Date: 2022-03-31T15:29:26+00:00

Actual source code: pciss.c
slepc-3.17.0 2022-03-31
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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 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:   A = (contour->pA)?contour->pA:pep->A;
     72:   K = (contour->pP)?contour->pP:ctx->Psplit;
     73:   PetscMalloc1(pep->nmat,&coeff);
     74:   if (deriv) PEPEvaluateBasisDerivative(pep,lambda,0,coeff,NULL);
     75:   else PEPEvaluateBasis(pep,lambda,0,coeff,NULL);
     76:   STGetMatStructure(pep->st,&str);
     77:   MatZeroEntries(T);
     78:   if (!deriv && T != P) {
     79:     STGetSplitPreconditionerInfo(pep->st,NULL,&strp);
     80:     MatZeroEntries(P);
     81:   }
     82:   i = deriv?1:0;
     83:   for (;i<pep->nmat;i++) {
     84:     MatAXPY(T,coeff[i],A[i],str);
     85:     if (!deriv && T != P) MatAXPY(P,coeff[i],K[i],strp);
     86:   }
     87:   PetscFree(coeff);
     88:   PetscFunctionReturn(0);
     89: }

     91: /*
     92:   Set up KSP solvers for every integration point
     93: */
     94: static PetscErrorCode PEPCISSSetUp(PEP pep,Mat T,Mat P)
     95: {
     96:   PEP_CISS         *ctx = (PEP_CISS*)pep->data;
     97:   SlepcContourData contour;
     98:   PetscInt         i,p_id;
     99:   Mat              Amat,Pmat;

    101:   if (!ctx->contour || !ctx->contour->ksp) PEPCISSGetKSPs(pep,NULL,NULL);
    102:   contour = ctx->contour;
    103:   for (i=0;i<contour->npoints;i++) {
    104:     p_id = i*contour->subcomm->n + contour->subcomm->color;
    105:     MatDuplicate(T,MAT_DO_NOT_COPY_VALUES,&Amat);
    106:     if (T != P) MatDuplicate(P,MAT_DO_NOT_COPY_VALUES,&Pmat); else Pmat = Amat;
    107:     PEPComputeFunction(pep,ctx->omega[p_id],Amat,Pmat,PETSC_FALSE);
    108:     PEP_KSPSetOperators(contour->ksp[i],Amat,Pmat);
    109:     MatDestroy(&Amat);
    110:     if (T != P) MatDestroy(&Pmat);
    111:   }
    112:   PetscFunctionReturn(0);
    113: }

    115: /*
    116:   Y_i = F(z_i)^{-1}Fp(z_i)V for every integration point, Y=[Y_i] is in the context
    117: */
    118: static PetscErrorCode PEPCISSSolve(PEP pep,Mat dT,BV V,PetscInt L_start,PetscInt L_end)
    119: {
    120:   PEP_CISS         *ctx = (PEP_CISS*)pep->data;
    121:   SlepcContourData contour;
    122:   PetscInt         i,p_id;
    123:   Mat              MV,BMV=NULL,MC;

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

    148: PetscErrorCode PEPSetUp_CISS(PEP pep)
    149: {
    150:   PEP_CISS         *ctx = (PEP_CISS*)pep->data;
    151:   SlepcContourData contour;
    152:   PetscInt         i,nwork,nsplit;
    153:   PetscBool        istrivial,isellipse,flg;
    154:   PetscObjectId    id;
    155:   PetscObjectState state;
    156:   Vec              v0;

    158:   if (pep->ncv==PETSC_DEFAULT) pep->ncv = ctx->L_max*ctx->M;
    159:   else {
    160:     ctx->L_max = pep->ncv/ctx->M;
    161:     if (!ctx->L_max) {
    162:       ctx->L_max = 1;
    163:       pep->ncv = ctx->L_max*ctx->M;
    164:     }
    165:   }
    166:   ctx->L = PetscMin(ctx->L,ctx->L_max);
    167:   if (pep->max_it==PETSC_DEFAULT) pep->max_it = 5;
    168:   if (pep->mpd==PETSC_DEFAULT) pep->mpd = pep->ncv;
    169:   if (!pep->which) pep->which = PEP_ALL;
    171:   PEPCheckUnsupported(pep,PEP_FEATURE_STOPPING);
    172:   PEPCheckIgnored(pep,PEP_FEATURE_SCALE);

    174:   /* check region */
    175:   RGIsTrivial(pep->rg,&istrivial);
    177:   RGGetComplement(pep->rg,&flg);
    179:   PetscObjectTypeCompare((PetscObject)pep->rg,RGELLIPSE,&isellipse);

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

    191:   /* create contour data structure */
    192:   if (!ctx->contour) {
    193:     RGCanUseConjugates(pep->rg,ctx->isreal,&ctx->useconj);
    194:     SlepcContourDataCreate(ctx->useconj?ctx->N/2:ctx->N,ctx->npart,(PetscObject)pep,&ctx->contour);
    195:   }

    197:   PEPAllocateSolution(pep,0);
    198:   if (ctx->weight) PetscFree4(ctx->weight,ctx->omega,ctx->pp,ctx->sigma);
    199:   PetscMalloc4(ctx->N,&ctx->weight,ctx->N,&ctx->omega,ctx->N,&ctx->pp,ctx->L_max*ctx->M,&ctx->sigma);
    200:   PetscLogObjectMemory((PetscObject)pep,3*ctx->N*sizeof(PetscScalar)+ctx->L_max*ctx->N*sizeof(PetscReal));

    202:   /* allocate basis vectors */
    203:   BVDestroy(&ctx->S);
    204:   BVDuplicateResize(pep->V,ctx->L*ctx->M,&ctx->S);
    205:   PetscLogObjectParent((PetscObject)pep,(PetscObject)ctx->S);
    206:   BVDestroy(&ctx->V);
    207:   BVDuplicateResize(pep->V,ctx->L,&ctx->V);
    208:   PetscLogObjectParent((PetscObject)pep,(PetscObject)ctx->V);

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

    218:   contour = ctx->contour;
    219:   SlepcContourRedundantMat(contour,pep->nmat,pep->A,ctx->Psplit);
    220:   if (!ctx->J) {
    221:     MatDuplicate(contour->pA?contour->pA[0]:pep->A[0],MAT_DO_NOT_COPY_VALUES,&ctx->J);
    222:     PetscLogObjectParent((PetscObject)pep,(PetscObject)ctx->J);
    223:   }
    224:   if (contour->pA) {
    225:     BVGetColumn(ctx->V,0,&v0);
    226:     SlepcContourScatterCreate(contour,v0);
    227:     BVRestoreColumn(ctx->V,0,&v0);
    228:     BVDestroy(&ctx->pV);
    229:     BVCreate(PetscObjectComm((PetscObject)contour->xsub),&ctx->pV);
    230:     BVSetSizesFromVec(ctx->pV,contour->xsub,pep->n);
    231:     BVSetFromOptions(ctx->pV);
    232:     BVResize(ctx->pV,ctx->L,PETSC_FALSE);
    233:     PetscLogObjectParent((PetscObject)pep,(PetscObject)ctx->pV);
    234:   }

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

    244:   if (ctx->extraction == PEP_CISS_EXTRACTION_HANKEL) DSSetType(pep->ds,DSGNHEP);
    245:   else if (ctx->extraction == PEP_CISS_EXTRACTION_CAA) DSSetType(pep->ds,DSNHEP);
    246:   else {
    247:     DSSetType(pep->ds,DSPEP);
    248:     DSPEPSetDegree(pep->ds,pep->nmat-1);
    249:     DSPEPSetCoefficients(pep->ds,pep->pbc);
    250:   }
    251:   DSAllocate(pep->ds,pep->ncv);
    252:   nwork = 2;
    253:   PEPSetWorkVecs(pep,nwork);
    254:   PetscFunctionReturn(0);
    255: }

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

    270:   DSSetFromOptions(pep->ds);
    271:   DSGetSlepcSC(pep->ds,&sc);
    272:   sc->comparison    = SlepcCompareLargestMagnitude;
    273:   sc->comparisonctx = NULL;
    274:   sc->map           = NULL;
    275:   sc->mapobj        = NULL;
    276:   DSGetLeadingDimension(pep->ds,&ld);
    277:   RGComputeQuadrature(pep->rg,RG_QUADRULE_TRAPEZOIDAL,ctx->N,ctx->omega,ctx->pp,ctx->weight);
    278:   STGetSplitPreconditionerInfo(pep->st,&nsplit,NULL);
    279:   if (contour->pA) {
    280:     T = contour->pA[0];
    281:     P = nsplit? contour->pP[0]: T;
    282:   } else {
    283:     T = pep->A[0];
    284:     P = nsplit? ctx->Psplit[0]: T;
    285:   }
    286:   PEPCISSSetUp(pep,T,P);
    287:   BVSetActiveColumns(ctx->V,0,ctx->L);
    288:   BVSetRandomSign(ctx->V);
    289:   BVGetRandomContext(ctx->V,&rand);
    290:   if (contour->pA) BVScatter(ctx->V,ctx->pV,contour->scatterin,contour->xdup);
    291:   PEPCISSSolve(pep,ctx->J,(contour->pA)?ctx->pV:ctx->V,0,ctx->L);
    292:   PetscObjectTypeCompare((PetscObject)pep->rg,RGELLIPSE,&isellipse);
    293:   if (isellipse) {
    294:     BVTraceQuadrature(ctx->Y,ctx->V,ctx->L,ctx->L,ctx->weight,contour->scatterin,contour->subcomm,contour->npoints,ctx->useconj,&est_eig);
    295:     PetscInfo(pep,"Estimated eigenvalue count: %f\n",(double)est_eig);
    296:     eta = PetscPowReal(10.0,-PetscLog10Real(pep->tol)/ctx->N);
    297:     L_add = PetscMax(0,(PetscInt)PetscCeilReal((est_eig*eta)/ctx->M)-ctx->L);
    298:     if (L_add>ctx->L_max-ctx->L) {
    299:       PetscInfo(pep,"Number of eigenvalues inside the contour path may be too large\n");
    300:       L_add = ctx->L_max-ctx->L;
    301:     }
    302:   }
    303:   /* Updates L after estimate the number of eigenvalue */
    304:   if (L_add>0) {
    305:     PetscInfo(pep,"Changing L %" PetscInt_FMT " -> %" PetscInt_FMT " by Estimate #Eig\n",ctx->L,ctx->L+L_add);
    306:     BVCISSResizeBases(ctx->S,contour->pA?ctx->pV:ctx->V,ctx->Y,ctx->L,ctx->L+L_add,ctx->M,contour->npoints);
    307:     BVSetActiveColumns(ctx->V,ctx->L,ctx->L+L_add);
    308:     BVSetRandomSign(ctx->V);
    309:     if (contour->pA) BVScatter(ctx->V,ctx->pV,contour->scatterin,contour->xdup);
    310:     ctx->L += L_add;
    311:     PEPCISSSolve(pep,ctx->J,(contour->pA)?ctx->pV:ctx->V,ctx->L-L_add,ctx->L);
    312:   }

    314:   PetscMalloc2(ctx->L*ctx->L*ctx->M*2,&Mu,ctx->L*ctx->M*ctx->L*ctx->M,&H0);
    315:   for (i=0;i<ctx->refine_blocksize;i++) {
    316:     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);
    317:     CISS_BlockHankel(Mu,0,ctx->L,ctx->M,H0);
    318:     PetscLogEventBegin(PEP_CISS_SVD,pep,0,0,0);
    319:     SlepcCISS_BH_SVD(H0,ctx->L*ctx->M,ctx->delta,ctx->sigma,&nv);
    320:     PetscLogEventEnd(PEP_CISS_SVD,pep,0,0,0);
    321:     if (ctx->sigma[0]<=ctx->delta || nv < ctx->L*ctx->M || ctx->L == ctx->L_max) break;
    322:     L_add = L_base;
    323:     if (ctx->L+L_add>ctx->L_max) L_add = ctx->L_max-ctx->L;
    324:     PetscInfo(pep,"Changing L %" PetscInt_FMT " -> %" PetscInt_FMT " by SVD(H0)\n",ctx->L,ctx->L+L_add);
    325:     BVCISSResizeBases(ctx->S,contour->pA?ctx->pV:ctx->V,ctx->Y,ctx->L,ctx->L+L_add,ctx->M,contour->npoints);
    326:     BVSetActiveColumns(ctx->V,ctx->L,ctx->L+L_add);
    327:     BVSetRandomSign(ctx->V);
    328:     if (contour->pA) BVScatter(ctx->V,ctx->pV,contour->scatterin,contour->xdup);
    329:     ctx->L += L_add;
    330:     PEPCISSSolve(pep,ctx->J,(contour->pA)?ctx->pV:ctx->V,ctx->L-L_add,ctx->L);
    331:     if (L_add) {
    332:       PetscFree2(Mu,H0);
    333:       PetscMalloc2(ctx->L*ctx->L*ctx->M*2,&Mu,ctx->L*ctx->M*ctx->L*ctx->M,&H0);
    334:     }
    335:   }

    337:   RGGetScale(pep->rg,&rgscale);
    338:   RGEllipseGetParameters(pep->rg,&center,&radius,NULL);

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

    342:   while (pep->reason == PEP_CONVERGED_ITERATING) {
    343:     pep->its++;
    344:     for (inner=0;inner<=ctx->refine_inner;inner++) {
    345:       if (ctx->extraction == PEP_CISS_EXTRACTION_HANKEL) {
    346:         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);
    347:         CISS_BlockHankel(Mu,0,ctx->L,ctx->M,H0);
    348:         PetscLogEventBegin(PEP_CISS_SVD,pep,0,0,0);
    349:         SlepcCISS_BH_SVD(H0,ctx->L*ctx->M,ctx->delta,ctx->sigma,&nv);
    350:         PetscLogEventEnd(PEP_CISS_SVD,pep,0,0,0);
    351:       } else {
    352:         BVSumQuadrature(ctx->S,ctx->Y,ctx->M,ctx->L,ctx->L,ctx->weight,ctx->pp,contour->scatterin,contour->subcomm,contour->npoints,ctx->useconj);
    353:         /* compute SVD of S */
    354:         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);
    355:       }
    356:       PetscInfo(pep,"Estimated rank: nv = %" PetscInt_FMT "\n",nv);
    357:       if (ctx->sigma[0]>ctx->delta && nv==ctx->L*ctx->M && inner!=ctx->refine_inner) {
    358:         BVSumQuadrature(ctx->S,ctx->Y,ctx->M,ctx->L,ctx->L,ctx->weight,ctx->pp,contour->scatterin,contour->subcomm,contour->npoints,ctx->useconj);
    359:         BVSetActiveColumns(ctx->S,0,ctx->L);
    360:         BVSetActiveColumns(ctx->V,0,ctx->L);
    361:         BVCopy(ctx->S,ctx->V);
    362:         if (contour->pA) BVScatter(ctx->V,ctx->pV,contour->scatterin,contour->xdup);
    363:         PEPCISSSolve(pep,ctx->J,(contour->pA)?ctx->pV:ctx->V,0,ctx->L);
    364:       } else break;
    365:     }
    366:     pep->nconv = 0;
    367:     if (nv == 0) { pep->reason = PEP_CONVERGED_TOL; break; }
    368:     else {
    369:       /* Extracting eigenpairs */
    370:       DSSetDimensions(pep->ds,nv,0,0);
    371:       DSSetState(pep->ds,DS_STATE_RAW);
    372:       if (ctx->extraction == PEP_CISS_EXTRACTION_HANKEL) {
    373:         CISS_BlockHankel(Mu,0,ctx->L,ctx->M,H0);
    374:         CISS_BlockHankel(Mu,1,ctx->L,ctx->M,H1);
    375:         DSGetArray(pep->ds,DS_MAT_A,&temp);
    376:         for (j=0;j<nv;j++)
    377:           for (i=0;i<nv;i++)
    378:             temp[i+j*ld] = H1[i+j*ctx->L*ctx->M];
    379:         DSRestoreArray(pep->ds,DS_MAT_A,&temp);
    380:         DSGetArray(pep->ds,DS_MAT_B,&temp);
    381:         for (j=0;j<nv;j++)
    382:           for (i=0;i<nv;i++)
    383:             temp[i+j*ld] = H0[i+j*ctx->L*ctx->M];
    384:         DSRestoreArray(pep->ds,DS_MAT_B,&temp);
    385:       } else if (ctx->extraction == PEP_CISS_EXTRACTION_CAA) {
    386:         BVSetActiveColumns(ctx->S,0,nv);
    387:         DSGetArray(pep->ds,DS_MAT_A,&temp);
    388:         for (i=0;i<nv;i++) PetscArraycpy(temp+i*ld,H0+i*nv,nv);
    389:         DSRestoreArray(pep->ds,DS_MAT_A,&temp);
    390:       } else {
    391:         BVSetActiveColumns(ctx->S,0,nv);
    392:         for (i=0;i<pep->nmat;i++) {
    393:           DSGetMat(pep->ds,DSMatExtra[i],&E);
    394:           BVMatProject(ctx->S,pep->A[i],ctx->S,E);
    395:           DSRestoreMat(pep->ds,DSMatExtra[i],&E);
    396:         }
    397:         nv = (pep->nmat-1)*nv;
    398:       }
    399:       DSSolve(pep->ds,pep->eigr,pep->eigi);
    400:       DSSynchronize(pep->ds,pep->eigr,pep->eigi);
    401:       if (ctx->extraction == PEP_CISS_EXTRACTION_CAA || ctx->extraction == PEP_CISS_EXTRACTION_HANKEL) {
    402:         for (i=0;i<nv;i++) {
    403:           pep->eigr[i] = (pep->eigr[i]*radius+center)*rgscale;
    404:         }
    405:       }
    406:       PetscMalloc3(nv,&fl1,nv,&inside,nv,&rr);
    407:       DSVectors(pep->ds,DS_MAT_X,NULL,NULL);
    408:       DSGetMat(pep->ds,DS_MAT_X,&X);
    409:       SlepcCISS_isGhost(X,nv,ctx->sigma,ctx->spurious_threshold,fl1);
    410:       MatDestroy(&X);
    411:       RGCheckInside(pep->rg,nv,pep->eigr,pep->eigi,inside);
    412:       for (i=0;i<nv;i++) {
    413:         if (fl1[i] && inside[i]>=0) {
    414:           rr[i] = 1.0;
    415:           pep->nconv++;
    416:         } else rr[i] = 0.0;
    417:       }
    418:       DSSort(pep->ds,pep->eigr,pep->eigi,rr,NULL,&pep->nconv);
    419:       DSSynchronize(pep->ds,pep->eigr,pep->eigi);
    420:       if (ctx->extraction == PEP_CISS_EXTRACTION_CAA || ctx->extraction == PEP_CISS_EXTRACTION_HANKEL) {
    421:         for (i=0;i<nv;i++) pep->eigr[i] = (pep->eigr[i]*radius+center)*rgscale;
    422:       }
    423:       PetscFree3(fl1,inside,rr);
    424:       BVSetActiveColumns(pep->V,0,nv);
    425:       DSVectors(pep->ds,DS_MAT_X,NULL,NULL);
    426:       if (ctx->extraction == PEP_CISS_EXTRACTION_HANKEL) {
    427:         BVSumQuadrature(ctx->S,ctx->Y,ctx->M,ctx->L,ctx->L,ctx->weight,ctx->pp,contour->scatterin,contour->subcomm,contour->npoints,ctx->useconj);
    428:         BVSetActiveColumns(ctx->S,0,nv);
    429:         BVCopy(ctx->S,pep->V);
    430:         DSGetMat(pep->ds,DS_MAT_X,&X);
    431:         BVMultInPlace(ctx->S,X,0,pep->nconv);
    432:         BVMultInPlace(pep->V,X,0,pep->nconv);
    433:         MatDestroy(&X);
    434:       } else {
    435:         DSGetMat(pep->ds,DS_MAT_X,&X);
    436:         BVMultInPlace(ctx->S,X,0,pep->nconv);
    437:         MatDestroy(&X);
    438:         BVSetActiveColumns(ctx->S,0,pep->nconv);
    439:         BVCopy(ctx->S,pep->V);
    440:       }
    441:       max_error = 0.0;
    442:       for (i=0;i<pep->nconv;i++) {
    443:         BVGetColumn(pep->V,i,&si);
    444:         VecNormalize(si,NULL);
    445:         PEPComputeResidualNorm_Private(pep,pep->eigr[i],0,si,NULL,pep->work,&error);
    446:         (*pep->converged)(pep,pep->eigr[i],0,error,&error,pep->convergedctx);
    447:         BVRestoreColumn(pep->V,i,&si);
    448:         max_error = PetscMax(max_error,error);
    449:       }
    450:       if (max_error <= pep->tol) pep->reason = PEP_CONVERGED_TOL;
    451:       else if (pep->its > pep->max_it) pep->reason = PEP_DIVERGED_ITS;
    452:       else {
    453:         if (pep->nconv > ctx->L) nv = pep->nconv;
    454:         else if (ctx->L > nv) nv = ctx->L;
    455:         nv = PetscMin(nv,ctx->L*ctx->M);
    456:         MatCreateSeqDense(PETSC_COMM_SELF,nv,ctx->L,NULL,&M);
    457:         MatSetRandom(M,rand);
    458:         BVSetActiveColumns(ctx->S,0,nv);
    459:         BVMultInPlace(ctx->S,M,0,ctx->L);
    460:         MatDestroy(&M);
    461:         BVSetActiveColumns(ctx->S,0,ctx->L);
    462:         BVSetActiveColumns(ctx->V,0,ctx->L);
    463:         BVCopy(ctx->S,ctx->V);
    464:         if (contour->pA) BVScatter(ctx->V,ctx->pV,contour->scatterin,contour->xdup);
    465:         PEPCISSSolve(pep,ctx->J,(contour->pA)?ctx->pV:ctx->V,0,ctx->L);
    466:       }
    467:     }
    468:   }
    469:   PetscFree2(Mu,H0);
    470:   if (ctx->extraction == PEP_CISS_EXTRACTION_HANKEL) PetscFree(H1);
    471:   PetscFunctionReturn(0);
    472: }

    474: static PetscErrorCode PEPCISSSetSizes_CISS(PEP pep,PetscInt ip,PetscInt bs,PetscInt ms,PetscInt npart,PetscInt bsmax,PetscBool realmats)
    475: {
    476:   PEP_CISS       *ctx = (PEP_CISS*)pep->data;
    477:   PetscInt       oN,oL,oM,oLmax,onpart;
    478:   PetscMPIInt    size;

    480:   oN = ctx->N;
    481:   if (ip == PETSC_DECIDE || ip == PETSC_DEFAULT) {
    482:     if (ctx->N!=32) { ctx->N =32; ctx->M = ctx->N/4; }
    483:   } else {
    486:     if (ctx->N!=ip) { ctx->N = ip; ctx->M = ctx->N/4; }
    487:   }
    488:   oL = ctx->L;
    489:   if (bs == PETSC_DECIDE || bs == PETSC_DEFAULT) {
    490:     ctx->L = 16;
    491:   } else {
    493:     ctx->L = bs;
    494:   }
    495:   oM = ctx->M;
    496:   if (ms == PETSC_DECIDE || ms == PETSC_DEFAULT) {
    497:     ctx->M = ctx->N/4;
    498:   } else {
    501:     ctx->M = PetscMax(ms,2);
    502:   }
    503:   onpart = ctx->npart;
    504:   if (npart == PETSC_DECIDE || npart == PETSC_DEFAULT) {
    505:     ctx->npart = 1;
    506:   } else {
    507:     MPI_Comm_size(PetscObjectComm((PetscObject)pep),&size);
    509:     ctx->npart = npart;
    510:   }
    511:   oLmax = ctx->L_max;
    512:   if (bsmax == PETSC_DECIDE || bsmax == PETSC_DEFAULT) {
    513:     ctx->L_max = 64;
    514:   } else {
    516:     ctx->L_max = PetscMax(bsmax,ctx->L);
    517:   }
    518:   if (onpart != ctx->npart || oN != ctx->N || realmats != ctx->isreal) {
    519:     SlepcContourDataDestroy(&ctx->contour);
    520:     PetscInfo(pep,"Resetting the contour data structure due to a change of parameters\n");
    521:     pep->state = PEP_STATE_INITIAL;
    522:   }
    523:   ctx->isreal = realmats;
    524:   if (oL != ctx->L || oM != ctx->M || oLmax != ctx->L_max) pep->state = PEP_STATE_INITIAL;
    525:   PetscFunctionReturn(0);
    526: }

    528: /*@
    529:    PEPCISSSetSizes - Sets the values of various size parameters in the CISS solver.

    531:    Logically Collective on pep

    533:    Input Parameters:
    534: +  pep   - the polynomial eigensolver context
    535: .  ip    - number of integration points
    536: .  bs    - block size
    537: .  ms    - moment size
    538: .  npart - number of partitions when splitting the communicator
    539: .  bsmax - max block size
    540: -  realmats - all coefficient matrices of P(.) are real

    542:    Options Database Keys:
    543: +  -pep_ciss_integration_points - Sets the number of integration points
    544: .  -pep_ciss_blocksize - Sets the block size
    545: .  -pep_ciss_moments - Sets the moment size
    546: .  -pep_ciss_partitions - Sets the number of partitions
    547: .  -pep_ciss_maxblocksize - Sets the maximum block size
    548: -  -pep_ciss_realmats - all coefficient matrices of P(.) are real

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

    555:    Level: advanced

    557: .seealso: PEPCISSGetSizes()
    558: @*/
    559: PetscErrorCode PEPCISSSetSizes(PEP pep,PetscInt ip,PetscInt bs,PetscInt ms,PetscInt npart,PetscInt bsmax,PetscBool realmats)
    560: {
    568:   PetscTryMethod(pep,"PEPCISSSetSizes_C",(PEP,PetscInt,PetscInt,PetscInt,PetscInt,PetscInt,PetscBool),(pep,ip,bs,ms,npart,bsmax,realmats));
    569:   PetscFunctionReturn(0);
    570: }

    572: static PetscErrorCode PEPCISSGetSizes_CISS(PEP pep,PetscInt *ip,PetscInt *bs,PetscInt *ms,PetscInt *npart,PetscInt *bsmax,PetscBool *realmats)
    573: {
    574:   PEP_CISS *ctx = (PEP_CISS*)pep->data;

    576:   if (ip) *ip = ctx->N;
    577:   if (bs) *bs = ctx->L;
    578:   if (ms) *ms = ctx->M;
    579:   if (npart) *npart = ctx->npart;
    580:   if (bsmax) *bsmax = ctx->L_max;
    581:   if (realmats) *realmats = ctx->isreal;
    582:   PetscFunctionReturn(0);
    583: }

    585: /*@
    586:    PEPCISSGetSizes - Gets the values of various size parameters in the CISS solver.

    588:    Not Collective

    590:    Input Parameter:
    591: .  pep - the polynomial eigensolver context

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

    601:    Level: advanced

    603: .seealso: PEPCISSSetSizes()
    604: @*/
    605: PetscErrorCode PEPCISSGetSizes(PEP pep,PetscInt *ip,PetscInt *bs,PetscInt *ms,PetscInt *npart,PetscInt *bsmax,PetscBool *realmats)
    606: {
    608:   PetscUseMethod(pep,"PEPCISSGetSizes_C",(PEP,PetscInt*,PetscInt*,PetscInt*,PetscInt*,PetscInt*,PetscBool*),(pep,ip,bs,ms,npart,bsmax,realmats));
    609:   PetscFunctionReturn(0);
    610: }

    612: static PetscErrorCode PEPCISSSetThreshold_CISS(PEP pep,PetscReal delta,PetscReal spur)
    613: {
    614:   PEP_CISS *ctx = (PEP_CISS*)pep->data;

    616:   if (delta == PETSC_DEFAULT) {
    617:     ctx->delta = SLEPC_DEFAULT_TOL*1e-4;
    618:   } else {
    620:     ctx->delta = delta;
    621:   }
    622:   if (spur == PETSC_DEFAULT) {
    623:     ctx->spurious_threshold = PetscSqrtReal(SLEPC_DEFAULT_TOL);
    624:   } else {
    626:     ctx->spurious_threshold = spur;
    627:   }
    628:   PetscFunctionReturn(0);
    629: }

    631: /*@
    632:    PEPCISSSetThreshold - Sets the values of various threshold parameters in
    633:    the CISS solver.

    635:    Logically Collective on pep

    637:    Input Parameters:
    638: +  pep   - the polynomial eigensolver context
    639: .  delta - threshold for numerical rank
    640: -  spur  - spurious threshold (to discard spurious eigenpairs)

    642:    Options Database Keys:
    643: +  -pep_ciss_delta - Sets the delta
    644: -  -pep_ciss_spurious_threshold - Sets the spurious threshold

    646:    Level: advanced

    648: .seealso: PEPCISSGetThreshold()
    649: @*/
    650: PetscErrorCode PEPCISSSetThreshold(PEP pep,PetscReal delta,PetscReal spur)
    651: {
    655:   PetscTryMethod(pep,"PEPCISSSetThreshold_C",(PEP,PetscReal,PetscReal),(pep,delta,spur));
    656:   PetscFunctionReturn(0);
    657: }

    659: static PetscErrorCode PEPCISSGetThreshold_CISS(PEP pep,PetscReal *delta,PetscReal *spur)
    660: {
    661:   PEP_CISS *ctx = (PEP_CISS*)pep->data;

    663:   if (delta) *delta = ctx->delta;
    664:   if (spur)  *spur = ctx->spurious_threshold;
    665:   PetscFunctionReturn(0);
    666: }

    668: /*@
    669:    PEPCISSGetThreshold - Gets the values of various threshold parameters in
    670:    the CISS solver.

    672:    Not Collective

    674:    Input Parameter:
    675: .  pep - the polynomial eigensolver context

    677:    Output Parameters:
    678: +  delta - threshold for numerical rank
    679: -  spur  - spurious threshold (to discard spurious eigenpairs)

    681:    Level: advanced

    683: .seealso: PEPCISSSetThreshold()
    684: @*/
    685: PetscErrorCode PEPCISSGetThreshold(PEP pep,PetscReal *delta,PetscReal *spur)
    686: {
    688:   PetscUseMethod(pep,"PEPCISSGetThreshold_C",(PEP,PetscReal*,PetscReal*),(pep,delta,spur));
    689:   PetscFunctionReturn(0);
    690: }

    692: static PetscErrorCode PEPCISSSetRefinement_CISS(PEP pep,PetscInt inner,PetscInt blsize)
    693: {
    694:   PEP_CISS *ctx = (PEP_CISS*)pep->data;

    696:   if (inner == PETSC_DEFAULT) {
    697:     ctx->refine_inner = 0;
    698:   } else {
    700:     ctx->refine_inner = inner;
    701:   }
    702:   if (blsize == PETSC_DEFAULT) {
    703:     ctx->refine_blocksize = 0;
    704:   } else {
    706:     ctx->refine_blocksize = blsize;
    707:   }
    708:   PetscFunctionReturn(0);
    709: }

    711: /*@
    712:    PEPCISSSetRefinement - Sets the values of various refinement parameters
    713:    in the CISS solver.

    715:    Logically Collective on pep

    717:    Input Parameters:
    718: +  pep    - the polynomial eigensolver context
    719: .  inner  - number of iterative refinement iterations (inner loop)
    720: -  blsize - number of iterative refinement iterations (blocksize loop)

    722:    Options Database Keys:
    723: +  -pep_ciss_refine_inner - Sets number of inner iterations
    724: -  -pep_ciss_refine_blocksize - Sets number of blocksize iterations

    726:    Level: advanced

    728: .seealso: PEPCISSGetRefinement()
    729: @*/
    730: PetscErrorCode PEPCISSSetRefinement(PEP pep,PetscInt inner,PetscInt blsize)
    731: {
    735:   PetscTryMethod(pep,"PEPCISSSetRefinement_C",(PEP,PetscInt,PetscInt),(pep,inner,blsize));
    736:   PetscFunctionReturn(0);
    737: }

    739: static PetscErrorCode PEPCISSGetRefinement_CISS(PEP pep,PetscInt *inner,PetscInt *blsize)
    740: {
    741:   PEP_CISS *ctx = (PEP_CISS*)pep->data;

    743:   if (inner)  *inner = ctx->refine_inner;
    744:   if (blsize) *blsize = ctx->refine_blocksize;
    745:   PetscFunctionReturn(0);
    746: }

    748: /*@
    749:    PEPCISSGetRefinement - Gets the values of various refinement parameters
    750:    in the CISS solver.

    752:    Not Collective

    754:    Input Parameter:
    755: .  pep - the polynomial eigensolver context

    757:    Output Parameters:
    758: +  inner  - number of iterative refinement iterations (inner loop)
    759: -  blsize - number of iterative refinement iterations (blocksize loop)

    761:    Level: advanced

    763: .seealso: PEPCISSSetRefinement()
    764: @*/
    765: PetscErrorCode PEPCISSGetRefinement(PEP pep, PetscInt *inner, PetscInt *blsize)
    766: {
    768:   PetscUseMethod(pep,"PEPCISSGetRefinement_C",(PEP,PetscInt*,PetscInt*),(pep,inner,blsize));
    769:   PetscFunctionReturn(0);
    770: }

    772: static PetscErrorCode PEPCISSSetExtraction_CISS(PEP pep,PEPCISSExtraction extraction)
    773: {
    774:   PEP_CISS *ctx = (PEP_CISS*)pep->data;

    776:   if (ctx->extraction != extraction) {
    777:     ctx->extraction = extraction;
    778:     pep->state      = PEP_STATE_INITIAL;
    779:   }
    780:   PetscFunctionReturn(0);
    781: }

    783: /*@
    784:    PEPCISSSetExtraction - Sets the extraction technique used in the CISS solver.

    786:    Logically Collective on pep

    788:    Input Parameters:
    789: +  pep        - the polynomial eigensolver context
    790: -  extraction - the extraction technique

    792:    Options Database Key:
    793: .  -pep_ciss_extraction - Sets the extraction technique (either 'ritz', 'hankel' or 'caa')

    795:    Notes:
    796:    By default, the Rayleigh-Ritz extraction is used (PEP_CISS_EXTRACTION_RITZ).

    798:    If the 'hankel' or the 'caa' option is specified (PEP_CISS_EXTRACTION_HANKEL or
    799:    PEP_CISS_EXTRACTION_CAA), then the Block Hankel method, or the Communication-avoiding
    800:    Arnoldi method, respectively, is used for extracting eigenpairs.

    802:    Level: advanced

    804: .seealso: PEPCISSGetExtraction(), PEPCISSExtraction
    805: @*/
    806: PetscErrorCode PEPCISSSetExtraction(PEP pep,PEPCISSExtraction extraction)
    807: {
    810:   PetscTryMethod(pep,"PEPCISSSetExtraction_C",(PEP,PEPCISSExtraction),(pep,extraction));
    811:   PetscFunctionReturn(0);
    812: }

    814: static PetscErrorCode PEPCISSGetExtraction_CISS(PEP pep,PEPCISSExtraction *extraction)
    815: {
    816:   PEP_CISS *ctx = (PEP_CISS*)pep->data;

    818:   *extraction = ctx->extraction;
    819:   PetscFunctionReturn(0);
    820: }

    822: /*@
    823:    PEPCISSGetExtraction - Gets the extraction technique used in the CISS solver.

    825:    Not Collective

    827:    Input Parameter:
    828: .  pep - the polynomial eigensolver context

    830:    Output Parameters:
    831: .  extraction - extraction technique

    833:    Level: advanced

    835: .seealso: PEPCISSSetExtraction() PEPCISSExtraction
    836: @*/
    837: PetscErrorCode PEPCISSGetExtraction(PEP pep,PEPCISSExtraction *extraction)
    838: {
    841:   PetscUseMethod(pep,"PEPCISSGetExtraction_C",(PEP,PEPCISSExtraction*),(pep,extraction));
    842:   PetscFunctionReturn(0);
    843: }

    845: static PetscErrorCode PEPCISSGetKSPs_CISS(PEP pep,PetscInt *nsolve,KSP **ksp)
    846: {
    847:   PEP_CISS         *ctx = (PEP_CISS*)pep->data;
    848:   SlepcContourData contour;
    849:   PetscInt         i,nsplit;
    850:   PC               pc;
    851:   MPI_Comm         child;

    853:   if (!ctx->contour) {  /* initialize contour data structure first */
    854:     RGCanUseConjugates(pep->rg,ctx->isreal,&ctx->useconj);
    855:     SlepcContourDataCreate(ctx->useconj?ctx->N/2:ctx->N,ctx->npart,(PetscObject)pep,&ctx->contour);
    856:   }
    857:   contour = ctx->contour;
    858:   if (!contour->ksp) {
    859:     PetscMalloc1(contour->npoints,&contour->ksp);
    860:     PEPGetST(pep,&pep->st);
    861:     STGetSplitPreconditionerInfo(pep->st,&nsplit,NULL);
    862:     PetscSubcommGetChild(contour->subcomm,&child);
    863:     for (i=0;i<contour->npoints;i++) {
    864:       KSPCreate(child,&contour->ksp[i]);
    865:       PetscObjectIncrementTabLevel((PetscObject)contour->ksp[i],(PetscObject)pep,1);
    866:       KSPSetOptionsPrefix(contour->ksp[i],((PetscObject)pep)->prefix);
    867:       KSPAppendOptionsPrefix(contour->ksp[i],"pep_ciss_");
    868:       PetscLogObjectParent((PetscObject)pep,(PetscObject)contour->ksp[i]);
    869:       PetscObjectSetOptions((PetscObject)contour->ksp[i],((PetscObject)pep)->options);
    870:       KSPSetErrorIfNotConverged(contour->ksp[i],PETSC_TRUE);
    871:       KSPSetTolerances(contour->ksp[i],SlepcDefaultTol(pep->tol),PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
    872:       KSPGetPC(contour->ksp[i],&pc);
    873:       if (nsplit) {
    874:         KSPSetType(contour->ksp[i],KSPBCGS);
    875:         PCSetType(pc,PCBJACOBI);
    876:       } else {
    877:         KSPSetType(contour->ksp[i],KSPPREONLY);
    878:         PCSetType(pc,PCLU);
    879:       }
    880:     }
    881:   }
    882:   if (nsolve) *nsolve = contour->npoints;
    883:   if (ksp)    *ksp    = contour->ksp;
    884:   PetscFunctionReturn(0);
    885: }

    887: /*@C
    888:    PEPCISSGetKSPs - Retrieve the array of linear solver objects associated with
    889:    the CISS solver.

    891:    Not Collective

    893:    Input Parameter:
    894: .  pep - polynomial eigenvalue solver

    896:    Output Parameters:
    897: +  nsolve - number of solver objects
    898: -  ksp - array of linear solver object

    900:    Notes:
    901:    The number of KSP solvers is equal to the number of integration points divided by
    902:    the number of partitions. This value is halved in the case of real matrices with
    903:    a region centered at the real axis.

    905:    Level: advanced

    907: .seealso: PEPCISSSetSizes()
    908: @*/
    909: PetscErrorCode PEPCISSGetKSPs(PEP pep,PetscInt *nsolve,KSP **ksp)
    910: {
    912:   PetscUseMethod(pep,"PEPCISSGetKSPs_C",(PEP,PetscInt*,KSP**),(pep,nsolve,ksp));
    913:   PetscFunctionReturn(0);
    914: }

    916: PetscErrorCode PEPReset_CISS(PEP pep)
    917: {
    918:   PEP_CISS       *ctx = (PEP_CISS*)pep->data;

    920:   BVDestroy(&ctx->S);
    921:   BVDestroy(&ctx->V);
    922:   BVDestroy(&ctx->Y);
    923:   SlepcContourDataReset(ctx->contour);
    924:   MatDestroy(&ctx->J);
    925:   BVDestroy(&ctx->pV);
    926:   PetscFree(ctx->Psplit);
    927:   PetscFunctionReturn(0);
    928: }

    930: PetscErrorCode PEPSetFromOptions_CISS(PetscOptionItems *PetscOptionsObject,PEP pep)
    931: {
    932:   PEP_CISS          *ctx = (PEP_CISS*)pep->data;
    933:   PetscReal         r1,r2;
    934:   PetscInt          i,i1,i2,i3,i4,i5,i6,i7;
    935:   PetscBool         b1,flg,flg2,flg3,flg4,flg5,flg6;
    936:   PEPCISSExtraction extraction;

    938:   PetscOptionsHead(PetscOptionsObject,"PEP CISS Options");

    940:     PEPCISSGetSizes(pep,&i1,&i2,&i3,&i4,&i5,&b1);
    941:     PetscOptionsInt("-pep_ciss_integration_points","Number of integration points","PEPCISSSetSizes",i1,&i1,&flg);
    942:     PetscOptionsInt("-pep_ciss_blocksize","Block size","PEPCISSSetSizes",i2,&i2,&flg2);
    943:     PetscOptionsInt("-pep_ciss_moments","Moment size","PEPCISSSetSizes",i3,&i3,&flg3);
    944:     PetscOptionsInt("-pep_ciss_partitions","Number of partitions","PEPCISSSetSizes",i4,&i4,&flg4);
    945:     PetscOptionsInt("-pep_ciss_maxblocksize","Maximum block size","PEPCISSSetSizes",i5,&i5,&flg5);
    946:     PetscOptionsBool("-pep_ciss_realmats","True if all coefficient matrices of P(.) are real","PEPCISSSetSizes",b1,&b1,&flg6);
    947:     if (flg || flg2 || flg3 || flg4 || flg5 || flg6) PEPCISSSetSizes(pep,i1,i2,i3,i4,i5,b1);

    949:     PEPCISSGetThreshold(pep,&r1,&r2);
    950:     PetscOptionsReal("-pep_ciss_delta","Threshold for numerical rank","PEPCISSSetThreshold",r1,&r1,&flg);
    951:     PetscOptionsReal("-pep_ciss_spurious_threshold","Threshold for the spurious eigenpairs","PEPCISSSetThreshold",r2,&r2,&flg2);
    952:     if (flg || flg2) PEPCISSSetThreshold(pep,r1,r2);

    954:     PEPCISSGetRefinement(pep,&i6,&i7);
    955:     PetscOptionsInt("-pep_ciss_refine_inner","Number of inner iterative refinement iterations","PEPCISSSetRefinement",i6,&i6,&flg);
    956:     PetscOptionsInt("-pep_ciss_refine_blocksize","Number of blocksize iterative refinement iterations","PEPCISSSetRefinement",i7,&i7,&flg2);
    957:     if (flg || flg2) PEPCISSSetRefinement(pep,i6,i7);

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

    962:   PetscOptionsTail();

    964:   if (!pep->rg) PEPGetRG(pep,&pep->rg);
    965:   RGSetFromOptions(pep->rg); /* this is necessary here to set useconj */
    966:   if (!ctx->contour || !ctx->contour->ksp) PEPCISSGetKSPs(pep,NULL,NULL);
    967:   for (i=0;i<ctx->contour->npoints;i++) KSPSetFromOptions(ctx->contour->ksp[i]);
    968:   PetscSubcommSetFromOptions(ctx->contour->subcomm);
    969:   PetscFunctionReturn(0);
    970: }

    972: PetscErrorCode PEPDestroy_CISS(PEP pep)
    973: {
    974:   PEP_CISS       *ctx = (PEP_CISS*)pep->data;

    976:   SlepcContourDataDestroy(&ctx->contour);
    977:   PetscFree4(ctx->weight,ctx->omega,ctx->pp,ctx->sigma);
    978:   PetscFree(pep->data);
    979:   PetscObjectComposeFunction((PetscObject)pep,"PEPCISSSetSizes_C",NULL);
    980:   PetscObjectComposeFunction((PetscObject)pep,"PEPCISSGetSizes_C",NULL);
    981:   PetscObjectComposeFunction((PetscObject)pep,"PEPCISSSetThreshold_C",NULL);
    982:   PetscObjectComposeFunction((PetscObject)pep,"PEPCISSGetThreshold_C",NULL);
    983:   PetscObjectComposeFunction((PetscObject)pep,"PEPCISSSetRefinement_C",NULL);
    984:   PetscObjectComposeFunction((PetscObject)pep,"PEPCISSGetRefinement_C",NULL);
    985:   PetscObjectComposeFunction((PetscObject)pep,"PEPCISSSetExtraction_C",NULL);
    986:   PetscObjectComposeFunction((PetscObject)pep,"PEPCISSGetExtraction_C",NULL);
    987:   PetscObjectComposeFunction((PetscObject)pep,"PEPCISSGetKSPs_C",NULL);
    988:   PetscFunctionReturn(0);
    989: }

    991: PetscErrorCode PEPView_CISS(PEP pep,PetscViewer viewer)
    992: {
    993:   PEP_CISS       *ctx = (PEP_CISS*)pep->data;
    994:   PetscBool      isascii;
    995:   PetscViewer    sviewer;

    997:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    998:   if (isascii) {
    999:     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);
    1000:     if (ctx->isreal) PetscViewerASCIIPrintf(viewer,"  exploiting symmetry of integration points\n");
    1001:     PetscViewerASCIIPrintf(viewer,"  threshold { delta: %g, spurious threshold: %g }\n",(double)ctx->delta,(double)ctx->spurious_threshold);
    1002:     PetscViewerASCIIPrintf(viewer,"  iterative refinement  { inner: %" PetscInt_FMT ", blocksize: %" PetscInt_FMT " }\n",ctx->refine_inner, ctx->refine_blocksize);
    1003:     PetscViewerASCIIPrintf(viewer,"  extraction: %s\n",PEPCISSExtractions[ctx->extraction]);
    1004:     if (!ctx->contour || !ctx->contour->ksp) PEPCISSGetKSPs(pep,NULL,NULL);
    1005:     PetscViewerASCIIPushTab(viewer);
    1006:     if (ctx->npart>1 && ctx->contour->subcomm) {
    1007:       PetscViewerGetSubViewer(viewer,ctx->contour->subcomm->child,&sviewer);
    1008:       if (!ctx->contour->subcomm->color) KSPView(ctx->contour->ksp[0],sviewer);
    1009:       PetscViewerFlush(sviewer);
    1010:       PetscViewerRestoreSubViewer(viewer,ctx->contour->subcomm->child,&sviewer);
    1011:       PetscViewerFlush(viewer);
    1012:       /* extra call needed because of the two calls to PetscViewerASCIIPushSynchronized() in PetscViewerGetSubViewer() */
    1013:       PetscViewerASCIIPopSynchronized(viewer);
    1014:     } else KSPView(ctx->contour->ksp[0],viewer);
    1015:     PetscViewerASCIIPopTab(viewer);
    1016:   }
    1017:   PetscFunctionReturn(0);
    1018: }

    1020: SLEPC_EXTERN PetscErrorCode PEPCreate_CISS(PEP pep)
    1021: {
    1022:   PEP_CISS       *ctx = (PEP_CISS*)pep->data;

    1024:   PetscNewLog(pep,&ctx);
    1025:   pep->data = ctx;
    1026:   /* set default values of parameters */
    1027:   ctx->N                  = 32;
    1028:   ctx->L                  = 16;
    1029:   ctx->M                  = ctx->N/4;
    1030:   ctx->delta              = SLEPC_DEFAULT_TOL*1e-4;
    1031:   ctx->L_max              = 64;
    1032:   ctx->spurious_threshold = PetscSqrtReal(SLEPC_DEFAULT_TOL);
    1033:   ctx->isreal             = PETSC_FALSE;
    1034:   ctx->npart              = 1;

    1036:   pep->ops->solve          = PEPSolve_CISS;
    1037:   pep->ops->setup          = PEPSetUp_CISS;
    1038:   pep->ops->setfromoptions = PEPSetFromOptions_CISS;
    1039:   pep->ops->reset          = PEPReset_CISS;
    1040:   pep->ops->destroy        = PEPDestroy_CISS;
    1041:   pep->ops->view           = PEPView_CISS;

    1043:   PetscObjectComposeFunction((PetscObject)pep,"PEPCISSSetSizes_C",PEPCISSSetSizes_CISS);
    1044:   PetscObjectComposeFunction((PetscObject)pep,"PEPCISSGetSizes_C",PEPCISSGetSizes_CISS);
    1045:   PetscObjectComposeFunction((PetscObject)pep,"PEPCISSSetThreshold_C",PEPCISSSetThreshold_CISS);
    1046:   PetscObjectComposeFunction((PetscObject)pep,"PEPCISSGetThreshold_C",PEPCISSGetThreshold_CISS);
    1047:   PetscObjectComposeFunction((PetscObject)pep,"PEPCISSSetRefinement_C",PEPCISSSetRefinement_CISS);
    1048:   PetscObjectComposeFunction((PetscObject)pep,"PEPCISSGetRefinement_C",PEPCISSGetRefinement_CISS);
    1049:   PetscObjectComposeFunction((PetscObject)pep,"PEPCISSSetExtraction_C",PEPCISSSetExtraction_CISS);
    1050:   PetscObjectComposeFunction((PetscObject)pep,"PEPCISSGetExtraction_C",PEPCISSGetExtraction_CISS);
    1051:   PetscObjectComposeFunction((PetscObject)pep,"PEPCISSGetKSPs_C",PEPCISSGetKSPs_CISS);
    1052:   PetscFunctionReturn(0);
    1053: }