Date: 2017-05-17T08:27:24+00:00

Actual source code: nciss.c
slepc-3.7.4 2017-05-17
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      1: /*

      3:    SLEPc eigensolver: "ciss"

      5:    Method: Contour Integral Spectral Slicing

      7:    Algorithm:

      9:        Contour integral based on Sakurai-Sugiura method to construct a
     10:        subspace, with various eigenpair extractions (Rayleigh-Ritz,
     11:        explicit moment).

     13:    Based on code contributed by Y. Maeda, T. Sakurai.

     15:    References:

     17:        [1] T. Sakurai and H. Sugiura, "A projection method for generalized
     18:            eigenvalue problems", J. Comput. Appl. Math. 159:119-128, 2003.

     20:        [2] T. Sakurai and H. Tadano, "CIRR: a Rayleigh-Ritz type method with
     21:            contour integral for generalized eigenvalue problems", Hokkaido
     22:            Math. J. 36:745-757, 2007.

     24:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     25:    SLEPc - Scalable Library for Eigenvalue Problem Computations
     26:    Copyright (c) 2002-2016, Universitat Politecnica de Valencia, Spain

     28:    This file is part of SLEPc.

     30:    SLEPc is free software: you can redistribute it and/or modify it under  the
     31:    terms of version 3 of the GNU Lesser General Public License as published by
     32:    the Free Software Foundation.

     34:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
     35:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
     36:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
     37:    more details.

     39:    You  should have received a copy of the GNU Lesser General  Public  License
     40:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
     41:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     42: */

     44: #include <slepc/private/nepimpl.h>         /*I "slepcnep.h" I*/
     45: #include <slepcblaslapack.h>

     47: typedef struct {
     48:   /* parameters */
     49:   PetscInt     N;          /* number of integration points (32) */
     50:   PetscInt     L;          /* block size (16) */
     51:   PetscInt     M;          /* moment degree (N/4 = 4) */
     52:   PetscReal    delta;      /* threshold of singular value (1e-12) */
     53:   PetscInt     L_max;      /* maximum number of columns of the source matrix V */
     54:   PetscReal    spurious_threshold; /* discard spurious eigenpairs */
     55:   PetscBool    isreal;     /* T(z) is real for real z */
     56:   PetscInt     refine_inner;
     57:   PetscInt     refine_blocksize;
     58:   /* private data */
     59:   PetscReal    *sigma;     /* threshold for numerical rank */
     60:   PetscInt     num_subcomm;
     61:   PetscInt     subcomm_id;
     62:   PetscInt     num_solve_point;
     63:   PetscScalar  *weight;
     64:   PetscScalar  *omega;
     65:   PetscScalar  *pp;
     66:   BV           V;
     67:   BV           S;
     68:   BV           Y;
     69:   KSP          *ksp;
     70:   Mat          *kspMat;
     71:   PetscBool    useconj;
     72:   PetscReal    est_eig;
     73:   PetscSubcomm subcomm;
     74:   PetscBool    usest;
     75: } NEP_CISS;

     79: static PetscErrorCode SetSolverComm(NEP nep)
     80: {
     82:   NEP_CISS       *ctx = (NEP_CISS*)nep->data;
     83:   PetscInt       N = ctx->N;

     86:   if (ctx->useconj) N = N/2;
     87:   if (!ctx->subcomm) {
     88:     PetscSubcommCreate(PetscObjectComm((PetscObject)nep),&ctx->subcomm);
     89:     PetscSubcommSetNumber(ctx->subcomm,ctx->num_subcomm);
     90:     PetscSubcommSetType(ctx->subcomm,PETSC_SUBCOMM_INTERLACED);
     91:     PetscLogObjectMemory((PetscObject)nep,sizeof(PetscSubcomm));
     92:     PetscSubcommSetFromOptions(ctx->subcomm);
     93:   }
     94:   ctx->subcomm_id = ctx->subcomm->color;
     95:   ctx->num_solve_point = N / ctx->num_subcomm;
     96:   if ((N%ctx->num_subcomm) > ctx->subcomm_id) ctx->num_solve_point+=1;
     97:   return(0);
     98: }

    102: static PetscErrorCode SetPathParameter(NEP nep)
    103: {
    105:   NEP_CISS       *ctx = (NEP_CISS*)nep->data;
    106:   PetscInt       i;
    107:   PetscScalar    center;
    108:   PetscReal      theta,radius,vscale,rgscale;
    109:   PetscBool      isellipse=PETSC_FALSE;

    112:   PetscObjectTypeCompare((PetscObject)nep->rg,RGELLIPSE,&isellipse);
    113:   RGGetScale(nep->rg,&rgscale);
    114:   if (isellipse) {
    115:     RGEllipseGetParameters(nep->rg,&center,&radius,&vscale);
    116:   } else SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"Region must be Ellipse");
    117:   for (i=0;i<ctx->N;i++) {
    118:     theta = ((2*PETSC_PI)/ctx->N)*(i+0.5);
    119:     ctx->pp[i] = PetscCosReal(theta) + PETSC_i*vscale*PetscSinReal(theta);
    120:     ctx->weight[i] = radius*(vscale*PetscCosReal(theta) + PETSC_i*PetscSinReal(theta))/(PetscReal)ctx->N;
    121:     ctx->omega[i] = rgscale*(center + radius*ctx->pp[i]);
    122:   }
    123:   return(0);
    124: }

    128: static PetscErrorCode CISSVecSetRandom(BV V,PetscInt i0,PetscInt i1)
    129: {
    131:   PetscInt       i,j,nlocal;
    132:   PetscScalar    *vdata;
    133:   Vec            x;

    136:   BVGetSizes(V,&nlocal,NULL,NULL);
    137:   for (i=i0;i<i1;i++) {
    138:     BVSetRandomColumn(V,i);
    139:     BVGetColumn(V,i,&x);
    140:     VecGetArray(x,&vdata);
    141:     for (j=0;j<nlocal;j++) {
    142:       vdata[j] = PetscRealPart(vdata[j]);
    143:       if (PetscRealPart(vdata[j]) < 0.5) vdata[j] = -1.0;
    144:       else vdata[j] = 1.0;
    145:     }
    146:     VecRestoreArray(x,&vdata);
    147:     BVRestoreColumn(V,i,&x);
    148:   }
    149:   return(0);
    150: }

    154: static PetscErrorCode SolveLinearSystem(NEP nep,Mat T,Mat dT,BV V,PetscInt L_start,PetscInt L_end,PetscBool initksp)
    155: {
    157:   NEP_CISS       *ctx = (NEP_CISS*)nep->data;
    158:   PetscInt       i,j,p_id;
    159:   Mat            Fz;
    160:   PC             pc;
    161:   Vec            Bvj,vj,yj;
    162:   KSP            ksp;

    165:   if (ctx->usest) {
    166:     NEPComputeFunction(nep,0,T,T);
    167:     MatDuplicate(T,MAT_DO_NOT_COPY_VALUES,&Fz);
    168:     KSPCreate(PetscObjectComm((PetscObject)nep),&ksp);
    169:   }
    170:   BVCreateVec(V,&Bvj);
    171:   for (i=0;i<ctx->num_solve_point;i++) {
    172:     p_id = i*ctx->subcomm->n + ctx->subcomm_id;
    173:     NEPComputeFunction(nep,ctx->omega[p_id],T,T);
    174:     NEPComputeJacobian(nep,ctx->omega[p_id],dT);
    175:     if (!ctx->usest && initksp == PETSC_TRUE) {
    176:       MatDuplicate(T,MAT_COPY_VALUES,&ctx->kspMat[i]);
    177:       KSPSetOperators(ctx->ksp[i],ctx->kspMat[i],ctx->kspMat[i]);
    178:       KSPSetType(ctx->ksp[i],KSPPREONLY);
    179:       KSPGetPC(ctx->ksp[i],&pc);
    180:       PCSetType(pc,PCLU);
    181:       KSPSetFromOptions(ctx->ksp[i]);
    182:     } else if (ctx->usest) {
    183:       MatCopy(T,Fz,DIFFERENT_NONZERO_PATTERN);
    184:       KSPSetOperators(ksp,Fz,Fz);
    185:       KSPSetType(ksp,KSPPREONLY);
    186:       KSPGetPC(ksp,&pc);
    187:       PCSetType(pc,PCLU);
    188:       KSPSetFromOptions(ksp);
    189:     }
    190:     for (j=L_start;j<L_end;j++) {
    191:       BVGetColumn(V,j,&vj);
    192:       BVGetColumn(ctx->Y,i*ctx->L_max+j,&yj);
    193:       MatMult(dT,vj,Bvj);
    194:       if (ctx->usest) {
    195:         KSPSolve(ksp,Bvj,yj);
    196:       } else {
    197:         KSPSolve(ctx->ksp[i],Bvj,yj);
    198:       }
    199:       BVRestoreColumn(V,j,&vj);
    200:       BVRestoreColumn(ctx->Y,i*ctx->L_max+j,&yj);
    201:     }
    202:     if (ctx->usest && i<ctx->num_solve_point-1) {  KSPReset(ksp); }
    203:   }
    204:   if (ctx->usest) {
    205:     MatDestroy(&Fz);
    206:     KSPDestroy(&ksp);
    207:   }
    208:   VecDestroy(&Bvj);
    209:   return(0);
    210: }

    214: static PetscErrorCode EstimateNumberEigs(NEP nep,PetscInt *L_add)
    215: {
    217:   NEP_CISS       *ctx = (NEP_CISS*)nep->data;
    218:   PetscInt       i,j,p_id;
    219:   PetscScalar    tmp,m = 1,sum = 0.0;
    220:   PetscReal      eta;
    221:   Vec            v,vtemp,vj,yj;

    224:   BVGetColumn(ctx->Y,0,&yj);
    225:   VecDuplicate(yj,&v);
    226:   BVRestoreColumn(ctx->Y,0,&yj);
    227:   BVCreateVec(ctx->V,&vtemp);
    228:   for (j=0;j<ctx->L;j++) {
    229:     VecSet(v,0);
    230:     for (i=0;i<ctx->num_solve_point; i++) {
    231:       p_id = i*ctx->subcomm->n + ctx->subcomm_id;
    232:       BVSetActiveColumns(ctx->Y,i*ctx->L_max+j,i*ctx->L_max+j+1);
    233:       BVMultVec(ctx->Y,ctx->weight[p_id],1,v,&m);
    234:     }
    235:     BVGetColumn(ctx->V,j,&vj);
    236:     VecDot(vj,v,&tmp);
    237:     BVRestoreColumn(ctx->V,j,&vj);
    238:     if (ctx->useconj) sum += PetscRealPart(tmp)*2;
    239:     else sum += tmp;
    240:   }
    241:   ctx->est_eig = PetscAbsScalar(sum/(PetscReal)ctx->L);
    242:   eta = PetscPowReal(10,-PetscLog10Real(nep->tol)/ctx->N);
    243:   PetscInfo1(nep,"Estimation_#Eig %f\n",(double)ctx->est_eig);
    244:   *L_add = (PetscInt)PetscCeilReal((ctx->est_eig*eta)/ctx->M) - ctx->L;
    245:   if (*L_add < 0) *L_add = 0;
    246:   if (*L_add>ctx->L_max-ctx->L) {
    247:     PetscInfo(nep,"Number of eigenvalues around the contour path may be too large\n");
    248:     *L_add = ctx->L_max-ctx->L;
    249:   }
    250:   VecDestroy(&v);
    251:   VecDestroy(&vtemp);
    252:   return(0);
    253: }

    257: static PetscErrorCode CalcMu(NEP nep, PetscScalar *Mu)
    258: {
    260:   PetscMPIInt    sub_size,len;
    261:   PetscInt       i,j,k,s;
    262:   PetscScalar    *m,*temp,*temp2,*ppk,alp;
    263:   NEP_CISS       *ctx = (NEP_CISS*)nep->data;
    264:   Mat            M;

    267:   MPI_Comm_size(PetscSubcommChild(ctx->subcomm),&sub_size);
    268:   PetscMalloc3(ctx->num_solve_point*ctx->L*(ctx->L+1),&temp,2*ctx->M*ctx->L*ctx->L,&temp2,ctx->num_solve_point,&ppk);
    269:   MatCreateSeqDense(PETSC_COMM_SELF,ctx->L,ctx->L_max*ctx->num_solve_point,NULL,&M);
    270:   for (i=0;i<2*ctx->M*ctx->L*ctx->L;i++) temp2[i] = 0;
    271:   BVSetActiveColumns(ctx->Y,0,ctx->L_max*ctx->num_solve_point);
    272:   BVSetActiveColumns(ctx->V,0,ctx->L);
    273:   BVDot(ctx->Y,ctx->V,M);
    274:   MatDenseGetArray(M,&m);
    275:   for (i=0;i<ctx->num_solve_point;i++) {
    276:     for (j=0;j<ctx->L;j++) {
    277:       for (k=0;k<ctx->L;k++) {
    278:         temp[k+j*ctx->L+i*ctx->L*ctx->L]=m[k+j*ctx->L+i*ctx->L*ctx->L_max];
    279:       }
    280:     }
    281:   }
    282:   MatDenseRestoreArray(M,&m);
    283:   for (i=0;i<ctx->num_solve_point;i++) ppk[i] = 1;
    284:   for (k=0;k<2*ctx->M;k++) {
    285:     for (j=0;j<ctx->L;j++) {
    286:       for (i=0;i<ctx->num_solve_point;i++) {
    287:         alp = ppk[i]*ctx->weight[i*ctx->subcomm->n + ctx->subcomm_id];
    288:         for (s=0;s<ctx->L;s++) {
    289:           if (ctx->useconj) temp2[s+(j+k*ctx->L)*ctx->L] += PetscRealPart(alp*temp[s+(j+i*ctx->L)*ctx->L])*2;
    290:           else temp2[s+(j+k*ctx->L)*ctx->L] += alp*temp[s+(j+i*ctx->L)*ctx->L];
    291:         }
    292:       }
    293:     }
    294:     for (i=0;i<ctx->num_solve_point;i++)
    295:       ppk[i] *= ctx->pp[i*ctx->subcomm->n + ctx->subcomm_id];
    296:   }
    297:   for (i=0;i<2*ctx->M*ctx->L*ctx->L;i++) temp2[i] /= sub_size;
    298:   PetscMPIIntCast(2*ctx->M*ctx->L*ctx->L,&len);
    299:   MPI_Allreduce(temp2,Mu,len,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)nep));
    300:   PetscFree3(temp,temp2,ppk);
    301:   MatDestroy(&M);
    302:   return(0);
    303: }

    307: static PetscErrorCode BlockHankel(NEP nep,PetscScalar *Mu,PetscInt s,PetscScalar *H)
    308: {
    309:   NEP_CISS *ctx = (NEP_CISS*)nep->data;
    310:   PetscInt  i,j,k,L=ctx->L,M=ctx->M;

    313:   for (k=0;k<L*M;k++)
    314:     for (j=0;j<M;j++)
    315:       for (i=0;i<L;i++)
    316:         H[j*L+i+k*L*M] = Mu[i+k*L+(j+s)*L*L];
    317:   return(0);
    318: }

    322: static PetscErrorCode SVD_H0(NEP nep,PetscScalar *S,PetscInt *K)
    323: {
    324: #if defined(PETSC_MISSING_LAPACK_GESVD)
    326:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GESVD - Lapack routine is unavailable");
    327: #else
    329:   NEP_CISS       *ctx = (NEP_CISS*)nep->data;
    330:   PetscInt       i,ml=ctx->L*ctx->M;
    331:   PetscBLASInt   m,n,lda,ldu,ldvt,lwork,info;
    332:   PetscScalar    *work;
    333: #if defined(PETSC_USE_COMPLEX)
    334:   PetscReal      *rwork;
    335: #endif

    338:   PetscMalloc1(5*ml,&work);
    339: #if defined(PETSC_USE_COMPLEX)
    340:   PetscMalloc1(5*ml,&rwork);
    341: #endif
    342:   PetscBLASIntCast(ml,&m);
    343:   n = m; lda = m; ldu = m; ldvt = m; lwork = 5*m;
    344:   PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    345: #if defined(PETSC_USE_COMPLEX)
    346:   PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("N","N",&m,&n,S,&lda,ctx->sigma,NULL,&ldu,NULL,&ldvt,work,&lwork,rwork,&info));
    347: #else
    348:   PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("N","N",&m,&n,S,&lda,ctx->sigma,NULL,&ldu,NULL,&ldvt,work,&lwork,&info));
    349: #endif
    350:   if (info) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in Lapack xGESVD %d",info);
    351:   PetscFPTrapPop();
    352:   (*K) = 0;
    353:   for (i=0;i<ml;i++) {
    354:     if (ctx->sigma[i]/PetscMax(ctx->sigma[0],1)>ctx->delta) (*K)++;
    355:   }
    356:   PetscFree(work);
    357: #if defined(PETSC_USE_COMPLEX)
    358:   PetscFree(rwork);
    359: #endif
    360:   return(0);
    361: #endif
    362: }

    366: static PetscErrorCode ConstructS(NEP nep)
    367: {
    369:   NEP_CISS       *ctx = (NEP_CISS*)nep->data;
    370:   PetscInt       i,j,k,vec_local_size,p_id;
    371:   Vec            v,sj,yj;
    372:   PetscScalar    *ppk, *v_data, m = 1;

    375:   BVGetSizes(ctx->Y,&vec_local_size,NULL,NULL);
    376:   PetscMalloc1(ctx->num_solve_point,&ppk);
    377:   for (i=0;i<ctx->num_solve_point;i++) ppk[i] = 1;
    378:   BVGetColumn(ctx->Y,0,&yj);
    379:   VecDuplicate(yj,&v);
    380:   BVRestoreColumn(ctx->Y,0,&yj);
    381:   for (k=0;k<ctx->M;k++) {
    382:     for (j=0;j<ctx->L;j++) {
    383:       VecSet(v,0);
    384:       for (i=0;i<ctx->num_solve_point;i++) {
    385:         p_id = i*ctx->subcomm->n + ctx->subcomm_id;
    386:         BVSetActiveColumns(ctx->Y,i*ctx->L_max+j,i*ctx->L_max+j+1);
    387:         BVMultVec(ctx->Y,ppk[i]*ctx->weight[p_id],1,v,&m);
    388:       }
    389:       if (ctx->useconj) {
    390:         VecGetArray(v,&v_data);
    391:         for (i=0;i<vec_local_size;i++) v_data[i] = PetscRealPart(v_data[i])*2;
    392:         VecRestoreArray(v,&v_data);
    393:       }
    394:       BVGetColumn(ctx->S,k*ctx->L+j,&sj);
    395:       VecCopy(v,sj);
    396:       BVRestoreColumn(ctx->S,k*ctx->L+j,&sj);
    397:     }
    398:     for (i=0;i<ctx->num_solve_point;i++) {
    399:       p_id = i*ctx->subcomm->n + ctx->subcomm_id;
    400:       ppk[i] *= ctx->pp[p_id];
    401:     }
    402:   }
    403:   PetscFree(ppk);
    404:   VecDestroy(&v);
    405:   return(0);
    406: }

    410: static PetscErrorCode isGhost(NEP nep,PetscInt ld,PetscInt nv,PetscBool *fl)
    411: {
    413:   NEP_CISS       *ctx = (NEP_CISS*)nep->data;
    414:   PetscInt       i,j;
    415:   PetscScalar    *pX;
    416:   PetscReal      *tau,s1,s2,tau_max=0.0;

    419:   PetscMalloc1(nv,&tau);
    420:   DSVectors(nep->ds,DS_MAT_X,NULL,NULL);
    421:   DSGetArray(nep->ds,DS_MAT_X,&pX);

    423:   for (i=0;i<nv;i++) {
    424:     s1 = 0;
    425:     s2 = 0;
    426:     for (j=0;j<nv;j++) {
    427:       s1 += PetscAbsScalar(PetscPowScalar(pX[i*ld+j],2));
    428:       s2 += PetscPowReal(PetscAbsScalar(pX[i*ld+j]),2)/ctx->sigma[j];
    429:     }
    430:     tau[i] = s1/s2;
    431:     tau_max = PetscMax(tau_max,tau[i]);
    432:   }
    433:   DSRestoreArray(nep->ds,DS_MAT_X,&pX);
    434:   for (i=0;i<nv;i++) {
    435:     tau[i] /= tau_max;
    436:   }
    437:   for (i=0;i<nv;i++) {
    438:     if (tau[i]>=ctx->spurious_threshold) fl[i] = PETSC_TRUE;
    439:     else fl[i] = PETSC_FALSE;
    440:   }
    441:   PetscFree(tau);
    442:   return(0);
    443: }

    447: PetscErrorCode NEPSetUp_CISS(NEP nep)
    448: {
    450:   NEP_CISS       *ctx = (NEP_CISS*)nep->data;
    451:   PetscInt       i,nwork;
    452:   PetscBool      istrivial,isellipse,flg;
    453:   PetscScalar    center;

    456:   if (!nep->ncv) nep->ncv = ctx->L_max*ctx->M;
    457:   else {
    458:     ctx->L_max = nep->ncv/ctx->M;
    459:     if (ctx->L_max == 0) {
    460:       ctx->L_max = 1;
    461:       nep->ncv = ctx->L_max*ctx->M;
    462:     }
    463:     if (ctx->L > ctx->L_max) ctx->L = ctx->L_max;
    464:   }
    465:   if (!nep->max_it) nep->max_it = 1;
    466:   if (!nep->mpd) nep->mpd = nep->ncv;
    467:   if (!nep->which) nep->which = NEP_ALL;
    468:   if (nep->stopping!=NEPStoppingBasic) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"This solver does not support user-defined stopping test");

    470:   /* check region */
    471:   RGIsTrivial(nep->rg,&istrivial);
    472:   if (istrivial) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"CISS requires a nontrivial region, e.g. -rg_type ellipse ...");
    473:   RGGetComplement(nep->rg,&flg);
    474:   if (flg) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"A region with complement flag set is not allowed");
    475:   PetscObjectTypeCompare((PetscObject)nep->rg,RGELLIPSE,&isellipse);
    476:   if (!isellipse) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"Currently only implemented for elliptic or arc regions");
    477:   RGEllipseGetParameters(nep->rg,&center,NULL,NULL);
    478:   if (ctx->isreal && PetscImaginaryPart(center) == 0.0) ctx->useconj = PETSC_TRUE;
    479:   else ctx->useconj = PETSC_FALSE;

    481:   /* create split comm */
    482:   ctx->num_subcomm = 1;
    483:   SetSolverComm(nep);

    485:   NEPAllocateSolution(nep,0);
    486:   PetscMalloc4(ctx->N,&ctx->weight,ctx->N,&ctx->omega,ctx->N,&ctx->pp,ctx->L_max*ctx->M,&ctx->sigma);
    487:   PetscLogObjectMemory((PetscObject)nep,3*ctx->N*sizeof(PetscScalar)+ctx->L_max*ctx->N*sizeof(PetscReal));

    489:   /* allocate basis vectors */
    490:   BVDuplicateResize(nep->V,ctx->L_max*ctx->M,&ctx->S);
    491:   PetscLogObjectParent((PetscObject)nep,(PetscObject)ctx->S);
    492:   BVDuplicateResize(nep->V,ctx->L_max,&ctx->V);
    493:   PetscLogObjectParent((PetscObject)nep,(PetscObject)ctx->V);

    495:   if (!ctx->usest) {
    496:     PetscMalloc2(ctx->num_solve_point,&ctx->ksp,ctx->num_solve_point,&ctx->kspMat);
    497:     PetscLogObjectMemory((PetscObject)nep,ctx->num_solve_point*sizeof(KSP)+ctx->num_solve_point*sizeof(Mat));
    498:     for (i=0;i<ctx->num_solve_point;i++) {
    499:       KSPCreate(PetscSubcommChild(ctx->subcomm),&ctx->ksp[i]);
    500:       PetscObjectIncrementTabLevel((PetscObject)ctx->ksp[i],(PetscObject)nep,1);
    501:       PetscLogObjectParent((PetscObject)nep,(PetscObject)ctx->ksp[i]);
    502:       KSPSetOptionsPrefix(ctx->ksp[i],((PetscObject)nep)->prefix);
    503:       KSPAppendOptionsPrefix(ctx->ksp[i],"nep_ciss_");
    504:       KSPSetErrorIfNotConverged(ctx->ksp[i],PETSC_TRUE);
    505:     }
    506:   }

    508:   BVDuplicateResize(nep->V,ctx->num_solve_point*ctx->L_max,&ctx->Y);

    510:   DSSetType(nep->ds,DSGNHEP);
    511:   DSAllocate(nep->ds,nep->ncv);
    512:   nwork = (nep->fui==NEP_USER_INTERFACE_SPLIT)? 2: 1;
    513:   NEPSetWorkVecs(nep,nwork);
    514:   return(0);
    515: }

    519: PetscErrorCode NEPSolve_CISS(NEP nep)
    520: {
    522:   NEP_CISS       *ctx = (NEP_CISS*)nep->data;
    523:   Mat            X,M;
    524:   PetscInt       i,j,ld,L_add=0,nv=0,L_base=ctx->L,inner,*inside;
    525:   PetscScalar    *Mu,*H0,*H1,*rr,*temp,center;
    526:   PetscReal      error,max_error,radius,rgscale;
    527:   PetscBool      *fl1;
    528:   Vec            si;
    529:   SlepcSC        sc;
    530:   PetscRandom    rand;

    533:   DSGetSlepcSC(nep->ds,&sc);
    534:   sc->comparison    = SlepcCompareLargestMagnitude;
    535:   sc->comparisonctx = NULL;
    536:   sc->map           = NULL;
    537:   sc->mapobj        = NULL;
    538:   DSGetLeadingDimension(nep->ds,&ld);
    539:   SetPathParameter(nep);
    540:   CISSVecSetRandom(ctx->V,0,ctx->L);
    541:   BVGetRandomContext(ctx->V,&rand);

    543:   SolveLinearSystem(nep,nep->function,nep->jacobian,ctx->V,0,ctx->L,PETSC_TRUE);
    544:   EstimateNumberEigs(nep,&L_add);
    545:   if (L_add>0) {
    546:     PetscInfo2(nep,"Changing L %D -> %D by Estimate #Eig\n",ctx->L,ctx->L+L_add);
    547:     CISSVecSetRandom(ctx->V,ctx->L,ctx->L+L_add);
    548:     SolveLinearSystem(nep,nep->function,nep->jacobian,ctx->V,ctx->L,ctx->L+L_add,PETSC_FALSE);
    549:     ctx->L += L_add;
    550:   }
    551:   PetscMalloc2(ctx->L*ctx->L*ctx->M*2,&Mu,ctx->L*ctx->M*ctx->L*ctx->M,&H0);
    552:   for (i=0;i<ctx->refine_blocksize;i++) {
    553:     CalcMu(nep,Mu);
    554:     BlockHankel(nep,Mu,0,H0);
    555:     SVD_H0(nep,H0,&nv);
    556:     if (ctx->sigma[0]<=ctx->delta || nv < ctx->L*ctx->M || ctx->L == ctx->L_max) break;
    557:     L_add = L_base;
    558:     if (ctx->L+L_add>ctx->L_max) L_add = ctx->L_max-ctx->L;
    559:     PetscInfo2(nep,"Changing L %D -> %D by SVD(H0)\n",ctx->L,ctx->L+L_add);
    560:     CISSVecSetRandom(ctx->V,ctx->L,ctx->L+L_add);
    561:     SolveLinearSystem(nep,nep->function,nep->jacobian,ctx->V,ctx->L,ctx->L+L_add,PETSC_FALSE);
    562:     ctx->L += L_add;
    563:   }
    564:   PetscFree2(Mu,H0);

    566:   RGGetScale(nep->rg,&rgscale);
    567:   RGEllipseGetParameters(nep->rg,&center,&radius,NULL);

    569:   PetscMalloc3(ctx->L*ctx->L*ctx->M*2,&Mu,ctx->L*ctx->M*ctx->L*ctx->M,&H0,ctx->L*ctx->M*ctx->L*ctx->M,&H1);
    570:   while (nep->reason == NEP_CONVERGED_ITERATING) {
    571:     nep->its++;
    572:     for (inner=0;inner<=ctx->refine_inner;inner++) {
    573:       CalcMu(nep,Mu);
    574:       BlockHankel(nep,Mu,0,H0);
    575:       SVD_H0(nep,H0,&nv);
    576:       if (ctx->sigma[0]>ctx->delta && nv==ctx->L*ctx->M && inner!=ctx->refine_inner) {
    577:         ConstructS(nep);
    578:         BVSetActiveColumns(ctx->S,0,ctx->L);
    579:         BVCopy(ctx->S,ctx->V);
    580:         SolveLinearSystem(nep,nep->function,nep->jacobian,ctx->V,0,ctx->L,PETSC_FALSE);
    581:       } else break;
    582:     }

    584:     nep->nconv = 0;
    585:     if (nv == 0) break;
    586:     BlockHankel(nep,Mu,0,H0);
    587:     BlockHankel(nep,Mu,1,H1);
    588:     DSSetDimensions(nep->ds,nv,0,0,0);
    589:     DSSetState(nep->ds,DS_STATE_RAW);
    590:     DSGetArray(nep->ds,DS_MAT_A,&temp);
    591:     for (j=0;j<nv;j++)
    592:       for (i=0;i<nv;i++)
    593:         temp[i+j*ld] = H1[i+j*ctx->L*ctx->M];
    594:     DSRestoreArray(nep->ds,DS_MAT_A,&temp);
    595:     DSGetArray(nep->ds,DS_MAT_B,&temp);
    596:     for (j=0;j<nv;j++)
    597:       for (i=0;i<nv;i++)
    598:         temp[i+j*ld] = H0[i+j*ctx->L*ctx->M];
    599:     DSRestoreArray(nep->ds,DS_MAT_B,&temp);
    600:     DSSolve(nep->ds,nep->eigr,nep->eigi);
    601:     DSVectors(nep->ds,DS_MAT_X,NULL,NULL);
    602:     for (i=0;i<nv;i++){
    603:       nep->eigr[i] = (nep->eigr[i]*radius+center)*rgscale;
    604: #if !defined(PETSC_USE_COMPLEX)
    605:       nep->eigi[i] = nep->eigi[i]*radius*rgscale;
    606: #endif
    607:     }
    608:     PetscMalloc3(nv,&fl1,nv,&inside,nv,&rr);
    609:     isGhost(nep,ld,nv,fl1);
    610:     RGCheckInside(nep->rg,nv,nep->eigr,nep->eigi,inside);
    611:     for (i=0;i<nv;i++) {
    612:       if (fl1[i] && inside[i]>0) {
    613:         rr[i] = 1.0;
    614:         nep->nconv++;
    615:       } else rr[i] = 0.0;
    616:     }
    617:     DSSort(nep->ds,nep->eigr,nep->eigi,rr,NULL,&nep->nconv);
    618:     for (i=0;i<nv;i++){
    619:       nep->eigr[i] = (nep->eigr[i]*radius+center)*rgscale;
    620: #if !defined(PETSC_USE_COMPLEX)
    621:       nep->eigi[i] = nep->eigi[i]*radius*rgscale;
    622: #endif
    623:     }
    624:     PetscFree3(fl1,inside,rr);
    625:     BVSetActiveColumns(nep->V,0,nv);
    626:     ConstructS(nep);
    627:     BVSetActiveColumns(ctx->S,0,nv);
    628:     BVCopy(ctx->S,nep->V);

    630:     DSVectors(nep->ds,DS_MAT_X,NULL,NULL);
    631:     DSGetMat(nep->ds,DS_MAT_X,&X);
    632:     BVMultInPlace(ctx->S,X,0,nep->nconv);
    633:     BVMultInPlace(nep->V,X,0,nep->nconv);
    634:     MatDestroy(&X);
    635:     max_error = 0.0;
    636:     for (i=0;i<nep->nconv;i++) {
    637:       BVGetColumn(nep->V,i,&si);
    638:       VecNormalize(si,NULL);
    639:       NEPComputeResidualNorm_Private(nep,nep->eigr[i],si,nep->work,&error);
    640:       (*nep->converged)(nep,nep->eigr[i],0,error,&error,nep->convergedctx);
    641:       BVRestoreColumn(nep->V,i,&si);
    642:       max_error = PetscMax(max_error,error);
    643:     }
    644:     if (max_error <= nep->tol) nep->reason = NEP_CONVERGED_TOL;
    645:     else if (nep->its > nep->max_it) nep->reason = NEP_DIVERGED_ITS;
    646:     else {
    647:       if (nep->nconv > ctx->L) nv = nep->nconv;
    648:       else if (ctx->L > nv) nv = ctx->L;
    649:       MatCreateSeqDense(PETSC_COMM_SELF,nv,ctx->L,NULL,&M);
    650:       MatDenseGetArray(M,&temp);
    651:       for (i=0;i<ctx->L*nv;i++) {
    652:         PetscRandomGetValue(rand,&temp[i]);
    653:         temp[i] = PetscRealPart(temp[i]);
    654:       }
    655:       MatDenseRestoreArray(M,&temp);
    656:       BVSetActiveColumns(ctx->S,0,nv);
    657:       BVMultInPlace(ctx->S,M,0,ctx->L);
    658:       MatDestroy(&M);
    659:       BVSetActiveColumns(ctx->S,0,ctx->L);
    660:       BVCopy(ctx->S,ctx->V);
    661:       SolveLinearSystem(nep,nep->function,nep->jacobian,ctx->V,0,ctx->L,PETSC_FALSE);
    662:     }
    663:   }
    664:   PetscFree3(Mu,H0,H1);
    665:   return(0);
    666: }

    670: static PetscErrorCode NEPCISSSetSizes_CISS(NEP nep,PetscInt ip,PetscInt bs,PetscInt ms,PetscInt npart,PetscInt bsmax,PetscBool realmats)
    671: {
    672:   NEP_CISS *ctx = (NEP_CISS*)nep->data;

    675:   if (ip == PETSC_DECIDE || ip == PETSC_DEFAULT) {
    676:     if (ctx->N!=32) { ctx->N =32; ctx->M = ctx->N/4; }
    677:   } else {
    678:     if (ip<1) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"The ip argument must be > 0");
    679:     if (ip%2) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"The ip argument must be an even number");
    680:     if (ctx->N!=ip) { ctx->N = ip; ctx->M = ctx->N/4; }
    681:   }
    682:   if (bs == PETSC_DECIDE || bs == PETSC_DEFAULT) {
    683:     ctx->L = 16;
    684:   } else {
    685:     if (bs<1) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"The bs argument must be > 0");
    686:     if (bs>ctx->L_max) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"The bs argument must be less than or equal to the maximum number of block size");
    687:     ctx->L = bs;
    688:   }
    689:   if (ms == PETSC_DECIDE || ms == PETSC_DEFAULT) {
    690:     ctx->M = ctx->N/4;
    691:   } else {
    692:     if (ms<1) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"The ms argument must be > 0");
    693:     if (ms>ctx->N) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"The ms argument must be less than or equal to the number of integration points");
    694:     ctx->M = ms;
    695:   }
    696:   if (npart == PETSC_DECIDE || npart == PETSC_DEFAULT) {
    697:     ctx->num_subcomm = 1;
    698:   } else {
    699:     if (npart<1) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"The npart argument must be > 0");
    700:     ctx->num_subcomm = npart;
    701:   }
    702:   if (bsmax == PETSC_DECIDE || bsmax == PETSC_DEFAULT) {
    703:     ctx->L = 256;
    704:   } else {
    705:     if (bsmax<1) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"The bsmax argument must be > 0");
    706:     if (bsmax<ctx->L) ctx->L_max = ctx->L;
    707:     else ctx->L_max = bsmax;
    708:   }
    709:   ctx->isreal = realmats;
    710:   return(0);
    711: }

    715: /*@
    716:    NEPCISSSetSizes - Sets the values of various size parameters in the CISS solver.

    718:    Logically Collective on NEP

    720:    Input Parameters:
    721: +  nep   - the eigenproblem solver context
    722: .  ip    - number of integration points
    723: .  bs    - block size
    724: .  ms    - moment size
    725: .  npart - number of partitions when splitting the communicator
    726: .  bsmax - max block size
    727: -  realmats - T(z) is real for real z

    729:    Options Database Keys:
    730: +  -nep_ciss_integration_points - Sets the number of integration points
    731: .  -nep_ciss_blocksize - Sets the block size
    732: .  -nep_ciss_moments - Sets the moment size
    733: .  -nep_ciss_partitions - Sets the number of partitions
    734: .  -nep_ciss_maxblocksize - Sets the maximum block size
    735: -  -nep_ciss_realmats - T(z) is real for real z

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

    742:    The realmats flag can be set to true when T(.) is guaranteed to be real
    743:    when the argument is a real value, for example, when all matrices in
    744:    the split form are real. When set to true, the solver avoids some computations.

    746:    Level: advanced

    748: .seealso: NEPCISSGetSizes()
    749: @*/
    750: PetscErrorCode NEPCISSSetSizes(NEP nep,PetscInt ip,PetscInt bs,PetscInt ms,PetscInt npart,PetscInt bsmax,PetscBool realmats)
    751: {

    762:   PetscTryMethod(nep,"NEPCISSSetSizes_C",(NEP,PetscInt,PetscInt,PetscInt,PetscInt,PetscInt,PetscBool),(nep,ip,bs,ms,npart,bsmax,realmats));
    763:   return(0);
    764: }

    768: static PetscErrorCode NEPCISSGetSizes_CISS(NEP nep,PetscInt *ip,PetscInt *bs,PetscInt *ms,PetscInt *npart,PetscInt *bsmax,PetscBool *realmats)
    769: {
    770:   NEP_CISS *ctx = (NEP_CISS*)nep->data;

    773:   if (ip) *ip = ctx->N;
    774:   if (bs) *bs = ctx->L;
    775:   if (ms) *ms = ctx->M;
    776:   if (npart) *npart = ctx->num_subcomm;
    777:   if (bsmax) *bsmax = ctx->L_max;
    778:   if (realmats) *realmats = ctx->isreal;
    779:   return(0);
    780: }

    784: /*@
    785:    NEPCISSGetSizes - Gets the values of various size parameters in the CISS solver.

    787:    Not Collective

    789:    Input Parameter:
    790: .  nep - the eigenproblem solver context

    792:    Output Parameters:
    793: +  ip    - number of integration points
    794: .  bs    - block size
    795: .  ms    - moment size
    796: .  npart - number of partitions when splitting the communicator
    797: .  bsmax - max block size
    798: -  realmats - T(z) is real for real z

    800:    Level: advanced

    802: .seealso: NEPCISSSetSizes()
    803: @*/
    804: PetscErrorCode NEPCISSGetSizes(NEP nep,PetscInt *ip,PetscInt *bs,PetscInt *ms,PetscInt *npart,PetscInt *bsmax,PetscBool *realmats)
    805: {

    810:   PetscUseMethod(nep,"NEPCISSGetSizes_C",(NEP,PetscInt*,PetscInt*,PetscInt*,PetscInt*,PetscInt*,PetscBool*),(nep,ip,bs,ms,npart,bsmax,realmats));
    811:   return(0);
    812: }

    816: static PetscErrorCode NEPCISSSetThreshold_CISS(NEP nep,PetscReal delta,PetscReal spur)
    817: {
    818:   NEP_CISS *ctx = (NEP_CISS*)nep->data;

    821:   if (delta == PETSC_DEFAULT) {
    822:     ctx->delta = 1e-12;
    823:   } else {
    824:     if (delta<=0.0) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"The delta argument must be > 0.0");
    825:     ctx->delta = delta;
    826:   }
    827:   if (spur == PETSC_DEFAULT) {
    828:     ctx->spurious_threshold = 1e-4;
    829:   } else {
    830:     if (spur<=0.0) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"The spurious threshold argument must be > 0.0");
    831:     ctx->spurious_threshold = spur;
    832:   }
    833:   return(0);
    834: }

    838: /*@
    839:    NEPCISSSetThreshold - Sets the values of various threshold parameters in
    840:    the CISS solver.

    842:    Logically Collective on NEP

    844:    Input Parameters:
    845: +  nep   - the eigenproblem solver context
    846: .  delta - threshold for numerical rank
    847: -  spur  - spurious threshold (to discard spurious eigenpairs)

    849:    Options Database Keys:
    850: +  -nep_ciss_delta - Sets the delta
    851: -  -nep_ciss_spurious_threshold - Sets the spurious threshold

    853:    Level: advanced

    855: .seealso: NEPCISSGetThreshold()
    856: @*/
    857: PetscErrorCode NEPCISSSetThreshold(NEP nep,PetscReal delta,PetscReal spur)
    858: {

    865:   PetscTryMethod(nep,"NEPCISSSetThreshold_C",(NEP,PetscReal,PetscReal),(nep,delta,spur));
    866:   return(0);
    867: }

    871: static PetscErrorCode NEPCISSGetThreshold_CISS(NEP nep,PetscReal *delta,PetscReal *spur)
    872: {
    873:   NEP_CISS *ctx = (NEP_CISS*)nep->data;

    876:   if (delta) *delta = ctx->delta;
    877:   if (spur)  *spur = ctx->spurious_threshold;
    878:   return(0);
    879: }

    883: /*@
    884:    NEPCISSGetThreshold - Gets the values of various threshold parameters in
    885:    the CISS solver.

    887:    Not Collective

    889:    Input Parameter:
    890: .  nep - the eigenproblem solver context

    892:    Output Parameters:
    893: +  delta - threshold for numerical rank
    894: -  spur  - spurious threshold (to discard spurious eigenpairs)

    896:    Level: advanced

    898: .seealso: NEPCISSSetThreshold()
    899: @*/
    900: PetscErrorCode NEPCISSGetThreshold(NEP nep,PetscReal *delta,PetscReal *spur)
    901: {

    906:   PetscUseMethod(nep,"NEPCISSGetThreshold_C",(NEP,PetscReal*,PetscReal*),(nep,delta,spur));
    907:   return(0);
    908: }

    912: static PetscErrorCode NEPCISSSetRefinement_CISS(NEP nep,PetscInt inner,PetscInt blsize)
    913: {
    914:   NEP_CISS *ctx = (NEP_CISS*)nep->data;

    917:   if (inner == PETSC_DEFAULT) {
    918:     ctx->refine_inner = 0;
    919:   } else {
    920:     if (inner<0) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"The refine inner argument must be >= 0");
    921:     ctx->refine_inner = inner;
    922:   }
    923:   if (blsize == PETSC_DEFAULT) {
    924:     ctx->refine_blocksize = 0;
    925:   } else {
    926:     if (blsize<0) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_ARG_OUTOFRANGE,"The refine blocksize argument must be >= 0");
    927:     ctx->refine_blocksize = blsize;
    928:   }
    929:   return(0);
    930: }

    934: /*@
    935:    NEPCISSSetRefinement - Sets the values of various refinement parameters
    936:    in the CISS solver.

    938:    Logically Collective on NEP

    940:    Input Parameters:
    941: +  nep    - the eigenproblem solver context
    942: .  inner  - number of iterative refinement iterations (inner loop)
    943: -  blsize - number of iterative refinement iterations (blocksize loop)

    945:    Options Database Keys:
    946: +  -nep_ciss_refine_inner - Sets number of inner iterations
    947: -  -nep_ciss_refine_blocksize - Sets number of blocksize iterations

    949:    Level: advanced

    951: .seealso: NEPCISSGetRefinement()
    952: @*/
    953: PetscErrorCode NEPCISSSetRefinement(NEP nep,PetscInt inner,PetscInt blsize)
    954: {

    961:   PetscTryMethod(nep,"NEPCISSSetRefinement_C",(NEP,PetscInt,PetscInt),(nep,inner,blsize));
    962:   return(0);
    963: }

    967: static PetscErrorCode NEPCISSGetRefinement_CISS(NEP nep,PetscInt *inner,PetscInt *blsize)
    968: {
    969:   NEP_CISS *ctx = (NEP_CISS*)nep->data;

    972:   if (inner)  *inner = ctx->refine_inner;
    973:   if (blsize) *blsize = ctx->refine_blocksize;
    974:   return(0);
    975: }

    979: /*@
    980:    NEPCISSGetRefinement - Gets the values of various refinement parameters
    981:    in the CISS solver.

    983:    Not Collective

    985:    Input Parameter:
    986: .  nep - the eigenproblem solver context

    988:    Output Parameters:
    989: +  inner  - number of iterative refinement iterations (inner loop)
    990: -  blsize - number of iterative refinement iterations (blocksize loop)

    992:    Level: advanced

    994: .seealso: NEPCISSSetRefinement()
    995: @*/
    996: PetscErrorCode NEPCISSGetRefinement(NEP nep, PetscInt *inner, PetscInt *blsize)
    997: {

    1002:   PetscUseMethod(nep,"NEPCISSGetRefinement_C",(NEP,PetscInt*,PetscInt*),(nep,inner,blsize));
    1003:   return(0);
    1004: }

    1008: PetscErrorCode NEPReset_CISS(NEP nep)
    1009: {
    1011:   PetscInt       i;
    1012:   NEP_CISS       *ctx = (NEP_CISS*)nep->data;

    1015:   PetscSubcommDestroy(&ctx->subcomm);
    1016:   PetscFree4(ctx->weight,ctx->omega,ctx->pp,ctx->sigma);
    1017:   BVDestroy(&ctx->S);
    1018:   BVDestroy(&ctx->V);
    1019:   BVDestroy(&ctx->Y);
    1020:   if (!ctx->usest) {
    1021:     for (i=0;i<ctx->num_solve_point;i++) {
    1022:       KSPDestroy(&ctx->ksp[i]);
    1023:     }
    1024:     for (i=0;i<ctx->num_solve_point;i++) {
    1025:       MatDestroy(&ctx->kspMat[i]);
    1026:     }
    1027:     PetscFree2(ctx->ksp,ctx->kspMat);
    1028:   }
    1029:   return(0);
    1030: }

    1034: PetscErrorCode NEPSetFromOptions_CISS(PetscOptionItems *PetscOptionsObject,NEP nep)
    1035: {
    1037:   PetscReal      r1,r2;
    1038:   PetscInt       i1,i2,i3,i4,i5,i6,i7;
    1039:   PetscBool      b1;

    1042:   PetscOptionsHead(PetscOptionsObject,"NEP CISS Options");

    1044:   NEPCISSGetSizes(nep,&i1,&i2,&i3,&i4,&i5,&b1);
    1045:   PetscOptionsInt("-nep_ciss_integration_points","CISS number of integration points","NEPCISSSetSizes",i1,&i1,NULL);
    1046:   PetscOptionsInt("-nep_ciss_blocksize","CISS block size","NEPCISSSetSizes",i2,&i2,NULL);
    1047:   PetscOptionsInt("-nep_ciss_moments","CISS moment size","NEPCISSSetSizes",i3,&i3,NULL);
    1048:   PetscOptionsInt("-nep_ciss_partitions","CISS number of partitions","NEPCISSSetSizes",i4,&i4,NULL);
    1049:   PetscOptionsInt("-nep_ciss_maxblocksize","CISS maximum block size","NEPCISSSetSizes",i5,&i5,NULL);
    1050:   PetscOptionsBool("-nep_ciss_realmats","CISS flag indicating that T(z) is real for real z","NEPCISSSetSizes",b1,&b1,NULL);
    1051:   NEPCISSSetSizes(nep,i1,i2,i3,i4,i5,b1);

    1053:   NEPCISSGetThreshold(nep,&r1,&r2);
    1054:   PetscOptionsReal("-nep_ciss_delta","CISS threshold for numerical rank","NEPCISSSetThreshold",r1,&r1,NULL);
    1055:   PetscOptionsReal("-nep_ciss_spurious_threshold","CISS threshold for the spurious eigenpairs","NEPCISSSetThreshold",r2,&r2,NULL);
    1056:   NEPCISSSetThreshold(nep,r1,r2);

    1058:   NEPCISSGetRefinement(nep,&i6,&i7);
    1059:   PetscOptionsInt("-nep_ciss_refine_inner","CISS number of inner iterative refinement iterations","NEPCISSSetRefinement",i6,&i6,NULL);
    1060:   PetscOptionsInt("-nep_ciss_refine_blocksize","CISS number of blocksize iterative refinement iterations","NEPCISSSetRefinement",i7,&i7,NULL);
    1061:   NEPCISSSetRefinement(nep,i6,i7);

    1063:   PetscOptionsTail();
    1064:   return(0);
    1065: }

    1069: PetscErrorCode NEPDestroy_CISS(NEP nep)
    1070: {

    1074:   PetscFree(nep->data);
    1075:   PetscObjectComposeFunction((PetscObject)nep,"NEPCISSSetSizes_C",NULL);
    1076:   PetscObjectComposeFunction((PetscObject)nep,"NEPCISSGetSizes_C",NULL);
    1077:   PetscObjectComposeFunction((PetscObject)nep,"NEPCISSSetThreshold_C",NULL);
    1078:   PetscObjectComposeFunction((PetscObject)nep,"NEPCISSGetThreshold_C",NULL);
    1079:   PetscObjectComposeFunction((PetscObject)nep,"NEPCISSSetRefinement_C",NULL);
    1080:   PetscObjectComposeFunction((PetscObject)nep,"NEPCISSGetRefinement_C",NULL);
    1081:   return(0);
    1082: }

    1086: PetscErrorCode NEPView_CISS(NEP nep,PetscViewer viewer)
    1087: {
    1089:   NEP_CISS       *ctx = (NEP_CISS*)nep->data;
    1090:   PetscBool      isascii;

    1093:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    1094:   if (isascii) {
    1095:     PetscViewerASCIIPrintf(viewer,"  CISS: sizes { integration points: %D, block size: %D, moment size: %D, partitions: %D, maximum block size: %D }\n",ctx->N,ctx->L,ctx->M,ctx->num_subcomm,ctx->L_max);
    1096:     if (ctx->isreal) {
    1097:       PetscViewerASCIIPrintf(viewer,"  CISS: exploiting symmetry of integration points\n");
    1098:     }
    1099:     PetscViewerASCIIPrintf(viewer,"  CISS: threshold { delta: %g, spurious threshold: %g }\n",(double)ctx->delta,(double)ctx->spurious_threshold);
    1100:     PetscViewerASCIIPrintf(viewer,"  CISS: iterative refinement  { inner: %D, blocksize: %D }\n",ctx->refine_inner, ctx->refine_blocksize);
    1101:     PetscViewerASCIIPushTab(viewer);
    1102:     if (!ctx->usest && ctx->ksp[0]) { KSPView(ctx->ksp[0],viewer); }
    1103:     PetscViewerASCIIPopTab(viewer);
    1104:   }
    1105:   return(0);
    1106: }

    1110: PETSC_EXTERN PetscErrorCode NEPCreate_CISS(NEP nep)
    1111: {
    1113:   NEP_CISS       *ctx = (NEP_CISS*)nep->data;

    1116:   PetscNewLog(nep,&ctx);
    1117:   nep->data = ctx;
    1118:   nep->ops->solve          = NEPSolve_CISS;
    1119:   nep->ops->setup          = NEPSetUp_CISS;
    1120:   nep->ops->setfromoptions = NEPSetFromOptions_CISS;
    1121:   nep->ops->reset          = NEPReset_CISS;
    1122:   nep->ops->destroy        = NEPDestroy_CISS;
    1123:   nep->ops->view           = NEPView_CISS;
    1124:   PetscObjectComposeFunction((PetscObject)nep,"NEPCISSSetSizes_C",NEPCISSSetSizes_CISS);
    1125:   PetscObjectComposeFunction((PetscObject)nep,"NEPCISSGetSizes_C",NEPCISSGetSizes_CISS);
    1126:   PetscObjectComposeFunction((PetscObject)nep,"NEPCISSSetThreshold_C",NEPCISSSetThreshold_CISS);
    1127:   PetscObjectComposeFunction((PetscObject)nep,"NEPCISSGetThreshold_C",NEPCISSGetThreshold_CISS);
    1128:   PetscObjectComposeFunction((PetscObject)nep,"NEPCISSSetRefinement_C",NEPCISSSetRefinement_CISS);
    1129:   PetscObjectComposeFunction((PetscObject)nep,"NEPCISSGetRefinement_C",NEPCISSGetRefinement_CISS);
    1130:   /* set default values of parameters */
    1131:   ctx->N       = 32;
    1132:   ctx->L       = 16;
    1133:   ctx->M       = ctx->N/4;
    1134:   ctx->delta   = 1e-12;
    1135:   ctx->L_max   = 64;
    1136:   ctx->spurious_threshold = 1e-4;
    1137:   ctx->usest   = PETSC_FALSE;
    1138:   ctx->isreal  = PETSC_FALSE;
    1139:   ctx->refine_inner = 0;
    1140:   ctx->refine_blocksize = 0;
    1141:   ctx->num_subcomm = 1;
    1142:   return(0);
    1143: }