Actual source code: nciss.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 nonlinear eigenvalue problems using contour
     27:            integrals", JSIAM Lett. 1:52-55, 2009.

     29:        [2] S. Yokota and T. Sakurai, "A projection method for nonlinear
     30:            eigenvalue problems using contour integrals", JSIAM Lett.
     31:            5:41-44, 2013.
     32: */

     34: #include <slepc/private/nepimpl.h>
     35: #include <slepc/private/slepccontour.h>

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

     67: struct _n_nep_ciss_project {
     68:   NEP  nep;
     69:   BV   Q;
     70: };

     72: static PetscErrorCode NEPContourDSComputeMatrix(DS ds,PetscScalar lambda,PetscBool deriv,DSMatType mat,void *ctx)
     73: {
     74:   NEP_CISS_PROJECT proj = (NEP_CISS_PROJECT)ctx;
     75:   Mat              M,fun;

     77:   PetscFunctionBegin;
     78:   if (!deriv) {
     79:     PetscCall(NEPComputeFunction(proj->nep,lambda,proj->nep->function,proj->nep->function));
     80:     fun = proj->nep->function;
     81:   } else {
     82:     PetscCall(NEPComputeJacobian(proj->nep,lambda,proj->nep->jacobian));
     83:     fun = proj->nep->jacobian;
     84:   }
     85:   PetscCall(DSGetMat(ds,mat,&M));
     86:   PetscCall(BVMatProject(proj->Q,fun,proj->Q,M));
     87:   PetscCall(DSRestoreMat(ds,mat,&M));
     88:   PetscFunctionReturn(PETSC_SUCCESS);
     89: }

     91: static PetscErrorCode NEPComputeFunctionSubcomm(NEP nep,PetscScalar lambda,Mat T,Mat P,PetscBool deriv)
     92: {
     93:   PetscInt       i;
     94:   PetscScalar    alpha;
     95:   NEP_CISS       *ctx = (NEP_CISS*)nep->data;

     97:   PetscFunctionBegin;
     98:   PetscAssert(nep->fui!=NEP_USER_INTERFACE_CALLBACK,PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_WRONGSTATE,"Should not arrive here with callbacks");
     99:   PetscCall(MatZeroEntries(T));
    100:   if (!deriv && T != P) PetscCall(MatZeroEntries(P));
    101:   for (i=0;i<nep->nt;i++) {
    102:     if (!deriv) PetscCall(FNEvaluateFunction(nep->f[i],lambda,&alpha));
    103:     else PetscCall(FNEvaluateDerivative(nep->f[i],lambda,&alpha));
    104:     PetscCall(MatAXPY(T,alpha,ctx->contour->pA[i],nep->mstr));
    105:     if (!deriv && T != P) PetscCall(MatAXPY(P,alpha,ctx->contour->pP[i],nep->mstrp));
    106:   }
    107:   PetscFunctionReturn(PETSC_SUCCESS);
    108: }

    110: /*
    111:   Set up KSP solvers for every integration point
    112: */
    113: static PetscErrorCode NEPCISSSetUp(NEP nep,Mat T,Mat P)
    114: {
    115:   NEP_CISS         *ctx = (NEP_CISS*)nep->data;
    116:   SlepcContourData contour;
    117:   PetscInt         i,p_id;
    118:   Mat              Amat,Pmat;

    120:   PetscFunctionBegin;
    121:   if (!ctx->contour || !ctx->contour->ksp) PetscCall(NEPCISSGetKSPs(nep,NULL,NULL));
    122:   contour = ctx->contour;
    123:   PetscAssert(ctx->contour && ctx->contour->ksp,PetscObjectComm((PetscObject)nep),PETSC_ERR_PLIB,"Something went wrong with NEPCISSGetKSPs()");
    124:   for (i=0;i<contour->npoints;i++) {
    125:     p_id = i*contour->subcomm->n + contour->subcomm->color;
    126:     PetscCall(MatDuplicate(T,MAT_DO_NOT_COPY_VALUES,&Amat));
    127:     if (T != P) PetscCall(MatDuplicate(P,MAT_DO_NOT_COPY_VALUES,&Pmat)); else Pmat = Amat;
    128:     if (contour->subcomm->n == 1 || nep->fui==NEP_USER_INTERFACE_CALLBACK) PetscCall(NEPComputeFunction(nep,ctx->omega[p_id],Amat,Pmat));
    129:     else PetscCall(NEPComputeFunctionSubcomm(nep,ctx->omega[p_id],Amat,Pmat,PETSC_FALSE));
    130:     PetscCall(NEP_KSPSetOperators(contour->ksp[i],Amat,Pmat));
    131:     PetscCall(MatDestroy(&Amat));
    132:     if (T != P) PetscCall(MatDestroy(&Pmat));
    133:   }
    134:   PetscFunctionReturn(PETSC_SUCCESS);
    135: }

    137: /*
    138:   Y_i = F(z_i)^{-1}Fp(z_i)V for every integration point, Y=[Y_i] is in the context
    139: */
    140: static PetscErrorCode NEPCISSSolve(NEP nep,Mat dT,BV V,PetscInt L_start,PetscInt L_end)
    141: {
    142:   NEP_CISS         *ctx = (NEP_CISS*)nep->data;
    143:   SlepcContourData contour = ctx->contour;
    144:   PetscInt         i,p_id;
    145:   Mat              MV,BMV=NULL,MC;

    147:   PetscFunctionBegin;
    148:   PetscCall(BVSetActiveColumns(V,L_start,L_end));
    149:   PetscCall(BVGetMat(V,&MV));
    150:   for (i=0;i<contour->npoints;i++) {
    151:     p_id = i*contour->subcomm->n + contour->subcomm->color;
    152:     if (contour->subcomm->n==1 || nep->fui==NEP_USER_INTERFACE_CALLBACK) PetscCall(NEPComputeJacobian(nep,ctx->omega[p_id],dT));
    153:     else PetscCall(NEPComputeFunctionSubcomm(nep,ctx->omega[p_id],dT,NULL,PETSC_TRUE));
    154:     PetscCall(BVSetActiveColumns(ctx->Y,i*ctx->L+L_start,i*ctx->L+L_end));
    155:     PetscCall(BVGetMat(ctx->Y,&MC));
    156:     if (!i) {
    157:       PetscCall(MatProductCreate(dT,MV,NULL,&BMV));
    158:       PetscCall(MatProductSetType(BMV,MATPRODUCT_AB));
    159:       PetscCall(MatProductSetFromOptions(BMV));
    160:       PetscCall(MatProductSymbolic(BMV));
    161:     }
    162:     PetscCall(MatProductNumeric(BMV));
    163:     PetscCall(KSPMatSolve(contour->ksp[i],BMV,MC));
    164:     PetscCall(BVRestoreMat(ctx->Y,&MC));
    165:   }
    166:   PetscCall(MatDestroy(&BMV));
    167:   PetscCall(BVRestoreMat(V,&MV));
    168:   PetscFunctionReturn(PETSC_SUCCESS);
    169: }

    171: static PetscErrorCode NEPSetUp_CISS(NEP nep)
    172: {
    173:   NEP_CISS         *ctx = (NEP_CISS*)nep->data;
    174:   SlepcContourData contour;
    175:   PetscInt         nwork;
    176:   PetscBool        istrivial,isellipse,flg;
    177:   NEP_CISS_PROJECT dsctxf;
    178:   PetscObjectId    id;
    179:   PetscObjectState state;
    180:   Vec              v0;

    182:   PetscFunctionBegin;
    183:   if (nep->ncv==PETSC_DETERMINE) nep->ncv = ctx->L_max*ctx->M;
    184:   else {
    185:     ctx->L_max = nep->ncv/ctx->M;
    186:     if (!ctx->L_max) {
    187:       ctx->L_max = 1;
    188:       nep->ncv = ctx->L_max*ctx->M;
    189:     }
    190:   }
    191:   ctx->L = PetscMin(ctx->L,ctx->L_max);
    192:   if (nep->max_it==PETSC_DETERMINE) nep->max_it = 5;
    193:   if (nep->mpd==PETSC_DETERMINE) nep->mpd = nep->ncv;
    194:   if (!nep->which) nep->which = NEP_ALL;
    195:   PetscCheck(nep->which==NEP_ALL,PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"This solver supports only computing all eigenvalues");
    196:   NEPCheckUnsupported(nep,NEP_FEATURE_STOPPING | NEP_FEATURE_TWOSIDED);

    198:   /* check region */
    199:   PetscCall(RGIsTrivial(nep->rg,&istrivial));
    200:   PetscCheck(!istrivial,PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"CISS requires a nontrivial region, e.g. -rg_type ellipse ...");
    201:   PetscCall(RGGetComplement(nep->rg,&flg));
    202:   PetscCheck(!flg,PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"A region with complement flag set is not allowed");
    203:   PetscCall(PetscObjectTypeCompare((PetscObject)nep->rg,RGELLIPSE,&isellipse));
    204:   PetscCheck(isellipse,PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"Currently only implemented for elliptic regions");

    206:   /* if the region has changed, then reset contour data */
    207:   PetscCall(PetscObjectGetId((PetscObject)nep->rg,&id));
    208:   PetscCall(PetscObjectStateGet((PetscObject)nep->rg,&state));
    209:   if (ctx->rgid && (id != ctx->rgid || state != ctx->rgstate)) {
    210:     PetscCall(SlepcContourDataDestroy(&ctx->contour));
    211:     PetscCall(PetscInfo(nep,"Resetting the contour data structure due to a change of region\n"));
    212:     ctx->rgid = id; ctx->rgstate = state;
    213:   }

    215:   /* create contour data structure */
    216:   if (!ctx->contour) {
    217:     PetscCall(RGCanUseConjugates(nep->rg,ctx->isreal,&ctx->useconj));
    218:     PetscCall(SlepcContourDataCreate(ctx->useconj?ctx->N/2:ctx->N,ctx->npart,(PetscObject)nep,&ctx->contour));
    219:   }

    221:   PetscCall(NEPAllocateSolution(nep,0));
    222:   if (ctx->weight) PetscCall(PetscFree4(ctx->weight,ctx->omega,ctx->pp,ctx->sigma));
    223:   PetscCall(PetscMalloc4(ctx->N,&ctx->weight,ctx->N,&ctx->omega,ctx->N,&ctx->pp,ctx->L_max*ctx->M,&ctx->sigma));

    225:   /* allocate basis vectors */
    226:   PetscCall(BVDestroy(&ctx->S));
    227:   PetscCall(BVDuplicateResize(nep->V,ctx->L*ctx->M,&ctx->S));
    228:   PetscCall(BVDestroy(&ctx->V));
    229:   PetscCall(BVDuplicateResize(nep->V,ctx->L,&ctx->V));

    231:   contour = ctx->contour;
    232:   if (contour->subcomm && contour->subcomm->n != 1 && nep->fui==NEP_USER_INTERFACE_CALLBACK) {
    233:     PetscCall(NEPComputeFunction(nep,0,nep->function,nep->function_pre));
    234:     PetscCall(SlepcContourRedundantMat(contour,1,&nep->function,(nep->function!=nep->function_pre)?&nep->function_pre:NULL));
    235:   } else PetscCall(SlepcContourRedundantMat(contour,nep->nt,nep->A,nep->P));
    236:   if (contour->pA) {
    237:     if (!ctx->J) PetscCall(MatDuplicate(contour->pA[0],MAT_DO_NOT_COPY_VALUES,&ctx->J));
    238:     PetscCall(BVGetColumn(ctx->V,0,&v0));
    239:     PetscCall(SlepcContourScatterCreate(contour,v0));
    240:     PetscCall(BVRestoreColumn(ctx->V,0,&v0));
    241:     PetscCall(BVDestroy(&ctx->pV));
    242:     PetscCall(BVCreate(PetscObjectComm((PetscObject)contour->xsub),&ctx->pV));
    243:     PetscCall(BVSetSizesFromVec(ctx->pV,contour->xsub,nep->n));
    244:     PetscCall(BVSetFromOptions(ctx->pV));
    245:     PetscCall(BVResize(ctx->pV,ctx->L,PETSC_FALSE));
    246:   }

    248:   PetscCall(BVDestroy(&ctx->Y));
    249:   if (contour->pA) {
    250:     PetscCall(BVCreate(PetscObjectComm((PetscObject)contour->xsub),&ctx->Y));
    251:     PetscCall(BVSetSizesFromVec(ctx->Y,contour->xsub,nep->n));
    252:     PetscCall(BVSetFromOptions(ctx->Y));
    253:     PetscCall(BVResize(ctx->Y,contour->npoints*ctx->L,PETSC_FALSE));
    254:   } else PetscCall(BVDuplicateResize(nep->V,contour->npoints*ctx->L,&ctx->Y));

    256:   if (ctx->extraction == NEP_CISS_EXTRACTION_RITZ)  {
    257:     PetscCall(DSSetMethod(nep->ds,1));
    258:     PetscCall(DSNEPSetRG(nep->ds,nep->rg));
    259:     if (nep->fui==NEP_USER_INTERFACE_SPLIT) PetscCall(DSNEPSetFN(nep->ds,nep->nt,nep->f));
    260:     else {
    261:       PetscCall(PetscNew(&dsctxf));
    262:       dsctxf->nep = nep;
    263:       PetscCall(DSNEPSetComputeMatrixFunction(nep->ds,NEPContourDSComputeMatrix,dsctxf,PetscCtxDestroyDefault));
    264:     }
    265:   }
    266:   PetscCall(DSAllocate(nep->ds,nep->ncv));
    267:   nwork = (nep->fui==NEP_USER_INTERFACE_SPLIT)? 2: 1;
    268:   PetscCall(NEPSetWorkVecs(nep,nwork));
    269:   PetscFunctionReturn(PETSC_SUCCESS);
    270: }

    272: static PetscErrorCode NEPSolve_CISS(NEP nep)
    273: {
    274:   NEP_CISS         *ctx = (NEP_CISS*)nep->data;
    275:   SlepcContourData contour = ctx->contour;
    276:   Mat              X,M,E,T,P,J;
    277:   BV               V;
    278:   PetscInt         i,j,ld,L_add=0,nv=0,L_base=ctx->L,inner,*inside;
    279:   PetscScalar      *Mu,*H0,*H1,*rr,*temp,center;
    280:   PetscReal        error,max_error,radius,rgscale,est_eig,eta;
    281:   PetscBool        isellipse,*fl1;
    282:   Vec              si;
    283:   SlepcSC          sc;
    284:   PetscRandom      rand;
    285:   NEP_CISS_PROJECT dsctxf;

    287:   PetscFunctionBegin;
    288:   PetscCall(DSGetSlepcSC(nep->ds,&sc));
    289:   sc->comparison    = SlepcCompareLargestMagnitude;
    290:   sc->comparisonctx = NULL;
    291:   sc->map           = NULL;
    292:   sc->mapobj        = NULL;
    293:   PetscCall(DSGetLeadingDimension(nep->ds,&ld));
    294:   PetscCall(RGComputeQuadrature(nep->rg,RG_QUADRULE_TRAPEZOIDAL,ctx->N,ctx->omega,ctx->pp,ctx->weight));
    295:   if (contour->pA) {
    296:     T = contour->pA[0];
    297:     P = ((nep->fui==NEP_USER_INTERFACE_SPLIT && nep->P) || (nep->fui==NEP_USER_INTERFACE_CALLBACK && contour->pP))? contour->pP[0]: T;
    298:   } else {
    299:     T = nep->function;
    300:     P = nep->function_pre? nep->function_pre: nep->function;
    301:   }
    302:   PetscCall(NEPCISSSetUp(nep,T,P));
    303:   PetscCall(BVSetActiveColumns(ctx->V,0,ctx->L));
    304:   PetscCall(BVSetRandomSign(ctx->V));
    305:   PetscCall(BVGetRandomContext(ctx->V,&rand));
    306:   if (contour->pA) {
    307:     J = ctx->J;
    308:     V = ctx->pV;
    309:     PetscCall(BVScatter(ctx->V,ctx->pV,contour->scatterin,contour->xdup));
    310:   } else {
    311:     J = nep->jacobian;
    312:     V = ctx->V;
    313:   }
    314:   PetscCall(NEPCISSSolve(nep,J,V,0,ctx->L));
    315:   PetscCall(PetscObjectTypeCompare((PetscObject)nep->rg,RGELLIPSE,&isellipse));
    316:   if (isellipse) {
    317:     PetscCall(BVTraceQuadrature(ctx->Y,ctx->V,ctx->L,ctx->L,ctx->weight,contour->scatterin,contour->subcomm,contour->npoints,ctx->useconj,&est_eig));
    318:     PetscCall(PetscInfo(nep,"Estimated eigenvalue count: %f\n",(double)est_eig));
    319:     eta = PetscPowReal(10.0,-PetscLog10Real(nep->tol)/ctx->N);
    320:     L_add = PetscMax(0,(PetscInt)PetscCeilReal((est_eig*eta)/ctx->M)-ctx->L);
    321:     if (L_add>ctx->L_max-ctx->L) {
    322:       PetscCall(PetscInfo(nep,"Number of eigenvalues inside the contour path may be too large\n"));
    323:       L_add = ctx->L_max-ctx->L;
    324:     }
    325:   }
    326:   /* Updates L after estimate the number of eigenvalue */
    327:   if (L_add>0) {
    328:     PetscCall(PetscInfo(nep,"Changing L %" PetscInt_FMT " -> %" PetscInt_FMT " by Estimate #Eig\n",ctx->L,ctx->L+L_add));
    329:     PetscCall(BVCISSResizeBases(ctx->S,contour->pA?ctx->pV:ctx->V,ctx->Y,ctx->L,ctx->L+L_add,ctx->M,contour->npoints));
    330:     PetscCall(BVSetActiveColumns(ctx->V,ctx->L,ctx->L+L_add));
    331:     PetscCall(BVSetRandomSign(ctx->V));
    332:     if (contour->pA) PetscCall(BVScatter(ctx->V,ctx->pV,contour->scatterin,contour->xdup));
    333:     ctx->L += L_add;
    334:     PetscCall(NEPCISSSolve(nep,J,V,ctx->L-L_add,ctx->L));
    335:   }

    337:   PetscCall(PetscMalloc2(ctx->L*ctx->L*ctx->M*2,&Mu,ctx->L*ctx->M*ctx->L*ctx->M,&H0));
    338:   for (i=0;i<ctx->refine_blocksize;i++) {
    339:     PetscCall(BVDotQuadrature(ctx->Y,V,Mu,ctx->M,ctx->L,ctx->L,ctx->weight,ctx->pp,contour->subcomm,contour->npoints,ctx->useconj));
    340:     PetscCall(CISS_BlockHankel(Mu,0,ctx->L,ctx->M,H0));
    341:     PetscCall(PetscLogEventBegin(NEP_CISS_SVD,nep,0,0,0));
    342:     PetscCall(SlepcCISS_BH_SVD(H0,ctx->L*ctx->M,ctx->delta,ctx->sigma,&nv));
    343:     PetscCall(PetscLogEventEnd(NEP_CISS_SVD,nep,0,0,0));
    344:     if (ctx->sigma[0]<=ctx->delta || nv < ctx->L*ctx->M || ctx->L == ctx->L_max) break;
    345:     L_add = L_base;
    346:     if (ctx->L+L_add>ctx->L_max) L_add = ctx->L_max-ctx->L;
    347:     PetscCall(PetscInfo(nep,"Changing L %" PetscInt_FMT " -> %" PetscInt_FMT " by SVD(H0)\n",ctx->L,ctx->L+L_add));
    348:     PetscCall(BVCISSResizeBases(ctx->S,contour->pA?ctx->pV:ctx->V,ctx->Y,ctx->L,ctx->L+L_add,ctx->M,contour->npoints));
    349:     PetscCall(BVSetActiveColumns(ctx->V,ctx->L,ctx->L+L_add));
    350:     PetscCall(BVSetRandomSign(ctx->V));
    351:     if (contour->pA) PetscCall(BVScatter(ctx->V,ctx->pV,contour->scatterin,contour->xdup));
    352:     ctx->L += L_add;
    353:     PetscCall(NEPCISSSolve(nep,J,V,ctx->L-L_add,ctx->L));
    354:     if (L_add) {
    355:       PetscCall(PetscFree2(Mu,H0));
    356:       PetscCall(PetscMalloc2(ctx->L*ctx->L*ctx->M*2,&Mu,ctx->L*ctx->M*ctx->L*ctx->M,&H0));
    357:     }
    358:   }

    360:   PetscCall(RGGetScale(nep->rg,&rgscale));
    361:   PetscCall(RGEllipseGetParameters(nep->rg,&center,&radius,NULL));

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

    365:   while (nep->reason == NEP_CONVERGED_ITERATING) {
    366:     nep->its++;
    367:     for (inner=0;inner<=ctx->refine_inner;inner++) {
    368:       if (ctx->extraction == NEP_CISS_EXTRACTION_HANKEL) {
    369:         PetscCall(BVDotQuadrature(ctx->Y,V,Mu,ctx->M,ctx->L,ctx->L,ctx->weight,ctx->pp,contour->subcomm,contour->npoints,ctx->useconj));
    370:         PetscCall(CISS_BlockHankel(Mu,0,ctx->L,ctx->M,H0));
    371:         PetscCall(PetscLogEventBegin(NEP_CISS_SVD,nep,0,0,0));
    372:         PetscCall(SlepcCISS_BH_SVD(H0,ctx->L*ctx->M,ctx->delta,ctx->sigma,&nv));
    373:         PetscCall(PetscLogEventEnd(NEP_CISS_SVD,nep,0,0,0));
    374:       } else {
    375:         PetscCall(BVSumQuadrature(ctx->S,ctx->Y,ctx->M,ctx->L,ctx->L,ctx->weight,ctx->pp,contour->scatterin,contour->subcomm,contour->npoints,ctx->useconj));
    376:         /* compute SVD of S */
    377:         PetscCall(BVSVDAndRank(ctx->S,ctx->M,ctx->L,ctx->delta,(ctx->extraction==NEP_CISS_EXTRACTION_CAA)?BV_SVD_METHOD_QR_CAA:BV_SVD_METHOD_QR,H0,ctx->sigma,&nv));
    378:       }
    379:       PetscCall(PetscInfo(nep,"Estimated rank: nv = %" PetscInt_FMT "\n",nv));
    380:       if (ctx->sigma[0]>ctx->delta && nv==ctx->L*ctx->M && inner!=ctx->refine_inner) {
    381:         PetscCall(BVSumQuadrature(ctx->S,ctx->Y,ctx->M,ctx->L,ctx->L,ctx->weight,ctx->pp,contour->scatterin,contour->subcomm,contour->npoints,ctx->useconj));
    382:         PetscCall(BVSetActiveColumns(ctx->S,0,ctx->L));
    383:         PetscCall(BVSetActiveColumns(ctx->V,0,ctx->L));
    384:         PetscCall(BVCopy(ctx->S,ctx->V));
    385:         if (contour->pA) PetscCall(BVScatter(ctx->V,ctx->pV,contour->scatterin,contour->xdup));
    386:         PetscCall(NEPCISSSolve(nep,J,V,0,ctx->L));
    387:       } else break;
    388:     }
    389:     nep->nconv = 0;
    390:     if (nv == 0) { nep->reason = NEP_CONVERGED_TOL; break; }
    391:     else {
    392:       /* Extracting eigenpairs */
    393:       PetscCall(DSSetDimensions(nep->ds,nv,0,0));
    394:       PetscCall(DSSetState(nep->ds,DS_STATE_RAW));
    395:       if (ctx->extraction == NEP_CISS_EXTRACTION_HANKEL) {
    396:         PetscCall(CISS_BlockHankel(Mu,0,ctx->L,ctx->M,H0));
    397:         PetscCall(CISS_BlockHankel(Mu,1,ctx->L,ctx->M,H1));
    398:         PetscCall(DSGetArray(nep->ds,DS_MAT_A,&temp));
    399:         for (j=0;j<nv;j++)
    400:           for (i=0;i<nv;i++)
    401:             temp[i+j*ld] = H1[i+j*ctx->L*ctx->M];
    402:         PetscCall(DSRestoreArray(nep->ds,DS_MAT_A,&temp));
    403:         PetscCall(DSGetArray(nep->ds,DS_MAT_B,&temp));
    404:         for (j=0;j<nv;j++)
    405:           for (i=0;i<nv;i++)
    406:             temp[i+j*ld] = H0[i+j*ctx->L*ctx->M];
    407:         PetscCall(DSRestoreArray(nep->ds,DS_MAT_B,&temp));
    408:       } else if (ctx->extraction == NEP_CISS_EXTRACTION_CAA) {
    409:         PetscCall(BVSetActiveColumns(ctx->S,0,nv));
    410:         PetscCall(DSGetArray(nep->ds,DS_MAT_A,&temp));
    411:         for (i=0;i<nv;i++) PetscCall(PetscArraycpy(temp+i*ld,H0+i*nv,nv));
    412:         PetscCall(DSRestoreArray(nep->ds,DS_MAT_A,&temp));
    413:       } else {
    414:         PetscCall(BVSetActiveColumns(ctx->S,0,nv));
    415:         if (nep->fui==NEP_USER_INTERFACE_SPLIT) {
    416:           for (i=0;i<nep->nt;i++) {
    417:             PetscCall(DSGetMat(nep->ds,DSMatExtra[i],&E));
    418:             PetscCall(BVMatProject(ctx->S,nep->A[i],ctx->S,E));
    419:             PetscCall(DSRestoreMat(nep->ds,DSMatExtra[i],&E));
    420:           }
    421:         } else {
    422:           PetscCall(DSNEPGetComputeMatrixFunction(nep->ds,NULL,(PetscCtxRt)&dsctxf,NULL));
    423:           dsctxf->Q = ctx->S;
    424:         }
    425:       }
    426:       PetscCall(DSSolve(nep->ds,nep->eigr,nep->eigi));
    427:       PetscCall(DSSynchronize(nep->ds,nep->eigr,nep->eigi));
    428:       PetscCall(DSGetDimensions(nep->ds,NULL,NULL,NULL,&nv));
    429:       if (ctx->extraction == NEP_CISS_EXTRACTION_CAA || ctx->extraction == NEP_CISS_EXTRACTION_HANKEL) {
    430:         for (i=0;i<nv;i++) {
    431:           nep->eigr[i] = (nep->eigr[i]*radius+center)*rgscale;
    432:         }
    433:       }
    434:       PetscCall(PetscMalloc3(nv,&fl1,nv,&inside,nv,&rr));
    435:       PetscCall(DSVectors(nep->ds,DS_MAT_X,NULL,NULL));
    436:       PetscCall(DSGetMat(nep->ds,DS_MAT_X,&X));
    437:       PetscCall(SlepcCISS_isGhost(X,nv,ctx->sigma,ctx->spurious_threshold,fl1));
    438:       PetscCall(DSRestoreMat(nep->ds,DS_MAT_X,&X));
    439:       PetscCall(RGCheckInside(nep->rg,nv,nep->eigr,nep->eigi,inside));
    440:       for (i=0;i<nv;i++) {
    441:         if (fl1[i] && inside[i]>=0) {
    442:           rr[i] = 1.0;
    443:           nep->nconv++;
    444:         } else rr[i] = 0.0;
    445:       }
    446:       PetscCall(DSSort(nep->ds,nep->eigr,nep->eigi,rr,NULL,&nep->nconv));
    447:       PetscCall(DSSynchronize(nep->ds,nep->eigr,nep->eigi));
    448:       if (ctx->extraction == NEP_CISS_EXTRACTION_CAA || ctx->extraction == NEP_CISS_EXTRACTION_HANKEL) {
    449:         for (i=0;i<nv;i++) nep->eigr[i] = (nep->eigr[i]*radius+center)*rgscale;
    450:       }
    451:       PetscCall(PetscFree3(fl1,inside,rr));
    452:       PetscCall(BVSetActiveColumns(nep->V,0,nv));
    453:       PetscCall(DSVectors(nep->ds,DS_MAT_X,NULL,NULL));
    454:       if (ctx->extraction == NEP_CISS_EXTRACTION_HANKEL) {
    455:         PetscCall(BVSumQuadrature(ctx->S,ctx->Y,ctx->M,ctx->L,ctx->L,ctx->weight,ctx->pp,contour->scatterin,contour->subcomm,contour->npoints,ctx->useconj));
    456:         PetscCall(BVSetActiveColumns(ctx->S,0,nv));
    457:         PetscCall(BVCopy(ctx->S,nep->V));
    458:         PetscCall(DSGetMat(nep->ds,DS_MAT_X,&X));
    459:         PetscCall(BVMultInPlace(ctx->S,X,0,nep->nconv));
    460:         PetscCall(BVMultInPlace(nep->V,X,0,nep->nconv));
    461:         PetscCall(DSRestoreMat(nep->ds,DS_MAT_X,&X));
    462:       } else {
    463:         PetscCall(DSGetMat(nep->ds,DS_MAT_X,&X));
    464:         PetscCall(BVMultInPlace(ctx->S,X,0,nep->nconv));
    465:         PetscCall(DSRestoreMat(nep->ds,DS_MAT_X,&X));
    466:         PetscCall(BVSetActiveColumns(ctx->S,0,nep->nconv));
    467:         PetscCall(BVCopy(ctx->S,nep->V));
    468:       }
    469:       max_error = 0.0;
    470:       for (i=0;i<nep->nconv;i++) {
    471:         PetscCall(BVGetColumn(nep->V,i,&si));
    472:         PetscCall(VecNormalize(si,NULL));
    473:         PetscCall(NEPComputeResidualNorm_Private(nep,PETSC_FALSE,nep->eigr[i],si,nep->work,&error));
    474:         PetscCall((*nep->converged)(nep,nep->eigr[i],0,error,&error,nep->convergedctx));
    475:         PetscCall(BVRestoreColumn(nep->V,i,&si));
    476:         max_error = PetscMax(max_error,error);
    477:       }
    478:       if (max_error <= nep->tol) nep->reason = NEP_CONVERGED_TOL;
    479:       else if (nep->its > nep->max_it) nep->reason = NEP_DIVERGED_ITS;
    480:       else {
    481:         if (nep->nconv > ctx->L) nv = nep->nconv;
    482:         else if (ctx->L > nv) nv = ctx->L;
    483:         nv = PetscMin(nv,ctx->L*ctx->M);
    484:         PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,nv,ctx->L,NULL,&M));
    485:         PetscCall(MatSetRandom(M,rand));
    486:         PetscCall(BVSetActiveColumns(ctx->S,0,nv));
    487:         PetscCall(BVMultInPlace(ctx->S,M,0,ctx->L));
    488:         PetscCall(MatDestroy(&M));
    489:         PetscCall(BVSetActiveColumns(ctx->S,0,ctx->L));
    490:         PetscCall(BVSetActiveColumns(ctx->V,0,ctx->L));
    491:         PetscCall(BVCopy(ctx->S,ctx->V));
    492:         if (contour->pA) PetscCall(BVScatter(ctx->V,ctx->pV,contour->scatterin,contour->xdup));
    493:         PetscCall(NEPCISSSolve(nep,J,V,0,ctx->L));
    494:       }
    495:     }
    496:   }
    497:   PetscCall(PetscFree2(Mu,H0));
    498:   if (ctx->extraction == NEP_CISS_EXTRACTION_HANKEL) PetscCall(PetscFree(H1));
    499:   PetscFunctionReturn(PETSC_SUCCESS);
    500: }

    502: static PetscErrorCode NEPCISSSetSizes_CISS(NEP nep,PetscInt ip,PetscInt bs,PetscInt ms,PetscInt npart,PetscInt bsmax,PetscBool realmats)
    503: {
    504:   NEP_CISS       *ctx = (NEP_CISS*)nep->data;
    505:   PetscInt       oN,oL,oM,oLmax,onpart;
    506:   PetscMPIInt    size;

    508:   PetscFunctionBegin;
    509:   oN = ctx->N;
    510:   if (ip == PETSC_DETERMINE) {
    511:     if (ctx->N!=32) { ctx->N =32; ctx->M = ctx->N/4; }
    512:   } else if (ip != PETSC_CURRENT) {
    513:     PetscCheck(ip>0,PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"The ip argument must be > 0");
    514:     PetscCheck(ip%2==0,PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"The ip argument must be an even number");
    515:     if (ctx->N!=ip) { ctx->N = ip; ctx->M = ctx->N/4; }
    516:   }
    517:   oL = ctx->L;
    518:   if (bs == PETSC_DETERMINE) {
    519:     ctx->L = 16;
    520:   } else if (bs != PETSC_CURRENT) {
    521:     PetscCheck(bs>0,PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"The bs argument must be > 0");
    522:     ctx->L = bs;
    523:   }
    524:   oM = ctx->M;
    525:   if (ms == PETSC_DETERMINE) {
    526:     ctx->M = ctx->N/4;
    527:   } else if (ms != PETSC_CURRENT) {
    528:     PetscCheck(ms>0,PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"The ms argument must be > 0");
    529:     PetscCheck(ms<=ctx->N,PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"The ms argument must be less than or equal to the number of integration points");
    530:     ctx->M = ms;
    531:   }
    532:   onpart = ctx->npart;
    533:   if (npart == PETSC_DETERMINE) {
    534:     ctx->npart = 1;
    535:   } else if (npart != PETSC_CURRENT) {
    536:     PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)nep),&size));
    537:     PetscCheck(npart>0 && npart<=size,PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"Illegal value of npart");
    538:     ctx->npart = npart;
    539:   }
    540:   oLmax = ctx->L_max;
    541:   if (bsmax == PETSC_DETERMINE) {
    542:     ctx->L_max = 64;
    543:   } else if (bsmax != PETSC_CURRENT) {
    544:     PetscCheck(bsmax>0,PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"The bsmax argument must be > 0");
    545:     ctx->L_max = PetscMax(bsmax,ctx->L);
    546:   }
    547:   if (onpart != ctx->npart || oN != ctx->N || realmats != ctx->isreal) {
    548:     PetscCall(SlepcContourDataDestroy(&ctx->contour));
    549:     PetscCall(PetscInfo(nep,"Resetting the contour data structure due to a change of parameters\n"));
    550:     nep->state = NEP_STATE_INITIAL;
    551:   }
    552:   ctx->isreal = realmats;
    553:   if (oL != ctx->L || oM != ctx->M || oLmax != ctx->L_max) nep->state = NEP_STATE_INITIAL;
    554:   PetscFunctionReturn(PETSC_SUCCESS);
    555: }

    557: /*@
    558:    NEPCISSSetSizes - Sets the values of various size parameters in the CISS solver.

    560:    Logically Collective

    562:    Input Parameters:
    563: +  nep      - the nonlinear eigensolver context
    564: .  ip       - number of integration points
    565: .  bs       - block size
    566: .  ms       - moment size
    567: .  npart    - number of partitions when splitting the communicator
    568: .  bsmax    - max block size
    569: -  realmats - $T(z)$ is real for real $z$

    571:    Options Database Keys:
    572: +  -nep_ciss_integration_points ip - sets the number of integration points
    573: .  -nep_ciss_blocksize bs          - sets the block size
    574: .  -nep_ciss_moments ms            - sets the moment size
    575: .  -nep_ciss_partitions npart      - sets the number of partitions
    576: .  -nep_ciss_maxblocksize bsmax    - sets the maximum block size
    577: -  -nep_ciss_realmats (true|false) - $T(z)$ is real for real $z$

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

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

    587:    The `realmats` flag can be set to `PETSC_TRUE` when $T(\cdot)$ is guaranteed to be real
    588:    when the argument is a real value, for example, when all matrices in
    589:    the split form are real. When set to `PETSC_TRUE`, the solver avoids some computations.

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

    593:    Level: advanced

    595: .seealso: [](ch:nep), `NEPCISS`, `NEPCISSGetSizes()`
    596: @*/
    597: PetscErrorCode NEPCISSSetSizes(NEP nep,PetscInt ip,PetscInt bs,PetscInt ms,PetscInt npart,PetscInt bsmax,PetscBool realmats)
    598: {
    599:   PetscFunctionBegin;
    607:   PetscTryMethod(nep,"NEPCISSSetSizes_C",(NEP,PetscInt,PetscInt,PetscInt,PetscInt,PetscInt,PetscBool),(nep,ip,bs,ms,npart,bsmax,realmats));
    608:   PetscFunctionReturn(PETSC_SUCCESS);
    609: }

    611: static PetscErrorCode NEPCISSGetSizes_CISS(NEP nep,PetscInt *ip,PetscInt *bs,PetscInt *ms,PetscInt *npart,PetscInt *bsmax,PetscBool *realmats)
    612: {
    613:   NEP_CISS *ctx = (NEP_CISS*)nep->data;

    615:   PetscFunctionBegin;
    616:   if (ip) *ip = ctx->N;
    617:   if (bs) *bs = ctx->L;
    618:   if (ms) *ms = ctx->M;
    619:   if (npart) *npart = ctx->npart;
    620:   if (bsmax) *bsmax = ctx->L_max;
    621:   if (realmats) *realmats = ctx->isreal;
    622:   PetscFunctionReturn(PETSC_SUCCESS);
    623: }

    625: /*@
    626:    NEPCISSGetSizes - Gets the values of various size parameters in the CISS solver.

    628:    Not Collective

    630:    Input Parameter:
    631: .  nep - the nonlinear eigensolver context

    633:    Output Parameters:
    634: +  ip       - number of integration points
    635: .  bs       - block size
    636: .  ms       - moment size
    637: .  npart    - number of partitions when splitting the communicator
    638: .  bsmax    - max block size
    639: -  realmats - $T(z)$ is real for real $z$

    641:    Level: advanced

    643: .seealso: [](ch:nep), `NEPCISS`, `NEPCISSSetSizes()`
    644: @*/
    645: PetscErrorCode NEPCISSGetSizes(NEP nep,PetscInt *ip,PetscInt *bs,PetscInt *ms,PetscInt *npart,PetscInt *bsmax,PetscBool *realmats)
    646: {
    647:   PetscFunctionBegin;
    649:   PetscUseMethod(nep,"NEPCISSGetSizes_C",(NEP,PetscInt*,PetscInt*,PetscInt*,PetscInt*,PetscInt*,PetscBool*),(nep,ip,bs,ms,npart,bsmax,realmats));
    650:   PetscFunctionReturn(PETSC_SUCCESS);
    651: }

    653: static PetscErrorCode NEPCISSSetThreshold_CISS(NEP nep,PetscReal delta,PetscReal spur)
    654: {
    655:   NEP_CISS *ctx = (NEP_CISS*)nep->data;

    657:   PetscFunctionBegin;
    658:   if (delta == (PetscReal)PETSC_DETERMINE) {
    659:     ctx->delta = SLEPC_DEFAULT_TOL*1e-4;
    660:   } else if (delta != (PetscReal)PETSC_CURRENT) {
    661:     PetscCheck(delta>0.0,PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"The delta argument must be > 0.0");
    662:     ctx->delta = delta;
    663:   }
    664:   if (spur == (PetscReal)PETSC_DETERMINE) {
    665:     ctx->spurious_threshold = PetscSqrtReal(SLEPC_DEFAULT_TOL);
    666:   } else if (spur != (PetscReal)PETSC_CURRENT) {
    667:     PetscCheck(spur>0.0,PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"The spurious threshold argument must be > 0.0");
    668:     ctx->spurious_threshold = spur;
    669:   }
    670:   PetscFunctionReturn(PETSC_SUCCESS);
    671: }

    673: /*@
    674:    NEPCISSSetThreshold - Sets the values of various threshold parameters in
    675:    the CISS solver.

    677:    Logically Collective

    679:    Input Parameters:
    680: +  nep   - the nonlinear eigensolver context
    681: .  delta - threshold for numerical rank
    682: -  spur  - spurious threshold (to discard spurious eigenpairs)

    684:    Options Database Keys:
    685: +  -nep_ciss_delta delta             - sets the delta
    686: -  -nep_ciss_spurious_threshold spur - sets the spurious threshold

    688:    Notes:
    689:    `PETSC_CURRENT` can be used to preserve the current value of any of the
    690:    arguments, and `PETSC_DETERMINE` to set them to a default value.

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

    694:    Level: advanced

    696: .seealso: [](ch:nep), `NEPCISS`, `NEPCISSGetThreshold()`
    697: @*/
    698: PetscErrorCode NEPCISSSetThreshold(NEP nep,PetscReal delta,PetscReal spur)
    699: {
    700:   PetscFunctionBegin;
    704:   PetscTryMethod(nep,"NEPCISSSetThreshold_C",(NEP,PetscReal,PetscReal),(nep,delta,spur));
    705:   PetscFunctionReturn(PETSC_SUCCESS);
    706: }

    708: static PetscErrorCode NEPCISSGetThreshold_CISS(NEP nep,PetscReal *delta,PetscReal *spur)
    709: {
    710:   NEP_CISS *ctx = (NEP_CISS*)nep->data;

    712:   PetscFunctionBegin;
    713:   if (delta) *delta = ctx->delta;
    714:   if (spur)  *spur = ctx->spurious_threshold;
    715:   PetscFunctionReturn(PETSC_SUCCESS);
    716: }

    718: /*@
    719:    NEPCISSGetThreshold - Gets the values of various threshold parameters in
    720:    the CISS solver.

    722:    Not Collective

    724:    Input Parameter:
    725: .  nep - the nonlinear eigensolver context

    727:    Output Parameters:
    728: +  delta - threshold for numerical rank
    729: -  spur  - spurious threshold (to discard spurious eigenpairs)

    731:    Level: advanced

    733: .seealso: [](ch:nep), `NEPCISS`, `NEPCISSSetThreshold()`
    734: @*/
    735: PetscErrorCode NEPCISSGetThreshold(NEP nep,PetscReal *delta,PetscReal *spur)
    736: {
    737:   PetscFunctionBegin;
    739:   PetscUseMethod(nep,"NEPCISSGetThreshold_C",(NEP,PetscReal*,PetscReal*),(nep,delta,spur));
    740:   PetscFunctionReturn(PETSC_SUCCESS);
    741: }

    743: static PetscErrorCode NEPCISSSetRefinement_CISS(NEP nep,PetscInt inner,PetscInt blsize)
    744: {
    745:   NEP_CISS *ctx = (NEP_CISS*)nep->data;

    747:   PetscFunctionBegin;
    748:   if (inner == PETSC_DETERMINE) {
    749:     ctx->refine_inner = 0;
    750:   } else if (inner != PETSC_CURRENT) {
    751:     PetscCheck(inner>=0,PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"The refine inner argument must be >= 0");
    752:     ctx->refine_inner = inner;
    753:   }
    754:   if (blsize == PETSC_DETERMINE) {
    755:     ctx->refine_blocksize = 0;
    756:   } else if (blsize != PETSC_CURRENT) {
    757:     PetscCheck(blsize>=0,PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"The refine blocksize argument must be >= 0");
    758:     ctx->refine_blocksize = blsize;
    759:   }
    760:   PetscFunctionReturn(PETSC_SUCCESS);
    761: }

    763: /*@
    764:    NEPCISSSetRefinement - Sets the values of various refinement parameters
    765:    in the CISS solver.

    767:    Logically Collective

    769:    Input Parameters:
    770: +  nep    - the nonlinear eigensolver context
    771: .  inner  - number of iterative refinement iterations (inner loop)
    772: -  blsize - number of iterative refinement iterations (blocksize loop)

    774:    Options Database Keys:
    775: +  -nep_ciss_refine_inner inner      - sets number of inner iterations
    776: -  -nep_ciss_refine_blocksize blsize - sets number of blocksize iterations

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

    782:    Level: advanced

    784: .seealso: [](ch:nep), `NEPCISS`, `NEPCISSGetRefinement()`
    785: @*/
    786: PetscErrorCode NEPCISSSetRefinement(NEP nep,PetscInt inner,PetscInt blsize)
    787: {
    788:   PetscFunctionBegin;
    792:   PetscTryMethod(nep,"NEPCISSSetRefinement_C",(NEP,PetscInt,PetscInt),(nep,inner,blsize));
    793:   PetscFunctionReturn(PETSC_SUCCESS);
    794: }

    796: static PetscErrorCode NEPCISSGetRefinement_CISS(NEP nep,PetscInt *inner,PetscInt *blsize)
    797: {
    798:   NEP_CISS *ctx = (NEP_CISS*)nep->data;

    800:   PetscFunctionBegin;
    801:   if (inner)  *inner = ctx->refine_inner;
    802:   if (blsize) *blsize = ctx->refine_blocksize;
    803:   PetscFunctionReturn(PETSC_SUCCESS);
    804: }

    806: /*@
    807:    NEPCISSGetRefinement - Gets the values of various refinement parameters
    808:    in the CISS solver.

    810:    Not Collective

    812:    Input Parameter:
    813: .  nep - the nonlinear eigensolver context

    815:    Output Parameters:
    816: +  inner  - number of iterative refinement iterations (inner loop)
    817: -  blsize - number of iterative refinement iterations (blocksize loop)

    819:    Level: advanced

    821: .seealso: [](ch:nep), `NEPCISS`, `NEPCISSSetRefinement()`
    822: @*/
    823: PetscErrorCode NEPCISSGetRefinement(NEP nep, PetscInt *inner, PetscInt *blsize)
    824: {
    825:   PetscFunctionBegin;
    827:   PetscUseMethod(nep,"NEPCISSGetRefinement_C",(NEP,PetscInt*,PetscInt*),(nep,inner,blsize));
    828:   PetscFunctionReturn(PETSC_SUCCESS);
    829: }

    831: static PetscErrorCode NEPCISSSetExtraction_CISS(NEP nep,NEPCISSExtraction extraction)
    832: {
    833:   NEP_CISS *ctx = (NEP_CISS*)nep->data;

    835:   PetscFunctionBegin;
    836:   if (ctx->extraction != extraction) {
    837:     ctx->extraction = extraction;
    838:     nep->state      = NEP_STATE_INITIAL;
    839:   }
    840:   PetscFunctionReturn(PETSC_SUCCESS);
    841: }

    843: /*@
    844:    NEPCISSSetExtraction - Sets the extraction technique used in the CISS solver.

    846:    Logically Collective

    848:    Input Parameters:
    849: +  nep        - the nonlinear eigensolver context
    850: -  extraction - the extraction technique, see `NEPCISSExtraction` for possible values

    852:    Options Database Key:
    853: .  -nep_ciss_extraction (ritz|hankel|caa) - sets the extraction technique

    855:    Notes:
    856:    By default, the Rayleigh-Ritz extraction is used (`NEP_CISS_EXTRACTION_RITZ`).

    858:    If the `hankel` or the `caa` option is specified (`NEP_CISS_EXTRACTION_HANKEL` or
    859:    `NEP_CISS_EXTRACTION_CAA`), then the block Hankel method, or the communication-avoiding
    860:    Arnoldi method, respectively, is used for extracting eigenpairs.

    862:    Level: advanced

    864: .seealso: [](ch:nep), `NEPCISS`, `NEPCISSGetExtraction()`, `NEPCISSExtraction`
    865: @*/
    866: PetscErrorCode NEPCISSSetExtraction(NEP nep,NEPCISSExtraction extraction)
    867: {
    868:   PetscFunctionBegin;
    871:   PetscTryMethod(nep,"NEPCISSSetExtraction_C",(NEP,NEPCISSExtraction),(nep,extraction));
    872:   PetscFunctionReturn(PETSC_SUCCESS);
    873: }

    875: static PetscErrorCode NEPCISSGetExtraction_CISS(NEP nep,NEPCISSExtraction *extraction)
    876: {
    877:   NEP_CISS *ctx = (NEP_CISS*)nep->data;

    879:   PetscFunctionBegin;
    880:   *extraction = ctx->extraction;
    881:   PetscFunctionReturn(PETSC_SUCCESS);
    882: }

    884: /*@
    885:    NEPCISSGetExtraction - Gets the extraction technique used in the CISS solver.

    887:    Not Collective

    889:    Input Parameter:
    890: .  nep - the nonlinear eigensolver context

    892:    Output Parameter:
    893: .  extraction - extraction technique

    895:    Level: advanced

    897: .seealso: [](ch:nep), `NEPCISS`, `NEPCISSSetExtraction()`, `NEPCISSExtraction`
    898: @*/
    899: PetscErrorCode NEPCISSGetExtraction(NEP nep,NEPCISSExtraction *extraction)
    900: {
    901:   PetscFunctionBegin;
    903:   PetscAssertPointer(extraction,2);
    904:   PetscUseMethod(nep,"NEPCISSGetExtraction_C",(NEP,NEPCISSExtraction*),(nep,extraction));
    905:   PetscFunctionReturn(PETSC_SUCCESS);
    906: }

    908: static PetscErrorCode NEPCISSGetKSPs_CISS(NEP nep,PetscInt *nsolve,KSP **ksp)
    909: {
    910:   NEP_CISS         *ctx = (NEP_CISS*)nep->data;
    911:   SlepcContourData contour;
    912:   PetscInt         i;
    913:   PC               pc;
    914:   MPI_Comm         child;

    916:   PetscFunctionBegin;
    917:   if (!ctx->contour) {  /* initialize contour data structure first */
    918:     PetscCall(RGCanUseConjugates(nep->rg,ctx->isreal,&ctx->useconj));
    919:     PetscCall(SlepcContourDataCreate(ctx->useconj?ctx->N/2:ctx->N,ctx->npart,(PetscObject)nep,&ctx->contour));
    920:   }
    921:   contour = ctx->contour;
    922:   if (!contour->ksp) {
    923:     PetscCall(PetscMalloc1(contour->npoints,&contour->ksp));
    924:     PetscCall(PetscSubcommGetChild(contour->subcomm,&child));
    925:     for (i=0;i<contour->npoints;i++) {
    926:       PetscCall(KSPCreate(child,&contour->ksp[i]));
    927:       PetscCall(PetscObjectIncrementTabLevel((PetscObject)contour->ksp[i],(PetscObject)nep,1));
    928:       PetscCall(KSPSetOptionsPrefix(contour->ksp[i],((PetscObject)nep)->prefix));
    929:       PetscCall(KSPAppendOptionsPrefix(contour->ksp[i],"nep_ciss_"));
    930:       PetscCall(PetscObjectSetOptions((PetscObject)contour->ksp[i],((PetscObject)nep)->options));
    931:       PetscCall(KSPSetErrorIfNotConverged(contour->ksp[i],PETSC_TRUE));
    932:       PetscCall(KSPSetTolerances(contour->ksp[i],SlepcDefaultTol(nep->tol),PETSC_CURRENT,PETSC_CURRENT,PETSC_CURRENT));
    933:       PetscCall(KSPGetPC(contour->ksp[i],&pc));
    934:       if ((nep->fui==NEP_USER_INTERFACE_SPLIT && nep->P) || (nep->fui==NEP_USER_INTERFACE_CALLBACK && nep->function_pre!=nep->function)) {
    935:         PetscCall(KSPSetType(contour->ksp[i],KSPBCGS));
    936:         PetscCall(PCSetType(pc,PCBJACOBI));
    937:       } else {
    938:         PetscCall(KSPSetType(contour->ksp[i],KSPPREONLY));
    939:         PetscCall(PCSetType(pc,PCLU));
    940:       }
    941:     }
    942:   }
    943:   if (nsolve) *nsolve = contour->npoints;
    944:   if (ksp)    *ksp    = contour->ksp;
    945:   PetscFunctionReturn(PETSC_SUCCESS);
    946: }

    948: /*@C
    949:    NEPCISSGetKSPs - Retrieve the array of linear solver objects associated with
    950:    the CISS solver.

    952:    Collective

    954:    Input Parameter:
    955: .  nep - the nonlinear eigensolver context

    957:    Output Parameters:
    958: +  nsolve - number of solver objects
    959: -  ksp - array of linear solver object

    961:    Notes:
    962:    The number of `KSP` solvers is equal to the number of integration points divided by
    963:    the number of partitions. This value is halved in the case of real matrices with
    964:    a region centered at the real axis.

    966:    Level: advanced

    968: .seealso: [](ch:nep), `NEPCISS`, `NEPCISSSetSizes()`
    969: @*/
    970: PetscErrorCode NEPCISSGetKSPs(NEP nep,PetscInt *nsolve,KSP **ksp)
    971: {
    972:   PetscFunctionBegin;
    974:   PetscUseMethod(nep,"NEPCISSGetKSPs_C",(NEP,PetscInt*,KSP**),(nep,nsolve,ksp));
    975:   PetscFunctionReturn(PETSC_SUCCESS);
    976: }

    978: static PetscErrorCode NEPReset_CISS(NEP nep)
    979: {
    980:   NEP_CISS       *ctx = (NEP_CISS*)nep->data;

    982:   PetscFunctionBegin;
    983:   PetscCall(BVDestroy(&ctx->S));
    984:   PetscCall(BVDestroy(&ctx->V));
    985:   PetscCall(BVDestroy(&ctx->Y));
    986:   PetscCall(SlepcContourDataReset(ctx->contour));
    987:   PetscCall(MatDestroy(&ctx->J));
    988:   PetscCall(BVDestroy(&ctx->pV));
    989:   PetscFunctionReturn(PETSC_SUCCESS);
    990: }

    992: static PetscErrorCode NEPSetFromOptions_CISS(NEP nep,PetscOptionItems PetscOptionsObject)
    993: {
    994:   NEP_CISS          *ctx = (NEP_CISS*)nep->data;
    995:   PetscReal         r1,r2;
    996:   PetscInt          i,i1,i2,i3,i4,i5,i6,i7;
    997:   PetscBool         b1,flg,flg2,flg3,flg4,flg5,flg6;
    998:   NEPCISSExtraction extraction;

    1000:   PetscFunctionBegin;
    1001:   PetscOptionsHeadBegin(PetscOptionsObject,"NEP CISS Options");

    1003:     PetscCall(NEPCISSGetSizes(nep,&i1,&i2,&i3,&i4,&i5,&b1));
    1004:     PetscCall(PetscOptionsInt("-nep_ciss_integration_points","Number of integration points","NEPCISSSetSizes",i1,&i1,&flg));
    1005:     PetscCall(PetscOptionsInt("-nep_ciss_blocksize","Block size","NEPCISSSetSizes",i2,&i2,&flg2));
    1006:     PetscCall(PetscOptionsInt("-nep_ciss_moments","Moment size","NEPCISSSetSizes",i3,&i3,&flg3));
    1007:     PetscCall(PetscOptionsInt("-nep_ciss_partitions","Number of partitions","NEPCISSSetSizes",i4,&i4,&flg4));
    1008:     PetscCall(PetscOptionsInt("-nep_ciss_maxblocksize","Maximum block size","NEPCISSSetSizes",i5,&i5,&flg5));
    1009:     PetscCall(PetscOptionsBool("-nep_ciss_realmats","True if T(z) is real for real z","NEPCISSSetSizes",b1,&b1,&flg6));
    1010:     if (flg || flg2 || flg3 || flg4 || flg5 || flg6) PetscCall(NEPCISSSetSizes(nep,i1,i2,i3,i4,i5,b1));

    1012:     PetscCall(NEPCISSGetThreshold(nep,&r1,&r2));
    1013:     PetscCall(PetscOptionsReal("-nep_ciss_delta","Threshold for numerical rank","NEPCISSSetThreshold",r1,&r1,&flg));
    1014:     PetscCall(PetscOptionsReal("-nep_ciss_spurious_threshold","Threshold for the spurious eigenpairs","NEPCISSSetThreshold",r2,&r2,&flg2));
    1015:     if (flg || flg2) PetscCall(NEPCISSSetThreshold(nep,r1,r2));

    1017:     PetscCall(NEPCISSGetRefinement(nep,&i6,&i7));
    1018:     PetscCall(PetscOptionsInt("-nep_ciss_refine_inner","Number of inner iterative refinement iterations","NEPCISSSetRefinement",i6,&i6,&flg));
    1019:     PetscCall(PetscOptionsInt("-nep_ciss_refine_blocksize","Number of blocksize iterative refinement iterations","NEPCISSSetRefinement",i7,&i7,&flg2));
    1020:     if (flg || flg2) PetscCall(NEPCISSSetRefinement(nep,i6,i7));

    1022:     PetscCall(PetscOptionsEnum("-nep_ciss_extraction","Extraction technique","NEPCISSSetExtraction",NEPCISSExtractions,(PetscEnum)ctx->extraction,(PetscEnum*)&extraction,&flg));
    1023:     if (flg) PetscCall(NEPCISSSetExtraction(nep,extraction));

    1025:   PetscOptionsHeadEnd();

    1027:   if (!nep->rg) PetscCall(NEPGetRG(nep,&nep->rg));
    1028:   PetscCall(RGSetFromOptions(nep->rg)); /* this is necessary here to set useconj */
    1029:   if (!ctx->contour || !ctx->contour->ksp) PetscCall(NEPCISSGetKSPs(nep,NULL,NULL));
    1030:   PetscAssert(ctx->contour && ctx->contour->ksp,PetscObjectComm((PetscObject)nep),PETSC_ERR_PLIB,"Something went wrong with NEPCISSGetKSPs()");
    1031:   for (i=0;i<ctx->contour->npoints;i++) PetscCall(KSPSetFromOptions(ctx->contour->ksp[i]));
    1032:   PetscCall(PetscSubcommSetFromOptions(ctx->contour->subcomm));
    1033:   PetscFunctionReturn(PETSC_SUCCESS);
    1034: }

    1036: static PetscErrorCode NEPDestroy_CISS(NEP nep)
    1037: {
    1038:   NEP_CISS       *ctx = (NEP_CISS*)nep->data;

    1040:   PetscFunctionBegin;
    1041:   PetscCall(SlepcContourDataDestroy(&ctx->contour));
    1042:   PetscCall(PetscFree4(ctx->weight,ctx->omega,ctx->pp,ctx->sigma));
    1043:   PetscCall(PetscFree(nep->data));
    1044:   PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSSetSizes_C",NULL));
    1045:   PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSGetSizes_C",NULL));
    1046:   PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSSetThreshold_C",NULL));
    1047:   PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSGetThreshold_C",NULL));
    1048:   PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSSetRefinement_C",NULL));
    1049:   PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSGetRefinement_C",NULL));
    1050:   PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSSetExtraction_C",NULL));
    1051:   PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSGetExtraction_C",NULL));
    1052:   PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSGetKSPs_C",NULL));
    1053:   PetscFunctionReturn(PETSC_SUCCESS);
    1054: }

    1056: static PetscErrorCode NEPView_CISS(NEP nep,PetscViewer viewer)
    1057: {
    1058:   NEP_CISS       *ctx = (NEP_CISS*)nep->data;
    1059:   PetscBool      isascii;
    1060:   PetscViewer    sviewer;

    1062:   PetscFunctionBegin;
    1063:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii));
    1064:   if (isascii) {
    1065:     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));
    1066:     if (ctx->isreal) PetscCall(PetscViewerASCIIPrintf(viewer,"  exploiting symmetry of integration points\n"));
    1067:     PetscCall(PetscViewerASCIIPrintf(viewer,"  threshold { delta: %g, spurious threshold: %g }\n",(double)ctx->delta,(double)ctx->spurious_threshold));
    1068:     PetscCall(PetscViewerASCIIPrintf(viewer,"  iterative refinement  { inner: %" PetscInt_FMT ", blocksize: %" PetscInt_FMT " }\n",ctx->refine_inner, ctx->refine_blocksize));
    1069:     PetscCall(PetscViewerASCIIPrintf(viewer,"  extraction: %s\n",NEPCISSExtractions[ctx->extraction]));
    1070:     if (!ctx->contour || !ctx->contour->ksp) PetscCall(NEPCISSGetKSPs(nep,NULL,NULL));
    1071:     PetscAssert(ctx->contour && ctx->contour->ksp,PetscObjectComm((PetscObject)nep),PETSC_ERR_PLIB,"Something went wrong with NEPCISSGetKSPs()");
    1072:     PetscCall(PetscViewerASCIIPushTab(viewer));
    1073:     if (ctx->npart>1 && ctx->contour->subcomm) {
    1074:       PetscCall(PetscViewerGetSubViewer(viewer,ctx->contour->subcomm->child,&sviewer));
    1075:       if (!ctx->contour->subcomm->color) PetscCall(KSPView(ctx->contour->ksp[0],sviewer));
    1076:       PetscCall(PetscViewerFlush(sviewer));
    1077:       PetscCall(PetscViewerRestoreSubViewer(viewer,ctx->contour->subcomm->child,&sviewer));
    1078:       /* extra call needed because of the two calls to PetscViewerASCIIPushSynchronized() in PetscViewerGetSubViewer() */
    1079:       PetscCall(PetscViewerASCIIPopSynchronized(viewer));
    1080:     } else PetscCall(KSPView(ctx->contour->ksp[0],viewer));
    1081:     PetscCall(PetscViewerASCIIPopTab(viewer));
    1082:   }
    1083:   PetscFunctionReturn(PETSC_SUCCESS);
    1084: }

    1086: static PetscErrorCode NEPSetDSType_CISS(NEP nep)
    1087: {
    1088:   NEP_CISS       *ctx = (NEP_CISS*)nep->data;

    1090:   PetscFunctionBegin;
    1091:   switch (ctx->extraction) {
    1092:     case NEP_CISS_EXTRACTION_RITZ:   PetscCall(DSSetType(nep->ds,DSNEP)); break;
    1093:     case NEP_CISS_EXTRACTION_HANKEL: PetscCall(DSSetType(nep->ds,DSGNHEP)); break;
    1094:     case NEP_CISS_EXTRACTION_CAA:    PetscCall(DSSetType(nep->ds,DSNHEP)); break;
    1095:   }
    1096:   PetscFunctionReturn(PETSC_SUCCESS);
    1097: }

    1099: /*MC
    1100:    NEPCISS - NEPCISS = "ciss" - A contour integral eigensolver based on the
    1101:    Sakurai-Sugiura scheme.

    1103:    Notes:
    1104:    This solver is based on the numerical contour integration idea
    1105:    proposed initially for linear problems by {cite:t}`Sak03`. In nonlinear
    1106:    eigenproblems, a Rayleigh-Ritz projection is done, resulting in
    1107:    a small dense nonlinear eigenproblem {cite:p}`Asa09,Yok13`.

    1109:    Contour integral methods are able to compute all eigenvalues
    1110:    lying inside a region of the complex plane. Use `NEPGetRG()` to
    1111:    specify the region. However, the computational cost is usually high
    1112:    because multiple linear systems must be solved. Use `NEPCISSGetKSPs()`
    1113:    to configure the `KSP` objects for this.

    1115:    Details of the implementation in SLEPc can be found in {cite:p}`Mae16`.

    1117:    Level: beginner

    1119: .seealso: [](ch:nep), `NEP`, `NEPType`, `NEPSetType()`, `NEPGetRG()`
    1120: M*/
    1121: SLEPC_EXTERN PetscErrorCode NEPCreate_CISS(NEP nep)
    1122: {
    1123:   NEP_CISS       *ctx = (NEP_CISS*)nep->data;

    1125:   PetscFunctionBegin;
    1126:   PetscCall(PetscNew(&ctx));
    1127:   nep->data = ctx;
    1128:   /* set default values of parameters */
    1129:   ctx->N                  = 32;
    1130:   ctx->L                  = 16;
    1131:   ctx->M                  = ctx->N/4;
    1132:   ctx->delta              = SLEPC_DEFAULT_TOL*1e-4;
    1133:   ctx->L_max              = 64;
    1134:   ctx->spurious_threshold = PetscSqrtReal(SLEPC_DEFAULT_TOL);
    1135:   ctx->isreal             = PETSC_FALSE;
    1136:   ctx->npart              = 1;

    1138:   nep->useds = PETSC_TRUE;

    1140:   nep->ops->solve          = NEPSolve_CISS;
    1141:   nep->ops->setup          = NEPSetUp_CISS;
    1142:   nep->ops->setfromoptions = NEPSetFromOptions_CISS;
    1143:   nep->ops->reset          = NEPReset_CISS;
    1144:   nep->ops->destroy        = NEPDestroy_CISS;
    1145:   nep->ops->view           = NEPView_CISS;
    1146:   nep->ops->setdstype      = NEPSetDSType_CISS;

    1148:   PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSSetSizes_C",NEPCISSSetSizes_CISS));
    1149:   PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSGetSizes_C",NEPCISSGetSizes_CISS));
    1150:   PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSSetThreshold_C",NEPCISSSetThreshold_CISS));
    1151:   PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSGetThreshold_C",NEPCISSGetThreshold_CISS));
    1152:   PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSSetRefinement_C",NEPCISSSetRefinement_CISS));
    1153:   PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSGetRefinement_C",NEPCISSGetRefinement_CISS));
    1154:   PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSSetExtraction_C",NEPCISSSetExtraction_CISS));
    1155:   PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSGetExtraction_C",NEPCISSGetExtraction_CISS));
    1156:   PetscCall(PetscObjectComposeFunction((PetscObject)nep,"NEPCISSGetKSPs_C",NEPCISSGetKSPs_CISS));
    1157:   PetscFunctionReturn(PETSC_SUCCESS);
    1158: }