Actual source code: pciss.c

  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 eigensolver: "ciss"

 13:    Method: Contour Integral Spectral Slicing

 15:    Algorithm:

 17:        Contour integral based on Sakurai-Sugiura method to construct a
 18:        subspace, with various eigenpair extractions (Rayleigh-Ritz,
 19:        explicit moment).

 21:    Based on code contributed by Y. Maeda, T. Sakurai.

 23:    References:

 25:        [1] J. Asakura, T. Sakurai, H. Tadano, T. Ikegami, K. Kimura, "A
 26:            numerical method for polynomial eigenvalue problems using contour
 27:            integral", Japan J. Indust. Appl. Math. 27:73-90, 2010.
 28: */

 30: #include <slepc/private/pepimpl.h>
 31: #include <slepc/private/slepccontour.h>

 33: typedef struct {
 34:   /* parameters */
 35:   PetscInt          N;             /* number of integration points (32) */
 36:   PetscInt          L;             /* block size (16) */
 37:   PetscInt          M;             /* moment degree (N/4 = 4) */
 38:   PetscReal         delta;         /* threshold of singular value (1e-12) */
 39:   PetscInt          L_max;         /* maximum number of columns of the source matrix V */
 40:   PetscReal         spurious_threshold; /* discard spurious eigenpairs */
 41:   PetscBool         isreal;        /* T(z) is real for real z */
 42:   PetscInt          npart;         /* number of partitions */
 43:   PetscInt          refine_inner;
 44:   PetscInt          refine_blocksize;
 45:   PEPCISSExtraction extraction;
 46:   /* private data */
 47:   SlepcContourData  contour;
 48:   PetscReal         *sigma;        /* threshold for numerical rank */
 49:   PetscScalar       *weight;
 50:   PetscScalar       *omega;
 51:   PetscScalar       *pp;
 52:   BV                V;
 53:   BV                S;
 54:   BV                Y;
 55:   PetscBool         useconj;
 56:   Mat               J,*Psplit;     /* auxiliary matrices */
 57:   BV                pV;
 58:   PetscObjectId     rgid;
 59:   PetscObjectState  rgstate;
 60: } PEP_CISS;

 62: static PetscErrorCode PEPComputeFunction(PEP pep,PetscScalar lambda,Mat T,Mat P,PetscBool deriv)
 63: {
 64:   PetscInt         i;
 65:   PetscScalar      *coeff;
 66:   Mat              *A,*K;
 67:   MatStructure     str,strp;
 68:   PEP_CISS         *ctx = (PEP_CISS*)pep->data;
 69:   SlepcContourData contour = ctx->contour;

 71:   PetscFunctionBegin;
 72:   A = (contour->pA)?contour->pA:pep->A;
 73:   K = (contour->pP)?contour->pP:ctx->Psplit;
 74:   PetscCall(PetscMalloc1(pep->nmat,&coeff));
 75:   if (deriv) PetscCall(PEPEvaluateBasisDerivative(pep,lambda,0,coeff,NULL));
 76:   else PetscCall(PEPEvaluateBasis(pep,lambda,0,coeff,NULL));
 77:   PetscCall(STGetMatStructure(pep->st,&str));
 78:   PetscCall(MatZeroEntries(T));
 79:   if (!deriv && T != P) {
 80:     PetscCall(STGetSplitPreconditionerInfo(pep->st,NULL,&strp));
 81:     PetscCall(MatZeroEntries(P));
 82:   }
 83:   i = deriv?1:0;
 84:   for (;i<pep->nmat;i++) {
 85:     PetscCall(MatAXPY(T,coeff[i],A[i],str));
 86:     if (!deriv && T != P) PetscCall(MatAXPY(P,coeff[i],K[i],strp));
 87:   }
 88:   PetscCall(PetscFree(coeff));
 89:   PetscFunctionReturn(PETSC_SUCCESS);
 90: }

 92: /*
 93:   Set up KSP solvers for every integration point
 94: */
 95: static PetscErrorCode PEPCISSSetUp(PEP pep,Mat T,Mat P)
 96: {
 97:   PEP_CISS         *ctx = (PEP_CISS*)pep->data;
 98:   SlepcContourData contour;
 99:   PetscInt         i,p_id;
100:   Mat              Amat,Pmat;

102:   PetscFunctionBegin;
103:   if (!ctx->contour || !ctx->contour->ksp) PetscCall(PEPCISSGetKSPs(pep,NULL,NULL));
104:   contour = ctx->contour;
105:   PetscAssert(ctx->contour && ctx->contour->ksp,PetscObjectComm((PetscObject)pep),PETSC_ERR_PLIB,"Something went wrong with PEPCISSGetKSPs()");
106:   for (i=0;i<contour->npoints;i++) {
107:     p_id = i*contour->subcomm->n + contour->subcomm->color;
108:     PetscCall(MatDuplicate(T,MAT_DO_NOT_COPY_VALUES,&Amat));
109:     if (T != P) PetscCall(MatDuplicate(P,MAT_DO_NOT_COPY_VALUES,&Pmat)); else Pmat = Amat;
110:     PetscCall(PEPComputeFunction(pep,ctx->omega[p_id],Amat,Pmat,PETSC_FALSE));
111:     PetscCall(PEP_KSPSetOperators(contour->ksp[i],Amat,Pmat));
112:     PetscCall(MatDestroy(&Amat));
113:     if (T != P) PetscCall(MatDestroy(&Pmat));
114:   }
115:   PetscFunctionReturn(PETSC_SUCCESS);
116: }

118: /*
119:   Y_i = F(z_i)^{-1}Fp(z_i)V for every integration point, Y=[Y_i] is in the context
120: */
121: static PetscErrorCode PEPCISSSolve(PEP pep,Mat dT,BV V,PetscInt L_start,PetscInt L_end)
122: {
123:   PEP_CISS         *ctx = (PEP_CISS*)pep->data;
124:   SlepcContourData contour;
125:   PetscInt         i,p_id;
126:   Mat              MV,BMV=NULL,MC;

128:   PetscFunctionBegin;
129:   contour = ctx->contour;
130:   PetscCall(BVSetActiveColumns(V,L_start,L_end));
131:   PetscCall(BVGetMat(V,&MV));
132:   for (i=0;i<contour->npoints;i++) {
133:     p_id = i*contour->subcomm->n + contour->subcomm->color;
134:     PetscCall(PEPComputeFunction(pep,ctx->omega[p_id],dT,NULL,PETSC_TRUE));
135:     PetscCall(BVSetActiveColumns(ctx->Y,i*ctx->L+L_start,i*ctx->L+L_end));
136:     PetscCall(BVGetMat(ctx->Y,&MC));
137:     if (!i) {
138:       PetscCall(MatProductCreate(dT,MV,NULL,&BMV));
139:       PetscCall(MatProductSetType(BMV,MATPRODUCT_AB));
140:       PetscCall(MatProductSetFromOptions(BMV));
141:       PetscCall(MatProductSymbolic(BMV));
142:     }
143:     PetscCall(MatProductNumeric(BMV));
144:     PetscCall(KSPMatSolve(contour->ksp[i],BMV,MC));
145:     PetscCall(BVRestoreMat(ctx->Y,&MC));
146:   }
147:   PetscCall(MatDestroy(&BMV));
148:   PetscCall(BVRestoreMat(V,&MV));
149:   PetscFunctionReturn(PETSC_SUCCESS);
150: }

152: static PetscErrorCode PEPSetUp_CISS(PEP pep)
153: {
154:   PEP_CISS         *ctx = (PEP_CISS*)pep->data;
155:   SlepcContourData contour;
156:   PetscInt         i,nwork,nsplit;
157:   PetscBool        istrivial,isellipse,flg;
158:   PetscObjectId    id;
159:   PetscObjectState state;
160:   Vec              v0;

162:   PetscFunctionBegin;
163:   if (pep->ncv==PETSC_DETERMINE) pep->ncv = ctx->L_max*ctx->M;
164:   else {
165:     ctx->L_max = pep->ncv/ctx->M;
166:     if (!ctx->L_max) {
167:       ctx->L_max = 1;
168:       pep->ncv = ctx->L_max*ctx->M;
169:     }
170:   }
171:   ctx->L = PetscMin(ctx->L,ctx->L_max);
172:   if (pep->max_it==PETSC_DETERMINE) pep->max_it = 5;
173:   if (pep->mpd==PETSC_DETERMINE) pep->mpd = pep->ncv;
174:   if (!pep->which) pep->which = PEP_ALL;
175:   PetscCheck(pep->which==PEP_ALL,PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"This solver supports only computing all eigenvalues");
176:   PEPCheckUnsupported(pep,PEP_FEATURE_STOPPING);
177:   PEPCheckIgnored(pep,PEP_FEATURE_SCALE);

179:   /* check region */
180:   PetscCall(RGIsTrivial(pep->rg,&istrivial));
181:   PetscCheck(!istrivial,PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"CISS requires a nontrivial region, e.g. -rg_type ellipse ...");
182:   PetscCall(RGGetComplement(pep->rg,&flg));
183:   PetscCheck(!flg,PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"A region with complement flag set is not allowed");
184:   PetscCall(PetscObjectTypeCompare((PetscObject)pep->rg,RGELLIPSE,&isellipse));
185:   PetscCheck(isellipse,PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Currently only implemented for elliptic regions");

187:   /* if the region has changed, then reset contour data */
188:   PetscCall(PetscObjectGetId((PetscObject)pep->rg,&id));
189:   PetscCall(PetscObjectStateGet((PetscObject)pep->rg,&state));
190:   if (ctx->rgid && (id != ctx->rgid || state != ctx->rgstate)) {
191:     PetscCall(SlepcContourDataDestroy(&ctx->contour));
192:     PetscCall(PetscInfo(pep,"Resetting the contour data structure due to a change of region\n"));
193:     ctx->rgid = id; ctx->rgstate = state;
194:   }

196:   /* create contour data structure */
197:   if (!ctx->contour) {
198:     PetscCall(RGCanUseConjugates(pep->rg,ctx->isreal,&ctx->useconj));
199:     PetscCall(SlepcContourDataCreate(ctx->useconj?ctx->N/2:ctx->N,ctx->npart,(PetscObject)pep,&ctx->contour));
200:   }

202:   PetscCall(PEPAllocateSolution(pep,0));
203:   if (ctx->weight) PetscCall(PetscFree4(ctx->weight,ctx->omega,ctx->pp,ctx->sigma));
204:   PetscCall(PetscMalloc4(ctx->N,&ctx->weight,ctx->N,&ctx->omega,ctx->N,&ctx->pp,ctx->L_max*ctx->M,&ctx->sigma));

206:   /* allocate basis vectors */
207:   PetscCall(BVDestroy(&ctx->S));
208:   PetscCall(BVDuplicateResize(pep->V,ctx->L*ctx->M,&ctx->S));
209:   PetscCall(BVDestroy(&ctx->V));
210:   PetscCall(BVDuplicateResize(pep->V,ctx->L,&ctx->V));

212:   /* check if a user-defined split preconditioner has been set */
213:   PetscCall(STGetSplitPreconditionerInfo(pep->st,&nsplit,NULL));
214:   if (nsplit) {
215:     PetscCall(PetscFree(ctx->Psplit));
216:     PetscCall(PetscMalloc1(nsplit,&ctx->Psplit));
217:     for (i=0;i<nsplit;i++) PetscCall(STGetSplitPreconditionerTerm(pep->st,i,&ctx->Psplit[i]));
218:   }

220:   contour = ctx->contour;
221:   PetscCall(SlepcContourRedundantMat(contour,pep->nmat,pep->A,ctx->Psplit));
222:   if (!ctx->J) PetscCall(MatDuplicate(contour->pA?contour->pA[0]:pep->A[0],MAT_DO_NOT_COPY_VALUES,&ctx->J));
223:   if (contour->pA) {
224:     PetscCall(BVGetColumn(ctx->V,0,&v0));
225:     PetscCall(SlepcContourScatterCreate(contour,v0));
226:     PetscCall(BVRestoreColumn(ctx->V,0,&v0));
227:     PetscCall(BVDestroy(&ctx->pV));
228:     PetscCall(BVCreate(PetscObjectComm((PetscObject)contour->xsub),&ctx->pV));
229:     PetscCall(BVSetSizesFromVec(ctx->pV,contour->xsub,pep->n));
230:     PetscCall(BVSetFromOptions(ctx->pV));
231:     PetscCall(BVResize(ctx->pV,ctx->L,PETSC_FALSE));
232:   }

234:   PetscCall(BVDestroy(&ctx->Y));
235:   if (contour->pA) {
236:     PetscCall(BVCreate(PetscObjectComm((PetscObject)contour->xsub),&ctx->Y));
237:     PetscCall(BVSetSizesFromVec(ctx->Y,contour->xsub,pep->n));
238:     PetscCall(BVSetFromOptions(ctx->Y));
239:     PetscCall(BVResize(ctx->Y,contour->npoints*ctx->L,PETSC_FALSE));
240:   } else PetscCall(BVDuplicateResize(pep->V,contour->npoints*ctx->L,&ctx->Y));

242:   if (ctx->extraction == PEP_CISS_EXTRACTION_RITZ) {
243:     PetscCall(DSPEPSetDegree(pep->ds,pep->nmat-1));
244:     PetscCall(DSPEPSetCoefficients(pep->ds,pep->pbc));
245:   }
246:   PetscCall(DSAllocate(pep->ds,pep->ncv));
247:   nwork = 2;
248:   PetscCall(PEPSetWorkVecs(pep,nwork));
249:   PetscFunctionReturn(PETSC_SUCCESS);
250: }

252: static PetscErrorCode PEPSolve_CISS(PEP pep)
253: {
254:   PEP_CISS         *ctx = (PEP_CISS*)pep->data;
255:   SlepcContourData contour = ctx->contour;
256:   Mat              X,M,E,T,P;
257:   PetscInt         i,j,ld,L_add=0,nv=0,L_base=ctx->L,inner,*inside,nsplit;
258:   PetscScalar      *Mu,*H0,*H1,*rr,*temp,center;
259:   PetscReal        error,max_error,radius,rgscale,est_eig,eta;
260:   PetscBool        isellipse,*fl1;
261:   Vec              si;
262:   SlepcSC          sc;
263:   PetscRandom      rand;

265:   PetscFunctionBegin;
266:   PetscCall(DSGetSlepcSC(pep->ds,&sc));
267:   sc->comparison    = SlepcCompareLargestMagnitude;
268:   sc->comparisonctx = NULL;
269:   sc->map           = NULL;
270:   sc->mapobj        = NULL;
271:   PetscCall(DSGetLeadingDimension(pep->ds,&ld));
272:   PetscCall(RGComputeQuadrature(pep->rg,RG_QUADRULE_TRAPEZOIDAL,ctx->N,ctx->omega,ctx->pp,ctx->weight));
273:   PetscCall(STGetSplitPreconditionerInfo(pep->st,&nsplit,NULL));
274:   if (contour->pA) {
275:     T = contour->pA[0];
276:     P = nsplit? contour->pP[0]: T;
277:   } else {
278:     T = pep->A[0];
279:     P = nsplit? ctx->Psplit[0]: T;
280:   }
281:   PetscCall(PEPCISSSetUp(pep,T,P));
282:   PetscCall(BVSetActiveColumns(ctx->V,0,ctx->L));
283:   PetscCall(BVSetRandomSign(ctx->V));
284:   PetscCall(BVGetRandomContext(ctx->V,&rand));
285:   if (contour->pA) PetscCall(BVScatter(ctx->V,ctx->pV,contour->scatterin,contour->xdup));
286:   PetscCall(PEPCISSSolve(pep,ctx->J,(contour->pA)?ctx->pV:ctx->V,0,ctx->L));
287:   PetscCall(PetscObjectTypeCompare((PetscObject)pep->rg,RGELLIPSE,&isellipse));
288:   if (isellipse) {
289:     PetscCall(BVTraceQuadrature(ctx->Y,ctx->V,ctx->L,ctx->L,ctx->weight,contour->scatterin,contour->subcomm,contour->npoints,ctx->useconj,&est_eig));
290:     PetscCall(PetscInfo(pep,"Estimated eigenvalue count: %f\n",(double)est_eig));
291:     eta = PetscPowReal(10.0,-PetscLog10Real(pep->tol)/ctx->N);
292:     L_add = PetscMax(0,(PetscInt)PetscCeilReal((est_eig*eta)/ctx->M)-ctx->L);
293:     if (L_add>ctx->L_max-ctx->L) {
294:       PetscCall(PetscInfo(pep,"Number of eigenvalues inside the contour path may be too large\n"));
295:       L_add = ctx->L_max-ctx->L;
296:     }
297:   }
298:   /* Updates L after estimate the number of eigenvalue */
299:   if (L_add>0) {
300:     PetscCall(PetscInfo(pep,"Changing L %" PetscInt_FMT " -> %" PetscInt_FMT " by Estimate #Eig\n",ctx->L,ctx->L+L_add));
301:     PetscCall(BVCISSResizeBases(ctx->S,contour->pA?ctx->pV:ctx->V,ctx->Y,ctx->L,ctx->L+L_add,ctx->M,contour->npoints));
302:     PetscCall(BVSetActiveColumns(ctx->V,ctx->L,ctx->L+L_add));
303:     PetscCall(BVSetRandomSign(ctx->V));
304:     if (contour->pA) PetscCall(BVScatter(ctx->V,ctx->pV,contour->scatterin,contour->xdup));
305:     ctx->L += L_add;
306:     PetscCall(PEPCISSSolve(pep,ctx->J,(contour->pA)?ctx->pV:ctx->V,ctx->L-L_add,ctx->L));
307:   }

309:   PetscCall(PetscMalloc2(ctx->L*ctx->L*ctx->M*2,&Mu,ctx->L*ctx->M*ctx->L*ctx->M,&H0));
310:   for (i=0;i<ctx->refine_blocksize;i++) {
311:     PetscCall(BVDotQuadrature(ctx->Y,(contour->pA)?ctx->pV:ctx->V,Mu,ctx->M,ctx->L,ctx->L,ctx->weight,ctx->pp,contour->subcomm,contour->npoints,ctx->useconj));
312:     PetscCall(CISS_BlockHankel(Mu,0,ctx->L,ctx->M,H0));
313:     PetscCall(PetscLogEventBegin(PEP_CISS_SVD,pep,0,0,0));
314:     PetscCall(SlepcCISS_BH_SVD(H0,ctx->L*ctx->M,ctx->delta,ctx->sigma,&nv));
315:     PetscCall(PetscLogEventEnd(PEP_CISS_SVD,pep,0,0,0));
316:     if (ctx->sigma[0]<=ctx->delta || nv < ctx->L*ctx->M || ctx->L == ctx->L_max) break;
317:     L_add = L_base;
318:     if (ctx->L+L_add>ctx->L_max) L_add = ctx->L_max-ctx->L;
319:     PetscCall(PetscInfo(pep,"Changing L %" PetscInt_FMT " -> %" PetscInt_FMT " by SVD(H0)\n",ctx->L,ctx->L+L_add));
320:     PetscCall(BVCISSResizeBases(ctx->S,contour->pA?ctx->pV:ctx->V,ctx->Y,ctx->L,ctx->L+L_add,ctx->M,contour->npoints));
321:     PetscCall(BVSetActiveColumns(ctx->V,ctx->L,ctx->L+L_add));
322:     PetscCall(BVSetRandomSign(ctx->V));
323:     if (contour->pA) PetscCall(BVScatter(ctx->V,ctx->pV,contour->scatterin,contour->xdup));
324:     ctx->L += L_add;
325:     PetscCall(PEPCISSSolve(pep,ctx->J,(contour->pA)?ctx->pV:ctx->V,ctx->L-L_add,ctx->L));
326:     if (L_add) {
327:       PetscCall(PetscFree2(Mu,H0));
328:       PetscCall(PetscMalloc2(ctx->L*ctx->L*ctx->M*2,&Mu,ctx->L*ctx->M*ctx->L*ctx->M,&H0));
329:     }
330:   }

332:   PetscCall(RGGetScale(pep->rg,&rgscale));
333:   PetscCall(RGEllipseGetParameters(pep->rg,&center,&radius,NULL));

335:   if (ctx->extraction == PEP_CISS_EXTRACTION_HANKEL) PetscCall(PetscMalloc1(ctx->L*ctx->M*ctx->L*ctx->M,&H1));

337:   while (pep->reason == PEP_CONVERGED_ITERATING) {
338:     pep->its++;
339:     for (inner=0;inner<=ctx->refine_inner;inner++) {
340:       if (ctx->extraction == PEP_CISS_EXTRACTION_HANKEL) {
341:         PetscCall(BVDotQuadrature(ctx->Y,(contour->pA)?ctx->pV:ctx->V,Mu,ctx->M,ctx->L,ctx->L,ctx->weight,ctx->pp,contour->subcomm,contour->npoints,ctx->useconj));
342:         PetscCall(CISS_BlockHankel(Mu,0,ctx->L,ctx->M,H0));
343:         PetscCall(PetscLogEventBegin(PEP_CISS_SVD,pep,0,0,0));
344:         PetscCall(SlepcCISS_BH_SVD(H0,ctx->L*ctx->M,ctx->delta,ctx->sigma,&nv));
345:         PetscCall(PetscLogEventEnd(PEP_CISS_SVD,pep,0,0,0));
346:       } else {
347:         PetscCall(BVSumQuadrature(ctx->S,ctx->Y,ctx->M,ctx->L,ctx->L,ctx->weight,ctx->pp,contour->scatterin,contour->subcomm,contour->npoints,ctx->useconj));
348:         /* compute SVD of S */
349:         PetscCall(BVSVDAndRank(ctx->S,ctx->M,ctx->L,ctx->delta,(ctx->extraction==PEP_CISS_EXTRACTION_CAA)?BV_SVD_METHOD_QR_CAA:BV_SVD_METHOD_QR,H0,ctx->sigma,&nv));
350:       }
351:       PetscCall(PetscInfo(pep,"Estimated rank: nv = %" PetscInt_FMT "\n",nv));
352:       if (ctx->sigma[0]>ctx->delta && nv==ctx->L*ctx->M && inner!=ctx->refine_inner) {
353:         PetscCall(BVSumQuadrature(ctx->S,ctx->Y,ctx->M,ctx->L,ctx->L,ctx->weight,ctx->pp,contour->scatterin,contour->subcomm,contour->npoints,ctx->useconj));
354:         PetscCall(BVSetActiveColumns(ctx->S,0,ctx->L));
355:         PetscCall(BVSetActiveColumns(ctx->V,0,ctx->L));
356:         PetscCall(BVCopy(ctx->S,ctx->V));
357:         if (contour->pA) PetscCall(BVScatter(ctx->V,ctx->pV,contour->scatterin,contour->xdup));
358:         PetscCall(PEPCISSSolve(pep,ctx->J,(contour->pA)?ctx->pV:ctx->V,0,ctx->L));
359:       } else break;
360:     }
361:     pep->nconv = 0;
362:     if (nv == 0) { pep->reason = PEP_CONVERGED_TOL; break; }
363:     else {
364:       /* Extracting eigenpairs */
365:       PetscCall(DSSetDimensions(pep->ds,nv,0,0));
366:       PetscCall(DSSetState(pep->ds,DS_STATE_RAW));
367:       if (ctx->extraction == PEP_CISS_EXTRACTION_HANKEL) {
368:         PetscCall(CISS_BlockHankel(Mu,0,ctx->L,ctx->M,H0));
369:         PetscCall(CISS_BlockHankel(Mu,1,ctx->L,ctx->M,H1));
370:         PetscCall(DSGetArray(pep->ds,DS_MAT_A,&temp));
371:         for (j=0;j<nv;j++)
372:           for (i=0;i<nv;i++)
373:             temp[i+j*ld] = H1[i+j*ctx->L*ctx->M];
374:         PetscCall(DSRestoreArray(pep->ds,DS_MAT_A,&temp));
375:         PetscCall(DSGetArray(pep->ds,DS_MAT_B,&temp));
376:         for (j=0;j<nv;j++)
377:           for (i=0;i<nv;i++)
378:             temp[i+j*ld] = H0[i+j*ctx->L*ctx->M];
379:         PetscCall(DSRestoreArray(pep->ds,DS_MAT_B,&temp));
380:       } else if (ctx->extraction == PEP_CISS_EXTRACTION_CAA) {
381:         PetscCall(BVSetActiveColumns(ctx->S,0,nv));
382:         PetscCall(DSGetArray(pep->ds,DS_MAT_A,&temp));
383:         for (i=0;i<nv;i++) PetscCall(PetscArraycpy(temp+i*ld,H0+i*nv,nv));
384:         PetscCall(DSRestoreArray(pep->ds,DS_MAT_A,&temp));
385:       } else {
386:         PetscCall(BVSetActiveColumns(ctx->S,0,nv));
387:         for (i=0;i<pep->nmat;i++) {
388:           PetscCall(DSGetMat(pep->ds,DSMatExtra[i],&E));
389:           PetscCall(BVMatProject(ctx->S,pep->A[i],ctx->S,E));
390:           PetscCall(DSRestoreMat(pep->ds,DSMatExtra[i],&E));
391:         }
392:         nv = (pep->nmat-1)*nv;
393:       }
394:       PetscCall(DSSolve(pep->ds,pep->eigr,pep->eigi));
395:       PetscCall(DSSynchronize(pep->ds,pep->eigr,pep->eigi));
396:       if (ctx->extraction == PEP_CISS_EXTRACTION_CAA || ctx->extraction == PEP_CISS_EXTRACTION_HANKEL) {
397:         for (i=0;i<nv;i++) {
398:           pep->eigr[i] = (pep->eigr[i]*radius+center)*rgscale;
399:         }
400:       }
401:       PetscCall(PetscMalloc3(nv,&fl1,nv,&inside,nv,&rr));
402:       PetscCall(DSVectors(pep->ds,DS_MAT_X,NULL,NULL));
403:       PetscCall(DSGetMat(pep->ds,DS_MAT_X,&X));
404:       PetscCall(SlepcCISS_isGhost(X,nv,ctx->sigma,ctx->spurious_threshold,fl1));
405:       PetscCall(DSRestoreMat(pep->ds,DS_MAT_X,&X));
406:       PetscCall(RGCheckInside(pep->rg,nv,pep->eigr,pep->eigi,inside));
407:       for (i=0;i<nv;i++) {
408:         if (fl1[i] && inside[i]>=0) {
409:           rr[i] = 1.0;
410:           pep->nconv++;
411:         } else rr[i] = 0.0;
412:       }
413:       PetscCall(DSSort(pep->ds,pep->eigr,pep->eigi,rr,NULL,&pep->nconv));
414:       PetscCall(DSSynchronize(pep->ds,pep->eigr,pep->eigi));
415:       if (ctx->extraction == PEP_CISS_EXTRACTION_CAA || ctx->extraction == PEP_CISS_EXTRACTION_HANKEL) {
416:         for (i=0;i<nv;i++) pep->eigr[i] = (pep->eigr[i]*radius+center)*rgscale;
417:       }
418:       PetscCall(PetscFree3(fl1,inside,rr));
419:       PetscCall(BVSetActiveColumns(pep->V,0,nv));
420:       PetscCall(DSVectors(pep->ds,DS_MAT_X,NULL,NULL));
421:       if (ctx->extraction == PEP_CISS_EXTRACTION_HANKEL) {
422:         PetscCall(BVSumQuadrature(ctx->S,ctx->Y,ctx->M,ctx->L,ctx->L,ctx->weight,ctx->pp,contour->scatterin,contour->subcomm,contour->npoints,ctx->useconj));
423:         PetscCall(BVSetActiveColumns(ctx->S,0,nv));
424:         PetscCall(BVCopy(ctx->S,pep->V));
425:         PetscCall(DSGetMat(pep->ds,DS_MAT_X,&X));
426:         PetscCall(BVMultInPlace(ctx->S,X,0,pep->nconv));
427:         PetscCall(BVMultInPlace(pep->V,X,0,pep->nconv));
428:         PetscCall(DSRestoreMat(pep->ds,DS_MAT_X,&X));
429:       } else {
430:         PetscCall(DSGetMat(pep->ds,DS_MAT_X,&X));
431:         PetscCall(BVMultInPlace(ctx->S,X,0,pep->nconv));
432:         PetscCall(DSRestoreMat(pep->ds,DS_MAT_X,&X));
433:         PetscCall(BVSetActiveColumns(ctx->S,0,pep->nconv));
434:         PetscCall(BVCopy(ctx->S,pep->V));
435:       }
436:       max_error = 0.0;
437:       for (i=0;i<pep->nconv;i++) {
438:         PetscCall(BVGetColumn(pep->V,i,&si));
439:         PetscCall(VecNormalize(si,NULL));
440:         PetscCall(PEPComputeResidualNorm_Private(pep,pep->eigr[i],0,si,NULL,pep->work,&error));
441:         PetscCall((*pep->converged)(pep,pep->eigr[i],0,error,&error,pep->convergedctx));
442:         PetscCall(BVRestoreColumn(pep->V,i,&si));
443:         max_error = PetscMax(max_error,error);
444:       }
445:       if (max_error <= pep->tol) pep->reason = PEP_CONVERGED_TOL;
446:       else if (pep->its > pep->max_it) pep->reason = PEP_DIVERGED_ITS;
447:       else {
448:         if (pep->nconv > ctx->L) nv = pep->nconv;
449:         else if (ctx->L > nv) nv = ctx->L;
450:         nv = PetscMin(nv,ctx->L*ctx->M);
451:         PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,nv,ctx->L,NULL,&M));
452:         PetscCall(MatSetRandom(M,rand));
453:         PetscCall(BVSetActiveColumns(ctx->S,0,nv));
454:         PetscCall(BVMultInPlace(ctx->S,M,0,ctx->L));
455:         PetscCall(MatDestroy(&M));
456:         PetscCall(BVSetActiveColumns(ctx->S,0,ctx->L));
457:         PetscCall(BVSetActiveColumns(ctx->V,0,ctx->L));
458:         PetscCall(BVCopy(ctx->S,ctx->V));
459:         if (contour->pA) PetscCall(BVScatter(ctx->V,ctx->pV,contour->scatterin,contour->xdup));
460:         PetscCall(PEPCISSSolve(pep,ctx->J,(contour->pA)?ctx->pV:ctx->V,0,ctx->L));
461:       }
462:     }
463:   }
464:   PetscCall(PetscFree2(Mu,H0));
465:   if (ctx->extraction == PEP_CISS_EXTRACTION_HANKEL) PetscCall(PetscFree(H1));
466:   PetscFunctionReturn(PETSC_SUCCESS);
467: }

469: static PetscErrorCode PEPCISSSetSizes_CISS(PEP pep,PetscInt ip,PetscInt bs,PetscInt ms,PetscInt npart,PetscInt bsmax,PetscBool realmats)
470: {
471:   PEP_CISS       *ctx = (PEP_CISS*)pep->data;
472:   PetscInt       oN,oL,oM,oLmax,onpart;
473:   PetscMPIInt    size;

475:   PetscFunctionBegin;
476:   oN = ctx->N;
477:   if (ip == PETSC_DETERMINE) {
478:     if (ctx->N!=32) { ctx->N =32; ctx->M = ctx->N/4; }
479:   } else if (ip != PETSC_CURRENT) {
480:     PetscCheck(ip>0,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"The ip argument must be > 0");
481:     PetscCheck(ip%2==0,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"The ip argument must be an even number");
482:     if (ctx->N!=ip) { ctx->N = ip; ctx->M = ctx->N/4; }
483:   }
484:   oL = ctx->L;
485:   if (bs == PETSC_DETERMINE) {
486:     ctx->L = 16;
487:   } else if (bs != PETSC_CURRENT) {
488:     PetscCheck(bs>0,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"The bs argument must be > 0");
489:     ctx->L = bs;
490:   }
491:   oM = ctx->M;
492:   if (ms == PETSC_DETERMINE) {
493:     ctx->M = ctx->N/4;
494:   } else if (ms != PETSC_CURRENT) {
495:     PetscCheck(ms>0,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"The ms argument must be > 0");
496:     PetscCheck(ms<=ctx->N,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"The ms argument must be less than or equal to the number of integration points");
497:     ctx->M = ms;
498:   }
499:   onpart = ctx->npart;
500:   if (npart == PETSC_DETERMINE) {
501:     ctx->npart = 1;
502:   } else if (npart != PETSC_CURRENT) {
503:     PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)pep),&size));
504:     PetscCheck(npart>0 && npart<=size,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"Illegal value of npart");
505:     ctx->npart = npart;
506:   }
507:   oLmax = ctx->L_max;
508:   if (bsmax == PETSC_DETERMINE) {
509:     ctx->L_max = 64;
510:   } else if (bsmax != PETSC_CURRENT) {
511:     PetscCheck(bsmax>0,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"The bsmax argument must be > 0");
512:     ctx->L_max = PetscMax(bsmax,ctx->L);
513:   }
514:   if (onpart != ctx->npart || oN != ctx->N || realmats != ctx->isreal) {
515:     PetscCall(SlepcContourDataDestroy(&ctx->contour));
516:     PetscCall(PetscInfo(pep,"Resetting the contour data structure due to a change of parameters\n"));
517:     pep->state = PEP_STATE_INITIAL;
518:   }
519:   ctx->isreal = realmats;
520:   if (oL != ctx->L || oM != ctx->M || oLmax != ctx->L_max) pep->state = PEP_STATE_INITIAL;
521:   PetscFunctionReturn(PETSC_SUCCESS);
522: }

524: /*@
525:    PEPCISSSetSizes - Sets the values of various size parameters in the CISS solver.

527:    Logically Collective

529:    Input Parameters:
530: +  pep      - the polynomial eigensolver context
531: .  ip       - number of integration points
532: .  bs       - block size
533: .  ms       - moment size
534: .  npart    - number of partitions when splitting the communicator
535: .  bsmax    - max block size
536: -  realmats - all coefficient matrices of $P(\cdot)$ are real

538:    Options Database Keys:
539: +  -pep_ciss_integration_points \<ip\> - sets the number of integration points
540: .  -pep_ciss_blocksize \<bs\>          - sets the block size
541: .  -pep_ciss_moments \<ms\>            - sets the moment size
542: .  -pep_ciss_partitions \<npart\>      - sets the number of partitions
543: .  -pep_ciss_maxblocksize \<bsmax\>    - sets the maximum block size
544: -  -pep_ciss_realmats                  - all coefficient matrices of $P(\cdot)$ are real

546:    Notes:
547:    For all integer arguments, you can use `PETSC_CURRENT` to keep the current value, and
548:    `PETSC_DETERMINE` to set them to a default value.

550:    The default number of partitions is 1. This means the internal `KSP` object is shared
551:    among all processes of the `PEP` communicator. Otherwise, the communicator is split
552:    into `npart` communicators, so that `npart` `KSP` solves proceed simultaneously.

554:    For a detailed description of the parameters see {cite:p}`Mae16`.

556:    Level: advanced

558: .seealso: [](ch:pep), `PEPCISS`, `PEPCISSGetSizes()`
559: @*/
560: PetscErrorCode PEPCISSSetSizes(PEP pep,PetscInt ip,PetscInt bs,PetscInt ms,PetscInt npart,PetscInt bsmax,PetscBool realmats)
561: {
562:   PetscFunctionBegin;
570:   PetscTryMethod(pep,"PEPCISSSetSizes_C",(PEP,PetscInt,PetscInt,PetscInt,PetscInt,PetscInt,PetscBool),(pep,ip,bs,ms,npart,bsmax,realmats));
571:   PetscFunctionReturn(PETSC_SUCCESS);
572: }

574: static PetscErrorCode PEPCISSGetSizes_CISS(PEP pep,PetscInt *ip,PetscInt *bs,PetscInt *ms,PetscInt *npart,PetscInt *bsmax,PetscBool *realmats)
575: {
576:   PEP_CISS *ctx = (PEP_CISS*)pep->data;

578:   PetscFunctionBegin;
579:   if (ip) *ip = ctx->N;
580:   if (bs) *bs = ctx->L;
581:   if (ms) *ms = ctx->M;
582:   if (npart) *npart = ctx->npart;
583:   if (bsmax) *bsmax = ctx->L_max;
584:   if (realmats) *realmats = ctx->isreal;
585:   PetscFunctionReturn(PETSC_SUCCESS);
586: }

588: /*@
589:    PEPCISSGetSizes - Gets the values of various size parameters in the CISS solver.

591:    Not Collective

593:    Input Parameter:
594: .  pep - the polynomial eigensolver context

596:    Output Parameters:
597: +  ip    - number of integration points
598: .  bs    - block size
599: .  ms    - moment size
600: .  npart - number of partitions when splitting the communicator
601: .  bsmax - max block size
602: -  realmats - all coefficient matrices of $P(\cdot)$ are real

604:    Level: advanced

606: .seealso: [](ch:pep), `PEPCISS`, `PEPCISSSetSizes()`
607: @*/
608: PetscErrorCode PEPCISSGetSizes(PEP pep,PetscInt *ip,PetscInt *bs,PetscInt *ms,PetscInt *npart,PetscInt *bsmax,PetscBool *realmats)
609: {
610:   PetscFunctionBegin;
612:   PetscUseMethod(pep,"PEPCISSGetSizes_C",(PEP,PetscInt*,PetscInt*,PetscInt*,PetscInt*,PetscInt*,PetscBool*),(pep,ip,bs,ms,npart,bsmax,realmats));
613:   PetscFunctionReturn(PETSC_SUCCESS);
614: }

616: static PetscErrorCode PEPCISSSetThreshold_CISS(PEP pep,PetscReal delta,PetscReal spur)
617: {
618:   PEP_CISS *ctx = (PEP_CISS*)pep->data;

620:   PetscFunctionBegin;
621:   if (delta == (PetscReal)PETSC_DETERMINE) {
622:     ctx->delta = SLEPC_DEFAULT_TOL*1e-4;
623:   } else if (delta != (PetscReal)PETSC_CURRENT) {
624:     PetscCheck(delta>0.0,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"The delta argument must be > 0.0");
625:     ctx->delta = delta;
626:   }
627:   if (spur == (PetscReal)PETSC_DETERMINE) {
628:     ctx->spurious_threshold = PetscSqrtReal(SLEPC_DEFAULT_TOL);
629:   } else if (spur != (PetscReal)PETSC_CURRENT) {
630:     PetscCheck(spur>0.0,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"The spurious threshold argument must be > 0.0");
631:     ctx->spurious_threshold = spur;
632:   }
633:   PetscFunctionReturn(PETSC_SUCCESS);
634: }

636: /*@
637:    PEPCISSSetThreshold - Sets the values of various threshold parameters in
638:    the CISS solver.

640:    Logically Collective

642:    Input Parameters:
643: +  pep   - the polynomial eigensolver context
644: .  delta - threshold for numerical rank
645: -  spur  - spurious threshold (to discard spurious eigenpairs)

647:    Options Database Keys:
648: +  -pep_ciss_delta \<delta\>             - sets the delta
649: -  -pep_ciss_spurious_threshold \<spur\> - sets the spurious threshold

651:    Notes:
652:    `PETSC_CURRENT` can be used to preserve the current value of any of the
653:    arguments, and `PETSC_DETERMINE` to set them to a default value.

655:    For a detailed description of the parameters see {cite:p}`Mae16`.

657:    Level: advanced

659: .seealso: [](ch:pep), `PEPCISS`, `PEPCISSGetThreshold()`
660: @*/
661: PetscErrorCode PEPCISSSetThreshold(PEP pep,PetscReal delta,PetscReal spur)
662: {
663:   PetscFunctionBegin;
667:   PetscTryMethod(pep,"PEPCISSSetThreshold_C",(PEP,PetscReal,PetscReal),(pep,delta,spur));
668:   PetscFunctionReturn(PETSC_SUCCESS);
669: }

671: static PetscErrorCode PEPCISSGetThreshold_CISS(PEP pep,PetscReal *delta,PetscReal *spur)
672: {
673:   PEP_CISS *ctx = (PEP_CISS*)pep->data;

675:   PetscFunctionBegin;
676:   if (delta) *delta = ctx->delta;
677:   if (spur)  *spur = ctx->spurious_threshold;
678:   PetscFunctionReturn(PETSC_SUCCESS);
679: }

681: /*@
682:    PEPCISSGetThreshold - Gets the values of various threshold parameters in
683:    the CISS solver.

685:    Not Collective

687:    Input Parameter:
688: .  pep - the polynomial eigensolver context

690:    Output Parameters:
691: +  delta - threshold for numerical rank
692: -  spur  - spurious threshold (to discard spurious eigenpairs)

694:    Level: advanced

696: .seealso: [](ch:pep), `PEPCISS`, `PEPCISSSetThreshold()`
697: @*/
698: PetscErrorCode PEPCISSGetThreshold(PEP pep,PetscReal *delta,PetscReal *spur)
699: {
700:   PetscFunctionBegin;
702:   PetscUseMethod(pep,"PEPCISSGetThreshold_C",(PEP,PetscReal*,PetscReal*),(pep,delta,spur));
703:   PetscFunctionReturn(PETSC_SUCCESS);
704: }

706: static PetscErrorCode PEPCISSSetRefinement_CISS(PEP pep,PetscInt inner,PetscInt blsize)
707: {
708:   PEP_CISS *ctx = (PEP_CISS*)pep->data;

710:   PetscFunctionBegin;
711:   if (inner == PETSC_DETERMINE) {
712:     ctx->refine_inner = 0;
713:   } else if (inner != PETSC_CURRENT) {
714:     PetscCheck(inner>=0,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"The refine inner argument must be >= 0");
715:     ctx->refine_inner = inner;
716:   }
717:   if (blsize == PETSC_DETERMINE) {
718:     ctx->refine_blocksize = 0;
719:   } else if (blsize != PETSC_CURRENT) {
720:     PetscCheck(blsize>=0,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"The refine blocksize argument must be >= 0");
721:     ctx->refine_blocksize = blsize;
722:   }
723:   PetscFunctionReturn(PETSC_SUCCESS);
724: }

726: /*@
727:    PEPCISSSetRefinement - Sets the values of various refinement parameters
728:    in the CISS solver.

730:    Logically Collective

732:    Input Parameters:
733: +  pep    - the polynomial eigensolver context
734: .  inner  - number of iterative refinement iterations (inner loop)
735: -  blsize - number of iterative refinement iterations (blocksize loop)

737:    Options Database Keys:
738: +  -pep_ciss_refine_inner \<inner\>      - sets number of inner iterations
739: -  -pep_ciss_refine_blocksize \<blsize\> - sets number of blocksize iterations

741:    Note:
742:    `PETSC_CURRENT` can be used to preserve the current value of any of the
743:    arguments, and `PETSC_DETERMINE` to set them to a default of 0 (no refinement).

745:    Level: advanced

747: .seealso: [](ch:pep), `PEPCISS`, `PEPCISSGetRefinement()`
748: @*/
749: PetscErrorCode PEPCISSSetRefinement(PEP pep,PetscInt inner,PetscInt blsize)
750: {
751:   PetscFunctionBegin;
755:   PetscTryMethod(pep,"PEPCISSSetRefinement_C",(PEP,PetscInt,PetscInt),(pep,inner,blsize));
756:   PetscFunctionReturn(PETSC_SUCCESS);
757: }

759: static PetscErrorCode PEPCISSGetRefinement_CISS(PEP pep,PetscInt *inner,PetscInt *blsize)
760: {
761:   PEP_CISS *ctx = (PEP_CISS*)pep->data;

763:   PetscFunctionBegin;
764:   if (inner)  *inner = ctx->refine_inner;
765:   if (blsize) *blsize = ctx->refine_blocksize;
766:   PetscFunctionReturn(PETSC_SUCCESS);
767: }

769: /*@
770:    PEPCISSGetRefinement - Gets the values of various refinement parameters
771:    in the CISS solver.

773:    Not Collective

775:    Input Parameter:
776: .  pep - the polynomial eigensolver context

778:    Output Parameters:
779: +  inner  - number of iterative refinement iterations (inner loop)
780: -  blsize - number of iterative refinement iterations (blocksize loop)

782:    Level: advanced

784: .seealso: [](ch:pep), `PEPCISS`, `PEPCISSSetRefinement()`
785: @*/
786: PetscErrorCode PEPCISSGetRefinement(PEP pep, PetscInt *inner, PetscInt *blsize)
787: {
788:   PetscFunctionBegin;
790:   PetscUseMethod(pep,"PEPCISSGetRefinement_C",(PEP,PetscInt*,PetscInt*),(pep,inner,blsize));
791:   PetscFunctionReturn(PETSC_SUCCESS);
792: }

794: static PetscErrorCode PEPCISSSetExtraction_CISS(PEP pep,PEPCISSExtraction extraction)
795: {
796:   PEP_CISS *ctx = (PEP_CISS*)pep->data;

798:   PetscFunctionBegin;
799:   if (ctx->extraction != extraction) {
800:     ctx->extraction = extraction;
801:     pep->state      = PEP_STATE_INITIAL;
802:   }
803:   PetscFunctionReturn(PETSC_SUCCESS);
804: }

806: /*@
807:    PEPCISSSetExtraction - Sets the extraction technique used in the CISS solver.

809:    Logically Collective

811:    Input Parameters:
812: +  pep        - the polynomial eigensolver context
813: -  extraction - the extraction technique, see `PEPCISSExtraction` for possible values

815:    Options Database Key:
816: .  -pep_ciss_extraction \<extraction\> - sets the extraction technique, either `ritz`, `hankel` or `caa`

818:    Notes:
819:    By default, the Rayleigh-Ritz extraction is used (`PEP_CISS_EXTRACTION_RITZ`),
820:    see {cite:p}`Asa10`.

822:    If the `hankel` or the `caa` option is specified (`PEP_CISS_EXTRACTION_HANKEL` or
823:    `PEP_CISS_EXTRACTION_CAA`), then the block Hankel method, or the communication-avoiding
824:    Arnoldi method, respectively, is used for extracting eigenpairs.

826:    Level: advanced

828: .seealso: [](ch:pep), `PEPCISS`, `PEPCISSGetExtraction()`, `PEPCISSExtraction`
829: @*/
830: PetscErrorCode PEPCISSSetExtraction(PEP pep,PEPCISSExtraction extraction)
831: {
832:   PetscFunctionBegin;
835:   PetscTryMethod(pep,"PEPCISSSetExtraction_C",(PEP,PEPCISSExtraction),(pep,extraction));
836:   PetscFunctionReturn(PETSC_SUCCESS);
837: }

839: static PetscErrorCode PEPCISSGetExtraction_CISS(PEP pep,PEPCISSExtraction *extraction)
840: {
841:   PEP_CISS *ctx = (PEP_CISS*)pep->data;

843:   PetscFunctionBegin;
844:   *extraction = ctx->extraction;
845:   PetscFunctionReturn(PETSC_SUCCESS);
846: }

848: /*@
849:    PEPCISSGetExtraction - Gets the extraction technique used in the CISS solver.

851:    Not Collective

853:    Input Parameter:
854: .  pep - the polynomial eigensolver context

856:    Output Parameter:
857: .  extraction - extraction technique

859:    Level: advanced

861: .seealso: [](ch:pep), `PEPCISS`, `PEPCISSSetExtraction()`, `PEPCISSExtraction`
862: @*/
863: PetscErrorCode PEPCISSGetExtraction(PEP pep,PEPCISSExtraction *extraction)
864: {
865:   PetscFunctionBegin;
867:   PetscAssertPointer(extraction,2);
868:   PetscUseMethod(pep,"PEPCISSGetExtraction_C",(PEP,PEPCISSExtraction*),(pep,extraction));
869:   PetscFunctionReturn(PETSC_SUCCESS);
870: }

872: static PetscErrorCode PEPCISSGetKSPs_CISS(PEP pep,PetscInt *nsolve,KSP **ksp)
873: {
874:   PEP_CISS         *ctx = (PEP_CISS*)pep->data;
875:   SlepcContourData contour;
876:   PetscInt         i,nsplit;
877:   PC               pc;
878:   MPI_Comm         child;

880:   PetscFunctionBegin;
881:   if (!ctx->contour) {  /* initialize contour data structure first */
882:     PetscCall(RGCanUseConjugates(pep->rg,ctx->isreal,&ctx->useconj));
883:     PetscCall(SlepcContourDataCreate(ctx->useconj?ctx->N/2:ctx->N,ctx->npart,(PetscObject)pep,&ctx->contour));
884:   }
885:   contour = ctx->contour;
886:   if (!contour->ksp) {
887:     PetscCall(PetscMalloc1(contour->npoints,&contour->ksp));
888:     PetscCall(PEPGetST(pep,&pep->st));
889:     PetscCall(STGetSplitPreconditionerInfo(pep->st,&nsplit,NULL));
890:     PetscCall(PetscSubcommGetChild(contour->subcomm,&child));
891:     for (i=0;i<contour->npoints;i++) {
892:       PetscCall(KSPCreate(child,&contour->ksp[i]));
893:       PetscCall(PetscObjectIncrementTabLevel((PetscObject)contour->ksp[i],(PetscObject)pep,1));
894:       PetscCall(KSPSetOptionsPrefix(contour->ksp[i],((PetscObject)pep)->prefix));
895:       PetscCall(KSPAppendOptionsPrefix(contour->ksp[i],"pep_ciss_"));
896:       PetscCall(PetscObjectSetOptions((PetscObject)contour->ksp[i],((PetscObject)pep)->options));
897:       PetscCall(KSPSetErrorIfNotConverged(contour->ksp[i],PETSC_TRUE));
898:       PetscCall(KSPSetTolerances(contour->ksp[i],SlepcDefaultTol(pep->tol),PETSC_CURRENT,PETSC_CURRENT,PETSC_CURRENT));
899:       PetscCall(KSPGetPC(contour->ksp[i],&pc));
900:       if (nsplit) {
901:         PetscCall(KSPSetType(contour->ksp[i],KSPBCGS));
902:         PetscCall(PCSetType(pc,PCBJACOBI));
903:       } else {
904:         PetscCall(KSPSetType(contour->ksp[i],KSPPREONLY));
905:         PetscCall(PCSetType(pc,PCLU));
906:       }
907:     }
908:   }
909:   if (nsolve) *nsolve = contour->npoints;
910:   if (ksp)    *ksp    = contour->ksp;
911:   PetscFunctionReturn(PETSC_SUCCESS);
912: }

914: /*@C
915:    PEPCISSGetKSPs - Retrieve the array of linear solver objects associated with
916:    the CISS solver.

918:    Collective

920:    Input Parameter:
921: .  pep - the polynomial eigensolver context

923:    Output Parameters:
924: +  nsolve - number of solver objects
925: -  ksp    - array of linear solver objects

927:    Notes:
928:    The number of `KSP` solvers is equal to the number of integration points divided by
929:    the number of partitions. This value is halved in the case of real matrices with
930:    a region centered at the real axis.

932:    Level: advanced

934: .seealso: [](ch:pep), `PEPCISS`, `PEPCISSSetSizes()`
935: @*/
936: PetscErrorCode PEPCISSGetKSPs(PEP pep,PetscInt *nsolve,KSP **ksp)
937: {
938:   PetscFunctionBegin;
940:   PetscUseMethod(pep,"PEPCISSGetKSPs_C",(PEP,PetscInt*,KSP**),(pep,nsolve,ksp));
941:   PetscFunctionReturn(PETSC_SUCCESS);
942: }

944: static PetscErrorCode PEPReset_CISS(PEP pep)
945: {
946:   PEP_CISS       *ctx = (PEP_CISS*)pep->data;

948:   PetscFunctionBegin;
949:   PetscCall(BVDestroy(&ctx->S));
950:   PetscCall(BVDestroy(&ctx->V));
951:   PetscCall(BVDestroy(&ctx->Y));
952:   PetscCall(SlepcContourDataReset(ctx->contour));
953:   PetscCall(MatDestroy(&ctx->J));
954:   PetscCall(BVDestroy(&ctx->pV));
955:   PetscCall(PetscFree(ctx->Psplit));
956:   PetscFunctionReturn(PETSC_SUCCESS);
957: }

959: static PetscErrorCode PEPSetFromOptions_CISS(PEP pep,PetscOptionItems PetscOptionsObject)
960: {
961:   PEP_CISS          *ctx = (PEP_CISS*)pep->data;
962:   PetscReal         r1,r2;
963:   PetscInt          i,i1,i2,i3,i4,i5,i6,i7;
964:   PetscBool         b1,flg,flg2,flg3,flg4,flg5,flg6;
965:   PEPCISSExtraction extraction;

967:   PetscFunctionBegin;
968:   PetscOptionsHeadBegin(PetscOptionsObject,"PEP CISS Options");

970:     PetscCall(PEPCISSGetSizes(pep,&i1,&i2,&i3,&i4,&i5,&b1));
971:     PetscCall(PetscOptionsInt("-pep_ciss_integration_points","Number of integration points","PEPCISSSetSizes",i1,&i1,&flg));
972:     PetscCall(PetscOptionsInt("-pep_ciss_blocksize","Block size","PEPCISSSetSizes",i2,&i2,&flg2));
973:     PetscCall(PetscOptionsInt("-pep_ciss_moments","Moment size","PEPCISSSetSizes",i3,&i3,&flg3));
974:     PetscCall(PetscOptionsInt("-pep_ciss_partitions","Number of partitions","PEPCISSSetSizes",i4,&i4,&flg4));
975:     PetscCall(PetscOptionsInt("-pep_ciss_maxblocksize","Maximum block size","PEPCISSSetSizes",i5,&i5,&flg5));
976:     PetscCall(PetscOptionsBool("-pep_ciss_realmats","True if all coefficient matrices of P(.) are real","PEPCISSSetSizes",b1,&b1,&flg6));
977:     if (flg || flg2 || flg3 || flg4 || flg5 || flg6) PetscCall(PEPCISSSetSizes(pep,i1,i2,i3,i4,i5,b1));

979:     PetscCall(PEPCISSGetThreshold(pep,&r1,&r2));
980:     PetscCall(PetscOptionsReal("-pep_ciss_delta","Threshold for numerical rank","PEPCISSSetThreshold",r1,&r1,&flg));
981:     PetscCall(PetscOptionsReal("-pep_ciss_spurious_threshold","Threshold for the spurious eigenpairs","PEPCISSSetThreshold",r2,&r2,&flg2));
982:     if (flg || flg2) PetscCall(PEPCISSSetThreshold(pep,r1,r2));

984:     PetscCall(PEPCISSGetRefinement(pep,&i6,&i7));
985:     PetscCall(PetscOptionsInt("-pep_ciss_refine_inner","Number of inner iterative refinement iterations","PEPCISSSetRefinement",i6,&i6,&flg));
986:     PetscCall(PetscOptionsInt("-pep_ciss_refine_blocksize","Number of blocksize iterative refinement iterations","PEPCISSSetRefinement",i7,&i7,&flg2));
987:     if (flg || flg2) PetscCall(PEPCISSSetRefinement(pep,i6,i7));

989:     PetscCall(PetscOptionsEnum("-pep_ciss_extraction","Extraction technique","PEPCISSSetExtraction",PEPCISSExtractions,(PetscEnum)ctx->extraction,(PetscEnum*)&extraction,&flg));
990:     if (flg) PetscCall(PEPCISSSetExtraction(pep,extraction));

992:   PetscOptionsHeadEnd();

994:   if (!pep->rg) PetscCall(PEPGetRG(pep,&pep->rg));
995:   PetscCall(RGSetFromOptions(pep->rg)); /* this is necessary here to set useconj */
996:   if (!ctx->contour || !ctx->contour->ksp) PetscCall(PEPCISSGetKSPs(pep,NULL,NULL));
997:   PetscAssert(ctx->contour && ctx->contour->ksp,PetscObjectComm((PetscObject)pep),PETSC_ERR_PLIB,"Something went wrong with PEPCISSGetKSPs()");
998:   for (i=0;i<ctx->contour->npoints;i++) PetscCall(KSPSetFromOptions(ctx->contour->ksp[i]));
999:   PetscCall(PetscSubcommSetFromOptions(ctx->contour->subcomm));
1000:   PetscFunctionReturn(PETSC_SUCCESS);
1001: }

1003: static PetscErrorCode PEPDestroy_CISS(PEP pep)
1004: {
1005:   PEP_CISS       *ctx = (PEP_CISS*)pep->data;

1007:   PetscFunctionBegin;
1008:   PetscCall(SlepcContourDataDestroy(&ctx->contour));
1009:   PetscCall(PetscFree4(ctx->weight,ctx->omega,ctx->pp,ctx->sigma));
1010:   PetscCall(PetscFree(pep->data));
1011:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPCISSSetSizes_C",NULL));
1012:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPCISSGetSizes_C",NULL));
1013:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPCISSSetThreshold_C",NULL));
1014:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPCISSGetThreshold_C",NULL));
1015:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPCISSSetRefinement_C",NULL));
1016:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPCISSGetRefinement_C",NULL));
1017:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPCISSSetExtraction_C",NULL));
1018:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPCISSGetExtraction_C",NULL));
1019:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPCISSGetKSPs_C",NULL));
1020:   PetscFunctionReturn(PETSC_SUCCESS);
1021: }

1023: static PetscErrorCode PEPView_CISS(PEP pep,PetscViewer viewer)
1024: {
1025:   PEP_CISS       *ctx = (PEP_CISS*)pep->data;
1026:   PetscBool      isascii;
1027:   PetscViewer    sviewer;

1029:   PetscFunctionBegin;
1030:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii));
1031:   if (isascii) {
1032:     PetscCall(PetscViewerASCIIPrintf(viewer,"  sizes { integration points: %" PetscInt_FMT ", block size: %" PetscInt_FMT ", moment size: %" PetscInt_FMT ", partitions: %" PetscInt_FMT ", maximum block size: %" PetscInt_FMT " }\n",ctx->N,ctx->L,ctx->M,ctx->npart,ctx->L_max));
1033:     if (ctx->isreal) PetscCall(PetscViewerASCIIPrintf(viewer,"  exploiting symmetry of integration points\n"));
1034:     PetscCall(PetscViewerASCIIPrintf(viewer,"  threshold { delta: %g, spurious threshold: %g }\n",(double)ctx->delta,(double)ctx->spurious_threshold));
1035:     PetscCall(PetscViewerASCIIPrintf(viewer,"  iterative refinement  { inner: %" PetscInt_FMT ", blocksize: %" PetscInt_FMT " }\n",ctx->refine_inner, ctx->refine_blocksize));
1036:     PetscCall(PetscViewerASCIIPrintf(viewer,"  extraction: %s\n",PEPCISSExtractions[ctx->extraction]));
1037:     if (!ctx->contour || !ctx->contour->ksp) PetscCall(PEPCISSGetKSPs(pep,NULL,NULL));
1038:     PetscAssert(ctx->contour && ctx->contour->ksp,PetscObjectComm((PetscObject)pep),PETSC_ERR_PLIB,"Something went wrong with PEPCISSGetKSPs()");
1039:     PetscCall(PetscViewerASCIIPushTab(viewer));
1040:     if (ctx->npart>1 && ctx->contour->subcomm) {
1041:       PetscCall(PetscViewerGetSubViewer(viewer,ctx->contour->subcomm->child,&sviewer));
1042:       if (!ctx->contour->subcomm->color) PetscCall(KSPView(ctx->contour->ksp[0],sviewer));
1043:       PetscCall(PetscViewerFlush(sviewer));
1044:       PetscCall(PetscViewerRestoreSubViewer(viewer,ctx->contour->subcomm->child,&sviewer));
1045:       /* extra call needed because of the two calls to PetscViewerASCIIPushSynchronized() in PetscViewerGetSubViewer() */
1046:       PetscCall(PetscViewerASCIIPopSynchronized(viewer));
1047:     } else PetscCall(KSPView(ctx->contour->ksp[0],viewer));
1048:     PetscCall(PetscViewerASCIIPopTab(viewer));
1049:   }
1050:   PetscFunctionReturn(PETSC_SUCCESS);
1051: }

1053: static PetscErrorCode PEPSetDSType_CISS(PEP pep)
1054: {
1055:   PEP_CISS       *ctx = (PEP_CISS*)pep->data;

1057:   PetscFunctionBegin;
1058:   switch (ctx->extraction) {
1059:     case PEP_CISS_EXTRACTION_RITZ:   PetscCall(DSSetType(pep->ds,DSPEP)); break;
1060:     case PEP_CISS_EXTRACTION_HANKEL: PetscCall(DSSetType(pep->ds,DSGNHEP)); break;
1061:     case PEP_CISS_EXTRACTION_CAA:    PetscCall(DSSetType(pep->ds,DSNHEP)); break;
1062:   }
1063:   PetscFunctionReturn(PETSC_SUCCESS);
1064: }

1066: /*MC
1067:    PEPCISS - PEPCISS = "ciss" - A contour integral eigensolver based on the
1068:    Sakurai-Sugiura scheme.

1070:    Notes:
1071:    This solver is based on the numerical contour integration idea
1072:    proposed initially for linear problems by {cite:t}`Sak03`. In polynomial
1073:    eigenproblems, a Rayleigh-Ritz projection is done, resulting in
1074:    a small dense polynomial eigenproblem {cite:p}`Asa10`.

1076:    Contour integral methods are able to compute all eigenvalues
1077:    lying inside a region of the complex plane. Use `PEPGetRG()` to
1078:    specify the region. However, the computational cost is usually high
1079:    because multiple linear systems must be solved. Use `PEPCISSGetKSPs()`
1080:    to configure the `KSP` objects for this.

1082:    Details of the implementation in SLEPc can be found in {cite:p}`Mae16`.

1084:    Level: beginner

1086: .seealso: [](ch:pep), `PEP`, `PEPType`, `PEPSetType()`, `PEPGetRG()`, `PEPCISSGetKSPs()`
1087: M*/
1088: SLEPC_EXTERN PetscErrorCode PEPCreate_CISS(PEP pep)
1089: {
1090:   PEP_CISS       *ctx = (PEP_CISS*)pep->data;

1092:   PetscFunctionBegin;
1093:   PetscCall(PetscNew(&ctx));
1094:   pep->data = ctx;
1095:   /* set default values of parameters */
1096:   ctx->N                  = 32;
1097:   ctx->L                  = 16;
1098:   ctx->M                  = ctx->N/4;
1099:   ctx->delta              = SLEPC_DEFAULT_TOL*1e-4;
1100:   ctx->L_max              = 64;
1101:   ctx->spurious_threshold = PetscSqrtReal(SLEPC_DEFAULT_TOL);
1102:   ctx->isreal             = PETSC_FALSE;
1103:   ctx->npart              = 1;

1105:   pep->ops->solve          = PEPSolve_CISS;
1106:   pep->ops->setup          = PEPSetUp_CISS;
1107:   pep->ops->setfromoptions = PEPSetFromOptions_CISS;
1108:   pep->ops->reset          = PEPReset_CISS;
1109:   pep->ops->destroy        = PEPDestroy_CISS;
1110:   pep->ops->view           = PEPView_CISS;
1111:   pep->ops->setdstype      = PEPSetDSType_CISS;

1113:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPCISSSetSizes_C",PEPCISSSetSizes_CISS));
1114:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPCISSGetSizes_C",PEPCISSGetSizes_CISS));
1115:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPCISSSetThreshold_C",PEPCISSSetThreshold_CISS));
1116:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPCISSGetThreshold_C",PEPCISSGetThreshold_CISS));
1117:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPCISSSetRefinement_C",PEPCISSSetRefinement_CISS));
1118:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPCISSGetRefinement_C",PEPCISSGetRefinement_CISS));
1119:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPCISSSetExtraction_C",PEPCISSSetExtraction_CISS));
1120:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPCISSGetExtraction_C",PEPCISSGetExtraction_CISS));
1121:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPCISSGetKSPs_C",PEPCISSGetKSPs_CISS));
1122:   PetscFunctionReturn(PETSC_SUCCESS);
1123: }