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C $Header: /u/gcmpack/MITgcm/pkg/admtlm/admtlm_dsvd.F,v 1.5 2005/11/01 04:09:46 heimbach Exp $ |
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C $Name: $ |
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|
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#include "CPP_OPTIONS.h" |
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|
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subroutine admtlm_dsvd ( mythid ) |
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c |
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c This example program is intended to illustrate the |
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c the use of ARPACK to compute the Singular Value Decomposition. |
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c |
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c This code shows how to use ARPACK to find a few of the |
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c largest singular values(sigma) and corresponding right singular |
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c vectors (v) for the the matrix A by solving the symmetric problem: |
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c |
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c (A'*A)*v = sigma*v |
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c |
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c where A is an m by n real matrix. |
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c |
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c This code may be easily modified to estimate the 2-norm |
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c condition number largest(sigma)/smallest(sigma) by setting |
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c which = 'BE' below. This will ask for a few of the smallest |
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c and a few of the largest singular values simultaneously. |
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c The condition number could then be estimated by taking |
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c the ratio of the largest and smallest singular values. |
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c |
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c This formulation is appropriate when m .ge. n. |
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c Reverse the roles of A and A' in the case that m .le. n. |
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c |
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c The main points illustrated here are |
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c |
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c 1) How to declare sufficient memory to find NEV |
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c largest singular values of A . |
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c |
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c 2) Illustration of the reverse communication interface |
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c needed to utilize the top level ARPACK routine DSAUPD |
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c that computes the quantities needed to construct |
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c the desired singular values and vectors(if requested). |
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c |
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c 3) How to extract the desired singular values and vectors |
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c using the ARPACK routine DSEUPD. |
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c |
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c 4) How to construct the left singular vectors U from the |
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c right singular vectors V to obtain the decomposition |
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c |
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c A*V = U*S |
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c |
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c where S = diag(sigma_1, sigma_2, ..., sigma_k). |
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c |
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c The only thing that must be supplied in order to use this |
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c routine on your problem is to change the array dimensions |
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c appropriately, to specify WHICH singular values you want to |
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c compute and to supply a the matrix-vector products |
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c |
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c w <- Ax |
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c y <- A'w |
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c |
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c in place of the calls to AV( ) and ATV( ) respectively below. |
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c |
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c Further documentation is available in the header of DSAUPD |
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c which may be found in the SRC directory. |
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c |
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c This codes implements |
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c |
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c\Example-1 |
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c ... Suppose we want to solve A'A*v = sigma*v in regular mode, |
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c where A is derived from the simplest finite difference |
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c discretization of the 2-dimensional kernel K(s,t)dt where |
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c |
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c K(s,t) = s(t-1) if 0 .le. s .le. t .le. 1, |
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c t(s-1) if 0 .le. t .lt. s .le. 1. |
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c |
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c See subroutines AV and ATV for details. |
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c ... OP = A'*A and B = I. |
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c ... Assume "call av (n,x,y)" computes y = A*x |
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c ... Assume "call atv (n,y,w)" computes w = A'*y |
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c ... Assume exact shifts are used |
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c ... |
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c |
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c\BeginLib |
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c |
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c\Routines called: |
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c dsaupd ARPACK reverse communication interface routine. |
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c dseupd ARPACK routine that returns Ritz values and (optionally) |
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c Ritz vectors. |
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c dnrm2 Level 1 BLAS that computes the norm of a vector. |
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c daxpy Level 1 BLAS that computes y <- alpha*x+y. |
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c dscal Level 1 BLAS thst computes x <- x*alpha. |
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c dcopy Level 1 BLAS thst computes y <- x. |
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c |
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c\Author |
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c Richard Lehoucq |
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c Danny Sorensen |
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c Chao Yang |
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c Dept. of Computational & |
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c Applied Mathematics |
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c Rice University |
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c Houston, Texas |
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c |
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c\SCCS Information: @(#) |
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c FILE: svd.F SID: 2.4 DATE OF SID: 10/17/00 RELEASE: 2 |
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c |
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c\Remarks |
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c 1. None |
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c |
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c\EndLib |
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c |
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c----------------------------------------------------------------------- |
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c |
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c %------------------------------------------------------% |
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c | Storage Declarations: | |
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c | | |
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c | It is assumed that A is M by N with M .ge. N. | |
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c | | |
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c | The maximum dimensions for all arrays are | |
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c | set here to accommodate a problem size of | |
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c | M .le. MAXM and N .le. MAXN | |
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c | | |
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c | The NEV right singular vectors will be computed in | |
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c | the N by NCV array V. | |
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c | | |
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c | The NEV left singular vectors will be computed in | |
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c | the M by NEV array U. | |
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c | | |
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c | NEV is the number of singular values requested. | |
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c | See specifications for ARPACK usage below. | |
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c | | |
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c | NCV is the largest number of basis vectors that will | |
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c | be used in the Implicitly Restarted Arnoldi | |
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c | Process. Work per major iteration is | |
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c | proportional to N*NCV*NCV. | |
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c | | |
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c | You must set: | |
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c | | |
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c | MAXM: Maximum number of rows of the A allowed. | |
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c | MAXN: Maximum number of columns of the A allowed. | |
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c | MAXNEV: Maximum NEV allowed | |
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c | MAXNCV: Maximum NCV allowed | |
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c %------------------------------------------------------% |
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c |
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C !USES: |
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C == Global variables === |
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#include "SIZE.h" |
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#include "EEPARAMS.h" |
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#include "PARAMS.h" |
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#ifdef ALLOW_ADMTLM |
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# include "tamc.h" |
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# include "ctrl.h" |
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# include "optim.h" |
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# include "cost.h" |
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# include "adcost.h" |
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# include "g_cost.h" |
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#endif |
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|
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C !INPUT/OUTPUT PARAMETERS: |
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C == Routine arguments == |
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INTEGER mythid |
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|
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C == PARAMETERS == |
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integer maxnev, maxncv, ldv, ldu |
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cph( |
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parameter ( maxnev=15, maxncv=30, ldu = maxm, ldv=maxn ) |
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character*(80) fnameGlobal |
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cph) |
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c |
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c %--------------% |
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c | Local Arrays | |
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c %--------------% |
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c |
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Double precision |
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& v(ldv,maxncv), u(ldu, maxnev), |
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& workl(maxncv*(maxncv+8)), workd(3*maxn), |
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& s(maxncv,2), resid(maxn), ax(maxm) |
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logical select(maxncv) |
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integer iparam(11), ipntr(11) |
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c |
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c %---------------% |
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c | Local Scalars | |
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c %---------------% |
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c |
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character bmat*1, which*2 |
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integer ido, m, n, nev, ncv, lworkl, info, ierr, |
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& j, ishfts, maxitr, mode, nconv |
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logical rvec |
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Double precision |
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& tol, sigma, temp |
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c |
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c %------------% |
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c | Parameters | |
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c %------------% |
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c |
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Double precision |
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& one, zero |
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parameter (one = 1.0D+0, zero = 0.0D+0) |
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c |
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c %-----------------------------% |
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c | BLAS & LAPACK routines used | |
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c %-----------------------------% |
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c |
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Double precision |
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& dnrm2 |
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external dnrm2, daxpy, dcopy, dscal |
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|
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cph( |
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integer l, ilinsysinfo, ii, jj |
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integer ipiv(maxn) |
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integer phiwork(maxn) |
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|
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double precision ferr, berr |
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double precision phtmpin(maxn), phtmpout(maxn) |
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double precision phxout(maxn) |
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double precision tmpvec1(maxn), tmpvec2(maxn) |
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double precision phrwork(3*maxn) |
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cph double precision metricLoc(maxn,maxn) |
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cph double precision metricTriag(maxn,maxn) |
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cph double precision metricInv(maxn,maxn) |
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|
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cph DATA (metricInv(ii,1),ii=1,maxn) |
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cph & / 9.9896D+07, 0.0519D+07, -0.0415D+07, |
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cph & 0.0486D+07, -0.2432D+07, 0.1945D+07 / |
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cph DATA (metricInv(ii,2),ii=1,maxn) |
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cph & / 0.0519D+07, 9.7403D+07, 0.2077D+07, |
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cph & -0.2432D+07, 1.2158D+07, -0.9726D+07 / |
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cph DATA (metricInv(ii,3),ii=1,maxn) |
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cph & / -0.0415D+07, 0.2077D+07, 9.8338D+07, |
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cph & 0.1945D+07, -0.9726D+07, 0.7781D+07 / |
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cph DATA (metricInv(ii,4),ii=1,maxn) |
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cph & / 0.0486D+07, -0.2432D+07, 0.1945D+07, |
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cph & 9.7723D+07, 1.1385D+07, -0.9108D+07 / |
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cph DATA (metricInv(ii,5),ii=1,maxn) |
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cph & / -0.2432D+07, 1.2158D+07, -0.9726D+07, |
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cph & 1.1385D+07, 4.3073D+07, 4.5542D+07 / |
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cph DATA (metricInv(ii,6),ii=1,maxn) |
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cph & / 0.1945D+07, -0.9726D+07, 0.7781D+07, |
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cph & -0.9108D+07, 4.5542D+07, 6.3567D+07 / |
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cph) |
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c |
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c %-----------------------% |
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c | Executable Statements | |
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c %-----------------------% |
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c |
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c %-------------------------------------------------% |
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c | The following include statement and assignments | |
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c | initiate trace output from the internal | |
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c | actions of ARPACK. See debug.doc in the | |
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c | DOCUMENTS directory for usage. Initially, the | |
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c | most useful information will be a breakdown of | |
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c | time spent in the various stages of computation | |
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c | given by setting msaupd = 1. | |
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c %-------------------------------------------------% |
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c |
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include 'arpack_debug.h' |
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ndigit = -3 |
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logfil = 6 |
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msgets = 0 |
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msaitr = 0 |
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msapps = 0 |
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msaupd = 1 |
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msaup2 = 0 |
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mseigt = 0 |
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mseupd = 0 |
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c |
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c %-------------------------------------------------% |
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c | The following sets dimensions for this problem. | |
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c %-------------------------------------------------% |
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c |
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cph( |
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m = admtlmrec |
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n = admtlmrec |
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cph) |
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c |
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c %------------------------------------------------% |
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c | Specifications for ARPACK usage are set | |
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c | below: | |
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c | | |
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c | 1) NEV = 4 asks for 4 singular values to be | |
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c | computed. | |
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c | | |
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c | 2) NCV = 20 sets the length of the Arnoldi | |
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c | factorization | |
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c | | |
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c | 3) This is a standard problem | |
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c | (indicated by bmat = 'I') | |
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c | | |
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c | 4) Ask for the NEV singular values of | |
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c | largest magnitude | |
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c | (indicated by which = 'LM') | |
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c | See documentation in DSAUPD for the | |
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c | other options SM, BE. | |
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c | | |
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c | Note: NEV and NCV must satisfy the following | |
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c | conditions: | |
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c | NEV <= MAXNEV, | |
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c | NEV + 1 <= NCV <= MAXNCV | |
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c %------------------------------------------------% |
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c |
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cph( |
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nev = 15 |
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ncv = 30 |
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bmat = 'I' |
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cph) |
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which = 'LM' |
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c |
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if ( n .gt. maxn ) then |
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print *, ' ERROR with _SVD: N is greater than MAXN ' |
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go to 9000 |
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else if ( m .gt. maxm ) then |
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print *, ' ERROR with _SVD: M is greater than MAXM ' |
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go to 9000 |
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else if ( nev .gt. maxnev ) then |
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print *, ' ERROR with _SVD: NEV is greater than MAXNEV ' |
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go to 9000 |
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else if ( ncv .gt. maxncv ) then |
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print *, ' ERROR with _SVD: NCV is greater than MAXNCV ' |
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go to 9000 |
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end if |
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c |
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c %-----------------------------------------------------% |
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c | Specification of stopping rules and initial | |
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c | conditions before calling DSAUPD | |
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c | | |
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c | abs(sigmaC - sigmaT) < TOL*abs(sigmaC) | |
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c | computed true | |
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c | | |
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c | If TOL .le. 0, then TOL <- macheps | |
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c | (machine precision) is used. | |
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c | | |
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c | IDO is the REVERSE COMMUNICATION parameter | |
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c | used to specify actions to be taken on return | |
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c | from DSAUPD. (See usage below.) | |
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c | | |
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c | It MUST initially be set to 0 before the first | |
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c | call to DSAUPD. | |
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c | | |
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c | INFO on entry specifies starting vector information | |
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c | and on return indicates error codes | |
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c | | |
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c | Initially, setting INFO=0 indicates that a | |
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c | random starting vector is requested to | |
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c | start the ARNOLDI iteration. Setting INFO to | |
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c | a nonzero value on the initial call is used | |
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c | if you want to specify your own starting | |
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c | vector (This vector must be placed in RESID.) | |
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c | | |
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c | The work array WORKL is used in DSAUPD as | |
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c | workspace. Its dimension LWORKL is set as | |
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c | illustrated below. | |
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c %-----------------------------------------------------% |
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c |
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lworkl = ncv*(ncv+8) |
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cph( |
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tol = zero |
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cph tol = 1.D-10 |
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cph) |
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info = 0 |
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ido = 0 |
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c |
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c %---------------------------------------------------% |
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c | Specification of Algorithm Mode: | |
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c | | |
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c | This program uses the exact shift strategy | |
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c | (indicated by setting IPARAM(1) = 1.) | |
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c | IPARAM(3) specifies the maximum number of Arnoldi | |
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c | iterations allowed. Mode 1 of DSAUPD is used | |
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c | (IPARAM(7) = 1). All these options can be changed | |
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c | by the user. For details see the documentation in | |
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c | DSAUPD. | |
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c %---------------------------------------------------% |
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c |
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ishfts = 1 |
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cph( |
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maxitr = 10 |
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c maxitr = 5 |
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c |
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mode = 1 |
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cph) |
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iparam(1) = ishfts |
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c |
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iparam(3) = maxitr |
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c |
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iparam(7) = mode |
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c |
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c %------------------------------------------------% |
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c | M A I N L O O P (Reverse communication loop) | |
| 384 |
c %------------------------------------------------% |
| 385 |
c |
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C-- Set model configuration (fixed arrays) |
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CALL INITIALISE_FIXED( myThid ) |
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c |
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10 continue |
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c |
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print *, 'ph----------------------------------------------------' |
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print *, 'ph----------------------------------------------------' |
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print *, 'ph----------------------------------------------------' |
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c |
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c %---------------------------------------------% |
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c | Repeatedly call the routine DSAUPD and take | |
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c | actions indicated by parameter IDO until | |
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c | either convergence is indicated or maxitr | |
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c | has been exceeded. | |
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c %---------------------------------------------% |
| 401 |
c |
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ctest( |
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CALL DSAUPD ( ido, bmat, n, which, nev, tol, resid, |
| 404 |
& ncv, v, ldv, iparam, ipntr, workd, workl, |
| 405 |
& lworkl, info ) |
| 406 |
ctest ido = -1 |
| 407 |
ctest) |
| 408 |
c |
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cph( |
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print *, 'ph-count: optimcycle, ido, info, ipntr(1) ', |
| 411 |
& optimcycle, ido, info, ipntr(1) |
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cph) |
| 413 |
|
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if (ido .eq. -1 .or. ido .eq. 1) then |
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c |
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c %---------------------------------------% |
| 417 |
c | Perform matrix vector multiplications | |
| 418 |
c | w <--- A*x (av()) | |
| 419 |
c | y <--- A'*w (atv()) | |
| 420 |
c | The user should supply his/her own | |
| 421 |
c | matrix vector multiplication routines | |
| 422 |
c | here that takes workd(ipntr(1)) as | |
| 423 |
c | the input, and returns the result in | |
| 424 |
c | workd(ipntr(2)). | |
| 425 |
c %---------------------------------------% |
| 426 |
c |
| 427 |
c call av (m, n, workd(ipntr(1)), ax) |
| 428 |
c call atv (m, n, ax, workd(ipntr(2))) |
| 429 |
c |
| 430 |
cph( |
| 431 |
c do l = 1, n |
| 432 |
c print *, 'ph-test A ', l, |
| 433 |
c & workd(ipntr(1)+l), workd(ipntr(2)+l), workd(l) |
| 434 |
c enddo |
| 435 |
cph) |
| 436 |
do l = 1, n |
| 437 |
phtmpadmtlm(l) = workd(ipntr(1)+l-1) |
| 438 |
enddo |
| 439 |
|
| 440 |
IF (optimcycle .GT. 0 ) THEN |
| 441 |
_BEGIN_MASTER( mythid ) |
| 442 |
IF ( myProcId .eq. 0 ) THEN |
| 443 |
call admtlm_dsvd2model( .FALSE., mythid ) |
| 444 |
ENDIF |
| 445 |
_END_MASTER( mythid ) |
| 446 |
cph CALL ADMTLM_UPXX( mythid ) |
| 447 |
ENDIF |
| 448 |
|
| 449 |
c-- MWMWMWMWMWMWMW |
| 450 |
CALL ADMTLM_DRIVER( mythid ) |
| 451 |
c-- MWMWMWMWMWMWMW |
| 452 |
|
| 453 |
_BEGIN_MASTER( mythid ) |
| 454 |
IF ( myProcId .eq. 0 ) THEN |
| 455 |
call admtlm_model2dsvd( .FALSE., mythid ) |
| 456 |
ENDIF |
| 457 |
_END_MASTER( mythid ) |
| 458 |
|
| 459 |
do l = 1, n |
| 460 |
workd(ipntr(2)+l-1) = phtmpadmtlm(l) |
| 461 |
enddo |
| 462 |
c |
| 463 |
|
| 464 |
if (optimcycle .EQ. 4) |
| 465 |
& STOP 'in ADMTLM_DSVD after the_model_main' |
| 466 |
|
| 467 |
cph( |
| 468 |
cph Since we solve for a generalized EV problem, we have to solve |
| 469 |
cph M*y=A*x for y with known matrix M and vector A*x |
| 470 |
c do ii = 1, n |
| 471 |
c phxout(ii) = 0. |
| 472 |
c do jj = 1, n |
| 473 |
c phxout(ii) = phxout(ii) + |
| 474 |
c & metricInv(ii,jj)*phtmpout(jj) |
| 475 |
c enddo |
| 476 |
c print *, 'ph-test C ', ii, phxout(ii) |
| 477 |
c enddo |
| 478 |
c |
| 479 |
c call dposvx ( |
| 480 |
c & 'E', 'U', maxn, 1, metricLoc, 6, metricTriag, 6, |
| 481 |
c & 'N', tmpvec1, phtmpout, 6, phxout, 6, tmpvec2, |
| 482 |
c & ferr, berr, phrwork, phiwork, ilinsysinfo) |
| 483 |
cph |
| 484 |
c call dgesv ( maxn, 1, metricLoc, maxn, |
| 485 |
c & ipiv, phtmpout, maxn, ilinsysinfo ) |
| 486 |
cph |
| 487 |
c |
| 488 |
cph Finally schift result y -> workd(ipntr(2)) |
| 489 |
cph call dcopy ( maxn, tmpvec1, 1, workd(ipntr(2)), 1 ) |
| 490 |
cph We have restored orig. standard EV problem |
| 491 |
cph OP*x = lambda*x for OP = INV(M)*A |
| 492 |
cph) |
| 493 |
c |
| 494 |
c %-----------------------------------------% |
| 495 |
c | L O O P B A C K to call DSAUPD again. | |
| 496 |
c %-----------------------------------------% |
| 497 |
c |
| 498 |
optimcycle = optimcycle + 1 |
| 499 |
|
| 500 |
go to 10 |
| 501 |
c |
| 502 |
end if |
| 503 |
c |
| 504 |
cph( |
| 505 |
1001 continue |
| 506 |
print *, 'ph-continue ', info, ierr |
| 507 |
cph) |
| 508 |
c |
| 509 |
c %----------------------------------------% |
| 510 |
c | Either we have convergence or there is | |
| 511 |
c | an error. | |
| 512 |
c %----------------------------------------% |
| 513 |
c |
| 514 |
if ( info .lt. 0 ) then |
| 515 |
c |
| 516 |
c %--------------------------% |
| 517 |
c | Error message. Check the | |
| 518 |
c | documentation in DSAUPD. | |
| 519 |
c %--------------------------% |
| 520 |
c |
| 521 |
print *, ' ' |
| 522 |
print *, ' Error with _saupd, info = ', info |
| 523 |
print *, ' Check documentation in _saupd ' |
| 524 |
print *, ' ' |
| 525 |
c |
| 526 |
else |
| 527 |
c |
| 528 |
c %--------------------------------------------% |
| 529 |
c | No fatal errors occurred. | |
| 530 |
c | Post-Process using DSEUPD. | |
| 531 |
c | | |
| 532 |
c | Computed singular values may be extracted. | |
| 533 |
c | | |
| 534 |
c | Singular vectors may also be computed now | |
| 535 |
c | if desired. (indicated by rvec = .true.) | |
| 536 |
c | | |
| 537 |
c | The routine DSEUPD now called to do this | |
| 538 |
c | post processing | |
| 539 |
c %--------------------------------------------% |
| 540 |
c |
| 541 |
rvec = .true. |
| 542 |
c |
| 543 |
call dseupd ( rvec, 'All', select, s, v, ldv, sigma, |
| 544 |
& bmat, n, which, nev, tol, resid, ncv, v, ldv, |
| 545 |
& iparam, ipntr, workd, workl, lworkl, ierr ) |
| 546 |
c |
| 547 |
c %-----------------------------------------------% |
| 548 |
c | Singular values are returned in the first | |
| 549 |
c | column of the two dimensional array S | |
| 550 |
c | and the corresponding right singular vectors | |
| 551 |
c | are returned in the first NEV columns of the | |
| 552 |
c | two dimensional array V as requested here. | |
| 553 |
c %-----------------------------------------------% |
| 554 |
c |
| 555 |
if ( ierr .ne. 0) then |
| 556 |
c |
| 557 |
c %------------------------------------% |
| 558 |
c | Error condition: | |
| 559 |
c | Check the documentation of DSEUPD. | |
| 560 |
c %------------------------------------% |
| 561 |
c |
| 562 |
print *, ' ' |
| 563 |
print *, ' Error with _seupd, info = ', ierr |
| 564 |
print *, ' Check the documentation of _seupd. ' |
| 565 |
print *, ' ' |
| 566 |
c |
| 567 |
else |
| 568 |
c |
| 569 |
nconv = iparam(5) |
| 570 |
cph( |
| 571 |
do j=1, nconv |
| 572 |
print *, 'ph-ev ', j, s(j,1), s(j,2) |
| 573 |
enddo |
| 574 |
|
| 575 |
STOP 'TEST AFTER dneupd' |
| 576 |
cph) |
| 577 |
do 20 j=1, nconv |
| 578 |
c |
| 579 |
s(j,1) = sqrt(s(j,1)) |
| 580 |
c |
| 581 |
c %-----------------------------% |
| 582 |
c | Compute the left singular | |
| 583 |
c | vectors from the formula | |
| 584 |
c | | |
| 585 |
c | u = Av/sigma | |
| 586 |
c | | |
| 587 |
c | u should have norm 1 so | |
| 588 |
c | divide by norm(Av) instead. | |
| 589 |
c %-----------------------------% |
| 590 |
c |
| 591 |
do l = 1, n |
| 592 |
tmpvec1(l) = v(l,j) |
| 593 |
enddo |
| 594 |
|
| 595 |
c |
| 596 |
c-- MWMWMWMWMWMWMW |
| 597 |
cph call box_main( tmpvec1, tmpvec2, metricLoc, ldoadjoint ) |
| 598 |
c-- MWMWMWMWMWMWMW |
| 599 |
c |
| 600 |
call dcopy( m, tmpvec2, 1, u(l,j), 1 ) |
| 601 |
temp = one / dnrm2( m, u(l,j), 1 ) |
| 602 |
cph( |
| 603 |
print *, 'ph-print ', j, dnrm2( m, u(l,j), 1 ) |
| 604 |
cph) |
| 605 |
call dscal(m , temp, u(l,j), 1 ) |
| 606 |
|
| 607 |
cph do l = 1, n |
| 608 |
cph u(l,j) = tmpvec2(l) |
| 609 |
cph enddo |
| 610 |
cph temp = one/dnrm2(m, tmpvec2, 1) |
| 611 |
cph call dscal(m, temp, tmpvec2, 1) |
| 612 |
c |
| 613 |
c %---------------------------% |
| 614 |
c | | |
| 615 |
c | Compute the residual norm | |
| 616 |
c | | |
| 617 |
c | || A*v - sigma*u || | |
| 618 |
c | | |
| 619 |
c | for the NCONV accurately | |
| 620 |
c | computed singular values | |
| 621 |
c | and vectors. (iparam(5) | |
| 622 |
c | indicates how many are | |
| 623 |
c | accurate to the requested | |
| 624 |
c | tolerance). | |
| 625 |
c | Store the result in 2nd | |
| 626 |
c | column of array S. | |
| 627 |
c %---------------------------% |
| 628 |
c |
| 629 |
call daxpy(m, -s(j,1), u(1,j), 1, tmpvec2, 1) |
| 630 |
s(j,2) = dnrm2(m, tmpvec2, 1) |
| 631 |
c |
| 632 |
20 continue |
| 633 |
c |
| 634 |
c %-------------------------------% |
| 635 |
c | Display computed residuals | |
| 636 |
c %-------------------------------% |
| 637 |
c |
| 638 |
call dmout(6, nconv, 2, s, maxncv, -6, |
| 639 |
& 'Singular values and direct residuals') |
| 640 |
end if |
| 641 |
c |
| 642 |
c %------------------------------------------% |
| 643 |
c | Print additional convergence information | |
| 644 |
c %------------------------------------------% |
| 645 |
c |
| 646 |
if ( info .eq. 1) then |
| 647 |
print *, ' ' |
| 648 |
print *, ' Maximum number of iterations reached.' |
| 649 |
print *, ' ' |
| 650 |
else if ( info .eq. 3) then |
| 651 |
print *, ' ' |
| 652 |
print *, ' No shifts could be applied during implicit', |
| 653 |
& ' Arnoldi update, try increasing NCV.' |
| 654 |
print *, ' ' |
| 655 |
end if |
| 656 |
c |
| 657 |
print *, ' ' |
| 658 |
print *, ' _SVD ' |
| 659 |
print *, ' ==== ' |
| 660 |
print *, ' ' |
| 661 |
print *, ' Size of the matrix is ', n |
| 662 |
print *, ' The number of Ritz values requested is ', nev |
| 663 |
print *, ' The number of Arnoldi vectors generated', |
| 664 |
& ' (NCV) is ', ncv |
| 665 |
print *, ' What portion of the spectrum: ', which |
| 666 |
print *, ' The number of converged Ritz values is ', |
| 667 |
& nconv |
| 668 |
print *, ' The number of Implicit Arnoldi update', |
| 669 |
& ' iterations taken is ', iparam(3) |
| 670 |
print *, ' The number of OP*x is ', iparam(9) |
| 671 |
print *, ' The convergence criterion is ', tol |
| 672 |
print *, ' ' |
| 673 |
c |
| 674 |
end if |
| 675 |
c |
| 676 |
c %-------------------------% |
| 677 |
c | Done with program dsvd. | |
| 678 |
c %-------------------------% |
| 679 |
c |
| 680 |
9000 continue |
| 681 |
c |
| 682 |
end |
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