Actual source code: trlanczos.c
slepc-3.7.0 2016-05-16
1: /*
3: SLEPc singular value solver: "trlanczos"
5: Method: Thick-restart Lanczos
7: Algorithm:
9: Golub-Kahan-Lanczos bidiagonalization with thick-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) 2002-2016, 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: static PetscBool cited = PETSC_FALSE;
45: static const char citation[] =
46: "@Article{slepc-svd,\n"
47: " author = \"V. Hern{\\'a}ndez and J. E. Rom{\\'a}n and A. Tom{\\'a}s\",\n"
48: " title = \"A robust and efficient parallel {SVD} solver based on restarted {Lanczos} bidiagonalization\",\n"
49: " journal = \"Electron. Trans. Numer. Anal.\",\n"
50: " volume = \"31\",\n"
51: " pages = \"68--85\",\n"
52: " year = \"2008\"\n"
53: "}\n";
55: typedef struct {
56: PetscBool oneside;
57: } SVD_TRLANCZOS;
61: PetscErrorCode SVDSetUp_TRLanczos(SVD svd)
62: {
64: PetscInt N;
67: SVDMatGetSize(svd,NULL,&N);
68: SVDSetDimensions_Default(svd);
69: if (svd->ncv>svd->nsv+svd->mpd) SETERRQ(PetscObjectComm((PetscObject)svd),1,"The value of ncv must not be larger than nev+mpd");
70: if (!svd->max_it) svd->max_it = PetscMax(N/svd->ncv,100);
71: svd->leftbasis = PETSC_TRUE;
72: SVDAllocateSolution(svd,1);
73: DSSetType(svd->ds,DSSVD);
74: DSSetCompact(svd->ds,PETSC_TRUE);
75: DSAllocate(svd->ds,svd->ncv);
76: return(0);
77: }
81: static PetscErrorCode SVDOneSideTRLanczosMGS(SVD svd,PetscReal *alpha,PetscReal *beta,BV V,BV U,PetscInt nconv,PetscInt l,PetscInt n,PetscScalar* work)
82: {
84: PetscReal a,b;
85: PetscInt i,k=nconv+l;
86: Vec ui,ui1,vi;
89: BVGetColumn(V,k,&vi);
90: BVGetColumn(U,k,&ui);
91: SVDMatMult(svd,PETSC_FALSE,vi,ui);
92: BVRestoreColumn(V,k,&vi);
93: BVRestoreColumn(U,k,&ui);
94: if (l>0) {
95: for (i=0;i<l;i++) work[i]=beta[i+nconv];
96: BVMultColumn(U,-1.0,1.0,k,work);
97: }
98: BVNormColumn(U,k,NORM_2,&a);
99: BVScaleColumn(U,k,1.0/a);
100: alpha[k] = a;
102: for (i=k+1;i<n;i++) {
103: BVGetColumn(V,i,&vi);
104: BVGetColumn(U,i-1,&ui1);
105: SVDMatMult(svd,PETSC_TRUE,ui1,vi);
106: BVRestoreColumn(V,i,&vi);
107: BVRestoreColumn(U,i-1,&ui1);
108: BVOrthogonalizeColumn(V,i,NULL,&b,NULL);
109: BVScaleColumn(V,i,1.0/b);
110: beta[i-1] = b;
112: BVGetColumn(V,i,&vi);
113: BVGetColumn(U,i,&ui);
114: SVDMatMult(svd,PETSC_FALSE,vi,ui);
115: BVRestoreColumn(V,i,&vi);
116: BVGetColumn(U,i-1,&ui1);
117: VecAXPY(ui,-b,ui1);
118: BVRestoreColumn(U,i-1,&ui1);
119: BVRestoreColumn(U,i,&ui);
120: BVNormColumn(U,i,NORM_2,&a);
121: BVScaleColumn(U,i,1.0/a);
122: alpha[i] = a;
123: }
125: BVGetColumn(V,n,&vi);
126: BVGetColumn(U,n-1,&ui1);
127: SVDMatMult(svd,PETSC_TRUE,ui1,vi);
128: BVRestoreColumn(V,n,&vi);
129: BVRestoreColumn(U,n-1,&ui1);
130: BVOrthogonalizeColumn(V,n,NULL,&b,NULL);
131: beta[n-1] = b;
132: return(0);
133: }
137: /*
138: Custom CGS orthogonalization, preprocess after first orthogonalization
139: */
140: static PetscErrorCode SVDOrthogonalizeCGS(BV V,PetscInt i,PetscScalar* h,PetscReal a,BVOrthogRefineType refine,PetscReal eta,PetscReal *norm)
141: {
143: PetscReal sum,onorm;
144: PetscScalar dot;
145: PetscInt j;
148: switch (refine) {
149: case BV_ORTHOG_REFINE_NEVER:
150: BVNormColumn(V,i,NORM_2,norm);
151: break;
152: case BV_ORTHOG_REFINE_ALWAYS:
153: BVSetActiveColumns(V,0,i);
154: BVDotColumn(V,i,h);
155: BVMultColumn(V,-1.0,1.0,i,h);
156: BVNormColumn(V,i,NORM_2,norm);
157: break;
158: case BV_ORTHOG_REFINE_IFNEEDED:
159: dot = h[i];
160: onorm = PetscSqrtReal(PetscRealPart(dot)) / a;
161: sum = 0.0;
162: for (j=0;j<i;j++) {
163: sum += PetscRealPart(h[j] * PetscConj(h[j]));
164: }
165: *norm = PetscRealPart(dot)/(a*a) - sum;
166: if (*norm>0.0) *norm = PetscSqrtReal(*norm);
167: else {
168: BVNormColumn(V,i,NORM_2,norm);
169: }
170: if (*norm < eta*onorm) {
171: BVSetActiveColumns(V,0,i);
172: BVDotColumn(V,i,h);
173: BVMultColumn(V,-1.0,1.0,i,h);
174: BVNormColumn(V,i,NORM_2,norm);
175: }
176: break;
177: }
178: return(0);
179: }
183: static PetscErrorCode SVDOneSideTRLanczosCGS(SVD svd,PetscReal *alpha,PetscReal *beta,BV V,BV U,PetscInt nconv,PetscInt l,PetscInt n,PetscScalar* work)
184: {
185: PetscErrorCode ierr;
186: PetscReal a,b,eta;
187: PetscInt i,j,k=nconv+l;
188: Vec ui,ui1,vi;
189: BVOrthogRefineType refine;
192: BVGetColumn(V,k,&vi);
193: BVGetColumn(U,k,&ui);
194: SVDMatMult(svd,PETSC_FALSE,vi,ui);
195: BVRestoreColumn(V,k,&vi);
196: BVRestoreColumn(U,k,&ui);
197: if (l>0) {
198: for (i=0;i<l;i++) work[i]=beta[i+nconv];
199: BVMultColumn(U,-1.0,1.0,k,work);
200: }
201: BVGetOrthogonalization(V,NULL,&refine,&eta,NULL);
203: for (i=k+1;i<n;i++) {
204: BVGetColumn(V,i,&vi);
205: BVGetColumn(U,i-1,&ui1);
206: SVDMatMult(svd,PETSC_TRUE,ui1,vi);
207: BVRestoreColumn(V,i,&vi);
208: BVRestoreColumn(U,i-1,&ui1);
209: BVNormColumnBegin(U,i-1,NORM_2,&a);
210: if (refine == BV_ORTHOG_REFINE_IFNEEDED) {
211: BVSetActiveColumns(V,0,i+1);
212: BVGetColumn(V,i,&vi);
213: BVDotVecBegin(V,vi,work);
214: } else {
215: BVSetActiveColumns(V,0,i);
216: BVDotColumnBegin(V,i,work);
217: }
218: BVNormColumnEnd(U,i-1,NORM_2,&a);
219: if (refine == BV_ORTHOG_REFINE_IFNEEDED) {
220: BVDotVecEnd(V,vi,work);
221: BVRestoreColumn(V,i,&vi);
222: BVSetActiveColumns(V,0,i);
223: } else {
224: BVDotColumnEnd(V,i,work);
225: }
227: BVScaleColumn(U,i-1,1.0/a);
228: for (j=0;j<i;j++) work[j] = work[j] / a;
229: BVMultColumn(V,-1.0,1.0/a,i,work);
230: SVDOrthogonalizeCGS(V,i,work,a,refine,eta,&b);
231: BVScaleColumn(V,i,1.0/b);
233: BVGetColumn(V,i,&vi);
234: BVGetColumn(U,i,&ui);
235: BVGetColumn(U,i-1,&ui1);
236: SVDMatMult(svd,PETSC_FALSE,vi,ui);
237: VecAXPY(ui,-b,ui1);
238: BVRestoreColumn(V,i,&vi);
239: BVRestoreColumn(U,i,&ui);
240: BVRestoreColumn(U,i-1,&ui1);
242: alpha[i-1] = a;
243: beta[i-1] = b;
244: }
246: BVGetColumn(V,n,&vi);
247: BVGetColumn(U,n-1,&ui1);
248: SVDMatMult(svd,PETSC_TRUE,ui1,vi);
249: BVRestoreColumn(V,n,&vi);
250: BVRestoreColumn(U,n-1,&ui1);
252: BVNormColumnBegin(svd->U,n-1,NORM_2,&a);
253: if (refine == BV_ORTHOG_REFINE_IFNEEDED) {
254: BVSetActiveColumns(V,0,n+1);
255: BVGetColumn(V,n,&vi);
256: BVDotVecBegin(V,vi,work);
257: } else {
258: BVSetActiveColumns(V,0,n);
259: BVDotColumnBegin(V,n,work);
260: }
261: BVNormColumnEnd(svd->U,n-1,NORM_2,&a);
262: if (refine == BV_ORTHOG_REFINE_IFNEEDED) {
263: BVDotVecEnd(V,vi,work);
264: BVRestoreColumn(V,n,&vi);
265: } else {
266: BVDotColumnEnd(V,n,work);
267: }
269: BVScaleColumn(U,n-1,1.0/a);
270: for (j=0;j<n;j++) work[j] = work[j] / a;
271: BVMultColumn(V,-1.0,1.0/a,n,work);
272: SVDOrthogonalizeCGS(V,n,work,a,refine,eta,&b);
273: BVSetActiveColumns(V,nconv,n);
274: alpha[n-1] = a;
275: beta[n-1] = b;
276: return(0);
277: }
281: PetscErrorCode SVDSolve_TRLanczos(SVD svd)
282: {
284: SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS*)svd->data;
285: PetscReal *alpha,*beta,lastbeta,norm,resnorm;
286: PetscScalar *Q,*swork=NULL,*w;
287: PetscInt i,k,l,nv,ld;
288: Mat U,VT;
289: PetscBool conv;
290: BVOrthogType orthog;
293: PetscCitationsRegister(citation,&cited);
294: /* allocate working space */
295: DSGetLeadingDimension(svd->ds,&ld);
296: BVGetOrthogonalization(svd->V,&orthog,NULL,NULL,NULL);
297: PetscMalloc1(ld,&w);
298: if (lanczos->oneside) {
299: PetscMalloc1(svd->ncv+1,&swork);
300: }
302: /* normalize start vector */
303: if (!svd->nini) {
304: BVSetRandomColumn(svd->V,0);
305: BVNormColumn(svd->V,0,NORM_2,&norm);
306: BVScaleColumn(svd->V,0,1.0/norm);
307: }
309: l = 0;
310: while (svd->reason == SVD_CONVERGED_ITERATING) {
311: svd->its++;
313: /* inner loop */
314: nv = PetscMin(svd->nconv+svd->mpd,svd->ncv);
315: BVSetActiveColumns(svd->V,svd->nconv,nv);
316: BVSetActiveColumns(svd->U,svd->nconv,nv);
317: DSGetArrayReal(svd->ds,DS_MAT_T,&alpha);
318: beta = alpha + ld;
319: if (lanczos->oneside) {
320: if (orthog == BV_ORTHOG_MGS) {
321: SVDOneSideTRLanczosMGS(svd,alpha,beta,svd->V,svd->U,svd->nconv,l,nv,swork);
322: } else {
323: SVDOneSideTRLanczosCGS(svd,alpha,beta,svd->V,svd->U,svd->nconv,l,nv,swork);
324: }
325: } else {
326: SVDTwoSideLanczos(svd,alpha,beta,svd->V,svd->U,svd->nconv+l,nv);
327: }
328: lastbeta = beta[nv-1];
329: DSRestoreArrayReal(svd->ds,DS_MAT_T,&alpha);
330: BVScaleColumn(svd->V,nv,1.0/lastbeta);
332: /* compute SVD of general matrix */
333: DSSetDimensions(svd->ds,nv,nv,svd->nconv,svd->nconv+l);
334: if (l==0) {
335: DSSetState(svd->ds,DS_STATE_INTERMEDIATE);
336: } else {
337: DSSetState(svd->ds,DS_STATE_RAW);
338: }
339: DSSolve(svd->ds,w,NULL);
340: DSSort(svd->ds,w,NULL,NULL,NULL,NULL);
342: /* compute error estimates */
343: k = 0;
344: conv = PETSC_TRUE;
345: DSGetArray(svd->ds,DS_MAT_U,&Q);
346: DSGetArrayReal(svd->ds,DS_MAT_T,&alpha);
347: beta = alpha + ld;
348: for (i=svd->nconv;i<nv;i++) {
349: svd->sigma[i] = PetscRealPart(w[i]);
350: beta[i] = PetscRealPart(Q[nv-1+i*ld])*lastbeta;
351: resnorm = PetscAbsReal(beta[i]);
352: (*svd->converged)(svd,svd->sigma[i],resnorm,&svd->errest[i],svd->convergedctx);
353: if (conv) {
354: if (svd->errest[i] < svd->tol) k++;
355: else conv = PETSC_FALSE;
356: }
357: }
358: DSRestoreArrayReal(svd->ds,DS_MAT_T,&alpha);
359: DSRestoreArray(svd->ds,DS_MAT_U,&Q);
361: /* check convergence and update l */
362: (*svd->stopping)(svd,svd->its,svd->max_it,svd->nconv+k,svd->nsv,&svd->reason,svd->stoppingctx);
363: if (svd->reason != SVD_CONVERGED_ITERATING) l = 0;
364: else l = PetscMax((nv-svd->nconv-k)/2,0);
366: /* compute converged singular vectors and restart vectors */
367: DSGetMat(svd->ds,DS_MAT_VT,&VT);
368: BVMultInPlaceTranspose(svd->V,VT,svd->nconv,svd->nconv+k+l);
369: MatDestroy(&VT);
370: DSGetMat(svd->ds,DS_MAT_U,&U);
371: BVMultInPlace(svd->U,U,svd->nconv,svd->nconv+k+l);
372: MatDestroy(&U);
374: /* copy the last vector to be the next initial vector */
375: if (svd->reason == SVD_CONVERGED_ITERATING) {
376: BVCopyColumn(svd->V,nv,svd->nconv+k+l);
377: }
379: svd->nconv += k;
380: SVDMonitor(svd,svd->its,svd->nconv,svd->sigma,svd->errest,nv);
381: }
383: /* orthonormalize U columns in one side method */
384: if (lanczos->oneside) {
385: for (i=0;i<svd->nconv;i++) {
386: BVOrthogonalizeColumn(svd->U,i,NULL,&norm,NULL);
387: BVScaleColumn(svd->U,i,1.0/norm);
388: }
389: }
391: /* free working space */
392: PetscFree(w);
393: if (swork) { PetscFree(swork); }
394: return(0);
395: }
399: PetscErrorCode SVDSetFromOptions_TRLanczos(PetscOptionItems *PetscOptionsObject,SVD svd)
400: {
402: PetscBool set,val;
403: SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS*)svd->data;
406: PetscOptionsHead(PetscOptionsObject,"SVD TRLanczos Options");
407: PetscOptionsBool("-svd_trlanczos_oneside","Lanczos one-side reorthogonalization","SVDTRLanczosSetOneSide",lanczos->oneside,&val,&set);
408: if (set) {
409: SVDTRLanczosSetOneSide(svd,val);
410: }
411: PetscOptionsTail();
412: return(0);
413: }
417: static PetscErrorCode SVDTRLanczosSetOneSide_TRLanczos(SVD svd,PetscBool oneside)
418: {
419: SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS*)svd->data;
422: lanczos->oneside = oneside;
423: return(0);
424: }
428: /*@
429: SVDTRLanczosSetOneSide - Indicate if the variant of the Lanczos method
430: to be used is one-sided or two-sided.
432: Logically Collective on SVD
434: Input Parameters:
435: + svd - singular value solver
436: - oneside - boolean flag indicating if the method is one-sided or not
438: Options Database Key:
439: . -svd_trlanczos_oneside <boolean> - Indicates the boolean flag
441: Note:
442: By default, a two-sided variant is selected, which is sometimes slightly
443: more robust. However, the one-sided variant is faster because it avoids
444: the orthogonalization associated to left singular vectors.
446: Level: advanced
448: .seealso: SVDLanczosSetOneSide()
449: @*/
450: PetscErrorCode SVDTRLanczosSetOneSide(SVD svd,PetscBool oneside)
451: {
457: PetscTryMethod(svd,"SVDTRLanczosSetOneSide_C",(SVD,PetscBool),(svd,oneside));
458: return(0);
459: }
463: static PetscErrorCode SVDTRLanczosGetOneSide_TRLanczos(SVD svd,PetscBool *oneside)
464: {
465: SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS*)svd->data;
468: *oneside = lanczos->oneside;
469: return(0);
470: }
474: /*@
475: SVDTRLanczosGetOneSide - Gets if the variant of the Lanczos method
476: to be used is one-sided or two-sided.
478: Not Collective
480: Input Parameters:
481: . svd - singular value solver
483: Output Parameters:
484: . oneside - boolean flag indicating if the method is one-sided or not
486: Level: advanced
488: .seealso: SVDTRLanczosSetOneSide()
489: @*/
490: PetscErrorCode SVDTRLanczosGetOneSide(SVD svd,PetscBool *oneside)
491: {
497: PetscUseMethod(svd,"SVDTRLanczosGetOneSide_C",(SVD,PetscBool*),(svd,oneside));
498: return(0);
499: }
503: PetscErrorCode SVDDestroy_TRLanczos(SVD svd)
504: {
508: PetscFree(svd->data);
509: PetscObjectComposeFunction((PetscObject)svd,"SVDTRLanczosSetOneSide_C",NULL);
510: PetscObjectComposeFunction((PetscObject)svd,"SVDTRLanczosGetOneSide_C",NULL);
511: return(0);
512: }
516: PetscErrorCode SVDView_TRLanczos(SVD svd,PetscViewer viewer)
517: {
519: SVD_TRLANCZOS *lanczos = (SVD_TRLANCZOS*)svd->data;
520: PetscBool isascii;
523: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
524: if (isascii) {
525: PetscViewerASCIIPrintf(viewer," TRLanczos: %s-sided reorthogonalization\n",lanczos->oneside? "one": "two");
526: }
527: return(0);
528: }
532: PETSC_EXTERN PetscErrorCode SVDCreate_TRLanczos(SVD svd)
533: {
535: SVD_TRLANCZOS *ctx;
538: PetscNewLog(svd,&ctx);
539: svd->data = (void*)ctx;
541: svd->ops->setup = SVDSetUp_TRLanczos;
542: svd->ops->solve = SVDSolve_TRLanczos;
543: svd->ops->destroy = SVDDestroy_TRLanczos;
544: svd->ops->setfromoptions = SVDSetFromOptions_TRLanczos;
545: svd->ops->view = SVDView_TRLanczos;
546: PetscObjectComposeFunction((PetscObject)svd,"SVDTRLanczosSetOneSide_C",SVDTRLanczosSetOneSide_TRLanczos);
547: PetscObjectComposeFunction((PetscObject)svd,"SVDTRLanczosGetOneSide_C",SVDTRLanczosGetOneSide_TRLanczos);
548: return(0);
549: }