Actual source code: qarnoldi.c

slepc-3.18.2 2023-01-26
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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 quadratic eigensolver: "qarnoldi"

 13:    Method: Q-Arnoldi

 15:    Algorithm:

 17:        Quadratic Arnoldi with Krylov-Schur type restart.

 19:    References:

 21:        [1] K. Meerbergen, "The Quadratic Arnoldi method for the solution
 22:            of the quadratic eigenvalue problem", SIAM J. Matrix Anal.
 23:            Appl. 30(4):1462-1482, 2008.
 24: */

 26: #include <slepc/private/pepimpl.h>
 27: #include <petscblaslapack.h>

 29: typedef struct {
 30:   PetscReal keep;         /* restart parameter */
 31:   PetscBool lock;         /* locking/non-locking variant */
 32: } PEP_QARNOLDI;

 34: PetscErrorCode PEPSetUp_QArnoldi(PEP pep)
 35: {
 36:   PEP_QARNOLDI   *ctx = (PEP_QARNOLDI*)pep->data;
 37:   PetscBool      flg;

 39:   PEPCheckQuadratic(pep);
 40:   PEPCheckShiftSinvert(pep);
 41:   PEPSetDimensions_Default(pep,pep->nev,&pep->ncv,&pep->mpd);
 43:   if (pep->max_it==PETSC_DEFAULT) pep->max_it = PetscMax(100,4*pep->n/pep->ncv);
 44:   if (!pep->which) PEPSetWhichEigenpairs_Default(pep);

 47:   STGetTransform(pep->st,&flg);

 50:   /* set default extraction */
 51:   if (!pep->extract) pep->extract = PEP_EXTRACT_NONE;
 52:   PEPCheckUnsupported(pep,PEP_FEATURE_NONMONOMIAL | PEP_FEATURE_EXTRACT);

 54:   if (!ctx->keep) ctx->keep = 0.5;

 56:   PEPAllocateSolution(pep,0);
 57:   PEPSetWorkVecs(pep,4);

 59:   DSSetType(pep->ds,DSNHEP);
 60:   DSSetExtraRow(pep->ds,PETSC_TRUE);
 61:   DSAllocate(pep->ds,pep->ncv+1);

 63:   return 0;
 64: }

 66: PetscErrorCode PEPExtractVectors_QArnoldi(PEP pep)
 67: {
 68:   PetscInt       k=pep->nconv;
 69:   Mat            X,X0;

 71:   if (pep->nconv==0) return 0;
 72:   DSVectors(pep->ds,DS_MAT_X,NULL,NULL);

 74:   /* update vectors V = V*X */
 75:   DSGetMat(pep->ds,DS_MAT_X,&X);
 76:   MatDenseGetSubMatrix(X,0,k,0,k,&X0);
 77:   BVMultInPlace(pep->V,X0,0,k);
 78:   MatDenseRestoreSubMatrix(X,&X0);
 79:   DSRestoreMat(pep->ds,DS_MAT_X,&X);
 80:   return 0;
 81: }

 83: /*
 84:   Compute a step of Classical Gram-Schmidt orthogonalization
 85: */
 86: 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)
 87: {
 88:   PetscBLASInt   ione = 1,j_1 = j+1;
 89:   PetscReal      x,y;
 90:   PetscScalar    dot,one = 1.0,zero = 0.0;

 92:   /* compute norm of v and w */
 93:   if (onorm) {
 94:     VecNorm(v,NORM_2,&x);
 95:     VecNorm(w,NORM_2,&y);
 96:     *onorm = SlepcAbs(x,y);
 97:   }

 99:   /* orthogonalize: compute h */
100:   BVDotVec(V,v,h);
101:   BVDotVec(V,w,work);
102:   if (j>0) PetscCallBLAS("BLASgemv",BLASgemv_("C",&j_1,&j,&one,H,&ldh,work,&ione,&one,h,&ione));
103:   VecDot(w,t,&dot);
104:   h[j] += dot;

106:   /* orthogonalize: update v and w */
107:   BVMultVec(V,-1.0,1.0,v,h);
108:   if (j>0) {
109:     PetscCallBLAS("BLASgemv",BLASgemv_("N",&j_1,&j,&one,H,&ldh,h,&ione,&zero,work,&ione));
110:     BVMultVec(V,-1.0,1.0,w,work);
111:   }
112:   VecAXPY(w,-h[j],t);

114:   /* compute norm of v and w */
115:   if (norm) {
116:     VecNorm(v,NORM_2,&x);
117:     VecNorm(w,NORM_2,&y);
118:     *norm = SlepcAbs(x,y);
119:   }
120:   return 0;
121: }

123: /*
124:   Compute a run of Q-Arnoldi iterations
125: */
126: static PetscErrorCode PEPQArnoldi(PEP pep,Mat A,PetscInt k,PetscInt *M,Vec v,Vec w,PetscReal *beta,PetscBool *breakdown,PetscScalar *work)
127: {
128:   PetscInt           i,j,l,m = *M,ldh;
129:   Vec                t = pep->work[2],u = pep->work[3];
130:   BVOrthogRefineType refinement;
131:   PetscReal          norm=0.0,onorm,eta;
132:   PetscScalar        *H,*c = work + m;

134:   *beta = 0.0;
135:   MatDenseGetArray(A,&H);
136:   MatDenseGetLDA(A,&ldh);
137:   BVGetOrthogonalization(pep->V,NULL,&refinement,&eta,NULL);
138:   BVInsertVec(pep->V,k,v);
139:   for (j=k;j<m;j++) {
140:     /* apply operator */
141:     VecCopy(w,t);
142:     if (pep->Dr) VecPointwiseMult(v,v,pep->Dr);
143:     STMatMult(pep->st,0,v,u);
144:     VecCopy(t,v);
145:     if (pep->Dr) VecPointwiseMult(t,t,pep->Dr);
146:     STMatMult(pep->st,1,t,w);
147:     VecAXPY(u,pep->sfactor,w);
148:     STMatSolve(pep->st,u,w);
149:     VecScale(w,-1.0/(pep->sfactor*pep->sfactor));
150:     if (pep->Dr) VecPointwiseDivide(w,w,pep->Dr);
151:     VecCopy(v,t);
152:     BVSetActiveColumns(pep->V,0,j+1);

154:     /* orthogonalize */
155:     switch (refinement) {
156:       case BV_ORTHOG_REFINE_NEVER:
157:         PEPQArnoldiCGS(pep,H,ldh,H+ldh*j,j,pep->V,t,v,w,NULL,&norm,work);
158:         *breakdown = PETSC_FALSE;
159:         break;
160:       case BV_ORTHOG_REFINE_ALWAYS:
161:         PEPQArnoldiCGS(pep,H,ldh,H+ldh*j,j,pep->V,t,v,w,NULL,NULL,work);
162:         PEPQArnoldiCGS(pep,H,ldh,c,j,pep->V,t,v,w,&onorm,&norm,work);
163:         for (i=0;i<=j;i++) H[ldh*j+i] += c[i];
164:         if (norm < eta * onorm) *breakdown = PETSC_TRUE;
165:         else *breakdown = PETSC_FALSE;
166:         break;
167:       case BV_ORTHOG_REFINE_IFNEEDED:
168:         PEPQArnoldiCGS(pep,H,ldh,H+ldh*j,j,pep->V,t,v,w,&onorm,&norm,work);
169:         /* ||q|| < eta ||h|| */
170:         l = 1;
171:         while (l<3 && norm < eta * onorm) {
172:           l++;
173:           onorm = norm;
174:           PEPQArnoldiCGS(pep,H,ldh,c,j,pep->V,t,v,w,NULL,&norm,work);
175:           for (i=0;i<=j;i++) H[ldh*j+i] += c[i];
176:         }
177:         if (norm < eta * onorm) *breakdown = PETSC_TRUE;
178:         else *breakdown = PETSC_FALSE;
179:         break;
180:     }
181:     VecScale(v,1.0/norm);
182:     VecScale(w,1.0/norm);

184:     H[j+1+ldh*j] = norm;
185:     if (j<m-1) BVInsertVec(pep->V,j+1,v);
186:   }
187:   *beta = norm;
188:   MatDenseRestoreArray(A,&H);
189:   return 0;
190: }

192: PetscErrorCode PEPSolve_QArnoldi(PEP pep)
193: {
194:   PEP_QARNOLDI   *ctx = (PEP_QARNOLDI*)pep->data;
195:   PetscInt       j,k,l,lwork,nv,nconv;
196:   Vec            v=pep->work[0],w=pep->work[1];
197:   Mat            Q,S;
198:   PetscScalar    *work;
199:   PetscReal      beta,norm,x,y;
200:   PetscBool      breakdown=PETSC_FALSE,sinv;

202:   lwork = 7*pep->ncv;
203:   PetscMalloc1(lwork,&work);
204:   PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinv);
205:   RGPushScale(pep->rg,sinv?pep->sfactor:1.0/pep->sfactor);
206:   STScaleShift(pep->st,sinv?pep->sfactor:1.0/pep->sfactor);

208:   /* Get the starting Arnoldi vector */
209:   for (j=0;j<2;j++) {
210:     if (j>=pep->nini) BVSetRandomColumn(pep->V,j);
211:   }
212:   BVCopyVec(pep->V,0,v);
213:   BVCopyVec(pep->V,1,w);
214:   VecNorm(v,NORM_2,&x);
215:   VecNorm(w,NORM_2,&y);
216:   norm = SlepcAbs(x,y);
217:   VecScale(v,1.0/norm);
218:   VecScale(w,1.0/norm);

220:   /* clean projected matrix (including the extra-arrow) */
221:   DSSetDimensions(pep->ds,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
222:   DSGetMat(pep->ds,DS_MAT_A,&S);
223:   MatZeroEntries(S);
224:   DSRestoreMat(pep->ds,DS_MAT_A,&S);

226:    /* Restart loop */
227:   l = 0;
228:   while (pep->reason == PEP_CONVERGED_ITERATING) {
229:     pep->its++;

231:     /* Compute an nv-step Arnoldi factorization */
232:     nv = PetscMin(pep->nconv+pep->mpd,pep->ncv);
233:     DSGetMat(pep->ds,DS_MAT_A,&S);
234:     PEPQArnoldi(pep,S,pep->nconv+l,&nv,v,w,&beta,&breakdown,work);
235:     DSRestoreMat(pep->ds,DS_MAT_A,&S);
236:     DSSetDimensions(pep->ds,nv,pep->nconv,pep->nconv+l);
237:     DSSetState(pep->ds,l?DS_STATE_RAW:DS_STATE_INTERMEDIATE);
238:     BVSetActiveColumns(pep->V,pep->nconv,nv);

240:     /* Solve projected problem */
241:     DSSolve(pep->ds,pep->eigr,pep->eigi);
242:     DSSort(pep->ds,pep->eigr,pep->eigi,NULL,NULL,NULL);
243:     DSUpdateExtraRow(pep->ds);
244:     DSSynchronize(pep->ds,pep->eigr,pep->eigi);

246:     /* Check convergence */
247:     PEPKrylovConvergence(pep,PETSC_FALSE,pep->nconv,nv-pep->nconv,beta,&k);
248:     (*pep->stopping)(pep,pep->its,pep->max_it,k,pep->nev,&pep->reason,pep->stoppingctx);
249:     nconv = k;

251:     /* Update l */
252:     if (pep->reason != PEP_CONVERGED_ITERATING || breakdown) l = 0;
253:     else {
254:       l = PetscMax(1,(PetscInt)((nv-k)*ctx->keep));
255:       DSGetTruncateSize(pep->ds,k,nv,&l);
256:     }
257:     if (!ctx->lock && l>0) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */
258:     if (l) PetscInfo(pep,"Preparing to restart keeping l=%" PetscInt_FMT " vectors\n",l);

260:     if (pep->reason == PEP_CONVERGED_ITERATING) {
261:       if (PetscUnlikely(breakdown)) {
262:         /* Stop if breakdown */
263:         PetscInfo(pep,"Breakdown Quadratic Arnoldi method (it=%" PetscInt_FMT " norm=%g)\n",pep->its,(double)beta);
264:         pep->reason = PEP_DIVERGED_BREAKDOWN;
265:       } else {
266:         /* Prepare the Rayleigh quotient for restart */
267:         DSTruncate(pep->ds,k+l,PETSC_FALSE);
268:       }
269:     }
270:     /* Update the corresponding vectors V(:,idx) = V*Q(:,idx) */
271:     DSGetMat(pep->ds,DS_MAT_Q,&Q);
272:     BVMultInPlace(pep->V,Q,pep->nconv,k+l);
273:     DSRestoreMat(pep->ds,DS_MAT_Q,&Q);

275:     pep->nconv = k;
276:     PEPMonitor(pep,pep->its,nconv,pep->eigr,pep->eigi,pep->errest,nv);
277:   }
278:   BVSetActiveColumns(pep->V,0,pep->nconv);
279:   for (j=0;j<pep->nconv;j++) {
280:     pep->eigr[j] *= pep->sfactor;
281:     pep->eigi[j] *= pep->sfactor;
282:   }

284:   STScaleShift(pep->st,sinv?1.0/pep->sfactor:pep->sfactor);
285:   RGPopScale(pep->rg);

287:   DSTruncate(pep->ds,pep->nconv,PETSC_TRUE);
288:   PetscFree(work);
289:   return 0;
290: }

292: static PetscErrorCode PEPQArnoldiSetRestart_QArnoldi(PEP pep,PetscReal keep)
293: {
294:   PEP_QARNOLDI *ctx = (PEP_QARNOLDI*)pep->data;

296:   if (keep==PETSC_DEFAULT) ctx->keep = 0.5;
297:   else {
299:     ctx->keep = keep;
300:   }
301:   return 0;
302: }

304: /*@
305:    PEPQArnoldiSetRestart - Sets the restart parameter for the Q-Arnoldi
306:    method, in particular the proportion of basis vectors that must be kept
307:    after restart.

309:    Logically Collective on pep

311:    Input Parameters:
312: +  pep  - the eigenproblem solver context
313: -  keep - the number of vectors to be kept at restart

315:    Options Database Key:
316: .  -pep_qarnoldi_restart - Sets the restart parameter

318:    Notes:
319:    Allowed values are in the range [0.1,0.9]. The default is 0.5.

321:    Level: advanced

323: .seealso: PEPQArnoldiGetRestart()
324: @*/
325: PetscErrorCode PEPQArnoldiSetRestart(PEP pep,PetscReal keep)
326: {
329:   PetscTryMethod(pep,"PEPQArnoldiSetRestart_C",(PEP,PetscReal),(pep,keep));
330:   return 0;
331: }

333: static PetscErrorCode PEPQArnoldiGetRestart_QArnoldi(PEP pep,PetscReal *keep)
334: {
335:   PEP_QARNOLDI *ctx = (PEP_QARNOLDI*)pep->data;

337:   *keep = ctx->keep;
338:   return 0;
339: }

341: /*@
342:    PEPQArnoldiGetRestart - Gets the restart parameter used in the Q-Arnoldi method.

344:    Not Collective

346:    Input Parameter:
347: .  pep - the eigenproblem solver context

349:    Output Parameter:
350: .  keep - the restart parameter

352:    Level: advanced

354: .seealso: PEPQArnoldiSetRestart()
355: @*/
356: PetscErrorCode PEPQArnoldiGetRestart(PEP pep,PetscReal *keep)
357: {
360:   PetscUseMethod(pep,"PEPQArnoldiGetRestart_C",(PEP,PetscReal*),(pep,keep));
361:   return 0;
362: }

364: static PetscErrorCode PEPQArnoldiSetLocking_QArnoldi(PEP pep,PetscBool lock)
365: {
366:   PEP_QARNOLDI *ctx = (PEP_QARNOLDI*)pep->data;

368:   ctx->lock = lock;
369:   return 0;
370: }

372: /*@
373:    PEPQArnoldiSetLocking - Choose between locking and non-locking variants of
374:    the Q-Arnoldi method.

376:    Logically Collective on pep

378:    Input Parameters:
379: +  pep  - the eigenproblem solver context
380: -  lock - true if the locking variant must be selected

382:    Options Database Key:
383: .  -pep_qarnoldi_locking - Sets the locking flag

385:    Notes:
386:    The default is to lock converged eigenpairs when the method restarts.
387:    This behaviour can be changed so that all directions are kept in the
388:    working subspace even if already converged to working accuracy (the
389:    non-locking variant).

391:    Level: advanced

393: .seealso: PEPQArnoldiGetLocking()
394: @*/
395: PetscErrorCode PEPQArnoldiSetLocking(PEP pep,PetscBool lock)
396: {
399:   PetscTryMethod(pep,"PEPQArnoldiSetLocking_C",(PEP,PetscBool),(pep,lock));
400:   return 0;
401: }

403: static PetscErrorCode PEPQArnoldiGetLocking_QArnoldi(PEP pep,PetscBool *lock)
404: {
405:   PEP_QARNOLDI *ctx = (PEP_QARNOLDI*)pep->data;

407:   *lock = ctx->lock;
408:   return 0;
409: }

411: /*@
412:    PEPQArnoldiGetLocking - Gets the locking flag used in the Q-Arnoldi method.

414:    Not Collective

416:    Input Parameter:
417: .  pep - the eigenproblem solver context

419:    Output Parameter:
420: .  lock - the locking flag

422:    Level: advanced

424: .seealso: PEPQArnoldiSetLocking()
425: @*/
426: PetscErrorCode PEPQArnoldiGetLocking(PEP pep,PetscBool *lock)
427: {
430:   PetscUseMethod(pep,"PEPQArnoldiGetLocking_C",(PEP,PetscBool*),(pep,lock));
431:   return 0;
432: }

434: PetscErrorCode PEPSetFromOptions_QArnoldi(PEP pep,PetscOptionItems *PetscOptionsObject)
435: {
436:   PetscBool      flg,lock;
437:   PetscReal      keep;

439:   PetscOptionsHeadBegin(PetscOptionsObject,"PEP Q-Arnoldi Options");

441:     PetscOptionsReal("-pep_qarnoldi_restart","Proportion of vectors kept after restart","PEPQArnoldiSetRestart",0.5,&keep,&flg);
442:     if (flg) PEPQArnoldiSetRestart(pep,keep);

444:     PetscOptionsBool("-pep_qarnoldi_locking","Choose between locking and non-locking variants","PEPQArnoldiSetLocking",PETSC_FALSE,&lock,&flg);
445:     if (flg) PEPQArnoldiSetLocking(pep,lock);

447:   PetscOptionsHeadEnd();
448:   return 0;
449: }

451: PetscErrorCode PEPView_QArnoldi(PEP pep,PetscViewer viewer)
452: {
453:   PEP_QARNOLDI   *ctx = (PEP_QARNOLDI*)pep->data;
454:   PetscBool      isascii;

456:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
457:   if (isascii) {
458:     PetscViewerASCIIPrintf(viewer,"  %d%% of basis vectors kept after restart\n",(int)(100*ctx->keep));
459:     PetscViewerASCIIPrintf(viewer,"  using the %slocking variant\n",ctx->lock?"":"non-");
460:   }
461:   return 0;
462: }

464: PetscErrorCode PEPDestroy_QArnoldi(PEP pep)
465: {
466:   PetscFree(pep->data);
467:   PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiSetRestart_C",NULL);
468:   PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiGetRestart_C",NULL);
469:   PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiSetLocking_C",NULL);
470:   PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiGetLocking_C",NULL);
471:   return 0;
472: }

474: SLEPC_EXTERN PetscErrorCode PEPCreate_QArnoldi(PEP pep)
475: {
476:   PEP_QARNOLDI   *ctx;

478:   PetscNew(&ctx);
479:   pep->data = (void*)ctx;

481:   pep->lineariz = PETSC_TRUE;
482:   ctx->lock     = PETSC_TRUE;

484:   pep->ops->solve          = PEPSolve_QArnoldi;
485:   pep->ops->setup          = PEPSetUp_QArnoldi;
486:   pep->ops->setfromoptions = PEPSetFromOptions_QArnoldi;
487:   pep->ops->destroy        = PEPDestroy_QArnoldi;
488:   pep->ops->view           = PEPView_QArnoldi;
489:   pep->ops->backtransform  = PEPBackTransform_Default;
490:   pep->ops->computevectors = PEPComputeVectors_Default;
491:   pep->ops->extractvectors = PEPExtractVectors_QArnoldi;
492:   pep->ops->setdefaultst   = PEPSetDefaultST_Transform;

494:   PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiSetRestart_C",PEPQArnoldiSetRestart_QArnoldi);
495:   PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiGetRestart_C",PEPQArnoldiGetRestart_QArnoldi);
496:   PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiSetLocking_C",PEPQArnoldiSetLocking_QArnoldi);
497:   PetscObjectComposeFunction((PetscObject)pep,"PEPQArnoldiGetLocking_C",PEPQArnoldiGetLocking_QArnoldi);
498:   return 0;
499: }