlfiles= for lib in $old_dlfiles; do case " $dlprefiles $dlfiles " in *" $lib "*) ;; *) dlfiles="$dlfiles $lib" ;; esac done # Make sure dlprefiles contains only unique files old_dlprefiles="$dlprefiles" dlprefiles= for lib in $old_dlprefiles; do case "$dlprefiles " in *" $lib "*) ;; *) dlprefiles="$dlprefiles $lib" ;; esac done if test "$build_libtool_libs" = yes; then if test -n "$rpath"; then case $host in *-*-cygwin* | *-*-mingw* | *-*-pw32* | *-*-os2* | *-*-beos* | *-cegcc*) # these systems don't actually have a c library (as such)! ;; *-*-rhapsody* | *-*-darwin1.[012]) # Rhapsody C library is in the System framework deplibs="$deplibs System.ltframework" ;; *-*-netbsd*) # Don't link with libc until the a.out ld.so is fixed. ;; *-*-openbsd* | *-*-freebsd* | *-*-dragonfly*) # Do not include libc due to us having libc/libc_r. ;; *-*-sco3.2v5* | *-*-sco5v6*) # Causes problems with __ctype ;; *-*-sysv4.2uw2* | *-*-sysv5* | *-*-unixware* | *-*-OpenUNIX*) # Compiler inserts libc in the correct place for threads to work ;; *) # Add libc to deplibs on all other systems if necessary. if test "$build_libtool_need_lc" = "yes"; then deplibs="$deplibs -lc" fi ;; esac fi # Transform deplibs into only deplibs that can be linked in shared. name_save=$name libname_save=$libname release_save=$release versuffix_save=$versuffix major_save=$major # I'm not sure if I'm treating the release correctly. I think # release should show up in the -l (ie -lgmp5) so we don't want to # add it in twice. Is that correct? release="" versuffix="" major="" newdeplibs= droppeddeps=no case $deplibs_check_method in pass_all) # Don't check for shared/static. Everything works. # This might be a little naive. We might want to check # whether the library exists or not. But this is on # osf3 & osf4 and I'm not really sure... Just # implementing what was already the behavior. newdeplibs=$deplibs ;; test_compile) # This code stresses the "libraries are programs" paradigm to its # limits. Maybe even breaks it. We compile a program, linking it # against the deplibs as a proxy for the library. Then we can check # whether they linked in statically or dynamically with ldd. $opt_dry_run || $RM conftest.c cat > conftest.c </dev/null` for potent_lib in $potential_libs; do # Follow soft links. if ls -lLd "$potent_lib" 2>/dev/null | $GREP " -> " >/dev/null; then continue fi # The statement above tries to avoid entering an # endless loop below, in case of cyclic links. # We might still enter an endless loop, since a link # loop can be closed while we follow links, # but so what? potlib="$potent_lib" while test -h "$potlib" 2>/dev/null; do potliblink=`ls -ld $potlib | ${SED} 's/.* -> //'` case $potliblink in [\\/]* | [A-Za-z]:[\\/]*) potlib="$potliblink";; *) potlib=`$ECHO "X$potlib" | $Xsed -e 's,[^/]*$,,'`"$potliblink";; esac done if eval $file_magic_cmd \"\$potlib\" 2>/dev/null | $SED -e 10q | $EGREP "$file_magic_regex" > /dev/null; then newdeplibs="$newdeplibs $a_deplib" a_deplib="" break 2 fi done done fi if test -n "$a_deplib" ; then droppeddeps=yes $ECHO $ECHO "*** Warning: linker path does not have real file for library $a_deplib." $ECHO "*** I have the capability to make that library automatically link in when" $ECHO "*** you link to this library. But I can only do this if you have a" $ECHO "*** shared version of the library, which you do not appear to have" $ECHO "*** because I did check the linker path looking for a file starting" if test -z "$potlib" ; then $ECHO "*** with $libname but no candidates were found. (...for file magic test)" else $ECHO "*** with $libname and none of the candidates passed a file format test" $ECHO "*** using a file magic. Last file checked: $potlib" fi fi ;; *) # Add a -L argument. newdeplibs="$newdeplibs $a_deplib" ;; esac done # Gone through all deplibs. ;; match_pattern*) set dummy $deplibs_check_method; shift match_pattern_regex=`expr "$deplibs_check_method" : "$1 \(.*\)"` for a_deplib in $deplibs; do case $a_deplib in -l*) func_stripname -l '' "$a_deplib" name=$func_stripname_result if test "X$allow_libtool_libs_with_static_runtimes" = "Xyes" ; then case " $predeps $postdeps " in *" $a_deplib "*) newdeplibs="$newdeplibs $a_deplib" a_deplib="" ;; esac fi if test -n "$a_deplib" ; then libname=`eval "\\$ECHO \"$libname_spec\""` for i in $lib_search_path $sys_lib_search_path $shlib_search_path; do potential_libs=`ls $i/$libname[.-]* 2>/dev/null` for potent_lib in $potential_libs; do potlib="$potent_lib" # see symlink-check above in file_magic test if eval "\$ECHO \"X$potent_lib\"" 2>/dev/null | $Xsed -e 10q | \ $EGREP "$match_pattern_regex" > /dev/null; then newdeplibs="$newdeplibs $a_deplib" a_deplib="" break 2 fi done done fi if test -n "$a_deplib" ; then droppeddeps=yes $ECHO $ECHO "*** Warning: linker path does not have real file for library $a_deplib." $ECHO "*** I have the capability to make that library automatically link in when" $ECHO "*** you link to this library. But I can only do this if you have a" $ECHO "*** shared version of the library, which you do not appear to have" $ECHO "*** because I did check the linker path looking for a file starting" if test -z "$potlib" ; then $ECHO "*** with $libname but no candidates were found. (...for regex pattern test)" else $ECHO "*** with $libname and none of the candidates passed a file format test" $ECHO "*** using a regex pattern. Last file checked: $potlib" fi fi ;; *) # Add a -L argument. newdeplibs="$newdeplibs $a_deplib" ;; esac done # Gone through all deplibs. ;; none | unknown | *) newdeplibs="" tmp_deplibs=`$ECHO "X $deplibs" | $Xsed \ -e 's/ -lc$//' -e 's/ -[LR][^ ]*//g'` if test "X$allow_libtool_libs_with_static_runtimes" = "Xyes" ; then for i in $predeps $postdeps ; do # can't use Xsed below, because $i might contain '/' tmp_deplibs=`$ECHO "X $tmp_deplibs" | $Xsed -e "s,$i,,"` done fi if $ECHO "X $tmp_deplibs" | $Xsed -e 's/[ ]//g' | $GREP . >/dev/null; then $ECHO if test "X$deplibs_check_method" = "Xnone"; then $ECHO "*** Warning: inter-library dependencies are not supported in this platform." else $ECHO "*** Warning: inter-library dependencies are not known to be supported." fi $ECHO "*** All declared inter-library dependencies are being dropped." droppeddeps=yes fi ;; esac versuffix=$versuffix_save major=$major_save release=$release_save libname=$libname_save name=$name_save case $host in *-*-rhapsody* | *-*-darwin1.[012]) # On Rhapsody replace the C library with the System framework newdeplibs=`$ECHO "X $newdeplibs" | $Xsed -e 's/ -lc / System.ltframework /'` ;; esac if test "$droppeddeps" = yes; then if test "$module" = yes; then $ECHO $ECHO "*** Warning: libtool could not satisfy all declared inter-library" $ECHO "*** dependencies of module $libname. Therefore, libtool will create" $ECHO "*** a static module, that should work as long as the dlopening" $ECHO "*** application is linked with the -dlopen flag." if test -z "$global_symbol_pipe"; then $ECHO $ECHO "*** However, this would only work if libtool was able to extract symbol" $ECHO "*** lists from a program, using \`nm' or equivalent, but libtool could" $ECHO "*** not find such a program. So, this module is probably useless." $ECHO "*** \`nm' from GNU binutils and a full rebuild may help." fi if test "$build_old_libs" = no; then oldlibs="$output_objdir/$libname.$libext" build_libtool_libs=module build_old_libs=yes else build_libtool_libs=no fi else $ECHO "*** The inter-library dependencies that have been dropped here will be" $ECHO "*** automatically added whenever a program is linked with this library" $ECHO "*** or is declared to -dlopen it." if test "$allow_undefined" = no; then $ECHO $ECHO "*** Since this library must not contain undefined symbols," $ECHO "*** because either the platform does not support them or" $ECHO "*** it was explicitly requested with -no-undefined," $ECHO "*** libtool will only create a static version of it." if test "$build_old_libs" = no; then oldlibs="$output_objdir/$libname.$libext" build_libtool_libs=module build_old_libs=yes else build_libtool_libs=no fi fi fi fi # Done checking deplibs! deplibs=$newdeplibs fi # Time to change all our "foo.ltframework" stuff back to "-framework foo" case $host in *-*-darwin*) newdeplibs=`$ECHO "X $newdeplibs" | $Xsed -e 's% \([^ $]*\).ltframework% -framework \1%g'` new_inherited_linker_flags=`$ECHO "X $new_inherited_linker_flags" | $Xsed -e 's% \([^ $]*\).ltframework% -framework \1%g'` deplibs=`$ECHO "X $deplibs" | $Xsed -e 's% \([^ $]*\).ltframework% -framework \1%g'` ;; esac # move library search paths that coincide with paths to not yet # installed libraries to the beginning of the library search list new_libs= for path in $notinst_path; do case " $new_libs " in *" -L$path/$objdir "*) ;; *) case " $deplibs " in *" -L$path/$objdir "*) new_libs="$new_libs -L$path/$objdir" ;; esac ;; esac done for deplib in $deplibs; do case $deplib in -L*) case " $new_libs " in *" $deplib "*) ;; *) new_libs="$new_libs $deplib" ;; esac ;; *) new_libs="$new_libs $deplib" ;; esac done deplibs="$new_libs" # All the library-specific variables (install_libdir is set above). library_names= old_library= dlname= # Test again, we may have decided not to build it any more if test "$build_libtool_libs" = yes; then if test "$hardcode_into_libs" = yes; then # Hardcode the library paths hardcode_libdirs= dep_rpath= rpath="$finalize_rpath" test "$mode" != relink && rpath="$compile_rpath$rpath" for libdir in $rpath; do if test -n "$hardcode_libdir_flag_spec"; then if test -n "$hardcode_libdir_separator"; then if test -z "$hardcode_libdirs"; then hardcode_libdirs="$libdir" else # Just accumulate the unique libdirs. case $hardcode_libdir_separator$hardcode_libdirs$hardcode_libdir_separator in *"$hardcode_libdir_separator$libdir$hardcode_libdir_separator"*) ;; *) hardcode_libdirs="$hardcode_libdirs$hardcode_libdir_separator$libdir" ;; esac fi else eval flag=\"$hardcode_libdir_flag_spec\" dep_rpath="$dep_rpath $flag" fi elif test -n "$runpath_var"; then case "$perm_rpath " in *" $libdir "*) ;; *) perm_rpath="$perm_rpath $libdir" ;; esac fi done # Substitute the hardcoded libdirs into the rpath. if test -n "$hardcode_libdir_separator" && test -n "$hardcode_libdirs"; then libdir="$hardcode_libdirs" if test -n "$hardcode_libdir_flag_spec_ld"; then eval dep_rpath=\"$hardcode_libdir_flag_spec_ld\" else eval dep_rpath=\"$hardcode_libdir_flag_spec\" fi fi if test -n "$runpath_var" && test -n "$perm_rpath"; then # We should set the runpath_var. rpath= for dir in $perm_rpath; do rpath="$rpath$dir:" done eval "$runpath_var='$rpath\$$runpath_var'; export $runpath_var" fi test -n "$dep_rpath" && deplibs="$dep_rpath $deplibs" fi shlibpath="$finalize_shlibpath" test "$mode" != relink && shlibpath="$compile_shlibpath$shlibpath" if test -n "$shlibpath"; then eval "$shlibpath_var='$shlibpath\$$shlibpath_var'; export $shlibpath_var" fi # Get the real and link names of the library. eval shared_ext=\"$shrext_cmds\" eval library_names=\"$library_names_spec\" set dummy $library_names shift realname="$1" shift if test -n "$soname_spec"; then eval soname=\"$soname_spec\" else soname="$realname" fi if test -z "$dlname"; then dlname=$soname fi lib="$output_objdir/$realname" linknames= for link do linknames="$linknames $link" done # Use standard objects if they are pic test -z "$pic_flag" && libobjs=`$ECHO "X$libobjs" | $SP2NL | $Xsed -e "$lo2o" | $NL2SP` test "X$libobjs" = "X " && libobjs= delfiles= if test -n "$export_symbols" && test -n "$include_expsyms"; then $opt_dry_run || cp "$export_symbols" "$output_objdir/$libname.uexp" export_symbols="$output_objdir/$libname.uexp" delfiles="$delfiles $export_symbols" fi orig_export_symbols= case $host_os in cygwin* | mingw* | cegcc*) if test -n "$export_symbols" && test -z "$export_symbols_regex"; then # exporting using user supplied symfile if test "x`$SED 1q $export_symbols`" != xEXPORTS; then # and it's NOT already a .def file. Must figure out # which of the given symbols are data symbols and tag # them as such. So, trigger use of export_symbols_cmds. # export_symbols gets reassigned inside the "prepare # the list of exported symbols" if statement, so the # include_expsyms logic still works. orig_export_symbols="$export_symbols" export_symbols= always_export_symbols=yes fi fi ;; esac # Prepare the list of exported symbols if test -z "$export_symbols"; then if test "$always_export_symbols" = yes || test -n "$export_symbols_regex"; then func_verbose "generating symbol list for \`$libname.la'" export_symbols="$output_objdir/$libname.exp" $opt_dry_run || $RM $export_symbols cmds=$export_symbols_cmds save_ifs="$IFS"; IFS='~' for cmd in $cmds; do IFS="$save_ifs" eval cmd=\"$cmd\" func_len " $cmd" len=$func_len_result if test "$len" -lt "$max_cmd_len" || test "$max_cmd_len" -le -1; then func_show_eval "$cmd" 'exit $?' skipped_export=false else # The command line is too long to execute in one step. func_verbose "using reloadable object file for export list..." skipped_export=: # Break out early, otherwise skipped_export may be # set to false by a later but shorter cmd. break fi done IFS="$save_ifs" if test -n "$export_symbols_regex" && test "X$skipped_export" != "X:"; then func_show_eval '$EGREP -e "$export_symbols_regex" "$export_symbols" > "${export_symbols}T"' func_show_eval '$MV "${export_symbols}T" "$export_symbols"' fi fi fi if test -n "$export_symbols" && test -n "$include_expsyms"; then tmp_export_symbols="$export_symbols" test -n "$orig_export_symbols" && tmp_export_symbols="$orig_export_symbols" $opt_dry_run || eval '$ECHO "X$include_expsyms" | $Xsed | $SP2NL >> "$tmp_export_symbols"' fi if test "X$skipped_export" != "X:" && test -n "$orig_export_symbols"; then # The given exports_symbols file has to be filtered, so filter it. func_verbose "filter symbol list for \`$libname.la' to tag DATA exports" # FIXME: $output_objdir/$libname.filter potentially contains lots of # 's' commands which not all seds can handle. GNU sed should be fine # though. Also, the filter scales superlinearly with the number of # global variables. join(1) would be nice here, but unfortunately # isn't a blessed tool. $opt_dry_run || $SED -e '/[ ,]DATA/!d;s,\(.*\)\([ \,].*\),s|^\1$|\1\2|,' < $export_symbols > $output_objdir/$libname.filter delfiles="$delfiles $export_symbols $output_objdir/$libname.filter" export_symbols=$output_objdir/$libname.def $opt_dry_run || $SED -f $output_objdir/$libname.filter < $orig_export_symbols > $export_symbols fi tmp_deplibs= for test_deplib in $deplibs; do case " $convenience " in *" $test_deplib "*) ;; *) tmp_deplibs="$tmp_deplibs $test_deplib" ;; esac done deplibs="$tmp_deplibs" if test -n "$convenience"; then if test -n "$whole_archive_flag_spec" && test "$compiler_needs_object" = yes && test -z "$libobjs"; then # extract the archives, so we have objects to list. # TODO: could optimize this to just extract one archive. whole_archive_flag_spec= fi if test -n "$whole_archive_flag_spec"; then save_libobjs=$libobjs eval libobjs=\"\$libobjs $whole_archive_flag_spec\" test "X$libobjs" = "X " && libobjs= else gentop="$output_objdir/${outputname}x" generated="$generated $gentop" func_extract_archives $gentop $convenience libobjs="$libobjs $func_extract_archives_result" test "X$libobjs" = "X " && libobjs= fi fi if test "$thread_safe" = yes && test -n "$thread_safe_flag_spec"; then eval flag=\"$thread_safe_flag_spec\" linker_flags="$linker_flags $flag" fi # Make a backup of the uninstalled library when relinking if test "$mode" = relink; then $opt_dry_run || eval '(cd $output_objdir && $RM ${realname}U && $MV $realname ${realname}U)' || exit $? fi # Do each of the archive commands. if test "$module" = yes && test -n "$module_cmds" ; then if test -n "$export_symbols" && test -n "$module_expsym_cmds"; then eval test_cmds=\"$module_expsym_cmds\" cmds=$module_expsym_cmds else eval test_cmds=\"$module_cmds\" cmds=$module_cmds fi else if test -n "$export_symbols" && test -n "$archive_expsym_cmds"; then eval test_cmds=\"$archive_expsym_cmds\" cmds=$archive_expsym_cmds else eval test_cmds=\"$archive_cmds\" cmds=$archive_cmds fi fi if test "X$skipped_export" != "X:" && func_len " $test_cmds" && len=$func_len_result && test "$len" -lt "$max_cmd_len" || test "$max_cmd_len" -le -1; then : else # The command line is too long to link in one step, link piecewise # or, if using GNU ld and skipped_export is not :, use a linker # script. # Save the value of $output and $libobjs because we want to # use them later. If we have whole_archive_flag_spec, we # want to use save_libobjs as it was before # whole_archive_flag_spec was expanded, because we can't # assume the linker understands whole_archive_flag_spec. # This may have to be revisited, in case too many # convenience libraries get linked in and end up exceeding # the spec. if test -z "$convenience" || test -z "$whole_archive_flag_spec"; then save_libobjs=$libobjs fi save_output=$output output_la=`$ECHO "X$output" | $Xsed -e "$basename"` # Clear the reloadable object creation command queue and # initialize k to one. test_cmds= concat_cmds= objlist= last_robj= k=1 if test -n "$save_libobjs" && test "X$skipped_export" != "X:" && test "$with_gnu_ld" = yes; then output=${output_objdir}/${output_la}.lnkscript func_verbose "creating GNU ld script: $output" $ECHO 'INPUT (' > $output for obj in $save_libobjs do $ECHO "$obj" >> $output done $ECHO ')' >> $output delfiles="$delfiles $output" elif test -n "$save_libobjs" && test "X$skipped_export" != "X:" && test "X$file_list_spec" != X; then output=${output_objdir}/${output_la}.lnk func_verbose "creating linker input file list: $output" : > $output set x $save_libobjs shift firstobj= if test "$compiler_needs_object" = yes; then firstobj="$1 " shift fi for obj do $ECHO "$obj" >> $output done delfiles="$delfiles $output" output=$firstobj\"$file_list_spec$output\" else if test -n "$save_libobjs"; then func_verbose "creating reloadable object files..." output=$output_objdir/$output_la-${k}.$objext eval test_cmds=\"$reload_cmds\" func_len " $test_cmds" len0=$func_len_result len=$len0 # Loop over the list of objects to be linked. for obj in $save_libobjs do func_len " $obj" func_arith $len + $func_len_result len=$func_arith_result if test "X$objlist" = X || test "$len" -lt "$max_cmd_len"; then func_append objlist " $obj" else # The command $test_cmds is almost too long, add a # command to the queue. if test "$k" -eq 1 ; then # The first file doesn't have a previous command to add. eval concat_cmds=\"$reload_cmds $objlist $last_robj\" else # All subsequent reloadable object files will link in # the last one created. eval concat_cmds=\"\$concat_cmds~$reload_cmds $objlist $last_robj~\$RM $last_robj\" fi last_robj=$output_objdir/$output_la-${k}.$objext func_arith $k + 1 k=$func_arith_result output=$output_objdir/$output_la-${k}.$objext objlist=$obj func_len " $last_robj" func_arith $len0 + $func_len_result len=$func_arith_result fi done # Handle the remaining objects by creating one last # reloadable object file. All subsequent reloadable object # files will link in the last one created. test -z "$concat_cmds" || concat_cmds=$concat_cmds~ eval concat_cmds=\"\${concat_cmds}$reload_cmds $objlist $last_robj\" if test -n "$last_robj"; then eval concat_cmds=\"\${concat_cmds}~\$RM $last_robj\" fi delfiles="$delfiles $output" else output= fi if ${skipped_export-false}; then func_verbose "generating symbol list for \`$libname.la'" export_symbols="$output_objdir/$libname.exp" $opt_dry_run || $RM $export_symbols libobjs=$output # Append the command to create the export file. test -z "$concat_cmds" || concat_cmds=$concat_cmds~ eval concat_cmds=\"\$concat_cmds$export_symbols_cmds\" if test -n "$last_robj"; then eval concat_cmds=\"\$concat_cmds~\$RM $last_robj\" fi fi test -n "$save_libobjs" && func_verbose "creating a temporary reloadable object file: $output" # Loop through the commands generated above and execute them. save_ifs="$IFS"; IFS='~' for cmd in $concat_cmds; do IFS="$save_ifs" $opt_silent || { func_quote_for_expand "$cmd" eval "func_echo $func_quote_for_expand_result" } $opt_dry_run || eval "$cmd" || { lt_exit=$? # Restore the uninstalled library and exit if test "$mode" = relink; then ( cd "$output_objdir" && \ $RM "${realname}T" && \ $MV "${realname}U" "$realname" ) fi exit $lt_exit } done IFS="$save_ifs" if test -n "$export_symbols_regex" && ${skipped_export-false}; then func_show_eval '$EGREP -e "$export_symbols_regex" "$export_symbols" > "${export_symbols}T"' func_show_eval '$MV "${export_symbols}T" "$export_symbols"' fi fi if ${skipped_export-false}; then if test -n "$export_symbols" && test -n "$include_expsyms"; then tmp_export_symbols="$export_symbols" test -n "$orig_export_symbols" && tmp_export_symbols="$orig_export_symbols" $opt_dry_run || eval '$ECHO "X$include_expsyms" | $Xsed | $SP2NL >> "$tmp_export_symbols"' fi if test -n "$orig_export_symbols"; then # The given exports_symbols file has to be filtered, so filter it. func_verbose "filter symbol list for \`$libname.la' to tag DATA exports" # FIXME: $output_objdir/$libname.filter potentially contains lots of # 's' commands which not all seds can handle. GNU sed should be fine # though. Also, the filter scales superlinearly with the number of # global variables. join(1) would be nice here, but unfortunately # isn't a blessed tool. $opt_dry_run || $SED -e '/[ ,]DATA/!d;s,\(.*\)\([ \,].*\),s|^\1$|\1\2|,' < $export_symbols > $output_objdir/$libname.filter delfiles="$delfiles $export_symbols $output_objdir/$libname.filter" export_symbols=$output_objdir/$libname.def $opt_dry_run || $SED -f $output_objdir/$libname.filter < $orig_export_symbols > $export_symbols fi fi libobjs=$output # Restore the value of output. output=$save_output if test -n "$convenience" && test -n "$whole_archive_flag_spec"; then eval libobjs=\"\$libobjs $whole_archive_flag_spec\" test "X$libobjs" = "X " && libobjs= fi # Expand the library linking commands again to reset the # value of $libobjs for piecewise linking. # Do each of the archive commands. if test "$module" = yes && test -n "$module_cmds" ; then if test -n "$export_symbols" && test -n "$module_expsym_cmds"; then cmds=$module_expsym_cmds else cmds=$module_cmds fi else if test -n "$export_symbols" && test -n "$archive_expsym_cmds"; then cmds=$archive_expsym_cmds else cmds=$archive_cmds fi fi fi if test -n "$delfiles"; then # Append the command to remove temporary files to $cmds. eval cmds=\"\$cmds~\$RM $delfiles\" fi # Add any objects from preloaded convenience libraries if test -n "$dlprefiles"; then gentop="$output_objdir/${outputname}x" generated="$generated $gentop" func_extract_archives $gentop $dlprefiles libobjs="$libobjs $func_extract_archives_result" test "X$libobjs" = "X " && libobjs= fi save_ifs="$IFS"; IFS='~' for cmd in $cmds; do IFS="$save_ifs" eval cmd=\"$cmd\" $opt_silent || { func_quote_for_expand "$cmd" eval "func_echo $func_quote_for_expand_result" } $opt_dry_run || eval "$cmd" || { lt_exit=$? # Restore the uninstalled library and exit if test "$mode" = relink; then ( cd "$output_objdir" && \ $RM "${realname}T" && \ $MV "${realname}U" "$realname" ) fi exit $lt_exit } done IFS="$save_ifs" # Restore the uninstalled library and exit if test "$mode" = relink; then $opt_dry_run || eval '(cd $output_objdir && $RM ${realname}T && $MV $realname ${realname}T && $MV ${realname}U $realname)' || exit $? if test -n "$convenience"; then if test -z "$whole_archive_flag_spec"; then func_show_eval '${RM}r "$gentop"' fi fi exit $EXIT_SUCCESS fi # Create links to the real library. for linkname in $linknames; do if test "$realname" != "$linkname"; then func_show_eval '(cd "$output_objdir" && $RM "$linkname" && $LN_S "$realname" "$linkname")' 'exit $?' fi done # If -module or -export-dynamic was specified, set the dlname. if test "$module" = yes || test "$export_dynamic" = yes; then # On all known operating systems, these are identical. dlname="$soname" fi fi ;; obj) if test -n "$dlfiles$dlprefiles" || test "$dlself" != no; then func_warning "\`-dlopen' is ignored for objects" fi case " $deplibs" in *\ -l* | *\ -L*) func_warning "\`-l' and \`-L' are ignored for objects" ;; esac test -n "$rpath" && \ func_warning "\`-rpath' is ignored for objects" test -n "$xrpath" && \ func_warning "\`-R' is ignored for objects" test -n "$vinfo" && \ func_warning "\`-version-info' is ignored for objects" test -n "$release" && \ func_warning "\`-release' is ignored for objects" case $output in *.lo) test -n "$objs$old_deplibs" && \ func_fatal_error "cannot build library object \`$output' from non-libtool objects" libobj=$output func_lo2o "$libobj" obj=$func_lo2o_result ;; *) libobj= obj="$output" ;; esac # Delete the old objects. $opt_dry_run || $RM $obj $libobj # Objects from convenience libraries. This assumes # single-version convenience libraries. Whenever we create # different ones for PIC/non-PIC, this we'll have to duplicate # the extraction. reload_conv_objs= gentop= # reload_cmds runs $LD directly, so let us get rid of # -Wl from whole_archive_flag_spec and hope we can get by with # turning comma into space.. wl= if test -n "$convenience"; then if test -n "$whole_archive_flag_spec"; then eval tmp_whole_archive_flags=\"$whole_archive_flag_spec\" reload_conv_objs=$reload_objs\ `$ECHO "X$tmp_whole_archive_flags" | $Xsed -e 's|,| |g'` else gentop="$output_objdir/${obj}x" generated="$generated $gentop" func_extract_archives $gentop $convenience reload_conv_objs="$reload_objs $func_extract_archives_result" fi fi # Create the old-style object. reload_objs="$objs$old_deplibs "`$ECHO "X$libobjs" | $SP2NL | $Xsed -e '/\.'${libext}$'/d' -e '/\.lib$/d' -e "$lo2o" | $NL2SP`" $reload_conv_objs" ### testsuite: skip nested quoting test output="$obj" func_execute_cmds "$reload_cmds" 'exit $?' # Exit if we aren't doing a library object file. if test -z "$libobj"; then if test -n "$gentop"; then func_show_eval '${RM}r "$gentop"' fi exit $EXIT_SUCCESS fi if test "$build_libtool_libs" != yes; then if test -n "$gentop"; then func_show_eval '${RM}r "$gentop"' fi # Create an invalid libtool object if no PIC, so that we don't # accidentally link it into a program. # $show "echo timestamp > $libobj" # $opt_dry_run || eval "echo timestamp > $libobj" || exit $? exit $EXIT_SUCCESS fi if test -n "$pic_flag" || test "$pic_mode" != default; then # Only do commands if we really have different PIC objects. reload_objs="$libobjs $reload_conv_objs" output="$libobj" func_execute_cmds "$reload_cmds" 'exit $?' fi if test -n "$gentop"; then func_show_eval '${RM}r "$gentop"' fi exit $EXIT_SUCCESS ;; prog) case $host in *cygwin*) func_stripname '' '.exe' "$output" output=$func_stripname_result.exe;; esac test -n "$vinfo" && \ func_warning "\`-version-info' is ignored for programs" test -n "$release" && \ func_warning "\`-release' is ignored for programs" test "$preload" = yes \ && test "$dlopen_support" = unknown \ && test "$dlopen_self" = unknown \ && test "$dlopen_self_static" = unknown && \ func_warning "\`LT_INIT([dlopen])' not used. Assuming no dlopen support." case $host in *-*-rhapsody* | *-*-darwin1.[012]) # On Rhapsody replace the C library is the System framework compile_deplibs=`$ECHO "X $compile_deplibs" | $Xsed -e 's/ -lc / System.ltframework /'` finalize_deplibs=`$ECHO "X $finalize_deplibs" | $Xsed -e 's/ -lc / System.ltframework /'` ;; esac case $host in *-*-darwin*) # Don't allow lazy linking, it breaks C++ global constructors # But is supposedly fixed on 10.4 or later (yay!). if test "$tagname" = CXX ; then case ${MACOSX_DEPLOYMENT_TARGET-10.0} in 10.[0123]) compile_command="$compile_command ${wl}-bind_at_load" finalize_command="$finalize_command ${wl}-bind_at_load" ;; esac fi # Time to change all our "foo.ltframework" stuff back to "-framework foo" compile_deplibs=`$ECHO "X $compile_deplibs" | $Xsed -e 's% \([^ $]*\).ltframework% -framework \1%g'` finalize_deplibs=`$ECHO "X $finalize_deplibs" | $Xsed -e 's% \([^ $]*\).ltframework% -framework \1%g'` ;; esac # move library search paths that coincide with paths to not yet # installed libraries to the beginning of the library search list new_libs= for path in $notinst_path; do case " $new_libs " in *" -L$path/$objdir "*) ;; *) case " $compile_deplibs " in *" -L$path/$objdir "*) new_libs="$new_libs -L$path/$objdir" ;; esac ;; esac done for deplib in $compile_deplibs; do case $deplib in -L*) case " $new_libs " in *" $deplib "*) ;; *) new_libs="$new_libs $deplib" ;; esac ;; *) new_libs="$new_libs $deplib" ;; esac done compile_deplibs="$new_libs" compile_command="$compile_command $compile_deplibs" finalize_command="$finalize_command $finalize_deplibs" if test -n "$rpath$xrpath"; then # If the user specified any rpath flags, then add them. for libdir in $rpath $xrpath; do # This is the magic to use -rpath. case "$finalize_rpath " in *" $libdir "*) ;; *) finalize_rpath="$finalize_rpath $libdir" ;; esac done fi # Now hardcode the library paths rpath= hardcode_libdirs= for libdir in $compile_rpath $finalize_rpath; do if test -n "$hardcode_libdir_flag_spec"; then if test -n "$hardcode_libdir_separator"; then if test -z "$hardcode_libdirs"; then hardcode_libdirs="$libdir" else # Just accumulate the unique libdirs. case $hardcode_libdir_separator$hardcode_libdirs$hardcode_libdir_separator in *"$hardcode_libdir_separator$libdir$hardcode_libdir_separator"*) ;; 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then finalize_command="$shlibpath_var=\"$finalize_shlibpath\$$shlibpath_var\" $finalize_command" fi compile_var= finalize_var= if test -n "$runpath_var"; then if test -n "$perm_rpath"; then # We should set the runpath_var. rpath= for dir in $perm_rpath; do rpath="$rpath$dir:" done compile_var="$runpath_var=\"$rpath\$$runpath_var\" " fi if test -n "$finalize_perm_rpath"; then # We should set the runpath_var. rpath= for dir in $finalize_perm_rpath; do rpath="$rpath$dir:" done finalize_var="$runpath_var=\"$rpath\$$runpath_var\" " fi fi if test "$no_install" = yes; then # We don't need to create a wrapper script. link_command="$compile_var$compile_command$compile_rpath" # Replace the output file specification. link_command=`$ECHO "X$link_command" | $Xsed -e 's%@OUTPUT@%'"$output"'%g'` # Delete the old output file. $opt_dry_run || $RM $output # Link the executable and exit func_show_eval "$link_command" 'exit $?' exit $EXIT_SUCCESS fi if test "$hardcode_action" = relink; then # Fast installation is not supported link_command="$compile_var$compile_command$compile_rpath" relink_command="$finalize_var$finalize_command$finalize_rpath" func_warning "this platform does not like uninstalled shared libraries" func_warning "\`$output' will be relinked during installation" else if test "$fast_install" != no; then link_command="$finalize_var$compile_command$finalize_rpath" if test "$fast_install" = yes; then relink_command=`$ECHO "X$compile_var$compile_command$compile_rpath" | $Xsed -e 's%@OUTPUT@%\$progdir/\$file%g'` else # fast_install is set to needless relink_command= fi else link_command="$compile_var$compile_command$compile_rpath" relink_command="$finalize_var$finalize_command$finalize_rpath" fi fi # Replace the output file specification. link_command=`$ECHO "X$link_command" | $Xsed -e 's%@OUTPUT@%'"$output_objdir/$outputname"'%g'` # Delete the old output files. $opt_dry_run || $RM $output $output_objdir/$outputname $output_objdir/lt-$outputname func_show_eval "$link_command" 'exit $?' # Now create the wrapper script. func_verbose "creating $output" # Quote the relink command for shipping. if test -n "$relink_command"; then # Preserve any variables that may affect compiler behavior for var in $variables_saved_for_relink; do if eval test -z \"\${$var+set}\"; then relink_command="{ test -z \"\${$var+set}\" || $lt_unset $var || { $var=; 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then eval exec "$exec_cmd" exit $EXIT_FAILURE fi exit $exit_status # The TAGs below are defined such that we never get into a situation # in which we disable both kinds of libraries. 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It does not imply ALL GNU software can. # # This file is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation; either version 2 of the License, or # (at your option) any later version. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program; if not, write to the Free Software # Foundation, Inc., 51 Franklin Street - Fifth Floor, Boston, MA # 02110-1301, USA. # # As a special exception to the GNU General Public License, if you # distribute this file as part of a program that contains a # configuration script generated by Autoconf, you may include it under # the same distribution terms that you use for the rest of that program. # Please send patches to . Submit a context # diff and a properly formatted GNU ChangeLog entry. # # Configuration subroutine to validate and canonicalize a configuration type. # Supply the specified configuration type as an argument. # If it is invalid, we print an error message on stderr and exit with code 1. # Otherwise, we print the canonical config type on stdout and succeed. # You can get the latest version of this script from: # http://git.savannah.gnu.org/gitweb/?p=config.git;a=blob_plain;f=config.sub;hb=HEAD # This file is supposed to be the same for all GNU packages # and recognize all the CPU types, system types and aliases # that are meaningful with *any* GNU software. # Each package is responsible for reporting which valid configurations # it does not support. The user should be able to distinguish # a failure to support a valid configuration from a meaningless # configuration. # The goal of this file is to map all the various variations of a given # machine specification into a single specification in the form: # CPU_TYPE-MANUFACTURER-OPERATING_SYSTEM # or in some cases, the newer four-part form: # CPU_TYPE-MANUFACTURER-KERNEL-OPERATING_SYSTEM # It is wrong to echo any other type of specification. me=`echo "$0" | sed -e 's,.*/,,'` usage="\ Usage: $0 [OPTION] CPU-MFR-OPSYS $0 [OPTION] ALIAS Canonicalize a configuration name. Operation modes: -h, --help print this help, then exit -t, --time-stamp print date of last modification, then exit -v, --version print version number, then exit Report bugs and patches to ." version="\ GNU config.sub ($timestamp) Copyright (C) 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 Free Software Foundation, Inc. This is free software; see the source for copying conditions. There is NO warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE." help=" Try \`$me --help' for more information." # Parse command line while test $# -gt 0 ; do case $1 in --time-stamp | --time* | -t ) echo "$timestamp" ; exit ;; --version | -v ) echo "$version" ; exit ;; --help | --h* | -h ) echo "$usage"; exit ;; -- ) # Stop option processing shift; break ;; - ) # Use stdin as input. break ;; -* ) echo "$me: invalid option $1$help" exit 1 ;; *local*) # First pass through any local machine types. echo $1 exit ;; * ) break ;; esac done case $# in 0) echo "$me: missing argument$help" >&2 exit 1;; 1) ;; *) echo "$me: too many arguments$help" >&2 exit 1;; esac # Separate what the user gave into CPU-COMPANY and OS or KERNEL-OS (if any). # Here we must recognize all the valid KERNEL-OS combinations. maybe_os=`echo $1 | sed 's/^\(.*\)-\([^-]*-[^-]*\)$/\2/'` case $maybe_os in nto-qnx* | linux-gnu* | linux-dietlibc | linux-newlib* | linux-uclibc* | \ uclinux-uclibc* | uclinux-gnu* | kfreebsd*-gnu* | knetbsd*-gnu* | netbsd*-gnu* | \ kopensolaris*-gnu* | \ storm-chaos* | os2-emx* | rtmk-nova*) os=-$maybe_os basic_machine=`echo $1 | sed 's/^\(.*\)-\([^-]*-[^-]*\)$/\1/'` ;; *) basic_machine=`echo $1 | sed 's/-[^-]*$//'` if [ $basic_machine != $1 ] then os=`echo $1 | sed 's/.*-/-/'` else os=; fi ;; esac ### Let's recognize common machines as not being operating systems so ### that things like config.sub decstation-3100 work. We also ### recognize some manufacturers as not being operating systems, so we ### can provide default operating systems below. case $os in -sun*os*) # Prevent following clause from handling this invalid input. ;; -dec* | -mips* | -sequent* | -encore* | -pc532* | -sgi* | -sony* | \ -att* | -7300* | -3300* | -delta* | -motorola* | -sun[234]* | \ -unicom* | -ibm* | -next | -hp | -isi* | -apollo | -altos* | \ -convergent* | -ncr* | -news | -32* | -3600* | -3100* | -hitachi* |\ -c[123]* | -convex* | -sun | -crds | -omron* | -dg | -ultra | -tti* | \ -harris | -dolphin | -highlevel | -gould | -cbm | -ns | -masscomp | \ -apple | -axis | -knuth | -cray | -microblaze) os= basic_machine=$1 ;; -bluegene*) os=-cnk ;; -sim | -cisco | -oki | -wec | -winbond) os= basic_machine=$1 ;; -scout) ;; -wrs) os=-vxworks basic_machine=$1 ;; -chorusos*) os=-chorusos basic_machine=$1 ;; -chorusrdb) os=-chorusrdb basic_machine=$1 ;; -hiux*) os=-hiuxwe2 ;; -sco6) os=-sco5v6 basic_machine=`echo $1 | sed -e 's/86-.*/86-pc/'` ;; -sco5) os=-sco3.2v5 basic_machine=`echo $1 | sed -e 's/86-.*/86-pc/'` ;; -sco4) os=-sco3.2v4 basic_machine=`echo $1 | sed -e 's/86-.*/86-pc/'` ;; -sco3.2.[4-9]*) os=`echo $os | sed -e 's/sco3.2./sco3.2v/'` basic_machine=`echo $1 | sed -e 's/86-.*/86-pc/'` ;; -sco3.2v[4-9]*) # Don't forget version if it is 3.2v4 or newer. basic_machine=`echo $1 | sed -e 's/86-.*/86-pc/'` ;; -sco5v6*) # Don't forget version if it is 3.2v4 or newer. basic_machine=`echo $1 | sed -e 's/86-.*/86-pc/'` ;; -sco*) os=-sco3.2v2 basic_machine=`echo $1 | sed -e 's/86-.*/86-pc/'` ;; -udk*) basic_machine=`echo $1 | sed -e 's/86-.*/86-pc/'` ;; -isc) os=-isc2.2 basic_machine=`echo $1 | sed -e 's/86-.*/86-pc/'` ;; -clix*) basic_machine=clipper-intergraph ;; -isc*) basic_machine=`echo $1 | sed -e 's/86-.*/86-pc/'` ;; -lynx*) os=-lynxos ;; -ptx*) basic_machine=`echo $1 | sed -e 's/86-.*/86-sequent/'` ;; -windowsnt*) os=`echo $os | sed -e 's/windowsnt/winnt/'` ;; -psos*) os=-psos ;; -mint | -mint[0-9]*) basic_machine=m68k-atari os=-mint ;; esac # Decode aliases for certain CPU-COMPANY combinations. case $basic_machine in # Recognize the basic CPU types without company name. # Some are omitted here because they have special meanings below. 1750a | 580 \ | a29k \ | alpha | alphaev[4-8] | alphaev56 | alphaev6[78] | alphapca5[67] \ | alpha64 | alpha64ev[4-8] | alpha64ev56 | alpha64ev6[78] | alpha64pca5[67] \ | am33_2.0 \ | arc | arm | arm[bl]e | arme[lb] | armv[2345] | armv[345][lb] | avr | avr32 \ | bfin \ | c4x | clipper \ | d10v | d30v | dlx | dsp16xx \ | fido | fr30 | frv \ | h8300 | h8500 | hppa | hppa1.[01] | hppa2.0 | hppa2.0[nw] | hppa64 \ | i370 | i860 | i960 | ia64 \ | ip2k | iq2000 \ | lm32 \ | m32c | m32r | m32rle | m68000 | m68k | m88k \ | maxq | mb | microblaze | mcore | mep | metag \ | mips | mipsbe | mipseb | mipsel | mipsle \ | mips16 \ | mips64 | mips64el \ | mips64octeon | mips64octeonel \ | mips64orion | mips64orionel \ | mips64r5900 | mips64r5900el \ | mips64vr | mips64vrel \ | mips64vr4100 | mips64vr4100el \ | mips64vr4300 | mips64vr4300el \ | mips64vr5000 | mips64vr5000el \ | mips64vr5900 | mips64vr5900el \ | mipsisa32 | mipsisa32el \ | mipsisa32r2 | mipsisa32r2el \ | mipsisa64 | mipsisa64el \ | mipsisa64r2 | mipsisa64r2el \ | mipsisa64sb1 | mipsisa64sb1el \ | mipsisa64sr71k | mipsisa64sr71kel \ | mipstx39 | mipstx39el \ | mn10200 | mn10300 \ | moxie \ | mt \ | msp430 \ | nios | nios2 \ | ns16k | ns32k \ | or32 \ | pdp10 | pdp11 | pj | pjl \ | powerpc | powerpc64 | powerpc64le | powerpcle | ppcbe \ | pyramid \ | rx \ | score \ | sh | sh[1234] | sh[24]a | sh[24]aeb | sh[23]e | sh[34]eb | sheb | shbe | shle | sh[1234]le | sh3ele \ | sh64 | sh64le \ | sparc | sparc64 | sparc64b | sparc64v | sparc86x | sparclet | sparclite \ | sparcv8 | sparcv9 | sparcv9b | sparcv9v \ | spu | strongarm \ | tahoe | thumb | tic4x | tic80 | tron \ | ubicom32 \ | v850 | v850e \ | we32k \ | x86 | xc16x | xscale | xscalee[bl] | xstormy16 | xtensa \ | z8k | z80) basic_machine=$basic_machine-unknown ;; m6811 | m68hc11 | m6812 | m68hc12 | picochip) # Motorola 68HC11/12. basic_machine=$basic_machine-unknown os=-none ;; m88110 | m680[12346]0 | m683?2 | m68360 | m5200 | v70 | w65 | z8k) ;; ms1) basic_machine=mt-unknown ;; # We use `pc' rather than `unknown' # because (1) that's what they normally are, and # (2) the word "unknown" tends to confuse beginning users. i*86 | x86_64) basic_machine=$basic_machine-pc ;; # Object if more than one company name word. *-*-*) echo Invalid configuration \`$1\': machine \`$basic_machine\' not recognized 1>&2 exit 1 ;; # Recognize the basic CPU types with company name. 580-* \ | a29k-* \ | alpha-* | alphaev[4-8]-* | alphaev56-* | alphaev6[78]-* \ | alpha64-* | alpha64ev[4-8]-* | alpha64ev56-* | alpha64ev6[78]-* \ | alphapca5[67]-* | alpha64pca5[67]-* | arc-* \ | arm-* | armbe-* | armle-* | armeb-* | armv*-* \ | avr-* | avr32-* \ | bfin-* | bs2000-* \ | c[123]* | c30-* | [cjt]90-* | c4x-* | c54x-* | c55x-* | c6x-* \ | clipper-* | craynv-* | cydra-* \ | d10v-* | d30v-* | dlx-* \ | elxsi-* \ | f30[01]-* | f700-* | fido-* | fr30-* | frv-* | fx80-* \ | h8300-* | h8500-* \ | hppa-* | hppa1.[01]-* | hppa2.0-* | hppa2.0[nw]-* | hppa64-* \ | i*86-* | i860-* | i960-* | ia64-* \ | ip2k-* | iq2000-* \ | lm32-* \ | m32c-* | m32r-* | m32rle-* \ | m68000-* | m680[012346]0-* | m68360-* | m683?2-* | m68k-* \ | m88110-* | m88k-* | maxq-* | mcore-* | metag-* | microblaze-* \ | mips-* | mipsbe-* | mipseb-* | mipsel-* | mipsle-* \ | mips16-* \ | mips64-* | mips64el-* \ | mips64octeon-* | mips64octeonel-* \ | mips64orion-* | mips64orionel-* \ | mips64r5900-* | mips64r5900el-* \ | mips64vr-* | mips64vrel-* \ | mips64vr4100-* | mips64vr4100el-* \ | mips64vr4300-* | mips64vr4300el-* \ | mips64vr5000-* | mips64vr5000el-* \ | mips64vr5900-* | mips64vr5900el-* \ | mipsisa32-* | mipsisa32el-* \ | mipsisa32r2-* | mipsisa32r2el-* \ | mipsisa64-* | mipsisa64el-* \ | mipsisa64r2-* | mipsisa64r2el-* \ | mipsisa64sb1-* | mipsisa64sb1el-* \ | mipsisa64sr71k-* | mipsisa64sr71kel-* \ | mipstx39-* | mipstx39el-* \ | mmix-* \ | mt-* \ | msp430-* \ | nios-* | nios2-* \ | none-* | np1-* | ns16k-* | ns32k-* \ | orion-* \ | pdp10-* | pdp11-* | pj-* | pjl-* | pn-* | power-* \ | powerpc-* | powerpc64-* | powerpc64le-* | powerpcle-* | ppcbe-* \ | pyramid-* \ | romp-* | rs6000-* | rx-* \ | sh-* | sh[1234]-* | sh[24]a-* | sh[24]aeb-* | sh[23]e-* | sh[34]eb-* | sheb-* | shbe-* \ | shle-* | sh[1234]le-* | sh3ele-* | sh64-* | sh64le-* \ | sparc-* | sparc64-* | sparc64b-* | sparc64v-* | sparc86x-* | sparclet-* \ | sparclite-* \ | sparcv8-* | sparcv9-* | sparcv9b-* | sparcv9v-* | strongarm-* | sv1-* | sx?-* \ | tahoe-* | thumb-* \ | tic30-* | tic4x-* | tic54x-* | tic55x-* | tic6x-* | tic80-* \ | tile-* | tilegx-* \ | tron-* \ | ubicom32-* \ | v850-* | v850e-* | vax-* \ | we32k-* \ | x86-* | x86_64-* | xc16x-* | xps100-* | xscale-* | xscalee[bl]-* \ | xstormy16-* | xtensa*-* \ | ymp-* \ | z8k-* | z80-*) ;; # Recognize the basic CPU types without company name, with glob match. xtensa*) basic_machine=$basic_machine-unknown ;; # Recognize the various machine names and aliases which stand # for a CPU type and a company and sometimes even an OS. 386bsd) basic_machine=i386-unknown os=-bsd ;; 3b1 | 7300 | 7300-att | att-7300 | pc7300 | safari | unixpc) basic_machine=m68000-att ;; 3b*) basic_machine=we32k-att ;; a29khif) basic_machine=a29k-amd os=-udi ;; abacus) basic_machine=abacus-unknown ;; adobe68k) basic_machine=m68010-adobe os=-scout ;; alliant | fx80) basic_machine=fx80-alliant ;; altos | altos3068) basic_machine=m68k-altos ;; am29k) basic_machine=a29k-none os=-bsd ;; amd64) basic_machine=x86_64-pc ;; amd64-*) basic_machine=x86_64-`echo $basic_machine | sed 's/^[^-]*-//'` ;; amdahl) basic_machine=580-amdahl os=-sysv ;; amiga | amiga-*) basic_machine=m68k-unknown ;; amigaos | amigados) basic_machine=m68k-unknown os=-amigaos ;; amigaunix | amix) basic_machine=m68k-unknown os=-sysv4 ;; apollo68) basic_machine=m68k-apollo os=-sysv ;; apollo68bsd) basic_machine=m68k-apollo os=-bsd ;; aros) basic_machine=i386-pc os=-aros ;; aux) basic_machine=m68k-apple os=-aux ;; balance) basic_machine=ns32k-sequent os=-dynix ;; blackfin) basic_machine=bfin-unknown os=-linux ;; blackfin-*) basic_machine=bfin-`echo $basic_machine | sed 's/^[^-]*-//'` os=-linux ;; bluegene*) basic_machine=powerpc-ibm os=-cnk ;; c90) basic_machine=c90-cray os=-unicos ;; cegcc) basic_machine=arm-unknown os=-cegcc ;; convex-c1) basic_machine=c1-convex os=-bsd ;; convex-c2) basic_machine=c2-convex os=-bsd ;; convex-c32) basic_machine=c32-convex os=-bsd ;; convex-c34) basic_machine=c34-convex os=-bsd ;; convex-c38) basic_machine=c38-convex os=-bsd ;; cray | j90) basic_machine=j90-cray os=-unicos ;; craynv) basic_machine=craynv-cray os=-unicosmp ;; cr16) basic_machine=cr16-unknown os=-elf ;; crds | unos) basic_machine=m68k-crds ;; crisv32 | crisv32-* | etraxfs*) basic_machine=crisv32-axis ;; cris | cris-* | etrax*) basic_machine=cris-axis ;; crx) basic_machine=crx-unknown os=-elf ;; da30 | da30-*) basic_machine=m68k-da30 ;; decstation | decstation-3100 | pmax | pmax-* | pmin | dec3100 | decstatn) basic_machine=mips-dec ;; decsystem10* | dec10*) basic_machine=pdp10-dec os=-tops10 ;; decsystem20* | dec20*) basic_machine=pdp10-dec os=-tops20 ;; delta | 3300 | motorola-3300 | motorola-delta \ | 3300-motorola | delta-motorola) basic_machine=m68k-motorola ;; delta88) basic_machine=m88k-motorola os=-sysv3 ;; dicos) basic_machine=i686-pc os=-dicos ;; djgpp) basic_machine=i586-pc os=-msdosdjgpp ;; dpx20 | dpx20-*) basic_machine=rs6000-bull os=-bosx ;; dpx2* | dpx2*-bull) basic_machine=m68k-bull os=-sysv3 ;; ebmon29k) basic_machine=a29k-amd os=-ebmon ;; elxsi) basic_machine=elxsi-elxsi os=-bsd ;; encore | umax | mmax) basic_machine=ns32k-encore ;; es1800 | OSE68k | ose68k | ose | OSE) basic_machine=m68k-ericsson os=-ose ;; fx2800) basic_machine=i860-alliant ;; genix) basic_machine=ns32k-ns ;; gmicro) basic_machine=tron-gmicro os=-sysv ;; go32) basic_machine=i386-pc os=-go32 ;; h3050r* | hiux*) basic_machine=hppa1.1-hitachi os=-hiuxwe2 ;; h8300hms) basic_machine=h8300-hitachi os=-hms ;; h8300xray) basic_machine=h8300-hitachi os=-xray ;; h8500hms) basic_machine=h8500-hitachi os=-hms ;; harris) basic_machine=m88k-harris os=-sysv3 ;; hp300-*) basic_machine=m68k-hp ;; hp300bsd) basic_machine=m68k-hp os=-bsd ;; hp300hpux) basic_machine=m68k-hp os=-hpux ;; hp3k9[0-9][0-9] | hp9[0-9][0-9]) basic_machine=hppa1.0-hp ;; hp9k2[0-9][0-9] | hp9k31[0-9]) basic_machine=m68000-hp ;; hp9k3[2-9][0-9]) basic_machine=m68k-hp ;; hp9k6[0-9][0-9] | hp6[0-9][0-9]) basic_machine=hppa1.0-hp ;; hp9k7[0-79][0-9] | hp7[0-79][0-9]) basic_machine=hppa1.1-hp ;; hp9k78[0-9] | hp78[0-9]) # FIXME: really hppa2.0-hp basic_machine=hppa1.1-hp ;; hp9k8[67]1 | hp8[67]1 | hp9k80[24] | hp80[24] | hp9k8[78]9 | hp8[78]9 | hp9k893 | hp893) # FIXME: really hppa2.0-hp basic_machine=hppa1.1-hp ;; hp9k8[0-9][13679] | hp8[0-9][13679]) basic_machine=hppa1.1-hp ;; hp9k8[0-9][0-9] | hp8[0-9][0-9]) basic_machine=hppa1.0-hp ;; hppa-next) os=-nextstep3 ;; hppaosf) basic_machine=hppa1.1-hp os=-osf ;; hppro) basic_machine=hppa1.1-hp os=-proelf ;; i370-ibm* | ibm*) basic_machine=i370-ibm ;; # I'm not sure what "Sysv32" means. Should this be sysv3.2? i*86v32) basic_machine=`echo $1 | sed -e 's/86.*/86-pc/'` os=-sysv32 ;; i*86v4*) basic_machine=`echo $1 | sed -e 's/86.*/86-pc/'` os=-sysv4 ;; i*86v) basic_machine=`echo $1 | sed -e 's/86.*/86-pc/'` os=-sysv ;; i*86sol2) basic_machine=`echo $1 | sed -e 's/86.*/86-pc/'` os=-solaris2 ;; i386mach) basic_machine=i386-mach os=-mach ;; i386-vsta | vsta) basic_machine=i386-unknown os=-vsta ;; iris | iris4d) basic_machine=mips-sgi case $os in -irix*) ;; *) os=-irix4 ;; esac ;; isi68 | isi) basic_machine=m68k-isi os=-sysv ;; m68knommu) basic_machine=m68k-unknown os=-linux ;; m68knommu-*) basic_machine=m68k-`echo $basic_machine | sed 's/^[^-]*-//'` os=-linux ;; m88k-omron*) basic_machine=m88k-omron ;; magnum | m3230) basic_machine=mips-mips os=-sysv ;; merlin) basic_machine=ns32k-utek os=-sysv ;; microblaze) basic_machine=microblaze-xilinx ;; mingw32) basic_machine=i386-pc os=-mingw32 ;; mingw32ce) basic_machine=arm-unknown os=-mingw32ce ;; miniframe) basic_machine=m68000-convergent ;; *mint | -mint[0-9]* | *MiNT | *MiNT[0-9]*) basic_machine=m68k-atari os=-mint ;; mips3*-*) basic_machine=`echo $basic_machine | sed -e 's/mips3/mips64/'` ;; mips3*) basic_machine=`echo $basic_machine | sed -e 's/mips3/mips64/'`-unknown ;; monitor) basic_machine=m68k-rom68k os=-coff ;; morphos) basic_machine=powerpc-unknown os=-morphos ;; msdos) basic_machine=i386-pc os=-msdos ;; ms1-*) basic_machine=`echo $basic_machine | sed -e 's/ms1-/mt-/'` ;; mvs) basic_machine=i370-ibm os=-mvs ;; ncr3000) basic_machine=i486-ncr os=-sysv4 ;; netbsd386) basic_machine=i386-unknown os=-netbsd ;; netwinder) basic_machine=armv4l-rebel os=-linux ;; news | news700 | news800 | news900) basic_machine=m68k-sony os=-newsos ;; news1000) basic_machine=m68030-sony os=-newsos ;; news-3600 | risc-news) basic_machine=mips-sony os=-newsos ;; necv70) basic_machine=v70-nec os=-sysv ;; next | m*-next ) basic_machine=m68k-next case $os in -nextstep* ) ;; -ns2*) os=-nextstep2 ;; *) os=-nextstep3 ;; esac ;; nh3000) basic_machine=m68k-harris os=-cxux ;; nh[45]000) basic_machine=m88k-harris os=-cxux ;; nindy960) basic_machine=i960-intel os=-nindy ;; mon960) basic_machine=i960-intel os=-mon960 ;; nonstopux) basic_machine=mips-compaq os=-nonstopux ;; np1) basic_machine=np1-gould ;; nsr-tandem) basic_machine=nsr-tandem ;; op50n-* | op60c-*) basic_machine=hppa1.1-oki os=-proelf ;; openrisc | openrisc-*) basic_machine=or32-unknown ;; os400) basic_machine=powerpc-ibm os=-os400 ;; OSE68000 | ose68000) basic_machine=m68000-ericsson os=-ose ;; os68k) basic_machine=m68k-none os=-os68k ;; pa-hitachi) basic_machine=hppa1.1-hitachi os=-hiuxwe2 ;; paragon) basic_machine=i860-intel os=-osf ;; parisc) basic_machine=hppa-unknown os=-linux ;; parisc-*) basic_machine=hppa-`echo $basic_machine | sed 's/^[^-]*-//'` os=-linux ;; pbd) basic_machine=sparc-tti ;; pbb) basic_machine=m68k-tti ;; pc532 | pc532-*) basic_machine=ns32k-pc532 ;; pc98) basic_machine=i386-pc ;; pc98-*) basic_machine=i386-`echo $basic_machine | sed 's/^[^-]*-//'` ;; pentium | p5 | k5 | k6 | nexgen | viac3) basic_machine=i586-pc ;; pentiumpro | p6 | 6x86 | athlon | athlon_*) basic_machine=i686-pc ;; pentiumii | pentium2 | pentiumiii | pentium3) basic_machine=i686-pc ;; pentium4) basic_machine=i786-pc ;; pentium-* | p5-* | k5-* | k6-* | nexgen-* | viac3-*) basic_machine=i586-`echo $basic_machine | sed 's/^[^-]*-//'` ;; pentiumpro-* | p6-* | 6x86-* | athlon-*) basic_machine=i686-`echo $basic_machine | sed 's/^[^-]*-//'` ;; pentiumii-* | pentium2-* | pentiumiii-* | pentium3-*) basic_machine=i686-`echo $basic_machine | sed 's/^[^-]*-//'` ;; pentium4-*) basic_machine=i786-`echo $basic_machine | sed 's/^[^-]*-//'` ;; pn) basic_machine=pn-gould ;; power) basic_machine=power-ibm ;; ppc) basic_machine=powerpc-unknown ;; ppc-*) basic_machine=powerpc-`echo $basic_machine | sed 's/^[^-]*-//'` ;; ppcle | powerpclittle | ppc-le | powerpc-little) basic_machine=powerpcle-unknown ;; ppcle-* | powerpclittle-*) basic_machine=powerpcle-`echo $basic_machine | sed 's/^[^-]*-//'` ;; ppc64) basic_machine=powerpc64-unknown ;; ppc64-*) basic_machine=powerpc64-`echo $basic_machine | sed 's/^[^-]*-//'` ;; ppc64le | powerpc64little | ppc64-le | powerpc64-little) basic_machine=powerpc64le-unknown ;; ppc64le-* | powerpc64little-*) basic_machine=powerpc64le-`echo $basic_machine | sed 's/^[^-]*-//'` ;; ps2) basic_machine=i386-ibm ;; pw32) basic_machine=i586-unknown os=-pw32 ;; rdos) basic_machine=i386-pc os=-rdos ;; rom68k) basic_machine=m68k-rom68k os=-coff ;; rm[46]00) basic_machine=mips-siemens ;; rtpc | rtpc-*) basic_machine=romp-ibm ;; s390 | s390-*) basic_machine=s390-ibm ;; s390x | s390x-*) basic_machine=s390x-ibm ;; sa29200) basic_machine=a29k-amd os=-udi ;; sb1) basic_machine=mipsisa64sb1-unknown ;; sb1el) basic_machine=mipsisa64sb1el-unknown ;; sde) basic_machine=mipsisa32-sde os=-elf ;; sei) basic_machine=mips-sei os=-seiux ;; sequent) basic_machine=i386-sequent ;; sh) basic_machine=sh-hitachi os=-hms ;; sh5el) basic_machine=sh5le-unknown ;; sh64) basic_machine=sh64-unknown ;; sparclite-wrs | simso-wrs) basic_machine=sparclite-wrs os=-vxworks ;; sps7) basic_machine=m68k-bull os=-sysv2 ;; spur) basic_machine=spur-unknown ;; st2000) basic_machine=m68k-tandem ;; stratus) basic_machine=i860-stratus os=-sysv4 ;; sun2) basic_machine=m68000-sun ;; sun2os3) basic_machine=m68000-sun os=-sunos3 ;; sun2os4) basic_machine=m68000-sun os=-sunos4 ;; sun3os3) basic_machine=m68k-sun os=-sunos3 ;; sun3os4) basic_machine=m68k-sun os=-sunos4 ;; sun4os3) basic_machine=sparc-sun os=-sunos3 ;; sun4os4) basic_machine=sparc-sun os=-sunos4 ;; sun4sol2) basic_machine=sparc-sun os=-solaris2 ;; sun3 | sun3-*) basic_machine=m68k-sun ;; sun4) basic_machine=sparc-sun ;; sun386 | sun386i | roadrunner) basic_machine=i386-sun ;; sv1) basic_machine=sv1-cray os=-unicos ;; symmetry) basic_machine=i386-sequent os=-dynix ;; t3e) basic_machine=alphaev5-cray os=-unicos ;; t90) basic_machine=t90-cray os=-unicos ;; tic54x | c54x*) basic_machine=tic54x-unknown os=-coff ;; tic55x | c55x*) basic_machine=tic55x-unknown os=-coff ;; tic6x | c6x*) basic_machine=tic6x-unknown os=-coff ;; # This must be matched before tile*. tilegx*) basic_machine=tilegx-unknown os=-linux-gnu ;; tile*) basic_machine=tile-unknown os=-linux-gnu ;; tx39) basic_machine=mipstx39-unknown ;; tx39el) basic_machine=mipstx39el-unknown ;; toad1) basic_machine=pdp10-xkl os=-tops20 ;; tower | tower-32) basic_machine=m68k-ncr ;; tpf) basic_machine=s390x-ibm os=-tpf ;; udi29k) basic_machine=a29k-amd os=-udi ;; ultra3) basic_machine=a29k-nyu os=-sym1 ;; v810 | necv810) basic_machine=v810-nec os=-none ;; vaxv) basic_machine=vax-dec os=-sysv ;; vms) basic_machine=vax-dec os=-vms ;; vpp*|vx|vx-*) basic_machine=f301-fujitsu ;; vxworks960) basic_machine=i960-wrs os=-vxworks ;; vxworks68) basic_machine=m68k-wrs os=-vxworks ;; vxworks29k) basic_machine=a29k-wrs os=-vxworks ;; w65*) basic_machine=w65-wdc os=-none ;; w89k-*) basic_machine=hppa1.1-winbond os=-proelf ;; xbox) basic_machine=i686-pc os=-mingw32 ;; xps | xps100) basic_machine=xps100-honeywell ;; ymp) basic_machine=ymp-cray os=-unicos ;; z8k-*-coff) basic_machine=z8k-unknown os=-sim ;; z80-*-coff) basic_machine=z80-unknown os=-sim ;; none) basic_machine=none-none os=-none ;; 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esac # Here we canonicalize certain aliases for manufacturers. case $basic_machine in *-digital*) basic_machine=`echo $basic_machine | sed 's/digital.*/dec/'` ;; *-commodore*) basic_machine=`echo $basic_machine | sed 's/commodore.*/cbm/'` ;; *) ;; esac # Decode manufacturer-specific aliases for certain operating systems. if [ x"$os" != x"" ] then case $os in # First match some system type aliases # that might get confused with valid system types. # -solaris* is a basic system type, with this one exception. -auroraux) os=-auroraux ;; -solaris1 | -solaris1.*) os=`echo $os | sed -e 's|solaris1|sunos4|'` ;; -solaris) os=-solaris2 ;; -svr4*) os=-sysv4 ;; -unixware*) os=-sysv4.2uw ;; -gnu/linux*) os=`echo $os | sed -e 's|gnu/linux|linux-gnu|'` ;; # First accept the basic system types. # The portable systems comes first. # Each alternative MUST END IN A *, to match a version number. # -sysv* is not here because it comes later, after sysvr4. -gnu* | -bsd* | -mach* | -minix* | -genix* | -ultrix* | -irix* \ | -*vms* | -sco* | -esix* | -isc* | -aix* | -cnk* | -sunos | -sunos[34]*\ | -hpux* | -unos* | -osf* | -luna* | -dgux* | -auroraux* | -solaris* \ | -sym* | -kopensolaris* \ | -amigaos* | -amigados* | -msdos* | -newsos* | -unicos* | -aof* \ | -aos* | -aros* \ | -nindy* | -vxsim* | -vxworks* | -ebmon* | -hms* | -mvs* \ | -clix* | -riscos* | -uniplus* | -iris* | -rtu* | -xenix* \ | -hiux* | -386bsd* | -knetbsd* | -mirbsd* | -netbsd* \ | -openbsd* | -solidbsd* \ | -ekkobsd* | -kfreebsd* | -freebsd* | -riscix* | -lynxos* \ | -bosx* | -nextstep* | -cxux* | -aout* | -elf* | -oabi* \ | -ptx* | -coff* | -ecoff* | -winnt* | -domain* | -vsta* \ | -udi* | -eabi* | -lites* | -ieee* | -go32* | -aux* \ | -chorusos* | -chorusrdb* | -cegcc* \ | -cygwin* | -pe* | -psos* | -moss* | -proelf* | -rtems* \ | -mingw32* | -linux-gnu* | -linux-newlib* | -linux-uclibc* \ | -uxpv* | -beos* | -mpeix* | -udk* \ | -interix* | -uwin* | -mks* | -rhapsody* | -darwin* | -opened* \ | -openstep* | -oskit* | -conix* | -pw32* | -nonstopux* \ | -storm-chaos* | -tops10* | -tenex* | -tops20* | -its* \ | -os2* | -vos* | -palmos* | -uclinux* | -nucleus* \ | -morphos* | -superux* | -rtmk* | -rtmk-nova* | -windiss* \ | -powermax* | -dnix* | -nx6 | -nx7 | -sei* | -dragonfly* \ | -skyos* | -haiku* | -rdos* | -toppers* | -drops* | -es*) # Remember, each alternative MUST END IN *, to match a version number. ;; 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