Date: 2026-01-20T11:35:19+00:00

Actual source code: gklanczos.c

      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-, 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: "lanczos"

     13:    Method: Explicitly restarted Lanczos

     15:    Algorithm:

     17:        Golub-Kahan-Lanczos bidiagonalization with explicit restart.

     19:    References:

     21:        [1] G.H. Golub and W. Kahan, "Calculating the singular values
     22:            and pseudo-inverse of a matrix", SIAM J. Numer. Anal. Ser.
     23:            B 2:205-224, 1965.

     25:        [2] V. Hernandez, J.E. Roman, and A. Tomas, "A robust and
     26:            efficient parallel SVD solver based on restarted Lanczos
     27:            bidiagonalization", Elec. Trans. Numer. Anal. 31:68-85,
     28:            2008.
     29: */

     31: #include <slepc/private/svdimpl.h>

     33: typedef struct {
     34:   PetscBool oneside;
     35: } SVD_LANCZOS;

     37: static PetscErrorCode SVDSetUp_Lanczos(SVD svd)
     38: {
     39:   SVD_LANCZOS    *lanczos = (SVD_LANCZOS*)svd->data;
     40:   PetscInt       N;

     42:   PetscFunctionBegin;
     43:   SVDCheckStandard(svd);
     44:   SVDCheckDefinite(svd);
     45:   PetscCall(MatGetSize(svd->A,NULL,&N));
     46:   PetscCall(SVDSetDimensions_Default(svd));
     47:   PetscCheck(svd->ncv<=svd->nsv+svd->mpd,PetscObjectComm((PetscObject)svd),PETSC_ERR_USER_INPUT,"The value of ncv must not be larger than nev+mpd");
     48:   if (svd->max_it==PETSC_DETERMINE) svd->max_it = PetscMax(N/svd->ncv,100)*((svd->stop==SVD_STOP_THRESHOLD)?10:1);
     49:   svd->leftbasis = PetscNot(lanczos->oneside);
     50:   PetscCall(SVDAllocateSolution(svd,1));
     51:   PetscCall(DSSetType(svd->ds,DSSVD));
     52:   PetscCall(DSSetCompact(svd->ds,PETSC_TRUE));
     53:   PetscCall(DSSetExtraRow(svd->ds,PETSC_TRUE));
     54:   PetscCall(DSAllocate(svd->ds,svd->ncv+1));
     55:   PetscFunctionReturn(PETSC_SUCCESS);
     56: }

     58: PetscErrorCode SVDTwoSideLanczos(SVD svd,PetscReal *alpha,PetscReal *beta,BV V,BV U,PetscInt k,PetscInt *n,PetscBool *breakdown)
     59: {
     60:   PetscInt       i;
     61:   Vec            u,v;
     62:   PetscBool      lindep=PETSC_FALSE;

     64:   PetscFunctionBegin;
     65:   PetscCall(BVGetColumn(svd->V,k,&v));
     66:   PetscCall(BVGetColumn(svd->U,k,&u));
     67:   PetscCall(MatMult(svd->A,v,u));
     68:   PetscCall(BVRestoreColumn(svd->V,k,&v));
     69:   PetscCall(BVRestoreColumn(svd->U,k,&u));
     70:   PetscCall(BVOrthonormalizeColumn(svd->U,k,PETSC_FALSE,alpha+k,&lindep));
     71:   if (PetscUnlikely(lindep)) {
     72:     *n = k;
     73:     if (breakdown) *breakdown = lindep;
     74:     PetscFunctionReturn(PETSC_SUCCESS);
     75:   }

     77:   for (i=k+1;i<*n;i++) {
     78:     PetscCall(BVGetColumn(svd->V,i,&v));
     79:     PetscCall(BVGetColumn(svd->U,i-1,&u));
     80:     PetscCall(MatMult(svd->AT,u,v));
     81:     PetscCall(BVRestoreColumn(svd->V,i,&v));
     82:     PetscCall(BVRestoreColumn(svd->U,i-1,&u));
     83:     PetscCall(BVOrthonormalizeColumn(svd->V,i,PETSC_FALSE,beta+i-1,&lindep));
     84:     if (PetscUnlikely(lindep)) {
     85:       *n = i;
     86:       break;
     87:     }
     88:     PetscCall(BVGetColumn(svd->V,i,&v));
     89:     PetscCall(BVGetColumn(svd->U,i,&u));
     90:     PetscCall(MatMult(svd->A,v,u));
     91:     PetscCall(BVRestoreColumn(svd->V,i,&v));
     92:     PetscCall(BVRestoreColumn(svd->U,i,&u));
     93:     PetscCall(BVOrthonormalizeColumn(svd->U,i,PETSC_FALSE,alpha+i,&lindep));
     94:     if (PetscUnlikely(lindep)) {
     95:       *n = i;
     96:       break;
     97:     }
     98:   }

    100:   if (!lindep) {
    101:     PetscCall(BVGetColumn(svd->V,*n,&v));
    102:     PetscCall(BVGetColumn(svd->U,*n-1,&u));
    103:     PetscCall(MatMult(svd->AT,u,v));
    104:     PetscCall(BVRestoreColumn(svd->V,*n,&v));
    105:     PetscCall(BVRestoreColumn(svd->U,*n-1,&u));
    106:     PetscCall(BVOrthogonalizeColumn(svd->V,*n,NULL,beta+*n-1,&lindep));
    107:   }
    108:   if (breakdown) *breakdown = lindep;
    109:   PetscFunctionReturn(PETSC_SUCCESS);
    110: }

    112: static PetscErrorCode SVDOneSideLanczos(SVD svd,PetscReal *alpha,PetscReal *beta,BV V,Vec u,Vec u_1,PetscInt k,PetscInt n,PetscScalar* work)
    113: {
    114:   PetscInt       i,bvl,bvk;
    115:   PetscReal      a,b;
    116:   Vec            z,temp;

    118:   PetscFunctionBegin;
    119:   PetscCall(BVGetActiveColumns(V,&bvl,&bvk));
    120:   PetscCall(BVGetColumn(V,k,&z));
    121:   PetscCall(MatMult(svd->A,z,u));
    122:   PetscCall(BVRestoreColumn(V,k,&z));

    124:   for (i=k+1;i<n;i++) {
    125:     PetscCall(BVGetColumn(V,i,&z));
    126:     PetscCall(MatMult(svd->AT,u,z));
    127:     PetscCall(BVRestoreColumn(V,i,&z));
    128:     PetscCall(VecNormBegin(u,NORM_2,&a));
    129:     PetscCall(BVSetActiveColumns(V,0,i));
    130:     PetscCall(BVDotColumnBegin(V,i,work));
    131:     PetscCall(VecNormEnd(u,NORM_2,&a));
    132:     PetscCall(BVDotColumnEnd(V,i,work));
    133:     PetscCall(VecScale(u,1.0/a));
    134:     PetscCall(BVMultColumn(V,-1.0/a,1.0/a,i,work));

    136:     /* h = V^* z, z = z - V h  */
    137:     PetscCall(BVDotColumn(V,i,work));
    138:     PetscCall(BVMultColumn(V,-1.0,1.0,i,work));
    139:     PetscCall(BVNormColumn(V,i,NORM_2,&b));
    140:     PetscCheck(PetscAbsReal(b)>10*PETSC_MACHINE_EPSILON,PetscObjectComm((PetscObject)svd),PETSC_ERR_PLIB,"Recurrence generated a zero vector; use a two-sided variant");
    141:     PetscCall(BVScaleColumn(V,i,1.0/b));

    143:     PetscCall(BVGetColumn(V,i,&z));
    144:     PetscCall(MatMult(svd->A,z,u_1));
    145:     PetscCall(BVRestoreColumn(V,i,&z));
    146:     PetscCall(VecAXPY(u_1,-b,u));
    147:     alpha[i-1] = a;
    148:     beta[i-1] = b;
    149:     temp = u;
    150:     u = u_1;
    151:     u_1 = temp;
    152:   }

    154:   PetscCall(BVGetColumn(V,n,&z));
    155:   PetscCall(MatMult(svd->AT,u,z));
    156:   PetscCall(BVRestoreColumn(V,n,&z));
    157:   PetscCall(VecNormBegin(u,NORM_2,&a));
    158:   PetscCall(BVDotColumnBegin(V,n,work));
    159:   PetscCall(VecNormEnd(u,NORM_2,&a));
    160:   PetscCall(BVDotColumnEnd(V,n,work));
    161:   PetscCall(VecScale(u,1.0/a));
    162:   PetscCall(BVMultColumn(V,-1.0/a,1.0/a,n,work));

    164:   /* h = V^* z, z = z - V h  */
    165:   PetscCall(BVDotColumn(V,n,work));
    166:   PetscCall(BVMultColumn(V,-1.0,1.0,n,work));
    167:   PetscCall(BVNormColumn(V,i,NORM_2,&b));

    169:   alpha[n-1] = a;
    170:   beta[n-1] = b;
    171:   PetscCall(BVSetActiveColumns(V,bvl,bvk));
    172:   PetscFunctionReturn(PETSC_SUCCESS);
    173: }

    175: /*
    176:    SVDKrylovConvergence - Implements the loop that checks for convergence
    177:    in Krylov methods.

    179:    Input Parameters:
    180:      svd     - the solver; some error estimates are updated in svd->errest
    181:      getall  - whether all residuals must be computed
    182:      kini    - initial value of k (the loop variable)
    183:      nits    - number of iterations of the loop
    184:      normr   - norm of triangular factor of qr([A;B]), used only in GSVD

    186:    Output Parameter:
    187:      kout  - the first index where the convergence test failed
    188: */
    189: PetscErrorCode SVDKrylovConvergence(SVD svd,PetscBool getall,PetscInt kini,PetscInt nits,PetscReal normr,PetscInt *kout)
    190: {
    191:   PetscInt       k,marker,ld;
    192:   PetscReal      *alpha,*beta,*betah,resnorm;
    193:   PetscBool      extra;

    195:   PetscFunctionBegin;
    196:   if (PetscUnlikely(svd->conv == SVD_CONV_MAXIT && svd->its >= svd->max_it)) *kout = svd->nsv;
    197:   else {
    198:     PetscCall(DSGetLeadingDimension(svd->ds,&ld));
    199:     PetscCall(DSGetExtraRow(svd->ds,&extra));
    200:     PetscCheck(extra,PetscObjectComm((PetscObject)svd),PETSC_ERR_SUP,"Only implemented for DS with extra row");
    201:     marker = -1;
    202:     if (svd->trackall) getall = PETSC_TRUE;
    203:     PetscCall(DSGetArrayReal(svd->ds,DS_MAT_T,&alpha));
    204:     beta = alpha + ld;
    205:     betah = alpha + 2*ld;
    206:     for (k=kini;k<kini+nits;k++) {
    207:       if (svd->isgeneralized) resnorm = SlepcAbs(beta[k],betah[k])*normr;
    208:       else resnorm = PetscAbsReal(beta[k]);
    209:       PetscCall((*svd->converged)(svd,svd->sigma[k],resnorm,&svd->errest[k],svd->convergedctx));
    210:       if (marker==-1 && svd->errest[k] >= svd->tol) marker = k;
    211:       if (marker!=-1 && !getall) break;
    212:     }
    213:     PetscCall(DSRestoreArrayReal(svd->ds,DS_MAT_T,&alpha));
    214:     if (marker!=-1) k = marker;
    215:     *kout = k;
    216:   }
    217:   PetscFunctionReturn(PETSC_SUCCESS);
    218: }

    220: static PetscErrorCode SVDSolve_Lanczos(SVD svd)
    221: {
    222:   SVD_LANCZOS    *lanczos = (SVD_LANCZOS*)svd->data;
    223:   PetscReal      *alpha,*beta;
    224:   PetscScalar    *swork,*w,*P,*aux1,*aux2;
    225:   PetscInt       i,k,j,nv,ld;
    226:   Vec            u=NULL,u_1=NULL;
    227:   Mat            U,V;

    229:   PetscFunctionBegin;
    230:   /* allocate working space */
    231:   PetscCall(DSGetLeadingDimension(svd->ds,&ld));
    232:   PetscCall(PetscMalloc2(ld,&w,svd->ncv,&swork));

    234:   if (lanczos->oneside) {
    235:     PetscCall(MatCreateVecs(svd->A,NULL,&u));
    236:     PetscCall(MatCreateVecs(svd->A,NULL,&u_1));
    237:   }

    239:   /* normalize start vector */
    240:   if (!svd->nini) {
    241:     PetscCall(BVSetRandomColumn(svd->V,0));
    242:     PetscCall(BVOrthonormalizeColumn(svd->V,0,PETSC_TRUE,NULL,NULL));
    243:   }

    245:   while (svd->reason == SVD_CONVERGED_ITERATING) {
    246:     svd->its++;

    248:     /* inner loop */
    249:     nv = PetscMin(svd->nconv+svd->mpd,svd->ncv);
    250:     PetscCall(DSGetArrayReal(svd->ds,DS_MAT_T,&alpha));
    251:     beta = alpha + ld;
    252:     if (lanczos->oneside) PetscCall(SVDOneSideLanczos(svd,alpha,beta,svd->V,u,u_1,svd->nconv,nv,swork));
    253:     else {
    254:       PetscCall(SVDTwoSideLanczos(svd,alpha,beta,svd->V,svd->U,svd->nconv,&nv,NULL));
    255:       PetscCall(BVSetActiveColumns(svd->U,svd->nconv,nv));
    256:     }
    257:     PetscCall(DSRestoreArrayReal(svd->ds,DS_MAT_T,&alpha));
    258:     PetscCall(BVSetActiveColumns(svd->V,svd->nconv,nv));

    260:     /* compute SVD of bidiagonal matrix */
    261:     PetscCall(DSSetDimensions(svd->ds,nv,svd->nconv,0));
    262:     PetscCall(DSSVDSetDimensions(svd->ds,nv));
    263:     PetscCall(DSSetState(svd->ds,DS_STATE_INTERMEDIATE));
    264:     PetscCall(DSSolve(svd->ds,w,NULL));
    265:     PetscCall(DSSort(svd->ds,w,NULL,NULL,NULL,NULL));
    266:     PetscCall(DSUpdateExtraRow(svd->ds));
    267:     PetscCall(DSSynchronize(svd->ds,w,NULL));
    268:     for (i=svd->nconv;i<nv;i++) svd->sigma[i] = PetscRealPart(w[i]);

    270:     /* check convergence */
    271:     PetscCall(SVDKrylovConvergence(svd,PETSC_FALSE,svd->nconv,nv-svd->nconv,1.0,&k));
    272:     SVDSetCtxThreshold(svd,svd->sigma,k);
    273:     PetscCall((*svd->stopping)(svd,svd->its,svd->max_it,k,svd->nsv,&svd->reason,svd->stoppingctx));

    275:     /* compute restart vector */
    276:     if (svd->reason == SVD_CONVERGED_ITERATING) {
    277:       if (k<nv) {
    278:         PetscCall(DSGetArray(svd->ds,DS_MAT_V,&P));
    279:         for (j=svd->nconv;j<nv;j++) swork[j-svd->nconv] = PetscConj(P[j+k*ld]);
    280:         PetscCall(DSRestoreArray(svd->ds,DS_MAT_V,&P));
    281:         PetscCall(BVMultColumn(svd->V,1.0,0.0,nv,swork));
    282:       } else {
    283:         /* all approximations have converged, generate a new initial vector */
    284:         PetscCall(BVSetRandomColumn(svd->V,nv));
    285:         PetscCall(BVOrthonormalizeColumn(svd->V,nv,PETSC_FALSE,NULL,NULL));
    286:       }
    287:     }

    289:     /* compute converged singular vectors */
    290:     PetscCall(DSGetMat(svd->ds,DS_MAT_V,&V));
    291:     PetscCall(BVMultInPlace(svd->V,V,svd->nconv,k));
    292:     PetscCall(DSRestoreMat(svd->ds,DS_MAT_V,&V));
    293:     if (!lanczos->oneside) {
    294:       PetscCall(DSGetMat(svd->ds,DS_MAT_U,&U));
    295:       PetscCall(BVMultInPlace(svd->U,U,svd->nconv,k));
    296:       PetscCall(DSRestoreMat(svd->ds,DS_MAT_U,&U));
    297:     }

    299:     if (svd->reason == SVD_CONVERGED_ITERATING) {
    300:       PetscCall(BVCopyColumn(svd->V,nv,k));  /* copy restart vector from the last column */
    301:       if (svd->stop==SVD_STOP_THRESHOLD && nv-k<5) {  /* reallocate */
    302:         svd->ncv = svd->mpd+k;
    303:         PetscCall(SVDReallocateSolution(svd,svd->ncv+1));
    304:         for (i=nv;i<svd->ncv;i++) svd->perm[i] = i;
    305:         PetscCall(DSReallocate(svd->ds,svd->ncv+1));
    306:         aux1 = w;
    307:         aux2 = swork;
    308:         PetscCall(PetscMalloc2(svd->ncv+1,&w,svd->ncv,&swork));
    309:         PetscCall(PetscArraycpy(w,aux1,ld));
    310:         PetscCall(PetscFree2(aux1,aux2));
    311:         PetscCall(DSGetLeadingDimension(svd->ds,&ld));
    312:       }
    313:     }

    315:     svd->nconv = k;
    316:     PetscCall(SVDMonitor(svd,svd->its,svd->nconv,svd->sigma,svd->errest,nv));
    317:   }

    319:   /* free working space */
    320:   PetscCall(VecDestroy(&u));
    321:   PetscCall(VecDestroy(&u_1));
    322:   PetscCall(PetscFree2(w,swork));
    323:   PetscFunctionReturn(PETSC_SUCCESS);
    324: }

    326: static PetscErrorCode SVDSetFromOptions_Lanczos(SVD svd,PetscOptionItems PetscOptionsObject)
    327: {
    328:   PetscBool      set,val;
    329:   SVD_LANCZOS    *lanczos = (SVD_LANCZOS*)svd->data;

    331:   PetscFunctionBegin;
    332:   PetscOptionsHeadBegin(PetscOptionsObject,"SVD Lanczos Options");

    334:     PetscCall(PetscOptionsBool("-svd_lanczos_oneside","Use one-side reorthogonalization","SVDLanczosSetOneSide",lanczos->oneside,&val,&set));
    335:     if (set) PetscCall(SVDLanczosSetOneSide(svd,val));

    337:   PetscOptionsHeadEnd();
    338:   PetscFunctionReturn(PETSC_SUCCESS);
    339: }

    341: static PetscErrorCode SVDLanczosSetOneSide_Lanczos(SVD svd,PetscBool oneside)
    342: {
    343:   SVD_LANCZOS *lanczos = (SVD_LANCZOS*)svd->data;

    345:   PetscFunctionBegin;
    346:   if (lanczos->oneside != oneside) {
    347:     lanczos->oneside = oneside;
    348:     svd->state = SVD_STATE_INITIAL;
    349:   }
    350:   PetscFunctionReturn(PETSC_SUCCESS);
    351: }

    353: /*@
    354:    SVDLanczosSetOneSide - Indicate if the variant of the Lanczos method
    355:    to be used is one-sided or two-sided.

    357:    Logically Collective

    359:    Input Parameters:
    360: +  svd     - the singular value solver context
    361: -  oneside - boolean flag indicating if the method is one-sided or not

    363:    Options Database Key:
    364: .  -svd_lanczos_oneside - enable the one-sided variant

    366:    Note:
    367:    By default, a two-sided variant is selected, which is sometimes slightly
    368:    more robust. However, the one-sided variant is faster because it avoids
    369:    the orthogonalization associated to left singular vectors. It also saves
    370:    the memory required for storing such vectors. See more details in
    371:    {cite:p}`Her07c,Her08`.

    373:    Level: advanced

    375: .seealso: [](ch:svd), `SVDTRLANCZOS`, `SVDTRLanczosSetOneSide()`
    376: @*/
    377: PetscErrorCode SVDLanczosSetOneSide(SVD svd,PetscBool oneside)
    378: {
    379:   PetscFunctionBegin;
    382:   PetscTryMethod(svd,"SVDLanczosSetOneSide_C",(SVD,PetscBool),(svd,oneside));
    383:   PetscFunctionReturn(PETSC_SUCCESS);
    384: }

    386: static PetscErrorCode SVDLanczosGetOneSide_Lanczos(SVD svd,PetscBool *oneside)
    387: {
    388:   SVD_LANCZOS *lanczos = (SVD_LANCZOS*)svd->data;

    390:   PetscFunctionBegin;
    391:   *oneside = lanczos->oneside;
    392:   PetscFunctionReturn(PETSC_SUCCESS);
    393: }

    395: /*@
    396:    SVDLanczosGetOneSide - Gets if the variant of the Lanczos method
    397:    to be used is one-sided or two-sided.

    399:    Not Collective

    401:    Input Parameter:
    402: .  svd - the singular value solver context

    404:    Output Parameter:
    405: .  oneside - boolean flag indicating if the method is one-sided or not

    407:    Level: advanced

    409: .seealso: [](ch:svd), `SVDTRLANCZOS`, `SVDLanczosSetOneSide()`
    410: @*/
    411: PetscErrorCode SVDLanczosGetOneSide(SVD svd,PetscBool *oneside)
    412: {
    413:   PetscFunctionBegin;
    415:   PetscAssertPointer(oneside,2);
    416:   PetscUseMethod(svd,"SVDLanczosGetOneSide_C",(SVD,PetscBool*),(svd,oneside));
    417:   PetscFunctionReturn(PETSC_SUCCESS);
    418: }

    420: static PetscErrorCode SVDDestroy_Lanczos(SVD svd)
    421: {
    422:   PetscFunctionBegin;
    423:   PetscCall(PetscFree(svd->data));
    424:   PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDLanczosSetOneSide_C",NULL));
    425:   PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDLanczosGetOneSide_C",NULL));
    426:   PetscFunctionReturn(PETSC_SUCCESS);
    427: }

    429: static PetscErrorCode SVDView_Lanczos(SVD svd,PetscViewer viewer)
    430: {
    431:   SVD_LANCZOS    *lanczos = (SVD_LANCZOS*)svd->data;
    432:   PetscBool      isascii;

    434:   PetscFunctionBegin;
    435:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii));
    436:   if (isascii) PetscCall(PetscViewerASCIIPrintf(viewer,"  %s-sided reorthogonalization\n",lanczos->oneside? "one": "two"));
    437:   PetscFunctionReturn(PETSC_SUCCESS);
    438: }

    440: /*MC
    441:    SVDLANCZOS - SVDLANCZOS = "lanczos" - A basic Golub-Kahan-Lanczos
    442:    bidiagonalization method with explicit restart.

    444:    Notes:
    445:    Only available for standard SVD problems.

    447:    This solver is very basic and is not recommended in general, since it
    448:    will not be competitive with respect to other solvers.

    450:    The implemented method is Lanczos bidiagonalization with explicit restart
    451:    and deflation. Generally, it is much better to use Lanczos with implicit
    452:    restart (also known as thick-restart Lanczos) as implemented in `SVDTRLANCZOS`.

    454:    The implementation includes a one-sided orthogonalization option, and
    455:    efficient parallel orthogonalization, see the details in {cite:p}`Her07c,Her08`.

    457:    Level: beginner

    459: .seealso: [](ch:svd), [](#sec:svdback), `SVD`, `SVDType`, `SVDSetType()`, `SVDSetProblemType()`, `SVDTRLANCZOS`
    460: M*/
    461: SLEPC_EXTERN PetscErrorCode SVDCreate_Lanczos(SVD svd)
    462: {
    463:   SVD_LANCZOS    *ctx;

    465:   PetscFunctionBegin;
    466:   PetscCall(PetscNew(&ctx));
    467:   svd->data = (void*)ctx;

    469:   svd->ops->setup          = SVDSetUp_Lanczos;
    470:   svd->ops->solve          = SVDSolve_Lanczos;
    471:   svd->ops->destroy        = SVDDestroy_Lanczos;
    472:   svd->ops->setfromoptions = SVDSetFromOptions_Lanczos;
    473:   svd->ops->view           = SVDView_Lanczos;
    474:   svd->ops->computevectors = SVDComputeVectors_Left;
    475:   PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDLanczosSetOneSide_C",SVDLanczosSetOneSide_Lanczos));
    476:   PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDLanczosGetOneSide_C",SVDLanczosGetOneSide_Lanczos));
    477:   PetscFunctionReturn(PETSC_SUCCESS);
    478: }