Actual source code: narnoldi.c

slepc-3.14.2 2021-02-01
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2020, 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 nonlinear eigensolver: "narnoldi"

 13:    Method: Nonlinear Arnoldi

 15:    Algorithm:

 17:        Arnoldi for nonlinear eigenproblems.

 19:    References:

 21:        [1] H. Voss, "An Arnoldi method for nonlinear eigenvalue problems",
 22:            BIT 44:387-401, 2004.
 23: */

 25: #include <slepc/private/nepimpl.h>
 26: #include <../src/nep/impls/nepdefl.h>

 28: typedef struct {
 29:   PetscInt lag;             /* interval to rebuild preconditioner */
 30:   KSP      ksp;             /* linear solver object */
 31: } NEP_NARNOLDI;

 33: PetscErrorCode NEPSetUp_NArnoldi(NEP nep)
 34: {

 38:   NEPSetDimensions_Default(nep,nep->nev,&nep->ncv,&nep->mpd);
 39:   if (nep->ncv>nep->nev+nep->mpd) SETERRQ(PetscObjectComm((PetscObject)nep),1,"The value of ncv must not be larger than nev+mpd");
 40:   if (nep->max_it==PETSC_DEFAULT) nep->max_it = nep->nev*nep->ncv;
 41:   if (!nep->which) nep->which = NEP_TARGET_MAGNITUDE;
 42:   if (nep->which!=NEP_TARGET_MAGNITUDE) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"This solver supports only target magnitude eigenvalues");
 43:   NEPCheckUnsupported(nep,NEP_FEATURE_CALLBACK | NEP_FEATURE_REGION | NEP_FEATURE_TWOSIDED);
 44:   NEPAllocateSolution(nep,0);
 45:   NEPSetWorkVecs(nep,3);
 46:   return(0);
 47: }

 49: PetscErrorCode NEPSolve_NArnoldi(NEP nep)
 50: {
 51:   PetscErrorCode     ierr;
 52:   NEP_NARNOLDI       *ctx = (NEP_NARNOLDI*)nep->data;
 53:   Mat                T,H;
 54:   Vec                f,r,u,uu;
 55:   PetscScalar        *X,lambda=0.0,lambda2=0.0,*eigr,*Hp,*Ap,sigma;
 56:   PetscReal          beta,resnorm=0.0,nrm,perr=0.0;
 57:   PetscInt           n,i,j,ldds,ldh;
 58:   PetscBool          breakdown,skip=PETSC_FALSE;
 59:   BV                 Vext;
 60:   DS                 ds;
 61:   NEP_EXT_OP         extop=NULL;
 62:   SlepcSC            sc;
 63:   KSPConvergedReason kspreason;

 66:   /* get initial space and shift */
 67:   NEPGetDefaultShift(nep,&sigma);
 68:   if (!nep->nini) {
 69:     BVSetRandomColumn(nep->V,0);
 70:     BVNormColumn(nep->V,0,NORM_2,&nrm);
 71:     BVScaleColumn(nep->V,0,1.0/nrm);
 72:     n = 1;
 73:   } else n = nep->nini;

 75:   if (!ctx->ksp) { NEPNArnoldiGetKSP(nep,&ctx->ksp); }
 76:   NEPDeflationInitialize(nep,nep->V,ctx->ksp,PETSC_FALSE,nep->nev,&extop);
 77:   NEPDeflationCreateBV(extop,nep->ncv,&Vext);

 79:   /* prepare linear solver */
 80:   NEPDeflationSolveSetUp(extop,sigma);

 82:   BVGetColumn(Vext,0,&f);
 83:   VecDuplicate(f,&r);
 84:   VecDuplicate(f,&u);
 85:   BVGetColumn(nep->V,0,&uu);
 86:   NEPDeflationCopyToExtendedVec(extop,uu,NULL,f,PETSC_FALSE);
 87:   BVRestoreColumn(nep->V,0,&uu);
 88:   VecCopy(f,r);
 89:   NEPDeflationFunctionSolve(extop,r,f);
 90:   VecNorm(f,NORM_2,&nrm);
 91:   VecScale(f,1.0/nrm);
 92:   BVRestoreColumn(Vext,0,&f);

 94:   DSCreate(PetscObjectComm((PetscObject)nep),&ds);
 95:   PetscLogObjectParent((PetscObject)nep,(PetscObject)ds);
 96:   DSSetType(ds,DSNEP);
 97:   DSNEPSetFN(ds,nep->nt,nep->f);
 98:   DSAllocate(ds,nep->ncv);
 99:   DSGetSlepcSC(ds,&sc);
100:   sc->comparison    = nep->sc->comparison;
101:   sc->comparisonctx = nep->sc->comparisonctx;
102:   DSSetFromOptions(ds);

104:   /* build projected matrices for initial space */
105:   DSSetDimensions(ds,n,0,0,0);
106:   NEPDeflationProjectOperator(extop,Vext,ds,0,n);

108:   PetscMalloc1(nep->ncv,&eigr);

110:   /* Restart loop */
111:   while (nep->reason == NEP_CONVERGED_ITERATING) {
112:     nep->its++;

114:     /* solve projected problem */
115:     DSSetDimensions(ds,n,0,0,0);
116:     DSSetState(ds,DS_STATE_RAW);
117:     DSSolve(ds,eigr,NULL);
118:     DSSynchronize(ds,eigr,NULL);
119:     if (nep->its>1) lambda2 = lambda;
120:     lambda = eigr[0];
121:     nep->eigr[nep->nconv] = lambda;

123:     /* compute Ritz vector, x = V*s */
124:     DSGetArray(ds,DS_MAT_X,&X);
125:     BVSetActiveColumns(Vext,0,n);
126:     BVMultVec(Vext,1.0,0.0,u,X);
127:     DSRestoreArray(ds,DS_MAT_X,&X);

129:     /* compute the residual, r = T(lambda)*x */
130:     NEPDeflationComputeFunction(extop,lambda,&T);
131:     MatMult(T,u,r);

133:     /* convergence test */
134:     VecNorm(r,NORM_2,&resnorm);
135:     if (nep->its>1) perr=nep->errest[nep->nconv];
136:     (*nep->converged)(nep,lambda,0,resnorm,&nep->errest[nep->nconv],nep->convergedctx);
137:     if (nep->errest[nep->nconv]<=nep->tol) {
138:       nep->nconv = nep->nconv + 1;
139:       NEPDeflationLocking(extop,u,lambda);
140:       skip = PETSC_TRUE;
141:     }
142:     (*nep->stopping)(nep,nep->its,nep->max_it,nep->nconv,nep->nev,&nep->reason,nep->stoppingctx);
143:     if (!skip || nep->reason>0) {
144:       NEPMonitor(nep,nep->its,nep->nconv,nep->eigr,nep->eigi,nep->errest,(nep->reason>0)?nep->nconv:nep->nconv+1);
145:     }

147:     if (nep->reason == NEP_CONVERGED_ITERATING) {
148:       if (!skip) {
149:         if (n>=nep->ncv) {
150:           nep->reason = NEP_DIVERGED_SUBSPACE_EXHAUSTED;
151:           break;
152:         }
153:         if (ctx->lag && !(nep->its%ctx->lag) && nep->its>=2*ctx->lag && perr && nep->errest[nep->nconv]>.5*perr) {
154:           NEPDeflationSolveSetUp(extop,lambda2);
155:         }

157:         /* continuation vector: f = T(sigma)\r */
158:         BVGetColumn(Vext,n,&f);
159:         NEPDeflationFunctionSolve(extop,r,f);
160:         BVRestoreColumn(Vext,n,&f);
161:         KSPGetConvergedReason(ctx->ksp,&kspreason);
162:         if (kspreason<0) {
163:           PetscInfo1(nep,"iter=%D, linear solve failed, stopping solve\n",nep->its);
164:           nep->reason = NEP_DIVERGED_LINEAR_SOLVE;
165:           break;
166:         }

168:         /* orthonormalize */
169:         BVOrthonormalizeColumn(Vext,n,PETSC_FALSE,&beta,&breakdown);
170:         if (breakdown || beta==0.0) {
171:           PetscInfo1(nep,"iter=%D, orthogonalization failed, stopping solve\n",nep->its);
172:           nep->reason = NEP_DIVERGED_BREAKDOWN;
173:           break;
174:         }

176:         /* update projected matrices */
177:         DSSetDimensions(ds,n+1,0,0,0);
178:         NEPDeflationProjectOperator(extop,Vext,ds,n,n+1);
179:         n++;
180:       } else {
181:         nep->its--;  /* do not count this as a full iteration */
182:         BVGetColumn(Vext,0,&f);
183:         NEPDeflationSetRandomVec(extop,f);
184:         NEPDeflationSolveSetUp(extop,sigma);
185:         VecCopy(f,r);
186:         NEPDeflationFunctionSolve(extop,r,f);
187:         VecNorm(f,NORM_2,&nrm);
188:         VecScale(f,1.0/nrm);
189:         BVRestoreColumn(Vext,0,&f);
190:         n = 1;
191:         DSSetDimensions(ds,n,0,0,0);
192:         NEPDeflationProjectOperator(extop,Vext,ds,n-1,n);
193:         skip = PETSC_FALSE;
194:       }
195:     }
196:   }

198:   NEPDeflationGetInvariantPair(extop,NULL,&H);
199:   MatGetSize(H,NULL,&ldh);
200:   DSSetType(nep->ds,DSNHEP);
201:   DSAllocate(nep->ds,PetscMax(nep->nconv,1));
202:   DSGetLeadingDimension(nep->ds,&ldds);
203:   MatDenseGetArray(H,&Hp);
204:   DSGetArray(nep->ds,DS_MAT_A,&Ap);
205:   for (j=0;j<nep->nconv;j++)
206:     for (i=0;i<nep->nconv;i++) Ap[j*ldds+i] = Hp[j*ldh+i];
207:   DSRestoreArray(nep->ds,DS_MAT_A,&Ap);
208:   MatDenseRestoreArray(H,&Hp);
209:   MatDestroy(&H);
210:   DSSetDimensions(nep->ds,nep->nconv,0,0,nep->nconv);
211:   DSSolve(nep->ds,nep->eigr,nep->eigi);
212:   NEPDeflationReset(extop);
213:   VecDestroy(&u);
214:   VecDestroy(&r);
215:   BVDestroy(&Vext);
216:   DSDestroy(&ds);
217:   PetscFree(eigr);
218:   return(0);
219: }

221: static PetscErrorCode NEPNArnoldiSetLagPreconditioner_NArnoldi(NEP nep,PetscInt lag)
222: {
223:   NEP_NARNOLDI *ctx = (NEP_NARNOLDI*)nep->data;

226:   if (lag<0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Lag must be non-negative");
227:   ctx->lag = lag;
228:   return(0);
229: }

231: /*@
232:    NEPNArnoldiSetLagPreconditioner - Determines when the preconditioner is rebuilt in the
233:    nonlinear solve.

235:    Logically Collective on nep

237:    Input Parameters:
238: +  nep - nonlinear eigenvalue solver
239: -  lag - 0 indicates NEVER rebuild, 1 means rebuild every time the Jacobian is
240:           computed within the nonlinear iteration, 2 means every second time
241:           the Jacobian is built, etc.

243:    Options Database Keys:
244: .  -nep_narnoldi_lag_preconditioner <lag>

246:    Notes:
247:    The default is 1.
248:    The preconditioner is ALWAYS built in the first iteration of a nonlinear solve.

250:    Level: intermediate

252: .seealso: NEPNArnoldiGetLagPreconditioner()
253: @*/
254: PetscErrorCode NEPNArnoldiSetLagPreconditioner(NEP nep,PetscInt lag)
255: {

261:   PetscTryMethod(nep,"NEPNArnoldiSetLagPreconditioner_C",(NEP,PetscInt),(nep,lag));
262:   return(0);
263: }

265: static PetscErrorCode NEPNArnoldiGetLagPreconditioner_NArnoldi(NEP nep,PetscInt *lag)
266: {
267:   NEP_NARNOLDI *ctx = (NEP_NARNOLDI*)nep->data;

270:   *lag = ctx->lag;
271:   return(0);
272: }

274: /*@
275:    NEPNArnoldiGetLagPreconditioner - Indicates how often the preconditioner is rebuilt.

277:    Not Collective

279:    Input Parameter:
280: .  nep - nonlinear eigenvalue solver

282:    Output Parameter:
283: .  lag - the lag parameter

285:    Level: intermediate

287: .seealso: NEPNArnoldiSetLagPreconditioner()
288: @*/
289: PetscErrorCode NEPNArnoldiGetLagPreconditioner(NEP nep,PetscInt *lag)
290: {

296:   PetscUseMethod(nep,"NEPNArnoldiGetLagPreconditioner_C",(NEP,PetscInt*),(nep,lag));
297:   return(0);
298: }

300: PetscErrorCode NEPSetFromOptions_NArnoldi(PetscOptionItems *PetscOptionsObject,NEP nep)
301: {
303:   PetscInt       i;
304:   PetscBool      flg;
305:   NEP_NARNOLDI   *ctx = (NEP_NARNOLDI*)nep->data;

308:   PetscOptionsHead(PetscOptionsObject,"NEP N-Arnoldi Options");
309:     i = 0;
310:     PetscOptionsInt("-nep_narnoldi_lag_preconditioner","Interval to rebuild preconditioner","NEPNArnoldiSetLagPreconditioner",ctx->lag,&i,&flg);
311:     if (flg) { NEPNArnoldiSetLagPreconditioner(nep,i); }

313:   PetscOptionsTail();

315:   if (!ctx->ksp) { NEPNArnoldiGetKSP(nep,&ctx->ksp); }
316:   KSPSetFromOptions(ctx->ksp);
317:   return(0);
318: }

320: static PetscErrorCode NEPNArnoldiSetKSP_NArnoldi(NEP nep,KSP ksp)
321: {
323:   NEP_NARNOLDI   *ctx = (NEP_NARNOLDI*)nep->data;

326:   PetscObjectReference((PetscObject)ksp);
327:   KSPDestroy(&ctx->ksp);
328:   ctx->ksp = ksp;
329:   PetscLogObjectParent((PetscObject)nep,(PetscObject)ctx->ksp);
330:   nep->state = NEP_STATE_INITIAL;
331:   return(0);
332: }

334: /*@
335:    NEPNArnoldiSetKSP - Associate a linear solver object (KSP) to the nonlinear
336:    eigenvalue solver.

338:    Collective on nep

340:    Input Parameters:
341: +  nep - eigenvalue solver
342: -  ksp - the linear solver object

344:    Level: advanced

346: .seealso: NEPNArnoldiGetKSP()
347: @*/
348: PetscErrorCode NEPNArnoldiSetKSP(NEP nep,KSP ksp)
349: {

356:   PetscTryMethod(nep,"NEPNArnoldiSetKSP_C",(NEP,KSP),(nep,ksp));
357:   return(0);
358: }

360: static PetscErrorCode NEPNArnoldiGetKSP_NArnoldi(NEP nep,KSP *ksp)
361: {
363:   NEP_NARNOLDI   *ctx = (NEP_NARNOLDI*)nep->data;

366:   if (!ctx->ksp) {
367:     KSPCreate(PetscObjectComm((PetscObject)nep),&ctx->ksp);
368:     PetscObjectIncrementTabLevel((PetscObject)ctx->ksp,(PetscObject)nep,1);
369:     KSPSetOptionsPrefix(ctx->ksp,((PetscObject)nep)->prefix);
370:     KSPAppendOptionsPrefix(ctx->ksp,"nep_narnoldi_");
371:     PetscLogObjectParent((PetscObject)nep,(PetscObject)ctx->ksp);
372:     PetscObjectSetOptions((PetscObject)ctx->ksp,((PetscObject)nep)->options);
373:     KSPSetErrorIfNotConverged(ctx->ksp,PETSC_TRUE);
374:     KSPSetTolerances(ctx->ksp,SLEPC_DEFAULT_TOL,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
375:   }
376:   *ksp = ctx->ksp;
377:   return(0);
378: }

380: /*@
381:    NEPNArnoldiGetKSP - Retrieve the linear solver object (KSP) associated with
382:    the nonlinear eigenvalue solver.

384:    Not Collective

386:    Input Parameter:
387: .  nep - nonlinear eigenvalue solver

389:    Output Parameter:
390: .  ksp - the linear solver object

392:    Level: advanced

394: .seealso: NEPNArnoldiSetKSP()
395: @*/
396: PetscErrorCode NEPNArnoldiGetKSP(NEP nep,KSP *ksp)
397: {

403:   PetscUseMethod(nep,"NEPNArnoldiGetKSP_C",(NEP,KSP*),(nep,ksp));
404:   return(0);
405: }

407: PetscErrorCode NEPView_NArnoldi(NEP nep,PetscViewer viewer)
408: {
410:   NEP_NARNOLDI   *ctx = (NEP_NARNOLDI*)nep->data;
411:   PetscBool      isascii;

414:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
415:   if (isascii) {
416:     if (ctx->lag) {
417:       PetscViewerASCIIPrintf(viewer,"  updating the preconditioner every %D iterations\n",ctx->lag);
418:     }
419:     if (!ctx->ksp) { NEPNArnoldiGetKSP(nep,&ctx->ksp); }
420:     PetscViewerASCIIPushTab(viewer);
421:     KSPView(ctx->ksp,viewer);
422:     PetscViewerASCIIPopTab(viewer);
423:   }
424:   return(0);
425: }

427: PetscErrorCode NEPReset_NArnoldi(NEP nep)
428: {
430:   NEP_NARNOLDI   *ctx = (NEP_NARNOLDI*)nep->data;

433:   KSPReset(ctx->ksp);
434:   return(0);
435: }

437: PetscErrorCode NEPDestroy_NArnoldi(NEP nep)
438: {
440:   NEP_NARNOLDI   *ctx = (NEP_NARNOLDI*)nep->data;

443:   KSPDestroy(&ctx->ksp);
444:   PetscFree(nep->data);
445:   PetscObjectComposeFunction((PetscObject)nep,"NEPNArnoldiSetLagPreconditioner_C",NULL);
446:   PetscObjectComposeFunction((PetscObject)nep,"NEPNArnoldiGetLagPreconditioner_C",NULL);
447:   PetscObjectComposeFunction((PetscObject)nep,"NEPNArnoldiSetKSP_C",NULL);
448:   PetscObjectComposeFunction((PetscObject)nep,"NEPNArnoldiGetKSP_C",NULL);
449:   return(0);
450: }

452: SLEPC_EXTERN PetscErrorCode NEPCreate_NArnoldi(NEP nep)
453: {
455:   NEP_NARNOLDI   *ctx;

458:   PetscNewLog(nep,&ctx);
459:   nep->data = (void*)ctx;
460:   ctx->lag  = 1;

462:   nep->useds = PETSC_TRUE;

464:   nep->ops->solve          = NEPSolve_NArnoldi;
465:   nep->ops->setup          = NEPSetUp_NArnoldi;
466:   nep->ops->setfromoptions = NEPSetFromOptions_NArnoldi;
467:   nep->ops->reset          = NEPReset_NArnoldi;
468:   nep->ops->destroy        = NEPDestroy_NArnoldi;
469:   nep->ops->view           = NEPView_NArnoldi;
470:   nep->ops->computevectors = NEPComputeVectors_Schur;

472:   PetscObjectComposeFunction((PetscObject)nep,"NEPNArnoldiSetLagPreconditioner_C",NEPNArnoldiSetLagPreconditioner_NArnoldi);
473:   PetscObjectComposeFunction((PetscObject)nep,"NEPNArnoldiGetLagPreconditioner_C",NEPNArnoldiGetLagPreconditioner_NArnoldi);
474:   PetscObjectComposeFunction((PetscObject)nep,"NEPNArnoldiSetKSP_C",NEPNArnoldiSetKSP_NArnoldi);
475:   PetscObjectComposeFunction((PetscObject)nep,"NEPNArnoldiGetKSP_C",NEPNArnoldiGetKSP_NArnoldi);
476:   return(0);
477: }