Date: 2020-01-13T12:00:27+00:00

Actual source code: ciss.c
slepc-3.12.2 2020-01-13
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2019, 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>                /*I "slepceps.h" I*/
     34: #include <slepcblaslapack.h>

     36: typedef struct {
     37:   /* parameters */
     38:   PetscInt          N;          /* number of integration points (32) */
     39:   PetscInt          L;          /* block size (16) */
     40:   PetscInt          M;          /* moment degree (N/4 = 4) */
     41:   PetscReal         delta;      /* threshold of singular value (1e-12) */
     42:   PetscInt          L_max;      /* maximum number of columns of the source matrix V */
     43:   PetscReal         spurious_threshold; /* discard spurious eigenpairs */
     44:   PetscBool         isreal;     /* A and B are real */
     45:   PetscInt          npart;      /* number of partitions */
     46:   PetscInt          refine_inner;
     47:   PetscInt          refine_blocksize;
     48:   /* private data */
     49:   PetscReal         *sigma;     /* threshold for numerical rank */
     50:   PetscInt          subcomm_id;
     51:   PetscInt          num_solve_point;
     52:   PetscScalar       *weight;
     53:   PetscScalar       *omega;
     54:   PetscScalar       *pp;
     55:   BV                V;
     56:   BV                S;
     57:   BV                pV;
     58:   BV                Y;
     59:   Vec               xsub;
     60:   Vec               xdup;
     61:   KSP               *ksp;       /* ksp array for storing factorizations at integration points */
     62:   PetscBool         useconj;
     63:   PetscReal         est_eig;
     64:   VecScatter        scatterin;
     65:   Mat               pA,pB;
     66:   PetscSubcomm      subcomm;
     67:   PetscBool         usest;
     68:   PetscBool         usest_set;  /* whether the user set the usest flag or not */
     69:   EPSCISSQuadRule   quad;
     70:   EPSCISSExtraction extraction;
     71: } EPS_CISS;

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

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

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

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

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

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

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

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

    154: static PetscErrorCode CISSRedundantMat(EPS eps)
    155: {
    157:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    158:   Mat            A,B;
    159:   PetscInt       nmat;

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

    179: static PetscErrorCode CISSScatterVec(EPS eps)
    180: {
    182:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    183:   IS             is1,is2;
    184:   Vec            v0;
    185:   PetscInt       i,j,k,mstart,mend,mlocal;
    186:   PetscInt       *idx1,*idx2,mloc_sub;

    189:   VecDestroy(&ctx->xsub);
    190:   MatCreateVecs(ctx->pA,&ctx->xsub,NULL);

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

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

    218: static PetscErrorCode SetPathParameter(EPS eps)
    219: {
    221:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    222:   PetscInt       i,j;
    223:   PetscScalar    center=0.0,tmp,tmp2,*omegai;
    224:   PetscReal      theta,radius=1.0,vscale,a,b,c,d,max_w=0.0,rgscale;
    225: #if defined(PETSC_USE_COMPLEX)
    226:   PetscReal      start_ang,end_ang;
    227: #endif
    228:   PetscBool      isring=PETSC_FALSE,isellipse=PETSC_FALSE,isinterval=PETSC_FALSE;

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

    306: static PetscErrorCode CISSVecSetRandom(BV V,PetscInt i0,PetscInt i1)
    307: {
    309:   PetscInt       i,j,nlocal;
    310:   PetscScalar    *vdata;
    311:   Vec            x;

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

    330: static PetscErrorCode VecScatterVecs(EPS eps,BV Vin,PetscInt n)
    331: {
    332:   PetscErrorCode    ierr;
    333:   EPS_CISS          *ctx = (EPS_CISS*)eps->data;
    334:   PetscInt          i;
    335:   Vec               vi,pvi;
    336:   const PetscScalar *array;

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

    355: static PetscErrorCode SolveLinearSystem(EPS eps,Mat A,Mat B,BV V,PetscInt L_start,PetscInt L_end,PetscBool initksp)
    356: {
    358:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    359:   PetscInt       i,j,p_id;
    360:   Mat            Fz,kspMat;
    361:   Vec            Bvj,vj,yj;
    362:   KSP            ksp;

    365:   if (!ctx->ksp) { EPSCISSGetKSPs(eps,&ctx->num_solve_point,&ctx->ksp); }
    366:   BVCreateVec(V,&Bvj);
    367:   if (ctx->usest) {
    368:     MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&Fz);
    369:   }
    370:   for (i=0;i<ctx->num_solve_point;i++) {
    371:     p_id = i*ctx->subcomm->n + ctx->subcomm_id;
    372:     if (!ctx->usest && initksp) {
    373:       MatDuplicate(A,MAT_COPY_VALUES,&kspMat);
    374:       if (B) {
    375:         MatAXPY(kspMat,-ctx->omega[p_id],B,DIFFERENT_NONZERO_PATTERN);
    376:       } else {
    377:         MatShift(kspMat,-ctx->omega[p_id]);
    378:       }
    379:       KSPSetOperators(ctx->ksp[i],kspMat,kspMat);
    380:       MatDestroy(&kspMat);
    381:     } else if (ctx->usest) {
    382:       STSetShift(eps->st,ctx->omega[p_id]);
    383:       STGetKSP(eps->st,&ksp);
    384:     }
    385:     for (j=L_start;j<L_end;j++) {
    386:       BVGetColumn(V,j,&vj);
    387:       BVGetColumn(ctx->Y,i*ctx->L_max+j,&yj);
    388:       if (B) {
    389:         MatMult(B,vj,Bvj);
    390:         if (ctx->usest) {
    391:           KSPSolve(ksp,Bvj,yj);
    392:         } else {
    393:           KSPSolve(ctx->ksp[i],Bvj,yj);
    394:         }
    395:       } else {
    396:         if (ctx->usest) {
    397:           KSPSolve(ksp,vj,yj);
    398:         } else {
    399:           KSPSolve(ctx->ksp[i],vj,yj);
    400:         }
    401:       }
    402:       BVRestoreColumn(V,j,&vj);
    403:       BVRestoreColumn(ctx->Y,i*ctx->L_max+j,&yj);
    404:     }
    405:     if (ctx->usest && i<ctx->num_solve_point-1) { KSPReset(ksp); }
    406:   }
    407:   if (ctx->usest) { MatDestroy(&Fz); }
    408:   VecDestroy(&Bvj);
    409:   return(0);
    410: }

    412: #if defined(PETSC_USE_COMPLEX)
    413: static PetscErrorCode EstimateNumberEigs(EPS eps,PetscInt *L_add)
    414: {
    416:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    417:   PetscInt       i,j,p_id;
    418:   PetscScalar    tmp,m = 1,sum = 0.0;
    419:   PetscReal      eta;
    420:   Vec            v,vtemp,vj,yj;

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

    462: static PetscErrorCode CalcMu(EPS eps,PetscScalar *Mu)
    463: {
    465:   PetscMPIInt    sub_size,len;
    466:   PetscInt       i,j,k,s;
    467:   PetscScalar    *m,*temp,*temp2,*ppk,alp;
    468:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    469:   Mat            M;

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

    515: static PetscErrorCode BlockHankel(EPS eps,PetscScalar *Mu,PetscInt s,PetscScalar *H)
    516: {
    517:   EPS_CISS *ctx = (EPS_CISS*)eps->data;
    518:   PetscInt i,j,k,L=ctx->L,M=ctx->M;

    521:   for (k=0;k<L*M;k++)
    522:     for (j=0;j<M;j++)
    523:       for (i=0;i<L;i++)
    524:         H[j*L+i+k*L*M] = Mu[i+k*L+(j+s)*L*L];
    525:   return(0);
    526: }

    528: static PetscErrorCode SVD_H0(EPS eps,PetscScalar *S,PetscInt *K)
    529: {
    530: #if defined(PETSC_MISSING_LAPACK_GESVD)
    532:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GESVD - Lapack routine is unavailable");
    533: #else
    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:   PetscMalloc1(5*ml,&work);
    545: #if defined(PETSC_USE_COMPLEX)
    546:   PetscMalloc1(5*ml,&rwork);
    547: #endif
    548:   PetscBLASIntCast(ml,&m);
    549:   n = m; lda = m; ldu = m; ldvt = m; lwork = 5*m;
    550:   PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    551: #if defined(PETSC_USE_COMPLEX)
    552:   PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("N","N",&m,&n,S,&lda,ctx->sigma,NULL,&ldu,NULL,&ldvt,work,&lwork,rwork,&info));
    553: #else
    554:   PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("N","N",&m,&n,S,&lda,ctx->sigma,NULL,&ldu,NULL,&ldvt,work,&lwork,&info));
    555: #endif
    556:   SlepcCheckLapackInfo("gesvd",info);
    557:   PetscFPTrapPop();
    558:   (*K) = 0;
    559:   for (i=0;i<ml;i++) {
    560:     if (ctx->sigma[i]/PetscMax(ctx->sigma[0],1)>ctx->delta) (*K)++;
    561:   }
    562:   PetscFree(work);
    563: #if defined(PETSC_USE_COMPLEX)
    564:   PetscFree(rwork);
    565: #endif
    566:   return(0);
    567: #endif
    568: }

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

    579:   BVGetSizes(ctx->Y,&vec_local_size,NULL,NULL);
    580:   PetscMalloc1(ctx->num_solve_point,&ppk);
    581:   for (i=0;i<ctx->num_solve_point;i++) ppk[i] = 1;
    582:   BVGetColumn(ctx->Y,0,&yj);
    583:   VecDuplicate(yj,&v);
    584:   BVRestoreColumn(ctx->Y,0,&yj);
    585:   for (k=0;k<ctx->M;k++) {
    586:     for (j=0;j<ctx->L;j++) {
    587:       VecSet(v,0);
    588:       for (i=0;i<ctx->num_solve_point;i++) {
    589:         p_id = i*ctx->subcomm->n + ctx->subcomm_id;
    590:         BVSetActiveColumns(ctx->Y,i*ctx->L_max+j,i*ctx->L_max+j+1);
    591:         BVMultVec(ctx->Y,ppk[i]*ctx->weight[p_id],1.0,v,&m);
    592:       }
    593:       if (ctx->useconj) {
    594:         VecGetArray(v,&v_data);
    595:         for (i=0;i<vec_local_size;i++) v_data[i] = PetscRealPart(v_data[i])*2;
    596:         VecRestoreArray(v,&v_data);
    597:       }
    598:       BVGetColumn(ctx->S,k*ctx->L+j,&sj);
    599:       if (ctx->pA) {
    600:         VecSet(sj,0);
    601:         VecScatterBegin(ctx->scatterin,v,sj,ADD_VALUES,SCATTER_REVERSE);
    602:         VecScatterEnd(ctx->scatterin,v,sj,ADD_VALUES,SCATTER_REVERSE);
    603:       } else {
    604:         VecCopy(v,sj);
    605:       }
    606:       BVRestoreColumn(ctx->S,k*ctx->L+j,&sj);
    607:     }
    608:     for (i=0;i<ctx->num_solve_point;i++) {
    609:       p_id = i*ctx->subcomm->n + ctx->subcomm_id;
    610:       ppk[i] *= ctx->pp[p_id];
    611:     }
    612:   }
    613:   PetscFree(ppk);
    614:   VecDestroy(&v);
    615:   return(0);
    616: }

    618: static PetscErrorCode SVD_S(BV S,PetscInt ml,PetscReal delta,PetscReal *sigma,PetscInt *K)
    619: {
    620: #if defined(PETSC_MISSING_LAPACK_GESVD)
    622:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GESVD - Lapack routine is unavailable");
    623: #else
    625:   PetscInt       i,j,k,local_size;
    626:   PetscMPIInt    len;
    627:   PetscScalar    *work,*temp,*B,*tempB,*s_data,*Q1,*Q2,*temp2,alpha=1,beta=0;
    628:   PetscBLASInt   l,m,n,lda,ldu,ldvt,lwork,info,ldb,ldc;
    629: #if defined(PETSC_USE_COMPLEX)
    630:   PetscReal      *rwork;
    631: #endif

    634:   BVGetSizes(S,&local_size,NULL,NULL);
    635:   BVGetArray(S,&s_data);
    636:   PetscMalloc7(ml*ml,&temp,ml*ml,&temp2,local_size*ml,&Q1,local_size*ml,&Q2,ml*ml,&B,ml*ml,&tempB,5*ml,&work);
    637:   PetscArrayzero(B,ml*ml);
    638: #if defined(PETSC_USE_COMPLEX)
    639:   PetscMalloc1(5*ml,&rwork);
    640: #endif
    641:   PetscFPTrapPush(PETSC_FP_TRAP_OFF);

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

    645:   for (k=0;k<2;k++) {
    646:     PetscBLASIntCast(local_size,&m);
    647:     PetscBLASIntCast(ml,&l);
    648:     n = l; lda = m; ldb = m; ldc = l;
    649:     if (k == 0) {
    650:       PetscStackCallBLAS("BLASgemm",BLASgemm_("C","N",&l,&n,&m,&alpha,s_data,&lda,s_data,&ldb,&beta,temp,&ldc));
    651:     } else if ((k%2)==1) {
    652:       PetscStackCallBLAS("BLASgemm",BLASgemm_("C","N",&l,&n,&m,&alpha,Q1,&lda,Q1,&ldb,&beta,temp,&ldc));
    653:     } else {
    654:       PetscStackCallBLAS("BLASgemm",BLASgemm_("C","N",&l,&n,&m,&alpha,Q2,&lda,Q2,&ldb,&beta,temp,&ldc));
    655:     }
    656:     PetscArrayzero(temp2,ml*ml);
    657:     PetscMPIIntCast(ml*ml,&len);
    658:     MPI_Allreduce(temp,temp2,len,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)S));

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

    669:     PetscBLASIntCast(local_size,&l);
    670:     PetscBLASIntCast(ml,&n);
    671:     m = n; lda = l; ldb = m; ldc = l;
    672:     if (k==0) {
    673:       PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&l,&n,&m,&alpha,s_data,&lda,temp2,&ldb,&beta,Q1,&ldc));
    674:     } else if ((k%2)==1) {
    675:       PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&l,&n,&m,&alpha,Q1,&lda,temp2,&ldb,&beta,Q2,&ldc));
    676:     } else {
    677:       PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&l,&n,&m,&alpha,Q2,&lda,temp2,&ldb,&beta,Q1,&ldc));
    678:     }

    680:     PetscBLASIntCast(ml,&l);
    681:     m = l; n = l; lda = l; ldb = m; ldc = l;
    682:     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&l,&n,&m,&alpha,B,&lda,temp2,&ldb,&beta,tempB,&ldc));
    683:     for (i=0;i<ml;i++) {
    684:       sigma[i] = sqrt(sigma[i]);
    685:       for (j=0;j<local_size;j++) {
    686:         if ((k%2)==1) Q2[j+i*local_size]/=sigma[i];
    687:         else Q1[j+i*local_size]/=sigma[i];
    688:       }
    689:       for (j=0;j<ml;j++) {
    690:         B[j+i*ml]=tempB[j+i*ml]*sigma[i];
    691:       }
    692:     }
    693:   }

    695:   PetscBLASIntCast(ml,&m);
    696:   n = m; lda = m; ldu=1; ldvt=1;
    697: #if defined(PETSC_USE_COMPLEX)
    698:   PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("N","O",&m,&n,B,&lda,sigma,NULL,&ldu,NULL,&ldvt,work,&lwork,rwork,&info));
    699: #else
    700:   PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("N","O",&m,&n,B,&lda,sigma,NULL,&ldu,NULL,&ldvt,work,&lwork,&info));
    701: #endif
    702:   SlepcCheckLapackInfo("gesvd",info);

    704:   PetscBLASIntCast(local_size,&l);
    705:   PetscBLASIntCast(ml,&n);
    706:   m = n; lda = l; ldb = m; ldc = l;
    707:   if ((k%2)==1) {
    708:     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","T",&l,&n,&m,&alpha,Q1,&lda,B,&ldb,&beta,s_data,&ldc));
    709:   } else {
    710:     PetscStackCallBLAS("BLASgemm",BLASgemm_("N","T",&l,&n,&m,&alpha,Q2,&lda,B,&ldb,&beta,s_data,&ldc));
    711:   }

    713:   PetscFPTrapPop();
    714:   BVRestoreArray(S,&s_data);

    716:   (*K) = 0;
    717:   for (i=0;i<ml;i++) {
    718:     if (sigma[i]/PetscMax(sigma[0],1)>delta) (*K)++;
    719:   }
    720:   PetscFree7(temp,temp2,Q1,Q2,B,tempB,work);
    721: #if defined(PETSC_USE_COMPLEX)
    722:   PetscFree(rwork);
    723: #endif
    724:   return(0);
    725: #endif
    726: }

    728: static PetscErrorCode isGhost(EPS eps,PetscInt ld,PetscInt nv,PetscBool *fl)
    729: {
    731:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    732:   PetscInt       i,j;
    733:   PetscScalar    *pX;
    734:   PetscReal      *tau,s1,s2,tau_max=0.0;

    737:   PetscMalloc1(nv,&tau);
    738:   DSVectors(eps->ds,DS_MAT_X,NULL,NULL);
    739:   DSGetArray(eps->ds,DS_MAT_X,&pX);

    741:   for (i=0;i<nv;i++) {
    742:     s1 = 0;
    743:     s2 = 0;
    744:     for (j=0;j<nv;j++) {
    745:       s1 += PetscAbsScalar(PetscPowScalarInt(pX[i*ld+j],2));
    746:       s2 += PetscPowRealInt(PetscAbsScalar(pX[i*ld+j]),2)/ctx->sigma[j];
    747:     }
    748:     tau[i] = s1/s2;
    749:     tau_max = PetscMax(tau_max,tau[i]);
    750:   }
    751:   DSRestoreArray(eps->ds,DS_MAT_X,&pX);
    752:   for (i=0;i<nv;i++) {
    753:     tau[i] /= tau_max;
    754:   }
    755:   for (i=0;i<nv;i++) {
    756:     if (tau[i]>=ctx->spurious_threshold) fl[i] = PETSC_TRUE;
    757:     else fl[i] = PETSC_FALSE;
    758:   }
    759:   PetscFree(tau);
    760:   return(0);
    761: }

    763: static PetscErrorCode rescale_eig(EPS eps,PetscInt nv)
    764: {
    766:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    767:   PetscInt       i;
    768:   PetscScalar    center;
    769:   PetscReal      radius,a,b,c,d,rgscale;
    770: #if defined(PETSC_USE_COMPLEX)
    771:   PetscReal      start_ang,end_ang,vscale,theta;
    772: #endif
    773:   PetscBool      isring,isellipse,isinterval;

    776:   PetscObjectTypeCompare((PetscObject)eps->rg,RGELLIPSE,&isellipse);
    777:   PetscObjectTypeCompare((PetscObject)eps->rg,RGRING,&isring);
    778:   PetscObjectTypeCompare((PetscObject)eps->rg,RGINTERVAL,&isinterval);
    779:   RGGetScale(eps->rg,&rgscale);
    780:   if (isinterval) {
    781:     RGIntervalGetEndpoints(eps->rg,NULL,NULL,&c,&d);
    782:     if (c==d) {
    783:       for (i=0;i<nv;i++) {
    784: #if defined(PETSC_USE_COMPLEX)
    785:         eps->eigr[i] = PetscRealPart(eps->eigr[i]);
    786: #else
    787:         eps->eigi[i] = 0;
    788: #endif
    789:       }
    790:     }
    791:   }
    792:   if (ctx->extraction == EPS_CISS_EXTRACTION_HANKEL) {
    793:     if (isellipse) {
    794:       RGEllipseGetParameters(eps->rg,&center,&radius,NULL);
    795:       for (i=0;i<nv;i++) eps->eigr[i] = rgscale*(center + radius*eps->eigr[i]);
    796:     } else if (isinterval) {
    797:       RGIntervalGetEndpoints(eps->rg,&a,&b,&c,&d);
    798:       if (ctx->quad == EPS_CISS_QUADRULE_CHEBYSHEV) {
    799:         for (i=0;i<nv;i++) {
    800:           if (c==d) eps->eigr[i] = ((b-a)*(eps->eigr[i]+1.0)/2.0+a)*rgscale;
    801:           if (a==b) {
    802: #if defined(PETSC_USE_COMPLEX)
    803:             eps->eigr[i] = ((d-c)*(eps->eigr[i]+1.0)/2.0+c)*rgscale*PETSC_i;
    804: #else
    805:             SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Integration points on a vertical line require complex arithmetic");
    806: #endif
    807:           }
    808:         }
    809:       } else {
    810:         center = (b+a)/2.0+(d+c)/2.0*PETSC_PI;
    811:         radius = PetscSqrtReal(PetscPowRealInt((b-a)/2.0,2)+PetscPowRealInt((d-c)/2.0,2));
    812:         for (i=0;i<nv;i++) eps->eigr[i] = center + radius*eps->eigr[i];
    813:       }
    814:     } else if (isring) {  /* only supported in complex scalars */
    815: #if defined(PETSC_USE_COMPLEX)
    816:       RGRingGetParameters(eps->rg,&center,&radius,&vscale,&start_ang,&end_ang,NULL);
    817:       if (ctx->quad == EPS_CISS_QUADRULE_CHEBYSHEV) {
    818:         for (i=0;i<nv;i++) {
    819:           theta = (start_ang*2.0+(end_ang-start_ang)*(PetscRealPart(eps->eigr[i])+1.0))*PETSC_PI;
    820:           eps->eigr[i] = rgscale*center + (rgscale*radius+PetscImaginaryPart(eps->eigr[i]))*PetscCMPLX(PetscCosReal(theta),vscale*PetscSinReal(theta));
    821:         }
    822:       } else {
    823:         for (i=0;i<nv;i++) eps->eigr[i] = rgscale*(center + radius*eps->eigr[i]);
    824:       }
    825: #endif
    826:     }
    827:   }
    828:   return(0);
    829: }

    831: PetscErrorCode EPSSetUp_CISS(EPS eps)
    832: {
    834:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    835:   PetscBool      issinvert,istrivial,isring,isellipse,isinterval,flg,useconj;
    836:   PetscReal      c,d;
    837:   Mat            A;

    840:   if (!eps->ncv) {
    841:     eps->ncv = ctx->L_max*ctx->M;
    842:     if (eps->ncv>eps->n) {
    843:       eps->ncv = eps->n;
    844:       ctx->L_max = eps->ncv/ctx->M;
    845:       if (!ctx->L_max) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Cannot adjust solver parameters, try setting a smaller value of M (moment size)");
    846:     }
    847:   } else {
    848:     EPSSetDimensions_Default(eps,eps->nev,&eps->ncv,&eps->mpd);
    849:     ctx->L_max = eps->ncv/ctx->M;
    850:     if (!ctx->L_max) {
    851:       ctx->L_max = 1;
    852:       eps->ncv = ctx->L_max*ctx->M;
    853:     }
    854:   }
    855:   ctx->L = PetscMin(ctx->L,ctx->L_max);
    856:   if (!eps->max_it) eps->max_it = 1;
    857:   if (!eps->mpd) eps->mpd = eps->ncv;
    858:   if (!eps->which) eps->which = EPS_ALL;
    859:   if (!eps->extraction) { EPSSetExtraction(eps,EPS_RITZ); }
    860:   else if (eps->extraction!=EPS_RITZ) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Unsupported extraction type");
    861:   if (eps->arbitrary) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Arbitrary selection of eigenpairs not supported in this solver");
    862:   if (eps->stopping!=EPSStoppingBasic) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"This solver does not support user-defined stopping test");

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

    877: #if !defined(PETSC_USE_COMPLEX)
    878:   if (isring) {
    879:     SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Ring region only supported for complex scalars");
    880:   }
    881: #endif
    882:   if (isinterval) {
    883:     RGIntervalGetEndpoints(eps->rg,NULL,NULL,&c,&d);
    884: #if !defined(PETSC_USE_COMPLEX)
    885:     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");
    886: #endif
    887:     if (!ctx->quad && c==d) ctx->quad = EPS_CISS_QUADRULE_CHEBYSHEV;
    888:   }
    889:   if (!ctx->quad) ctx->quad = EPS_CISS_QUADRULE_TRAPEZOIDAL;

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

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

    899:   /* allocate basis vectors */
    900:   BVDestroy(&ctx->S);
    901:   BVDuplicateResize(eps->V,ctx->L_max*ctx->M,&ctx->S);
    902:   PetscLogObjectParent((PetscObject)eps,(PetscObject)ctx->S);
    903:   BVDestroy(&ctx->V);
    904:   BVDuplicateResize(eps->V,ctx->L_max,&ctx->V);
    905:   PetscLogObjectParent((PetscObject)eps,(PetscObject)ctx->V);

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

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

    914:   CISSRedundantMat(eps);
    915:   if (ctx->pA) {
    916:     CISSScatterVec(eps);
    917:     BVDestroy(&ctx->pV);
    918:     BVCreate(PetscObjectComm((PetscObject)ctx->xsub),&ctx->pV);
    919:     BVSetSizesFromVec(ctx->pV,ctx->xsub,eps->n);
    920:     BVSetFromOptions(ctx->pV);
    921:     BVResize(ctx->pV,ctx->L_max,PETSC_FALSE);
    922:     PetscLogObjectParent((PetscObject)eps,(PetscObject)ctx->pV);
    923:   }

    925:   if (ctx->usest) {
    926:     PetscObjectTypeCompare((PetscObject)eps->st,STSINVERT,&issinvert);
    927:     if (!issinvert) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"If the usest flag is set, you must select the STSINVERT spectral transformation");
    928:   }

    930:   BVDestroy(&ctx->Y);
    931:   if (ctx->pA) {
    932:     BVCreate(PetscObjectComm((PetscObject)ctx->xsub),&ctx->Y);
    933:     BVSetSizesFromVec(ctx->Y,ctx->xsub,eps->n);
    934:     BVSetFromOptions(ctx->Y);
    935:     BVResize(ctx->Y,ctx->num_solve_point*ctx->L_max,PETSC_FALSE);
    936:   } else {
    937:     BVDuplicateResize(eps->V,ctx->num_solve_point*ctx->L_max,&ctx->Y);
    938:   }
    939:   PetscLogObjectParent((PetscObject)eps,(PetscObject)ctx->Y);

    941:   if (ctx->extraction == EPS_CISS_EXTRACTION_HANKEL) {
    942:     DSSetType(eps->ds,DSGNHEP);
    943:   } else if (eps->isgeneralized) {
    944:     if (eps->ishermitian && eps->ispositive) {
    945:       DSSetType(eps->ds,DSGHEP);
    946:     } else {
    947:       DSSetType(eps->ds,DSGNHEP);
    948:     }
    949:   } else {
    950:     if (eps->ishermitian) {
    951:       DSSetType(eps->ds,DSHEP);
    952:     } else {
    953:       DSSetType(eps->ds,DSNHEP);
    954:     }
    955:   }
    956:   DSAllocate(eps->ds,eps->ncv);
    957:   EPSSetWorkVecs(eps,2);

    959: #if !defined(PETSC_USE_COMPLEX)
    960:   if (!eps->ishermitian) { PetscInfo(eps,"Warning: complex eigenvalues are not calculated exactly without --with-scalar-type=complex in PETSc\n"); }
    961: #endif
    962:   return(0);
    963: }

    965: PetscErrorCode EPSSolve_CISS(EPS eps)
    966: {
    968:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    969:   Mat            A,B,X,M,pA,pB;
    970:   PetscInt       i,j,ld,nmat,L_add=0,nv=0,L_base=ctx->L,inner,nlocal,*inside;
    971:   PetscScalar    *Mu,*H0,*H1=NULL,*rr,*temp;
    972:   PetscReal      error,max_error;
    973:   PetscBool      *fl1;
    974:   Vec            si,w[3];
    975:   SlepcSC        sc;
    976:   PetscRandom    rand;
    977: #if defined(PETSC_USE_COMPLEX)
    978:   PetscBool      isellipse;
    979: #endif

    982:   w[0] = eps->work[0];
    983:   w[1] = NULL;
    984:   w[2] = eps->work[1];
    985:   /* override SC settings */
    986:   DSGetSlepcSC(eps->ds,&sc);
    987:   sc->comparison    = SlepcCompareLargestMagnitude;
    988:   sc->comparisonctx = NULL;
    989:   sc->map           = NULL;
    990:   sc->mapobj        = NULL;
    991:   VecGetLocalSize(w[0],&nlocal);
    992:   DSGetLeadingDimension(eps->ds,&ld);
    993:   STGetNumMatrices(eps->st,&nmat);
    994:   STGetMatrix(eps->st,0,&A);
    995:   if (nmat>1) { STGetMatrix(eps->st,1,&B); }
    996:   else B = NULL;
    997:   SetPathParameter(eps);
    998:   CISSVecSetRandom(ctx->V,0,ctx->L);
    999:   BVGetRandomContext(ctx->V,&rand);

    1001:   if (ctx->pA) {
    1002:     VecScatterVecs(eps,ctx->V,ctx->L);
    1003:     SolveLinearSystem(eps,ctx->pA,ctx->pB,ctx->pV,0,ctx->L,PETSC_TRUE);
    1004:   } else {
    1005:     SolveLinearSystem(eps,A,B,ctx->V,0,ctx->L,PETSC_TRUE);
    1006:   }
    1007: #if defined(PETSC_USE_COMPLEX)
    1008:   PetscObjectTypeCompare((PetscObject)eps->rg,RGELLIPSE,&isellipse);
    1009:   if (isellipse) {
    1010:     EstimateNumberEigs(eps,&L_add);
    1011:   } else {
    1012:     L_add = 0;
    1013:   }
    1014: #else
    1015:   L_add = 0;
    1016: #endif
    1017:   if (L_add>0) {
    1018:     PetscInfo2(eps,"Changing L %D -> %D by Estimate #Eig\n",ctx->L,ctx->L+L_add);
    1019:     CISSVecSetRandom(ctx->V,ctx->L,ctx->L+L_add);
    1020:     if (ctx->pA) {
    1021:       VecScatterVecs(eps,ctx->V,ctx->L+L_add);
    1022:       SolveLinearSystem(eps,ctx->pA,ctx->pB,ctx->pV,ctx->L,ctx->L+L_add,PETSC_FALSE);
    1023:     } else {
    1024:       SolveLinearSystem(eps,A,B,ctx->V,ctx->L,ctx->L+L_add,PETSC_FALSE);
    1025:     }
    1026:     ctx->L += L_add;
    1027:   }
    1028:   PetscMalloc2(ctx->L*ctx->L*ctx->M*2,&Mu,ctx->L*ctx->M*ctx->L*ctx->M,&H0);
    1029:   for (i=0;i<ctx->refine_blocksize;i++) {
    1030:     CalcMu(eps,Mu);
    1031:     BlockHankel(eps,Mu,0,H0);
    1032:     SVD_H0(eps,H0,&nv);
    1033:     if (ctx->sigma[0]<=ctx->delta || nv < ctx->L*ctx->M || ctx->L == ctx->L_max) break;
    1034:     L_add = L_base;
    1035:     if (ctx->L+L_add>ctx->L_max) L_add = ctx->L_max-ctx->L;
    1036:     PetscInfo2(eps,"Changing L %D -> %D by SVD(H0)\n",ctx->L,ctx->L+L_add);
    1037:     CISSVecSetRandom(ctx->V,ctx->L,ctx->L+L_add);
    1038:     if (ctx->pA) {
    1039:       VecScatterVecs(eps,ctx->V,ctx->L+L_add);
    1040:       SolveLinearSystem(eps,ctx->pA,ctx->pB,ctx->pV,ctx->L,ctx->L+L_add,PETSC_FALSE);
    1041:     } else {
    1042:       SolveLinearSystem(eps,A,B,ctx->V,ctx->L,ctx->L+L_add,PETSC_FALSE);
    1043:     }
    1044:     ctx->L += L_add;
    1045:   }
    1046:   if (ctx->extraction == EPS_CISS_EXTRACTION_HANKEL) {
    1047:     PetscMalloc1(ctx->L*ctx->M*ctx->L*ctx->M,&H1);
    1048:   }

    1050:   while (eps->reason == EPS_CONVERGED_ITERATING) {
    1051:     eps->its++;
    1052:     for (inner=0;inner<=ctx->refine_inner;inner++) {
    1053:       if (ctx->extraction == EPS_CISS_EXTRACTION_HANKEL) {
    1054:         CalcMu(eps,Mu);
    1055:         BlockHankel(eps,Mu,0,H0);
    1056:         SVD_H0(eps,H0,&nv);
    1057:         break;
    1058:       } else {
    1059:         ConstructS(eps);
    1060:         BVSetActiveColumns(ctx->S,0,ctx->L);
    1061:         BVCopy(ctx->S,ctx->V);
    1062:         SVD_S(ctx->S,ctx->L*ctx->M,ctx->delta,ctx->sigma,&nv);
    1063:         if (ctx->sigma[0]>ctx->delta && nv==ctx->L*ctx->M && inner!=ctx->refine_inner) {
    1064:           if (ctx->pA) {
    1065:             VecScatterVecs(eps,ctx->V,ctx->L);
    1066:             SolveLinearSystem(eps,ctx->pA,ctx->pB,ctx->pV,0,ctx->L,PETSC_FALSE);
    1067:           } else {
    1068:             SolveLinearSystem(eps,A,B,ctx->V,0,ctx->L,PETSC_FALSE);
    1069:           }
    1070:         } else break;
    1071:       }
    1072:     }
    1073:     eps->nconv = 0;
    1074:     if (nv == 0) eps->reason = EPS_CONVERGED_TOL;
    1075:     else {
    1076:       DSSetDimensions(eps->ds,nv,0,0,0);
    1077:       DSSetState(eps->ds,DS_STATE_RAW);

    1079:       if (ctx->extraction == EPS_CISS_EXTRACTION_HANKEL) {
    1080:         BlockHankel(eps,Mu,0,H0);
    1081:         BlockHankel(eps,Mu,1,H1);
    1082:         DSGetArray(eps->ds,DS_MAT_A,&temp);
    1083:         for (j=0;j<nv;j++) {
    1084:           for (i=0;i<nv;i++) {
    1085:             temp[i+j*ld] = H1[i+j*ctx->L*ctx->M];
    1086:           }
    1087:         }
    1088:         DSRestoreArray(eps->ds,DS_MAT_A,&temp);
    1089:         DSGetArray(eps->ds,DS_MAT_B,&temp);
    1090:         for (j=0;j<nv;j++) {
    1091:           for (i=0;i<nv;i++) {
    1092:             temp[i+j*ld] = H0[i+j*ctx->L*ctx->M];
    1093:           }
    1094:         }
    1095:         DSRestoreArray(eps->ds,DS_MAT_B,&temp);
    1096:       } else {
    1097:         BVSetActiveColumns(ctx->S,0,nv);
    1098:         DSGetMat(eps->ds,DS_MAT_A,&pA);
    1099:         MatZeroEntries(pA);
    1100:         BVMatProject(ctx->S,A,ctx->S,pA);
    1101:         DSRestoreMat(eps->ds,DS_MAT_A,&pA);
    1102:         if (B) {
    1103:           DSGetMat(eps->ds,DS_MAT_B,&pB);
    1104:           MatZeroEntries(pB);
    1105:           BVMatProject(ctx->S,B,ctx->S,pB);
    1106:           DSRestoreMat(eps->ds,DS_MAT_B,&pB);
    1107:         }
    1108:       }

    1110:       DSSolve(eps->ds,eps->eigr,eps->eigi);
    1111:       DSSynchronize(eps->ds,eps->eigr,eps->eigi);

    1113:       PetscMalloc3(nv,&fl1,nv,&inside,nv,&rr);
    1114:       rescale_eig(eps,nv);
    1115:       isGhost(eps,ld,nv,fl1);
    1116:       RGCheckInside(eps->rg,nv,eps->eigr,eps->eigi,inside);
    1117:       for (i=0;i<nv;i++) {
    1118:         if (fl1[i] && inside[i]>=0) {
    1119:           rr[i] = 1.0;
    1120:           eps->nconv++;
    1121:         } else rr[i] = 0.0;
    1122:       }
    1123:       DSSort(eps->ds,eps->eigr,eps->eigi,rr,NULL,&eps->nconv);
    1124:       DSSynchronize(eps->ds,eps->eigr,eps->eigi);
    1125:       rescale_eig(eps,nv);
    1126:       PetscFree3(fl1,inside,rr);
    1127:       BVSetActiveColumns(eps->V,0,nv);
    1128:       if (ctx->extraction == EPS_CISS_EXTRACTION_HANKEL) {
    1129:         ConstructS(eps);
    1130:         BVSetActiveColumns(ctx->S,0,ctx->L);
    1131:         BVCopy(ctx->S,ctx->V);
    1132:         BVSetActiveColumns(ctx->S,0,nv);
    1133:       }
    1134:       BVCopy(ctx->S,eps->V);

    1136:       DSVectors(eps->ds,DS_MAT_X,NULL,NULL);
    1137:       DSGetMat(eps->ds,DS_MAT_X,&X);
    1138:       BVMultInPlace(ctx->S,X,0,eps->nconv);
    1139:       if (eps->ishermitian) {
    1140:         BVMultInPlace(eps->V,X,0,eps->nconv);
    1141:       }
    1142:       MatDestroy(&X);
    1143:       max_error = 0.0;
    1144:       for (i=0;i<eps->nconv;i++) {
    1145:         BVGetColumn(ctx->S,i,&si);
    1146:         EPSComputeResidualNorm_Private(eps,PETSC_FALSE,eps->eigr[i],eps->eigi[i],si,NULL,w,&error);
    1147:         (*eps->converged)(eps,eps->eigr[i],eps->eigi[i],error,&error,eps->convergedctx);
    1148:         BVRestoreColumn(ctx->S,i,&si);
    1149:         max_error = PetscMax(max_error,error);
    1150:       }

    1152:       if (max_error <= eps->tol) eps->reason = EPS_CONVERGED_TOL;
    1153:       else if (eps->its >= eps->max_it) eps->reason = EPS_DIVERGED_ITS;
    1154:       else {
    1155:         if (eps->nconv > ctx->L) {
    1156:           MatCreateSeqDense(PETSC_COMM_SELF,eps->nconv,ctx->L,NULL,&M);
    1157:           MatDenseGetArray(M,&temp);
    1158:           for (i=0;i<ctx->L*eps->nconv;i++) {
    1159:             PetscRandomGetValue(rand,&temp[i]);
    1160:             temp[i] = PetscRealPart(temp[i]);
    1161:           }
    1162:           MatDenseRestoreArray(M,&temp);
    1163:           BVSetActiveColumns(ctx->S,0,eps->nconv);
    1164:           BVMultInPlace(ctx->S,M,0,ctx->L);
    1165:           MatDestroy(&M);
    1166:           BVSetActiveColumns(ctx->S,0,ctx->L);
    1167:           BVCopy(ctx->S,ctx->V);
    1168:         }
    1169:         if (ctx->pA) {
    1170:           VecScatterVecs(eps,ctx->V,ctx->L);
    1171:           SolveLinearSystem(eps,ctx->pA,ctx->pB,ctx->pV,0,ctx->L,PETSC_FALSE);
    1172:         } else {
    1173:           SolveLinearSystem(eps,A,B,ctx->V,0,ctx->L,PETSC_FALSE);
    1174:         }
    1175:       }
    1176:     }
    1177:   }
    1178:   if (ctx->extraction == EPS_CISS_EXTRACTION_HANKEL) {
    1179:     PetscFree(H1);
    1180:   }
    1181:   PetscFree2(Mu,H0);
    1182:   return(0);
    1183: }

    1185: static PetscErrorCode EPSCISSSetSizes_CISS(EPS eps,PetscInt ip,PetscInt bs,PetscInt ms,PetscInt npart,PetscInt bsmax,PetscBool realmats)
    1186: {
    1188:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    1189:   PetscInt       oN,onpart;

    1192:   oN = ctx->N;
    1193:   if (ip == PETSC_DECIDE || ip == PETSC_DEFAULT) {
    1194:     if (ctx->N!=32) { ctx->N =32; ctx->M = ctx->N/4; }
    1195:   } else {
    1196:     if (ip<1) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The ip argument must be > 0");
    1197:     if (ip%2) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The ip argument must be an even number");
    1198:     if (ctx->N!=ip) { ctx->N = ip; ctx->M = ctx->N/4; }
    1199:   }
    1200:   if (bs == PETSC_DECIDE || bs == PETSC_DEFAULT) {
    1201:     ctx->L = 16;
    1202:   } else {
    1203:     if (bs<1) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The bs argument must be > 0");
    1204:     ctx->L = bs;
    1205:   }
    1206:   if (ms == PETSC_DECIDE || ms == PETSC_DEFAULT) {
    1207:     ctx->M = ctx->N/4;
    1208:   } else {
    1209:     if (ms<1) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The ms argument must be > 0");
    1210:     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");
    1211:     ctx->M = ms;
    1212:   }
    1213:   onpart = ctx->npart;
    1214:   if (npart == PETSC_DECIDE || npart == PETSC_DEFAULT) {
    1215:     ctx->npart = 1;
    1216:   } else {
    1217:     if (npart<1) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The npart argument must be > 0");
    1218:     ctx->npart = npart;
    1219:   }
    1220:   if (bsmax == PETSC_DECIDE || bsmax == PETSC_DEFAULT) {
    1221:     ctx->L_max = 64;
    1222:   } else {
    1223:     if (bsmax<1) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The bsmax argument must be > 0");
    1224:     ctx->L_max = PetscMax(bsmax,ctx->L);
    1225:   }
    1226:   if (onpart != ctx->npart || oN != ctx->N || realmats != ctx->isreal) { EPSCISSResetSubcomm(eps); }
    1227:   ctx->isreal = realmats;
    1228:   eps->state = EPS_STATE_INITIAL;
    1229:   return(0);
    1230: }

    1232: /*@
    1233:    EPSCISSSetSizes - Sets the values of various size parameters in the CISS solver.

    1235:    Logically Collective on eps

    1237:    Input Parameters:
    1238: +  eps   - the eigenproblem solver context
    1239: .  ip    - number of integration points
    1240: .  bs    - block size
    1241: .  ms    - moment size
    1242: .  npart - number of partitions when splitting the communicator
    1243: .  bsmax - max block size
    1244: -  realmats - A and B are real

    1246:    Options Database Keys:
    1247: +  -eps_ciss_integration_points - Sets the number of integration points
    1248: .  -eps_ciss_blocksize - Sets the block size
    1249: .  -eps_ciss_moments - Sets the moment size
    1250: .  -eps_ciss_partitions - Sets the number of partitions
    1251: .  -eps_ciss_maxblocksize - Sets the maximum block size
    1252: -  -eps_ciss_realmats - A and B are real

    1254:    Note:
    1255:    The default number of partitions is 1. This means the internal KSP object is shared
    1256:    among all processes of the EPS communicator. Otherwise, the communicator is split
    1257:    into npart communicators, so that npart KSP solves proceed simultaneously.

    1259:    Level: advanced

    1261: .seealso: EPSCISSGetSizes()
    1262: @*/
    1263: PetscErrorCode EPSCISSSetSizes(EPS eps,PetscInt ip,PetscInt bs,PetscInt ms,PetscInt npart,PetscInt bsmax,PetscBool realmats)
    1264: {

    1275:   PetscTryMethod(eps,"EPSCISSSetSizes_C",(EPS,PetscInt,PetscInt,PetscInt,PetscInt,PetscInt,PetscBool),(eps,ip,bs,ms,npart,bsmax,realmats));
    1276:   return(0);
    1277: }

    1279: static PetscErrorCode EPSCISSGetSizes_CISS(EPS eps,PetscInt *ip,PetscInt *bs,PetscInt *ms,PetscInt *npart,PetscInt *bsmax,PetscBool *realmats)
    1280: {
    1281:   EPS_CISS *ctx = (EPS_CISS*)eps->data;

    1284:   if (ip) *ip = ctx->N;
    1285:   if (bs) *bs = ctx->L;
    1286:   if (ms) *ms = ctx->M;
    1287:   if (npart) *npart = ctx->npart;
    1288:   if (bsmax) *bsmax = ctx->L_max;
    1289:   if (realmats) *realmats = ctx->isreal;
    1290:   return(0);
    1291: }

    1293: /*@
    1294:    EPSCISSGetSizes - Gets the values of various size parameters in the CISS solver.

    1296:    Not Collective

    1298:    Input Parameter:
    1299: .  eps - the eigenproblem solver context

    1301:    Output Parameters:
    1302: +  ip    - number of integration points
    1303: .  bs    - block size
    1304: .  ms    - moment size
    1305: .  npart - number of partitions when splitting the communicator
    1306: .  bsmax - max block size
    1307: -  realmats - A and B are real

    1309:    Level: advanced

    1311: .seealso: EPSCISSSetSizes()
    1312: @*/
    1313: PetscErrorCode EPSCISSGetSizes(EPS eps,PetscInt *ip,PetscInt *bs,PetscInt *ms,PetscInt *npart,PetscInt *bsmax,PetscBool *realmats)
    1314: {

    1319:   PetscUseMethod(eps,"EPSCISSGetSizes_C",(EPS,PetscInt*,PetscInt*,PetscInt*,PetscInt*,PetscInt*,PetscBool*),(eps,ip,bs,ms,npart,bsmax,realmats));
    1320:   return(0);
    1321: }

    1323: static PetscErrorCode EPSCISSSetThreshold_CISS(EPS eps,PetscReal delta,PetscReal spur)
    1324: {
    1325:   EPS_CISS *ctx = (EPS_CISS*)eps->data;

    1328:   if (delta == PETSC_DEFAULT) {
    1329:     ctx->delta = 1e-12;
    1330:   } else {
    1331:     if (delta<=0.0) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The delta argument must be > 0.0");
    1332:     ctx->delta = delta;
    1333:   }
    1334:   if (spur == PETSC_DEFAULT) {
    1335:     ctx->spurious_threshold = 1e-4;
    1336:   } else {
    1337:     if (spur<=0.0) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The spurious threshold argument must be > 0.0");
    1338:     ctx->spurious_threshold = spur;
    1339:   }
    1340:   return(0);
    1341: }

    1343: /*@
    1344:    EPSCISSSetThreshold - Sets the values of various threshold parameters in
    1345:    the CISS solver.

    1347:    Logically Collective on eps

    1349:    Input Parameters:
    1350: +  eps   - the eigenproblem solver context
    1351: .  delta - threshold for numerical rank
    1352: -  spur  - spurious threshold (to discard spurious eigenpairs)

    1354:    Options Database Keys:
    1355: +  -eps_ciss_delta - Sets the delta
    1356: -  -eps_ciss_spurious_threshold - Sets the spurious threshold

    1358:    Level: advanced

    1360: .seealso: EPSCISSGetThreshold()
    1361: @*/
    1362: PetscErrorCode EPSCISSSetThreshold(EPS eps,PetscReal delta,PetscReal spur)
    1363: {

    1370:   PetscTryMethod(eps,"EPSCISSSetThreshold_C",(EPS,PetscReal,PetscReal),(eps,delta,spur));
    1371:   return(0);
    1372: }

    1374: static PetscErrorCode EPSCISSGetThreshold_CISS(EPS eps,PetscReal *delta,PetscReal *spur)
    1375: {
    1376:   EPS_CISS *ctx = (EPS_CISS*)eps->data;

    1379:   if (delta) *delta = ctx->delta;
    1380:   if (spur)  *spur = ctx->spurious_threshold;
    1381:   return(0);
    1382: }

    1384: /*@
    1385:    EPSCISSGetThreshold - Gets the values of various threshold parameters
    1386:    in the CISS solver.

    1388:    Not Collective

    1390:    Input Parameter:
    1391: .  eps - the eigenproblem solver context

    1393:    Output Parameters:
    1394: +  delta - threshold for numerical rank
    1395: -  spur  - spurious threshold (to discard spurious eigenpairs)

    1397:    Level: advanced

    1399: .seealso: EPSCISSSetThreshold()
    1400: @*/
    1401: PetscErrorCode EPSCISSGetThreshold(EPS eps,PetscReal *delta,PetscReal *spur)
    1402: {

    1407:   PetscUseMethod(eps,"EPSCISSGetThreshold_C",(EPS,PetscReal*,PetscReal*),(eps,delta,spur));
    1408:   return(0);
    1409: }

    1411: static PetscErrorCode EPSCISSSetRefinement_CISS(EPS eps,PetscInt inner,PetscInt blsize)
    1412: {
    1413:   EPS_CISS *ctx = (EPS_CISS*)eps->data;

    1416:   if (inner == PETSC_DEFAULT) {
    1417:     ctx->refine_inner = 0;
    1418:   } else {
    1419:     if (inner<0) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The refine inner argument must be >= 0");
    1420:     ctx->refine_inner = inner;
    1421:   }
    1422:   if (blsize == PETSC_DEFAULT) {
    1423:     ctx->refine_blocksize = 0;
    1424:   } else {
    1425:     if (blsize<0) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The refine blocksize argument must be >= 0");
    1426:     ctx->refine_blocksize = blsize;
    1427:   }
    1428:   return(0);
    1429: }

    1431: /*@
    1432:    EPSCISSSetRefinement - Sets the values of various refinement parameters
    1433:    in the CISS solver.

    1435:    Logically Collective on eps

    1437:    Input Parameters:
    1438: +  eps    - the eigenproblem solver context
    1439: .  inner  - number of iterative refinement iterations (inner loop)
    1440: -  blsize - number of iterative refinement iterations (blocksize loop)

    1442:    Options Database Keys:
    1443: +  -eps_ciss_refine_inner - Sets number of inner iterations
    1444: -  -eps_ciss_refine_blocksize - Sets number of blocksize iterations

    1446:    Level: advanced

    1448: .seealso: EPSCISSGetRefinement()
    1449: @*/
    1450: PetscErrorCode EPSCISSSetRefinement(EPS eps,PetscInt inner,PetscInt blsize)
    1451: {

    1458:   PetscTryMethod(eps,"EPSCISSSetRefinement_C",(EPS,PetscInt,PetscInt),(eps,inner,blsize));
    1459:   return(0);
    1460: }

    1462: static PetscErrorCode EPSCISSGetRefinement_CISS(EPS eps,PetscInt *inner,PetscInt *blsize)
    1463: {
    1464:   EPS_CISS *ctx = (EPS_CISS*)eps->data;

    1467:   if (inner)  *inner = ctx->refine_inner;
    1468:   if (blsize) *blsize = ctx->refine_blocksize;
    1469:   return(0);
    1470: }

    1472: /*@
    1473:    EPSCISSGetRefinement - Gets the values of various refinement parameters
    1474:    in the CISS solver.

    1476:    Not Collective

    1478:    Input Parameter:
    1479: .  eps - the eigenproblem solver context

    1481:    Output Parameters:
    1482: +  inner  - number of iterative refinement iterations (inner loop)
    1483: -  blsize - number of iterative refinement iterations (blocksize loop)

    1485:    Level: advanced

    1487: .seealso: EPSCISSSetRefinement()
    1488: @*/
    1489: PetscErrorCode EPSCISSGetRefinement(EPS eps, PetscInt *inner, PetscInt *blsize)
    1490: {

    1495:   PetscUseMethod(eps,"EPSCISSGetRefinement_C",(EPS,PetscInt*,PetscInt*),(eps,inner,blsize));
    1496:   return(0);
    1497: }

    1499: static PetscErrorCode EPSCISSSetUseST_CISS(EPS eps,PetscBool usest)
    1500: {
    1501:   EPS_CISS *ctx = (EPS_CISS*)eps->data;

    1504:   ctx->usest     = usest;
    1505:   ctx->usest_set = PETSC_TRUE;
    1506:   eps->state     = EPS_STATE_INITIAL;
    1507:   return(0);
    1508: }

    1510: /*@
    1511:    EPSCISSSetUseST - Sets a flag indicating that the CISS solver will
    1512:    use the ST object for the linear solves.

    1514:    Logically Collective on eps

    1516:    Input Parameters:
    1517: +  eps    - the eigenproblem solver context
    1518: -  usest  - boolean flag to use the ST object or not

    1520:    Options Database Keys:
    1521: .  -eps_ciss_usest <bool> - whether the ST object will be used or not

    1523:    Level: advanced

    1525: .seealso: EPSCISSGetUseST()
    1526: @*/
    1527: PetscErrorCode EPSCISSSetUseST(EPS eps,PetscBool usest)
    1528: {

    1534:   PetscTryMethod(eps,"EPSCISSSetUseST_C",(EPS,PetscBool),(eps,usest));
    1535:   return(0);
    1536: }

    1538: static PetscErrorCode EPSCISSGetUseST_CISS(EPS eps,PetscBool *usest)
    1539: {
    1540:   EPS_CISS *ctx = (EPS_CISS*)eps->data;

    1543:   *usest = ctx->usest;
    1544:   return(0);
    1545: }

    1547: /*@
    1548:    EPSCISSGetUseST - Gets the flag for using the ST object
    1549:    in the CISS solver.

    1551:    Not Collective

    1553:    Input Parameter:
    1554: .  eps - the eigenproblem solver context

    1556:    Output Parameters:
    1557: .  usest - boolean flag indicating if the ST object is being used

    1559:    Level: advanced

    1561: .seealso: EPSCISSSetUseST()
    1562: @*/
    1563: PetscErrorCode EPSCISSGetUseST(EPS eps,PetscBool *usest)
    1564: {

    1570:   PetscUseMethod(eps,"EPSCISSGetUseST_C",(EPS,PetscBool*),(eps,usest));
    1571:   return(0);
    1572: }

    1574: static PetscErrorCode EPSCISSSetQuadRule_CISS(EPS eps,EPSCISSQuadRule quad)
    1575: {
    1576:   EPS_CISS *ctx = (EPS_CISS*)eps->data;

    1579:   ctx->quad = quad;
    1580:   return(0);
    1581: }

    1583: /*@
    1584:    EPSCISSSetQuadRule - Sets the quadrature rule used in the CISS solver.

    1586:    Logically Collective on eps

    1588:    Input Parameters:
    1589: +  eps  - the eigenproblem solver context
    1590: -  quad - the quadrature rule

    1592:    Options Database Key:
    1593: .  -eps_ciss_quadrule - Sets the quadrature rule (either 'trapezoidal' or
    1594:                            'chebyshev')

    1596:    Notes:
    1597:    By default, the trapezoidal rule is used (EPS_CISS_QUADRULE_TRAPEZOIDAL).

    1599:    If the 'chebyshev' option is specified (EPS_CISS_QUADRULE_CHEBYSHEV), then
    1600:    Chebyshev points are used as quadrature points.

    1602:    Level: advanced

    1604: .seealso: EPSCISSGetQuadRule(), EPSCISSQuadRule
    1605: @*/
    1606: PetscErrorCode EPSCISSSetQuadRule(EPS eps,EPSCISSQuadRule quad)
    1607: {

    1613:   PetscTryMethod(eps,"EPSCISSSetQuadRule_C",(EPS,EPSCISSQuadRule),(eps,quad));
    1614:   return(0);
    1615: }

    1617: static PetscErrorCode EPSCISSGetQuadRule_CISS(EPS eps,EPSCISSQuadRule *quad)
    1618: {
    1619:   EPS_CISS *ctx = (EPS_CISS*)eps->data;

    1622:   *quad = ctx->quad;
    1623:   return(0);
    1624: }

    1626: /*@
    1627:    EPSCISSGetQuadRule - Gets the quadrature rule used in the CISS solver.

    1629:    Not Collective

    1631:    Input Parameter:
    1632: .  eps - the eigenproblem solver context

    1634:    Output Parameters:
    1635: .  quad - quadrature rule

    1637:    Level: advanced

    1639: .seealso: EPSCISSSetQuadRule() EPSCISSQuadRule
    1640: @*/
    1641: PetscErrorCode EPSCISSGetQuadRule(EPS eps,EPSCISSQuadRule *quad)
    1642: {

    1648:   PetscUseMethod(eps,"EPSCISSGetQuadRule_C",(EPS,EPSCISSQuadRule*),(eps,quad));
    1649:   return(0);
    1650: }

    1652: static PetscErrorCode EPSCISSSetExtraction_CISS(EPS eps,EPSCISSExtraction extraction)
    1653: {
    1654:   EPS_CISS *ctx = (EPS_CISS*)eps->data;

    1657:   ctx->extraction = extraction;
    1658:   return(0);
    1659: }

    1661: /*@
    1662:    EPSCISSSetExtraction - Sets the extraction technique used in the CISS solver.

    1664:    Logically Collective on eps

    1666:    Input Parameters:
    1667: +  eps        - the eigenproblem solver context
    1668: -  extraction - the extraction technique

    1670:    Options Database Key:
    1671: .  -eps_ciss_extraction - Sets the extraction technique (either 'ritz' or
    1672:                            'hankel')

    1674:    Notes:
    1675:    By default, the Rayleigh-Ritz extraction is used (EPS_CISS_EXTRACTION_RITZ).

    1677:    If the 'hankel' option is specified (EPS_CISS_EXTRACTION_HANKEL), then
    1678:    the Block Hankel method is used for extracting eigenpairs.

    1680:    Level: advanced

    1682: .seealso: EPSCISSGetExtraction(), EPSCISSExtraction
    1683: @*/
    1684: PetscErrorCode EPSCISSSetExtraction(EPS eps,EPSCISSExtraction extraction)
    1685: {

    1691:   PetscTryMethod(eps,"EPSCISSSetExtraction_C",(EPS,EPSCISSExtraction),(eps,extraction));
    1692:   return(0);
    1693: }

    1695: static PetscErrorCode EPSCISSGetExtraction_CISS(EPS eps,EPSCISSExtraction *extraction)
    1696: {
    1697:   EPS_CISS *ctx = (EPS_CISS*)eps->data;

    1700:   *extraction = ctx->extraction;
    1701:   return(0);
    1702: }

    1704: /*@
    1705:    EPSCISSGetExtraction - Gets the extraction technique used in the CISS solver.

    1707:    Not Collective

    1709:    Input Parameter:
    1710: .  eps - the eigenproblem solver context

    1712:    Output Parameters:
    1713: +  extraction - extraction technique

    1715:    Level: advanced

    1717: .seealso: EPSCISSSetExtraction() EPSCISSExtraction
    1718: @*/
    1719: PetscErrorCode EPSCISSGetExtraction(EPS eps,EPSCISSExtraction *extraction)
    1720: {

    1726:   PetscUseMethod(eps,"EPSCISSGetExtraction_C",(EPS,EPSCISSExtraction*),(eps,extraction));
    1727:   return(0);
    1728: }

    1730: static PetscErrorCode EPSCISSGetKSPs_CISS(EPS eps,PetscInt *nsolve,KSP **ksp)
    1731: {
    1733:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    1734:   PetscInt       i;
    1735:   PC             pc;

    1738:   if (!ctx->ksp) {
    1739:     if (!ctx->subcomm) {  /* initialize subcomm first */
    1740:       EPSCISSSetUseConj(eps,&ctx->useconj);
    1741:       EPSCISSSetUpSubComm(eps,&ctx->num_solve_point);
    1742:     }
    1743:     PetscMalloc1(ctx->num_solve_point,&ctx->ksp);
    1744:     for (i=0;i<ctx->num_solve_point;i++) {
    1745:       KSPCreate(PetscSubcommChild(ctx->subcomm),&ctx->ksp[i]);
    1746:       PetscObjectIncrementTabLevel((PetscObject)ctx->ksp[i],(PetscObject)eps,1);
    1747:       KSPSetOptionsPrefix(ctx->ksp[i],((PetscObject)eps)->prefix);
    1748:       KSPAppendOptionsPrefix(ctx->ksp[i],"eps_ciss_");
    1749:       PetscLogObjectParent((PetscObject)eps,(PetscObject)ctx->ksp[i]);
    1750:       PetscObjectSetOptions((PetscObject)ctx->ksp[i],((PetscObject)eps)->options);
    1751:       KSPSetErrorIfNotConverged(ctx->ksp[i],PETSC_TRUE);
    1752:       KSPSetTolerances(ctx->ksp[i],SLEPC_DEFAULT_TOL,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
    1753:       KSPGetPC(ctx->ksp[i],&pc);
    1754:       KSPSetType(ctx->ksp[i],KSPPREONLY);
    1755:       PCSetType(pc,PCLU);
    1756:     }
    1757:   }
    1758:   if (nsolve) *nsolve = ctx->num_solve_point;
    1759:   if (ksp)    *ksp    = ctx->ksp;
    1760:   return(0);
    1761: }

    1763: /*@C
    1764:    EPSCISSGetKSPs - Retrieve the array of linear solver objects associated with
    1765:    the CISS solver.

    1767:    Not Collective

    1769:    Input Parameter:
    1770: .  eps - the eigenproblem solver solver

    1772:    Output Parameters:
    1773: +  nsolve - number of solver objects
    1774: -  ksp - array of linear solver object

    1776:    Notes:
    1777:    The number of KSP solvers is equal to the number of integration points divided by
    1778:    the number of partitions. This value is halved in the case of real matrices with
    1779:    a region centered at the real axis.

    1781:    Level: advanced

    1783: .seealso: EPSCISSSetSizes()
    1784: @*/
    1785: PetscErrorCode EPSCISSGetKSPs(EPS eps,PetscInt *nsolve,KSP **ksp)
    1786: {

    1791:   PetscUseMethod(eps,"EPSCISSGetKSPs_C",(EPS,PetscInt*,KSP**),(eps,nsolve,ksp));
    1792:   return(0);
    1793: }

    1795: PetscErrorCode EPSReset_CISS(EPS eps)
    1796: {
    1798:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    1799:   PetscInt       i;

    1802:   BVDestroy(&ctx->S);
    1803:   BVDestroy(&ctx->V);
    1804:   BVDestroy(&ctx->Y);
    1805:   if (!ctx->usest) {
    1806:     for (i=0;i<ctx->num_solve_point;i++) {
    1807:       KSPReset(ctx->ksp[i]);
    1808:     }
    1809:   }
    1810:   VecScatterDestroy(&ctx->scatterin);
    1811:   VecDestroy(&ctx->xsub);
    1812:   VecDestroy(&ctx->xdup);
    1813:   if (ctx->pA) {
    1814:     MatDestroy(&ctx->pA);
    1815:     MatDestroy(&ctx->pB);
    1816:     BVDestroy(&ctx->pV);
    1817:   }
    1818:   return(0);
    1819: }

    1821: PetscErrorCode EPSSetFromOptions_CISS(PetscOptionItems *PetscOptionsObject,EPS eps)
    1822: {
    1823:   PetscErrorCode    ierr;
    1824:   PetscReal         r3,r4;
    1825:   PetscInt          i,i1,i2,i3,i4,i5,i6,i7;
    1826:   PetscBool         b1,b2,flg;
    1827:   EPS_CISS          *ctx = (EPS_CISS*)eps->data;
    1828:   EPSCISSQuadRule   quad;
    1829:   EPSCISSExtraction extraction;

    1832:   PetscOptionsHead(PetscOptionsObject,"EPS CISS Options");

    1834:     EPSCISSGetSizes(eps,&i1,&i2,&i3,&i4,&i5,&b1);
    1835:     PetscOptionsInt("-eps_ciss_integration_points","Number of integration points","EPSCISSSetSizes",i1,&i1,NULL);
    1836:     PetscOptionsInt("-eps_ciss_blocksize","Block size","EPSCISSSetSizes",i2,&i2,NULL);
    1837:     PetscOptionsInt("-eps_ciss_moments","Moment size","EPSCISSSetSizes",i3,&i3,NULL);
    1838:     PetscOptionsInt("-eps_ciss_partitions","Number of partitions","EPSCISSSetSizes",i4,&i4,NULL);
    1839:     PetscOptionsInt("-eps_ciss_maxblocksize","Maximum block size","EPSCISSSetSizes",i5,&i5,NULL);
    1840:     PetscOptionsBool("-eps_ciss_realmats","True if A and B are real","EPSCISSSetSizes",b1,&b1,NULL);
    1841:     EPSCISSSetSizes(eps,i1,i2,i3,i4,i5,b1);

    1843:     EPSCISSGetThreshold(eps,&r3,&r4);
    1844:     PetscOptionsReal("-eps_ciss_delta","Threshold for numerical rank","EPSCISSSetThreshold",r3,&r3,NULL);
    1845:     PetscOptionsReal("-eps_ciss_spurious_threshold","Threshold for the spurious eigenpairs","EPSCISSSetThreshold",r4,&r4,NULL);
    1846:     EPSCISSSetThreshold(eps,r3,r4);

    1848:     EPSCISSGetRefinement(eps,&i6,&i7);
    1849:     PetscOptionsInt("-eps_ciss_refine_inner","Number of inner iterative refinement iterations","EPSCISSSetRefinement",i6,&i6,NULL);
    1850:     PetscOptionsInt("-eps_ciss_refine_blocksize","Number of blocksize iterative refinement iterations","EPSCISSSetRefinement",i7,&i7,NULL);
    1851:     EPSCISSSetRefinement(eps,i6,i7);

    1853:     EPSCISSGetUseST(eps,&b2);
    1854:     PetscOptionsBool("-eps_ciss_usest","Use ST for linear solves","EPSCISSSetUseST",b2,&b2,&flg);
    1855:     if (flg) { EPSCISSSetUseST(eps,b2); }

    1857:     PetscOptionsEnum("-eps_ciss_quadrule","Quadrature rule","EPSCISSSetQuadRule",EPSCISSQuadRules,(PetscEnum)ctx->quad,(PetscEnum*)&quad,&flg);
    1858:     if (flg) { EPSCISSSetQuadRule(eps,quad); }

    1860:     PetscOptionsEnum("-eps_ciss_extraction","Extraction technique","EPSCISSSetExtraction",EPSCISSExtractions,(PetscEnum)ctx->extraction,(PetscEnum*)&extraction,&flg);
    1861:     if (flg) { EPSCISSSetExtraction(eps,extraction); }

    1863:   PetscOptionsTail();

    1865:   if (!eps->rg) { EPSGetRG(eps,&eps->rg); }
    1866:   RGSetFromOptions(eps->rg); /* this is necessary here to set useconj */
    1867:   if (!ctx->ksp) { EPSCISSGetKSPs(eps,&ctx->num_solve_point,&ctx->ksp); }
    1868:   for (i=0;i<ctx->num_solve_point;i++) {
    1869:     KSPSetFromOptions(ctx->ksp[i]);
    1870:   }
    1871:   PetscSubcommSetFromOptions(ctx->subcomm);
    1872:   return(0);
    1873: }

    1875: PetscErrorCode EPSDestroy_CISS(EPS eps)
    1876: {
    1878:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;

    1881:   EPSCISSResetSubcomm(eps);
    1882:   PetscFree4(ctx->weight,ctx->omega,ctx->pp,ctx->sigma);
    1883:   PetscFree(eps->data);
    1884:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetSizes_C",NULL);
    1885:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetSizes_C",NULL);
    1886:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetThreshold_C",NULL);
    1887:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetThreshold_C",NULL);
    1888:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetRefinement_C",NULL);
    1889:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetRefinement_C",NULL);
    1890:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetUseST_C",NULL);
    1891:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetUseST_C",NULL);
    1892:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetQuadRule_C",NULL);
    1893:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetQuadRule_C",NULL);
    1894:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetExtraction_C",NULL);
    1895:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetExtraction_C",NULL);
    1896:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetKSPs_C",NULL);
    1897:   return(0);
    1898: }

    1900: PetscErrorCode EPSView_CISS(EPS eps,PetscViewer viewer)
    1901: {
    1903:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    1904:   PetscBool      isascii;

    1907:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    1908:   if (isascii) {
    1909:     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);
    1910:     if (ctx->isreal) {
    1911:       PetscViewerASCIIPrintf(viewer,"  exploiting symmetry of integration points\n");
    1912:     }
    1913:     PetscViewerASCIIPrintf(viewer,"  threshold { delta: %g, spurious threshold: %g }\n",(double)ctx->delta,(double)ctx->spurious_threshold);
    1914:     PetscViewerASCIIPrintf(viewer,"  iterative refinement { inner: %D, blocksize: %D }\n",ctx->refine_inner, ctx->refine_blocksize);
    1915:     PetscViewerASCIIPrintf(viewer,"  extraction: %s\n",EPSCISSExtractions[ctx->extraction]);
    1916:     PetscViewerASCIIPrintf(viewer,"  quadrature rule: %s\n",EPSCISSQuadRules[ctx->quad]);
    1917:     if (ctx->usest) {
    1918:       PetscViewerASCIIPrintf(viewer,"  using ST for linear solves\n");
    1919:     } else {
    1920:       if (!ctx->ksp) { EPSCISSGetKSPs(eps,&ctx->num_solve_point,&ctx->ksp); }
    1921:       PetscViewerASCIIPushTab(viewer);
    1922:       KSPView(ctx->ksp[0],viewer);
    1923:       PetscViewerASCIIPopTab(viewer);
    1924:     }
    1925:   }
    1926:   return(0);
    1927: }

    1929: PetscErrorCode EPSSetDefaultST_CISS(EPS eps)
    1930: {
    1932:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;
    1933:   PetscBool      usest = ctx->usest;

    1936:   if (!((PetscObject)eps->st)->type_name) {
    1937:     if (!ctx->usest_set) usest = (ctx->npart>1)? PETSC_FALSE: PETSC_TRUE;
    1938:     if (usest) {
    1939:       STSetType(eps->st,STSINVERT);
    1940:     } else {
    1941:       /* we are not going to use ST, so avoid factorizing the matrix */
    1942:       STSetType(eps->st,STSHIFT);
    1943:     }
    1944:   }
    1945:   return(0);
    1946: }

    1948: SLEPC_EXTERN PetscErrorCode EPSCreate_CISS(EPS eps)
    1949: {
    1951:   EPS_CISS       *ctx = (EPS_CISS*)eps->data;

    1954:   PetscNewLog(eps,&ctx);
    1955:   eps->data = ctx;

    1957:   eps->useds = PETSC_TRUE;
    1958:   eps->categ = EPS_CATEGORY_CONTOUR;

    1960:   eps->ops->solve          = EPSSolve_CISS;
    1961:   eps->ops->setup          = EPSSetUp_CISS;
    1962:   eps->ops->setfromoptions = EPSSetFromOptions_CISS;
    1963:   eps->ops->destroy        = EPSDestroy_CISS;
    1964:   eps->ops->reset          = EPSReset_CISS;
    1965:   eps->ops->view           = EPSView_CISS;
    1966:   eps->ops->computevectors = EPSComputeVectors_Schur;
    1967:   eps->ops->setdefaultst   = EPSSetDefaultST_CISS;

    1969:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetSizes_C",EPSCISSSetSizes_CISS);
    1970:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetSizes_C",EPSCISSGetSizes_CISS);
    1971:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetThreshold_C",EPSCISSSetThreshold_CISS);
    1972:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetThreshold_C",EPSCISSGetThreshold_CISS);
    1973:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetRefinement_C",EPSCISSSetRefinement_CISS);
    1974:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetRefinement_C",EPSCISSGetRefinement_CISS);
    1975:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetUseST_C",EPSCISSSetUseST_CISS);
    1976:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetUseST_C",EPSCISSGetUseST_CISS);
    1977:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetQuadRule_C",EPSCISSSetQuadRule_CISS);
    1978:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetQuadRule_C",EPSCISSGetQuadRule_CISS);
    1979:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSSetExtraction_C",EPSCISSSetExtraction_CISS);
    1980:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetExtraction_C",EPSCISSGetExtraction_CISS);
    1981:   PetscObjectComposeFunction((PetscObject)eps,"EPSCISSGetKSPs_C",EPSCISSGetKSPs_CISS);
    1982:   /* set default values of parameters */
    1983:   ctx->N                  = 32;
    1984:   ctx->L                  = 16;
    1985:   ctx->M                  = ctx->N/4;
    1986:   ctx->delta              = 1e-12;
    1987:   ctx->L_max              = 64;
    1988:   ctx->spurious_threshold = 1e-4;
    1989:   ctx->usest              = PETSC_TRUE;
    1990:   ctx->usest_set          = PETSC_FALSE;
    1991:   ctx->isreal             = PETSC_FALSE;
    1992:   ctx->refine_inner       = 0;
    1993:   ctx->refine_blocksize   = 0;
    1994:   ctx->npart              = 1;
    1995:   ctx->quad               = (EPSCISSQuadRule)0;
    1996:   ctx->extraction         = EPS_CISS_EXTRACTION_RITZ;
    1997:   return(0);
    1998: }