Date: 2023-09-05T10:18:37+00:00

Actual source code: gklanczos.c
slepc-3.19.2 2023-09-05
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      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: 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_DEFAULT) svd->max_it = PetscMax(N/svd->ncv,100);
     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: PetscErrorCode SVDSolve_Lanczos(SVD svd)
    221: {
    222:   SVD_LANCZOS    *lanczos = (SVD_LANCZOS*)svd->data;
    223:   PetscReal      *alpha,*beta;
    224:   PetscScalar    *swork,*w,*P;
    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(BVSetActiveColumns(svd->V,svd->nconv,nv));
    251:     PetscCall(DSGetArrayReal(svd->ds,DS_MAT_T,&alpha));
    252:     beta = alpha + ld;
    253:     if (lanczos->oneside) PetscCall(SVDOneSideLanczos(svd,alpha,beta,svd->V,u,u_1,svd->nconv,nv,swork));
    254:     else {
    255:       PetscCall(BVSetActiveColumns(svd->U,svd->nconv,nv));
    256:       PetscCall(SVDTwoSideLanczos(svd,alpha,beta,svd->V,svd->U,svd->nconv,&nv,NULL));
    257:     }
    258:     PetscCall(DSRestoreArrayReal(svd->ds,DS_MAT_T,&alpha));

    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:     PetscCall((*svd->stopping)(svd,svd->its,svd->max_it,k,svd->nsv,&svd->reason,svd->stoppingctx));

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

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

    298:     /* copy restart vector from the last column */
    299:     if (svd->reason == SVD_CONVERGED_ITERATING) PetscCall(BVCopyColumn(svd->V,nv,k));

    301:     svd->nconv = k;
    302:     PetscCall(SVDMonitor(svd,svd->its,svd->nconv,svd->sigma,svd->errest,nv));
    303:   }

    305:   /* free working space */
    306:   PetscCall(VecDestroy(&u));
    307:   PetscCall(VecDestroy(&u_1));
    308:   PetscCall(PetscFree2(w,swork));
    309:   PetscFunctionReturn(PETSC_SUCCESS);
    310: }

    312: PetscErrorCode SVDSetFromOptions_Lanczos(SVD svd,PetscOptionItems *PetscOptionsObject)
    313: {
    314:   PetscBool      set,val;
    315:   SVD_LANCZOS    *lanczos = (SVD_LANCZOS*)svd->data;

    317:   PetscFunctionBegin;
    318:   PetscOptionsHeadBegin(PetscOptionsObject,"SVD Lanczos Options");

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

    323:   PetscOptionsHeadEnd();
    324:   PetscFunctionReturn(PETSC_SUCCESS);
    325: }

    327: static PetscErrorCode SVDLanczosSetOneSide_Lanczos(SVD svd,PetscBool oneside)
    328: {
    329:   SVD_LANCZOS *lanczos = (SVD_LANCZOS*)svd->data;

    331:   PetscFunctionBegin;
    332:   if (lanczos->oneside != oneside) {
    333:     lanczos->oneside = oneside;
    334:     svd->state = SVD_STATE_INITIAL;
    335:   }
    336:   PetscFunctionReturn(PETSC_SUCCESS);
    337: }

    339: /*@
    340:    SVDLanczosSetOneSide - Indicate if the variant of the Lanczos method
    341:    to be used is one-sided or two-sided.

    343:    Logically Collective

    345:    Input Parameters:
    346: +  svd     - singular value solver
    347: -  oneside - boolean flag indicating if the method is one-sided or not

    349:    Options Database Key:
    350: .  -svd_lanczos_oneside <boolean> - Indicates the boolean flag

    352:    Note:
    353:    By default, a two-sided variant is selected, which is sometimes slightly
    354:    more robust. However, the one-sided variant is faster because it avoids
    355:    the orthogonalization associated to left singular vectors. It also saves
    356:    the memory required for storing such vectors.

    358:    Level: advanced

    360: .seealso: SVDTRLanczosSetOneSide()
    361: @*/
    362: PetscErrorCode SVDLanczosSetOneSide(SVD svd,PetscBool oneside)
    363: {
    364:   PetscFunctionBegin;
    367:   PetscTryMethod(svd,"SVDLanczosSetOneSide_C",(SVD,PetscBool),(svd,oneside));
    368:   PetscFunctionReturn(PETSC_SUCCESS);
    369: }

    371: static PetscErrorCode SVDLanczosGetOneSide_Lanczos(SVD svd,PetscBool *oneside)
    372: {
    373:   SVD_LANCZOS *lanczos = (SVD_LANCZOS*)svd->data;

    375:   PetscFunctionBegin;
    376:   *oneside = lanczos->oneside;
    377:   PetscFunctionReturn(PETSC_SUCCESS);
    378: }

    380: /*@
    381:    SVDLanczosGetOneSide - Gets if the variant of the Lanczos method
    382:    to be used is one-sided or two-sided.

    384:    Not Collective

    386:    Input Parameters:
    387: .  svd     - singular value solver

    389:    Output Parameters:
    390: .  oneside - boolean flag indicating if the method is one-sided or not

    392:    Level: advanced

    394: .seealso: SVDLanczosSetOneSide()
    395: @*/
    396: PetscErrorCode SVDLanczosGetOneSide(SVD svd,PetscBool *oneside)
    397: {
    398:   PetscFunctionBegin;
    401:   PetscUseMethod(svd,"SVDLanczosGetOneSide_C",(SVD,PetscBool*),(svd,oneside));
    402:   PetscFunctionReturn(PETSC_SUCCESS);
    403: }

    405: PetscErrorCode SVDDestroy_Lanczos(SVD svd)
    406: {
    407:   PetscFunctionBegin;
    408:   PetscCall(PetscFree(svd->data));
    409:   PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDLanczosSetOneSide_C",NULL));
    410:   PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDLanczosGetOneSide_C",NULL));
    411:   PetscFunctionReturn(PETSC_SUCCESS);
    412: }

    414: PetscErrorCode SVDView_Lanczos(SVD svd,PetscViewer viewer)
    415: {
    416:   SVD_LANCZOS    *lanczos = (SVD_LANCZOS*)svd->data;
    417:   PetscBool      isascii;

    419:   PetscFunctionBegin;
    420:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii));
    421:   if (isascii) PetscCall(PetscViewerASCIIPrintf(viewer,"  %s-sided reorthogonalization\n",lanczos->oneside? "one": "two"));
    422:   PetscFunctionReturn(PETSC_SUCCESS);
    423: }

    425: SLEPC_EXTERN PetscErrorCode SVDCreate_Lanczos(SVD svd)
    426: {
    427:   SVD_LANCZOS    *ctx;

    429:   PetscFunctionBegin;
    430:   PetscCall(PetscNew(&ctx));
    431:   svd->data = (void*)ctx;

    433:   svd->ops->setup          = SVDSetUp_Lanczos;
    434:   svd->ops->solve          = SVDSolve_Lanczos;
    435:   svd->ops->destroy        = SVDDestroy_Lanczos;
    436:   svd->ops->setfromoptions = SVDSetFromOptions_Lanczos;
    437:   svd->ops->view           = SVDView_Lanczos;
    438:   svd->ops->computevectors = SVDComputeVectors_Left;
    439:   PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDLanczosSetOneSide_C",SVDLanczosSetOneSide_Lanczos));
    440:   PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDLanczosGetOneSide_C",SVDLanczosGetOneSide_Lanczos));
    441:   PetscFunctionReturn(PETSC_SUCCESS);
    442: }