Actual source code: gklanczos.c

slepc-3.15.1 2021-05-28
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2021, 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:   SVDCheckStandard(svd);
 45:   MatGetSize(svd->A,NULL,&N);
 46:   SVDSetDimensions_Default(svd);
 47:   if (svd->ncv>svd->nsv+svd->mpd) SETERRQ(PetscObjectComm((PetscObject)svd),1,"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:   SVDAllocateSolution(svd,1);
 51:   DSSetType(svd->ds,DSSVD);
 52:   DSSetCompact(svd->ds,PETSC_TRUE);
 53:   DSAllocate(svd->ds,svd->ncv);
 54:   return(0);
 55: }

 57: PetscErrorCode SVDTwoSideLanczos(SVD svd,PetscReal *alpha,PetscReal *beta,BV V,BV U,PetscInt k,PetscInt n)
 58: {
 60:   PetscInt       i;
 61:   Vec            u,v;

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

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

 81:     BVGetColumn(svd->V,i,&v);
 82:     BVGetColumn(svd->U,i,&u);
 83:     MatMult(svd->A,v,u);
 84:     BVRestoreColumn(svd->V,i,&v);
 85:     BVRestoreColumn(svd->U,i,&u);
 86:     BVOrthogonalizeColumn(svd->U,i,NULL,alpha+i,NULL);
 87:     BVScaleColumn(U,i,1.0/alpha[i]);
 88:   }

 90:   BVGetColumn(svd->V,n,&v);
 91:   BVGetColumn(svd->U,n-1,&u);
 92:   MatMult(svd->AT,u,v);
 93:   BVRestoreColumn(svd->V,n,&v);
 94:   BVRestoreColumn(svd->U,n-1,&u);
 95:   BVOrthogonalizeColumn(svd->V,n,NULL,beta+n-1,NULL);
 96:   return(0);
 97: }

 99: static PetscErrorCode SVDOneSideLanczos(SVD svd,PetscReal *alpha,PetscReal *beta,BV V,Vec u,Vec u_1,PetscInt k,PetscInt n,PetscScalar* work)
100: {
102:   PetscInt       i,bvl,bvk;
103:   PetscReal      a,b;
104:   Vec            z,temp;

107:   BVGetActiveColumns(V,&bvl,&bvk);
108:   BVGetColumn(V,k,&z);
109:   MatMult(svd->A,z,u);
110:   BVRestoreColumn(V,k,&z);

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

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

131:     BVGetColumn(V,i,&z);
132:     MatMult(svd->A,z,u_1);
133:     BVRestoreColumn(V,i,&z);
134:     VecAXPY(u_1,-b,u);
135:     alpha[i-1] = a;
136:     beta[i-1] = b;
137:     temp = u;
138:     u = u_1;
139:     u_1 = temp;
140:   }

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

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

157:   alpha[n-1] = a;
158:   beta[n-1] = b;
159:   BVSetActiveColumns(V,bvl,bvk);
160:   return(0);
161: }

163: PetscErrorCode SVDSolve_Lanczos(SVD svd)
164: {
166:   SVD_LANCZOS    *lanczos = (SVD_LANCZOS*)svd->data;
167:   PetscReal      *alpha,*beta,lastbeta,norm,resnorm;
168:   PetscScalar    *swork,*w,*Q,*PT;
169:   PetscInt       i,k,j,nv,ld;
170:   Vec            u=0,u_1=0;
171:   Mat            U,VT;
172:   PetscBool      conv;

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

179:   if (lanczos->oneside) {
180:     MatCreateVecs(svd->A,NULL,&u);
181:     MatCreateVecs(svd->A,NULL,&u_1);
182:   }

184:   /* normalize start vector */
185:   if (!svd->nini) {
186:     BVSetRandomColumn(svd->V,0);
187:     BVNormColumn(svd->V,0,NORM_2,&norm);
188:     BVScaleColumn(svd->V,0,1.0/norm);
189:   }

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

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

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

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

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

234:     /* compute restart vector */
235:     DSGetArray(svd->ds,DS_MAT_VT,&PT);
236:     if (svd->reason == SVD_CONVERGED_ITERATING) {
237:       if (k<nv-svd->nconv) {
238:         for (j=svd->nconv;j<nv;j++) swork[j-svd->nconv] = PT[k+svd->nconv+j*ld];
239:         BVMultColumn(svd->V,1.0,0.0,nv,swork);
240:       } else {
241:         /* all approximations have converged, generate a new initial vector */
242:         BVSetRandomColumn(svd->V,nv);
243:         BVOrthogonalizeColumn(svd->V,nv,NULL,&norm,NULL);
244:         BVScaleColumn(svd->V,nv,1.0/norm);
245:       }
246:     }
247:     DSRestoreArray(svd->ds,DS_MAT_VT,&PT);

249:     /* compute converged singular vectors */
250:     DSGetMat(svd->ds,DS_MAT_VT,&VT);
251:     BVMultInPlaceTranspose(svd->V,VT,svd->nconv,svd->nconv+k);
252:     MatDestroy(&VT);
253:     if (!lanczos->oneside) {
254:       DSGetMat(svd->ds,DS_MAT_U,&U);
255:       BVMultInPlace(svd->U,U,svd->nconv,svd->nconv+k);
256:       MatDestroy(&U);
257:     }

259:     /* copy restart vector from the last column */
260:     if (svd->reason == SVD_CONVERGED_ITERATING) {
261:       BVCopyColumn(svd->V,nv,svd->nconv+k);
262:     }

264:     svd->nconv += k;
265:     SVDMonitor(svd,svd->its,svd->nconv,svd->sigma,svd->errest,nv);
266:   }

268:   /* free working space */
269:   VecDestroy(&u);
270:   VecDestroy(&u_1);
271:   PetscFree2(w,swork);
272:   return(0);
273: }

275: PetscErrorCode SVDSetFromOptions_Lanczos(PetscOptionItems *PetscOptionsObject,SVD svd)
276: {
278:   PetscBool      set,val;
279:   SVD_LANCZOS    *lanczos = (SVD_LANCZOS*)svd->data;

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

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

287:   PetscOptionsTail();
288:   return(0);
289: }

291: static PetscErrorCode SVDLanczosSetOneSide_Lanczos(SVD svd,PetscBool oneside)
292: {
293:   SVD_LANCZOS *lanczos = (SVD_LANCZOS*)svd->data;

296:   if (lanczos->oneside != oneside) {
297:     lanczos->oneside = oneside;
298:     svd->state = SVD_STATE_INITIAL;
299:   }
300:   return(0);
301: }

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

307:    Logically Collective on svd

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

313:    Options Database Key:
314: .  -svd_lanczos_oneside <boolean> - Indicates the boolean flag

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

322:    Level: advanced

324: .seealso: SVDTRLanczosSetOneSide()
325: @*/
326: PetscErrorCode SVDLanczosSetOneSide(SVD svd,PetscBool oneside)
327: {

333:   PetscTryMethod(svd,"SVDLanczosSetOneSide_C",(SVD,PetscBool),(svd,oneside));
334:   return(0);
335: }

337: static PetscErrorCode SVDLanczosGetOneSide_Lanczos(SVD svd,PetscBool *oneside)
338: {
339:   SVD_LANCZOS *lanczos = (SVD_LANCZOS*)svd->data;

342:   *oneside = lanczos->oneside;
343:   return(0);
344: }

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

350:    Not Collective

352:    Input Parameters:
353: .  svd     - singular value solver

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

358:    Level: advanced

360: .seealso: SVDLanczosSetOneSide()
361: @*/
362: PetscErrorCode SVDLanczosGetOneSide(SVD svd,PetscBool *oneside)
363: {

369:   PetscUseMethod(svd,"SVDLanczosGetOneSide_C",(SVD,PetscBool*),(svd,oneside));
370:   return(0);
371: }

373: PetscErrorCode SVDDestroy_Lanczos(SVD svd)
374: {

378:   PetscFree(svd->data);
379:   PetscObjectComposeFunction((PetscObject)svd,"SVDLanczosSetOneSide_C",NULL);
380:   PetscObjectComposeFunction((PetscObject)svd,"SVDLanczosGetOneSide_C",NULL);
381:   return(0);
382: }

384: PetscErrorCode SVDView_Lanczos(SVD svd,PetscViewer viewer)
385: {
387:   SVD_LANCZOS    *lanczos = (SVD_LANCZOS*)svd->data;
388:   PetscBool      isascii;

391:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
392:   if (isascii) {
393:     PetscViewerASCIIPrintf(viewer,"  %s-sided reorthogonalization\n",lanczos->oneside? "one": "two");
394:   }
395:   return(0);
396: }

398: SLEPC_EXTERN PetscErrorCode SVDCreate_Lanczos(SVD svd)
399: {
401:   SVD_LANCZOS    *ctx;

404:   PetscNewLog(svd,&ctx);
405:   svd->data = (void*)ctx;

407:   svd->ops->setup          = SVDSetUp_Lanczos;
408:   svd->ops->solve          = SVDSolve_Lanczos;
409:   svd->ops->destroy        = SVDDestroy_Lanczos;
410:   svd->ops->setfromoptions = SVDSetFromOptions_Lanczos;
411:   svd->ops->view           = SVDView_Lanczos;
412:   svd->ops->computevectors = SVDComputeVectors_Left;
413:   PetscObjectComposeFunction((PetscObject)svd,"SVDLanczosSetOneSide_C",SVDLanczosSetOneSide_Lanczos);
414:   PetscObjectComposeFunction((PetscObject)svd,"SVDLanczosGetOneSide_C",SVDLanczosGetOneSide_Lanczos);
415:   return(0);
416: }