Date: 2026-05-01T10:02:36+00:00

Actual source code: ciss.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] T. Sakurai and H. Sugiura, "A projection method for generalized
     26:            eigenvalue problems", J. Comput. Appl. Math. 159:119-128, 2003.

     28:        [2] T. Sakurai and H. Tadano, "CIRR: a Rayleigh-Ritz type method with
     29:            contour integral for generalized eigenvalue problems", Hokkaido
     30:            Math. J. 36:745-757, 2007.
     31: */

     33: #include <slepc/private/epsimpl.h>
     34: #include <slepc/private/slepccontour.h>
     35: #include <slepcblaslapack.h>

     37: typedef struct {
     38:   /* user parameters */
     39:   PetscInt          N;          /* number of integration points (32) */
     40:   PetscInt          L;          /* block size (16) */
     41:   PetscInt          M;          /* moment degree (N/4 = 4) */
     42:   PetscReal         delta;      /* threshold of singular value (1e-12) */
     43:   PetscInt          L_max;      /* maximum number of columns of the source matrix V */
     44:   PetscReal         spurious_threshold; /* discard spurious eigenpairs */
     45:   PetscBool         isreal;     /* A and B are real */
     46:   PetscInt          npart;      /* number of partitions */
     47:   PetscInt          refine_inner;
     48:   PetscInt          refine_blocksize;
     49:   EPSCISSQuadRule   quad;
     50:   EPSCISSExtraction extraction;
     51:   PetscBool         usest;
     52:   /* private data */
     53:   SlepcContourData  contour;
     54:   PetscReal         *sigma;     /* threshold for numerical rank */
     55:   PetscScalar       *weight;
     56:   PetscScalar       *omega;
     57:   PetscScalar       *pp;
     58:   BV                V;
     59:   BV                S;
     60:   BV                pV;
     61:   BV                Y;
     62:   PetscBool         useconj;
     63:   PetscBool         usest_set;  /* whether the user set the usest flag or not */
     64:   PetscObjectId     rgid;
     65:   PetscObjectState  rgstate;
     66: } EPS_CISS;

     68: /*
     69:   Set up KSP solvers for every integration point, only called if !ctx->usest
     70: */
     71: static PetscErrorCode EPSCISSSetUp(EPS eps,Mat A,Mat B,Mat Pa,Mat Pb)
     72: {
     73:   EPS_CISS         *ctx = (EPS_CISS*)eps->data;
     74:   SlepcContourData contour;
     75:   PetscInt         i,p_id,nsplit;
     76:   Mat              Amat,Pmat;
     77:   MatStructure     str,strp;

     79:   PetscFunctionBegin;
     80:   if (!ctx->contour || !ctx->contour->ksp) PetscCall(EPSCISSGetKSPs(eps,NULL,NULL));
     81:   PetscAssert(ctx->contour && ctx->contour->ksp,PetscObjectComm((PetscObject)eps),PETSC_ERR_PLIB,"Something went wrong with EPSCISSGetKSPs()");
     82:   contour = ctx->contour;
     83:   PetscCall(STGetMatStructure(eps->st,&str));
     84:   PetscCall(STGetSplitPreconditionerInfo(eps->st,&nsplit,&strp));
     85:   for (i=0;i<contour->npoints;i++) {
     86:     p_id = i*contour->subcomm->n + contour->subcomm->color;
     87:     PetscCall(MatDuplicate(A,MAT_COPY_VALUES,&Amat));
     88:     if (B) PetscCall(MatAXPY(Amat,-ctx->omega[p_id],B,str));
     89:     else PetscCall(MatShift(Amat,-ctx->omega[p_id]));
     90:     if (nsplit) {
     91:       PetscCall(MatDuplicate(Pa,MAT_COPY_VALUES,&Pmat));
     92:       if (Pb) PetscCall(MatAXPY(Pmat,-ctx->omega[p_id],Pb,strp));
     93:       else PetscCall(MatShift(Pmat,-ctx->omega[p_id]));
     94:     } else Pmat = Amat;
     95:     PetscCall(EPS_KSPSetOperators(contour->ksp[i],Amat,Amat));
     96:     PetscCall(MatDestroy(&Amat));
     97:     if (nsplit) PetscCall(MatDestroy(&Pmat));
     98:   }
     99:   PetscFunctionReturn(PETSC_SUCCESS);
    100: }

    102: /*
    103:   Y_i = (A-z_i B)^{-1}BV for every integration point, Y=[Y_i] is in the context
    104: */
    105: static PetscErrorCode EPSCISSSolve(EPS eps,Mat B,BV V,PetscInt L_start,PetscInt L_end)
    106: {
    107:   EPS_CISS         *ctx = (EPS_CISS*)eps->data;
    108:   SlepcContourData contour;
    109:   PetscInt         i,p_id;
    110:   Mat              MV,BMV=NULL,MC;
    111:   KSP              ksp;

    113:   PetscFunctionBegin;
    114:   if (!ctx->contour || !ctx->contour->ksp) PetscCall(EPSCISSGetKSPs(eps,NULL,NULL));
    115:   contour = ctx->contour;
    116:   PetscAssert(ctx->contour && ctx->contour->ksp,PetscObjectComm((PetscObject)eps),PETSC_ERR_PLIB,"Something went wrong with EPSCISSGetKSPs()");
    117:   PetscCall(BVSetActiveColumns(V,L_start,L_end));
    118:   PetscCall(BVGetMat(V,&MV));
    119:   for (i=0;i<contour->npoints;i++) {
    120:     p_id = i*contour->subcomm->n + contour->subcomm->color;
    121:     if (ctx->usest)  {
    122:       PetscCall(STSetShift(eps->st,ctx->omega[p_id]));
    123:       PetscCall(STGetKSP(eps->st,&ksp));
    124:     } else ksp = contour->ksp[i];
    125:     PetscCall(BVSetActiveColumns(ctx->Y,i*ctx->L+L_start,i*ctx->L+L_end));
    126:     PetscCall(BVGetMat(ctx->Y,&MC));
    127:     if (B) {
    128:       if (!i) {
    129:         PetscCall(MatProductCreate(B,MV,NULL,&BMV));
    130:         PetscCall(MatProductSetType(BMV,MATPRODUCT_AB));
    131:         PetscCall(MatProductSetFromOptions(BMV));
    132:         PetscCall(MatProductSymbolic(BMV));
    133:       }
    134:       PetscCall(MatProductNumeric(BMV));
    135:       PetscCall(KSPMatSolve(ksp,BMV,MC));
    136:     } else PetscCall(KSPMatSolve(ksp,MV,MC));
    137:     PetscCall(BVRestoreMat(ctx->Y,&MC));
    138:     if (ctx->usest && i<contour->npoints-1) PetscCall(KSPReset(ksp));
    139:   }
    140:   PetscCall(MatDestroy(&BMV));
    141:   PetscCall(BVRestoreMat(V,&MV));
    142:   PetscFunctionReturn(PETSC_SUCCESS);
    143: }

    145: static PetscErrorCode rescale_eig(EPS eps,PetscInt nv)
    146: {
    147:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    148:   PetscInt       i;
    149:   PetscScalar    center;
    150:   PetscReal      radius,a,b,c,d,rgscale;
    151: #if defined(PETSC_USE_COMPLEX)
    152:   PetscReal      start_ang,end_ang,vscale,theta;
    153: #endif
    154:   PetscBool      isring,isellipse,isinterval;

    156:   PetscFunctionBegin;
    157:   PetscCall(PetscObjectTypeCompare((PetscObject)eps->rg,RGELLIPSE,&isellipse));
    158:   PetscCall(PetscObjectTypeCompare((PetscObject)eps->rg,RGRING,&isring));
    159:   PetscCall(PetscObjectTypeCompare((PetscObject)eps->rg,RGINTERVAL,&isinterval));
    160:   PetscCall(RGGetScale(eps->rg,&rgscale));
    161:   if (isinterval) {
    162:     PetscCall(RGIntervalGetEndpoints(eps->rg,NULL,NULL,&c,&d));
    163:     if (c==d) {
    164:       for (i=0;i<nv;i++) {
    165: #if defined(PETSC_USE_COMPLEX)
    166:         eps->eigr[i] = PetscRealPart(eps->eigr[i]);
    167: #else
    168:         eps->eigi[i] = 0;
    169: #endif
    170:       }
    171:     }
    172:   }
    173:   if (ctx->extraction == EPS_CISS_EXTRACTION_HANKEL) {
    174:     if (isellipse) {
    175:       PetscCall(RGEllipseGetParameters(eps->rg,&center,&radius,NULL));
    176:       for (i=0;i<nv;i++) eps->eigr[i] = rgscale*(center + radius*eps->eigr[i]);
    177:     } else if (isinterval) {
    178:       PetscCall(RGIntervalGetEndpoints(eps->rg,&a,&b,&c,&d));
    179:       if (ctx->quad == EPS_CISS_QUADRULE_CHEBYSHEV) {
    180:         for (i=0;i<nv;i++) {
    181:           if (c==d) eps->eigr[i] = ((eps->eigr[i]+1.0)*(b-a)/2.0+a)*rgscale;
    182:           if (a==b) {
    183: #if defined(PETSC_USE_COMPLEX)
    184:             eps->eigr[i] = ((eps->eigr[i]+1.0)*(d-c)/2.0+c)*rgscale*PETSC_i;
    185: #else
    186:             SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Integration points on a vertical line require complex arithmetic");
    187: #endif
    188:           }
    189:         }
    190:       } else {
    191:         center = (b+a)/2.0+(d+c)/2.0*PETSC_PI;
    192:         radius = PetscSqrtReal(PetscPowRealInt((b-a)/2.0,2)+PetscPowRealInt((d-c)/2.0,2));
    193:         for (i=0;i<nv;i++) eps->eigr[i] = center + radius*eps->eigr[i];
    194:       }
    195:     } else if (isring) {  /* only supported in complex scalars */
    196: #if defined(PETSC_USE_COMPLEX)
    197:       PetscCall(RGRingGetParameters(eps->rg,&center,&radius,&vscale,&start_ang,&end_ang,NULL));
    198:       if (ctx->quad == EPS_CISS_QUADRULE_CHEBYSHEV) {
    199:         for (i=0;i<nv;i++) {
    200:           theta = (start_ang*2.0+(end_ang-start_ang)*(PetscRealPart(eps->eigr[i])+1.0))*PETSC_PI;
    201:           eps->eigr[i] = rgscale*center + (rgscale*radius+PetscImaginaryPart(eps->eigr[i]))*PetscCMPLX(PetscCosReal(theta),vscale*PetscSinReal(theta));
    202:         }
    203:       } else {
    204:         for (i=0;i<nv;i++) eps->eigr[i] = rgscale*(center + radius*eps->eigr[i]);
    205:       }
    206: #endif
    207:     }
    208:   }
    209:   PetscFunctionReturn(PETSC_SUCCESS);
    210: }

    212: static PetscErrorCode EPSSetUp_CISS(EPS eps)
    213: {
    214:   EPS_CISS         *ctx = (EPS_CISS*)eps->data;
    215:   SlepcContourData contour;
    216:   PetscBool        istrivial,isring,isellipse,isinterval,flg;
    217:   PetscReal        c,d;
    218:   PetscInt         nsplit;
    219:   PetscRandom      rand;
    220:   PetscObjectId    id;
    221:   PetscObjectState state;
    222:   Mat              A[2],Psplit[2];
    223:   Vec              v0;

    225:   PetscFunctionBegin;
    226:   EPSCheckNotStructured(eps);
    227:   if (eps->ncv==PETSC_DETERMINE) {
    228:     eps->ncv = ctx->L_max*ctx->M;
    229:     if (eps->ncv>eps->n) {
    230:       eps->ncv = eps->n;
    231:       ctx->L_max = eps->ncv/ctx->M;
    232:       PetscCheck(ctx->L_max,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Cannot adjust solver parameters, try setting a smaller value of M (moment size)");
    233:     }
    234:   } else {
    235:     PetscCall(EPSSetDimensions_Default(eps,&eps->nev,&eps->ncv,&eps->mpd));
    236:     ctx->L_max = eps->ncv/ctx->M;
    237:     if (!ctx->L_max) {
    238:       ctx->L_max = 1;
    239:       eps->ncv = ctx->L_max*ctx->M;
    240:     }
    241:   }
    242:   ctx->L = PetscMin(ctx->L,ctx->L_max);
    243:   if (eps->max_it==PETSC_DETERMINE) eps->max_it = 5;
    244:   if (eps->mpd==PETSC_DETERMINE) eps->mpd = eps->ncv;
    245:   if (!eps->which) eps->which = EPS_ALL;
    246:   PetscCheck(eps->which==EPS_ALL,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"This solver supports only computing all eigenvalues");
    247:   EPSCheckUnsupported(eps,EPS_FEATURE_BALANCE | EPS_FEATURE_ARBITRARY | EPS_FEATURE_EXTRACTION | EPS_FEATURE_STOPPING | EPS_FEATURE_TWOSIDED);

    249:   /* check region */
    250:   PetscCall(RGIsTrivial(eps->rg,&istrivial));
    251:   PetscCheck(!istrivial,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"CISS requires a nontrivial region, e.g. -rg_type ellipse ...");
    252:   PetscCall(RGGetComplement(eps->rg,&flg));
    253:   PetscCheck(!flg,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"A region with complement flag set is not allowed");
    254:   PetscCall(PetscObjectTypeCompare((PetscObject)eps->rg,RGELLIPSE,&isellipse));
    255:   PetscCall(PetscObjectTypeCompare((PetscObject)eps->rg,RGRING,&isring));
    256:   PetscCall(PetscObjectTypeCompare((PetscObject)eps->rg,RGINTERVAL,&isinterval));
    257:   PetscCheck(isellipse || isring || isinterval,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Currently only implemented for interval, elliptic or ring regions");

    259:   /* if the region has changed, then reset contour data */
    260:   PetscCall(PetscObjectGetId((PetscObject)eps->rg,&id));
    261:   PetscCall(PetscObjectStateGet((PetscObject)eps->rg,&state));
    262:   if (ctx->rgid && (id != ctx->rgid || state != ctx->rgstate)) {
    263:     PetscCall(SlepcContourDataDestroy(&ctx->contour));
    264:     PetscCall(PetscInfo(eps,"Resetting the contour data structure due to a change of region\n"));
    265:     ctx->rgid = id; ctx->rgstate = state;
    266:   }

    268: #if !defined(PETSC_USE_COMPLEX)
    269:   PetscCheck(!isring,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Ring region only supported for complex scalars");
    270: #endif
    271:   if (isinterval) {
    272:     PetscCall(RGIntervalGetEndpoints(eps->rg,NULL,NULL,&c,&d));
    273: #if !defined(PETSC_USE_COMPLEX)
    274:     PetscCheck(c==d && c==0.0,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"In real scalars, endpoints of the imaginary axis must be both zero");
    275: #endif
    276:     if (!ctx->quad && c==d) ctx->quad = EPS_CISS_QUADRULE_CHEBYSHEV;
    277:   }
    278:   if (!ctx->quad) ctx->quad = EPS_CISS_QUADRULE_TRAPEZOIDAL;

    280:   /* create contour data structure */
    281:   if (!ctx->contour) {
    282:     PetscCall(RGCanUseConjugates(eps->rg,ctx->isreal,&ctx->useconj));
    283:     PetscCall(SlepcContourDataCreate(ctx->useconj?ctx->N/2:ctx->N,ctx->npart,(PetscObject)eps,&ctx->contour));
    284:   }

    286:   PetscCall(EPSAllocateSolution(eps,0));
    287:   PetscCall(BVGetRandomContext(eps->V,&rand));  /* make sure the random context is available when duplicating */
    288:   if (ctx->weight) PetscCall(PetscFree4(ctx->weight,ctx->omega,ctx->pp,ctx->sigma));
    289:   PetscCall(PetscMalloc4(ctx->N,&ctx->weight,ctx->N+1,&ctx->omega,ctx->N,&ctx->pp,ctx->L_max*ctx->M,&ctx->sigma));

    291:   /* allocate basis vectors */
    292:   PetscCall(BVDestroy(&ctx->S));
    293:   PetscCall(BVDuplicateResize(eps->V,ctx->L*ctx->M,&ctx->S));
    294:   PetscCall(BVDestroy(&ctx->V));
    295:   PetscCall(BVDuplicateResize(eps->V,ctx->L,&ctx->V));

    297:   PetscCall(STGetMatrix(eps->st,0,&A[0]));
    298:   PetscCall(MatIsShell(A[0],&flg));
    299:   PetscCheck(!flg,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Matrix type shell is not supported in this solver");
    300:   if (eps->isgeneralized) PetscCall(STGetMatrix(eps->st,1,&A[1]));

    302:   if (!ctx->usest_set) ctx->usest = (ctx->npart>1)? PETSC_FALSE: PETSC_TRUE;
    303:   PetscCheck(!ctx->usest || ctx->npart==1,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"The usest flag is not supported when partitions > 1");

    305:   /* check if a user-defined split preconditioner has been set */
    306:   PetscCall(STGetSplitPreconditionerInfo(eps->st,&nsplit,NULL));
    307:   if (nsplit) {
    308:     PetscCall(STGetSplitPreconditionerTerm(eps->st,0,&Psplit[0]));
    309:     if (eps->isgeneralized) PetscCall(STGetSplitPreconditionerTerm(eps->st,1,&Psplit[1]));
    310:   }

    312:   contour = ctx->contour;
    313:   PetscCall(SlepcContourRedundantMat(contour,eps->isgeneralized?2:1,A,nsplit?Psplit:NULL));
    314:   if (contour->pA) {
    315:     PetscCall(BVGetColumn(ctx->V,0,&v0));
    316:     PetscCall(SlepcContourScatterCreate(contour,v0));
    317:     PetscCall(BVRestoreColumn(ctx->V,0,&v0));
    318:     PetscCall(BVDestroy(&ctx->pV));
    319:     PetscCall(BVCreate(PetscObjectComm((PetscObject)contour->xsub),&ctx->pV));
    320:     PetscCall(BVSetSizesFromVec(ctx->pV,contour->xsub,eps->n));
    321:     PetscCall(BVSetFromOptions(ctx->pV));
    322:     PetscCall(BVResize(ctx->pV,ctx->L,PETSC_FALSE));
    323:   }

    325:   EPSCheckDefinite(eps);
    326:   EPSCheckSinvertCondition(eps,ctx->usest," (with the usest flag set)");

    328:   PetscCall(BVDestroy(&ctx->Y));
    329:   if (contour->pA) {
    330:     PetscCall(BVCreate(PetscObjectComm((PetscObject)contour->xsub),&ctx->Y));
    331:     PetscCall(BVSetSizesFromVec(ctx->Y,contour->xsub,eps->n));
    332:     PetscCall(BVSetFromOptions(ctx->Y));
    333:     PetscCall(BVResize(ctx->Y,contour->npoints*ctx->L,PETSC_FALSE));
    334:   } else PetscCall(BVDuplicateResize(eps->V,contour->npoints*ctx->L,&ctx->Y));

    336:   if (ctx->extraction == EPS_CISS_EXTRACTION_HANKEL) PetscCall(DSSetType(eps->ds,DSGNHEP));
    337:   else if (eps->isgeneralized) {
    338:     if (eps->ishermitian && eps->ispositive) PetscCall(DSSetType(eps->ds,DSGHEP));
    339:     else PetscCall(DSSetType(eps->ds,DSGNHEP));
    340:   } else {
    341:     if (eps->ishermitian) PetscCall(DSSetType(eps->ds,DSHEP));
    342:     else PetscCall(DSSetType(eps->ds,DSNHEP));
    343:   }
    344:   PetscCall(DSAllocate(eps->ds,eps->ncv));

    346: #if !defined(PETSC_USE_COMPLEX)
    347:   PetscCall(EPSSetWorkVecs(eps,3));
    348:   if (!eps->ishermitian) PetscCall(PetscInfo(eps,"Warning: complex eigenvalues are not calculated exactly without --with-scalar-type=complex in PETSc\n"));
    349: #else
    350:   PetscCall(EPSSetWorkVecs(eps,2));
    351: #endif
    352:   PetscFunctionReturn(PETSC_SUCCESS);
    353: }

    355: static PetscErrorCode EPSSetUpSort_CISS(EPS eps)
    356: {
    357:   SlepcSC        sc;

    359:   PetscFunctionBegin;
    360:   /* fill sorting criterion context */
    361:   eps->sc->comparison    = SlepcCompareSmallestReal;
    362:   eps->sc->comparisonctx = NULL;
    363:   eps->sc->map           = NULL;
    364:   eps->sc->mapobj        = NULL;

    366:   /* fill sorting criterion for DS */
    367:   PetscCall(DSGetSlepcSC(eps->ds,&sc));
    368:   sc->comparison    = SlepcCompareLargestMagnitude;
    369:   sc->comparisonctx = NULL;
    370:   sc->map           = NULL;
    371:   sc->mapobj        = NULL;
    372:   PetscFunctionReturn(PETSC_SUCCESS);
    373: }

    375: static PetscErrorCode EPSSolve_CISS(EPS eps)
    376: {
    377:   EPS_CISS         *ctx = (EPS_CISS*)eps->data;
    378:   SlepcContourData contour = ctx->contour;
    379:   Mat              A,B,X,M,pA,pB,T,J,Pa=NULL,Pb=NULL;
    380:   BV               V;
    381:   PetscInt         i,j,ld,nmat,L_add=0,nv=0,L_base=ctx->L,inner,nlocal,*inside,nsplit;
    382:   PetscScalar      *Mu,*H0,*H1=NULL,*rr,*temp;
    383:   PetscReal        error,max_error,norm;
    384:   PetscBool        *fl1;
    385:   Vec              si,si1=NULL,w[3];
    386:   PetscRandom      rand;
    387: #if defined(PETSC_USE_COMPLEX)
    388:   PetscBool        isellipse;
    389:   PetscReal        est_eig,eta;
    390: #else
    391:   PetscReal        normi;
    392: #endif

    394:   PetscFunctionBegin;
    395:   w[0] = eps->work[0];
    396: #if defined(PETSC_USE_COMPLEX)
    397:   w[1] = NULL;
    398: #else
    399:   w[1] = eps->work[2];
    400: #endif
    401:   w[2] = eps->work[1];
    402:   PetscCall(VecGetLocalSize(w[0],&nlocal));
    403:   PetscCall(DSGetLeadingDimension(eps->ds,&ld));
    404:   PetscCall(RGComputeQuadrature(eps->rg,ctx->quad==EPS_CISS_QUADRULE_CHEBYSHEV?RG_QUADRULE_CHEBYSHEV:RG_QUADRULE_TRAPEZOIDAL,ctx->N,ctx->omega,ctx->pp,ctx->weight));
    405:   PetscCall(STGetNumMatrices(eps->st,&nmat));
    406:   PetscCall(STGetMatrix(eps->st,0,&A));
    407:   if (nmat>1) PetscCall(STGetMatrix(eps->st,1,&B));
    408:   else B = NULL;
    409:   J = (contour->pA && nmat>1)? contour->pA[1]: B;
    410:   V = contour->pA? ctx->pV: ctx->V;
    411:   if (!ctx->usest) {
    412:     T = contour->pA? contour->pA[0]: A;
    413:     PetscCall(STGetSplitPreconditionerInfo(eps->st,&nsplit,NULL));
    414:     if (nsplit) {
    415:       if (contour->pA) {
    416:         Pa = contour->pP[0];
    417:         if (nsplit>1) Pb = contour->pP[1];
    418:       } else {
    419:         PetscCall(STGetSplitPreconditionerTerm(eps->st,0,&Pa));
    420:         if (nsplit>1) PetscCall(STGetSplitPreconditionerTerm(eps->st,1,&Pb));
    421:       }
    422:     }
    423:     PetscCall(EPSCISSSetUp(eps,T,J,Pa,Pb));
    424:   }
    425:   PetscCall(BVSetActiveColumns(ctx->V,0,ctx->L));
    426:   PetscCall(BVSetRandomSign(ctx->V));
    427:   PetscCall(BVGetRandomContext(ctx->V,&rand));

    429:   if (contour->pA) PetscCall(BVScatter(ctx->V,ctx->pV,contour->scatterin,contour->xdup));
    430:   PetscCall(EPSCISSSolve(eps,J,V,0,ctx->L));
    431: #if defined(PETSC_USE_COMPLEX)
    432:   PetscCall(PetscObjectTypeCompare((PetscObject)eps->rg,RGELLIPSE,&isellipse));
    433:   if (isellipse) {
    434:     PetscCall(BVTraceQuadrature(ctx->Y,ctx->V,ctx->L,ctx->L,ctx->weight,contour->scatterin,contour->subcomm,contour->npoints,ctx->useconj,&est_eig));
    435:     PetscCall(PetscInfo(eps,"Estimated eigenvalue count: %f\n",(double)est_eig));
    436:     eta = PetscPowReal(10.0,-PetscLog10Real(eps->tol)/ctx->N);
    437:     L_add = PetscMax(0,(PetscInt)PetscCeilReal((est_eig*eta)/ctx->M)-ctx->L);
    438:     if (L_add>ctx->L_max-ctx->L) {
    439:       PetscCall(PetscInfo(eps,"Number of eigenvalues inside the contour path may be too large\n"));
    440:       L_add = ctx->L_max-ctx->L;
    441:     }
    442:   }
    443: #endif
    444:   if (L_add>0) {
    445:     PetscCall(PetscInfo(eps,"Changing L %" PetscInt_FMT " -> %" PetscInt_FMT " by Estimate #Eig\n",ctx->L,ctx->L+L_add));
    446:     PetscCall(BVCISSResizeBases(ctx->S,contour->pA?ctx->pV:ctx->V,ctx->Y,ctx->L,ctx->L+L_add,ctx->M,contour->npoints));
    447:     PetscCall(BVSetActiveColumns(ctx->V,ctx->L,ctx->L+L_add));
    448:     PetscCall(BVSetRandomSign(ctx->V));
    449:     if (contour->pA) PetscCall(BVScatter(ctx->V,ctx->pV,contour->scatterin,contour->xdup));
    450:     ctx->L += L_add;
    451:     PetscCall(EPSCISSSolve(eps,J,V,ctx->L-L_add,ctx->L));
    452:   }
    453:   PetscCall(PetscMalloc2(ctx->L*ctx->L*ctx->M*2,&Mu,ctx->L*ctx->M*ctx->L*ctx->M,&H0));
    454:   for (i=0;i<ctx->refine_blocksize;i++) {
    455:     PetscCall(BVDotQuadrature(ctx->Y,(contour->pA)?ctx->pV:ctx->V,Mu,ctx->M,ctx->L,ctx->L,ctx->weight,ctx->pp,contour->subcomm,contour->npoints,ctx->useconj));
    456:     PetscCall(CISS_BlockHankel(Mu,0,ctx->L,ctx->M,H0));
    457:     PetscCall(PetscLogEventBegin(EPS_CISS_SVD,eps,0,0,0));
    458:     PetscCall(SlepcCISS_BH_SVD(H0,ctx->L*ctx->M,ctx->delta,ctx->sigma,&nv));
    459:     PetscCall(PetscLogEventEnd(EPS_CISS_SVD,eps,0,0,0));
    460:     if (ctx->sigma[0]<=ctx->delta || nv < ctx->L*ctx->M || ctx->L == ctx->L_max) break;
    461:     L_add = L_base;
    462:     if (ctx->L+L_add>ctx->L_max) L_add = ctx->L_max-ctx->L;
    463:     PetscCall(PetscInfo(eps,"Changing L %" PetscInt_FMT " -> %" PetscInt_FMT " by SVD(H0)\n",ctx->L,ctx->L+L_add));
    464:     PetscCall(BVCISSResizeBases(ctx->S,contour->pA?ctx->pV:ctx->V,ctx->Y,ctx->L,ctx->L+L_add,ctx->M,contour->npoints));
    465:     PetscCall(BVSetActiveColumns(ctx->V,ctx->L,ctx->L+L_add));
    466:     PetscCall(BVSetRandomSign(ctx->V));
    467:     if (contour->pA) PetscCall(BVScatter(ctx->V,ctx->pV,contour->scatterin,contour->xdup));
    468:     ctx->L += L_add;
    469:     PetscCall(EPSCISSSolve(eps,J,V,ctx->L-L_add,ctx->L));
    470:     if (L_add) {
    471:       PetscCall(PetscFree2(Mu,H0));
    472:       PetscCall(PetscMalloc2(ctx->L*ctx->L*ctx->M*2,&Mu,ctx->L*ctx->M*ctx->L*ctx->M,&H0));
    473:     }
    474:   }
    475:   if (ctx->extraction == EPS_CISS_EXTRACTION_HANKEL) PetscCall(PetscMalloc1(ctx->L*ctx->M*ctx->L*ctx->M,&H1));

    477:   while (eps->reason == EPS_CONVERGED_ITERATING) {
    478:     eps->its++;
    479:     for (inner=0;inner<=ctx->refine_inner;inner++) {
    480:       if (ctx->extraction == EPS_CISS_EXTRACTION_HANKEL) {
    481:         PetscCall(BVDotQuadrature(ctx->Y,(contour->pA)?ctx->pV:ctx->V,Mu,ctx->M,ctx->L,ctx->L,ctx->weight,ctx->pp,contour->subcomm,contour->npoints,ctx->useconj));
    482:         PetscCall(CISS_BlockHankel(Mu,0,ctx->L,ctx->M,H0));
    483:         PetscCall(PetscLogEventBegin(EPS_CISS_SVD,eps,0,0,0));
    484:         PetscCall(SlepcCISS_BH_SVD(H0,ctx->L*ctx->M,ctx->delta,ctx->sigma,&nv));
    485:         PetscCall(PetscLogEventEnd(EPS_CISS_SVD,eps,0,0,0));
    486:         break;
    487:       } else {
    488:         PetscCall(BVSumQuadrature(ctx->S,ctx->Y,ctx->M,ctx->L,ctx->L,ctx->weight,ctx->pp,contour->scatterin,contour->subcomm,contour->npoints,ctx->useconj));
    489:         PetscCall(BVSetActiveColumns(ctx->S,0,ctx->L));
    490:         PetscCall(BVSetActiveColumns(ctx->V,0,ctx->L));
    491:         PetscCall(BVCopy(ctx->S,ctx->V));
    492:         PetscCall(BVSVDAndRank(ctx->S,ctx->M,ctx->L,ctx->delta,BV_SVD_METHOD_REFINE,H0,ctx->sigma,&nv));
    493:         if (ctx->sigma[0]>ctx->delta && nv==ctx->L*ctx->M && inner!=ctx->refine_inner) {
    494:           if (contour->pA) PetscCall(BVScatter(ctx->V,ctx->pV,contour->scatterin,contour->xdup));
    495:           PetscCall(EPSCISSSolve(eps,J,V,0,ctx->L));
    496:         } else break;
    497:       }
    498:     }
    499:     eps->nconv = 0;
    500:     if (nv == 0) eps->reason = EPS_CONVERGED_TOL;
    501:     else {
    502:       PetscCall(DSSetDimensions(eps->ds,nv,0,0));
    503:       PetscCall(DSSetState(eps->ds,DS_STATE_RAW));

    505:       if (ctx->extraction == EPS_CISS_EXTRACTION_HANKEL) {
    506:         PetscCall(CISS_BlockHankel(Mu,0,ctx->L,ctx->M,H0));
    507:         PetscCall(CISS_BlockHankel(Mu,1,ctx->L,ctx->M,H1));
    508:         PetscCall(DSGetArray(eps->ds,DS_MAT_A,&temp));
    509:         for (j=0;j<nv;j++) {
    510:           for (i=0;i<nv;i++) {
    511:             temp[i+j*ld] = H1[i+j*ctx->L*ctx->M];
    512:           }
    513:         }
    514:         PetscCall(DSRestoreArray(eps->ds,DS_MAT_A,&temp));
    515:         PetscCall(DSGetArray(eps->ds,DS_MAT_B,&temp));
    516:         for (j=0;j<nv;j++) {
    517:           for (i=0;i<nv;i++) {
    518:             temp[i+j*ld] = H0[i+j*ctx->L*ctx->M];
    519:           }
    520:         }
    521:         PetscCall(DSRestoreArray(eps->ds,DS_MAT_B,&temp));
    522:       } else {
    523:         PetscCall(BVSetActiveColumns(ctx->S,0,nv));
    524:         PetscCall(DSGetMat(eps->ds,DS_MAT_A,&pA));
    525:         PetscCall(MatZeroEntries(pA));
    526:         PetscCall(BVMatProject(ctx->S,A,ctx->S,pA));
    527:         PetscCall(DSRestoreMat(eps->ds,DS_MAT_A,&pA));
    528:         if (B) {
    529:           PetscCall(DSGetMat(eps->ds,DS_MAT_B,&pB));
    530:           PetscCall(MatZeroEntries(pB));
    531:           PetscCall(BVMatProject(ctx->S,B,ctx->S,pB));
    532:           PetscCall(DSRestoreMat(eps->ds,DS_MAT_B,&pB));
    533:         }
    534:       }

    536:       PetscCall(DSSolve(eps->ds,eps->eigr,eps->eigi));
    537:       PetscCall(DSSynchronize(eps->ds,eps->eigr,eps->eigi));

    539:       PetscCall(PetscMalloc3(nv,&fl1,nv,&inside,nv,&rr));
    540:       PetscCall(rescale_eig(eps,nv));
    541:       PetscCall(DSVectors(eps->ds,DS_MAT_X,NULL,NULL));
    542:       PetscCall(DSGetMat(eps->ds,DS_MAT_X,&X));
    543:       PetscCall(SlepcCISS_isGhost(X,nv,ctx->sigma,ctx->spurious_threshold,fl1));
    544:       PetscCall(DSRestoreMat(eps->ds,DS_MAT_X,&X));
    545:       PetscCall(RGCheckInside(eps->rg,nv,eps->eigr,eps->eigi,inside));
    546:       for (i=0;i<nv;i++) {
    547:         if (fl1[i] && inside[i]>=0) {
    548:           rr[i] = 1.0;
    549:           eps->nconv++;
    550:         } else rr[i] = 0.0;
    551:       }
    552:       PetscCall(DSSort(eps->ds,eps->eigr,eps->eigi,rr,NULL,&eps->nconv));
    553:       PetscCall(DSSynchronize(eps->ds,eps->eigr,eps->eigi));
    554:       PetscCall(rescale_eig(eps,nv));
    555:       PetscCall(PetscFree3(fl1,inside,rr));
    556:       PetscCall(BVSetActiveColumns(eps->V,0,nv));
    557:       if (ctx->extraction == EPS_CISS_EXTRACTION_HANKEL) {
    558:         PetscCall(BVSumQuadrature(ctx->S,ctx->Y,ctx->M,ctx->L,ctx->L,ctx->weight,ctx->pp,contour->scatterin,contour->subcomm,contour->npoints,ctx->useconj));
    559:         PetscCall(BVSetActiveColumns(ctx->S,0,ctx->L));
    560:         PetscCall(BVCopy(ctx->S,ctx->V));
    561:         PetscCall(BVSetActiveColumns(ctx->S,0,nv));
    562:       }
    563:       PetscCall(BVCopy(ctx->S,eps->V));

    565:       PetscCall(DSVectors(eps->ds,DS_MAT_X,NULL,NULL));
    566:       PetscCall(DSGetMat(eps->ds,DS_MAT_X,&X));
    567:       PetscCall(BVMultInPlace(ctx->S,X,0,eps->nconv));
    568:       if (eps->ishermitian) PetscCall(BVMultInPlace(eps->V,X,0,eps->nconv));
    569:       PetscCall(DSRestoreMat(eps->ds,DS_MAT_X,&X));
    570:       max_error = 0.0;
    571:       for (i=0;i<eps->nconv;i++) {
    572:         PetscCall(BVGetColumn(ctx->S,i,&si));
    573: #if !defined(PETSC_USE_COMPLEX)
    574:         if (eps->eigi[i]!=0.0) PetscCall(BVGetColumn(ctx->S,i+1,&si1));
    575: #endif
    576:         PetscCall(EPSComputeResidualNorm_Private(eps,PETSC_FALSE,eps->eigr[i],eps->eigi[i],si,si1,w,&error));
    577:         if (ctx->extraction == EPS_CISS_EXTRACTION_HANKEL) {  /* vector is not normalized */
    578:           PetscCall(VecNorm(si,NORM_2,&norm));
    579: #if !defined(PETSC_USE_COMPLEX)
    580:           if (eps->eigi[i]!=0.0) {
    581:             PetscCall(VecNorm(si1,NORM_2,&normi));
    582:             norm = SlepcAbsEigenvalue(norm,normi);
    583:           }
    584: #endif
    585:           error /= norm;
    586:         }
    587:         PetscCall((*eps->converged)(eps,eps->eigr[i],eps->eigi[i],error,&error,eps->convergedctx));
    588:         PetscCall(BVRestoreColumn(ctx->S,i,&si));
    589: #if !defined(PETSC_USE_COMPLEX)
    590:         if (eps->eigi[i]!=0.0) {
    591:           PetscCall(BVRestoreColumn(ctx->S,i+1,&si1));
    592:           i++;
    593:         }
    594: #endif
    595:         max_error = PetscMax(max_error,error);
    596:       }

    598:       if (max_error <= eps->tol) eps->reason = EPS_CONVERGED_TOL;
    599:       else if (eps->its >= eps->max_it) eps->reason = EPS_DIVERGED_ITS;
    600:       else {
    601:         if (eps->nconv > ctx->L) nv = eps->nconv;
    602:         else if (ctx->L > nv) nv = ctx->L;
    603:         nv = PetscMin(nv,ctx->L*ctx->M);
    604:         PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,nv,ctx->L,NULL,&M));
    605:         PetscCall(MatSetRandom(M,rand));
    606:         PetscCall(BVSetActiveColumns(ctx->S,0,nv));
    607:         PetscCall(BVMultInPlace(ctx->S,M,0,ctx->L));
    608:         PetscCall(MatDestroy(&M));
    609:         PetscCall(BVSetActiveColumns(ctx->S,0,ctx->L));
    610:         PetscCall(BVSetActiveColumns(ctx->V,0,ctx->L));
    611:         PetscCall(BVCopy(ctx->S,ctx->V));
    612:         if (contour->pA) PetscCall(BVScatter(ctx->V,ctx->pV,contour->scatterin,contour->xdup));
    613:         PetscCall(EPSCISSSolve(eps,J,V,0,ctx->L));
    614:       }
    615:     }
    616:   }
    617:   if (ctx->extraction == EPS_CISS_EXTRACTION_HANKEL) PetscCall(PetscFree(H1));
    618:   PetscCall(PetscFree2(Mu,H0));
    619:   PetscFunctionReturn(PETSC_SUCCESS);
    620: }

    622: static PetscErrorCode EPSComputeVectors_CISS(EPS eps)
    623: {
    624:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    625:   PetscInt       n;
    626:   Mat            Z,B=NULL;

    628:   PetscFunctionBegin;
    629:   if (eps->ishermitian) {
    630:     if (eps->isgeneralized && !eps->ispositive) PetscCall(EPSComputeVectors_Indefinite(eps));
    631:     else PetscCall(EPSComputeVectors_Hermitian(eps));
    632:     if (eps->isgeneralized && eps->ispositive && ctx->extraction == EPS_CISS_EXTRACTION_HANKEL) {
    633:       /* normalize to have unit B-norm */
    634:       PetscCall(STGetMatrix(eps->st,1,&B));
    635:       PetscCall(BVSetMatrix(eps->V,B,PETSC_FALSE));
    636:       PetscCall(BVNormalize(eps->V,NULL));
    637:       PetscCall(BVSetMatrix(eps->V,NULL,PETSC_FALSE));
    638:     }
    639:     PetscFunctionReturn(PETSC_SUCCESS);
    640:   }
    641:   PetscCall(DSGetDimensions(eps->ds,&n,NULL,NULL,NULL));
    642:   PetscCall(BVSetActiveColumns(eps->V,0,n));

    644:   /* right eigenvectors */
    645:   PetscCall(DSVectors(eps->ds,DS_MAT_X,NULL,NULL));

    647:   /* V = V * Z */
    648:   PetscCall(DSGetMat(eps->ds,DS_MAT_X,&Z));
    649:   PetscCall(BVMultInPlace(eps->V,Z,0,n));
    650:   PetscCall(DSRestoreMat(eps->ds,DS_MAT_X,&Z));
    651:   PetscCall(BVSetActiveColumns(eps->V,0,eps->nconv));

    653:   /* normalize */
    654:   if (ctx->extraction == EPS_CISS_EXTRACTION_HANKEL) PetscCall(BVNormalize(eps->V,NULL));
    655:   PetscFunctionReturn(PETSC_SUCCESS);
    656: }

    658: static PetscErrorCode EPSCISSSetSizes_CISS(EPS eps,PetscInt ip,PetscInt bs,PetscInt ms,PetscInt npart,PetscInt bsmax,PetscBool realmats)
    659: {
    660:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    661:   PetscInt       oN,oL,oM,oLmax,onpart;
    662:   PetscMPIInt    size;

    664:   PetscFunctionBegin;
    665:   oN = ctx->N;
    666:   if (ip == PETSC_DETERMINE) {
    667:     if (ctx->N!=32) { ctx->N =32; ctx->M = ctx->N/4; }
    668:   } else if (ip != PETSC_CURRENT) {
    669:     PetscCheck(ip>0,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The ip argument must be > 0");
    670:     PetscCheck(ip%2==0,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The ip argument must be an even number");
    671:     if (ctx->N!=ip) { ctx->N = ip; ctx->M = ctx->N/4; }
    672:   }
    673:   oL = ctx->L;
    674:   if (bs == PETSC_DETERMINE) {
    675:     ctx->L = 16;
    676:   } else if (bs != PETSC_CURRENT) {
    677:     PetscCheck(bs>0,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The bs argument must be > 0");
    678:     ctx->L = bs;
    679:   }
    680:   oM = ctx->M;
    681:   if (ms == PETSC_DETERMINE) {
    682:     ctx->M = ctx->N/4;
    683:   } else if (ms != PETSC_CURRENT) {
    684:     PetscCheck(ms>0,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The ms argument must be > 0");
    685:     PetscCheck(ms<=ctx->N,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The ms argument must be less than or equal to the number of integration points");
    686:     ctx->M = ms;
    687:   }
    688:   onpart = ctx->npart;
    689:   if (npart == PETSC_DETERMINE) {
    690:     ctx->npart = 1;
    691:   } else if (npart != PETSC_CURRENT) {
    692:     PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)eps),&size));
    693:     PetscCheck(npart>0 && npart<=size,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"Illegal value of npart");
    694:     ctx->npart = npart;
    695:   }
    696:   oLmax = ctx->L_max;
    697:   if (bsmax == PETSC_DETERMINE) {
    698:     ctx->L_max = 64;
    699:   } else if (bsmax != PETSC_CURRENT) {
    700:     PetscCheck(bsmax>0,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The bsmax argument must be > 0");
    701:     ctx->L_max = PetscMax(bsmax,ctx->L);
    702:   }
    703:   if (onpart != ctx->npart || oN != ctx->N || realmats != ctx->isreal) {
    704:     PetscCall(SlepcContourDataDestroy(&ctx->contour));
    705:     PetscCall(PetscInfo(eps,"Resetting the contour data structure due to a change of parameters\n"));
    706:     eps->state = EPS_STATE_INITIAL;
    707:   }
    708:   ctx->isreal = realmats;
    709:   if (oL != ctx->L || oM != ctx->M || oLmax != ctx->L_max) eps->state = EPS_STATE_INITIAL;
    710:   PetscFunctionReturn(PETSC_SUCCESS);
    711: }

    713: /*@
    714:    EPSCISSSetSizes - Sets the values of various size parameters in the CISS solver.

    716:    Logically Collective

    718:    Input Parameters:
    719: +  eps      - the linear eigensolver context
    720: .  ip       - number of integration points
    721: .  bs       - block size
    722: .  ms       - moment size
    723: .  npart    - number of partitions when splitting the communicator
    724: .  bsmax    - max block size
    725: -  realmats - $A$ and $B$ are real

    727:    Options Database Keys:
    728: +  -eps_ciss_integration_points ip - sets the number of integration points
    729: .  -eps_ciss_blocksize bs          - sets the block size
    730: .  -eps_ciss_moments ms            - sets the moment size
    731: .  -eps_ciss_partitions npart      - sets the number of partitions
    732: .  -eps_ciss_maxblocksize bsmax    - sets the maximum block size
    733: -  -eps_ciss_realmats (true|false) - $A$ and $B$ are real

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

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

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

    745:    Level: advanced

    747: .seealso: [](ch:eps), `EPSCISS`, `EPSCISSGetSizes()`, `EPSCISSSetThreshold()`, `EPSCISSSetRefinement()`
    748: @*/
    749: PetscErrorCode EPSCISSSetSizes(EPS eps,PetscInt ip,PetscInt bs,PetscInt ms,PetscInt npart,PetscInt bsmax,PetscBool realmats)
    750: {
    751:   PetscFunctionBegin;
    759:   PetscTryMethod(eps,"EPSCISSSetSizes_C",(EPS,PetscInt,PetscInt,PetscInt,PetscInt,PetscInt,PetscBool),(eps,ip,bs,ms,npart,bsmax,realmats));
    760:   PetscFunctionReturn(PETSC_SUCCESS);
    761: }

    763: static PetscErrorCode EPSCISSGetSizes_CISS(EPS eps,PetscInt *ip,PetscInt *bs,PetscInt *ms,PetscInt *npart,PetscInt *bsmax,PetscBool *realmats)
    764: {
    765:   EPS_CISS *ctx = (EPS_CISS*)eps->data;

    767:   PetscFunctionBegin;
    768:   if (ip) *ip = ctx->N;
    769:   if (bs) *bs = ctx->L;
    770:   if (ms) *ms = ctx->M;
    771:   if (npart) *npart = ctx->npart;
    772:   if (bsmax) *bsmax = ctx->L_max;
    773:   if (realmats) *realmats = ctx->isreal;
    774:   PetscFunctionReturn(PETSC_SUCCESS);
    775: }

    777: /*@
    778:    EPSCISSGetSizes - Gets the values of various size parameters in the CISS solver.

    780:    Not Collective

    782:    Input Parameter:
    783: .  eps - the linear eigensolver context

    785:    Output Parameters:
    786: +  ip    - number of integration points
    787: .  bs    - block size
    788: .  ms    - moment size
    789: .  npart - number of partitions when splitting the communicator
    790: .  bsmax - max block size
    791: -  realmats - $A$ and $B$ are real

    793:    Level: advanced

    795: .seealso: [](ch:eps), `EPSCISS`, `EPSCISSSetSizes()`
    796: @*/
    797: PetscErrorCode EPSCISSGetSizes(EPS eps,PetscInt *ip,PetscInt *bs,PetscInt *ms,PetscInt *npart,PetscInt *bsmax,PetscBool *realmats)
    798: {
    799:   PetscFunctionBegin;
    801:   PetscUseMethod(eps,"EPSCISSGetSizes_C",(EPS,PetscInt*,PetscInt*,PetscInt*,PetscInt*,PetscInt*,PetscBool*),(eps,ip,bs,ms,npart,bsmax,realmats));
    802:   PetscFunctionReturn(PETSC_SUCCESS);
    803: }

    805: static PetscErrorCode EPSCISSSetThreshold_CISS(EPS eps,PetscReal delta,PetscReal spur)
    806: {
    807:   EPS_CISS *ctx = (EPS_CISS*)eps->data;

    809:   PetscFunctionBegin;
    810:   if (delta == (PetscReal)PETSC_DETERMINE) {
    811:     ctx->delta = SLEPC_DEFAULT_TOL*1e-4;
    812:   } else if (delta != (PetscReal)PETSC_CURRENT) {
    813:     PetscCheck(delta>0.0,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The delta argument must be > 0.0");
    814:     ctx->delta = delta;
    815:   }
    816:   if (spur == (PetscReal)PETSC_DETERMINE) {
    817:     ctx->spurious_threshold = PetscSqrtReal(SLEPC_DEFAULT_TOL);
    818:   } else if (spur != (PetscReal)PETSC_CURRENT) {
    819:     PetscCheck(spur>0.0,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The spurious threshold argument must be > 0.0");
    820:     ctx->spurious_threshold = spur;
    821:   }
    822:   PetscFunctionReturn(PETSC_SUCCESS);
    823: }

    825: /*@
    826:    EPSCISSSetThreshold - Sets the values of various threshold parameters in
    827:    the CISS solver.

    829:    Logically Collective

    831:    Input Parameters:
    832: +  eps   - the linear eigensolver context
    833: .  delta - threshold for numerical rank
    834: -  spur  - spurious threshold (to discard spurious eigenpairs)

    836:    Options Database Keys:
    837: +  -eps_ciss_delta delta             - sets the delta
    838: -  -eps_ciss_spurious_threshold spur - sets the spurious threshold

    840:    Notes:
    841:    `PETSC_CURRENT` can be used to preserve the current value of any of the
    842:    arguments, and `PETSC_DETERMINE` to set them to a default value.

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

    846:    Level: advanced

    848: .seealso: [](ch:eps), `EPSCISS`, `EPSCISSGetThreshold()`, `EPSCISSSetSizes()`, `EPSCISSSetRefinement()`
    849: @*/
    850: PetscErrorCode EPSCISSSetThreshold(EPS eps,PetscReal delta,PetscReal spur)
    851: {
    852:   PetscFunctionBegin;
    856:   PetscTryMethod(eps,"EPSCISSSetThreshold_C",(EPS,PetscReal,PetscReal),(eps,delta,spur));
    857:   PetscFunctionReturn(PETSC_SUCCESS);
    858: }

    860: static PetscErrorCode EPSCISSGetThreshold_CISS(EPS eps,PetscReal *delta,PetscReal *spur)
    861: {
    862:   EPS_CISS *ctx = (EPS_CISS*)eps->data;

    864:   PetscFunctionBegin;
    865:   if (delta) *delta = ctx->delta;
    866:   if (spur)  *spur = ctx->spurious_threshold;
    867:   PetscFunctionReturn(PETSC_SUCCESS);
    868: }

    870: /*@
    871:    EPSCISSGetThreshold - Gets the values of various threshold parameters
    872:    in the CISS solver.

    874:    Not Collective

    876:    Input Parameter:
    877: .  eps - the linear eigensolver context

    879:    Output Parameters:
    880: +  delta - threshold for numerical rank
    881: -  spur  - spurious threshold (to discard spurious eigenpairs)

    883:    Level: advanced

    885: .seealso: [](ch:eps), `EPSCISS`, `EPSCISSSetThreshold()`
    886: @*/
    887: PetscErrorCode EPSCISSGetThreshold(EPS eps,PetscReal *delta,PetscReal *spur)
    888: {
    889:   PetscFunctionBegin;
    891:   PetscUseMethod(eps,"EPSCISSGetThreshold_C",(EPS,PetscReal*,PetscReal*),(eps,delta,spur));
    892:   PetscFunctionReturn(PETSC_SUCCESS);
    893: }

    895: static PetscErrorCode EPSCISSSetRefinement_CISS(EPS eps,PetscInt inner,PetscInt blsize)
    896: {
    897:   EPS_CISS *ctx = (EPS_CISS*)eps->data;

    899:   PetscFunctionBegin;
    900:   if (inner == PETSC_DETERMINE) {
    901:     ctx->refine_inner = 0;
    902:   } else if (inner != PETSC_CURRENT) {
    903:     PetscCheck(inner>=0,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The refine inner argument must be >= 0");
    904:     ctx->refine_inner = inner;
    905:   }
    906:   if (blsize == PETSC_DETERMINE) {
    907:     ctx->refine_blocksize = 0;
    908:   } else if (blsize != PETSC_CURRENT) {
    909:     PetscCheck(blsize>=0,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The refine blocksize argument must be >= 0");
    910:     ctx->refine_blocksize = blsize;
    911:   }
    912:   PetscFunctionReturn(PETSC_SUCCESS);
    913: }

    915: /*@
    916:    EPSCISSSetRefinement - Sets the values of various refinement parameters
    917:    in the CISS solver.

    919:    Logically Collective

    921:    Input Parameters:
    922: +  eps    - the linear eigensolver context
    923: .  inner  - number of iterative refinement iterations (inner loop)
    924: -  blsize - number of iterative refinement iterations (blocksize loop)

    926:    Options Database Keys:
    927: +  -eps_ciss_refine_inner inner      - sets number of inner iterations
    928: -  -eps_ciss_refine_blocksize blsize - sets number of blocksize iterations

    930:    Notes:
    931:    `PETSC_CURRENT` can be used to preserve the current value of any of the
    932:    arguments, and `PETSC_DETERMINE` to set them to a default of 0 (no refinement).

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

    936:    Level: advanced

    938: .seealso: [](ch:eps), `EPSCISS`, `EPSCISSGetRefinement()`, `EPSCISSSetSizes()`, `EPSCISSSetThreshold()`
    939: @*/
    940: PetscErrorCode EPSCISSSetRefinement(EPS eps,PetscInt inner,PetscInt blsize)
    941: {
    942:   PetscFunctionBegin;
    946:   PetscTryMethod(eps,"EPSCISSSetRefinement_C",(EPS,PetscInt,PetscInt),(eps,inner,blsize));
    947:   PetscFunctionReturn(PETSC_SUCCESS);
    948: }

    950: static PetscErrorCode EPSCISSGetRefinement_CISS(EPS eps,PetscInt *inner,PetscInt *blsize)
    951: {
    952:   EPS_CISS *ctx = (EPS_CISS*)eps->data;

    954:   PetscFunctionBegin;
    955:   if (inner)  *inner = ctx->refine_inner;
    956:   if (blsize) *blsize = ctx->refine_blocksize;
    957:   PetscFunctionReturn(PETSC_SUCCESS);
    958: }

    960: /*@
    961:    EPSCISSGetRefinement - Gets the values of various refinement parameters
    962:    in the CISS solver.

    964:    Not Collective

    966:    Input Parameter:
    967: .  eps - the linear eigensolver context

    969:    Output Parameters:
    970: +  inner  - number of iterative refinement iterations (inner loop)
    971: -  blsize - number of iterative refinement iterations (blocksize loop)

    973:    Level: advanced

    975: .seealso: [](ch:eps), `EPSCISS`, `EPSCISSSetRefinement()`
    976: @*/
    977: PetscErrorCode EPSCISSGetRefinement(EPS eps, PetscInt *inner, PetscInt *blsize)
    978: {
    979:   PetscFunctionBegin;
    981:   PetscUseMethod(eps,"EPSCISSGetRefinement_C",(EPS,PetscInt*,PetscInt*),(eps,inner,blsize));
    982:   PetscFunctionReturn(PETSC_SUCCESS);
    983: }

    985: static PetscErrorCode EPSCISSSetUseST_CISS(EPS eps,PetscBool usest)
    986: {
    987:   EPS_CISS *ctx = (EPS_CISS*)eps->data;

    989:   PetscFunctionBegin;
    990:   ctx->usest     = usest;
    991:   ctx->usest_set = PETSC_TRUE;
    992:   eps->state     = EPS_STATE_INITIAL;
    993:   PetscFunctionReturn(PETSC_SUCCESS);
    994: }

    996: /*@
    997:    EPSCISSSetUseST - Sets a flag indicating that the CISS solver will
    998:    use the `ST` object for the linear solves.

    1000:    Logically Collective

    1002:    Input Parameters:
    1003: +  eps    - the linear eigensolver context
    1004: -  usest  - boolean flag to use the `ST` object or not

    1006:    Options Database Key:
    1007: .  -eps_ciss_usest (true|false) - whether the `ST` object will be used or not

    1009:    Note:
    1010:    When this option is set, the linear solves can be configured by
    1011:    setting options for the `KSP` object obtained with `STGetKSP()`.
    1012:    Otherwise, several `KSP` objects are created, which can be accessed
    1013:    with `EPSCISSGetKSPs()`.

    1015:    The default is to use the `ST`, unless several partitions have been
    1016:    specified, see `EPSCISSSetSizes()`.

    1018:    Level: advanced

    1020: .seealso: [](ch:eps), `EPSCISS`, `EPSCISSGetUseST()`, `EPSCISSSetSizes()`, `EPSCISSGetKSPs()`, `STGetKSP()`
    1021: @*/
    1022: PetscErrorCode EPSCISSSetUseST(EPS eps,PetscBool usest)
    1023: {
    1024:   PetscFunctionBegin;
    1027:   PetscTryMethod(eps,"EPSCISSSetUseST_C",(EPS,PetscBool),(eps,usest));
    1028:   PetscFunctionReturn(PETSC_SUCCESS);
    1029: }

    1031: static PetscErrorCode EPSCISSGetUseST_CISS(EPS eps,PetscBool *usest)
    1032: {
    1033:   EPS_CISS *ctx = (EPS_CISS*)eps->data;

    1035:   PetscFunctionBegin;
    1036:   *usest = ctx->usest;
    1037:   PetscFunctionReturn(PETSC_SUCCESS);
    1038: }

    1040: /*@
    1041:    EPSCISSGetUseST - Gets the flag for using the `ST` object
    1042:    in the CISS solver.

    1044:    Not Collective

    1046:    Input Parameter:
    1047: .  eps - the linear eigensolver context

    1049:    Output Parameter:
    1050: .  usest - boolean flag indicating if the `ST` object is being used

    1052:    Level: advanced

    1054: .seealso: [](ch:eps), `EPSCISS`, `EPSCISSSetUseST()`
    1055: @*/
    1056: PetscErrorCode EPSCISSGetUseST(EPS eps,PetscBool *usest)
    1057: {
    1058:   PetscFunctionBegin;
    1060:   PetscAssertPointer(usest,2);
    1061:   PetscUseMethod(eps,"EPSCISSGetUseST_C",(EPS,PetscBool*),(eps,usest));
    1062:   PetscFunctionReturn(PETSC_SUCCESS);
    1063: }

    1065: static PetscErrorCode EPSCISSSetQuadRule_CISS(EPS eps,EPSCISSQuadRule quad)
    1066: {
    1067:   EPS_CISS *ctx = (EPS_CISS*)eps->data;

    1069:   PetscFunctionBegin;
    1070:   if (ctx->quad != quad) {
    1071:     ctx->quad  = quad;
    1072:     eps->state = EPS_STATE_INITIAL;
    1073:   }
    1074:   PetscFunctionReturn(PETSC_SUCCESS);
    1075: }

    1077: /*@
    1078:    EPSCISSSetQuadRule - Sets the quadrature rule used in the CISS solver.

    1080:    Logically Collective

    1082:    Input Parameters:
    1083: +  eps  - the linear eigensolver context
    1084: -  quad - the quadrature rule, see `EPSCISSQuadRule` for possible values

    1086:    Options Database Key:
    1087: .  -eps_ciss_quadrule (trapezoidal|chebyshev) - sets the quadrature rule

    1089:    Notes:
    1090:    By default, the trapezoidal rule is used (`EPS_CISS_QUADRULE_TRAPEZOIDAL`).

    1092:    If the `chebyshev` option is specified (`EPS_CISS_QUADRULE_CHEBYSHEV`), then
    1093:    Chebyshev points are used as quadrature points.

    1095:    Level: advanced

    1097: .seealso: [](ch:eps), `EPSCISS`, `EPSCISSGetQuadRule()`, `EPSCISSQuadRule`
    1098: @*/
    1099: PetscErrorCode EPSCISSSetQuadRule(EPS eps,EPSCISSQuadRule quad)
    1100: {
    1101:   PetscFunctionBegin;
    1104:   PetscTryMethod(eps,"EPSCISSSetQuadRule_C",(EPS,EPSCISSQuadRule),(eps,quad));
    1105:   PetscFunctionReturn(PETSC_SUCCESS);
    1106: }

    1108: static PetscErrorCode EPSCISSGetQuadRule_CISS(EPS eps,EPSCISSQuadRule *quad)
    1109: {
    1110:   EPS_CISS *ctx = (EPS_CISS*)eps->data;

    1112:   PetscFunctionBegin;
    1113:   *quad = ctx->quad;
    1114:   PetscFunctionReturn(PETSC_SUCCESS);
    1115: }

    1117: /*@
    1118:    EPSCISSGetQuadRule - Gets the quadrature rule used in the CISS solver.

    1120:    Not Collective

    1122:    Input Parameter:
    1123: .  eps - the linear eigensolver context

    1125:    Output Parameter:
    1126: .  quad - quadrature rule

    1128:    Level: advanced

    1130: .seealso: [](ch:eps), `EPSCISS`, `EPSCISSSetQuadRule()`, `EPSCISSQuadRule`
    1131: @*/
    1132: PetscErrorCode EPSCISSGetQuadRule(EPS eps,EPSCISSQuadRule *quad)
    1133: {
    1134:   PetscFunctionBegin;
    1136:   PetscAssertPointer(quad,2);
    1137:   PetscUseMethod(eps,"EPSCISSGetQuadRule_C",(EPS,EPSCISSQuadRule*),(eps,quad));
    1138:   PetscFunctionReturn(PETSC_SUCCESS);
    1139: }

    1141: static PetscErrorCode EPSCISSSetExtraction_CISS(EPS eps,EPSCISSExtraction extraction)
    1142: {
    1143:   EPS_CISS *ctx = (EPS_CISS*)eps->data;

    1145:   PetscFunctionBegin;
    1146:   if (ctx->extraction != extraction) {
    1147:     ctx->extraction = extraction;
    1148:     eps->state      = EPS_STATE_INITIAL;
    1149:   }
    1150:   PetscFunctionReturn(PETSC_SUCCESS);
    1151: }

    1153: /*@
    1154:    EPSCISSSetExtraction - Sets the extraction technique used in the CISS solver.

    1156:    Logically Collective

    1158:    Input Parameters:
    1159: +  eps        - the linear eigensolver context
    1160: -  extraction - the extraction technique, see `EPSCISSExtraction` for possible values

    1162:    Options Database Key:
    1163: .  -eps_ciss_extraction (ritz|hankel) - sets the extraction technique

    1165:    Notes:
    1166:    By default, the Rayleigh-Ritz extraction is used (`EPS_CISS_EXTRACTION_RITZ`),
    1167:    see {cite:p}`Sak07`.

    1169:    If the `hankel` option is specified (`EPS_CISS_EXTRACTION_HANKEL`), then
    1170:    the block Hankel method is used for extracting eigenpairs {cite:p}`Sak03`.

    1172:    Level: advanced

    1174: .seealso: [](ch:eps), `EPSCISS`, `EPSCISSGetExtraction()`, `EPSCISSExtraction`
    1175: @*/
    1176: PetscErrorCode EPSCISSSetExtraction(EPS eps,EPSCISSExtraction extraction)
    1177: {
    1178:   PetscFunctionBegin;
    1181:   PetscTryMethod(eps,"EPSCISSSetExtraction_C",(EPS,EPSCISSExtraction),(eps,extraction));
    1182:   PetscFunctionReturn(PETSC_SUCCESS);
    1183: }

    1185: static PetscErrorCode EPSCISSGetExtraction_CISS(EPS eps,EPSCISSExtraction *extraction)
    1186: {
    1187:   EPS_CISS *ctx = (EPS_CISS*)eps->data;

    1189:   PetscFunctionBegin;
    1190:   *extraction = ctx->extraction;
    1191:   PetscFunctionReturn(PETSC_SUCCESS);
    1192: }

    1194: /*@
    1195:    EPSCISSGetExtraction - Gets the extraction technique used in the CISS solver.

    1197:    Not Collective

    1199:    Input Parameter:
    1200: .  eps - the linear eigensolver context

    1202:    Output Parameter:
    1203: .  extraction - extraction technique

    1205:    Level: advanced

    1207: .seealso: [](ch:eps), `EPSCISS`, `EPSCISSSetExtraction()`, `EPSCISSExtraction`
    1208: @*/
    1209: PetscErrorCode EPSCISSGetExtraction(EPS eps,EPSCISSExtraction *extraction)
    1210: {
    1211:   PetscFunctionBegin;
    1213:   PetscAssertPointer(extraction,2);
    1214:   PetscUseMethod(eps,"EPSCISSGetExtraction_C",(EPS,EPSCISSExtraction*),(eps,extraction));
    1215:   PetscFunctionReturn(PETSC_SUCCESS);
    1216: }

    1218: static PetscErrorCode EPSCISSGetKSPs_CISS(EPS eps,PetscInt *nsolve,KSP **ksp)
    1219: {
    1220:   EPS_CISS         *ctx = (EPS_CISS*)eps->data;
    1221:   SlepcContourData contour;
    1222:   PetscInt         i,nsplit;
    1223:   PC               pc;
    1224:   MPI_Comm         child;

    1226:   PetscFunctionBegin;
    1227:   if (!ctx->contour) {  /* initialize contour data structure first */
    1228:     PetscCall(RGCanUseConjugates(eps->rg,ctx->isreal,&ctx->useconj));
    1229:     PetscCall(SlepcContourDataCreate(ctx->useconj?ctx->N/2:ctx->N,ctx->npart,(PetscObject)eps,&ctx->contour));
    1230:   }
    1231:   contour = ctx->contour;
    1232:   if (!contour->ksp) {
    1233:     PetscCall(PetscMalloc1(contour->npoints,&contour->ksp));
    1234:     PetscCall(EPSGetST(eps,&eps->st));
    1235:     PetscCall(STGetSplitPreconditionerInfo(eps->st,&nsplit,NULL));
    1236:     PetscCall(PetscSubcommGetChild(contour->subcomm,&child));
    1237:     for (i=0;i<contour->npoints;i++) {
    1238:       PetscCall(KSPCreate(child,&contour->ksp[i]));
    1239:       PetscCall(PetscObjectIncrementTabLevel((PetscObject)contour->ksp[i],(PetscObject)eps,1));
    1240:       PetscCall(KSPSetOptionsPrefix(contour->ksp[i],((PetscObject)eps)->prefix));
    1241:       PetscCall(KSPAppendOptionsPrefix(contour->ksp[i],"eps_ciss_"));
    1242:       PetscCall(PetscObjectSetOptions((PetscObject)contour->ksp[i],((PetscObject)eps)->options));
    1243:       PetscCall(KSPSetErrorIfNotConverged(contour->ksp[i],PETSC_TRUE));
    1244:       PetscCall(KSPSetTolerances(contour->ksp[i],SlepcDefaultTol(eps->tol),PETSC_CURRENT,PETSC_CURRENT,PETSC_CURRENT));
    1245:       PetscCall(KSPGetPC(contour->ksp[i],&pc));
    1246:       if (nsplit) {
    1247:         PetscCall(KSPSetType(contour->ksp[i],KSPBCGS));
    1248:         PetscCall(PCSetType(pc,PCBJACOBI));
    1249:       } else {
    1250:         PetscCall(KSPSetType(contour->ksp[i],KSPPREONLY));
    1251:         PetscCall(PCSetType(pc,PCLU));
    1252:       }
    1253:     }
    1254:   }
    1255:   if (nsolve) *nsolve = contour->npoints;
    1256:   if (ksp)    *ksp    = contour->ksp;
    1257:   PetscFunctionReturn(PETSC_SUCCESS);
    1258: }

    1260: /*@C
    1261:    EPSCISSGetKSPs - Retrieve the array of linear solver objects associated with
    1262:    the CISS solver.

    1264:    Not Collective

    1266:    Input Parameter:
    1267: .  eps - the linear eigensolver context

    1269:    Output Parameters:
    1270: +  nsolve - number of solver objects
    1271: -  ksp - array of linear solver object

    1273:    Note:
    1274:    The number of `KSP` solvers is equal to the number of integration points divided by
    1275:    the number of partitions, see `EPSCISSSetSizes()`. This value is halved in the case
    1276:    of real matrices with a region centered at the real axis.

    1278:    Level: advanced

    1280: .seealso: [](ch:eps), `EPSCISS`, `EPSCISSSetSizes()`
    1281: @*/
    1282: PetscErrorCode EPSCISSGetKSPs(EPS eps,PetscInt *nsolve,KSP **ksp)
    1283: {
    1284:   PetscFunctionBegin;
    1286:   PetscUseMethod(eps,"EPSCISSGetKSPs_C",(EPS,PetscInt*,KSP**),(eps,nsolve,ksp));
    1287:   PetscFunctionReturn(PETSC_SUCCESS);
    1288: }

    1290: static PetscErrorCode EPSReset_CISS(EPS eps)
    1291: {
    1292:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;

    1294:   PetscFunctionBegin;
    1295:   PetscCall(BVDestroy(&ctx->S));
    1296:   PetscCall(BVDestroy(&ctx->V));
    1297:   PetscCall(BVDestroy(&ctx->Y));
    1298:   if (!ctx->usest) PetscCall(SlepcContourDataReset(ctx->contour));
    1299:   PetscCall(BVDestroy(&ctx->pV));
    1300:   PetscFunctionReturn(PETSC_SUCCESS);
    1301: }

    1303: static PetscErrorCode EPSSetFromOptions_CISS(EPS eps,PetscOptionItems PetscOptionsObject)
    1304: {
    1305:   PetscReal         r3,r4;
    1306:   PetscInt          i,i1,i2,i3,i4,i5,i6,i7;
    1307:   PetscBool         b1,b2,flg,flg2,flg3,flg4,flg5,flg6;
    1308:   EPS_CISS          *ctx = (EPS_CISS*)eps->data;
    1309:   EPSCISSQuadRule   quad;
    1310:   EPSCISSExtraction extraction;

    1312:   PetscFunctionBegin;
    1313:   PetscOptionsHeadBegin(PetscOptionsObject,"EPS CISS Options");

    1315:     PetscCall(EPSCISSGetSizes(eps,&i1,&i2,&i3,&i4,&i5,&b1));
    1316:     PetscCall(PetscOptionsInt("-eps_ciss_integration_points","Number of integration points","EPSCISSSetSizes",i1,&i1,&flg));
    1317:     PetscCall(PetscOptionsInt("-eps_ciss_blocksize","Block size","EPSCISSSetSizes",i2,&i2,&flg2));
    1318:     PetscCall(PetscOptionsInt("-eps_ciss_moments","Moment size","EPSCISSSetSizes",i3,&i3,&flg3));
    1319:     PetscCall(PetscOptionsInt("-eps_ciss_partitions","Number of partitions","EPSCISSSetSizes",i4,&i4,&flg4));
    1320:     PetscCall(PetscOptionsInt("-eps_ciss_maxblocksize","Maximum block size","EPSCISSSetSizes",i5,&i5,&flg5));
    1321:     PetscCall(PetscOptionsBool("-eps_ciss_realmats","True if A and B are real","EPSCISSSetSizes",b1,&b1,&flg6));
    1322:     if (flg || flg2 || flg3 || flg4 || flg5 || flg6) PetscCall(EPSCISSSetSizes(eps,i1,i2,i3,i4,i5,b1));

    1324:     PetscCall(EPSCISSGetThreshold(eps,&r3,&r4));
    1325:     PetscCall(PetscOptionsReal("-eps_ciss_delta","Threshold for numerical rank","EPSCISSSetThreshold",r3,&r3,&flg));
    1326:     PetscCall(PetscOptionsReal("-eps_ciss_spurious_threshold","Threshold for the spurious eigenpairs","EPSCISSSetThreshold",r4,&r4,&flg2));
    1327:     if (flg || flg2) PetscCall(EPSCISSSetThreshold(eps,r3,r4));

    1329:     PetscCall(EPSCISSGetRefinement(eps,&i6,&i7));
    1330:     PetscCall(PetscOptionsInt("-eps_ciss_refine_inner","Number of inner iterative refinement iterations","EPSCISSSetRefinement",i6,&i6,&flg));
    1331:     PetscCall(PetscOptionsInt("-eps_ciss_refine_blocksize","Number of blocksize iterative refinement iterations","EPSCISSSetRefinement",i7,&i7,&flg2));
    1332:     if (flg || flg2) PetscCall(EPSCISSSetRefinement(eps,i6,i7));

    1334:     PetscCall(EPSCISSGetUseST(eps,&b2));
    1335:     PetscCall(PetscOptionsBool("-eps_ciss_usest","Use ST for linear solves","EPSCISSSetUseST",b2,&b2,&flg));
    1336:     if (flg) PetscCall(EPSCISSSetUseST(eps,b2));

    1338:     PetscCall(PetscOptionsEnum("-eps_ciss_quadrule","Quadrature rule","EPSCISSSetQuadRule",EPSCISSQuadRules,(PetscEnum)ctx->quad,(PetscEnum*)&quad,&flg));
    1339:     if (flg) PetscCall(EPSCISSSetQuadRule(eps,quad));

    1341:     PetscCall(PetscOptionsEnum("-eps_ciss_extraction","Extraction technique","EPSCISSSetExtraction",EPSCISSExtractions,(PetscEnum)ctx->extraction,(PetscEnum*)&extraction,&flg));
    1342:     if (flg) PetscCall(EPSCISSSetExtraction(eps,extraction));

    1344:   PetscOptionsHeadEnd();

    1346:   if (!eps->rg) PetscCall(EPSGetRG(eps,&eps->rg));
    1347:   PetscCall(RGSetFromOptions(eps->rg)); /* this is necessary here to set useconj */
    1348:   if (!ctx->contour || !ctx->contour->ksp) PetscCall(EPSCISSGetKSPs(eps,NULL,NULL));
    1349:   PetscAssert(ctx->contour && ctx->contour->ksp,PetscObjectComm((PetscObject)eps),PETSC_ERR_PLIB,"Something went wrong with EPSCISSGetKSPs()");
    1350:   for (i=0;i<ctx->contour->npoints;i++) PetscCall(KSPSetFromOptions(ctx->contour->ksp[i]));
    1351:   PetscCall(PetscSubcommSetFromOptions(ctx->contour->subcomm));
    1352:   PetscFunctionReturn(PETSC_SUCCESS);
    1353: }

    1355: static PetscErrorCode EPSDestroy_CISS(EPS eps)
    1356: {
    1357:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;

    1359:   PetscFunctionBegin;
    1360:   PetscCall(SlepcContourDataDestroy(&ctx->contour));
    1361:   PetscCall(PetscFree4(ctx->weight,ctx->omega,ctx->pp,ctx->sigma));
    1362:   PetscCall(PetscFree(eps->data));
    1363:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetSizes_C",NULL));
    1364:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetSizes_C",NULL));
    1365:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetThreshold_C",NULL));
    1366:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetThreshold_C",NULL));
    1367:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetRefinement_C",NULL));
    1368:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetRefinement_C",NULL));
    1369:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetUseST_C",NULL));
    1370:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetUseST_C",NULL));
    1371:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetQuadRule_C",NULL));
    1372:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetQuadRule_C",NULL));
    1373:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetExtraction_C",NULL));
    1374:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetExtraction_C",NULL));
    1375:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetKSPs_C",NULL));
    1376:   PetscFunctionReturn(PETSC_SUCCESS);
    1377: }

    1379: static PetscErrorCode EPSView_CISS(EPS eps,PetscViewer viewer)
    1380: {
    1381:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    1382:   PetscBool      isascii;
    1383:   PetscViewer    sviewer;

    1385:   PetscFunctionBegin;
    1386:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii));
    1387:   if (isascii) {
    1388:     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));
    1389:     if (ctx->isreal) PetscCall(PetscViewerASCIIPrintf(viewer,"  exploiting symmetry of integration points\n"));
    1390:     PetscCall(PetscViewerASCIIPrintf(viewer,"  threshold { delta: %g, spurious threshold: %g }\n",(double)ctx->delta,(double)ctx->spurious_threshold));
    1391:     PetscCall(PetscViewerASCIIPrintf(viewer,"  iterative refinement { inner: %" PetscInt_FMT ", blocksize: %" PetscInt_FMT " }\n",ctx->refine_inner, ctx->refine_blocksize));
    1392:     PetscCall(PetscViewerASCIIPrintf(viewer,"  extraction: %s\n",EPSCISSExtractions[ctx->extraction]));
    1393:     PetscCall(PetscViewerASCIIPrintf(viewer,"  quadrature rule: %s\n",EPSCISSQuadRules[ctx->quad]));
    1394:     if (ctx->usest) PetscCall(PetscViewerASCIIPrintf(viewer,"  using ST for linear solves\n"));
    1395:     else {
    1396:       if (!ctx->contour || !ctx->contour->ksp) PetscCall(EPSCISSGetKSPs(eps,NULL,NULL));
    1397:       PetscAssert(ctx->contour && ctx->contour->ksp,PetscObjectComm((PetscObject)eps),PETSC_ERR_PLIB,"Something went wrong with EPSCISSGetKSPs()");
    1398:       PetscCall(PetscViewerASCIIPushTab(viewer));
    1399:       if (ctx->npart>1 && ctx->contour->subcomm) {
    1400:         PetscCall(PetscViewerGetSubViewer(viewer,ctx->contour->subcomm->child,&sviewer));
    1401:         if (!ctx->contour->subcomm->color) PetscCall(KSPView(ctx->contour->ksp[0],sviewer));
    1402:         PetscCall(PetscViewerFlush(sviewer));
    1403:         PetscCall(PetscViewerRestoreSubViewer(viewer,ctx->contour->subcomm->child,&sviewer));
    1404:         /* extra call needed because of the two calls to PetscViewerASCIIPushSynchronized() in PetscViewerGetSubViewer() */
    1405:         PetscCall(PetscViewerASCIIPopSynchronized(viewer));
    1406:       } else PetscCall(KSPView(ctx->contour->ksp[0],viewer));
    1407:       PetscCall(PetscViewerASCIIPopTab(viewer));
    1408:     }
    1409:   }
    1410:   PetscFunctionReturn(PETSC_SUCCESS);
    1411: }

    1413: static PetscErrorCode EPSSetDefaultST_CISS(EPS eps)
    1414: {
    1415:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    1416:   PetscBool      usest = ctx->usest;
    1417:   KSP            ksp;
    1418:   PC             pc;

    1420:   PetscFunctionBegin;
    1421:   if (!((PetscObject)eps->st)->type_name) {
    1422:     if (!ctx->usest_set) usest = (ctx->npart>1)? PETSC_FALSE: PETSC_TRUE;
    1423:     if (usest) PetscCall(STSetType(eps->st,STSINVERT));
    1424:     else {
    1425:       /* we are not going to use ST, so avoid factorizing the matrix */
    1426:       PetscCall(STSetType(eps->st,STSHIFT));
    1427:       if (eps->isgeneralized) {
    1428:         PetscCall(STGetKSP(eps->st,&ksp));
    1429:         PetscCall(KSPGetPC(ksp,&pc));
    1430:         PetscCall(PCSetType(pc,PCNONE));
    1431:       }
    1432:     }
    1433:   }
    1434:   PetscFunctionReturn(PETSC_SUCCESS);
    1435: }

    1437: /*MC
    1438:    EPSCISS - EPSCISS = "ciss" - A contour integral eigensolver based on the
    1439:    Sakurai-Sugiura scheme.

    1441:    Notes:
    1442:    This solver is based on the numerical contour integration idea
    1443:    proposed initially by {cite:t}`Sak03` and improved later by adding
    1444:    a Rayleigh-Ritz projection step {cite:p}`Sak07`.

    1446:    Contour integral methods are able to compute all eigenvalues
    1447:    lying inside a region of the complex plane. Use `EPSGetRG()` to
    1448:    specify the region. However, the computational cost is usually high
    1449:    because multiple linear systems must be solved. For this, we can
    1450:    use the `KSP` object inside `ST`, or several independent `KSP`s,
    1451:    see `EPSCISSSetUseST()`.

    1453:    Details of the implementation in SLEPc can be found in {cite:p}`Mae16`.

    1455:    Level: beginner

    1457: .seealso: [](ch:eps), `EPS`, `EPSType`, `EPSSetType()`, `EPSGetRG()`
    1458: M*/
    1459: SLEPC_EXTERN PetscErrorCode EPSCreate_CISS(EPS eps)
    1460: {
    1461:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;

    1463:   PetscFunctionBegin;
    1464:   PetscCall(PetscNew(&ctx));
    1465:   eps->data = ctx;

    1467:   eps->useds = PETSC_TRUE;
    1468:   eps->categ = EPS_CATEGORY_CONTOUR;

    1470:   eps->ops->solve          = EPSSolve_CISS;
    1471:   eps->ops->setup          = EPSSetUp_CISS;
    1472:   eps->ops->setupsort      = EPSSetUpSort_CISS;
    1473:   eps->ops->setfromoptions = EPSSetFromOptions_CISS;
    1474:   eps->ops->destroy        = EPSDestroy_CISS;
    1475:   eps->ops->reset          = EPSReset_CISS;
    1476:   eps->ops->view           = EPSView_CISS;
    1477:   eps->ops->computevectors = EPSComputeVectors_CISS;
    1478:   eps->ops->setdefaultst   = EPSSetDefaultST_CISS;

    1480:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetSizes_C",EPSCISSSetSizes_CISS));
    1481:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetSizes_C",EPSCISSGetSizes_CISS));
    1482:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetThreshold_C",EPSCISSSetThreshold_CISS));
    1483:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetThreshold_C",EPSCISSGetThreshold_CISS));
    1484:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetRefinement_C",EPSCISSSetRefinement_CISS));
    1485:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetRefinement_C",EPSCISSGetRefinement_CISS));
    1486:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetUseST_C",EPSCISSSetUseST_CISS));
    1487:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetUseST_C",EPSCISSGetUseST_CISS));
    1488:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetQuadRule_C",EPSCISSSetQuadRule_CISS));
    1489:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetQuadRule_C",EPSCISSGetQuadRule_CISS));
    1490:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetExtraction_C",EPSCISSSetExtraction_CISS));
    1491:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetExtraction_C",EPSCISSGetExtraction_CISS));
    1492:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetKSPs_C",EPSCISSGetKSPs_CISS));

    1494:   /* set default values of parameters */
    1495:   ctx->N                  = 32;
    1496:   ctx->L                  = 16;
    1497:   ctx->M                  = ctx->N/4;
    1498:   ctx->delta              = SLEPC_DEFAULT_TOL*1e-4;
    1499:   ctx->L_max              = 64;
    1500:   ctx->spurious_threshold = PetscSqrtReal(SLEPC_DEFAULT_TOL);
    1501:   ctx->usest              = PETSC_TRUE;
    1502:   ctx->usest_set          = PETSC_FALSE;
    1503:   ctx->isreal             = PETSC_FALSE;
    1504:   ctx->refine_inner       = 0;
    1505:   ctx->refine_blocksize   = 0;
    1506:   ctx->npart              = 1;
    1507:   ctx->quad               = (EPSCISSQuadRule)0;
    1508:   ctx->extraction         = EPS_CISS_EXTRACTION_RITZ;
    1509:   PetscFunctionReturn(PETSC_SUCCESS);
    1510: }