Date: 2021-02-01T14:41:57+00:00

Actual source code: ciss.c
slepc-3.14.2 2021-02-01
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2020, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.
      7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
      8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      9: */
     10: /*
     11:    SLEPc 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 <slepcblaslapack.h>

     36: PetscLogEvent EPS_CISS_SVD;

     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;     /* A and B are real */
     47:   PetscInt          npart;      /* number of partitions */
     48:   PetscInt          refine_inner;
     49:   PetscInt          refine_blocksize;
     50:   /* private data */
     51:   PetscReal         *sigma;     /* threshold for numerical rank */
     52:   PetscInt          subcomm_id;
     53:   PetscInt          num_solve_point;
     54:   PetscScalar       *weight;
     55:   PetscScalar       *omega;
     56:   PetscScalar       *pp;
     57:   BV                V;
     58:   BV                S;
     59:   BV                pV;
     60:   BV                Y;
     61:   Vec               xsub;
     62:   Vec               xdup;
     63:   KSP               *ksp;       /* ksp array for storing factorizations at integration points */
     64:   PetscBool         useconj;
     65:   PetscReal         est_eig;
     66:   VecScatter        scatterin;
     67:   Mat               pA,pB;
     68:   PetscSubcomm      subcomm;
     69:   PetscBool         usest;
     70:   PetscBool         usest_set;  /* whether the user set the usest flag or not */
     71:   EPSCISSQuadRule   quad;
     72:   EPSCISSExtraction extraction;
     73: } EPS_CISS;

     75: /* destroy KSP objects when the number of solve points changes */
     76: PETSC_STATIC_INLINE PetscErrorCode EPSCISSResetSolvers(EPS eps)
     77: {
     79:   PetscInt       i;
     80:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;

     83:   if (ctx->ksp) {
     84:     for (i=0;i<ctx->num_solve_point;i++) {
     85:       KSPDestroy(&ctx->ksp[i]);
     86:     }
     87:     PetscFree(ctx->ksp);
     88:   }
     89:   return(0);
     90: }

     92: /* clean PetscSubcomm object when the number of partitions changes */
     93: PETSC_STATIC_INLINE PetscErrorCode EPSCISSResetSubcomm(EPS eps)
     94: {
     96:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;

     99:   EPSCISSResetSolvers(eps);
    100:   PetscSubcommDestroy(&ctx->subcomm);
    101:   return(0);
    102: }

    104: /* determine whether half of integration points can be avoided (use its conjugates);
    105:    depends on isreal and the center of the region */
    106: PETSC_STATIC_INLINE PetscErrorCode EPSCISSSetUseConj(EPS eps,PetscBool *useconj)
    107: {
    109:   PetscScalar    center;
    110:   PetscReal      c,d;
    111:   PetscBool      isellipse,isinterval;
    112: #if defined(PETSC_USE_COMPLEX)
    113:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    114: #endif

    117:   *useconj = PETSC_FALSE;
    118:   PetscObjectTypeCompare((PetscObject)eps->rg,RGELLIPSE,&isellipse);
    119:   if (isellipse) {
    120:     RGEllipseGetParameters(eps->rg,&center,NULL,NULL);
    121: #if defined(PETSC_USE_COMPLEX)
    122:     *useconj = (ctx->isreal && PetscImaginaryPart(center) == 0.0)? PETSC_TRUE: PETSC_FALSE;
    123: #endif
    124:   } else {
    125:     PetscObjectTypeCompare((PetscObject)eps->rg,RGINTERVAL,&isinterval);
    126:     if (isinterval) {
    127:       RGIntervalGetEndpoints(eps->rg,NULL,NULL,&c,&d);
    128: #if defined(PETSC_USE_COMPLEX)
    129:       *useconj = (ctx->isreal && c==d)? PETSC_TRUE: PETSC_FALSE;
    130: #endif
    131:     }
    132:   }
    133:   return(0);
    134: }

    136: /* create PetscSubcomm object and determine num_solve_point (depends on npart, N, useconj) */
    137: PETSC_STATIC_INLINE PetscErrorCode EPSCISSSetUpSubComm(EPS eps,PetscInt *num_solve_point)
    138: {
    140:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    141:   PetscInt       N = ctx->N;

    144:   PetscSubcommCreate(PetscObjectComm((PetscObject)eps),&ctx->subcomm);
    145:   PetscSubcommSetNumber(ctx->subcomm,ctx->npart);
    146:   PetscSubcommSetType(ctx->subcomm,PETSC_SUBCOMM_INTERLACED);
    147:   PetscLogObjectMemory((PetscObject)eps,sizeof(PetscSubcomm));
    148:   ctx->subcomm_id = ctx->subcomm->color;
    149:   EPSCISSSetUseConj(eps,&ctx->useconj);
    150:   if (ctx->useconj) N = N/2;
    151:   *num_solve_point = N / ctx->npart;
    152:   if (N%ctx->npart > ctx->subcomm_id) (*num_solve_point)++;
    153:   return(0);
    154: }

    156: static PetscErrorCode CISSRedundantMat(EPS eps)
    157: {
    159:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    160:   Mat            A,B;
    161:   PetscInt       nmat;

    164:   STGetNumMatrices(eps->st,&nmat);
    165:   if (ctx->subcomm->n != 1) {
    166:     STGetMatrix(eps->st,0,&A);
    167:     MatDestroy(&ctx->pA);
    168:     MatCreateRedundantMatrix(A,ctx->subcomm->n,PetscSubcommChild(ctx->subcomm),MAT_INITIAL_MATRIX,&ctx->pA);
    169:     if (nmat>1) {
    170:       STGetMatrix(eps->st,1,&B);
    171:       MatDestroy(&ctx->pB);
    172:       MatCreateRedundantMatrix(B,ctx->subcomm->n,PetscSubcommChild(ctx->subcomm),MAT_INITIAL_MATRIX,&ctx->pB);
    173:     } else ctx->pB = NULL;
    174:   } else {
    175:     ctx->pA = NULL;
    176:     ctx->pB = NULL;
    177:   }
    178:   return(0);
    179: }

    181: static PetscErrorCode CISSScatterVec(EPS eps)
    182: {
    184:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    185:   IS             is1,is2;
    186:   Vec            v0;
    187:   PetscInt       i,j,k,mstart,mend,mlocal;
    188:   PetscInt       *idx1,*idx2,mloc_sub;

    191:   VecDestroy(&ctx->xsub);
    192:   MatCreateVecs(ctx->pA,&ctx->xsub,NULL);

    194:   VecDestroy(&ctx->xdup);
    195:   MatGetLocalSize(ctx->pA,&mloc_sub,NULL);
    196:   VecCreateMPI(PetscSubcommContiguousParent(ctx->subcomm),mloc_sub,PETSC_DECIDE,&ctx->xdup);

    198:   VecScatterDestroy(&ctx->scatterin);
    199:   BVGetColumn(ctx->V,0,&v0);
    200:   VecGetOwnershipRange(v0,&mstart,&mend);
    201:   mlocal = mend - mstart;
    202:   PetscMalloc2(ctx->subcomm->n*mlocal,&idx1,ctx->subcomm->n*mlocal,&idx2);
    203:   j = 0;
    204:   for (k=0;k<ctx->subcomm->n;k++) {
    205:     for (i=mstart;i<mend;i++) {
    206:       idx1[j]   = i;
    207:       idx2[j++] = i + eps->n*k;
    208:     }
    209:   }
    210:   ISCreateGeneral(PetscObjectComm((PetscObject)eps),ctx->subcomm->n*mlocal,idx1,PETSC_COPY_VALUES,&is1);
    211:   ISCreateGeneral(PetscObjectComm((PetscObject)eps),ctx->subcomm->n*mlocal,idx2,PETSC_COPY_VALUES,&is2);
    212:   VecScatterCreate(v0,is1,ctx->xdup,is2,&ctx->scatterin);
    213:   ISDestroy(&is1);
    214:   ISDestroy(&is2);
    215:   PetscFree2(idx1,idx2);
    216:   BVRestoreColumn(ctx->V,0,&v0);
    217:   return(0);
    218: }

    220: static PetscErrorCode SetPathParameter(EPS eps)
    221: {
    223:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    224:   PetscInt       i,j;
    225:   PetscScalar    center=0.0,tmp,tmp2,*omegai;
    226:   PetscReal      theta,radius=1.0,vscale,a,b,c,d,max_w=0.0,rgscale;
    227: #if defined(PETSC_USE_COMPLEX)
    228:   PetscReal      start_ang,end_ang;
    229: #endif
    230:   PetscBool      isring=PETSC_FALSE,isellipse=PETSC_FALSE,isinterval=PETSC_FALSE;

    233:   PetscObjectTypeCompare((PetscObject)eps->rg,RGELLIPSE,&isellipse);
    234:   PetscObjectTypeCompare((PetscObject)eps->rg,RGRING,&isring);
    235:   PetscObjectTypeCompare((PetscObject)eps->rg,RGINTERVAL,&isinterval);
    236:   RGGetScale(eps->rg,&rgscale);
    237:   PetscMalloc1(ctx->N+1l,&omegai);
    238:   RGComputeContour(eps->rg,ctx->N,ctx->omega,omegai);
    239:   if (isellipse) {
    240:     RGEllipseGetParameters(eps->rg,&center,&radius,&vscale);
    241:     for (i=0;i<ctx->N;i++) {
    242: #if defined(PETSC_USE_COMPLEX)
    243:       theta = 2.0*PETSC_PI*(i+0.5)/ctx->N;
    244:       ctx->pp[i] = PetscCMPLX(PetscCosReal(theta),vscale*PetscSinReal(theta));
    245:       ctx->weight[i] = rgscale*radius*(PetscCMPLX(vscale*PetscCosReal(theta),PetscSinReal(theta)))/(PetscReal)ctx->N;
    246: #else
    247:       theta = (PETSC_PI/ctx->N)*(i+0.5);
    248:       ctx->pp[i] = PetscCosReal(theta);
    249:       ctx->weight[i] = PetscCosReal((ctx->N-1)*theta)/ctx->N;
    250:       ctx->omega[i] = rgscale*(center + radius*ctx->pp[i]);
    251: #endif
    252:     }
    253:   } else if (ctx->quad == EPS_CISS_QUADRULE_CHEBYSHEV) {
    254:     for (i=0;i<ctx->N;i++) {
    255:       theta = (PETSC_PI/ctx->N)*(i+0.5);
    256:       ctx->pp[i] = PetscCosReal(theta);
    257:       ctx->weight[i] = PetscCosReal((ctx->N-1)*theta)/ctx->N;
    258:     }
    259:     if (isinterval) {
    260:       RGIntervalGetEndpoints(eps->rg,&a,&b,&c,&d);
    261:       if ((c!=d || c!=0.0) && (a!=b || a!=0.0)) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Endpoints of the imaginary axis or the real axis must be both zero");
    262:       for (i=0;i<ctx->N;i++) {
    263:         if (c==d) ctx->omega[i] = ((b-a)*(ctx->pp[i]+1.0)/2.0+a)*rgscale;
    264:         if (a==b) {
    265: #if defined(PETSC_USE_COMPLEX)
    266:           ctx->omega[i] = ((d-c)*(ctx->pp[i]+1.0)/2.0+c)*rgscale*PETSC_i;
    267: #else
    268:           SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Integration points on a vertical line require complex arithmetic");
    269: #endif
    270:         }
    271:       }
    272:     }
    273:     if (isring) {  /* only supported in complex scalars */
    274: #if defined(PETSC_USE_COMPLEX)
    275:       RGRingGetParameters(eps->rg,&center,&radius,&vscale,&start_ang,&end_ang,NULL);
    276:       for (i=0;i<ctx->N;i++) {
    277:         theta = (start_ang*2.0+(end_ang-start_ang)*(PetscRealPart(ctx->pp[i])+1.0))*PETSC_PI;
    278:         ctx->omega[i] = rgscale*(center + radius*PetscCMPLX(PetscCosReal(theta),vscale*PetscSinReal(theta)));
    279:       }
    280: #endif
    281:     }
    282:   } else {
    283:     if (isinterval) {
    284:       RGIntervalGetEndpoints(eps->rg,&a,&b,&c,&d);
    285:       center = rgscale*((b+a)/2.0+(d+c)/2.0*PETSC_PI);
    286:       radius = PetscSqrtReal(PetscPowRealInt(rgscale*(b-a)/2.0,2)+PetscPowRealInt(rgscale*(d-c)/2.0,2));
    287:     } else if (isring) {
    288:       RGRingGetParameters(eps->rg,&center,&radius,NULL,NULL,NULL,NULL);
    289:       center *= rgscale;
    290:       radius *= rgscale;
    291:     }
    292:     for (i=0;i<ctx->N;i++) {
    293:       ctx->pp[i] = (ctx->omega[i]-center)/radius;
    294:       tmp = 1; tmp2 = 1;
    295:       for (j=0;j<ctx->N;j++) {
    296:         tmp *= ctx->omega[j];
    297:         if (i != j) tmp2 *= ctx->omega[j]-ctx->omega[i];
    298:       }
    299:       ctx->weight[i] = tmp/tmp2;
    300:       max_w = PetscMax(PetscAbsScalar(ctx->weight[i]),max_w);
    301:     }
    302:     for (i=0;i<ctx->N;i++) ctx->weight[i] /= (PetscScalar)max_w;
    303:   }
    304:   PetscFree(omegai);
    305:   return(0);
    306: }

    308: static PetscErrorCode CISSVecSetRandom(BV V,PetscInt i0,PetscInt i1)
    309: {
    311:   PetscInt       i,j,nlocal;
    312:   PetscScalar    *vdata;
    313:   Vec            x;

    316:   BVGetSizes(V,&nlocal,NULL,NULL);
    317:   for (i=i0;i<i1;i++) {
    318:     BVSetRandomColumn(V,i);
    319:     BVGetColumn(V,i,&x);
    320:     VecGetArray(x,&vdata);
    321:     for (j=0;j<nlocal;j++) {
    322:       vdata[j] = PetscRealPart(vdata[j]);
    323:       if (PetscRealPart(vdata[j]) < 0.5) vdata[j] = -1.0;
    324:       else vdata[j] = 1.0;
    325:     }
    326:     VecRestoreArray(x,&vdata);
    327:     BVRestoreColumn(V,i,&x);
    328:   }
    329:   return(0);
    330: }

    332: static PetscErrorCode VecScatterVecs(EPS eps,BV Vin,PetscInt n)
    333: {
    334:   PetscErrorCode    ierr;
    335:   EPS_CISS          *ctx = (EPS_CISS*)eps->data;
    336:   PetscInt          i;
    337:   Vec               vi,pvi;
    338:   const PetscScalar *array;

    341:   for (i=0;i<n;i++) {
    342:     BVGetColumn(Vin,i,&vi);
    343:     VecScatterBegin(ctx->scatterin,vi,ctx->xdup,INSERT_VALUES,SCATTER_FORWARD);
    344:     VecScatterEnd(ctx->scatterin,vi,ctx->xdup,INSERT_VALUES,SCATTER_FORWARD);
    345:     BVRestoreColumn(Vin,i,&vi);
    346:     VecGetArrayRead(ctx->xdup,&array);
    347:     VecPlaceArray(ctx->xsub,array);
    348:     BVGetColumn(ctx->pV,i,&pvi);
    349:     VecCopy(ctx->xsub,pvi);
    350:     BVRestoreColumn(ctx->pV,i,&pvi);
    351:     VecResetArray(ctx->xsub);
    352:     VecRestoreArrayRead(ctx->xdup,&array);
    353:   }
    354:   return(0);
    355: }

    357: static PetscErrorCode SolveLinearSystem(EPS eps,Mat A,Mat B,BV V,PetscInt L_start,PetscInt L_end,PetscBool initksp)
    358: {
    360:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    361:   PetscInt       i,p_id;
    362:   Mat            Fz,kspMat,MV,BMV=NULL,MC;
    363:   KSP            ksp;

    366:   if (!ctx->ksp) { EPSCISSGetKSPs(eps,&ctx->num_solve_point,&ctx->ksp); }
    367:   if (ctx->usest) {
    368:     MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&Fz);
    369:   }
    370:   BVSetActiveColumns(V,L_start,L_end);
    371:   BVGetMat(V,&MV);
    372:   if (B) {
    373:     MatProductCreate(B,MV,NULL,&BMV);
    374:     MatProductSetType(BMV,MATPRODUCT_AB);
    375:     MatProductSetFromOptions(BMV);
    376:     MatProductSymbolic(BMV);
    377:   }
    378:   for (i=0;i<ctx->num_solve_point;i++) {
    379:     p_id = i*ctx->subcomm->n + ctx->subcomm_id;
    380:     if (!ctx->usest && initksp) {
    381:       MatDuplicate(A,MAT_COPY_VALUES,&kspMat);
    382:       if (B) {
    383:         MatAXPY(kspMat,-ctx->omega[p_id],B,DIFFERENT_NONZERO_PATTERN);
    384:       } else {
    385:         MatShift(kspMat,-ctx->omega[p_id]);
    386:       }
    387:       KSPSetOperators(ctx->ksp[i],kspMat,kspMat);
    388:       MatDestroy(&kspMat);
    389:     } else if (ctx->usest) {
    390:       STSetShift(eps->st,ctx->omega[p_id]);
    391:       STGetKSP(eps->st,&ksp);
    392:     }
    393:     BVSetActiveColumns(ctx->Y,i*ctx->L_max+L_start,i*ctx->L_max+L_end);
    394:     BVGetMat(ctx->Y,&MC);
    395:     if (B) {
    396:       MatProductNumeric(BMV);
    397:       if (ctx->usest) {
    398:         KSPMatSolve(ksp,BMV,MC);
    399:       } else {
    400:         KSPMatSolve(ctx->ksp[i],BMV,MC);
    401:       }
    402:     } else {
    403:       if (ctx->usest) {
    404:         KSPMatSolve(ksp,MV,MC);
    405:       } else {
    406:         KSPMatSolve(ctx->ksp[i],MV,MC);
    407:       }
    408:     }
    409:     if (ctx->usest && i<ctx->num_solve_point-1) { KSPReset(ksp); }
    410:     BVRestoreMat(ctx->Y,&MC);
    411:   }
    412:   MatDestroy(&BMV);
    413:   BVRestoreMat(V,&MV);
    414:   if (ctx->usest) { MatDestroy(&Fz); }
    415:   return(0);
    416: }

    418: #if defined(PETSC_USE_COMPLEX)
    419: static PetscErrorCode EstimateNumberEigs(EPS eps,PetscInt *L_add)
    420: {
    422:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    423:   PetscInt       i,j,p_id;
    424:   PetscScalar    tmp,m = 1,sum = 0.0;
    425:   PetscReal      eta;
    426:   Vec            v,vtemp,vj;

    429:   BVCreateVec(ctx->Y,&v);
    430:   BVCreateVec(ctx->V,&vtemp);
    431:   for (j=0;j<ctx->L;j++) {
    432:     VecSet(v,0);
    433:     for (i=0;i<ctx->num_solve_point; i++) {
    434:       p_id = i*ctx->subcomm->n + ctx->subcomm_id;
    435:       BVSetActiveColumns(ctx->Y,i*ctx->L_max+j,i*ctx->L_max+j+1);
    436:       BVMultVec(ctx->Y,ctx->weight[p_id],1,v,&m);
    437:     }
    438:     BVGetColumn(ctx->V,j,&vj);
    439:     if (ctx->pA) {
    440:       VecSet(vtemp,0);
    441:       VecScatterBegin(ctx->scatterin,v,vtemp,ADD_VALUES,SCATTER_REVERSE);
    442:       VecScatterEnd(ctx->scatterin,v,vtemp,ADD_VALUES,SCATTER_REVERSE);
    443:       VecDot(vj,vtemp,&tmp);
    444:     } else {
    445:       VecDot(vj,v,&tmp);
    446:     }
    447:     BVRestoreColumn(ctx->V,j,&vj);
    448:     if (ctx->useconj) sum += PetscRealPart(tmp)*2;
    449:     else sum += tmp;
    450:   }
    451:   ctx->est_eig = PetscAbsScalar(sum/(PetscReal)ctx->L);
    452:   eta = PetscPowReal(10.0,-PetscLog10Real(eps->tol)/ctx->N);
    453:   PetscInfo1(eps,"Estimation_#Eig %f\n",(double)ctx->est_eig);
    454:   *L_add = (PetscInt)PetscCeilReal((ctx->est_eig*eta)/ctx->M) - ctx->L;
    455:   if (*L_add < 0) *L_add = 0;
    456:   if (*L_add>ctx->L_max-ctx->L) {
    457:     PetscInfo(eps,"Number of eigenvalues around the contour path may be too large\n");
    458:     *L_add = ctx->L_max-ctx->L;
    459:   }
    460:   VecDestroy(&v);
    461:   VecDestroy(&vtemp);
    462:   return(0);
    463: }
    464: #endif

    466: static PetscErrorCode CalcMu(EPS eps,PetscScalar *Mu)
    467: {
    469:   PetscMPIInt    sub_size,len;
    470:   PetscInt       i,j,k,s;
    471:   PetscScalar    *m,*temp,*temp2,*ppk,alp;
    472:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    473:   Mat            M;

    476:   MPI_Comm_size(PetscSubcommChild(ctx->subcomm),&sub_size);
    477:   PetscMalloc3(ctx->num_solve_point*ctx->L*(ctx->L+1),&temp,2*ctx->M*ctx->L*ctx->L,&temp2,ctx->num_solve_point,&ppk);
    478:   MatCreateSeqDense(PETSC_COMM_SELF,ctx->L,ctx->L_max*ctx->num_solve_point,NULL,&M);
    479:   for (i=0;i<2*ctx->M*ctx->L*ctx->L;i++) temp2[i] = 0;
    480:   BVSetActiveColumns(ctx->Y,0,ctx->L_max*ctx->num_solve_point);
    481:   if (ctx->pA) {
    482:     BVSetActiveColumns(ctx->pV,0,ctx->L);
    483:     BVDot(ctx->Y,ctx->pV,M);
    484:   } else {
    485:     BVSetActiveColumns(ctx->V,0,ctx->L);
    486:     BVDot(ctx->Y,ctx->V,M);
    487:   }
    488:   MatDenseGetArray(M,&m);
    489:   for (i=0;i<ctx->num_solve_point;i++) {
    490:     for (j=0;j<ctx->L;j++) {
    491:       for (k=0;k<ctx->L;k++) {
    492:         temp[k+j*ctx->L+i*ctx->L*ctx->L]=m[k+j*ctx->L+i*ctx->L*ctx->L_max];
    493:       }
    494:     }
    495:   }
    496:   MatDenseRestoreArray(M,&m);
    497:   for (i=0;i<ctx->num_solve_point;i++) ppk[i] = 1;
    498:   for (k=0;k<2*ctx->M;k++) {
    499:     for (j=0;j<ctx->L;j++) {
    500:       for (i=0;i<ctx->num_solve_point;i++) {
    501:         alp = ppk[i]*ctx->weight[i*ctx->subcomm->n + ctx->subcomm_id];
    502:         for (s=0;s<ctx->L;s++) {
    503:           if (ctx->useconj) temp2[s+(j+k*ctx->L)*ctx->L] += PetscRealPart(alp*temp[s+(j+i*ctx->L)*ctx->L])*2;
    504:           else temp2[s+(j+k*ctx->L)*ctx->L] += alp*temp[s+(j+i*ctx->L)*ctx->L];
    505:         }
    506:       }
    507:     }
    508:     for (i=0;i<ctx->num_solve_point;i++)
    509:       ppk[i] *= ctx->pp[i*ctx->subcomm->n + ctx->subcomm_id];
    510:   }
    511:   for (i=0;i<2*ctx->M*ctx->L*ctx->L;i++) temp2[i] /= sub_size;
    512:   PetscMPIIntCast(2*ctx->M*ctx->L*ctx->L,&len);
    513:   MPIU_Allreduce(temp2,Mu,len,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)eps));
    514:   PetscFree3(temp,temp2,ppk);
    515:   MatDestroy(&M);
    516:   return(0);
    517: }

    519: static PetscErrorCode BlockHankel(EPS eps,PetscScalar *Mu,PetscInt s,PetscScalar *H)
    520: {
    521:   EPS_CISS *ctx = (EPS_CISS*)eps->data;
    522:   PetscInt i,j,k,L=ctx->L,M=ctx->M;

    525:   for (k=0;k<L*M;k++)
    526:     for (j=0;j<M;j++)
    527:       for (i=0;i<L;i++)
    528:         H[j*L+i+k*L*M] = Mu[i+k*L+(j+s)*L*L];
    529:   return(0);
    530: }

    532: static PetscErrorCode SVD_H0(EPS eps,PetscScalar *S,PetscInt *K)
    533: {
    535:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    536:   PetscInt       i,ml=ctx->L*ctx->M;
    537:   PetscBLASInt   m,n,lda,ldu,ldvt,lwork,info;
    538:   PetscScalar    *work;
    539: #if defined(PETSC_USE_COMPLEX)
    540:   PetscReal      *rwork;
    541: #endif

    544:   PetscLogEventBegin(EPS_CISS_SVD,eps,0,0,0);
    545:   PetscMalloc1(5*ml,&work);
    546: #if defined(PETSC_USE_COMPLEX)
    547:   PetscMalloc1(5*ml,&rwork);
    548: #endif
    549:   PetscBLASIntCast(ml,&m);
    550:   n = m; lda = m; ldu = m; ldvt = m; lwork = 5*m;
    551:   PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    552: #if defined(PETSC_USE_COMPLEX)
    553:   PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("N","N",&m,&n,S,&lda,ctx->sigma,NULL,&ldu,NULL,&ldvt,work,&lwork,rwork,&info));
    554: #else
    555:   PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("N","N",&m,&n,S,&lda,ctx->sigma,NULL,&ldu,NULL,&ldvt,work,&lwork,&info));
    556: #endif
    557:   SlepcCheckLapackInfo("gesvd",info);
    558:   PetscFPTrapPop();
    559:   (*K) = 0;
    560:   for (i=0;i<ml;i++) {
    561:     if (ctx->sigma[i]/PetscMax(ctx->sigma[0],1)>ctx->delta) (*K)++;
    562:   }
    563:   PetscFree(work);
    564: #if defined(PETSC_USE_COMPLEX)
    565:   PetscFree(rwork);
    566: #endif
    567:   PetscLogEventEnd(EPS_CISS_SVD,eps,0,0,0);
    568:   return(0);
    569: }

    571: static PetscErrorCode ConstructS(EPS eps)
    572: {
    574:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    575:   PetscInt       i,j,k,vec_local_size,p_id;
    576:   Vec            v,sj;
    577:   PetscScalar    *ppk, *v_data, m = 1;

    580:   BVGetSizes(ctx->Y,&vec_local_size,NULL,NULL);
    581:   PetscMalloc1(ctx->num_solve_point,&ppk);
    582:   for (i=0;i<ctx->num_solve_point;i++) ppk[i] = 1;
    583:   BVCreateVec(ctx->Y,&v);
    584:   for (k=0;k<ctx->M;k++) {
    585:     for (j=0;j<ctx->L;j++) {
    586:       VecSet(v,0);
    587:       for (i=0;i<ctx->num_solve_point;i++) {
    588:         p_id = i*ctx->subcomm->n + ctx->subcomm_id;
    589:         BVSetActiveColumns(ctx->Y,i*ctx->L_max+j,i*ctx->L_max+j+1);
    590:         BVMultVec(ctx->Y,ppk[i]*ctx->weight[p_id],1.0,v,&m);
    591:       }
    592:       if (ctx->useconj) {
    593:         VecGetArray(v,&v_data);
    594:         for (i=0;i<vec_local_size;i++) v_data[i] = PetscRealPart(v_data[i])*2;
    595:         VecRestoreArray(v,&v_data);
    596:       }
    597:       BVGetColumn(ctx->S,k*ctx->L+j,&sj);
    598:       if (ctx->pA) {
    599:         VecSet(sj,0);
    600:         VecScatterBegin(ctx->scatterin,v,sj,ADD_VALUES,SCATTER_REVERSE);
    601:         VecScatterEnd(ctx->scatterin,v,sj,ADD_VALUES,SCATTER_REVERSE);
    602:       } else {
    603:         VecCopy(v,sj);
    604:       }
    605:       BVRestoreColumn(ctx->S,k*ctx->L+j,&sj);
    606:     }
    607:     for (i=0;i<ctx->num_solve_point;i++) {
    608:       p_id = i*ctx->subcomm->n + ctx->subcomm_id;
    609:       ppk[i] *= ctx->pp[p_id];
    610:     }
    611:   }
    612:   PetscFree(ppk);
    613:   VecDestroy(&v);
    614:   return(0);
    615: }

    617: static PetscErrorCode SVD_S(BV S,PetscInt ml,PetscReal delta,PetscReal *sigma,PetscInt *K)
    618: {
    620:   PetscInt       i,j,k,local_size;
    621:   PetscMPIInt    len;
    622:   PetscScalar    *work,*temp,*B,*tempB,*s_data,*Q1,*Q2,*temp2,alpha=1,beta=0;
    623:   PetscBLASInt   l,m,n,lda,ldu,ldvt,lwork,info,ldb,ldc;
    624: #if defined(PETSC_USE_COMPLEX)
    625:   PetscReal      *rwork;
    626: #endif

    629:   BVGetSizes(S,&local_size,NULL,NULL);
    630:   BVGetArray(S,&s_data);
    631:   PetscMalloc7(ml*ml,&temp,ml*ml,&temp2,local_size*ml,&Q1,local_size*ml,&Q2,ml*ml,&B,ml*ml,&tempB,5*ml,&work);
    632:   PetscArrayzero(B,ml*ml);
    633: #if defined(PETSC_USE_COMPLEX)
    634:   PetscMalloc1(5*ml,&rwork);
    635: #endif
    636:   PetscFPTrapPush(PETSC_FP_TRAP_OFF);

    638:   for (i=0;i<ml;i++) B[i*ml+i]=1;

    640:   for (k=0;k<2;k++) {
    641:     PetscBLASIntCast(local_size,&m);
    642:     PetscBLASIntCast(ml,&l);
    643:     n = l; lda = m; ldb = m; ldc = l;
    644:     if (k == 0) {
    645:       PetscStackCallBLAS("BLASgemm",BLASgemm_("C","N",&l,&n,&m,&alpha,s_data,&lda,s_data,&ldb,&beta,temp,&ldc));
    646:     } else if ((k%2)==1) {
    647:       PetscStackCallBLAS("BLASgemm",BLASgemm_("C","N",&l,&n,&m,&alpha,Q1,&lda,Q1,&ldb,&beta,temp,&ldc));
    648:     } else {
    649:       PetscStackCallBLAS("BLASgemm",BLASgemm_("C","N",&l,&n,&m,&alpha,Q2,&lda,Q2,&ldb,&beta,temp,&ldc));
    650:     }
    651:     PetscArrayzero(temp2,ml*ml);
    652:     PetscMPIIntCast(ml*ml,&len);
    653:     MPIU_Allreduce(temp,temp2,len,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)S));

    655:     PetscBLASIntCast(ml,&m);
    656:     n = m; lda = m; lwork = 5*m, ldu = 1; ldvt = 1;
    657: #if defined(PETSC_USE_COMPLEX)
    658:     PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&m,&n,temp2,&lda,sigma,NULL,&ldu,NULL,&ldvt,work,&lwork,rwork,&info));
    659: #else
    660:     PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("O","N",&m,&n,temp2,&lda,sigma,NULL,&ldu,NULL,&ldvt,work,&lwork,&info));
    661: #endif
    662:     SlepcCheckLapackInfo("gesvd",info);

    664:     PetscBLASIntCast(local_size,&l);
    665:     PetscBLASIntCast(ml,&n);
    666:     m = n; lda = l; ldb = m; ldc = l;
    667:     if (k==0) {
    668:       PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&l,&n,&m,&alpha,s_data,&lda,temp2,&ldb,&beta,Q1,&ldc));
    669:     } else if ((k%2)==1) {
    670:       PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&l,&n,&m,&alpha,Q1,&lda,temp2,&ldb,&beta,Q2,&ldc));
    671:     } else {
    672:       PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&l,&n,&m,&alpha,Q2,&lda,temp2,&ldb,&beta,Q1,&ldc));
    673:     }

    675:     PetscBLASIntCast(ml,&l);
    676:     m = l; n = l; lda = l; ldb = m; ldc = l;
    677:     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&l,&n,&m,&alpha,B,&lda,temp2,&ldb,&beta,tempB,&ldc));
    678:     for (i=0;i<ml;i++) {
    679:       sigma[i] = sqrt(sigma[i]);
    680:       for (j=0;j<local_size;j++) {
    681:         if ((k%2)==1) Q2[j+i*local_size]/=sigma[i];
    682:         else Q1[j+i*local_size]/=sigma[i];
    683:       }
    684:       for (j=0;j<ml;j++) {
    685:         B[j+i*ml]=tempB[j+i*ml]*sigma[i];
    686:       }
    687:     }
    688:   }

    690:   PetscBLASIntCast(ml,&m);
    691:   n = m; lda = m; ldu=1; ldvt=1;
    692: #if defined(PETSC_USE_COMPLEX)
    693:   PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("N","O",&m,&n,B,&lda,sigma,NULL,&ldu,NULL,&ldvt,work,&lwork,rwork,&info));
    694: #else
    695:   PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("N","O",&m,&n,B,&lda,sigma,NULL,&ldu,NULL,&ldvt,work,&lwork,&info));
    696: #endif
    697:   SlepcCheckLapackInfo("gesvd",info);

    699:   PetscBLASIntCast(local_size,&l);
    700:   PetscBLASIntCast(ml,&n);
    701:   m = n; lda = l; ldb = m; ldc = l;
    702:   if ((k%2)==1) {
    703:     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","T",&l,&n,&m,&alpha,Q1,&lda,B,&ldb,&beta,s_data,&ldc));
    704:   } else {
    705:     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","T",&l,&n,&m,&alpha,Q2,&lda,B,&ldb,&beta,s_data,&ldc));
    706:   }

    708:   PetscFPTrapPop();
    709:   BVRestoreArray(S,&s_data);

    711:   (*K) = 0;
    712:   for (i=0;i<ml;i++) {
    713:     if (sigma[i]/PetscMax(sigma[0],1)>delta) (*K)++;
    714:   }
    715:   PetscFree7(temp,temp2,Q1,Q2,B,tempB,work);
    716: #if defined(PETSC_USE_COMPLEX)
    717:   PetscFree(rwork);
    718: #endif
    719:   return(0);
    720: }

    722: static PetscErrorCode isGhost(EPS eps,PetscInt ld,PetscInt nv,PetscBool *fl)
    723: {
    725:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    726:   PetscInt       i,j;
    727:   PetscScalar    *pX;
    728:   PetscReal      *tau,s1,s2,tau_max=0.0;

    731:   PetscMalloc1(nv,&tau);
    732:   DSVectors(eps->ds,DS_MAT_X,NULL,NULL);
    733:   DSGetArray(eps->ds,DS_MAT_X,&pX);

    735:   for (i=0;i<nv;i++) {
    736:     s1 = 0;
    737:     s2 = 0;
    738:     for (j=0;j<nv;j++) {
    739:       s1 += PetscAbsScalar(PetscPowScalarInt(pX[i*ld+j],2));
    740:       s2 += PetscPowRealInt(PetscAbsScalar(pX[i*ld+j]),2)/ctx->sigma[j];
    741:     }
    742:     tau[i] = s1/s2;
    743:     tau_max = PetscMax(tau_max,tau[i]);
    744:   }
    745:   DSRestoreArray(eps->ds,DS_MAT_X,&pX);
    746:   for (i=0;i<nv;i++) {
    747:     tau[i] /= tau_max;
    748:   }
    749:   for (i=0;i<nv;i++) {
    750:     if (tau[i]>=ctx->spurious_threshold) fl[i] = PETSC_TRUE;
    751:     else fl[i] = PETSC_FALSE;
    752:   }
    753:   PetscFree(tau);
    754:   return(0);
    755: }

    757: static PetscErrorCode rescale_eig(EPS eps,PetscInt nv)
    758: {
    760:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    761:   PetscInt       i;
    762:   PetscScalar    center;
    763:   PetscReal      radius,a,b,c,d,rgscale;
    764: #if defined(PETSC_USE_COMPLEX)
    765:   PetscReal      start_ang,end_ang,vscale,theta;
    766: #endif
    767:   PetscBool      isring,isellipse,isinterval;

    770:   PetscObjectTypeCompare((PetscObject)eps->rg,RGELLIPSE,&isellipse);
    771:   PetscObjectTypeCompare((PetscObject)eps->rg,RGRING,&isring);
    772:   PetscObjectTypeCompare((PetscObject)eps->rg,RGINTERVAL,&isinterval);
    773:   RGGetScale(eps->rg,&rgscale);
    774:   if (isinterval) {
    775:     RGIntervalGetEndpoints(eps->rg,NULL,NULL,&c,&d);
    776:     if (c==d) {
    777:       for (i=0;i<nv;i++) {
    778: #if defined(PETSC_USE_COMPLEX)
    779:         eps->eigr[i] = PetscRealPart(eps->eigr[i]);
    780: #else
    781:         eps->eigi[i] = 0;
    782: #endif
    783:       }
    784:     }
    785:   }
    786:   if (ctx->extraction == EPS_CISS_EXTRACTION_HANKEL) {
    787:     if (isellipse) {
    788:       RGEllipseGetParameters(eps->rg,&center,&radius,NULL);
    789:       for (i=0;i<nv;i++) eps->eigr[i] = rgscale*(center + radius*eps->eigr[i]);
    790:     } else if (isinterval) {
    791:       RGIntervalGetEndpoints(eps->rg,&a,&b,&c,&d);
    792:       if (ctx->quad == EPS_CISS_QUADRULE_CHEBYSHEV) {
    793:         for (i=0;i<nv;i++) {
    794:           if (c==d) eps->eigr[i] = ((b-a)*(eps->eigr[i]+1.0)/2.0+a)*rgscale;
    795:           if (a==b) {
    796: #if defined(PETSC_USE_COMPLEX)
    797:             eps->eigr[i] = ((d-c)*(eps->eigr[i]+1.0)/2.0+c)*rgscale*PETSC_i;
    798: #else
    799:             SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Integration points on a vertical line require complex arithmetic");
    800: #endif
    801:           }
    802:         }
    803:       } else {
    804:         center = (b+a)/2.0+(d+c)/2.0*PETSC_PI;
    805:         radius = PetscSqrtReal(PetscPowRealInt((b-a)/2.0,2)+PetscPowRealInt((d-c)/2.0,2));
    806:         for (i=0;i<nv;i++) eps->eigr[i] = center + radius*eps->eigr[i];
    807:       }
    808:     } else if (isring) {  /* only supported in complex scalars */
    809: #if defined(PETSC_USE_COMPLEX)
    810:       RGRingGetParameters(eps->rg,&center,&radius,&vscale,&start_ang,&end_ang,NULL);
    811:       if (ctx->quad == EPS_CISS_QUADRULE_CHEBYSHEV) {
    812:         for (i=0;i<nv;i++) {
    813:           theta = (start_ang*2.0+(end_ang-start_ang)*(PetscRealPart(eps->eigr[i])+1.0))*PETSC_PI;
    814:           eps->eigr[i] = rgscale*center + (rgscale*radius+PetscImaginaryPart(eps->eigr[i]))*PetscCMPLX(PetscCosReal(theta),vscale*PetscSinReal(theta));
    815:         }
    816:       } else {
    817:         for (i=0;i<nv;i++) eps->eigr[i] = rgscale*(center + radius*eps->eigr[i]);
    818:       }
    819: #endif
    820:     }
    821:   }
    822:   return(0);
    823: }

    825: PetscErrorCode EPSSetUp_CISS(EPS eps)
    826: {
    828:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    829:   PetscBool      istrivial,isring,isellipse,isinterval,flg,useconj;
    830:   PetscReal      c,d;
    831:   Mat            A;

    834:   if (eps->ncv==PETSC_DEFAULT) {
    835:     eps->ncv = ctx->L_max*ctx->M;
    836:     if (eps->ncv>eps->n) {
    837:       eps->ncv = eps->n;
    838:       ctx->L_max = eps->ncv/ctx->M;
    839:       if (!ctx->L_max) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Cannot adjust solver parameters, try setting a smaller value of M (moment size)");
    840:     }
    841:   } else {
    842:     EPSSetDimensions_Default(eps,eps->nev,&eps->ncv,&eps->mpd);
    843:     ctx->L_max = eps->ncv/ctx->M;
    844:     if (!ctx->L_max) {
    845:       ctx->L_max = 1;
    846:       eps->ncv = ctx->L_max*ctx->M;
    847:     }
    848:   }
    849:   ctx->L = PetscMin(ctx->L,ctx->L_max);
    850:   if (eps->max_it==PETSC_DEFAULT) eps->max_it = 1;
    851:   if (eps->mpd==PETSC_DEFAULT) eps->mpd = eps->ncv;
    852:   if (!eps->which) eps->which = EPS_ALL;
    853:   if (eps->which!=EPS_ALL) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"This solver supports only computing all eigenvalues");
    854:   EPSCheckUnsupported(eps,EPS_FEATURE_BALANCE | EPS_FEATURE_ARBITRARY | EPS_FEATURE_EXTRACTION | EPS_FEATURE_STOPPING | EPS_FEATURE_TWOSIDED);

    856:   /* check region */
    857:   RGIsTrivial(eps->rg,&istrivial);
    858:   if (istrivial) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"CISS requires a nontrivial region, e.g. -rg_type ellipse ...");
    859:   RGGetComplement(eps->rg,&flg);
    860:   if (flg) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"A region with complement flag set is not allowed");
    861:   PetscObjectTypeCompare((PetscObject)eps->rg,RGELLIPSE,&isellipse);
    862:   PetscObjectTypeCompare((PetscObject)eps->rg,RGRING,&isring);
    863:   PetscObjectTypeCompare((PetscObject)eps->rg,RGINTERVAL,&isinterval);
    864:   if (!isellipse && !isring && !isinterval) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Currently only implemented for interval, elliptic or ring regions");
    865:   /* if useconj has changed, then reset subcomm data */
    866:   EPSCISSSetUseConj(eps,&useconj);
    867:   if (useconj!=ctx->useconj) { EPSCISSResetSubcomm(eps); }

    869: #if !defined(PETSC_USE_COMPLEX)
    870:   if (isring) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Ring region only supported for complex scalars");
    871: #endif
    872:   if (isinterval) {
    873:     RGIntervalGetEndpoints(eps->rg,NULL,NULL,&c,&d);
    874: #if !defined(PETSC_USE_COMPLEX)
    875:     if (c!=d || c!=0.0) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"In real scalars, endpoints of the imaginary axis must be both zero");
    876: #endif
    877:     if (!ctx->quad && c==d) ctx->quad = EPS_CISS_QUADRULE_CHEBYSHEV;
    878:   }
    879:   if (!ctx->quad) ctx->quad = EPS_CISS_QUADRULE_TRAPEZOIDAL;

    881:   /* create split comm */
    882:   if (!ctx->subcomm) { EPSCISSSetUpSubComm(eps,&ctx->num_solve_point); }

    884:   EPSAllocateSolution(eps,0);
    885:   if (ctx->weight) { PetscFree4(ctx->weight,ctx->omega,ctx->pp,ctx->sigma); }
    886:   PetscMalloc4(ctx->N,&ctx->weight,ctx->N+1,&ctx->omega,ctx->N,&ctx->pp,ctx->L_max*ctx->M,&ctx->sigma);
    887:   PetscLogObjectMemory((PetscObject)eps,3*ctx->N*sizeof(PetscScalar)+ctx->L_max*ctx->N*sizeof(PetscReal));

    889:   /* allocate basis vectors */
    890:   BVDestroy(&ctx->S);
    891:   BVDuplicateResize(eps->V,ctx->L_max*ctx->M,&ctx->S);
    892:   PetscLogObjectParent((PetscObject)eps,(PetscObject)ctx->S);
    893:   BVDestroy(&ctx->V);
    894:   BVDuplicateResize(eps->V,ctx->L_max,&ctx->V);
    895:   PetscLogObjectParent((PetscObject)eps,(PetscObject)ctx->V);

    897:   STGetMatrix(eps->st,0,&A);
    898:   PetscObjectTypeCompare((PetscObject)A,MATSHELL,&flg);
    899:   if (flg) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Matrix type shell is not supported in this solver");

    901:   if (!ctx->usest_set) ctx->usest = (ctx->npart>1)? PETSC_FALSE: PETSC_TRUE;
    902:   if (ctx->usest && ctx->npart>1) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"The usest flag is not supported when partitions > 1");

    904:   CISSRedundantMat(eps);
    905:   if (ctx->pA) {
    906:     CISSScatterVec(eps);
    907:     BVDestroy(&ctx->pV);
    908:     BVCreate(PetscObjectComm((PetscObject)ctx->xsub),&ctx->pV);
    909:     BVSetSizesFromVec(ctx->pV,ctx->xsub,eps->n);
    910:     BVSetFromOptions(ctx->pV);
    911:     BVResize(ctx->pV,ctx->L_max,PETSC_FALSE);
    912:     PetscLogObjectParent((PetscObject)eps,(PetscObject)ctx->pV);
    913:   }

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

    917:   BVDestroy(&ctx->Y);
    918:   if (ctx->pA) {
    919:     BVCreate(PetscObjectComm((PetscObject)ctx->xsub),&ctx->Y);
    920:     BVSetSizesFromVec(ctx->Y,ctx->xsub,eps->n);
    921:     BVSetFromOptions(ctx->Y);
    922:     BVResize(ctx->Y,ctx->num_solve_point*ctx->L_max,PETSC_FALSE);
    923:   } else {
    924:     BVDuplicateResize(eps->V,ctx->num_solve_point*ctx->L_max,&ctx->Y);
    925:   }
    926:   PetscLogObjectParent((PetscObject)eps,(PetscObject)ctx->Y);

    928:   if (ctx->extraction == EPS_CISS_EXTRACTION_HANKEL) {
    929:     DSSetType(eps->ds,DSGNHEP);
    930:   } else if (eps->isgeneralized) {
    931:     if (eps->ishermitian && eps->ispositive) {
    932:       DSSetType(eps->ds,DSGHEP);
    933:     } else {
    934:       DSSetType(eps->ds,DSGNHEP);
    935:     }
    936:   } else {
    937:     if (eps->ishermitian) {
    938:       DSSetType(eps->ds,DSHEP);
    939:     } else {
    940:       DSSetType(eps->ds,DSNHEP);
    941:     }
    942:   }
    943:   DSAllocate(eps->ds,eps->ncv);
    944:   EPSSetWorkVecs(eps,2);

    946: #if !defined(PETSC_USE_COMPLEX)
    947:   if (!eps->ishermitian) { PetscInfo(eps,"Warning: complex eigenvalues are not calculated exactly without --with-scalar-type=complex in PETSc\n"); }
    948: #endif
    949:   return(0);
    950: }

    952: PetscErrorCode EPSSetUpSort_CISS(EPS eps)
    953: {
    955:   SlepcSC        sc;

    958:   /* fill sorting criterion context */
    959:   eps->sc->comparison    = SlepcCompareSmallestReal;
    960:   eps->sc->comparisonctx = NULL;
    961:   eps->sc->map           = NULL;
    962:   eps->sc->mapobj        = NULL;

    964:   /* fill sorting criterion for DS */
    965:   DSGetSlepcSC(eps->ds,&sc);
    966:   sc->comparison    = SlepcCompareLargestMagnitude;
    967:   sc->comparisonctx = NULL;
    968:   sc->map           = NULL;
    969:   sc->mapobj        = NULL;
    970:   return(0);
    971: }

    973: PetscErrorCode EPSSolve_CISS(EPS eps)
    974: {
    976:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    977:   Mat            A,B,X,M,pA,pB;
    978:   PetscInt       i,j,ld,nmat,L_add=0,nv=0,L_base=ctx->L,inner,nlocal,*inside;
    979:   PetscScalar    *Mu,*H0,*H1=NULL,*rr,*temp;
    980:   PetscReal      error,max_error,norm;
    981:   PetscBool      *fl1;
    982:   Vec            si,w[3];
    983:   PetscRandom    rand;
    984: #if defined(PETSC_USE_COMPLEX)
    985:   PetscBool      isellipse;
    986: #endif

    989:   w[0] = eps->work[0];
    990:   w[1] = NULL;
    991:   w[2] = eps->work[1];
    992:   VecGetLocalSize(w[0],&nlocal);
    993:   DSGetLeadingDimension(eps->ds,&ld);
    994:   STGetNumMatrices(eps->st,&nmat);
    995:   STGetMatrix(eps->st,0,&A);
    996:   if (nmat>1) { STGetMatrix(eps->st,1,&B); }
    997:   else B = NULL;
    998:   SetPathParameter(eps);
    999:   CISSVecSetRandom(ctx->V,0,ctx->L);
    1000:   BVGetRandomContext(ctx->V,&rand);

    1002:   if (ctx->pA) {
    1003:     VecScatterVecs(eps,ctx->V,ctx->L);
    1004:     SolveLinearSystem(eps,ctx->pA,ctx->pB,ctx->pV,0,ctx->L,PETSC_TRUE);
    1005:   } else {
    1006:     SolveLinearSystem(eps,A,B,ctx->V,0,ctx->L,PETSC_TRUE);
    1007:   }
    1008: #if defined(PETSC_USE_COMPLEX)
    1009:   PetscObjectTypeCompare((PetscObject)eps->rg,RGELLIPSE,&isellipse);
    1010:   if (isellipse) {
    1011:     EstimateNumberEigs(eps,&L_add);
    1012:   } else {
    1013:     L_add = 0;
    1014:   }
    1015: #else
    1016:   L_add = 0;
    1017: #endif
    1018:   if (L_add>0) {
    1019:     PetscInfo2(eps,"Changing L %D -> %D by Estimate #Eig\n",ctx->L,ctx->L+L_add);
    1020:     CISSVecSetRandom(ctx->V,ctx->L,ctx->L+L_add);
    1021:     if (ctx->pA) {
    1022:       VecScatterVecs(eps,ctx->V,ctx->L+L_add);
    1023:       SolveLinearSystem(eps,ctx->pA,ctx->pB,ctx->pV,ctx->L,ctx->L+L_add,PETSC_FALSE);
    1024:     } else {
    1025:       SolveLinearSystem(eps,A,B,ctx->V,ctx->L,ctx->L+L_add,PETSC_FALSE);
    1026:     }
    1027:     ctx->L += L_add;
    1028:   }
    1029:   PetscMalloc2(ctx->L*ctx->L*ctx->M*2,&Mu,ctx->L*ctx->M*ctx->L*ctx->M,&H0);
    1030:   for (i=0;i<ctx->refine_blocksize;i++) {
    1031:     CalcMu(eps,Mu);
    1032:     BlockHankel(eps,Mu,0,H0);
    1033:     SVD_H0(eps,H0,&nv);
    1034:     if (ctx->sigma[0]<=ctx->delta || nv < ctx->L*ctx->M || ctx->L == ctx->L_max) break;
    1035:     L_add = L_base;
    1036:     if (ctx->L+L_add>ctx->L_max) L_add = ctx->L_max-ctx->L;
    1037:     PetscInfo2(eps,"Changing L %D -> %D by SVD(H0)\n",ctx->L,ctx->L+L_add);
    1038:     CISSVecSetRandom(ctx->V,ctx->L,ctx->L+L_add);
    1039:     if (ctx->pA) {
    1040:       VecScatterVecs(eps,ctx->V,ctx->L+L_add);
    1041:       SolveLinearSystem(eps,ctx->pA,ctx->pB,ctx->pV,ctx->L,ctx->L+L_add,PETSC_FALSE);
    1042:     } else {
    1043:       SolveLinearSystem(eps,A,B,ctx->V,ctx->L,ctx->L+L_add,PETSC_FALSE);
    1044:     }
    1045:     ctx->L += L_add;
    1046:   }
    1047:   if (ctx->extraction == EPS_CISS_EXTRACTION_HANKEL) {
    1048:     PetscMalloc1(ctx->L*ctx->M*ctx->L*ctx->M,&H1);
    1049:   }

    1051:   while (eps->reason == EPS_CONVERGED_ITERATING) {
    1052:     eps->its++;
    1053:     for (inner=0;inner<=ctx->refine_inner;inner++) {
    1054:       if (ctx->extraction == EPS_CISS_EXTRACTION_HANKEL) {
    1055:         CalcMu(eps,Mu);
    1056:         BlockHankel(eps,Mu,0,H0);
    1057:         SVD_H0(eps,H0,&nv);
    1058:         break;
    1059:       } else {
    1060:         ConstructS(eps);
    1061:         BVSetActiveColumns(ctx->S,0,ctx->L);
    1062:         BVCopy(ctx->S,ctx->V);
    1063:         PetscLogEventBegin(EPS_CISS_SVD,eps,0,0,0);
    1064:         SVD_S(ctx->S,ctx->L*ctx->M,ctx->delta,ctx->sigma,&nv);
    1065:         PetscLogEventEnd(EPS_CISS_SVD,eps,0,0,0);
    1066:         if (ctx->sigma[0]>ctx->delta && nv==ctx->L*ctx->M && inner!=ctx->refine_inner) {
    1067:           if (ctx->pA) {
    1068:             VecScatterVecs(eps,ctx->V,ctx->L);
    1069:             SolveLinearSystem(eps,ctx->pA,ctx->pB,ctx->pV,0,ctx->L,PETSC_FALSE);
    1070:           } else {
    1071:             SolveLinearSystem(eps,A,B,ctx->V,0,ctx->L,PETSC_FALSE);
    1072:           }
    1073:         } else break;
    1074:       }
    1075:     }
    1076:     eps->nconv = 0;
    1077:     if (nv == 0) eps->reason = EPS_CONVERGED_TOL;
    1078:     else {
    1079:       DSSetDimensions(eps->ds,nv,0,0,0);
    1080:       DSSetState(eps->ds,DS_STATE_RAW);

    1082:       if (ctx->extraction == EPS_CISS_EXTRACTION_HANKEL) {
    1083:         BlockHankel(eps,Mu,0,H0);
    1084:         BlockHankel(eps,Mu,1,H1);
    1085:         DSGetArray(eps->ds,DS_MAT_A,&temp);
    1086:         for (j=0;j<nv;j++) {
    1087:           for (i=0;i<nv;i++) {
    1088:             temp[i+j*ld] = H1[i+j*ctx->L*ctx->M];
    1089:           }
    1090:         }
    1091:         DSRestoreArray(eps->ds,DS_MAT_A,&temp);
    1092:         DSGetArray(eps->ds,DS_MAT_B,&temp);
    1093:         for (j=0;j<nv;j++) {
    1094:           for (i=0;i<nv;i++) {
    1095:             temp[i+j*ld] = H0[i+j*ctx->L*ctx->M];
    1096:           }
    1097:         }
    1098:         DSRestoreArray(eps->ds,DS_MAT_B,&temp);
    1099:       } else {
    1100:         BVSetActiveColumns(ctx->S,0,nv);
    1101:         DSGetMat(eps->ds,DS_MAT_A,&pA);
    1102:         MatZeroEntries(pA);
    1103:         BVMatProject(ctx->S,A,ctx->S,pA);
    1104:         DSRestoreMat(eps->ds,DS_MAT_A,&pA);
    1105:         if (B) {
    1106:           DSGetMat(eps->ds,DS_MAT_B,&pB);
    1107:           MatZeroEntries(pB);
    1108:           BVMatProject(ctx->S,B,ctx->S,pB);
    1109:           DSRestoreMat(eps->ds,DS_MAT_B,&pB);
    1110:         }
    1111:       }

    1113:       DSSolve(eps->ds,eps->eigr,eps->eigi);
    1114:       DSSynchronize(eps->ds,eps->eigr,eps->eigi);

    1116:       PetscMalloc3(nv,&fl1,nv,&inside,nv,&rr);
    1117:       rescale_eig(eps,nv);
    1118:       isGhost(eps,ld,nv,fl1);
    1119:       RGCheckInside(eps->rg,nv,eps->eigr,eps->eigi,inside);
    1120:       for (i=0;i<nv;i++) {
    1121:         if (fl1[i] && inside[i]>=0) {
    1122:           rr[i] = 1.0;
    1123:           eps->nconv++;
    1124:         } else rr[i] = 0.0;
    1125:       }
    1126:       DSSort(eps->ds,eps->eigr,eps->eigi,rr,NULL,&eps->nconv);
    1127:       DSSynchronize(eps->ds,eps->eigr,eps->eigi);
    1128:       rescale_eig(eps,nv);
    1129:       PetscFree3(fl1,inside,rr);
    1130:       BVSetActiveColumns(eps->V,0,nv);
    1131:       if (ctx->extraction == EPS_CISS_EXTRACTION_HANKEL) {
    1132:         ConstructS(eps);
    1133:         BVSetActiveColumns(ctx->S,0,ctx->L);
    1134:         BVCopy(ctx->S,ctx->V);
    1135:         BVSetActiveColumns(ctx->S,0,nv);
    1136:       }
    1137:       BVCopy(ctx->S,eps->V);

    1139:       DSVectors(eps->ds,DS_MAT_X,NULL,NULL);
    1140:       DSGetMat(eps->ds,DS_MAT_X,&X);
    1141:       BVMultInPlace(ctx->S,X,0,eps->nconv);
    1142:       if (eps->ishermitian) {
    1143:         BVMultInPlace(eps->V,X,0,eps->nconv);
    1144:       }
    1145:       MatDestroy(&X);
    1146:       max_error = 0.0;
    1147:       for (i=0;i<eps->nconv;i++) {
    1148:         BVGetColumn(ctx->S,i,&si);
    1149:         EPSComputeResidualNorm_Private(eps,PETSC_FALSE,eps->eigr[i],eps->eigi[i],si,NULL,w,&error);
    1150:         if (ctx->extraction == EPS_CISS_EXTRACTION_HANKEL) {  /* vector is not normalized */
    1151:           VecNorm(si,NORM_2,&norm);
    1152:           error /= norm;
    1153:         }
    1154:         (*eps->converged)(eps,eps->eigr[i],eps->eigi[i],error,&error,eps->convergedctx);
    1155:         BVRestoreColumn(ctx->S,i,&si);
    1156:         max_error = PetscMax(max_error,error);
    1157:       }

    1159:       if (max_error <= eps->tol) eps->reason = EPS_CONVERGED_TOL;
    1160:       else if (eps->its >= eps->max_it) eps->reason = EPS_DIVERGED_ITS;
    1161:       else {
    1162:         if (eps->nconv > ctx->L) {
    1163:           MatCreateSeqDense(PETSC_COMM_SELF,eps->nconv,ctx->L,NULL,&M);
    1164:           MatDenseGetArray(M,&temp);
    1165:           for (i=0;i<ctx->L*eps->nconv;i++) {
    1166:             PetscRandomGetValue(rand,&temp[i]);
    1167:             temp[i] = PetscRealPart(temp[i]);
    1168:           }
    1169:           MatDenseRestoreArray(M,&temp);
    1170:           BVSetActiveColumns(ctx->S,0,eps->nconv);
    1171:           BVMultInPlace(ctx->S,M,0,ctx->L);
    1172:           MatDestroy(&M);
    1173:           BVSetActiveColumns(ctx->S,0,ctx->L);
    1174:           BVCopy(ctx->S,ctx->V);
    1175:         }
    1176:         if (ctx->pA) {
    1177:           VecScatterVecs(eps,ctx->V,ctx->L);
    1178:           SolveLinearSystem(eps,ctx->pA,ctx->pB,ctx->pV,0,ctx->L,PETSC_FALSE);
    1179:         } else {
    1180:           SolveLinearSystem(eps,A,B,ctx->V,0,ctx->L,PETSC_FALSE);
    1181:         }
    1182:       }
    1183:     }
    1184:   }
    1185:   if (ctx->extraction == EPS_CISS_EXTRACTION_HANKEL) {
    1186:     PetscFree(H1);
    1187:   }
    1188:   PetscFree2(Mu,H0);
    1189:   return(0);
    1190: }

    1192: PetscErrorCode EPSComputeVectors_CISS(EPS eps)
    1193: {
    1195:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    1196:   PetscInt       n;
    1197:   Mat            Z,B=NULL;

    1200:   if (eps->ishermitian) {
    1201:     if (eps->isgeneralized && !eps->ispositive) {
    1202:       EPSComputeVectors_Indefinite(eps);
    1203:     } else {
    1204:       EPSComputeVectors_Hermitian(eps);
    1205:     }
    1206:     return(0);
    1207:   }
    1208:   DSGetDimensions(eps->ds,&n,NULL,NULL,NULL,NULL);
    1209:   BVSetActiveColumns(eps->V,0,n);

    1211:   /* right eigenvectors */
    1212:   DSVectors(eps->ds,DS_MAT_X,NULL,NULL);

    1214:   /* V = V * Z */
    1215:   DSGetMat(eps->ds,DS_MAT_X,&Z);
    1216:   BVMultInPlace(eps->V,Z,0,n);
    1217:   MatDestroy(&Z);
    1218:   BVSetActiveColumns(eps->V,0,eps->nconv);

    1220:   /* normalize */
    1221:   if (ctx->extraction == EPS_CISS_EXTRACTION_HANKEL) {
    1222:     if (eps->isgeneralized && eps->ishermitian && eps->ispositive) {
    1223:       STGetMatrix(eps->st,1,&B);
    1224:       BVSetMatrix(eps->V,B,PETSC_FALSE);
    1225:     }
    1226:     BVNormalize(eps->V,NULL);
    1227:     if (B) { BVSetMatrix(eps->V,NULL,PETSC_FALSE); }
    1228:   }
    1229:   return(0);
    1230: }

    1232: static PetscErrorCode EPSCISSSetSizes_CISS(EPS eps,PetscInt ip,PetscInt bs,PetscInt ms,PetscInt npart,PetscInt bsmax,PetscBool realmats)
    1233: {
    1235:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    1236:   PetscInt       oN,onpart;

    1239:   oN = ctx->N;
    1240:   if (ip == PETSC_DECIDE || ip == PETSC_DEFAULT) {
    1241:     if (ctx->N!=32) { ctx->N =32; ctx->M = ctx->N/4; }
    1242:   } else {
    1243:     if (ip<1) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The ip argument must be > 0");
    1244:     if (ip%2) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The ip argument must be an even number");
    1245:     if (ctx->N!=ip) { ctx->N = ip; ctx->M = ctx->N/4; }
    1246:   }
    1247:   if (bs == PETSC_DECIDE || bs == PETSC_DEFAULT) {
    1248:     ctx->L = 16;
    1249:   } else {
    1250:     if (bs<1) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The bs argument must be > 0");
    1251:     ctx->L = bs;
    1252:   }
    1253:   if (ms == PETSC_DECIDE || ms == PETSC_DEFAULT) {
    1254:     ctx->M = ctx->N/4;
    1255:   } else {
    1256:     if (ms<1) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The ms argument must be > 0");
    1257:     if (ms>ctx->N) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The ms argument must be less than or equal to the number of integration points");
    1258:     ctx->M = ms;
    1259:   }
    1260:   onpart = ctx->npart;
    1261:   if (npart == PETSC_DECIDE || npart == PETSC_DEFAULT) {
    1262:     ctx->npart = 1;
    1263:   } else {
    1264:     if (npart<1) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The npart argument must be > 0");
    1265:     ctx->npart = npart;
    1266:   }
    1267:   if (bsmax == PETSC_DECIDE || bsmax == PETSC_DEFAULT) {
    1268:     ctx->L_max = 64;
    1269:   } else {
    1270:     if (bsmax<1) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The bsmax argument must be > 0");
    1271:     ctx->L_max = PetscMax(bsmax,ctx->L);
    1272:   }
    1273:   if (onpart != ctx->npart || oN != ctx->N || realmats != ctx->isreal) { EPSCISSResetSubcomm(eps); }
    1274:   ctx->isreal = realmats;
    1275:   eps->state = EPS_STATE_INITIAL;
    1276:   return(0);
    1277: }

    1279: /*@
    1280:    EPSCISSSetSizes - Sets the values of various size parameters in the CISS solver.

    1282:    Logically Collective on eps

    1284:    Input Parameters:
    1285: +  eps   - the eigenproblem solver context
    1286: .  ip    - number of integration points
    1287: .  bs    - block size
    1288: .  ms    - moment size
    1289: .  npart - number of partitions when splitting the communicator
    1290: .  bsmax - max block size
    1291: -  realmats - A and B are real

    1293:    Options Database Keys:
    1294: +  -eps_ciss_integration_points - Sets the number of integration points
    1295: .  -eps_ciss_blocksize - Sets the block size
    1296: .  -eps_ciss_moments - Sets the moment size
    1297: .  -eps_ciss_partitions - Sets the number of partitions
    1298: .  -eps_ciss_maxblocksize - Sets the maximum block size
    1299: -  -eps_ciss_realmats - A and B are real

    1301:    Note:
    1302:    The default number of partitions is 1. This means the internal KSP object is shared
    1303:    among all processes of the EPS communicator. Otherwise, the communicator is split
    1304:    into npart communicators, so that npart KSP solves proceed simultaneously.

    1306:    Level: advanced

    1308: .seealso: EPSCISSGetSizes()
    1309: @*/
    1310: PetscErrorCode EPSCISSSetSizes(EPS eps,PetscInt ip,PetscInt bs,PetscInt ms,PetscInt npart,PetscInt bsmax,PetscBool realmats)
    1311: {

    1322:   PetscTryMethod(eps,"EPSCISSSetSizes_C",(EPS,PetscInt,PetscInt,PetscInt,PetscInt,PetscInt,PetscBool),(eps,ip,bs,ms,npart,bsmax,realmats));
    1323:   return(0);
    1324: }

    1326: static PetscErrorCode EPSCISSGetSizes_CISS(EPS eps,PetscInt *ip,PetscInt *bs,PetscInt *ms,PetscInt *npart,PetscInt *bsmax,PetscBool *realmats)
    1327: {
    1328:   EPS_CISS *ctx = (EPS_CISS*)eps->data;

    1331:   if (ip) *ip = ctx->N;
    1332:   if (bs) *bs = ctx->L;
    1333:   if (ms) *ms = ctx->M;
    1334:   if (npart) *npart = ctx->npart;
    1335:   if (bsmax) *bsmax = ctx->L_max;
    1336:   if (realmats) *realmats = ctx->isreal;
    1337:   return(0);
    1338: }

    1340: /*@
    1341:    EPSCISSGetSizes - Gets the values of various size parameters in the CISS solver.

    1343:    Not Collective

    1345:    Input Parameter:
    1346: .  eps - the eigenproblem solver context

    1348:    Output Parameters:
    1349: +  ip    - number of integration points
    1350: .  bs    - block size
    1351: .  ms    - moment size
    1352: .  npart - number of partitions when splitting the communicator
    1353: .  bsmax - max block size
    1354: -  realmats - A and B are real

    1356:    Level: advanced

    1358: .seealso: EPSCISSSetSizes()
    1359: @*/
    1360: PetscErrorCode EPSCISSGetSizes(EPS eps,PetscInt *ip,PetscInt *bs,PetscInt *ms,PetscInt *npart,PetscInt *bsmax,PetscBool *realmats)
    1361: {

    1366:   PetscUseMethod(eps,"EPSCISSGetSizes_C",(EPS,PetscInt*,PetscInt*,PetscInt*,PetscInt*,PetscInt*,PetscBool*),(eps,ip,bs,ms,npart,bsmax,realmats));
    1367:   return(0);
    1368: }

    1370: static PetscErrorCode EPSCISSSetThreshold_CISS(EPS eps,PetscReal delta,PetscReal spur)
    1371: {
    1372:   EPS_CISS *ctx = (EPS_CISS*)eps->data;

    1375:   if (delta == PETSC_DEFAULT) {
    1376:     ctx->delta = 1e-12;
    1377:   } else {
    1378:     if (delta<=0.0) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The delta argument must be > 0.0");
    1379:     ctx->delta = delta;
    1380:   }
    1381:   if (spur == PETSC_DEFAULT) {
    1382:     ctx->spurious_threshold = 1e-4;
    1383:   } else {
    1384:     if (spur<=0.0) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The spurious threshold argument must be > 0.0");
    1385:     ctx->spurious_threshold = spur;
    1386:   }
    1387:   return(0);
    1388: }

    1390: /*@
    1391:    EPSCISSSetThreshold - Sets the values of various threshold parameters in
    1392:    the CISS solver.

    1394:    Logically Collective on eps

    1396:    Input Parameters:
    1397: +  eps   - the eigenproblem solver context
    1398: .  delta - threshold for numerical rank
    1399: -  spur  - spurious threshold (to discard spurious eigenpairs)

    1401:    Options Database Keys:
    1402: +  -eps_ciss_delta - Sets the delta
    1403: -  -eps_ciss_spurious_threshold - Sets the spurious threshold

    1405:    Level: advanced

    1407: .seealso: EPSCISSGetThreshold()
    1408: @*/
    1409: PetscErrorCode EPSCISSSetThreshold(EPS eps,PetscReal delta,PetscReal spur)
    1410: {

    1417:   PetscTryMethod(eps,"EPSCISSSetThreshold_C",(EPS,PetscReal,PetscReal),(eps,delta,spur));
    1418:   return(0);
    1419: }

    1421: static PetscErrorCode EPSCISSGetThreshold_CISS(EPS eps,PetscReal *delta,PetscReal *spur)
    1422: {
    1423:   EPS_CISS *ctx = (EPS_CISS*)eps->data;

    1426:   if (delta) *delta = ctx->delta;
    1427:   if (spur)  *spur = ctx->spurious_threshold;
    1428:   return(0);
    1429: }

    1431: /*@
    1432:    EPSCISSGetThreshold - Gets the values of various threshold parameters
    1433:    in the CISS solver.

    1435:    Not Collective

    1437:    Input Parameter:
    1438: .  eps - the eigenproblem solver context

    1440:    Output Parameters:
    1441: +  delta - threshold for numerical rank
    1442: -  spur  - spurious threshold (to discard spurious eigenpairs)

    1444:    Level: advanced

    1446: .seealso: EPSCISSSetThreshold()
    1447: @*/
    1448: PetscErrorCode EPSCISSGetThreshold(EPS eps,PetscReal *delta,PetscReal *spur)
    1449: {

    1454:   PetscUseMethod(eps,"EPSCISSGetThreshold_C",(EPS,PetscReal*,PetscReal*),(eps,delta,spur));
    1455:   return(0);
    1456: }

    1458: static PetscErrorCode EPSCISSSetRefinement_CISS(EPS eps,PetscInt inner,PetscInt blsize)
    1459: {
    1460:   EPS_CISS *ctx = (EPS_CISS*)eps->data;

    1463:   if (inner == PETSC_DEFAULT) {
    1464:     ctx->refine_inner = 0;
    1465:   } else {
    1466:     if (inner<0) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The refine inner argument must be >= 0");
    1467:     ctx->refine_inner = inner;
    1468:   }
    1469:   if (blsize == PETSC_DEFAULT) {
    1470:     ctx->refine_blocksize = 0;
    1471:   } else {
    1472:     if (blsize<0) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The refine blocksize argument must be >= 0");
    1473:     ctx->refine_blocksize = blsize;
    1474:   }
    1475:   return(0);
    1476: }

    1478: /*@
    1479:    EPSCISSSetRefinement - Sets the values of various refinement parameters
    1480:    in the CISS solver.

    1482:    Logically Collective on eps

    1484:    Input Parameters:
    1485: +  eps    - the eigenproblem solver context
    1486: .  inner  - number of iterative refinement iterations (inner loop)
    1487: -  blsize - number of iterative refinement iterations (blocksize loop)

    1489:    Options Database Keys:
    1490: +  -eps_ciss_refine_inner - Sets number of inner iterations
    1491: -  -eps_ciss_refine_blocksize - Sets number of blocksize iterations

    1493:    Level: advanced

    1495: .seealso: EPSCISSGetRefinement()
    1496: @*/
    1497: PetscErrorCode EPSCISSSetRefinement(EPS eps,PetscInt inner,PetscInt blsize)
    1498: {

    1505:   PetscTryMethod(eps,"EPSCISSSetRefinement_C",(EPS,PetscInt,PetscInt),(eps,inner,blsize));
    1506:   return(0);
    1507: }

    1509: static PetscErrorCode EPSCISSGetRefinement_CISS(EPS eps,PetscInt *inner,PetscInt *blsize)
    1510: {
    1511:   EPS_CISS *ctx = (EPS_CISS*)eps->data;

    1514:   if (inner)  *inner = ctx->refine_inner;
    1515:   if (blsize) *blsize = ctx->refine_blocksize;
    1516:   return(0);
    1517: }

    1519: /*@
    1520:    EPSCISSGetRefinement - Gets the values of various refinement parameters
    1521:    in the CISS solver.

    1523:    Not Collective

    1525:    Input Parameter:
    1526: .  eps - the eigenproblem solver context

    1528:    Output Parameters:
    1529: +  inner  - number of iterative refinement iterations (inner loop)
    1530: -  blsize - number of iterative refinement iterations (blocksize loop)

    1532:    Level: advanced

    1534: .seealso: EPSCISSSetRefinement()
    1535: @*/
    1536: PetscErrorCode EPSCISSGetRefinement(EPS eps, PetscInt *inner, PetscInt *blsize)
    1537: {

    1542:   PetscUseMethod(eps,"EPSCISSGetRefinement_C",(EPS,PetscInt*,PetscInt*),(eps,inner,blsize));
    1543:   return(0);
    1544: }

    1546: static PetscErrorCode EPSCISSSetUseST_CISS(EPS eps,PetscBool usest)
    1547: {
    1548:   EPS_CISS *ctx = (EPS_CISS*)eps->data;

    1551:   ctx->usest     = usest;
    1552:   ctx->usest_set = PETSC_TRUE;
    1553:   eps->state     = EPS_STATE_INITIAL;
    1554:   return(0);
    1555: }

    1557: /*@
    1558:    EPSCISSSetUseST - Sets a flag indicating that the CISS solver will
    1559:    use the ST object for the linear solves.

    1561:    Logically Collective on eps

    1563:    Input Parameters:
    1564: +  eps    - the eigenproblem solver context
    1565: -  usest  - boolean flag to use the ST object or not

    1567:    Options Database Keys:
    1568: .  -eps_ciss_usest <bool> - whether the ST object will be used or not

    1570:    Level: advanced

    1572: .seealso: EPSCISSGetUseST()
    1573: @*/
    1574: PetscErrorCode EPSCISSSetUseST(EPS eps,PetscBool usest)
    1575: {

    1581:   PetscTryMethod(eps,"EPSCISSSetUseST_C",(EPS,PetscBool),(eps,usest));
    1582:   return(0);
    1583: }

    1585: static PetscErrorCode EPSCISSGetUseST_CISS(EPS eps,PetscBool *usest)
    1586: {
    1587:   EPS_CISS *ctx = (EPS_CISS*)eps->data;

    1590:   *usest = ctx->usest;
    1591:   return(0);
    1592: }

    1594: /*@
    1595:    EPSCISSGetUseST - Gets the flag for using the ST object
    1596:    in the CISS solver.

    1598:    Not Collective

    1600:    Input Parameter:
    1601: .  eps - the eigenproblem solver context

    1603:    Output Parameters:
    1604: .  usest - boolean flag indicating if the ST object is being used

    1606:    Level: advanced

    1608: .seealso: EPSCISSSetUseST()
    1609: @*/
    1610: PetscErrorCode EPSCISSGetUseST(EPS eps,PetscBool *usest)
    1611: {

    1617:   PetscUseMethod(eps,"EPSCISSGetUseST_C",(EPS,PetscBool*),(eps,usest));
    1618:   return(0);
    1619: }

    1621: static PetscErrorCode EPSCISSSetQuadRule_CISS(EPS eps,EPSCISSQuadRule quad)
    1622: {
    1623:   EPS_CISS *ctx = (EPS_CISS*)eps->data;

    1626:   ctx->quad = quad;
    1627:   return(0);
    1628: }

    1630: /*@
    1631:    EPSCISSSetQuadRule - Sets the quadrature rule used in the CISS solver.

    1633:    Logically Collective on eps

    1635:    Input Parameters:
    1636: +  eps  - the eigenproblem solver context
    1637: -  quad - the quadrature rule

    1639:    Options Database Key:
    1640: .  -eps_ciss_quadrule - Sets the quadrature rule (either 'trapezoidal' or
    1641:                            'chebyshev')

    1643:    Notes:
    1644:    By default, the trapezoidal rule is used (EPS_CISS_QUADRULE_TRAPEZOIDAL).

    1646:    If the 'chebyshev' option is specified (EPS_CISS_QUADRULE_CHEBYSHEV), then
    1647:    Chebyshev points are used as quadrature points.

    1649:    Level: advanced

    1651: .seealso: EPSCISSGetQuadRule(), EPSCISSQuadRule
    1652: @*/
    1653: PetscErrorCode EPSCISSSetQuadRule(EPS eps,EPSCISSQuadRule quad)
    1654: {

    1660:   PetscTryMethod(eps,"EPSCISSSetQuadRule_C",(EPS,EPSCISSQuadRule),(eps,quad));
    1661:   return(0);
    1662: }

    1664: static PetscErrorCode EPSCISSGetQuadRule_CISS(EPS eps,EPSCISSQuadRule *quad)
    1665: {
    1666:   EPS_CISS *ctx = (EPS_CISS*)eps->data;

    1669:   *quad = ctx->quad;
    1670:   return(0);
    1671: }

    1673: /*@
    1674:    EPSCISSGetQuadRule - Gets the quadrature rule used in the CISS solver.

    1676:    Not Collective

    1678:    Input Parameter:
    1679: .  eps - the eigenproblem solver context

    1681:    Output Parameters:
    1682: .  quad - quadrature rule

    1684:    Level: advanced

    1686: .seealso: EPSCISSSetQuadRule() EPSCISSQuadRule
    1687: @*/
    1688: PetscErrorCode EPSCISSGetQuadRule(EPS eps,EPSCISSQuadRule *quad)
    1689: {

    1695:   PetscUseMethod(eps,"EPSCISSGetQuadRule_C",(EPS,EPSCISSQuadRule*),(eps,quad));
    1696:   return(0);
    1697: }

    1699: static PetscErrorCode EPSCISSSetExtraction_CISS(EPS eps,EPSCISSExtraction extraction)
    1700: {
    1701:   EPS_CISS *ctx = (EPS_CISS*)eps->data;

    1704:   ctx->extraction = extraction;
    1705:   return(0);
    1706: }

    1708: /*@
    1709:    EPSCISSSetExtraction - Sets the extraction technique used in the CISS solver.

    1711:    Logically Collective on eps

    1713:    Input Parameters:
    1714: +  eps        - the eigenproblem solver context
    1715: -  extraction - the extraction technique

    1717:    Options Database Key:
    1718: .  -eps_ciss_extraction - Sets the extraction technique (either 'ritz' or
    1719:                            'hankel')

    1721:    Notes:
    1722:    By default, the Rayleigh-Ritz extraction is used (EPS_CISS_EXTRACTION_RITZ).

    1724:    If the 'hankel' option is specified (EPS_CISS_EXTRACTION_HANKEL), then
    1725:    the Block Hankel method is used for extracting eigenpairs.

    1727:    Level: advanced

    1729: .seealso: EPSCISSGetExtraction(), EPSCISSExtraction
    1730: @*/
    1731: PetscErrorCode EPSCISSSetExtraction(EPS eps,EPSCISSExtraction extraction)
    1732: {

    1738:   PetscTryMethod(eps,"EPSCISSSetExtraction_C",(EPS,EPSCISSExtraction),(eps,extraction));
    1739:   return(0);
    1740: }

    1742: static PetscErrorCode EPSCISSGetExtraction_CISS(EPS eps,EPSCISSExtraction *extraction)
    1743: {
    1744:   EPS_CISS *ctx = (EPS_CISS*)eps->data;

    1747:   *extraction = ctx->extraction;
    1748:   return(0);
    1749: }

    1751: /*@
    1752:    EPSCISSGetExtraction - Gets the extraction technique used in the CISS solver.

    1754:    Not Collective

    1756:    Input Parameter:
    1757: .  eps - the eigenproblem solver context

    1759:    Output Parameters:
    1760: .  extraction - extraction technique

    1762:    Level: advanced

    1764: .seealso: EPSCISSSetExtraction() EPSCISSExtraction
    1765: @*/
    1766: PetscErrorCode EPSCISSGetExtraction(EPS eps,EPSCISSExtraction *extraction)
    1767: {

    1773:   PetscUseMethod(eps,"EPSCISSGetExtraction_C",(EPS,EPSCISSExtraction*),(eps,extraction));
    1774:   return(0);
    1775: }

    1777: static PetscErrorCode EPSCISSGetKSPs_CISS(EPS eps,PetscInt *nsolve,KSP **ksp)
    1778: {
    1780:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    1781:   PetscInt       i;
    1782:   PC             pc;

    1785:   if (!ctx->ksp) {
    1786:     if (!ctx->subcomm) {  /* initialize subcomm first */
    1787:       EPSCISSSetUseConj(eps,&ctx->useconj);
    1788:       EPSCISSSetUpSubComm(eps,&ctx->num_solve_point);
    1789:     }
    1790:     PetscMalloc1(ctx->num_solve_point,&ctx->ksp);
    1791:     for (i=0;i<ctx->num_solve_point;i++) {
    1792:       KSPCreate(PetscSubcommChild(ctx->subcomm),&ctx->ksp[i]);
    1793:       PetscObjectIncrementTabLevel((PetscObject)ctx->ksp[i],(PetscObject)eps,1);
    1794:       KSPSetOptionsPrefix(ctx->ksp[i],((PetscObject)eps)->prefix);
    1795:       KSPAppendOptionsPrefix(ctx->ksp[i],"eps_ciss_");
    1796:       PetscLogObjectParent((PetscObject)eps,(PetscObject)ctx->ksp[i]);
    1797:       PetscObjectSetOptions((PetscObject)ctx->ksp[i],((PetscObject)eps)->options);
    1798:       KSPSetErrorIfNotConverged(ctx->ksp[i],PETSC_TRUE);
    1799:       KSPSetTolerances(ctx->ksp[i],SLEPC_DEFAULT_TOL,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
    1800:       KSPGetPC(ctx->ksp[i],&pc);
    1801:       KSPSetType(ctx->ksp[i],KSPPREONLY);
    1802:       PCSetType(pc,PCLU);
    1803:     }
    1804:   }
    1805:   if (nsolve) *nsolve = ctx->num_solve_point;
    1806:   if (ksp)    *ksp    = ctx->ksp;
    1807:   return(0);
    1808: }

    1810: /*@C
    1811:    EPSCISSGetKSPs - Retrieve the array of linear solver objects associated with
    1812:    the CISS solver.

    1814:    Not Collective

    1816:    Input Parameter:
    1817: .  eps - the eigenproblem solver solver

    1819:    Output Parameters:
    1820: +  nsolve - number of solver objects
    1821: -  ksp - array of linear solver object

    1823:    Notes:
    1824:    The number of KSP solvers is equal to the number of integration points divided by
    1825:    the number of partitions. This value is halved in the case of real matrices with
    1826:    a region centered at the real axis.

    1828:    Level: advanced

    1830: .seealso: EPSCISSSetSizes()
    1831: @*/
    1832: PetscErrorCode EPSCISSGetKSPs(EPS eps,PetscInt *nsolve,KSP **ksp)
    1833: {

    1838:   PetscUseMethod(eps,"EPSCISSGetKSPs_C",(EPS,PetscInt*,KSP**),(eps,nsolve,ksp));
    1839:   return(0);
    1840: }

    1842: PetscErrorCode EPSReset_CISS(EPS eps)
    1843: {
    1845:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    1846:   PetscInt       i;

    1849:   BVDestroy(&ctx->S);
    1850:   BVDestroy(&ctx->V);
    1851:   BVDestroy(&ctx->Y);
    1852:   if (!ctx->usest) {
    1853:     for (i=0;i<ctx->num_solve_point;i++) {
    1854:       KSPReset(ctx->ksp[i]);
    1855:     }
    1856:   }
    1857:   VecScatterDestroy(&ctx->scatterin);
    1858:   VecDestroy(&ctx->xsub);
    1859:   VecDestroy(&ctx->xdup);
    1860:   if (ctx->pA) {
    1861:     MatDestroy(&ctx->pA);
    1862:     MatDestroy(&ctx->pB);
    1863:     BVDestroy(&ctx->pV);
    1864:   }
    1865:   return(0);
    1866: }

    1868: PetscErrorCode EPSSetFromOptions_CISS(PetscOptionItems *PetscOptionsObject,EPS eps)
    1869: {
    1870:   PetscErrorCode    ierr;
    1871:   PetscReal         r3,r4;
    1872:   PetscInt          i,i1,i2,i3,i4,i5,i6,i7;
    1873:   PetscBool         b1,b2,flg;
    1874:   EPS_CISS          *ctx = (EPS_CISS*)eps->data;
    1875:   EPSCISSQuadRule   quad;
    1876:   EPSCISSExtraction extraction;

    1879:   PetscOptionsHead(PetscOptionsObject,"EPS CISS Options");

    1881:     EPSCISSGetSizes(eps,&i1,&i2,&i3,&i4,&i5,&b1);
    1882:     PetscOptionsInt("-eps_ciss_integration_points","Number of integration points","EPSCISSSetSizes",i1,&i1,NULL);
    1883:     PetscOptionsInt("-eps_ciss_blocksize","Block size","EPSCISSSetSizes",i2,&i2,NULL);
    1884:     PetscOptionsInt("-eps_ciss_moments","Moment size","EPSCISSSetSizes",i3,&i3,NULL);
    1885:     PetscOptionsInt("-eps_ciss_partitions","Number of partitions","EPSCISSSetSizes",i4,&i4,NULL);
    1886:     PetscOptionsInt("-eps_ciss_maxblocksize","Maximum block size","EPSCISSSetSizes",i5,&i5,NULL);
    1887:     PetscOptionsBool("-eps_ciss_realmats","True if A and B are real","EPSCISSSetSizes",b1,&b1,NULL);
    1888:     EPSCISSSetSizes(eps,i1,i2,i3,i4,i5,b1);

    1890:     EPSCISSGetThreshold(eps,&r3,&r4);
    1891:     PetscOptionsReal("-eps_ciss_delta","Threshold for numerical rank","EPSCISSSetThreshold",r3,&r3,NULL);
    1892:     PetscOptionsReal("-eps_ciss_spurious_threshold","Threshold for the spurious eigenpairs","EPSCISSSetThreshold",r4,&r4,NULL);
    1893:     EPSCISSSetThreshold(eps,r3,r4);

    1895:     EPSCISSGetRefinement(eps,&i6,&i7);
    1896:     PetscOptionsInt("-eps_ciss_refine_inner","Number of inner iterative refinement iterations","EPSCISSSetRefinement",i6,&i6,NULL);
    1897:     PetscOptionsInt("-eps_ciss_refine_blocksize","Number of blocksize iterative refinement iterations","EPSCISSSetRefinement",i7,&i7,NULL);
    1898:     EPSCISSSetRefinement(eps,i6,i7);

    1900:     EPSCISSGetUseST(eps,&b2);
    1901:     PetscOptionsBool("-eps_ciss_usest","Use ST for linear solves","EPSCISSSetUseST",b2,&b2,&flg);
    1902:     if (flg) { EPSCISSSetUseST(eps,b2); }

    1904:     PetscOptionsEnum("-eps_ciss_quadrule","Quadrature rule","EPSCISSSetQuadRule",EPSCISSQuadRules,(PetscEnum)ctx->quad,(PetscEnum*)&quad,&flg);
    1905:     if (flg) { EPSCISSSetQuadRule(eps,quad); }

    1907:     PetscOptionsEnum("-eps_ciss_extraction","Extraction technique","EPSCISSSetExtraction",EPSCISSExtractions,(PetscEnum)ctx->extraction,(PetscEnum*)&extraction,&flg);
    1908:     if (flg) { EPSCISSSetExtraction(eps,extraction); }

    1910:   PetscOptionsTail();

    1912:   if (!eps->rg) { EPSGetRG(eps,&eps->rg); }
    1913:   RGSetFromOptions(eps->rg); /* this is necessary here to set useconj */
    1914:   if (!ctx->ksp) { EPSCISSGetKSPs(eps,&ctx->num_solve_point,&ctx->ksp); }
    1915:   for (i=0;i<ctx->num_solve_point;i++) {
    1916:     KSPSetFromOptions(ctx->ksp[i]);
    1917:   }
    1918:   PetscSubcommSetFromOptions(ctx->subcomm);
    1919:   return(0);
    1920: }

    1922: PetscErrorCode EPSDestroy_CISS(EPS eps)
    1923: {
    1925:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;

    1928:   EPSCISSResetSubcomm(eps);
    1929:   PetscFree4(ctx->weight,ctx->omega,ctx->pp,ctx->sigma);
    1930:   PetscFree(eps->data);
    1931:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetSizes_C",NULL);
    1932:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetSizes_C",NULL);
    1933:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetThreshold_C",NULL);
    1934:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetThreshold_C",NULL);
    1935:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetRefinement_C",NULL);
    1936:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetRefinement_C",NULL);
    1937:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetUseST_C",NULL);
    1938:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetUseST_C",NULL);
    1939:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetQuadRule_C",NULL);
    1940:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetQuadRule_C",NULL);
    1941:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetExtraction_C",NULL);
    1942:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetExtraction_C",NULL);
    1943:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetKSPs_C",NULL);
    1944:   return(0);
    1945: }

    1947: PetscErrorCode EPSView_CISS(EPS eps,PetscViewer viewer)
    1948: {
    1950:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    1951:   PetscBool      isascii;

    1954:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    1955:   if (isascii) {
    1956:     PetscViewerASCIIPrintf(viewer,"  sizes { integration points: %D, block size: %D, moment size: %D, partitions: %D, maximum block size: %D }\n",ctx->N,ctx->L,ctx->M,ctx->npart,ctx->L_max);
    1957:     if (ctx->isreal) {
    1958:       PetscViewerASCIIPrintf(viewer,"  exploiting symmetry of integration points\n");
    1959:     }
    1960:     PetscViewerASCIIPrintf(viewer,"  threshold { delta: %g, spurious threshold: %g }\n",(double)ctx->delta,(double)ctx->spurious_threshold);
    1961:     PetscViewerASCIIPrintf(viewer,"  iterative refinement { inner: %D, blocksize: %D }\n",ctx->refine_inner, ctx->refine_blocksize);
    1962:     PetscViewerASCIIPrintf(viewer,"  extraction: %s\n",EPSCISSExtractions[ctx->extraction]);
    1963:     PetscViewerASCIIPrintf(viewer,"  quadrature rule: %s\n",EPSCISSQuadRules[ctx->quad]);
    1964:     if (ctx->usest) {
    1965:       PetscViewerASCIIPrintf(viewer,"  using ST for linear solves\n");
    1966:     } else {
    1967:       if (!ctx->ksp) { EPSCISSGetKSPs(eps,&ctx->num_solve_point,&ctx->ksp); }
    1968:       PetscViewerASCIIPushTab(viewer);
    1969:       KSPView(ctx->ksp[0],viewer);
    1970:       PetscViewerASCIIPopTab(viewer);
    1971:     }
    1972:   }
    1973:   return(0);
    1974: }

    1976: PetscErrorCode EPSSetDefaultST_CISS(EPS eps)
    1977: {
    1979:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    1980:   PetscBool      usest = ctx->usest;

    1983:   if (!((PetscObject)eps->st)->type_name) {
    1984:     if (!ctx->usest_set) usest = (ctx->npart>1)? PETSC_FALSE: PETSC_TRUE;
    1985:     if (usest) {
    1986:       STSetType(eps->st,STSINVERT);
    1987:     } else {
    1988:       /* we are not going to use ST, so avoid factorizing the matrix */
    1989:       STSetType(eps->st,STSHIFT);
    1990:     }
    1991:   }
    1992:   return(0);
    1993: }

    1995: SLEPC_EXTERN PetscErrorCode EPSCreate_CISS(EPS eps)
    1996: {
    1998:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;

    2001:   PetscNewLog(eps,&ctx);
    2002:   eps->data = ctx;

    2004:   eps->useds = PETSC_TRUE;
    2005:   eps->categ = EPS_CATEGORY_CONTOUR;

    2007:   eps->ops->solve          = EPSSolve_CISS;
    2008:   eps->ops->setup          = EPSSetUp_CISS;
    2009:   eps->ops->setupsort      = EPSSetUpSort_CISS;
    2010:   eps->ops->setfromoptions = EPSSetFromOptions_CISS;
    2011:   eps->ops->destroy        = EPSDestroy_CISS;
    2012:   eps->ops->reset          = EPSReset_CISS;
    2013:   eps->ops->view           = EPSView_CISS;
    2014:   eps->ops->computevectors = EPSComputeVectors_CISS;
    2015:   eps->ops->setdefaultst   = EPSSetDefaultST_CISS;

    2017:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetSizes_C",EPSCISSSetSizes_CISS);
    2018:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetSizes_C",EPSCISSGetSizes_CISS);
    2019:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetThreshold_C",EPSCISSSetThreshold_CISS);
    2020:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetThreshold_C",EPSCISSGetThreshold_CISS);
    2021:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetRefinement_C",EPSCISSSetRefinement_CISS);
    2022:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetRefinement_C",EPSCISSGetRefinement_CISS);
    2023:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetUseST_C",EPSCISSSetUseST_CISS);
    2024:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetUseST_C",EPSCISSGetUseST_CISS);
    2025:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetQuadRule_C",EPSCISSSetQuadRule_CISS);
    2026:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetQuadRule_C",EPSCISSGetQuadRule_CISS);
    2027:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetExtraction_C",EPSCISSSetExtraction_CISS);
    2028:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetExtraction_C",EPSCISSGetExtraction_CISS);
    2029:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetKSPs_C",EPSCISSGetKSPs_CISS);

    2031:   /* log events */
    2032:   PetscLogEventRegister("EPSCISS_SVD",EPS_CLASSID,&EPS_CISS_SVD);

    2034:   /* set default values of parameters */
    2035:   ctx->N                  = 32;
    2036:   ctx->L                  = 16;
    2037:   ctx->M                  = ctx->N/4;
    2038:   ctx->delta              = 1e-12;
    2039:   ctx->L_max              = 64;
    2040:   ctx->spurious_threshold = 1e-4;
    2041:   ctx->usest              = PETSC_TRUE;
    2042:   ctx->usest_set          = PETSC_FALSE;
    2043:   ctx->isreal             = PETSC_FALSE;
    2044:   ctx->refine_inner       = 0;
    2045:   ctx->refine_blocksize   = 0;
    2046:   ctx->npart              = 1;
    2047:   ctx->quad               = (EPSCISSQuadRule)0;
    2048:   ctx->extraction         = EPS_CISS_EXTRACTION_RITZ;
    2049:   return(0);
    2050: }