Actual source code: gklanczos.c

slepc-3.6.1 2015-09-03
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  1: /*

  3:    SLEPc singular value solver: "lanczos"

  5:    Method: Explicitly restarted Lanczos

  7:    Algorithm:

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

 11:    References:

 13:        [1] G.H. Golub and W. Kahan, "Calculating the singular values
 14:            and pseudo-inverse of a matrix", SIAM J. Numer. Anal. Ser.
 15:            B 2:205-224, 1965.

 17:        [2] V. Hernandez, J.E. Roman, and A. Tomas, "A robust and
 18:            efficient parallel SVD solver based on restarted Lanczos
 19:            bidiagonalization", Elec. Trans. Numer. Anal. 31:68-85,
 20:            2008.

 22:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 23:    SLEPc - Scalable Library for Eigenvalue Problem Computations
 24:    Copyright (c) 2002-2015, Universitat Politecnica de Valencia, Spain

 26:    This file is part of SLEPc.

 28:    SLEPc is free software: you can redistribute it and/or modify it under  the
 29:    terms of version 3 of the GNU Lesser General Public License as published by
 30:    the Free Software Foundation.

 32:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
 33:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
 34:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
 35:    more details.

 37:    You  should have received a copy of the GNU Lesser General  Public  License
 38:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
 39:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 40: */

 42: #include <slepc/private/svdimpl.h>                /*I "slepcsvd.h" I*/

 44: typedef struct {
 45:   PetscBool oneside;
 46: } SVD_LANCZOS;

 50: PetscErrorCode SVDSetUp_Lanczos(SVD svd)
 51: {
 53:   SVD_LANCZOS    *lanczos = (SVD_LANCZOS*)svd->data;
 54:   PetscInt       N;

 57:   SVDMatGetSize(svd,NULL,&N);
 58:   SVDSetDimensions_Default(svd);
 59:   if (svd->ncv>svd->nsv+svd->mpd) SETERRQ(PetscObjectComm((PetscObject)svd),1,"The value of ncv must not be larger than nev+mpd");
 60:   if (!svd->max_it) svd->max_it = PetscMax(N/svd->ncv,100);
 61:   svd->leftbasis = (lanczos->oneside)? PETSC_FALSE: PETSC_TRUE;
 62:   SVDAllocateSolution(svd,1);
 63:   DSSetType(svd->ds,DSSVD);
 64:   DSSetCompact(svd->ds,PETSC_TRUE);
 65:   DSAllocate(svd->ds,svd->ncv);
 66:   return(0);
 67: }

 71: PetscErrorCode SVDTwoSideLanczos(SVD svd,PetscReal *alpha,PetscReal *beta,BV V,BV U,PetscInt k,PetscInt n)
 72: {
 74:   PetscInt       i;
 75:   Vec            u,v;

 78:   BVGetColumn(svd->V,k,&v);
 79:   BVGetColumn(svd->U,k,&u);
 80:   SVDMatMult(svd,PETSC_FALSE,v,u);
 81:   BVRestoreColumn(svd->V,k,&v);
 82:   BVRestoreColumn(svd->U,k,&u);
 83:   BVOrthogonalizeColumn(svd->U,k,NULL,alpha+k,NULL);
 84:   BVScaleColumn(U,k,1.0/alpha[k]);

 86:   for (i=k+1;i<n;i++) {
 87:     BVGetColumn(svd->V,i,&v);
 88:     BVGetColumn(svd->U,i-1,&u);
 89:     SVDMatMult(svd,PETSC_TRUE,u,v);
 90:     BVRestoreColumn(svd->V,i,&v);
 91:     BVRestoreColumn(svd->U,i-1,&u);
 92:     BVOrthogonalizeColumn(svd->V,i,NULL,beta+i-1,NULL);
 93:     BVScaleColumn(V,i,1.0/beta[i-1]);

 95:     BVGetColumn(svd->V,i,&v);
 96:     BVGetColumn(svd->U,i,&u);
 97:     SVDMatMult(svd,PETSC_FALSE,v,u);
 98:     BVRestoreColumn(svd->V,i,&v);
 99:     BVRestoreColumn(svd->U,i,&u);
100:     BVOrthogonalizeColumn(svd->U,i,NULL,alpha+i,NULL);
101:     BVScaleColumn(U,i,1.0/alpha[i]);
102:   }

104:   BVGetColumn(svd->V,n,&v);
105:   BVGetColumn(svd->U,n-1,&u);
106:   SVDMatMult(svd,PETSC_TRUE,u,v);
107:   BVRestoreColumn(svd->V,n,&v);
108:   BVRestoreColumn(svd->U,n-1,&u);
109:   BVOrthogonalizeColumn(svd->V,n,NULL,beta+n-1,NULL);
110:   return(0);
111: }

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

123:   BVGetActiveColumns(V,&bvl,&bvk);
124:   BVGetColumn(V,k,&z);
125:   SVDMatMult(svd,PETSC_FALSE,z,u);
126:   BVRestoreColumn(V,k,&z);

128:   for (i=k+1;i<n;i++) {
129:     BVGetColumn(V,i,&z);
130:     SVDMatMult(svd,PETSC_TRUE,u,z);
131:     BVRestoreColumn(V,i,&z);
132:     VecNormBegin(u,NORM_2,&a);
133:     BVSetActiveColumns(V,0,i);
134:     BVDotColumnBegin(V,i,work);
135:     VecNormEnd(u,NORM_2,&a);
136:     BVDotColumnEnd(V,i,work);
137:     VecScale(u,1.0/a);
138:     BVMultColumn(V,-1.0/a,1.0/a,i,work);

140:     /* h = V^* z, z = z - V h  */
141:     BVDotColumn(V,i,work);
142:     BVMultColumn(V,-1.0,1.0,i,work);
143:     BVNormColumn(V,i,NORM_2,&b);
144:     BVScaleColumn(V,i,1.0/b);

146:     BVGetColumn(V,i,&z);
147:     SVDMatMult(svd,PETSC_FALSE,z,u_1);
148:     BVRestoreColumn(V,i,&z);
149:     VecAXPY(u_1,-b,u);
150:     alpha[i-1] = a;
151:     beta[i-1] = b;
152:     temp = u;
153:     u = u_1;
154:     u_1 = temp;
155:   }

157:   BVGetColumn(V,n,&z);
158:   SVDMatMult(svd,PETSC_TRUE,u,z);
159:   BVRestoreColumn(V,n,&z);
160:   VecNormBegin(u,NORM_2,&a);
161:   BVDotColumnBegin(V,n,work);
162:   VecNormEnd(u,NORM_2,&a);
163:   BVDotColumnEnd(V,n,work);
164:   VecScale(u,1.0/a);
165:   BVMultColumn(V,-1.0/a,1.0/a,n,work);

167:   /* h = V^* z, z = z - V h  */
168:   BVDotColumn(V,n,work);
169:   BVMultColumn(V,-1.0,1.0,n,work);
170:   BVNormColumn(V,i,NORM_2,&b);

172:   alpha[n-1] = a;
173:   beta[n-1] = b;
174:   BVSetActiveColumns(V,bvl,bvk);
175:   return(0);
176: }

180: PetscErrorCode SVDSolve_Lanczos(SVD svd)
181: {
183:   SVD_LANCZOS    *lanczos = (SVD_LANCZOS*)svd->data;
184:   PetscReal      *alpha,*beta,lastbeta,norm;
185:   PetscScalar    *swork,*w,*Q,*PT;
186:   PetscInt       i,k,j,nv,ld;
187:   Vec            u=0,u_1=0;
188:   Mat            U,VT;
189:   PetscBool      conv;

192:   /* allocate working space */
193:   DSGetLeadingDimension(svd->ds,&ld);
194:   PetscMalloc2(ld,&w,svd->ncv,&swork);

196:   if (lanczos->oneside) {
197:     SVDMatCreateVecs(svd,NULL,&u);
198:     SVDMatCreateVecs(svd,NULL,&u_1);
199:   }

201:   /* normalize start vector */
202:   if (!svd->nini) {
203:     BVSetRandomColumn(svd->V,0,svd->rand);
204:     BVNormColumn(svd->V,0,NORM_2,&norm);
205:     BVScaleColumn(svd->V,0,1.0/norm);
206:   }

208:   while (svd->reason == SVD_CONVERGED_ITERATING) {
209:     svd->its++;

211:     /* inner loop */
212:     nv = PetscMin(svd->nconv+svd->mpd,svd->ncv);
213:     BVSetActiveColumns(svd->V,svd->nconv,nv);
214:     DSGetArrayReal(svd->ds,DS_MAT_T,&alpha);
215:     beta = alpha + ld;
216:     if (lanczos->oneside) {
217:       SVDOneSideLanczos(svd,alpha,beta,svd->V,u,u_1,svd->nconv,nv,swork);
218:     } else {
219:       BVSetActiveColumns(svd->U,svd->nconv,nv);
220:       SVDTwoSideLanczos(svd,alpha,beta,svd->V,svd->U,svd->nconv,nv);
221:     }
222:     lastbeta = beta[nv-1];
223:     DSRestoreArrayReal(svd->ds,DS_MAT_T,&alpha);

225:     /* compute SVD of bidiagonal matrix */
226:     DSSetDimensions(svd->ds,nv,nv,svd->nconv,0);
227:     DSSetState(svd->ds,DS_STATE_INTERMEDIATE);
228:     DSSolve(svd->ds,w,NULL);
229:     DSSort(svd->ds,w,NULL,NULL,NULL,NULL);

231:     /* compute error estimates */
232:     k = 0;
233:     conv = PETSC_TRUE;
234:     DSGetArray(svd->ds,DS_MAT_U,&Q);
235:     for (i=svd->nconv;i<nv;i++) {
236:       svd->sigma[i] = PetscRealPart(w[i]);
237:       svd->errest[i] = PetscAbsScalar(Q[nv-1+i*ld])*lastbeta;
238:       if (svd->sigma[i] > svd->tol) svd->errest[i] /= svd->sigma[i];
239:       if (conv) {
240:         if (svd->errest[i] < svd->tol) k++;
241:         else conv = PETSC_FALSE;
242:       }
243:     }
244:     DSRestoreArray(svd->ds,DS_MAT_U,&Q);

246:     /* check convergence */
247:     if (svd->its >= svd->max_it) svd->reason = SVD_DIVERGED_ITS;
248:     if (svd->nconv+k >= svd->nsv) svd->reason = SVD_CONVERGED_TOL;

250:     /* compute restart vector */
251:     DSGetArray(svd->ds,DS_MAT_VT,&PT);
252:     if (svd->reason == SVD_CONVERGED_ITERATING) {
253:       for (j=svd->nconv;j<nv;j++) swork[j-svd->nconv] = PT[k+svd->nconv+j*ld];
254:       BVMultColumn(svd->V,1.0,0.0,nv,swork);
255:     }
256:     DSRestoreArray(svd->ds,DS_MAT_VT,&PT);

258:     /* compute converged singular vectors */
259:     DSGetMat(svd->ds,DS_MAT_VT,&VT);
260:     BVMultInPlaceTranspose(svd->V,VT,svd->nconv,svd->nconv+k);
261:     MatDestroy(&VT);
262:     if (!lanczos->oneside) {
263:       DSGetMat(svd->ds,DS_MAT_U,&U);
264:       BVMultInPlace(svd->U,U,svd->nconv,svd->nconv+k);
265:       MatDestroy(&U);
266:     }

268:     /* copy restart vector from the last column */
269:     if (svd->reason == SVD_CONVERGED_ITERATING) {
270:       BVCopyColumn(svd->V,nv,svd->nconv+k);
271:     }

273:     svd->nconv += k;
274:     SVDMonitor(svd,svd->its,svd->nconv,svd->sigma,svd->errest,nv);
275:   }

277:   /* free working space */
278:   VecDestroy(&u);
279:   VecDestroy(&u_1);
280:   PetscFree2(w,swork);
281:   return(0);
282: }

286: PetscErrorCode SVDSetFromOptions_Lanczos(PetscOptions *PetscOptionsObject,SVD svd)
287: {
289:   PetscBool      set,val;
290:   SVD_LANCZOS    *lanczos = (SVD_LANCZOS*)svd->data;

293:   PetscOptionsHead(PetscOptionsObject,"SVD Lanczos Options");
294:   PetscOptionsBool("-svd_lanczos_oneside","Lanczos one-side reorthogonalization","SVDLanczosSetOneSide",lanczos->oneside,&val,&set);
295:   if (set) {
296:     SVDLanczosSetOneSide(svd,val);
297:   }
298:   PetscOptionsTail();
299:   return(0);
300: }

304: static PetscErrorCode SVDLanczosSetOneSide_Lanczos(SVD svd,PetscBool oneside)
305: {
306:   SVD_LANCZOS *lanczos = (SVD_LANCZOS*)svd->data;

309:   if (lanczos->oneside != oneside) {
310:     lanczos->oneside = oneside;
311:     svd->state = SVD_STATE_INITIAL;
312:   }
313:   return(0);
314: }

318: /*@
319:    SVDLanczosSetOneSide - Indicate if the variant of the Lanczos method
320:    to be used is one-sided or two-sided.

322:    Logically Collective on SVD

324:    Input Parameters:
325: +  svd     - singular value solver
326: -  oneside - boolean flag indicating if the method is one-sided or not

328:    Options Database Key:
329: .  -svd_lanczos_oneside <boolean> - Indicates the boolean flag

331:    Note:
332:    By default, a two-sided variant is selected, which is sometimes slightly
333:    more robust. However, the one-sided variant is faster because it avoids
334:    the orthogonalization associated to left singular vectors. It also saves
335:    the memory required for storing such vectors.

337:    Level: advanced

339: .seealso: SVDTRLanczosSetOneSide()
340: @*/
341: PetscErrorCode SVDLanczosSetOneSide(SVD svd,PetscBool oneside)
342: {

348:   PetscTryMethod(svd,"SVDLanczosSetOneSide_C",(SVD,PetscBool),(svd,oneside));
349:   return(0);
350: }

354: /*@
355:    SVDLanczosGetOneSide - Gets if the variant of the Lanczos method
356:    to be used is one-sided or two-sided.

358:    Not Collective

360:    Input Parameters:
361: .  svd     - singular value solver

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

366:    Level: advanced

368: .seealso: SVDLanczosSetOneSide()
369: @*/
370: PetscErrorCode SVDLanczosGetOneSide(SVD svd,PetscBool *oneside)
371: {

377:   PetscTryMethod(svd,"SVDLanczosGetOneSide_C",(SVD,PetscBool*),(svd,oneside));
378:   return(0);
379: }

383: static PetscErrorCode SVDLanczosGetOneSide_Lanczos(SVD svd,PetscBool *oneside)
384: {
385:   SVD_LANCZOS *lanczos = (SVD_LANCZOS*)svd->data;

388:   *oneside = lanczos->oneside;
389:   return(0);
390: }

394: PetscErrorCode SVDDestroy_Lanczos(SVD svd)
395: {

399:   PetscFree(svd->data);
400:   PetscObjectComposeFunction((PetscObject)svd,"SVDLanczosSetOneSide_C",NULL);
401:   PetscObjectComposeFunction((PetscObject)svd,"SVDLanczosGetOneSide_C",NULL);
402:   return(0);
403: }

407: PetscErrorCode SVDView_Lanczos(SVD svd,PetscViewer viewer)
408: {
410:   SVD_LANCZOS    *lanczos = (SVD_LANCZOS*)svd->data;

413:   PetscViewerASCIIPrintf(viewer,"  Lanczos: %s-sided reorthogonalization\n",lanczos->oneside? "one": "two");
414:   return(0);
415: }

419: PETSC_EXTERN PetscErrorCode SVDCreate_Lanczos(SVD svd)
420: {
422:   SVD_LANCZOS    *ctx;

425:   PetscNewLog(svd,&ctx);
426:   svd->data = (void*)ctx;

428:   svd->ops->setup          = SVDSetUp_Lanczos;
429:   svd->ops->solve          = SVDSolve_Lanczos;
430:   svd->ops->destroy        = SVDDestroy_Lanczos;
431:   svd->ops->setfromoptions = SVDSetFromOptions_Lanczos;
432:   svd->ops->view           = SVDView_Lanczos;
433:   PetscObjectComposeFunction((PetscObject)svd,"SVDLanczosSetOneSide_C",SVDLanczosSetOneSide_Lanczos);
434:   PetscObjectComposeFunction((PetscObject)svd,"SVDLanczosGetOneSide_C",SVDLanczosGetOneSide_Lanczos);
435:   return(0);
436: }