Actual source code: gklanczos.c

slepc-3.5.2 2014-10-10
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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) 2002-2014, 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:     VecNorm(u,NORM_2,&a);
133:     BVSetActiveColumns(V,0,i);
134:     BVDotColumn(V,i,work);
135:     VecScale(u,1.0/a);
136:     BVMultColumn(V,-1.0/a,1.0/a,i,work);

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

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

155:   BVGetColumn(V,n,&z);
156:   SVDMatMult(svd,PETSC_TRUE,u,z);
157:   BVRestoreColumn(V,n,&z);
158:   VecNorm(u,NORM_2,&a);
159:   BVDotColumn(V,n,work);
160:   VecScale(u,1.0/a);
161:   BVMultColumn(V,-1.0/a,1.0/a,n,work);

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

168:   alpha[n-1] = a;
169:   beta[n-1] = b;
170:   BVSetActiveColumns(V,bvl,bvk);
171:   return(0);
172: }

176: PetscErrorCode SVDSolve_Lanczos(SVD svd)
177: {
179:   SVD_LANCZOS    *lanczos = (SVD_LANCZOS*)svd->data;
180:   PetscReal      *alpha,*beta,lastbeta,norm;
181:   PetscScalar    *swork,*w,*Q,*PT;
182:   PetscInt       i,k,j,nv,ld;
183:   Vec            u=0,u_1=0;
184:   Mat            U,VT;
185:   PetscBool      conv;

188:   /* allocate working space */
189:   DSGetLeadingDimension(svd->ds,&ld);
190:   PetscMalloc2(ld,&w,svd->ncv,&swork);

192:   if (lanczos->oneside) {
193:     SVDMatGetVecs(svd,NULL,&u);
194:     SVDMatGetVecs(svd,NULL,&u_1);
195:   }

197:   /* normalize start vector */
198:   if (!svd->nini) {
199:     BVSetRandomColumn(svd->V,0,svd->rand);
200:     BVNormColumn(svd->V,0,NORM_2,&norm);
201:     BVScaleColumn(svd->V,0,1.0/norm);
202:   }

204:   while (svd->reason == SVD_CONVERGED_ITERATING) {
205:     svd->its++;

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

221:     /* compute SVD of bidiagonal matrix */
222:     DSSetDimensions(svd->ds,nv,nv,svd->nconv,0);
223:     DSSetState(svd->ds,DS_STATE_INTERMEDIATE);
224:     DSSolve(svd->ds,w,NULL);
225:     DSSort(svd->ds,w,NULL,NULL,NULL,NULL);

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

242:     /* check convergence */
243:     if (svd->its >= svd->max_it) svd->reason = SVD_DIVERGED_ITS;
244:     if (svd->nconv+k >= svd->nsv) svd->reason = SVD_CONVERGED_TOL;

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

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

264:     /* copy restart vector from the last column */
265:     if (svd->reason == SVD_CONVERGED_ITERATING) {
266:       BVCopyColumn(svd->V,nv,svd->nconv+k);
267:     }

269:     svd->nconv += k;
270:     SVDMonitor(svd,svd->its,svd->nconv,svd->sigma,svd->errest,nv);
271:   }

273:   /* free working space */
274:   VecDestroy(&u);
275:   VecDestroy(&u_1);
276:   PetscFree2(w,swork);
277:   return(0);
278: }

282: PetscErrorCode SVDSetFromOptions_Lanczos(SVD svd)
283: {
285:   PetscBool      set,val;
286:   SVD_LANCZOS    *lanczos = (SVD_LANCZOS*)svd->data;

289:   PetscOptionsHead("SVD Lanczos Options");
290:   PetscOptionsBool("-svd_lanczos_oneside","Lanczos one-side reorthogonalization","SVDLanczosSetOneSide",lanczos->oneside,&val,&set);
291:   if (set) {
292:     SVDLanczosSetOneSide(svd,val);
293:   }
294:   PetscOptionsTail();
295:   return(0);
296: }

300: static PetscErrorCode SVDLanczosSetOneSide_Lanczos(SVD svd,PetscBool oneside)
301: {
302:   SVD_LANCZOS *lanczos = (SVD_LANCZOS*)svd->data;

305:   if (lanczos->oneside != oneside) {
306:     lanczos->oneside = oneside;
307:     svd->setupcalled = 0;
308:   }
309:   return(0);
310: }

314: /*@
315:    SVDLanczosSetOneSide - Indicate if the variant of the Lanczos method
316:    to be used is one-sided or two-sided.

318:    Logically Collective on SVD

320:    Input Parameters:
321: +  svd     - singular value solver
322: -  oneside - boolean flag indicating if the method is one-sided or not

324:    Options Database Key:
325: .  -svd_lanczos_oneside <boolean> - Indicates the boolean flag

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

333:    Level: advanced

335: .seealso: SVDTRLanczosSetOneSide()
336: @*/
337: PetscErrorCode SVDLanczosSetOneSide(SVD svd,PetscBool oneside)
338: {

344:   PetscTryMethod(svd,"SVDLanczosSetOneSide_C",(SVD,PetscBool),(svd,oneside));
345:   return(0);
346: }

350: /*@
351:    SVDLanczosGetOneSide - Gets if the variant of the Lanczos method
352:    to be used is one-sided or two-sided.

354:    Not Collective

356:    Input Parameters:
357: .  svd     - singular value solver

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

362:    Level: advanced

364: .seealso: SVDLanczosSetOneSide()
365: @*/
366: PetscErrorCode SVDLanczosGetOneSide(SVD svd,PetscBool *oneside)
367: {

373:   PetscTryMethod(svd,"SVDLanczosGetOneSide_C",(SVD,PetscBool*),(svd,oneside));
374:   return(0);
375: }

379: static PetscErrorCode SVDLanczosGetOneSide_Lanczos(SVD svd,PetscBool *oneside)
380: {
381:   SVD_LANCZOS *lanczos = (SVD_LANCZOS*)svd->data;

384:   *oneside = lanczos->oneside;
385:   return(0);
386: }

390: PetscErrorCode SVDDestroy_Lanczos(SVD svd)
391: {

395:   PetscFree(svd->data);
396:   PetscObjectComposeFunction((PetscObject)svd,"SVDLanczosSetOneSide_C",NULL);
397:   PetscObjectComposeFunction((PetscObject)svd,"SVDLanczosGetOneSide_C",NULL);
398:   return(0);
399: }

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

409:   PetscViewerASCIIPrintf(viewer,"  Lanczos: %s-sided reorthogonalization\n",lanczos->oneside? "one": "two");
410:   return(0);
411: }

415: PETSC_EXTERN PetscErrorCode SVDCreate_Lanczos(SVD svd)
416: {
418:   SVD_LANCZOS    *ctx;

421:   PetscNewLog(svd,&ctx);
422:   svd->data = (void*)ctx;

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