Actual source code: qarnoldi.c
slepc-3.7.4 2017-05-17
1: /*
3: SLEPc quadratic eigensolver: "qarnoldi"
5: Method: Q-Arnoldi
7: Algorithm:
9: Quadratic Arnoldi with Krylov-Schur type restart.
11: References:
13: [1] K. Meerbergen, "The Quadratic Arnoldi method for the solution
14: of the quadratic eigenvalue problem", SIAM J. Matrix Anal.
15: Appl. 30(4):1462-1482, 2008.
17: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
18: SLEPc - Scalable Library for Eigenvalue Problem Computations
19: Copyright (c) 2002-2016, Universitat Politecnica de Valencia, Spain
21: This file is part of SLEPc.
23: SLEPc is free software: you can redistribute it and/or modify it under the
24: terms of version 3 of the GNU Lesser General Public License as published by
25: the Free Software Foundation.
27: SLEPc is distributed in the hope that it will be useful, but WITHOUT ANY
28: WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
29: FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for
30: more details.
32: You should have received a copy of the GNU Lesser General Public License
33: along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
34: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
35: */
37: #include <slepc/private/pepimpl.h> /*I "slepcpep.h" I*/
38: #include <petscblaslapack.h>
40: typedef struct {
41: PetscReal keep; /* restart parameter */
42: PetscBool lock; /* locking/non-locking variant */
43: } PEP_QARNOLDI;
47: PetscErrorCode PEPSetUp_QArnoldi(PEP pep)
48: {
50: PEP_QARNOLDI *ctx = (PEP_QARNOLDI*)pep->data;
51: PetscBool shift,sinv,flg;
54: pep->lineariz = PETSC_TRUE;
55: PEPSetDimensions_Default(pep,pep->nev,&pep->ncv,&pep->mpd);
56: if (!ctx->lock && pep->mpd<pep->ncv) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Should not use mpd parameter in non-locking variant");
57: if (!pep->max_it) pep->max_it = PetscMax(100,4*pep->n/pep->ncv);
58: /* Set STSHIFT as the default ST */
59: if (!((PetscObject)pep->st)->type_name) {
60: STSetType(pep->st,STSHIFT);
61: }
62: PetscObjectTypeCompare((PetscObject)pep->st,STSHIFT,&shift);
63: PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinv);
64: if (!shift && !sinv) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Only STSHIFT and STSINVERT spectral transformations can be used");
65: if (!pep->which) {
66: if (sinv) pep->which = PEP_TARGET_MAGNITUDE;
67: else pep->which = PEP_LARGEST_MAGNITUDE;
68: }
70: if (pep->nmat!=3) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Solver only available for quadratic problems");
71: if (pep->basis!=PEP_BASIS_MONOMIAL) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Solver not implemented for non-monomial bases");
72: STGetTransform(pep->st,&flg);
73: if (!flg) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Solver requires the ST transformation flag set, see STSetTransform()");
75: /* set default extraction */
76: if (!pep->extract) {
77: pep->extract = PEP_EXTRACT_NONE;
78: }
79: if (pep->extract!=PEP_EXTRACT_NONE) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Solver does not support requested extraction");
80:
81: if (!ctx->keep) ctx->keep = 0.5;
83: PEPAllocateSolution(pep,0);
84: PEPSetWorkVecs(pep,4);
86: DSSetType(pep->ds,DSNHEP);
87: DSSetExtraRow(pep->ds,PETSC_TRUE);
88: DSAllocate(pep->ds,pep->ncv+1);
90: /* process starting vector */
91: if (pep->nini>-2) {
92: BVSetRandomColumn(pep->V,0);
93: BVSetRandomColumn(pep->V,1);
94: } else {
95: BVInsertVec(pep->V,0,pep->IS[0]);
96: BVInsertVec(pep->V,1,pep->IS[1]);
97: }
98: if (pep->nini<0) {
99: SlepcBasisDestroy_Private(&pep->nini,&pep->IS);
100: }
101: return(0);
102: }
106: PetscErrorCode PEPExtractVectors_QArnoldi(PEP pep)
107: {
109: PetscInt i,k=pep->nconv,ldds;
110: PetscScalar *X,*pX0;
111: Mat X0;
114: if (pep->nconv==0) return(0);
115: DSGetLeadingDimension(pep->ds,&ldds);
116: DSVectors(pep->ds,DS_MAT_X,NULL,NULL);
117: DSGetArray(pep->ds,DS_MAT_X,&X);
119: /* update vectors V = V*X */
120: MatCreateSeqDense(PETSC_COMM_SELF,k,k,NULL,&X0);
121: MatDenseGetArray(X0,&pX0);
122: for (i=0;i<k;i++) {
123: PetscMemcpy(pX0+i*k,X+i*ldds,k*sizeof(PetscScalar));
124: }
125: MatDenseRestoreArray(X0,&pX0);
126: BVMultInPlace(pep->V,X0,0,k);
127: MatDestroy(&X0);
128: DSRestoreArray(pep->ds,DS_MAT_X,&X);
129: return(0);
130: }
134: /*
135: Compute a step of Classical Gram-Schmidt orthogonalization
136: */
137: static PetscErrorCode PEPQArnoldiCGS(PEP pep,PetscScalar *H,PetscBLASInt ldh,PetscScalar *h,PetscBLASInt j,BV V,Vec t,Vec v,Vec w,PetscReal *onorm,PetscReal *norm,PetscScalar *work)
138: {
140: PetscBLASInt ione = 1,j_1 = j+1;
141: PetscReal x,y;
142: PetscScalar dot,one = 1.0,zero = 0.0;
145: /* compute norm of v and w */
146: if (onorm) {
147: VecNorm(v,NORM_2,&x);
148: VecNorm(w,NORM_2,&y);
149: *onorm = PetscSqrtReal(x*x+y*y);
150: }
152: /* orthogonalize: compute h */
153: BVDotVec(V,v,h);
154: BVDotVec(V,w,work);
155: if (j>0)
156: PetscStackCallBLAS("BLASgemv",BLASgemv_("C",&j_1,&j,&one,H,&ldh,work,&ione,&one,h,&ione));
157: VecDot(w,t,&dot);
158: h[j] += dot;
160: /* orthogonalize: update v and w */
161: BVMultVec(V,-1.0,1.0,v,h);
162: if (j>0) {
163: PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&j_1,&j,&one,H,&ldh,h,&ione,&zero,work,&ione));
164: BVMultVec(V,-1.0,1.0,w,work);
165: }
166: VecAXPY(w,-h[j],t);
168: /* compute norm of v and w */
169: if (norm) {
170: VecNorm(v,NORM_2,&x);
171: VecNorm(w,NORM_2,&y);
172: *norm = PetscSqrtReal(x*x+y*y);
173: }
174: return(0);
175: }
179: /*
180: Compute a run of Q-Arnoldi iterations
181: */
182: static PetscErrorCode PEPQArnoldi(PEP pep,PetscScalar *H,PetscInt ldh,PetscInt k,PetscInt *M,Vec v,Vec w,PetscReal *beta,PetscBool *breakdown,PetscScalar *work)
183: {
184: PetscErrorCode ierr;
185: PetscInt i,j,l,m = *M;
186: Vec t = pep->work[2],u = pep->work[3];
187: BVOrthogRefineType refinement;
188: PetscReal norm=0.0,onorm,eta;
189: PetscScalar *c = work + m;
192: BVGetOrthogonalization(pep->V,NULL,&refinement,&eta,NULL);
193: BVInsertVec(pep->V,k,v);
194: for (j=k;j<m;j++) {
195: /* apply operator */
196: VecCopy(w,t);
197: if (pep->Dr) {
198: VecPointwiseMult(v,v,pep->Dr);
199: }
200: STMatMult(pep->st,0,v,u);
201: VecCopy(t,v);
202: if (pep->Dr) {
203: VecPointwiseMult(t,t,pep->Dr);
204: }
205: STMatMult(pep->st,1,t,w);
206: VecAXPY(u,pep->sfactor,w);
207: STMatSolve(pep->st,u,w);
208: VecScale(w,-1.0/(pep->sfactor*pep->sfactor));
209: if (pep->Dr) {
210: VecPointwiseDivide(w,w,pep->Dr);
211: }
212: VecCopy(v,t);
213: BVSetActiveColumns(pep->V,0,j+1);
215: /* orthogonalize */
216: switch (refinement) {
217: case BV_ORTHOG_REFINE_NEVER:
218: PEPQArnoldiCGS(pep,H,ldh,H+ldh*j,j,pep->V,t,v,w,NULL,&norm,work);
219: *breakdown = PETSC_FALSE;
220: break;
221: case BV_ORTHOG_REFINE_ALWAYS:
222: PEPQArnoldiCGS(pep,H,ldh,H+ldh*j,j,pep->V,t,v,w,NULL,NULL,work);
223: PEPQArnoldiCGS(pep,H,ldh,c,j,pep->V,t,v,w,&onorm,&norm,work);
224: for (i=0;i<=j;i++) H[ldh*j+i] += c[i];
225: if (norm < eta * onorm) *breakdown = PETSC_TRUE;
226: else *breakdown = PETSC_FALSE;
227: break;
228: case BV_ORTHOG_REFINE_IFNEEDED:
229: PEPQArnoldiCGS(pep,H,ldh,H+ldh*j,j,pep->V,t,v,w,&onorm,&norm,work);
230: /* ||q|| < eta ||h|| */
231: l = 1;
232: while (l<3 && norm < eta * onorm) {
233: l++;
234: onorm = norm;
235: PEPQArnoldiCGS(pep,H,ldh,c,j,pep->V,t,v,w,NULL,&norm,work);
236: for (i=0;i<=j;i++) H[ldh*j+i] += c[i];
237: }
238: if (norm < eta * onorm) *breakdown = PETSC_TRUE;
239: else *breakdown = PETSC_FALSE;
240: break;
241: default: SETERRQ(PetscObjectComm((PetscObject)pep),1,"Wrong value of ip->orth_ref");
242: }
243: VecScale(v,1.0/norm);
244: VecScale(w,1.0/norm);
246: H[j+1+ldh*j] = norm;
247: if (j<m-1) {
248: BVInsertVec(pep->V,j+1,v);
249: }
250: }
251: *beta = norm;
252: return(0);
253: }
257: PetscErrorCode PEPSolve_QArnoldi(PEP pep)
258: {
260: PEP_QARNOLDI *ctx = (PEP_QARNOLDI*)pep->data;
261: PetscInt j,k,l,lwork,nv,ld,newn,nconv;
262: Vec v=pep->work[0],w=pep->work[1];
263: Mat Q;
264: PetscScalar *S,*work;
265: PetscReal beta=0.0,norm,x,y;
266: PetscBool breakdown=PETSC_FALSE,sinv;
269: DSGetLeadingDimension(pep->ds,&ld);
270: lwork = 7*pep->ncv;
271: PetscMalloc1(lwork,&work);
272: PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinv);
273: RGPushScale(pep->rg,sinv?pep->sfactor:1.0/pep->sfactor);
274: STScaleShift(pep->st,sinv?pep->sfactor:1.0/pep->sfactor);
276: /* Get the starting Arnoldi vector */
277: BVCopyVec(pep->V,0,v);
278: BVCopyVec(pep->V,1,w);
279: VecNorm(v,NORM_2,&x);
280: VecNorm(w,NORM_2,&y);
281: norm = PetscSqrtReal(x*x+y*y);
282: VecScale(v,1.0/norm);
283: VecScale(w,1.0/norm);
285: /* Restart loop */
286: l = 0;
287: while (pep->reason == PEP_CONVERGED_ITERATING) {
288: pep->its++;
290: /* Compute an nv-step Arnoldi factorization */
291: nv = PetscMin(pep->nconv+pep->mpd,pep->ncv);
292: DSGetArray(pep->ds,DS_MAT_A,&S);
293: PEPQArnoldi(pep,S,ld,pep->nconv+l,&nv,v,w,&beta,&breakdown,work);
294: DSRestoreArray(pep->ds,DS_MAT_A,&S);
295: DSSetDimensions(pep->ds,nv,0,pep->nconv,pep->nconv+l);
296: if (l==0) {
297: DSSetState(pep->ds,DS_STATE_INTERMEDIATE);
298: } else {
299: DSSetState(pep->ds,DS_STATE_RAW);
300: }
301: BVSetActiveColumns(pep->V,pep->nconv,nv);
303: /* Solve projected problem */
304: DSSolve(pep->ds,pep->eigr,pep->eigi);
305: DSSort(pep->ds,pep->eigr,pep->eigi,NULL,NULL,NULL);
306: DSUpdateExtraRow(pep->ds);
308: /* Check convergence */
309: PEPKrylovConvergence(pep,PETSC_FALSE,pep->nconv,nv-pep->nconv,beta,&k);
310: (*pep->stopping)(pep,pep->its,pep->max_it,k,pep->nev,&pep->reason,pep->stoppingctx);
311: nconv = k;
313: /* Update l */
314: if (pep->reason != PEP_CONVERGED_ITERATING || breakdown) l = 0;
315: else l = PetscMax(1,(PetscInt)((nv-k)*ctx->keep));
316: if (!ctx->lock && l>0) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */
318: if (pep->reason == PEP_CONVERGED_ITERATING) {
319: if (breakdown) {
320: /* Stop if breakdown */
321: PetscInfo2(pep,"Breakdown Quadratic Arnoldi method (it=%D norm=%g)\n",pep->its,(double)beta);
322: pep->reason = PEP_DIVERGED_BREAKDOWN;
323: } else {
324: /* Prepare the Rayleigh quotient for restart */
325: DSTruncate(pep->ds,k+l);
326: DSGetDimensions(pep->ds,&newn,NULL,NULL,NULL,NULL);
327: l = newn-k;
328: }
329: }
330: /* Update the corresponding vectors V(:,idx) = V*Q(:,idx) */
331: DSGetMat(pep->ds,DS_MAT_Q,&Q);
332: BVMultInPlace(pep->V,Q,pep->nconv,k+l);
333: MatDestroy(&Q);
335: pep->nconv = k;
336: PEPMonitor(pep,pep->its,nconv,pep->eigr,pep->eigi,pep->errest,nv);
337: }
339: for (j=0;j<pep->nconv;j++) {
340: pep->eigr[j] *= pep->sfactor;
341: pep->eigi[j] *= pep->sfactor;
342: }
344: STScaleShift(pep->st,sinv?1.0/pep->sfactor:pep->sfactor);
345: RGPopScale(pep->rg);
347: /* truncate Schur decomposition and change the state to raw so that
348: DSVectors() computes eigenvectors from scratch */
349: DSSetDimensions(pep->ds,pep->nconv,0,0,0);
350: DSSetState(pep->ds,DS_STATE_RAW);
351: PetscFree(work);
352: return(0);
353: }
357: static PetscErrorCode PEPQArnoldiSetRestart_QArnoldi(PEP pep,PetscReal keep)
358: {
359: PEP_QARNOLDI *ctx = (PEP_QARNOLDI*)pep->data;
362: if (keep==PETSC_DEFAULT) ctx->keep = 0.5;
363: else {
364: if (keep<0.1 || keep>0.9) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"The keep argument must be in the range [0.1,0.9]");
365: ctx->keep = keep;
366: }
367: return(0);
368: }
372: /*@
373: PEPQArnoldiSetRestart - Sets the restart parameter for the Q-Arnoldi
374: method, in particular the proportion of basis vectors that must be kept
375: after restart.
377: Logically Collective on PEP
379: Input Parameters:
380: + pep - the eigenproblem solver context
381: - keep - the number of vectors to be kept at restart
383: Options Database Key:
384: . -pep_qarnoldi_restart - Sets the restart parameter
386: Notes:
387: Allowed values are in the range [0.1,0.9]. The default is 0.5.
389: Level: advanced
391: .seealso: PEPQArnoldiGetRestart()
392: @*/
393: PetscErrorCode PEPQArnoldiSetRestart(PEP pep,PetscReal keep)
394: {
400: PetscTryMethod(pep,"PEPQArnoldiSetRestart_C",(PEP,PetscReal),(pep,keep));
401: return(0);
402: }
406: static PetscErrorCode PEPQArnoldiGetRestart_QArnoldi(PEP pep,PetscReal *keep)
407: {
408: PEP_QARNOLDI *ctx = (PEP_QARNOLDI*)pep->data;
411: *keep = ctx->keep;
412: return(0);
413: }
417: /*@
418: PEPQArnoldiGetRestart - Gets the restart parameter used in the Q-Arnoldi method.
420: Not Collective
422: Input Parameter:
423: . pep - the eigenproblem solver context
425: Output Parameter:
426: . keep - the restart parameter
428: Level: advanced
430: .seealso: PEPQArnoldiSetRestart()
431: @*/
432: PetscErrorCode PEPQArnoldiGetRestart(PEP pep,PetscReal *keep)
433: {
439: PetscUseMethod(pep,"PEPQArnoldiGetRestart_C",(PEP,PetscReal*),(pep,keep));
440: return(0);
441: }
445: static PetscErrorCode PEPQArnoldiSetLocking_QArnoldi(PEP pep,PetscBool lock)
446: {
447: PEP_QARNOLDI *ctx = (PEP_QARNOLDI*)pep->data;
450: ctx->lock = lock;
451: return(0);
452: }
456: /*@
457: PEPQArnoldiSetLocking - Choose between locking and non-locking variants of
458: the Q-Arnoldi method.
460: Logically Collective on PEP
462: Input Parameters:
463: + pep - the eigenproblem solver context
464: - lock - true if the locking variant must be selected
466: Options Database Key:
467: . -pep_qarnoldi_locking - Sets the locking flag
469: Notes:
470: The default is to keep all directions in the working subspace even if
471: already converged to working accuracy (the non-locking variant).
472: This behaviour can be changed so that converged eigenpairs are locked
473: when the method restarts.
475: Note that the default behaviour is the opposite to Krylov solvers in EPS.
477: Level: advanced
479: .seealso: PEPQArnoldiGetLocking()
480: @*/
481: PetscErrorCode PEPQArnoldiSetLocking(PEP pep,PetscBool lock)
482: {
488: PetscTryMethod(pep,"PEPQArnoldiSetLocking_C",(PEP,PetscBool),(pep,lock));
489: return(0);
490: }
494: static PetscErrorCode PEPQArnoldiGetLocking_QArnoldi(PEP pep,PetscBool *lock)
495: {
496: PEP_QARNOLDI *ctx = (PEP_QARNOLDI*)pep->data;
499: *lock = ctx->lock;
500: return(0);
501: }
505: /*@
506: PEPQArnoldiGetLocking - Gets the locking flag used in the Q-Arnoldi method.
508: Not Collective
510: Input Parameter:
511: . pep - the eigenproblem solver context
513: Output Parameter:
514: . lock - the locking flag
516: Level: advanced
518: .seealso: PEPQArnoldiSetLocking()
519: @*/
520: PetscErrorCode PEPQArnoldiGetLocking(PEP pep,PetscBool *lock)
521: {
527: PetscUseMethod(pep,"PEPQArnoldiGetLocking_C",(PEP,PetscBool*),(pep,lock));
528: return(0);
529: }
533: PetscErrorCode PEPSetFromOptions_QArnoldi(PetscOptionItems *PetscOptionsObject,PEP pep)
534: {
536: PetscBool flg,lock;
537: PetscReal keep;
540: PetscOptionsHead(PetscOptionsObject,"PEP Q-Arnoldi Options");
541: PetscOptionsReal("-pep_qarnoldi_restart","Proportion of vectors kept after restart","PEPQArnoldiSetRestart",0.5,&keep,&flg);
542: if (flg) {
543: PEPQArnoldiSetRestart(pep,keep);
544: }
545: PetscOptionsBool("-pep_qarnoldi_locking","Choose between locking and non-locking variants","PEPQArnoldiSetLocking",PETSC_FALSE,&lock,&flg);
546: if (flg) {
547: PEPQArnoldiSetLocking(pep,lock);
548: }
549: PetscOptionsTail();
550: return(0);
551: }
555: PetscErrorCode PEPView_QArnoldi(PEP pep,PetscViewer viewer)
556: {
558: PEP_QARNOLDI *ctx = (PEP_QARNOLDI*)pep->data;
559: PetscBool isascii;
562: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
563: if (isascii) {
564: PetscViewerASCIIPrintf(viewer," Q-Arnoldi: %d%% of basis vectors kept after restart\n",(int)(100*ctx->keep));
565: PetscViewerASCIIPrintf(viewer," Q-Arnoldi: using the %slocking variant\n",ctx->lock?"":"non-");
566: }
567: return(0);
568: }
572: PetscErrorCode PEPDestroy_QArnoldi(PEP pep)
573: {
577: PetscFree(pep->data);
578: PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiSetRestart_C",NULL);
579: PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiGetRestart_C",NULL);
580: PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiSetLocking_C",NULL);
581: PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiGetLocking_C",NULL);
582: return(0);
583: }
587: PETSC_EXTERN PetscErrorCode PEPCreate_QArnoldi(PEP pep)
588: {
589: PEP_QARNOLDI *ctx;
593: PetscNewLog(pep,&ctx);
594: pep->data = (void*)ctx;
595: ctx->lock = PETSC_TRUE;
597: pep->ops->solve = PEPSolve_QArnoldi;
598: pep->ops->setup = PEPSetUp_QArnoldi;
599: pep->ops->setfromoptions = PEPSetFromOptions_QArnoldi;
600: pep->ops->destroy = PEPDestroy_QArnoldi;
601: pep->ops->view = PEPView_QArnoldi;
602: pep->ops->backtransform = PEPBackTransform_Default;
603: pep->ops->computevectors = PEPComputeVectors_Default;
604: pep->ops->extractvectors = PEPExtractVectors_QArnoldi;
605: PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiSetRestart_C",PEPQArnoldiSetRestart_QArnoldi);
606: PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiGetRestart_C",PEPQArnoldiGetRestart_QArnoldi);
607: PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiSetLocking_C",PEPQArnoldiSetLocking_QArnoldi);
608: PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiGetLocking_C",PEPQArnoldiGetLocking_QArnoldi);
609: return(0);
610: }