Date: 2021-02-01T14:42:07+00:00

Actual source code: gklanczos.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: "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: {
     40:   SVD_LANCZOS    *lanczos = (SVD_LANCZOS*)svd->data;
     41:   PetscInt       N;

     44:   SVDMatGetSize(svd,NULL,&N);
     45:   SVDSetDimensions_Default(svd);
     46:   if (svd->ncv>svd->nsv+svd->mpd) SETERRQ(PetscObjectComm((PetscObject)svd),1,"The value of ncv must not be larger than nev+mpd");
     47:   if (svd->max_it==PETSC_DEFAULT) svd->max_it = PetscMax(N/svd->ncv,100);
     48:   svd->leftbasis = PetscNot(lanczos->oneside);
     49:   SVDAllocateSolution(svd,1);
     50:   DSSetType(svd->ds,DSSVD);
     51:   DSSetCompact(svd->ds,PETSC_TRUE);
     52:   DSAllocate(svd->ds,svd->ncv);
     53:   return(0);
     54: }

     56: PetscErrorCode SVDTwoSideLanczos(SVD svd,PetscReal *alpha,PetscReal *beta,BV V,BV U,PetscInt k,PetscInt n)
     57: {
     59:   PetscInt       i;
     60:   Vec            u,v;

     63:   BVGetColumn(svd->V,k,&v);
     64:   BVGetColumn(svd->U,k,&u);
     65:   SVDMatMult(svd,PETSC_FALSE,v,u);
     66:   BVRestoreColumn(svd->V,k,&v);
     67:   BVRestoreColumn(svd->U,k,&u);
     68:   BVOrthogonalizeColumn(svd->U,k,NULL,alpha+k,NULL);
     69:   BVScaleColumn(U,k,1.0/alpha[k]);

     71:   for (i=k+1;i<n;i++) {
     72:     BVGetColumn(svd->V,i,&v);
     73:     BVGetColumn(svd->U,i-1,&u);
     74:     SVDMatMult(svd,PETSC_TRUE,u,v);
     75:     BVRestoreColumn(svd->V,i,&v);
     76:     BVRestoreColumn(svd->U,i-1,&u);
     77:     BVOrthogonalizeColumn(svd->V,i,NULL,beta+i-1,NULL);
     78:     BVScaleColumn(V,i,1.0/beta[i-1]);

     80:     BVGetColumn(svd->V,i,&v);
     81:     BVGetColumn(svd->U,i,&u);
     82:     SVDMatMult(svd,PETSC_FALSE,v,u);
     83:     BVRestoreColumn(svd->V,i,&v);
     84:     BVRestoreColumn(svd->U,i,&u);
     85:     BVOrthogonalizeColumn(svd->U,i,NULL,alpha+i,NULL);
     86:     BVScaleColumn(U,i,1.0/alpha[i]);
     87:   }

     89:   BVGetColumn(svd->V,n,&v);
     90:   BVGetColumn(svd->U,n-1,&u);
     91:   SVDMatMult(svd,PETSC_TRUE,u,v);
     92:   BVRestoreColumn(svd->V,n,&v);
     93:   BVRestoreColumn(svd->U,n-1,&u);
     94:   BVOrthogonalizeColumn(svd->V,n,NULL,beta+n-1,NULL);
     95:   return(0);
     96: }

     98: static PetscErrorCode SVDOneSideLanczos(SVD svd,PetscReal *alpha,PetscReal *beta,BV V,Vec u,Vec u_1,PetscInt k,PetscInt n,PetscScalar* work)
     99: {
    101:   PetscInt       i,bvl,bvk;
    102:   PetscReal      a,b;
    103:   Vec            z,temp;

    106:   BVGetActiveColumns(V,&bvl,&bvk);
    107:   BVGetColumn(V,k,&z);
    108:   SVDMatMult(svd,PETSC_FALSE,z,u);
    109:   BVRestoreColumn(V,k,&z);

    111:   for (i=k+1;i<n;i++) {
    112:     BVGetColumn(V,i,&z);
    113:     SVDMatMult(svd,PETSC_TRUE,u,z);
    114:     BVRestoreColumn(V,i,&z);
    115:     VecNormBegin(u,NORM_2,&a);
    116:     BVSetActiveColumns(V,0,i);
    117:     BVDotColumnBegin(V,i,work);
    118:     VecNormEnd(u,NORM_2,&a);
    119:     BVDotColumnEnd(V,i,work);
    120:     VecScale(u,1.0/a);
    121:     BVMultColumn(V,-1.0/a,1.0/a,i,work);

    123:     /* h = V^* z, z = z - V h  */
    124:     BVDotColumn(V,i,work);
    125:     BVMultColumn(V,-1.0,1.0,i,work);
    126:     BVNormColumn(V,i,NORM_2,&b);
    127:     if (PetscAbsReal(b)<10*PETSC_MACHINE_EPSILON) SETERRQ(PetscObjectComm((PetscObject)svd),1,"Recurrence generated a zero vector; use a two-sided variant");
    128:     BVScaleColumn(V,i,1.0/b);

    130:     BVGetColumn(V,i,&z);
    131:     SVDMatMult(svd,PETSC_FALSE,z,u_1);
    132:     BVRestoreColumn(V,i,&z);
    133:     VecAXPY(u_1,-b,u);
    134:     alpha[i-1] = a;
    135:     beta[i-1] = b;
    136:     temp = u;
    137:     u = u_1;
    138:     u_1 = temp;
    139:   }

    141:   BVGetColumn(V,n,&z);
    142:   SVDMatMult(svd,PETSC_TRUE,u,z);
    143:   BVRestoreColumn(V,n,&z);
    144:   VecNormBegin(u,NORM_2,&a);
    145:   BVDotColumnBegin(V,n,work);
    146:   VecNormEnd(u,NORM_2,&a);
    147:   BVDotColumnEnd(V,n,work);
    148:   VecScale(u,1.0/a);
    149:   BVMultColumn(V,-1.0/a,1.0/a,n,work);

    151:   /* h = V^* z, z = z - V h  */
    152:   BVDotColumn(V,n,work);
    153:   BVMultColumn(V,-1.0,1.0,n,work);
    154:   BVNormColumn(V,i,NORM_2,&b);

    156:   alpha[n-1] = a;
    157:   beta[n-1] = b;
    158:   BVSetActiveColumns(V,bvl,bvk);
    159:   return(0);
    160: }

    162: PetscErrorCode SVDSolve_Lanczos(SVD svd)
    163: {
    165:   SVD_LANCZOS    *lanczos = (SVD_LANCZOS*)svd->data;
    166:   PetscReal      *alpha,*beta,lastbeta,norm,resnorm;
    167:   PetscScalar    *swork,*w,*Q,*PT;
    168:   PetscInt       i,k,j,nv,ld;
    169:   Vec            u=0,u_1=0;
    170:   Mat            U,VT;
    171:   PetscBool      conv;

    174:   /* allocate working space */
    175:   DSGetLeadingDimension(svd->ds,&ld);
    176:   PetscMalloc2(ld,&w,svd->ncv,&swork);

    178:   if (lanczos->oneside) {
    179:     SVDMatCreateVecs(svd,NULL,&u);
    180:     SVDMatCreateVecs(svd,NULL,&u_1);
    181:   }

    183:   /* normalize start vector */
    184:   if (!svd->nini) {
    185:     BVSetRandomColumn(svd->V,0);
    186:     BVNormColumn(svd->V,0,NORM_2,&norm);
    187:     BVScaleColumn(svd->V,0,1.0/norm);
    188:   }

    190:   while (svd->reason == SVD_CONVERGED_ITERATING) {
    191:     svd->its++;

    193:     /* inner loop */
    194:     nv = PetscMin(svd->nconv+svd->mpd,svd->ncv);
    195:     BVSetActiveColumns(svd->V,svd->nconv,nv);
    196:     DSGetArrayReal(svd->ds,DS_MAT_T,&alpha);
    197:     beta = alpha + ld;
    198:     if (lanczos->oneside) {
    199:       SVDOneSideLanczos(svd,alpha,beta,svd->V,u,u_1,svd->nconv,nv,swork);
    200:     } else {
    201:       BVSetActiveColumns(svd->U,svd->nconv,nv);
    202:       SVDTwoSideLanczos(svd,alpha,beta,svd->V,svd->U,svd->nconv,nv);
    203:     }
    204:     lastbeta = beta[nv-1];
    205:     DSRestoreArrayReal(svd->ds,DS_MAT_T,&alpha);

    207:     /* compute SVD of bidiagonal matrix */
    208:     DSSetDimensions(svd->ds,nv,nv,svd->nconv,0);
    209:     DSSetState(svd->ds,DS_STATE_INTERMEDIATE);
    210:     DSSolve(svd->ds,w,NULL);
    211:     DSSort(svd->ds,w,NULL,NULL,NULL,NULL);
    212:     DSSynchronize(svd->ds,w,NULL);

    214:     /* compute error estimates */
    215:     k = 0;
    216:     conv = PETSC_TRUE;
    217:     DSGetArray(svd->ds,DS_MAT_U,&Q);
    218:     for (i=svd->nconv;i<nv;i++) {
    219:       svd->sigma[i] = PetscRealPart(w[i]);
    220:       resnorm = PetscAbsScalar(Q[nv-1+i*ld])*lastbeta;
    221:       (*svd->converged)(svd,svd->sigma[i],resnorm,&svd->errest[i],svd->convergedctx);
    222:       if (conv) {
    223:         if (svd->errest[i] < svd->tol) k++;
    224:         else conv = PETSC_FALSE;
    225:       }
    226:     }
    227:     DSRestoreArray(svd->ds,DS_MAT_U,&Q);

    229:     /* check convergence */
    230:     (*svd->stopping)(svd,svd->its,svd->max_it,svd->nconv+k,svd->nsv,&svd->reason,svd->stoppingctx);

    232:     /* compute restart vector */
    233:     DSGetArray(svd->ds,DS_MAT_VT,&PT);
    234:     if (svd->reason == SVD_CONVERGED_ITERATING) {
    235:       if (k<nv-svd->nconv) {
    236:         for (j=svd->nconv;j<nv;j++) swork[j-svd->nconv] = PT[k+svd->nconv+j*ld];
    237:         BVMultColumn(svd->V,1.0,0.0,nv,swork);
    238:       } else {
    239:         /* all approximations have converged, generate a new initial vector */
    240:         BVSetRandomColumn(svd->V,nv);
    241:         BVOrthogonalizeColumn(svd->V,nv,NULL,&norm,NULL);
    242:         BVScaleColumn(svd->V,nv,1.0/norm);
    243:       }
    244:     }
    245:     DSRestoreArray(svd->ds,DS_MAT_VT,&PT);

    247:     /* compute converged singular vectors */
    248:     DSGetMat(svd->ds,DS_MAT_VT,&VT);
    249:     BVMultInPlaceTranspose(svd->V,VT,svd->nconv,svd->nconv+k);
    250:     MatDestroy(&VT);
    251:     if (!lanczos->oneside) {
    252:       DSGetMat(svd->ds,DS_MAT_U,&U);
    253:       BVMultInPlace(svd->U,U,svd->nconv,svd->nconv+k);
    254:       MatDestroy(&U);
    255:     }

    257:     /* copy restart vector from the last column */
    258:     if (svd->reason == SVD_CONVERGED_ITERATING) {
    259:       BVCopyColumn(svd->V,nv,svd->nconv+k);
    260:     }

    262:     svd->nconv += k;
    263:     SVDMonitor(svd,svd->its,svd->nconv,svd->sigma,svd->errest,nv);
    264:   }

    266:   /* free working space */
    267:   VecDestroy(&u);
    268:   VecDestroy(&u_1);
    269:   PetscFree2(w,swork);
    270:   return(0);
    271: }

    273: PetscErrorCode SVDSetFromOptions_Lanczos(PetscOptionItems *PetscOptionsObject,SVD svd)
    274: {
    276:   PetscBool      set,val;
    277:   SVD_LANCZOS    *lanczos = (SVD_LANCZOS*)svd->data;

    280:   PetscOptionsHead(PetscOptionsObject,"SVD Lanczos Options");

    282:     PetscOptionsBool("-svd_lanczos_oneside","Use one-side reorthogonalization","SVDLanczosSetOneSide",lanczos->oneside,&val,&set);
    283:     if (set) { SVDLanczosSetOneSide(svd,val); }

    285:   PetscOptionsTail();
    286:   return(0);
    287: }

    289: static PetscErrorCode SVDLanczosSetOneSide_Lanczos(SVD svd,PetscBool oneside)
    290: {
    291:   SVD_LANCZOS *lanczos = (SVD_LANCZOS*)svd->data;

    294:   if (lanczos->oneside != oneside) {
    295:     lanczos->oneside = oneside;
    296:     svd->state = SVD_STATE_INITIAL;
    297:   }
    298:   return(0);
    299: }

    301: /*@
    302:    SVDLanczosSetOneSide - Indicate if the variant of the Lanczos method
    303:    to be used is one-sided or two-sided.

    305:    Logically Collective on svd

    307:    Input Parameters:
    308: +  svd     - singular value solver
    309: -  oneside - boolean flag indicating if the method is one-sided or not

    311:    Options Database Key:
    312: .  -svd_lanczos_oneside <boolean> - Indicates the boolean flag

    314:    Note:
    315:    By default, a two-sided variant is selected, which is sometimes slightly
    316:    more robust. However, the one-sided variant is faster because it avoids
    317:    the orthogonalization associated to left singular vectors. It also saves
    318:    the memory required for storing such vectors.

    320:    Level: advanced

    322: .seealso: SVDTRLanczosSetOneSide()
    323: @*/
    324: PetscErrorCode SVDLanczosSetOneSide(SVD svd,PetscBool oneside)
    325: {

    331:   PetscTryMethod(svd,"SVDLanczosSetOneSide_C",(SVD,PetscBool),(svd,oneside));
    332:   return(0);
    333: }

    335: static PetscErrorCode SVDLanczosGetOneSide_Lanczos(SVD svd,PetscBool *oneside)
    336: {
    337:   SVD_LANCZOS *lanczos = (SVD_LANCZOS*)svd->data;

    340:   *oneside = lanczos->oneside;
    341:   return(0);
    342: }

    344: /*@
    345:    SVDLanczosGetOneSide - Gets if the variant of the Lanczos method
    346:    to be used is one-sided or two-sided.

    348:    Not Collective

    350:    Input Parameters:
    351: .  svd     - singular value solver

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

    356:    Level: advanced

    358: .seealso: SVDLanczosSetOneSide()
    359: @*/
    360: PetscErrorCode SVDLanczosGetOneSide(SVD svd,PetscBool *oneside)
    361: {

    367:   PetscUseMethod(svd,"SVDLanczosGetOneSide_C",(SVD,PetscBool*),(svd,oneside));
    368:   return(0);
    369: }

    371: PetscErrorCode SVDDestroy_Lanczos(SVD svd)
    372: {

    376:   PetscFree(svd->data);
    377:   PetscObjectComposeFunction((PetscObject)svd,"SVDLanczosSetOneSide_C",NULL);
    378:   PetscObjectComposeFunction((PetscObject)svd,"SVDLanczosGetOneSide_C",NULL);
    379:   return(0);
    380: }

    382: PetscErrorCode SVDView_Lanczos(SVD svd,PetscViewer viewer)
    383: {
    385:   SVD_LANCZOS    *lanczos = (SVD_LANCZOS*)svd->data;
    386:   PetscBool      isascii;

    389:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    390:   if (isascii) {
    391:     PetscViewerASCIIPrintf(viewer,"  %s-sided reorthogonalization\n",lanczos->oneside? "one": "two");
    392:   }
    393:   return(0);
    394: }

    396: SLEPC_EXTERN PetscErrorCode SVDCreate_Lanczos(SVD svd)
    397: {
    399:   SVD_LANCZOS    *ctx;

    402:   PetscNewLog(svd,&ctx);
    403:   svd->data = (void*)ctx;

    405:   svd->ops->setup          = SVDSetUp_Lanczos;
    406:   svd->ops->solve          = SVDSolve_Lanczos;
    407:   svd->ops->destroy        = SVDDestroy_Lanczos;
    408:   svd->ops->setfromoptions = SVDSetFromOptions_Lanczos;
    409:   svd->ops->view           = SVDView_Lanczos;
    410:   PetscObjectComposeFunction((PetscObject)svd,"SVDLanczosSetOneSide_C",SVDLanczosSetOneSide_Lanczos);
    411:   PetscObjectComposeFunction((PetscObject)svd,"SVDLanczosGetOneSide_C",SVDLanczosGetOneSide_Lanczos);
    412:   return(0);
    413: }