Date: 2021-02-01T14:42:06+00:00

Actual source code: cyclic.c
slepc-3.14.2 2021-02-01
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2020, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.
      7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
      8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      9: */
     10: /*
     11:    SLEPc singular value solver: "cyclic"

     13:    Method: Uses a Hermitian eigensolver for H(A) = [ 0  A ; A^T 0 ]
     14: */

     16: #include <slepc/private/svdimpl.h>
     17: #include <slepc/private/epsimpl.h>
     18: #include "cyclic.h"

     20: static PetscErrorCode MatMult_Cyclic(Mat B,Vec x,Vec y)
     21: {
     22:   PetscErrorCode    ierr;
     23:   SVD               svd;
     24:   SVD_CYCLIC        *cyclic;
     25:   const PetscScalar *px;
     26:   PetscScalar       *py;
     27:   PetscInt          m;

     30:   MatShellGetContext(B,(void**)&svd);
     31:   cyclic = (SVD_CYCLIC*)svd->data;
     32:   SVDMatGetLocalSize(svd,&m,NULL);
     33:   VecGetArrayRead(x,&px);
     34:   VecGetArray(y,&py);
     35:   VecPlaceArray(cyclic->x1,px);
     36:   VecPlaceArray(cyclic->x2,px+m);
     37:   VecPlaceArray(cyclic->y1,py);
     38:   VecPlaceArray(cyclic->y2,py+m);
     39:   SVDMatMult(svd,PETSC_FALSE,cyclic->x2,cyclic->y1);
     40:   SVDMatMult(svd,PETSC_TRUE,cyclic->x1,cyclic->y2);
     41:   VecResetArray(cyclic->x1);
     42:   VecResetArray(cyclic->x2);
     43:   VecResetArray(cyclic->y1);
     44:   VecResetArray(cyclic->y2);
     45:   VecRestoreArrayRead(x,&px);
     46:   VecRestoreArray(y,&py);
     47:   return(0);
     48: }

     50: static PetscErrorCode MatGetDiagonal_Cyclic(Mat B,Vec diag)
     51: {

     55:   VecSet(diag,0.0);
     56:   return(0);
     57: }

     59: PetscErrorCode SVDSetUp_Cyclic(SVD svd)
     60: {
     61:   PetscErrorCode    ierr;
     62:   SVD_CYCLIC        *cyclic = (SVD_CYCLIC*)svd->data;
     63:   PetscInt          M,N,m,n,i,isl,Istart,Iend;
     64:   const PetscScalar *isa;
     65:   PetscScalar       *va;
     66:   PetscBool         trackall,issinv;
     67:   Vec               v;
     68:   Mat               Zm,Zn;
     69:   ST                st;
     70: #if defined(PETSC_HAVE_CUDA)
     71:   PetscBool         cuda;
     72: #endif

     75:   SVDMatGetSize(svd,&M,&N);
     76:   SVDMatGetLocalSize(svd,&m,&n);
     77:   if (!cyclic->mat) {
     78:     if (cyclic->explicitmatrix) {
     79:       if (!svd->A || !svd->AT) SETERRQ(PetscObjectComm((PetscObject)svd),PETSC_ERR_SUP,"Cannot use explicit cyclic matrix with implicit transpose");
     80:       MatCreate(PetscObjectComm((PetscObject)svd),&Zm);
     81:       MatSetSizes(Zm,m,m,M,M);
     82:       MatSetFromOptions(Zm);
     83:       MatSetUp(Zm);
     84:       MatGetOwnershipRange(Zm,&Istart,&Iend);
     85:       for (i=Istart;i<Iend;i++) {
     86:         MatSetValue(Zm,i,i,0.0,INSERT_VALUES);
     87:       }
     88:       MatAssemblyBegin(Zm,MAT_FINAL_ASSEMBLY);
     89:       MatAssemblyEnd(Zm,MAT_FINAL_ASSEMBLY);
     90:       MatCreate(PetscObjectComm((PetscObject)svd),&Zn);
     91:       MatSetSizes(Zn,n,n,N,N);
     92:       MatSetFromOptions(Zn);
     93:       MatSetUp(Zn);
     94:       MatGetOwnershipRange(Zn,&Istart,&Iend);
     95:       for (i=Istart;i<Iend;i++) {
     96:         MatSetValue(Zn,i,i,0.0,INSERT_VALUES);
     97:       }
     98:       MatAssemblyBegin(Zn,MAT_FINAL_ASSEMBLY);
     99:       MatAssemblyEnd(Zn,MAT_FINAL_ASSEMBLY);
    100:       MatCreateTile(1.0,Zm,1.0,svd->A,1.0,svd->AT,1.0,Zn,&cyclic->mat);
    101:       PetscLogObjectParent((PetscObject)svd,(PetscObject)cyclic->mat);
    102:       MatDestroy(&Zm);
    103:       MatDestroy(&Zn);
    104:     } else {
    105:       SVDMatCreateVecsEmpty(svd,&cyclic->x2,&cyclic->x1);
    106:       SVDMatCreateVecsEmpty(svd,&cyclic->y2,&cyclic->y1);
    107:       PetscLogObjectParent((PetscObject)svd,(PetscObject)cyclic->x1);
    108:       PetscLogObjectParent((PetscObject)svd,(PetscObject)cyclic->x2);
    109:       PetscLogObjectParent((PetscObject)svd,(PetscObject)cyclic->y1);
    110:       PetscLogObjectParent((PetscObject)svd,(PetscObject)cyclic->y2);
    111:       MatCreateShell(PetscObjectComm((PetscObject)svd),m+n,m+n,M+N,M+N,svd,&cyclic->mat);
    112:       MatShellSetOperation(cyclic->mat,MATOP_GET_DIAGONAL,(void(*)(void))MatGetDiagonal_Cyclic);
    113: #if defined(PETSC_HAVE_CUDA)
    114:       PetscObjectTypeCompareAny((PetscObject)(svd->A?svd->A:svd->AT),&cuda,MATSEQAIJCUSPARSE,MATMPIAIJCUSPARSE,"");
    115:       if (cuda) {
    116:         MatShellSetOperation(cyclic->mat,MATOP_CREATE_VECS,(void(*)(void))MatCreateVecs_Cyclic_CUDA);
    117:         MatShellSetOperation(cyclic->mat,MATOP_MULT,(void(*)(void))MatMult_Cyclic_CUDA);
    118:       } else
    119: #endif
    120:       {
    121:         MatShellSetOperation(cyclic->mat,MATOP_MULT,(void(*)(void))MatMult_Cyclic);
    122:       }
    123:     }
    124:     PetscLogObjectParent((PetscObject)svd,(PetscObject)cyclic->mat);
    125:   }

    127:   if (!cyclic->eps) { SVDCyclicGetEPS(svd,&cyclic->eps); }
    128:   EPSSetOperators(cyclic->eps,cyclic->mat,NULL);
    129:   EPSSetProblemType(cyclic->eps,EPS_HEP);
    130:   if (!cyclic->usereps) {
    131:     if (svd->which == SVD_LARGEST) {
    132:       EPSGetST(cyclic->eps,&st);
    133:       PetscObjectTypeCompare((PetscObject)st,STSINVERT,&issinv);
    134:       if (issinv) {
    135:         EPSSetWhichEigenpairs(cyclic->eps,EPS_TARGET_MAGNITUDE);
    136:       } else {
    137:         EPSSetWhichEigenpairs(cyclic->eps,EPS_LARGEST_REAL);
    138:       }
    139:     } else {
    140:       EPSSetEigenvalueComparison(cyclic->eps,SlepcCompareSmallestPosReal,NULL);
    141:       EPSSetTarget(cyclic->eps,0.0);
    142:     }
    143:     EPSSetDimensions(cyclic->eps,svd->nsv,svd->ncv,svd->mpd);
    144:     EPSSetTolerances(cyclic->eps,svd->tol==PETSC_DEFAULT?SLEPC_DEFAULT_TOL/10.0:svd->tol,svd->max_it);
    145:     switch (svd->conv) {
    146:     case SVD_CONV_ABS:
    147:       EPSSetConvergenceTest(cyclic->eps,EPS_CONV_ABS);break;
    148:     case SVD_CONV_REL:
    149:       EPSSetConvergenceTest(cyclic->eps,EPS_CONV_REL);break;
    150:     case SVD_CONV_USER:
    151:       SETERRQ(PetscObjectComm((PetscObject)svd),PETSC_ERR_SUP,"User-defined convergence test not supported in this solver");
    152:     }
    153:   }
    154:   SVDCheckUnsupported(svd,SVD_FEATURE_STOPPING);
    155:   /* Transfer the trackall option from svd to eps */
    156:   SVDGetTrackAll(svd,&trackall);
    157:   EPSSetTrackAll(cyclic->eps,trackall);
    158:   /* Transfer the initial subspace from svd to eps */
    159:   if (svd->nini<0 || svd->ninil<0) {
    160:     for (i=0;i<-PetscMin(svd->nini,svd->ninil);i++) {
    161:       MatCreateVecs(cyclic->mat,&v,NULL);
    162:       VecGetArray(v,&va);
    163:       if (i<-svd->ninil) {
    164:         VecGetSize(svd->ISL[i],&isl);
    165:         if (isl!=m) SETERRQ(PetscObjectComm((PetscObject)svd),PETSC_ERR_SUP,"Size mismatch for left initial vector");
    166:         VecGetArrayRead(svd->ISL[i],&isa);
    167:         PetscArraycpy(va,isa,m);
    168:         VecRestoreArrayRead(svd->IS[i],&isa);
    169:       } else {
    170:         PetscArrayzero(&va,m);
    171:       }
    172:       if (i<-svd->nini) {
    173:         VecGetSize(svd->IS[i],&isl);
    174:         if (isl!=n) SETERRQ(PetscObjectComm((PetscObject)svd),PETSC_ERR_SUP,"Size mismatch for right initial vector");
    175:         VecGetArrayRead(svd->IS[i],&isa);
    176:         PetscArraycpy(va+m,isa,n);
    177:         VecRestoreArrayRead(svd->IS[i],&isa);
    178:       } else {
    179:         PetscArrayzero(va+m,n);
    180:       }
    181:       VecRestoreArray(v,&va);
    182:       VecDestroy(&svd->IS[i]);
    183:       svd->IS[i] = v;
    184:     }
    185:     svd->nini = PetscMin(svd->nini,svd->ninil);
    186:     EPSSetInitialSpace(cyclic->eps,-svd->nini,svd->IS);
    187:     SlepcBasisDestroy_Private(&svd->nini,&svd->IS);
    188:     SlepcBasisDestroy_Private(&svd->ninil,&svd->ISL);
    189:   }
    190:   EPSSetUp(cyclic->eps);
    191:   EPSGetDimensions(cyclic->eps,NULL,&svd->ncv,&svd->mpd);
    192:   svd->ncv = PetscMin(svd->ncv,PetscMin(M,N));
    193:   EPSGetTolerances(cyclic->eps,NULL,&svd->max_it);
    194:   if (svd->tol==PETSC_DEFAULT) svd->tol = SLEPC_DEFAULT_TOL;

    196:   svd->leftbasis = PETSC_TRUE;
    197:   SVDAllocateSolution(svd,0);
    198:   return(0);
    199: }

    201: PetscErrorCode SVDSolve_Cyclic(SVD svd)
    202: {
    203:   PetscErrorCode    ierr;
    204:   SVD_CYCLIC        *cyclic = (SVD_CYCLIC*)svd->data;
    205:   PetscInt          i,j,M,N,m,n;
    206:   PetscScalar       sigma;
    207:   const PetscScalar *px;
    208:   Vec               x,x1,x2;

    211:   EPSSolve(cyclic->eps);
    212:   EPSGetConverged(cyclic->eps,&svd->nconv);
    213:   EPSGetIterationNumber(cyclic->eps,&svd->its);
    214:   EPSGetConvergedReason(cyclic->eps,(EPSConvergedReason*)&svd->reason);

    216:   MatCreateVecs(cyclic->mat,&x,NULL);
    217:   SVDMatGetSize(svd,&M,&N);
    218:   SVDMatGetLocalSize(svd,&m,&n);
    219:   SVDMatCreateVecsEmpty(svd,&x2,&x1);
    220:   for (i=0,j=0;i<svd->nconv;i++) {
    221:     EPSGetEigenpair(cyclic->eps,i,&sigma,NULL,x,NULL);
    222:     if (PetscRealPart(sigma) > 0.0) {
    223:       svd->sigma[j] = PetscRealPart(sigma);
    224:       VecGetArrayRead(x,&px);
    225:       VecPlaceArray(x1,px);
    226:       VecPlaceArray(x2,px+m);
    227:       BVInsertVec(svd->U,j,x1);
    228:       BVScaleColumn(svd->U,j,1.0/PetscSqrtReal(2.0));
    229:       BVInsertVec(svd->V,j,x2);
    230:       BVScaleColumn(svd->V,j,1.0/PetscSqrtReal(2.0));
    231:       VecResetArray(x1);
    232:       VecResetArray(x2);
    233:       VecRestoreArrayRead(x,&px);
    234:       j++;
    235:     }
    236:   }
    237:   svd->nconv = j;

    239:   VecDestroy(&x);
    240:   VecDestroy(&x1);
    241:   VecDestroy(&x2);
    242:   return(0);
    243: }

    245: static PetscErrorCode EPSMonitor_Cyclic(EPS eps,PetscInt its,PetscInt nconv,PetscScalar *eigr,PetscScalar *eigi,PetscReal *errest,PetscInt nest,void *ctx)
    246: {
    247:   PetscInt       i,j;
    248:   SVD            svd = (SVD)ctx;
    249:   PetscScalar    er,ei;

    253:   nconv = 0;
    254:   for (i=0,j=0;i<PetscMin(nest,svd->ncv);i++) {
    255:     er = eigr[i]; ei = eigi[i];
    256:     STBackTransform(eps->st,1,&er,&ei);
    257:     if (PetscRealPart(er) > 0.0) {
    258:       svd->sigma[j] = PetscRealPart(er);
    259:       svd->errest[j] = errest[i];
    260:       if (errest[i] && errest[i] < svd->tol) nconv++;
    261:       j++;
    262:     }
    263:   }
    264:   nest = j;
    265:   SVDMonitor(svd,its,nconv,svd->sigma,svd->errest,nest);
    266:   return(0);
    267: }

    269: PetscErrorCode SVDSetFromOptions_Cyclic(PetscOptionItems *PetscOptionsObject,SVD svd)
    270: {
    272:   PetscBool      set,val;
    273:   SVD_CYCLIC     *cyclic = (SVD_CYCLIC*)svd->data;
    274:   ST             st;

    277:   PetscOptionsHead(PetscOptionsObject,"SVD Cyclic Options");

    279:     PetscOptionsBool("-svd_cyclic_explicitmatrix","Use cyclic explicit matrix","SVDCyclicSetExplicitMatrix",cyclic->explicitmatrix,&val,&set);
    280:     if (set) { SVDCyclicSetExplicitMatrix(svd,val); }

    282:   PetscOptionsTail();

    284:   if (!cyclic->eps) { SVDCyclicGetEPS(svd,&cyclic->eps); }
    285:   if (!cyclic->explicitmatrix && !cyclic->usereps) {
    286:     /* use as default an ST with shell matrix and Jacobi */
    287:     EPSGetST(cyclic->eps,&st);
    288:     STSetMatMode(st,ST_MATMODE_SHELL);
    289:   }
    290:   EPSSetFromOptions(cyclic->eps);
    291:   return(0);
    292: }

    294: static PetscErrorCode SVDCyclicSetExplicitMatrix_Cyclic(SVD svd,PetscBool explicitmatrix)
    295: {
    296:   SVD_CYCLIC *cyclic = (SVD_CYCLIC*)svd->data;

    299:   if (cyclic->explicitmatrix != explicitmatrix) {
    300:     cyclic->explicitmatrix = explicitmatrix;
    301:     svd->state = SVD_STATE_INITIAL;
    302:   }
    303:   return(0);
    304: }

    306: /*@
    307:    SVDCyclicSetExplicitMatrix - Indicate if the eigensolver operator
    308:    H(A) = [ 0  A ; A^T 0 ] must be computed explicitly.

    310:    Logically Collective on svd

    312:    Input Parameters:
    313: +  svd      - singular value solver
    314: -  explicit - boolean flag indicating if H(A) is built explicitly

    316:    Options Database Key:
    317: .  -svd_cyclic_explicitmatrix <boolean> - Indicates the boolean flag

    319:    Level: advanced

    321: .seealso: SVDCyclicGetExplicitMatrix()
    322: @*/
    323: PetscErrorCode SVDCyclicSetExplicitMatrix(SVD svd,PetscBool explicitmatrix)
    324: {

    330:   PetscTryMethod(svd,"SVDCyclicSetExplicitMatrix_C",(SVD,PetscBool),(svd,explicitmatrix));
    331:   return(0);
    332: }

    334: static PetscErrorCode SVDCyclicGetExplicitMatrix_Cyclic(SVD svd,PetscBool *explicitmatrix)
    335: {
    336:   SVD_CYCLIC *cyclic = (SVD_CYCLIC*)svd->data;

    339:   *explicitmatrix = cyclic->explicitmatrix;
    340:   return(0);
    341: }

    343: /*@
    344:    SVDCyclicGetExplicitMatrix - Returns the flag indicating if H(A) is built explicitly.

    346:    Not Collective

    348:    Input Parameter:
    349: .  svd  - singular value solver

    351:    Output Parameter:
    352: .  explicit - the mode flag

    354:    Level: advanced

    356: .seealso: SVDCyclicSetExplicitMatrix()
    357: @*/
    358: PetscErrorCode SVDCyclicGetExplicitMatrix(SVD svd,PetscBool *explicitmatrix)
    359: {

    365:   PetscUseMethod(svd,"SVDCyclicGetExplicitMatrix_C",(SVD,PetscBool*),(svd,explicitmatrix));
    366:   return(0);
    367: }

    369: static PetscErrorCode SVDCyclicSetEPS_Cyclic(SVD svd,EPS eps)
    370: {
    371:   PetscErrorCode  ierr;
    372:   SVD_CYCLIC      *cyclic = (SVD_CYCLIC*)svd->data;

    375:   PetscObjectReference((PetscObject)eps);
    376:   EPSDestroy(&cyclic->eps);
    377:   cyclic->eps = eps;
    378:   cyclic->usereps = PETSC_TRUE;
    379:   PetscLogObjectParent((PetscObject)svd,(PetscObject)cyclic->eps);
    380:   svd->state = SVD_STATE_INITIAL;
    381:   return(0);
    382: }

    384: /*@
    385:    SVDCyclicSetEPS - Associate an eigensolver object (EPS) to the
    386:    singular value solver.

    388:    Collective on svd

    390:    Input Parameters:
    391: +  svd - singular value solver
    392: -  eps - the eigensolver object

    394:    Level: advanced

    396: .seealso: SVDCyclicGetEPS()
    397: @*/
    398: PetscErrorCode SVDCyclicSetEPS(SVD svd,EPS eps)
    399: {

    406:   PetscTryMethod(svd,"SVDCyclicSetEPS_C",(SVD,EPS),(svd,eps));
    407:   return(0);
    408: }

    410: static PetscErrorCode SVDCyclicGetEPS_Cyclic(SVD svd,EPS *eps)
    411: {
    413:   SVD_CYCLIC     *cyclic = (SVD_CYCLIC*)svd->data;

    416:   if (!cyclic->eps) {
    417:     EPSCreate(PetscObjectComm((PetscObject)svd),&cyclic->eps);
    418:     PetscObjectIncrementTabLevel((PetscObject)cyclic->eps,(PetscObject)svd,1);
    419:     EPSSetOptionsPrefix(cyclic->eps,((PetscObject)svd)->prefix);
    420:     EPSAppendOptionsPrefix(cyclic->eps,"svd_cyclic_");
    421:     PetscLogObjectParent((PetscObject)svd,(PetscObject)cyclic->eps);
    422:     PetscObjectSetOptions((PetscObject)cyclic->eps,((PetscObject)svd)->options);
    423:     EPSSetWhichEigenpairs(cyclic->eps,EPS_LARGEST_REAL);
    424:     EPSMonitorSet(cyclic->eps,EPSMonitor_Cyclic,svd,NULL);
    425:   }
    426:   *eps = cyclic->eps;
    427:   return(0);
    428: }

    430: /*@
    431:    SVDCyclicGetEPS - Retrieve the eigensolver object (EPS) associated
    432:    to the singular value solver.

    434:    Not Collective

    436:    Input Parameter:
    437: .  svd - singular value solver

    439:    Output Parameter:
    440: .  eps - the eigensolver object

    442:    Level: advanced

    444: .seealso: SVDCyclicSetEPS()
    445: @*/
    446: PetscErrorCode SVDCyclicGetEPS(SVD svd,EPS *eps)
    447: {

    453:   PetscUseMethod(svd,"SVDCyclicGetEPS_C",(SVD,EPS*),(svd,eps));
    454:   return(0);
    455: }

    457: PetscErrorCode SVDView_Cyclic(SVD svd,PetscViewer viewer)
    458: {
    460:   SVD_CYCLIC     *cyclic = (SVD_CYCLIC*)svd->data;
    461:   PetscBool      isascii;

    464:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    465:   if (isascii) {
    466:     if (!cyclic->eps) { SVDCyclicGetEPS(svd,&cyclic->eps); }
    467:     PetscViewerASCIIPrintf(viewer,"  %s matrix\n",cyclic->explicitmatrix?"explicit":"implicit");
    468:     PetscViewerASCIIPushTab(viewer);
    469:     EPSView(cyclic->eps,viewer);
    470:     PetscViewerASCIIPopTab(viewer);
    471:   }
    472:   return(0);
    473: }

    475: PetscErrorCode SVDReset_Cyclic(SVD svd)
    476: {
    478:   SVD_CYCLIC     *cyclic = (SVD_CYCLIC*)svd->data;

    481:   EPSReset(cyclic->eps);
    482:   MatDestroy(&cyclic->mat);
    483:   VecDestroy(&cyclic->x1);
    484:   VecDestroy(&cyclic->x2);
    485:   VecDestroy(&cyclic->y1);
    486:   VecDestroy(&cyclic->y2);
    487:   return(0);
    488: }

    490: PetscErrorCode SVDDestroy_Cyclic(SVD svd)
    491: {
    493:   SVD_CYCLIC     *cyclic = (SVD_CYCLIC*)svd->data;

    496:   EPSDestroy(&cyclic->eps);
    497:   PetscFree(svd->data);
    498:   PetscObjectComposeFunction((PetscObject)svd,"SVDCyclicSetEPS_C",NULL);
    499:   PetscObjectComposeFunction((PetscObject)svd,"SVDCyclicGetEPS_C",NULL);
    500:   PetscObjectComposeFunction((PetscObject)svd,"SVDCyclicSetExplicitMatrix_C",NULL);
    501:   PetscObjectComposeFunction((PetscObject)svd,"SVDCyclicGetExplicitMatrix_C",NULL);
    502:   return(0);
    503: }

    505: SLEPC_EXTERN PetscErrorCode SVDCreate_Cyclic(SVD svd)
    506: {
    508:   SVD_CYCLIC     *cyclic;

    511:   PetscNewLog(svd,&cyclic);
    512:   svd->data                      = (void*)cyclic;
    513:   svd->ops->solve                = SVDSolve_Cyclic;
    514:   svd->ops->setup                = SVDSetUp_Cyclic;
    515:   svd->ops->setfromoptions       = SVDSetFromOptions_Cyclic;
    516:   svd->ops->destroy              = SVDDestroy_Cyclic;
    517:   svd->ops->reset                = SVDReset_Cyclic;
    518:   svd->ops->view                 = SVDView_Cyclic;
    519:   PetscObjectComposeFunction((PetscObject)svd,"SVDCyclicSetEPS_C",SVDCyclicSetEPS_Cyclic);
    520:   PetscObjectComposeFunction((PetscObject)svd,"SVDCyclicGetEPS_C",SVDCyclicGetEPS_Cyclic);
    521:   PetscObjectComposeFunction((PetscObject)svd,"SVDCyclicSetExplicitMatrix_C",SVDCyclicSetExplicitMatrix_Cyclic);
    522:   PetscObjectComposeFunction((PetscObject)svd,"SVDCyclicGetExplicitMatrix_C",SVDCyclicGetExplicitMatrix_Cyclic);
    523:   return(0);
    524: }