Date: 2016-03-29T14:57:58+00:00

Actual source code: ks-slice.c
slepc-3.6.3 2016-03-29
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      1: /*

      3:    SLEPc eigensolver: "krylovschur"

      5:    Method: Krylov-Schur with spectrum slicing for symmetric eigenproblems

      7:    References:

      9:        [1] R.G. Grimes et al., "A shifted block Lanczos algorithm for
     10:            solving sparse symmetric generalized eigenproblems", SIAM J.
     11:            Matrix Anal. Appl. 15(1):228-272, 1994.

     13:        [2] C. Campos and J.E. Roman, "Spectrum slicing strategies based
     14:            on restarted Lanczos methods", Numer. Algor. 60(2):279-295,
     15:            2012.

     17:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     18:    SLEPc - Scalable Library for Eigenvalue Problem Computations
     19:    Copyright (c) 2002-2015, Universitat Politecnica de Valencia, Spain

     21:    This file is part of SLEPc.

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

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

     32:    You  should have received a copy of the GNU Lesser General  Public  License
     33:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
     34:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     35: */

     37: #include <slepc/private/epsimpl.h>
     38:  #include krylovschur.h

     40: #define SLICE_PTOL PETSC_SQRT_MACHINE_EPSILON

     44: static PetscErrorCode EPSSliceResetSR(EPS eps) {
     45:   PetscErrorCode  ierr;
     46:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
     47:   EPS_SR          sr=ctx->sr;
     48:   EPS_shift       s;

     51:   if (sr) {
     52:     if (ctx->npart>1) {
     53:       BVDestroy(&sr->V);
     54:       PetscFree4(sr->eigr,sr->eigi,sr->errest,sr->perm);
     55:     }
     56:     /* Reviewing list of shifts to free memory */
     57:     s = sr->s0;
     58:     if (s) {
     59:       while (s->neighb[1]) {
     60:         s = s->neighb[1];
     61:         PetscFree(s->neighb[0]);
     62:       }
     63:       PetscFree(s);
     64:     }
     65:     PetscFree(sr);
     66:   }
     67:   ctx->sr = PETSC_NULL;
     68:   return(0);
     69: }

     73: PetscErrorCode EPSReset_KrylovSchur_Slice(EPS eps)
     74: {
     75:   PetscErrorCode  ierr;
     76:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;

     79:   if (!ctx->global) return(0);
     80:   /* Destroy auxiliary EPS */
     81:   EPSSliceResetSR(ctx->eps);
     82:   EPSDestroy(&ctx->eps);
     83:   if (ctx->npart>1) {
     84:     PetscSubcommDestroy(&ctx->subc);
     85:     if (ctx->commset) {
     86:       MPI_Comm_free(&ctx->commrank);
     87:       ctx->commset = PETSC_FALSE;
     88:     }
     89:   }
     90:   PetscFree(ctx->subintervals);
     91:   PetscFree(ctx->nconv_loc);
     92:   EPSSliceResetSR(eps);
     93:   PetscFree(ctx->inertias);
     94:   PetscFree(ctx->shifts);
     95:   return(0);
     96: }

    100: /*
    101:   EPSSliceAllocateSolution - Allocate memory storage for common variables such
    102:   as eigenvalues and eigenvectors. The argument extra is used for methods
    103:   that require a working basis slightly larger than ncv.
    104: */
    105: static PetscErrorCode EPSSliceAllocateSolution(EPS eps,PetscInt extra)
    106: {
    107:   PetscErrorCode     ierr;
    108:   EPS_KRYLOVSCHUR    *ctx=(EPS_KRYLOVSCHUR*)eps->data;
    109:   PetscReal          eta;
    110:   PetscInt           k;
    111:   PetscLogDouble     cnt;
    112:   BVType             type;
    113:   BVOrthogType       orthog_type;
    114:   BVOrthogRefineType orthog_ref;
    115:   BVOrthogBlockType  ob_type;
    116:   Mat                matrix;
    117:   Vec                t;
    118:   EPS_SR             sr = ctx->sr;

    121:   /* allocate space for eigenvalues and friends */
    122:   k = PetscMax(1,sr->numEigs);
    123:   PetscFree4(sr->eigr,sr->eigi,sr->errest,sr->perm);
    124:   PetscMalloc4(k,&sr->eigr,k,&sr->eigi,k,&sr->errest,k,&sr->perm);
    125:   cnt = 2*k*sizeof(PetscScalar) + 2*k*sizeof(PetscReal) + k*sizeof(PetscInt);
    126:   PetscLogObjectMemory((PetscObject)eps,cnt);

    128:   /* allocate sr->V and transfer options from eps->V */
    129:   BVDestroy(&sr->V);
    130:   BVCreate(PetscObjectComm((PetscObject)eps),&sr->V);
    131:   PetscLogObjectParent((PetscObject)eps,(PetscObject)sr->V);
    132:   if (!eps->V) { EPSGetBV(eps,&eps->V); }
    133:   if (!((PetscObject)(eps->V))->type_name) {
    134:     BVSetType(sr->V,BVSVEC);
    135:   } else {
    136:     BVGetType(eps->V,&type);
    137:     BVSetType(sr->V,type);
    138:   }
    139:   STMatCreateVecs(eps->st,&t,NULL);
    140:   BVSetSizesFromVec(sr->V,t,k);
    141:   VecDestroy(&t);
    142:   EPS_SetInnerProduct(eps);
    143:   BVGetMatrix(eps->V,&matrix,NULL);
    144:   BVSetMatrix(sr->V,matrix,PETSC_FALSE);
    145:   BVGetOrthogonalization(eps->V,&orthog_type,&orthog_ref,&eta,&ob_type);
    146:   BVSetOrthogonalization(sr->V,orthog_type,orthog_ref,eta,ob_type);
    147:   return(0);
    148: }

    152: static PetscErrorCode EPSSliceGetEPS(EPS eps)
    153: {
    154:   PetscErrorCode     ierr;
    155:   EPS_KRYLOVSCHUR    *ctx=(EPS_KRYLOVSCHUR*)eps->data,*ctx_local;
    156:   BV                 V;
    157:   BVType             type;
    158:   PetscReal          eta;
    159:   BVOrthogType       orthog_type;
    160:   BVOrthogRefineType orthog_ref;
    161:   BVOrthogBlockType  ob_type;
    162:   Mat                A,B=NULL,Ar,Br=NULL;
    163:   PetscInt           i;
    164:   PetscReal          h,a,b;
    165:   PetscMPIInt        rank;
    166:   EPS_SR             sr=ctx->sr;
    167:   PC                 pc;
    168:   PCType             pctype;
    169:   KSP                ksp;
    170:   KSPType            ksptype;
    171:   STType             sttype;
    172:   const MatSolverPackage stype;

    175:   EPSGetOperators(eps,&A,&B);
    176:   if (ctx->npart==1) {
    177:     if (!ctx->eps) { EPSCreate(((PetscObject)eps)->comm,&ctx->eps); }
    178:     EPSSetType(ctx->eps,((PetscObject)eps)->type_name);
    179:     EPSSetST(ctx->eps,eps->st);
    180:     a = eps->inta; b = eps->intb;
    181:   } else {
    182:     if (!ctx->subc) {
    183:       /* Create context for subcommunicators */
    184:       PetscSubcommCreate(PetscObjectComm((PetscObject)eps),&ctx->subc);
    185:       PetscSubcommSetNumber(ctx->subc,ctx->npart);
    186:       PetscSubcommSetType(ctx->subc,PETSC_SUBCOMM_CONTIGUOUS);
    187:       PetscLogObjectMemory((PetscObject)eps,sizeof(PetscSubcomm));

    189:       /* Duplicate matrices */
    190:       MatCreateRedundantMatrix(A,0,PetscSubcommChild(ctx->subc),MAT_INITIAL_MATRIX,&Ar);
    191:       if (B) { MatCreateRedundantMatrix(B,0,PetscSubcommChild(ctx->subc),MAT_INITIAL_MATRIX,&Br); }
    192:     }

    194:     /* Determine subintervals */
    195:     if (!ctx->subintset) { /* uniform distribution if no set by user */
    196:       if (!sr->hasEnd) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"Global interval must be bounded for splitting it in uniform subintervals");
    197:       h = (eps->intb-eps->inta)/ctx->npart;
    198:       a = eps->inta+ctx->subc->color*h;
    199:       b = (ctx->subc->color==ctx->npart-1)?eps->intb:eps->inta+(ctx->subc->color+1)*h;
    200:       PetscFree(ctx->subintervals);
    201:       PetscMalloc1(ctx->npart+1,&ctx->subintervals);
    202:       for (i=0;i<ctx->npart;i++) ctx->subintervals[i] = eps->inta+h*i;
    203:       ctx->subintervals[ctx->npart] = eps->intb;
    204:     } else {
    205:       a = ctx->subintervals[ctx->subc->color];
    206:       b = ctx->subintervals[ctx->subc->color+1];
    207:     }

    209:     if (!ctx->eps) {
    210:       /* Create auxiliary EPS */
    211:       EPSCreate(PetscSubcommChild(ctx->subc),&ctx->eps);
    212:       EPSSetOperators(ctx->eps,Ar,Br);
    213:       MatDestroy(&Ar);
    214:       MatDestroy(&Br);
    215:     }
    216:     EPSSetType(ctx->eps,((PetscObject)eps)->type_name);

    218:     /* Transfer options for ST, KSP and PC */
    219:     STGetType(eps->st,&sttype);
    220:     STSetType(ctx->eps->st,sttype);
    221:     STGetKSP(eps->st,&ksp);
    222:     KSPGetType(ksp,&ksptype);
    223:     KSPGetPC(ksp,&pc);
    224:     PCGetType(pc,&pctype);
    225:     PCFactorGetMatSolverPackage(pc,&stype);
    226:     STGetKSP(ctx->eps->st,&ksp);
    227:     KSPSetType(ksp,ksptype);
    228:     KSPGetPC(ksp,&pc);
    229:     PCSetType(pc,pctype);
    230:     PCFactorSetMatSolverPackage(pc,stype);

    232:     /* Create subcommunicator grouping processes with same rank */
    233:     if (ctx->commset) { MPI_Comm_free(&ctx->commrank); }
    234:     MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);
    235:     MPI_Comm_split(((PetscObject)eps)->comm,rank,ctx->subc->color,&ctx->commrank);
    236:     ctx->commset = PETSC_TRUE;
    237:   }
    238:   EPSSetConvergenceTest(ctx->eps,eps->conv);
    239:   EPSSetInterval(ctx->eps,a,b);
    240:   ctx_local = (EPS_KRYLOVSCHUR*)ctx->eps->data;
    241:   ctx_local->npart = ctx->npart;
    242:   ctx_local->detect = ctx->detect;
    243:   ctx_local->global = PETSC_FALSE;
    244:   ctx_local->eps = eps;
    245:   ctx_local->subc = ctx->subc;
    246:   ctx_local->commrank = ctx->commrank;

    248:   EPSSetDimensions(ctx->eps,ctx->nev,ctx->ncv,ctx->mpd);
    249:   EPSKrylovSchurSetLocking(ctx->eps,ctx->lock);

    251:   /* transfer options from eps->V */
    252:   EPSGetBV(ctx->eps,&V);
    253:   if (!eps->V) { EPSGetBV(eps,&eps->V); }
    254:   if (!((PetscObject)(eps->V))->type_name) {
    255:     BVSetType(V,BVSVEC);
    256:   } else {
    257:     BVGetType(eps->V,&type);
    258:     BVSetType(V,type);
    259:   }
    260:   BVGetOrthogonalization(eps->V,&orthog_type,&orthog_ref,&eta,&ob_type);
    261:   BVSetOrthogonalization(V,orthog_type,orthog_ref,eta,ob_type);
    262:   ctx->eps->which = eps->which;
    263:   ctx->eps->max_it = eps->max_it;
    264:   ctx->eps->tol = eps->tol;
    265:   ctx->eps->purify = eps->purify;
    266:   if (eps->tol==PETSC_DEFAULT) eps->tol = SLEPC_DEFAULT_TOL;
    267:   EPSSetProblemType(ctx->eps,eps->problem_type);
    268:   EPSSetUp(ctx->eps);
    269:   ctx->eps->nconv = 0;
    270:   ctx->eps->its   = 0;
    271:   for (i=0;i<ctx->eps->ncv;i++) {
    272:     ctx->eps->eigr[i]   = 0.0;
    273:     ctx->eps->eigi[i]   = 0.0;
    274:     ctx->eps->errest[i] = 0.0;
    275:   }
    276:   return(0);
    277: }

    281: static PetscErrorCode EPSSliceGetInertia(EPS eps,PetscReal shift,PetscInt *inertia,PetscInt *zeros)
    282: {
    284:   KSP            ksp;
    285:   PC             pc;
    286:   Mat            F;

    289:   if (shift >= PETSC_MAX_REAL) { /* Right-open interval */
    290:     if (inertia) *inertia = eps->n;
    291:   } else if (shift <= PETSC_MIN_REAL) {
    292:     if (inertia) *inertia = 0;
    293:     if (zeros) *zeros = 0;
    294:   } else {
    295:     STSetShift(eps->st,shift);
    296:     STSetUp(eps->st);
    297:     STGetKSP(eps->st,&ksp);
    298:     KSPGetPC(ksp,&pc);
    299:     PCFactorGetMatrix(pc,&F);
    300:     MatGetInertia(F,inertia,zeros,NULL);
    301:   }
    302:   return(0);
    303: }

    307: PetscErrorCode EPSSetUp_KrylovSchur_Slice(EPS eps)
    308: {
    309:   PetscErrorCode  ierr;
    310:   PetscBool       issinv;
    311:   EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data,*ctx_glob;
    312:   EPS_SR          sr,sr_loc,sr_glob;
    313:   PetscInt        nEigs,dssz=1,i,zeros=0,off=0;
    314:   PetscMPIInt     nproc,rank,aux;
    315:   MPI_Request     req;

    318:   if (ctx->global) {
    319:     if (eps->inta==0.0 && eps->intb==0.0) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"Must define a computational interval when using EPS_ALL");
    320:     if (eps->intb >= PETSC_MAX_REAL && eps->inta <= PETSC_MIN_REAL) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"The defined computational interval should have at least one of their sides bounded");
    321:     if (!eps->ishermitian) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Spectrum slicing only available for symmetric/Hermitian eigenproblems");
    322:     if (eps->arbitrary) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Arbitrary selection of eigenpairs cannot be used with spectrum slicing");
    323:     if (!((PetscObject)(eps->st))->type_name) { /* default to shift-and-invert */
    324:       STSetType(eps->st,STSINVERT);
    325:     }
    326:     PetscObjectTypeCompareAny((PetscObject)eps->st,&issinv,STSINVERT,STCAYLEY,"");
    327:     if (!issinv) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Shift-and-invert or Cayley ST is needed for spectrum slicing");
    328:     if (eps->tol==PETSC_DEFAULT) eps->tol = SLEPC_DEFAULT_TOL*1e-2;  /* use tighter tolerance */
    329:     if (!eps->max_it) eps->max_it = 100;
    330:     if (ctx->nev==1) ctx->nev = 40;  /* nev not set, use default value */
    331:     if (ctx->nev<10) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"nev cannot be less than 10 in spectrum slicing runs");
    332:   }
    333:   eps->ops->backtransform = NULL;

    335:   /* create spectrum slicing context and initialize it */
    336:   EPSSliceResetSR(eps);
    337:   PetscNewLog(eps,&sr);
    338:   ctx->sr = sr;
    339:   sr->itsKs = 0;
    340:   sr->nleap = 0;
    341:   sr->nMAXCompl = eps->nev/4;
    342:   sr->iterCompl = eps->max_it/4;
    343:   sr->sPres = NULL;
    344:   sr->nS = 0;

    346:   if (ctx->npart==1 || ctx->global) {
    347:     /* check presence of ends and finding direction */
    348:     if ((eps->inta > PETSC_MIN_REAL && eps->inta != 0.0) || eps->intb >= PETSC_MAX_REAL) {
    349:       sr->int0 = eps->inta;
    350:       sr->int1 = eps->intb;
    351:       sr->dir = 1;
    352:       if (eps->intb >= PETSC_MAX_REAL) { /* Right-open interval */
    353:         sr->hasEnd = PETSC_FALSE;
    354:       } else sr->hasEnd = PETSC_TRUE;
    355:     } else {
    356:       sr->int0 = eps->intb;
    357:       sr->int1 = eps->inta;
    358:       sr->dir = -1;
    359:       sr->hasEnd = (eps->inta <= PETSC_MIN_REAL)?PETSC_FALSE:PETSC_TRUE;
    360:     }
    361:   }
    362:   if (ctx->global) {
    363:     if (ctx->npart>1) {
    364:       /* prevent computation of factorization in global eps unless npart==1 */
    365:       STSetTransform(eps->st,PETSC_FALSE);
    366:     }
    367:     EPSSetDimensions_Default(eps,ctx->nev,&ctx->ncv,&ctx->mpd);
    368:     /* create subintervals and initialize auxiliary eps for slicing runs */
    369:     EPSSliceGetEPS(eps);
    370:     sr_loc = ((EPS_KRYLOVSCHUR*)ctx->eps->data)->sr;
    371:     if (ctx->npart>1) {
    372:       if ((sr->dir>0&&ctx->subc->color==0)||(sr->dir<0&&ctx->subc->color==ctx->npart-1)) sr->inertia0 = sr_loc->inertia0;
    373:       MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);
    374:       if (rank==0) {
    375:         MPI_Bcast(&sr->inertia0,1,MPIU_INT,(sr->dir>0)?0:ctx->npart-1,ctx->commrank);
    376:       }
    377:       MPI_Bcast(&sr->inertia0,1,MPIU_INT,0,PetscSubcommChild(ctx->subc));
    378:       PetscFree(ctx->nconv_loc);
    379:       PetscMalloc1(ctx->npart,&ctx->nconv_loc);
    380:       MPI_Comm_size(((PetscObject)eps)->comm,&nproc);
    381:       if (sr->dir<0) off = 1;
    382:       if (nproc%ctx->npart==0) { /* subcommunicators with the same size */
    383:         PetscMPIIntCast(sr_loc->numEigs,&aux);
    384:         MPI_Allgather(&aux,1,MPI_INT,ctx->nconv_loc,1,MPI_INT,ctx->commrank);
    385:         MPI_Allgather(&sr_loc->int0,1,MPIU_REAL,ctx->subintervals+off,1,MPIU_REAL,ctx->commrank);
    386:       } else {
    387:         MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);
    388:         if (!rank) {
    389:           PetscMPIIntCast(sr_loc->numEigs,&aux);
    390:           MPI_Allgather(&aux,1,MPI_INT,ctx->nconv_loc,1,MPI_INT,ctx->commrank);
    391:           MPI_Allgather(&sr_loc->int0,1,MPIU_REAL,ctx->subintervals+off,1,MPIU_REAL,ctx->commrank);
    392:         }
    393:         PetscMPIIntCast(ctx->npart,&aux);
    394:         MPI_Bcast(ctx->nconv_loc,aux,MPI_INT,0,PetscSubcommChild(ctx->subc));
    395:         MPI_Bcast(ctx->subintervals+off,aux,MPIU_REAL,0,PetscSubcommChild(ctx->subc));
    396:       }
    397:       nEigs = 0;
    398:       for (i=0;i<ctx->npart;i++) nEigs += ctx->nconv_loc[i];
    399:     } else {
    400:       nEigs = sr_loc->numEigs;
    401:       sr->inertia0 = sr_loc->inertia0;
    402:     }
    403:     sr->inertia1 = sr->inertia0+sr->dir*nEigs;
    404:     sr->numEigs = nEigs;
    405:     eps->nev = nEigs;
    406:     eps->ncv = nEigs;
    407:     eps->mpd = nEigs;
    408:   } else {
    409:     ctx_glob = (EPS_KRYLOVSCHUR*)ctx->eps->data;
    410:     sr_glob = ctx_glob->sr;
    411:     if (ctx->npart>1) {
    412:       sr->dir = sr_glob->dir;
    413:       sr->int0 = (sr->dir==1)?eps->inta:eps->intb;
    414:       sr->int1 = (sr->dir==1)?eps->intb:eps->inta;
    415:       if ((sr->dir>0&&ctx->subc->color==ctx->npart-1)||(sr->dir<0&&ctx->subc->color==0)) sr->hasEnd = sr_glob->hasEnd;
    416:       else sr->hasEnd = PETSC_TRUE;
    417:     }

    419:     /* last process in eps comm computes inertia1 */
    420:     if (ctx->npart==1 || ((sr->dir>0 && ctx->subc->color==ctx->npart-1) || (sr->dir<0 && ctx->subc->color==0))) {
    421:       EPSSliceGetInertia(eps,sr->int1,&sr->inertia1,ctx->detect?&zeros:NULL);
    422:       if (zeros) SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_USER,"Found singular matrix for the transformed problem in an interval endpoint defined by user");
    423:     }

    425:     /* compute inertia0 */
    426:     EPSSliceGetInertia(eps,sr->int0,&sr->inertia0,ctx->detect?&zeros:NULL);
    427:     if (zeros) { /* error in factorization */
    428:       if (ctx->npart==1 || ctx_glob->subintset || ((sr->dir>0 && ctx->subc->color==0) || (sr->dir<0 && ctx->subc->color==ctx->npart-1))) SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_USER,"Found singular matrix for the transformed problem in an interval endpoint defined by user");
    429:       else { /* perturb shift */
    430:         sr->int0 *= (1.0+SLICE_PTOL);
    431:         EPSSliceGetInertia(eps,sr->int0,&sr->inertia0,&zeros);
    432:         if (zeros) SETERRQ1(((PetscObject)eps)->comm,PETSC_ERR_CONV_FAILED,"Inertia computation fails in %g",sr->int1);
    433:       }
    434:     }
    435:     if (ctx->npart>1) {
    436:       /* inertia1 is received from neighbour */
    437:       MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);
    438:       if (!rank) {
    439:         if ((sr->dir>0 && ctx->subc->color>0) || (sr->dir<0 && ctx->subc->color<ctx->npart-1)) { /* send inertia0 to neighbour0 */
    440:           MPI_Isend(&(sr->inertia0),1,MPIU_INT,ctx->subc->color-sr->dir,0,ctx->commrank,&req);
    441:           MPI_Isend(&(sr->int0),1,MPIU_REAL,ctx->subc->color-sr->dir,0,ctx->commrank,&req);
    442:         }
    443:         if ((sr->dir>0 && ctx->subc->color<ctx->npart-1)|| (sr->dir<0 && ctx->subc->color>0)) { /* receive inertia1 from neighbour1 */
    444:           MPI_Recv(&(sr->inertia1),1,MPIU_INT,ctx->subc->color+sr->dir,0,ctx->commrank,MPI_STATUS_IGNORE);
    445:           MPI_Recv(&(sr->int1),1,MPIU_REAL,ctx->subc->color+sr->dir,0,ctx->commrank,MPI_STATUS_IGNORE);
    446:         }
    447:       }
    448:       if ((sr->dir>0 && ctx->subc->color<ctx->npart-1)||(sr->dir<0 && ctx->subc->color>0)) {
    449:         MPI_Bcast(&sr->inertia1,1,MPIU_INT,0,PetscSubcommChild(ctx->subc));
    450:         MPI_Bcast(&sr->int1,1,MPIU_REAL,0,PetscSubcommChild(ctx->subc));
    451:       } else sr_glob->inertia1 = sr->inertia1;
    452:     }

    454:     /* number of eigenvalues in interval */
    455:     sr->numEigs = (sr->dir)*(sr->inertia1 - sr->inertia0);
    456:     if (ctx->npart>1) {
    457:       /* memory allocate for subinterval eigenpairs */
    458:       EPSSliceAllocateSolution(eps,1);
    459:     }
    460:     dssz = eps->ncv+1;
    461:   }
    462:   DSSetType(eps->ds,DSHEP);
    463:   DSSetCompact(eps->ds,PETSC_TRUE);
    464:   DSAllocate(eps->ds,dssz);
    465:   return(0);
    466: }

    470: static PetscErrorCode EPSSliceGatherEigenVectors(EPS eps)
    471: {
    472:   PetscErrorCode  ierr;
    473:   Vec             v,vg,v_loc;
    474:   IS              is1,is2;
    475:   VecScatter      vec_sc;
    476:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
    477:   PetscInt        nloc,m0,n0,i,si,idx,*idx1,*idx2,j;
    478:   PetscScalar     *array;
    479:   EPS_SR          sr_loc;
    480:   BV              V_loc;

    483:   sr_loc = ((EPS_KRYLOVSCHUR*)ctx->eps->data)->sr;
    484:   V_loc = sr_loc->V;

    486:   /* Gather parallel eigenvectors */
    487:   BVGetColumn(eps->V,0,&v);
    488:   VecGetOwnershipRange(v,&n0,&m0);
    489:   BVRestoreColumn(eps->V,0,&v);
    490:   BVGetColumn(ctx->eps->V,0,&v);
    491:   VecGetLocalSize(v,&nloc);
    492:   BVRestoreColumn(ctx->eps->V,0,&v);
    493:   PetscMalloc2(m0-n0,&idx1,m0-n0,&idx2);
    494:   VecCreateMPI(PetscObjectComm((PetscObject)eps),nloc,PETSC_DECIDE,&vg);
    495:   idx = -1;
    496:   for (si=0;si<ctx->npart;si++) {
    497:     j = 0;
    498:     for (i=n0;i<m0;i++) {
    499:       idx1[j]   = i;
    500:       idx2[j++] = i+eps->n*si;
    501:     }
    502:     ISCreateGeneral(PetscObjectComm((PetscObject)eps),(m0-n0),idx1,PETSC_COPY_VALUES,&is1);
    503:     ISCreateGeneral(PetscObjectComm((PetscObject)eps),(m0-n0),idx2,PETSC_COPY_VALUES,&is2);
    504:     BVGetColumn(eps->V,0,&v);
    505:     VecScatterCreate(v,is1,vg,is2,&vec_sc);
    506:     BVRestoreColumn(eps->V,0,&v);
    507:     ISDestroy(&is1);
    508:     ISDestroy(&is2);
    509:     for (i=0;i<ctx->nconv_loc[si];i++) {
    510:       BVGetColumn(eps->V,++idx,&v);
    511:       if (ctx->subc->color==si) {
    512:         BVGetColumn(V_loc,i,&v_loc);
    513:         VecGetArray(v_loc,&array);
    514:         VecPlaceArray(vg,array);
    515:       }
    516:       VecScatterBegin(vec_sc,vg,v,INSERT_VALUES,SCATTER_REVERSE);
    517:       VecScatterEnd(vec_sc,vg,v,INSERT_VALUES,SCATTER_REVERSE);
    518:       if (ctx->subc->color==si) {
    519:         VecResetArray(vg);
    520:         VecRestoreArray(v_loc,&array);
    521:         BVRestoreColumn(V_loc,i,&v_loc);
    522:       }
    523:       BVRestoreColumn(eps->V,idx,&v);
    524:     }
    525:     VecScatterDestroy(&vec_sc);
    526:   }
    527:   PetscFree2(idx1,idx2);
    528:   VecDestroy(&vg);
    529:   return(0);
    530: }

    534: /*
    535:   EPSComputeVectors_Slice - Recover Eigenvectors from subcomunicators
    536:  */
    537: PetscErrorCode EPSComputeVectors_Slice(EPS eps)
    538: {
    539:   PetscErrorCode  ierr;
    540:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;

    543:   if (ctx->global && ctx->npart>1) {
    544:     EPSComputeVectors(ctx->eps);
    545:     EPSSliceGatherEigenVectors(eps);
    546:   }
    547:   return(0);
    548: }

    550: #define SWAP(a,b,t) {t=a;a=b;b=t;}

    554: static PetscErrorCode EPSSliceGetInertias(EPS eps,PetscInt *n,PetscReal **shifts,PetscInt **inertias)
    555: {
    556:   PetscErrorCode  ierr;
    557:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
    558:   PetscInt        i=0,j,tmpi;
    559:   PetscReal       v,tmpr;
    560:   EPS_shift       s;

    563:   if (!eps->state) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONGSTATE,"Must call EPSSetUp() first");
    564:   if (!ctx->sr) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONGSTATE,"Only available in interval computations, see EPSSetInterval()");
    565:   if (!ctx->sr->s0) {  /* EPSSolve not called yet */
    566:     *n = 2;
    567:   } else {
    568:     *n = 1;
    569:     s = ctx->sr->s0;
    570:     while (s) {
    571:       (*n)++;
    572:       s = s->neighb[1];
    573:     }
    574:   }
    575:   PetscMalloc1(*n,shifts);
    576:   PetscMalloc1(*n,inertias);
    577:   if (!ctx->sr->s0) {  /* EPSSolve not called yet */
    578:     (*shifts)[0]   = ctx->sr->int0;
    579:     (*shifts)[1]   = ctx->sr->int1;
    580:     (*inertias)[0] = ctx->sr->inertia0;
    581:     (*inertias)[1] = ctx->sr->inertia1;
    582:   } else {
    583:     s = ctx->sr->s0;
    584:     while (s) {
    585:       (*shifts)[i]     = s->value;
    586:       (*inertias)[i++] = s->inertia;
    587:       s = s->neighb[1];
    588:     }
    589:     (*shifts)[i]   = ctx->sr->int1;
    590:     (*inertias)[i] = ctx->sr->inertia1;
    591:   }
    592:   /* remove possible duplicate in last position */
    593:   if ((*shifts)[(*n)-1]==(*shifts)[(*n)-2]) (*n)--;
    594:   /* sort result */
    595:   for (i=0;i<*n;i++) {
    596:     v = (*shifts)[i];
    597:     for (j=i+1;j<*n;j++) {
    598:       if (v > (*shifts)[j]) {
    599:         SWAP((*shifts)[i],(*shifts)[j],tmpr);
    600:         SWAP((*inertias)[i],(*inertias)[j],tmpi);
    601:         v = (*shifts)[i];
    602:       }
    603:     }
    604:   }
    605:   return(0);
    606: }

    610: static PetscErrorCode EPSSliceGatherSolution(EPS eps)
    611: {
    612:   PetscErrorCode  ierr;
    613:   PetscMPIInt     rank,nproc;
    614:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
    615:   PetscInt        i,idx,j;
    616:   PetscInt        *perm_loc,off=0,*inertias_loc,ns;
    617:   PetscScalar     *eigr_loc;
    618:   EPS_SR          sr_loc;
    619:   PetscReal       *shifts_loc;
    620:   PetscMPIInt     *disp,*ns_loc,aux;

    623:   eps->nconv = 0;
    624:   for (i=0;i<ctx->npart;i++) eps->nconv += ctx->nconv_loc[i];
    625:   sr_loc = ((EPS_KRYLOVSCHUR*)ctx->eps->data)->sr;

    627:   /* Gather the shifts used and the inertias computed */
    628:   EPSSliceGetInertias(ctx->eps,&ns,&shifts_loc,&inertias_loc);
    629:   if (ctx->sr->dir>0 && shifts_loc[ns-1]==sr_loc->int1 && ctx->subc->color<ctx->npart-1) ns--;
    630:   if (ctx->sr->dir<0 && shifts_loc[ns-1]==sr_loc->int0 && ctx->subc->color>0) {
    631:     ns--;
    632:     for (i=0;i<ns;i++) {
    633:       inertias_loc[i] = inertias_loc[i+1];
    634:       shifts_loc[i] = shifts_loc[i+1];
    635:     }
    636:   }
    637:   PetscMalloc1(ctx->npart,&ns_loc);
    638:   MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);
    639:   PetscMPIIntCast(ns,&aux);
    640:   if (rank==0) { MPI_Allgather(&aux,1,MPI_INT,ns_loc,1,MPI_INT,ctx->commrank); }
    641:   PetscMPIIntCast(ctx->npart,&aux);
    642:   MPI_Bcast(ns_loc,aux,MPI_INT,0,PetscSubcommChild(ctx->subc));
    643:   ctx->nshifts = 0;
    644:   for (i=0;i<ctx->npart;i++) ctx->nshifts += ns_loc[i];
    645:   PetscFree(ctx->inertias);
    646:   PetscFree(ctx->shifts);
    647:   PetscMalloc1(ctx->nshifts,&ctx->inertias);
    648:   PetscMalloc1(ctx->nshifts,&ctx->shifts);

    650:   /* Gather eigenvalues (same ranks have fully set of eigenvalues)*/
    651:   eigr_loc = sr_loc->eigr;
    652:   perm_loc = sr_loc->perm;
    653:   MPI_Comm_size(((PetscObject)eps)->comm,&nproc);
    654:   PetscMalloc1(ctx->npart,&disp);
    655:   disp[0] = 0;
    656:   for (i=1;i<ctx->npart;i++) disp[i] = disp[i-1]+ctx->nconv_loc[i-1];
    657:   if (nproc%ctx->npart==0) { /* subcommunicators with the same size */
    658:     PetscMPIIntCast(sr_loc->numEigs,&aux);
    659:     MPI_Allgatherv(eigr_loc,aux,MPIU_SCALAR,eps->eigr,ctx->nconv_loc,disp,MPIU_SCALAR,ctx->commrank); /* eigenvalues */
    660:     MPI_Allgatherv(perm_loc,aux,MPIU_INT,eps->perm,ctx->nconv_loc,disp,MPIU_INT,ctx->commrank); /* perm */
    661:     for (i=1;i<ctx->npart;i++) disp[i] = disp[i-1]+ns_loc[i-1];
    662:     PetscMPIIntCast(ns,&aux);
    663:     MPI_Allgatherv(shifts_loc,aux,MPIU_REAL,ctx->shifts,ns_loc,disp,MPIU_REAL,ctx->commrank); /* shifts */
    664:     MPI_Allgatherv(inertias_loc,aux,MPIU_INT,ctx->inertias,ns_loc,disp,MPIU_INT,ctx->commrank); /* inertias */
    665:     MPI_Allreduce(&sr_loc->itsKs,&eps->its,1,MPIU_INT,MPI_SUM,ctx->commrank);
    666:   } else { /* subcommunicators with different size */
    667:     MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);
    668:     if (rank==0) {
    669:       PetscMPIIntCast(sr_loc->numEigs,&aux);
    670:       MPI_Allgatherv(eigr_loc,aux,MPIU_SCALAR,eps->eigr,ctx->nconv_loc,disp,MPIU_SCALAR,ctx->commrank); /* eigenvalues */
    671:       MPI_Allgatherv(perm_loc,aux,MPIU_INT,eps->perm,ctx->nconv_loc,disp,MPIU_INT,ctx->commrank); /* perm */
    672:       for (i=1;i<ctx->npart;i++) disp[i] = disp[i-1]+ns_loc[i-1];
    673:       PetscMPIIntCast(ns,&aux);
    674:       MPI_Allgatherv(shifts_loc,aux,MPIU_REAL,ctx->shifts,ns_loc,disp,MPIU_REAL,ctx->commrank); /* shifts */
    675:       MPI_Allgatherv(inertias_loc,aux,MPIU_INT,ctx->inertias,ns_loc,disp,MPIU_INT,ctx->commrank); /* inertias */
    676:       MPI_Allreduce(&sr_loc->itsKs,&eps->its,1,MPIU_INT,MPI_SUM,ctx->commrank);
    677:     }
    678:     PetscMPIIntCast(eps->nconv,&aux);
    679:     MPI_Bcast(eps->eigr,aux,MPIU_SCALAR,0,PetscSubcommChild(ctx->subc));
    680:     MPI_Bcast(eps->perm,aux,MPIU_INT,0,PetscSubcommChild(ctx->subc));
    681:     MPI_Bcast(ctx->shifts,ctx->nshifts,MPIU_REAL,0,PetscSubcommChild(ctx->subc));
    682:     PetscMPIIntCast(ctx->nshifts,&aux);
    683:     MPI_Bcast(ctx->inertias,aux,MPIU_INT,0,PetscSubcommChild(ctx->subc));
    684:     MPI_Bcast(&eps->its,1,MPIU_INT,0,PetscSubcommChild(ctx->subc));
    685:   }
    686:   /* Update global array eps->perm */
    687:   idx = ctx->nconv_loc[0];
    688:   for (i=1;i<ctx->npart;i++) {
    689:     off += ctx->nconv_loc[i-1];
    690:     for (j=0;j<ctx->nconv_loc[i];j++) eps->perm[idx++] += off;
    691:   }

    693:   /* Gather parallel eigenvectors */
    694:   PetscFree(ns_loc);
    695:   PetscFree(disp);
    696:   PetscFree(shifts_loc);
    697:   PetscFree(inertias_loc);
    698:   return(0);
    699: }

    701: /*
    702:    Fills the fields of a shift structure
    703: */
    706: static PetscErrorCode EPSCreateShift(EPS eps,PetscReal val,EPS_shift neighb0,EPS_shift neighb1)
    707: {
    708:   PetscErrorCode  ierr;
    709:   EPS_shift       s,*pending2;
    710:   PetscInt        i;
    711:   EPS_SR          sr;
    712:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;

    715:   sr = ctx->sr;
    716:   PetscNewLog(eps,&s);
    717:   s->value = val;
    718:   s->neighb[0] = neighb0;
    719:   if (neighb0) neighb0->neighb[1] = s;
    720:   s->neighb[1] = neighb1;
    721:   if (neighb1) neighb1->neighb[0] = s;
    722:   s->comp[0] = PETSC_FALSE;
    723:   s->comp[1] = PETSC_FALSE;
    724:   s->index = -1;
    725:   s->neigs = 0;
    726:   s->nconv[0] = s->nconv[1] = 0;
    727:   s->nsch[0] = s->nsch[1]=0;
    728:   /* Inserts in the stack of pending shifts */
    729:   /* If needed, the array is resized */
    730:   if (sr->nPend >= sr->maxPend) {
    731:     sr->maxPend *= 2;
    732:     PetscMalloc1(sr->maxPend,&pending2);
    733:     PetscLogObjectMemory((PetscObject)eps,sizeof(EPS_shift));
    734:     for (i=0;i<sr->nPend;i++) pending2[i] = sr->pending[i];
    735:     PetscFree(sr->pending);
    736:     sr->pending = pending2;
    737:   }
    738:   sr->pending[sr->nPend++]=s;
    739:   return(0);
    740: }

    742: /* Prepare for Rational Krylov update */
    745: static PetscErrorCode EPSPrepareRational(EPS eps)
    746: {
    747:   EPS_KRYLOVSCHUR  *ctx=(EPS_KRYLOVSCHUR*)eps->data;
    748:   PetscErrorCode   ierr;
    749:   PetscInt         dir,i,k,ld,nv;
    750:   PetscScalar      *A;
    751:   EPS_SR           sr = ctx->sr;
    752:   Vec              v;

    755:   DSGetLeadingDimension(eps->ds,&ld);
    756:   dir = (sr->sPres->neighb[0] == sr->sPrev)?1:-1;
    757:   dir*=sr->dir;
    758:   k = 0;
    759:   for (i=0;i<sr->nS;i++) {
    760:     if (dir*PetscRealPart(sr->S[i])>0.0) {
    761:       sr->S[k] = sr->S[i];
    762:       sr->S[sr->nS+k] = sr->S[sr->nS+i];
    763:       BVGetColumn(sr->Vnext,k,&v);
    764:       BVCopyVec(eps->V,eps->nconv+i,v);
    765:       BVRestoreColumn(sr->Vnext,k,&v);
    766:       k++;
    767:       if (k>=sr->nS/2)break;
    768:     }
    769:   }
    770:   /* Copy to DS */
    771:   DSGetArray(eps->ds,DS_MAT_A,&A);
    772:   PetscMemzero(A,ld*ld*sizeof(PetscScalar));
    773:   for (i=0;i<k;i++) {
    774:     A[i*(1+ld)] = sr->S[i];
    775:     A[k+i*ld] = sr->S[sr->nS+i];
    776:   }
    777:   sr->nS = k;
    778:   DSRestoreArray(eps->ds,DS_MAT_A,&A);
    779:   DSGetDimensions(eps->ds,&nv,NULL,NULL,NULL,NULL);
    780:   DSSetDimensions(eps->ds,nv,0,0,k);
    781:   /* Append u to V */
    782:   BVGetColumn(sr->Vnext,sr->nS,&v);
    783:   BVCopyVec(eps->V,sr->nv,v);
    784:   BVRestoreColumn(sr->Vnext,sr->nS,&v);
    785:   return(0);
    786: }

    788: /* Provides next shift to be computed */
    791: static PetscErrorCode EPSExtractShift(EPS eps)
    792: {
    793:   PetscErrorCode   ierr;
    794:   PetscInt         iner,zeros=0;
    795:   EPS_KRYLOVSCHUR  *ctx=(EPS_KRYLOVSCHUR*)eps->data;
    796:   EPS_SR           sr;
    797:   PetscReal        newShift;
    798:   EPS_shift        sPres;

    801:   sr = ctx->sr;
    802:   if (sr->nPend > 0) {
    803:     sr->sPrev = sr->sPres;
    804:     sr->sPres = sr->pending[--sr->nPend];
    805:     sPres = sr->sPres;
    806:     EPSSliceGetInertia(eps,sPres->value,&iner,ctx->detect?&zeros:NULL);
    807:     if (zeros) {
    808:       newShift = sPres->value*(1.0+SLICE_PTOL);
    809:       if (sr->dir*(sPres->neighb[0] && newShift-sPres->neighb[0]->value) < 0) newShift = (sPres->value+sPres->neighb[0]->value)/2;
    810:       else if (sPres->neighb[1] && sr->dir*(sPres->neighb[1]->value-newShift) < 0) newShift = (sPres->value+sPres->neighb[1]->value)/2;
    811:       EPSSliceGetInertia(eps,newShift,&iner,&zeros);
    812:       if (zeros) SETERRQ1(((PetscObject)eps)->comm,PETSC_ERR_CONV_FAILED,"Inertia computation fails in %g",newShift);
    813:       sPres->value = newShift;
    814:     }
    815:     sr->sPres->inertia = iner;
    816:     eps->target = sr->sPres->value;
    817:     eps->reason = EPS_CONVERGED_ITERATING;
    818:     eps->its = 0;
    819:   } else sr->sPres = NULL;
    820:   return(0);
    821: }

    823: /*
    824:    Symmetric KrylovSchur adapted to spectrum slicing:
    825:    Allows searching an specific amount of eigenvalues in the subintervals left and right.
    826:    Returns whether the search has succeeded
    827: */
    830: static PetscErrorCode EPSKrylovSchur_Slice(EPS eps)
    831: {
    832:   PetscErrorCode  ierr;
    833:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
    834:   PetscInt        i,conv,k,l,ld,nv,*iwork,j,p;
    835:   Mat             U;
    836:   PetscScalar     *Q,*A,rtmp;
    837:   PetscReal       *a,*b,beta;
    838:   PetscBool       breakdown;
    839:   PetscInt        count0,count1;
    840:   PetscReal       lambda;
    841:   EPS_shift       sPres;
    842:   PetscBool       complIterating;
    843:   PetscBool       sch0,sch1;
    844:   PetscInt        iterCompl=0,n0,n1;
    845:   EPS_SR          sr = ctx->sr;

    848:   /* Spectrum slicing data */
    849:   sPres = sr->sPres;
    850:   complIterating =PETSC_FALSE;
    851:   sch1 = sch0 = PETSC_TRUE;
    852:   DSGetLeadingDimension(eps->ds,&ld);
    853:   PetscMalloc1(2*ld,&iwork);
    854:   count0=0;count1=0; /* Found on both sides */
    855:   if (sr->nS > 0 && (sPres->neighb[0] == sr->sPrev || sPres->neighb[1] == sr->sPrev)) {
    856:     /* Rational Krylov */
    857:     DSTranslateRKS(eps->ds,sr->sPrev->value-sPres->value);
    858:     DSGetDimensions(eps->ds,NULL,NULL,NULL,&l,NULL);
    859:     DSSetDimensions(eps->ds,l+1,0,0,0);
    860:     BVSetActiveColumns(eps->V,0,l+1);
    861:     DSGetMat(eps->ds,DS_MAT_Q,&U);
    862:     BVMultInPlace(eps->V,U,0,l+1);
    863:     MatDestroy(&U);
    864:   } else {
    865:     /* Get the starting Lanczos vector */
    866:     EPSGetStartVector(eps,0,NULL);
    867:     l = 0;
    868:   }
    869:   /* Restart loop */
    870:   while (eps->reason == EPS_CONVERGED_ITERATING) {
    871:     eps->its++; sr->itsKs++;
    872:     /* Compute an nv-step Lanczos factorization */
    873:     nv = PetscMin(eps->nconv+eps->mpd,eps->ncv);
    874:     DSGetArrayReal(eps->ds,DS_MAT_T,&a);
    875:     b = a + ld;
    876:     EPSFullLanczos(eps,a,b,eps->nconv+l,&nv,&breakdown);
    877:     sr->nv = nv;
    878:     beta = b[nv-1];
    879:     DSRestoreArrayReal(eps->ds,DS_MAT_T,&a);
    880:     DSSetDimensions(eps->ds,nv,0,eps->nconv,eps->nconv+l);
    881:     if (l==0) {
    882:       DSSetState(eps->ds,DS_STATE_INTERMEDIATE);
    883:     } else {
    884:       DSSetState(eps->ds,DS_STATE_RAW);
    885:     }
    886:     BVSetActiveColumns(eps->V,eps->nconv,nv);

    888:     /* Solve projected problem and compute residual norm estimates */
    889:     if (eps->its == 1 && l > 0) {/* After rational update */
    890:       DSGetArray(eps->ds,DS_MAT_A,&A);
    891:       DSGetArrayReal(eps->ds,DS_MAT_T,&a);
    892:       b = a + ld;
    893:       k = eps->nconv+l;
    894:       A[k*ld+k-1] = A[(k-1)*ld+k];
    895:       A[k*ld+k] = a[k];
    896:       for (j=k+1; j< nv; j++) {
    897:         A[j*ld+j] = a[j];
    898:         A[j*ld+j-1] = b[j-1] ;
    899:         A[(j-1)*ld+j] = b[j-1];
    900:       }
    901:       DSRestoreArray(eps->ds,DS_MAT_A,&A);
    902:       DSRestoreArrayReal(eps->ds,DS_MAT_T,&a);
    903:       DSSolve(eps->ds,eps->eigr,NULL);
    904:       DSSort(eps->ds,eps->eigr,NULL,NULL,NULL,NULL);
    905:       DSSetCompact(eps->ds,PETSC_TRUE);
    906:     } else { /* Restart */
    907:       DSSolve(eps->ds,eps->eigr,NULL);
    908:       DSSort(eps->ds,eps->eigr,NULL,NULL,NULL,NULL);
    909:     }
    910:     /* Residual */
    911:     EPSKrylovConvergence(eps,PETSC_TRUE,eps->nconv,nv-eps->nconv,beta,1.0,&k);

    913:     if (ctx->lock) {
    914:       /* Check convergence */
    915:       DSGetArrayReal(eps->ds,DS_MAT_T,&a);
    916:       b = a + ld;
    917:       conv = 0;
    918:       j = k = eps->nconv;
    919:       for (i=eps->nconv;i<nv;i++) if (eps->errest[i] < eps->tol) conv++;
    920:       for (i=eps->nconv;i<nv;i++) {
    921:         if (eps->errest[i] < eps->tol) {
    922:           iwork[j++]=i;
    923:         } else iwork[conv+k++]=i;
    924:       }
    925:       for (i=eps->nconv;i<nv;i++) {
    926:         a[i]=PetscRealPart(eps->eigr[i]);
    927:         b[i]=eps->errest[i];
    928:       }
    929:       for (i=eps->nconv;i<nv;i++) {
    930:         eps->eigr[i] = a[iwork[i]];
    931:         eps->errest[i] = b[iwork[i]];
    932:       }
    933:       for (i=eps->nconv;i<nv;i++) {
    934:         a[i]=PetscRealPart(eps->eigr[i]);
    935:         b[i]=eps->errest[i];
    936:       }
    937:       DSRestoreArrayReal(eps->ds,DS_MAT_T,&a);
    938:       DSGetArray(eps->ds,DS_MAT_Q,&Q);
    939:       for (i=eps->nconv;i<nv;i++) {
    940:         p=iwork[i];
    941:         if (p!=i) {
    942:           j=i+1;
    943:           while (iwork[j]!=i) j++;
    944:           iwork[j]=p;iwork[i]=i;
    945:           for (k=0;k<nv;k++) {
    946:             rtmp=Q[k+p*ld];Q[k+p*ld]=Q[k+i*ld];Q[k+i*ld]=rtmp;
    947:           }
    948:         }
    949:       }
    950:       DSRestoreArray(eps->ds,DS_MAT_Q,&Q);
    951:       k=eps->nconv+conv;
    952:     }

    954:     /* Checking values obtained for completing */
    955:     for (i=0;i<k;i++) {
    956:       sr->back[i]=eps->eigr[i];
    957:     }
    958:     STBackTransform(eps->st,k,sr->back,eps->eigi);
    959:     count0=count1=0;
    960:     for (i=0;i<k;i++) {
    961:       lambda = PetscRealPart(sr->back[i]);
    962:       if (((sr->dir)*(sPres->value - lambda) > 0) && ((sr->dir)*(lambda - sPres->ext[0]) > 0)) count0++;
    963:       if (((sr->dir)*(lambda - sPres->value) > 0) && ((sr->dir)*(sPres->ext[1] - lambda) > 0)) count1++;
    964:     }
    965:     if (k>eps->nev && eps->ncv-k<5) eps->reason = EPS_CONVERGED_TOL;
    966:     else {
    967:       /* Checks completion */
    968:       if ((!sch0||count0 >= sPres->nsch[0]) && (!sch1 ||count1 >= sPres->nsch[1])) {
    969:         eps->reason = EPS_CONVERGED_TOL;
    970:       } else {
    971:         if (!complIterating && eps->its >= eps->max_it) eps->reason = EPS_DIVERGED_ITS;
    972:         if (complIterating) {
    973:           if (--iterCompl <= 0) eps->reason = EPS_DIVERGED_ITS;
    974:         } else if (k >= eps->nev) {
    975:           n0 = sPres->nsch[0]-count0;
    976:           n1 = sPres->nsch[1]-count1;
    977:           if (sr->iterCompl>0 && ((n0>0 && n0<= sr->nMAXCompl)||(n1>0&&n1<=sr->nMAXCompl))) {
    978:             /* Iterating for completion*/
    979:             complIterating = PETSC_TRUE;
    980:             if (n0 >sr->nMAXCompl)sch0 = PETSC_FALSE;
    981:             if (n1 >sr->nMAXCompl)sch1 = PETSC_FALSE;
    982:             iterCompl = sr->iterCompl;
    983:           } else eps->reason = EPS_CONVERGED_TOL;
    984:         }
    985:       }
    986:     }
    987:     /* Update l */
    988:     if (eps->reason == EPS_CONVERGED_ITERATING) l = PetscMax(1,(PetscInt)((nv-k)*ctx->keep));
    989:     else l = 0;
    990:     if (!ctx->lock && l>0) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */
    991:     if (breakdown) l=0;

    993:     if (eps->reason == EPS_CONVERGED_ITERATING) {
    994:       if (breakdown) {
    995:         /* Start a new Lanczos factorization */
    996:         PetscInfo2(eps,"Breakdown in Krylov-Schur method (it=%D norm=%g)\n",eps->its,(double)beta);
    997:         EPSGetStartVector(eps,k,&breakdown);
    998:         if (breakdown) {
    999:           eps->reason = EPS_DIVERGED_BREAKDOWN;
    1000:           PetscInfo(eps,"Unable to generate more start vectors\n");
    1001:         }
    1002:       } else {
    1003:         /* Prepare the Rayleigh quotient for restart */
    1004:         DSGetArrayReal(eps->ds,DS_MAT_T,&a);
    1005:         DSGetArray(eps->ds,DS_MAT_Q,&Q);
    1006:         b = a + ld;
    1007:         for (i=k;i<k+l;i++) {
    1008:           a[i] = PetscRealPart(eps->eigr[i]);
    1009:           b[i] = PetscRealPart(Q[nv-1+i*ld]*beta);
    1010:         }
    1011:         DSRestoreArrayReal(eps->ds,DS_MAT_T,&a);
    1012:         DSRestoreArray(eps->ds,DS_MAT_Q,&Q);
    1013:       }
    1014:     }
    1015:     /* Update the corresponding vectors V(:,idx) = V*Q(:,idx) */
    1016:     DSGetMat(eps->ds,DS_MAT_Q,&U);
    1017:     BVMultInPlace(eps->V,U,eps->nconv,k+l);
    1018:     MatDestroy(&U);

    1020:     /* Normalize u and append it to V */
    1021:     if (eps->reason == EPS_CONVERGED_ITERATING && !breakdown) {
    1022:       BVCopyColumn(eps->V,nv,k+l);
    1023:     }
    1024:     eps->nconv = k;
    1025:     if (eps->reason != EPS_CONVERGED_ITERATING) {
    1026:       /* Store approximated values for next shift */
    1027:       DSGetArray(eps->ds,DS_MAT_Q,&Q);
    1028:       sr->nS = l;
    1029:       for (i=0;i<l;i++) {
    1030:         sr->S[i] = eps->eigr[i+k];/* Diagonal elements */
    1031:         sr->S[i+l] = Q[nv-1+(i+k)*ld]*beta; /* Out of diagonal elements */
    1032:       }
    1033:       DSRestoreArray(eps->ds,DS_MAT_Q,&Q);
    1034:     }
    1035:   }
    1036:   /* Check for completion */
    1037:   for (i=0;i< eps->nconv; i++) {
    1038:     if ((sr->dir)*PetscRealPart(eps->eigr[i])>0) sPres->nconv[1]++;
    1039:     else sPres->nconv[0]++;
    1040:   }
    1041:   sPres->comp[0] = (count0 >= sPres->nsch[0])?PETSC_TRUE:PETSC_FALSE;
    1042:   sPres->comp[1] = (count1 >= sPres->nsch[1])?PETSC_TRUE:PETSC_FALSE;
    1043:   if (count0 > sPres->nsch[0] || count1 > sPres->nsch[1])SETERRQ(PetscObjectComm((PetscObject)eps),1,"Mismatch between number of values found and information from inertia, consider using EPSKrylovSchurSetDetectZeros()");
    1044:   PetscFree(iwork);
    1045:   return(0);
    1046: }

    1048: /*
    1049:   Obtains value of subsequent shift
    1050: */
    1053: static PetscErrorCode EPSGetNewShiftValue(EPS eps,PetscInt side,PetscReal *newS)
    1054: {
    1055:   PetscReal       lambda,d_prev;
    1056:   PetscInt        i,idxP;
    1057:   EPS_SR          sr;
    1058:   EPS_shift       sPres,s;
    1059:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;

    1062:   sr = ctx->sr;
    1063:   sPres = sr->sPres;
    1064:   if (sPres->neighb[side]) {
    1065:   /* Completing a previous interval */
    1066:     if (!sPres->neighb[side]->neighb[side] && sPres->neighb[side]->nconv[side]==0) { /* One of the ends might be too far from eigenvalues */
    1067:       if (side) *newS = (sPres->value + PetscRealPart(sr->eigr[sr->perm[sr->indexEig-1]]))/2;
    1068:       else *newS = (sPres->value + PetscRealPart(sr->eigr[sr->perm[0]]))/2;
    1069:     } else *newS=(sPres->value + sPres->neighb[side]->value)/2;
    1070:   } else { /* (Only for side=1). Creating a new interval. */
    1071:     if (sPres->neigs==0) {/* No value has been accepted*/
    1072:       if (sPres->neighb[0]) {
    1073:         /* Multiplying by 10 the previous distance */
    1074:         *newS = sPres->value + 10*(sr->dir)*PetscAbsReal(sPres->value - sPres->neighb[0]->value);
    1075:         sr->nleap++;
    1076:         /* Stops when the interval is open and no values are found in the last 5 shifts (there might be infinite eigenvalues) */
    1077:         if (!sr->hasEnd && sr->nleap > 5) SETERRQ(PetscObjectComm((PetscObject)eps),1,"Unable to compute the wanted eigenvalues with open interval");
    1078:       } else { /* First shift */
    1079:         if (eps->nconv != 0) {
    1080:           /* Unaccepted values give information for next shift */
    1081:           idxP=0;/* Number of values left from shift */
    1082:           for (i=0;i<eps->nconv;i++) {
    1083:             lambda = PetscRealPart(sr->eigr[i]);
    1084:             if ((sr->dir)*(lambda - sPres->value) <0) idxP++;
    1085:             else break;
    1086:           }
    1087:           /* Avoiding subtraction of eigenvalues (might be the same).*/
    1088:           if (idxP>0) {
    1089:             d_prev = PetscAbsReal(sPres->value - PetscRealPart(sr->eigr[0]))/(idxP+0.3);
    1090:           } else {
    1091:             d_prev = PetscAbsReal(sPres->value - PetscRealPart(sr->eigr[eps->nconv-1]))/(eps->nconv+0.3);
    1092:           }
    1093:           *newS = sPres->value + ((sr->dir)*d_prev*eps->nev)/2;
    1094:         } else { /* No values found, no information for next shift */
    1095:           SETERRQ(PetscObjectComm((PetscObject)eps),1,"First shift renders no information");
    1096:         }
    1097:       }
    1098:     } else { /* Accepted values found */
    1099:       sr->nleap = 0;
    1100:       /* Average distance of values in previous subinterval */
    1101:       s = sPres->neighb[0];
    1102:       while (s && PetscAbs(s->inertia - sPres->inertia)==0) {
    1103:         s = s->neighb[0];/* Looking for previous shifts with eigenvalues within */
    1104:       }
    1105:       if (s) {
    1106:         d_prev = PetscAbsReal((sPres->value - s->value)/(sPres->inertia - s->inertia));
    1107:       } else { /* First shift. Average distance obtained with values in this shift */
    1108:         /* first shift might be too far from first wanted eigenvalue (no values found outside the interval)*/
    1109:         if ((sr->dir)*(PetscRealPart(sr->eigr[0])-sPres->value)>0 && PetscAbsReal((PetscRealPart(sr->eigr[sr->indexEig-1]) - PetscRealPart(sr->eigr[0]))/PetscRealPart(sr->eigr[0])) > PetscSqrtReal(eps->tol)) {
    1110:           d_prev =  PetscAbsReal((PetscRealPart(sr->eigr[sr->indexEig-1]) - PetscRealPart(sr->eigr[0])))/(sPres->neigs+0.3);
    1111:         } else {
    1112:           d_prev = PetscAbsReal(PetscRealPart(sr->eigr[sr->indexEig-1]) - sPres->value)/(sPres->neigs+0.3);
    1113:         }
    1114:       }
    1115:       /* Average distance is used for next shift by adding it to value on the right or to shift */
    1116:       if ((sr->dir)*(PetscRealPart(sr->eigr[sPres->index + sPres->neigs -1]) - sPres->value)>0) {
    1117:         *newS = PetscRealPart(sr->eigr[sPres->index + sPres->neigs -1])+ ((sr->dir)*d_prev*(eps->nev))/2;
    1118:       } else { /* Last accepted value is on the left of shift. Adding to shift */
    1119:         *newS = sPres->value + ((sr->dir)*d_prev*(eps->nev))/2;
    1120:       }
    1121:     }
    1122:     /* End of interval can not be surpassed */
    1123:     if ((sr->dir)*(sr->int1 - *newS) < 0) *newS = sr->int1;
    1124:   }/* of neighb[side]==null */
    1125:   return(0);
    1126: }

    1128: /*
    1129:   Function for sorting an array of real values
    1130: */
    1133: static PetscErrorCode sortRealEigenvalues(PetscScalar *r,PetscInt *perm,PetscInt nr,PetscBool prev,PetscInt dir)
    1134: {
    1135:   PetscReal      re;
    1136:   PetscInt       i,j,tmp;

    1139:   if (!prev) for (i=0;i<nr;i++) perm[i] = i;
    1140:   /* Insertion sort */
    1141:   for (i=1;i<nr;i++) {
    1142:     re = PetscRealPart(r[perm[i]]);
    1143:     j = i-1;
    1144:     while (j>=0 && dir*(re - PetscRealPart(r[perm[j]])) <= 0) {
    1145:       tmp = perm[j]; perm[j] = perm[j+1]; perm[j+1] = tmp; j--;
    1146:     }
    1147:   }
    1148:   return(0);
    1149: }

    1151: /* Stores the pairs obtained since the last shift in the global arrays */
    1154: static PetscErrorCode EPSStoreEigenpairs(EPS eps)
    1155: {
    1156:   PetscErrorCode  ierr;
    1157:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
    1158:   PetscReal       lambda,err,norm;
    1159:   PetscInt        i,count;
    1160:   PetscBool       iscayley;
    1161:   EPS_SR          sr = ctx->sr;
    1162:   EPS_shift       sPres;
    1163:   Vec             v,w;

    1166:   sPres = sr->sPres;
    1167:   sPres->index = sr->indexEig;
    1168:   count = sr->indexEig;
    1169:   /* Back-transform */
    1170:   STBackTransform(eps->st,eps->nconv,eps->eigr,eps->eigi);
    1171:   PetscObjectTypeCompare((PetscObject)eps->st,STCAYLEY,&iscayley);
    1172:   /* Sort eigenvalues */
    1173:   sortRealEigenvalues(eps->eigr,eps->perm,eps->nconv,PETSC_FALSE,sr->dir);
    1174:   /* Values stored in global array */
    1175:   for (i=0;i<eps->nconv;i++) {
    1176:     lambda = PetscRealPart(eps->eigr[eps->perm[i]]);
    1177:     err = eps->errest[eps->perm[i]];

    1179:     if ((sr->dir)*(lambda - sPres->ext[0]) > 0 && (sr->dir)*(sPres->ext[1] - lambda) > 0) {/* Valid value */
    1180:       if (count>=sr->numEigs) SETERRQ(PetscObjectComm((PetscObject)eps),1,"Unexpected error in Spectrum Slicing");
    1181:       sr->eigr[count] = lambda;
    1182:       sr->errest[count] = err;
    1183:       /* Explicit purification */
    1184:       if (eps->purify) {
    1185:         BVGetColumn(sr->V,count,&v);
    1186:         BVGetColumn(eps->V,eps->perm[i],&w);
    1187:         STApply(eps->st,w,v);
    1188:         BVRestoreColumn(sr->V,count,&v);
    1189:         BVRestoreColumn(eps->V,eps->perm[i],&w);
    1190:         BVNormColumn(sr->V,count,NORM_2,&norm);
    1191:         BVScaleColumn(sr->V,count,1.0/norm);
    1192:       } else {
    1193:         BVGetColumn(eps->V,eps->perm[i],&w);
    1194:         BVInsertVec(sr->V,count,w);
    1195:         BVRestoreColumn(eps->V,eps->perm[i],&w);
    1196:         BVNormColumn(sr->V,count,NORM_2,&norm);
    1197:         BVScaleColumn(sr->V,count,1.0/norm);
    1198:       }
    1199:       count++;
    1200:     }
    1201:   }
    1202:   sPres->neigs = count - sr->indexEig;
    1203:   sr->indexEig = count;
    1204:   /* Global ordering array updating */
    1205:   sortRealEigenvalues(sr->eigr,sr->perm,count,PETSC_TRUE,sr->dir);
    1206:   return(0);
    1207: }

    1211: static PetscErrorCode EPSLookForDeflation(EPS eps)
    1212: {
    1213:   PetscErrorCode  ierr;
    1214:   PetscReal       val;
    1215:   PetscInt        i,count0=0,count1=0;
    1216:   EPS_shift       sPres;
    1217:   PetscInt        ini,fin,k,idx0,idx1;
    1218:   EPS_SR          sr;
    1219:   Vec             v;
    1220:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;

    1223:   sr = ctx->sr;
    1224:   sPres = sr->sPres;

    1226:   if (sPres->neighb[0]) ini = (sr->dir)*(sPres->neighb[0]->inertia - sr->inertia0);
    1227:   else ini = 0;
    1228:   fin = sr->indexEig;
    1229:   /* Selection of ends for searching new values */
    1230:   if (!sPres->neighb[0]) sPres->ext[0] = sr->int0;/* First shift */
    1231:   else sPres->ext[0] = sPres->neighb[0]->value;
    1232:   if (!sPres->neighb[1]) {
    1233:     if (sr->hasEnd) sPres->ext[1] = sr->int1;
    1234:     else sPres->ext[1] = (sr->dir > 0)?PETSC_MAX_REAL:PETSC_MIN_REAL;
    1235:   } else sPres->ext[1] = sPres->neighb[1]->value;
    1236:   /* Selection of values between right and left ends */
    1237:   for (i=ini;i<fin;i++) {
    1238:     val=PetscRealPart(sr->eigr[sr->perm[i]]);
    1239:     /* Values to the right of left shift */
    1240:     if ((sr->dir)*(val - sPres->ext[1]) < 0) {
    1241:       if ((sr->dir)*(val - sPres->value) < 0) count0++;
    1242:       else count1++;
    1243:     } else break;
    1244:   }
    1245:   /* The number of values on each side are found */
    1246:   if (sPres->neighb[0]) {
    1247:     sPres->nsch[0] = (sr->dir)*(sPres->inertia - sPres->neighb[0]->inertia)-count0;
    1248:     if (sPres->nsch[0]<0)SETERRQ(PetscObjectComm((PetscObject)eps),1,"Mismatch between number of values found and information from inertia, consider using EPSKrylovSchurSetDetectZeros()");
    1249:   } else sPres->nsch[0] = 0;

    1251:   if (sPres->neighb[1]) {
    1252:     sPres->nsch[1] = (sr->dir)*(sPres->neighb[1]->inertia - sPres->inertia) - count1;
    1253:     if (sPres->nsch[1]<0)SETERRQ(PetscObjectComm((PetscObject)eps),1,"Mismatch between number of values found and information from inertia, consider using EPSKrylovSchurSetDetectZeros()");
    1254:   } else sPres->nsch[1] = (sr->dir)*(sr->inertia1 - sPres->inertia);

    1256:   /* Completing vector of indexes for deflation */
    1257:   idx0 = ini;
    1258:   idx1 = ini+count0+count1;
    1259:   k=0;
    1260:   for (i=idx0;i<idx1;i++) sr->idxDef[k++]=sr->perm[i];
    1261:   BVDuplicateResize(eps->V,k+eps->ncv+1,&sr->Vnext);
    1262:   BVSetNumConstraints(sr->Vnext,k);
    1263:   for (i=0;i<k;i++) {
    1264:     BVGetColumn(sr->Vnext,-i-1,&v);
    1265:     BVCopyVec(sr->V,sr->idxDef[i],v);
    1266:     BVRestoreColumn(sr->Vnext,-i-1,&v);
    1267:   }

    1269:   /* For rational Krylov */
    1270:   if (sr->nS>0 && (sr->sPrev == sr->sPres->neighb[0] || sr->sPrev == sr->sPres->neighb[1])) {
    1271:     EPSPrepareRational(eps);
    1272:   }
    1273:   eps->nconv = 0;
    1274:   /* Get rid of temporary Vnext */
    1275:   BVDestroy(&eps->V);
    1276:   eps->V = sr->Vnext;
    1277:   sr->Vnext = NULL;
    1278:   return(0);
    1279: }

    1283: PetscErrorCode EPSSolve_KrylovSchur_Slice(EPS eps)
    1284: {
    1285:   PetscErrorCode  ierr;
    1286:   PetscInt        i,lds;
    1287:   PetscReal       newS;
    1288:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
    1289:   EPS_SR          sr=ctx->sr;

    1292:   if (ctx->global) {
    1293:     EPSSolve_KrylovSchur_Slice(ctx->eps);
    1294:     ctx->eps->state = EPS_STATE_SOLVED;
    1295:     eps->reason = EPS_CONVERGED_TOL;
    1296:     if (ctx->npart>1) {
    1297:       /* Gather solution from subsolvers */
    1298:       EPSSliceGatherSolution(eps);
    1299:     } else {
    1300:       eps->nconv = sr->numEigs;
    1301:       eps->its   = ctx->eps->its;
    1302:       PetscFree(ctx->inertias);
    1303:       PetscFree(ctx->shifts);
    1304:       EPSSliceGetInertias(ctx->eps,&ctx->nshifts,&ctx->shifts,&ctx->inertias);
    1305:     }
    1306:   } else {
    1307:     if (ctx->npart==1) {
    1308:       sr->eigr   = ctx->eps->eigr;
    1309:       sr->eigi   = ctx->eps->eigi;
    1310:       sr->perm   = ctx->eps->perm;
    1311:       sr->errest = ctx->eps->errest;
    1312:       sr->V      = ctx->eps->V;
    1313:     }
    1314:     /* Only with eigenvalues present in the interval ...*/
    1315:     if (sr->numEigs==0) {
    1316:       eps->reason = EPS_CONVERGED_TOL;
    1317:       return(0);
    1318:     }
    1319:     /* Array of pending shifts */
    1320:     sr->maxPend = 100; /* Initial size */
    1321:     sr->nPend = 0;
    1322:     PetscMalloc1(sr->maxPend,&sr->pending);
    1323:     PetscLogObjectMemory((PetscObject)eps,(sr->maxPend)*sizeof(EPS_shift));
    1324:     EPSCreateShift(eps,sr->int0,NULL,NULL);
    1325:     /* extract first shift */
    1326:     sr->sPrev = NULL;
    1327:     sr->sPres = sr->pending[--sr->nPend];
    1328:     sr->sPres->inertia = sr->inertia0;
    1329:     eps->target = sr->sPres->value;
    1330:     sr->s0 = sr->sPres;
    1331:     sr->indexEig = 0;
    1332:     /* Memory reservation for auxiliary variables */
    1333:     lds = PetscMin(eps->mpd,eps->ncv);
    1334:     PetscCalloc1(lds*lds,&sr->S);
    1335:     PetscMalloc1(eps->ncv,&sr->back);
    1336:     PetscLogObjectMemory((PetscObject)eps,(sr->numEigs+2*eps->ncv)*sizeof(PetscScalar));
    1337:     for (i=0;i<sr->numEigs;i++) {
    1338:       sr->eigr[i]   = 0.0;
    1339:       sr->eigi[i]   = 0.0;
    1340:       sr->errest[i] = 0.0;
    1341:       sr->perm[i]   = i;
    1342:     }
    1343:     /* Vectors for deflation */
    1344:     PetscMalloc1(sr->numEigs,&sr->idxDef);
    1345:     PetscLogObjectMemory((PetscObject)eps,sr->numEigs*sizeof(PetscInt));
    1346:     sr->indexEig = 0;
    1347:     /* Main loop */
    1348:     while (sr->sPres) {
    1349:       /* Search for deflation */
    1350:       EPSLookForDeflation(eps);
    1351:       /* KrylovSchur */
    1352:       EPSKrylovSchur_Slice(eps);

    1354:       EPSStoreEigenpairs(eps);
    1355:       /* Select new shift */
    1356:       if (!sr->sPres->comp[1]) {
    1357:         EPSGetNewShiftValue(eps,1,&newS);
    1358:         EPSCreateShift(eps,newS,sr->sPres,sr->sPres->neighb[1]);
    1359:       }
    1360:       if (!sr->sPres->comp[0]) {
    1361:         /* Completing earlier interval */
    1362:         EPSGetNewShiftValue(eps,0,&newS);
    1363:         EPSCreateShift(eps,newS,sr->sPres->neighb[0],sr->sPres);
    1364:       }
    1365:       /* Preparing for a new search of values */
    1366:       EPSExtractShift(eps);
    1367:     }

    1369:     /* Updating eps values prior to exit */
    1370:     PetscFree(sr->S);
    1371:     PetscFree(sr->idxDef);
    1372:     PetscFree(sr->pending);
    1373:     PetscFree(sr->back);
    1374:     BVDuplicateResize(eps->V,eps->ncv+1,&sr->Vnext);
    1375:     BVSetNumConstraints(sr->Vnext,0);
    1376:     BVDestroy(&eps->V);
    1377:     eps->V      = sr->Vnext;
    1378:     eps->nconv  = sr->indexEig;
    1379:     eps->reason = EPS_CONVERGED_TOL;
    1380:     eps->its    = sr->itsKs;
    1381:     eps->nds    = 0;
    1382:   }
    1383:   return(0);
    1384: }