Actual source code: gklanczos.c

slepc-3.17.1 2022-04-11
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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:   SVDCheckStandard(svd);
 43:   MatGetSize(svd->A,NULL,&N);
 44:   SVDSetDimensions_Default(svd);
 46:   if (svd->max_it==PETSC_DEFAULT) svd->max_it = PetscMax(N/svd->ncv,100);
 47:   svd->leftbasis = PetscNot(lanczos->oneside);
 48:   SVDAllocateSolution(svd,1);
 49:   DSSetType(svd->ds,DSSVD);
 50:   DSSetCompact(svd->ds,PETSC_TRUE);
 51:   DSSetExtraRow(svd->ds,PETSC_TRUE);
 52:   DSAllocate(svd->ds,svd->ncv+1);
 53:   PetscFunctionReturn(0);
 54: }

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

 62:   BVGetColumn(svd->V,k,&v);
 63:   BVGetColumn(svd->U,k,&u);
 64:   MatMult(svd->A,v,u);
 65:   BVRestoreColumn(svd->V,k,&v);
 66:   BVRestoreColumn(svd->U,k,&u);
 67:   BVOrthonormalizeColumn(svd->U,k,PETSC_FALSE,alpha+k,&lindep);
 68:   if (PetscUnlikely(lindep)) {
 69:     *n = k;
 70:     if (breakdown) *breakdown = lindep;
 71:     PetscFunctionReturn(0);
 72:   }

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

 97:   if (!lindep) {
 98:     BVGetColumn(svd->V,*n,&v);
 99:     BVGetColumn(svd->U,*n-1,&u);
100:     MatMult(svd->AT,u,v);
101:     BVRestoreColumn(svd->V,*n,&v);
102:     BVRestoreColumn(svd->U,*n-1,&u);
103:     BVOrthogonalizeColumn(svd->V,*n,NULL,beta+*n-1,&lindep);
104:   }
105:   if (PetscUnlikely(breakdown)) *breakdown = lindep;
106:   PetscFunctionReturn(0);
107: }

109: static PetscErrorCode SVDOneSideLanczos(SVD svd,PetscReal *alpha,PetscReal *beta,BV V,Vec u,Vec u_1,PetscInt k,PetscInt n,PetscScalar* work)
110: {
111:   PetscInt       i,bvl,bvk;
112:   PetscReal      a,b;
113:   Vec            z,temp;

115:   BVGetActiveColumns(V,&bvl,&bvk);
116:   BVGetColumn(V,k,&z);
117:   MatMult(svd->A,z,u);
118:   BVRestoreColumn(V,k,&z);

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

132:     /* h = V^* z, z = z - V h  */
133:     BVDotColumn(V,i,work);
134:     BVMultColumn(V,-1.0,1.0,i,work);
135:     BVNormColumn(V,i,NORM_2,&b);
137:     BVScaleColumn(V,i,1.0/b);

139:     BVGetColumn(V,i,&z);
140:     MatMult(svd->A,z,u_1);
141:     BVRestoreColumn(V,i,&z);
142:     VecAXPY(u_1,-b,u);
143:     alpha[i-1] = a;
144:     beta[i-1] = b;
145:     temp = u;
146:     u = u_1;
147:     u_1 = temp;
148:   }

150:   BVGetColumn(V,n,&z);
151:   MatMult(svd->AT,u,z);
152:   BVRestoreColumn(V,n,&z);
153:   VecNormBegin(u,NORM_2,&a);
154:   BVDotColumnBegin(V,n,work);
155:   VecNormEnd(u,NORM_2,&a);
156:   BVDotColumnEnd(V,n,work);
157:   VecScale(u,1.0/a);
158:   BVMultColumn(V,-1.0/a,1.0/a,n,work);

160:   /* h = V^* z, z = z - V h  */
161:   BVDotColumn(V,n,work);
162:   BVMultColumn(V,-1.0,1.0,n,work);
163:   BVNormColumn(V,i,NORM_2,&b);

165:   alpha[n-1] = a;
166:   beta[n-1] = b;
167:   BVSetActiveColumns(V,bvl,bvk);
168:   PetscFunctionReturn(0);
169: }

171: /*
172:    SVDKrylovConvergence - Implements the loop that checks for convergence
173:    in Krylov methods.

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

182:    Output Parameter:
183:      kout  - the first index where the convergence test failed
184: */
185: PetscErrorCode SVDKrylovConvergence(SVD svd,PetscBool getall,PetscInt kini,PetscInt nits,PetscReal normr,PetscInt *kout)
186: {
187:   PetscInt       k,marker,ld;
188:   PetscReal      *alpha,*beta,*betah,resnorm;
189:   PetscBool      extra;

191:   if (PetscUnlikely(svd->conv == SVD_CONV_MAXIT && svd->its >= svd->max_it)) *kout = svd->nsv;
192:   else {
193:     DSGetLeadingDimension(svd->ds,&ld);
194:     DSGetExtraRow(svd->ds,&extra);
196:     marker = -1;
197:     if (svd->trackall) getall = PETSC_TRUE;
198:     DSGetArrayReal(svd->ds,DS_MAT_T,&alpha);
199:     beta = alpha + ld;
200:     betah = alpha + 2*ld;
201:     for (k=kini;k<kini+nits;k++) {
202:       if (svd->isgeneralized) resnorm = SlepcAbs(beta[k],betah[k])*normr;
203:       else resnorm = PetscAbsReal(beta[k]);
204:       (*svd->converged)(svd,svd->sigma[k],resnorm,&svd->errest[k],svd->convergedctx);
205:       if (marker==-1 && svd->errest[k] >= svd->tol) marker = k;
206:       if (marker!=-1 && !getall) break;
207:     }
208:     DSRestoreArrayReal(svd->ds,DS_MAT_T,&alpha);
209:     if (marker!=-1) k = marker;
210:     *kout = k;
211:   }
212:   PetscFunctionReturn(0);
213: }

215: PetscErrorCode SVDSolve_Lanczos(SVD svd)
216: {
217:   SVD_LANCZOS    *lanczos = (SVD_LANCZOS*)svd->data;
218:   PetscReal      *alpha,*beta;
219:   PetscScalar    *swork,*w,*P;
220:   PetscInt       i,k,j,nv,ld;
221:   Vec            u=0,u_1=0;
222:   Mat            U,V;

224:   /* allocate working space */
225:   DSGetLeadingDimension(svd->ds,&ld);
226:   PetscMalloc2(ld,&w,svd->ncv,&swork);

228:   if (lanczos->oneside) {
229:     MatCreateVecs(svd->A,NULL,&u);
230:     MatCreateVecs(svd->A,NULL,&u_1);
231:   }

233:   /* normalize start vector */
234:   if (!svd->nini) {
235:     BVSetRandomColumn(svd->V,0);
236:     BVOrthonormalizeColumn(svd->V,0,PETSC_TRUE,NULL,NULL);
237:   }

239:   while (svd->reason == SVD_CONVERGED_ITERATING) {
240:     svd->its++;

242:     /* inner loop */
243:     nv = PetscMin(svd->nconv+svd->mpd,svd->ncv);
244:     BVSetActiveColumns(svd->V,svd->nconv,nv);
245:     DSGetArrayReal(svd->ds,DS_MAT_T,&alpha);
246:     beta = alpha + ld;
247:     if (lanczos->oneside) SVDOneSideLanczos(svd,alpha,beta,svd->V,u,u_1,svd->nconv,nv,swork);
248:     else {
249:       BVSetActiveColumns(svd->U,svd->nconv,nv);
250:       SVDTwoSideLanczos(svd,alpha,beta,svd->V,svd->U,svd->nconv,&nv,NULL);
251:     }
252:     DSRestoreArrayReal(svd->ds,DS_MAT_T,&alpha);

254:     /* compute SVD of bidiagonal matrix */
255:     DSSetDimensions(svd->ds,nv,svd->nconv,0);
256:     DSSVDSetDimensions(svd->ds,nv);
257:     DSSetState(svd->ds,DS_STATE_INTERMEDIATE);
258:     DSSolve(svd->ds,w,NULL);
259:     DSSort(svd->ds,w,NULL,NULL,NULL,NULL);
260:     DSUpdateExtraRow(svd->ds);
261:     DSSynchronize(svd->ds,w,NULL);
262:     for (i=svd->nconv;i<nv;i++) svd->sigma[i] = PetscRealPart(w[i]);

264:     /* check convergence */
265:     SVDKrylovConvergence(svd,PETSC_FALSE,svd->nconv,nv-svd->nconv,1.0,&k);
266:     (*svd->stopping)(svd,svd->its,svd->max_it,k,svd->nsv,&svd->reason,svd->stoppingctx);

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

282:     /* compute converged singular vectors */
283:     DSGetMat(svd->ds,DS_MAT_V,&V);
284:     BVMultInPlace(svd->V,V,svd->nconv,k);
285:     MatDestroy(&V);
286:     if (!lanczos->oneside) {
287:       DSGetMat(svd->ds,DS_MAT_U,&U);
288:       BVMultInPlace(svd->U,U,svd->nconv,k);
289:       MatDestroy(&U);
290:     }

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

295:     svd->nconv = k;
296:     SVDMonitor(svd,svd->its,svd->nconv,svd->sigma,svd->errest,nv);
297:   }

299:   /* free working space */
300:   VecDestroy(&u);
301:   VecDestroy(&u_1);
302:   PetscFree2(w,swork);
303:   PetscFunctionReturn(0);
304: }

306: PetscErrorCode SVDSetFromOptions_Lanczos(PetscOptionItems *PetscOptionsObject,SVD svd)
307: {
308:   PetscBool      set,val;
309:   SVD_LANCZOS    *lanczos = (SVD_LANCZOS*)svd->data;

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

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

316:   PetscOptionsTail();
317:   PetscFunctionReturn(0);
318: }

320: static PetscErrorCode SVDLanczosSetOneSide_Lanczos(SVD svd,PetscBool oneside)
321: {
322:   SVD_LANCZOS *lanczos = (SVD_LANCZOS*)svd->data;

324:   if (lanczos->oneside != oneside) {
325:     lanczos->oneside = oneside;
326:     svd->state = SVD_STATE_INITIAL;
327:   }
328:   PetscFunctionReturn(0);
329: }

331: /*@
332:    SVDLanczosSetOneSide - Indicate if the variant of the Lanczos method
333:    to be used is one-sided or two-sided.

335:    Logically Collective on svd

337:    Input Parameters:
338: +  svd     - singular value solver
339: -  oneside - boolean flag indicating if the method is one-sided or not

341:    Options Database Key:
342: .  -svd_lanczos_oneside <boolean> - Indicates the boolean flag

344:    Note:
345:    By default, a two-sided variant is selected, which is sometimes slightly
346:    more robust. However, the one-sided variant is faster because it avoids
347:    the orthogonalization associated to left singular vectors. It also saves
348:    the memory required for storing such vectors.

350:    Level: advanced

352: .seealso: SVDTRLanczosSetOneSide()
353: @*/
354: PetscErrorCode SVDLanczosSetOneSide(SVD svd,PetscBool oneside)
355: {
358:   PetscTryMethod(svd,"SVDLanczosSetOneSide_C",(SVD,PetscBool),(svd,oneside));
359:   PetscFunctionReturn(0);
360: }

362: static PetscErrorCode SVDLanczosGetOneSide_Lanczos(SVD svd,PetscBool *oneside)
363: {
364:   SVD_LANCZOS *lanczos = (SVD_LANCZOS*)svd->data;

366:   *oneside = lanczos->oneside;
367:   PetscFunctionReturn(0);
368: }

370: /*@
371:    SVDLanczosGetOneSide - Gets if the variant of the Lanczos method
372:    to be used is one-sided or two-sided.

374:    Not Collective

376:    Input Parameters:
377: .  svd     - singular value solver

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

382:    Level: advanced

384: .seealso: SVDLanczosSetOneSide()
385: @*/
386: PetscErrorCode SVDLanczosGetOneSide(SVD svd,PetscBool *oneside)
387: {
390:   PetscUseMethod(svd,"SVDLanczosGetOneSide_C",(SVD,PetscBool*),(svd,oneside));
391:   PetscFunctionReturn(0);
392: }

394: PetscErrorCode SVDDestroy_Lanczos(SVD svd)
395: {
396:   PetscFree(svd->data);
397:   PetscObjectComposeFunction((PetscObject)svd,"SVDLanczosSetOneSide_C",NULL);
398:   PetscObjectComposeFunction((PetscObject)svd,"SVDLanczosGetOneSide_C",NULL);
399:   PetscFunctionReturn(0);
400: }

402: PetscErrorCode SVDView_Lanczos(SVD svd,PetscViewer viewer)
403: {
404:   SVD_LANCZOS    *lanczos = (SVD_LANCZOS*)svd->data;
405:   PetscBool      isascii;

407:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
408:   if (isascii) PetscViewerASCIIPrintf(viewer,"  %s-sided reorthogonalization\n",lanczos->oneside? "one": "two");
409:   PetscFunctionReturn(0);
410: }

412: SLEPC_EXTERN PetscErrorCode SVDCreate_Lanczos(SVD svd)
413: {
414:   SVD_LANCZOS    *ctx;

416:   PetscNewLog(svd,&ctx);
417:   svd->data = (void*)ctx;

419:   svd->ops->setup          = SVDSetUp_Lanczos;
420:   svd->ops->solve          = SVDSolve_Lanczos;
421:   svd->ops->destroy        = SVDDestroy_Lanczos;
422:   svd->ops->setfromoptions = SVDSetFromOptions_Lanczos;
423:   svd->ops->view           = SVDView_Lanczos;
424:   svd->ops->computevectors = SVDComputeVectors_Left;
425:   PetscObjectComposeFunction((PetscObject)svd,"SVDLanczosSetOneSide_C",SVDLanczosSetOneSide_Lanczos);
426:   PetscObjectComposeFunction((PetscObject)svd,"SVDLanczosGetOneSide_C",SVDLanczosGetOneSide_Lanczos);
427:   PetscFunctionReturn(0);
428: }