Date: 2017-05-17T08:25:49+00:00

Actual source code: ks-slice.c
slepc-3.7.4 2017-05-17
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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) 2002-2016, 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: static PetscBool  cited = PETSC_FALSE;
     41: static const char citation[] =
     42:   "@Article{slepc-slice,\n"
     43:   "   author = \"C. Campos and J. E. Roman\",\n"
     44:   "   title = \"Strategies for spectrum slicing based on restarted {Lanczos} methods\",\n"
     45:   "   journal = \"Numer. Algorithms\",\n"
     46:   "   volume = \"60\",\n"
     47:   "   number = \"2\",\n"
     48:   "   pages = \"279--295\",\n"
     49:   "   year = \"2012,\"\n"
     50:   "   doi = \"http://dx.doi.org/10.1007/s11075-012-9564-z\"\n"
     51:   "}\n";

     53: #define SLICE_PTOL PETSC_SQRT_MACHINE_EPSILON

     57: static PetscErrorCode EPSSliceResetSR(EPS eps) {
     58:   PetscErrorCode  ierr;
     59:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
     60:   EPS_SR          sr=ctx->sr;
     61:   EPS_shift       s;

     64:   if (sr) {
     65:     if (ctx->npart>1) {
     66:       BVDestroy(&sr->V);
     67:       PetscFree4(sr->eigr,sr->eigi,sr->errest,sr->perm);
     68:     }
     69:     /* Reviewing list of shifts to free memory */
     70:     s = sr->s0;
     71:     if (s) {
     72:       while (s->neighb[1]) {
     73:         s = s->neighb[1];
     74:         PetscFree(s->neighb[0]);
     75:       }
     76:       PetscFree(s);
     77:     }
     78:     PetscFree(sr);
     79:   }
     80:   ctx->sr = NULL;
     81:   return(0);
     82: }

     86: PetscErrorCode EPSReset_KrylovSchur_Slice(EPS eps)
     87: {
     88:   PetscErrorCode  ierr;
     89:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;

     92:   if (!ctx->global) return(0);
     93:   /* Destroy auxiliary EPS */
     94:   EPSSliceResetSR(ctx->eps);
     95:   EPSDestroy(&ctx->eps);
     96:   if (ctx->npart>1) {
     97:     PetscSubcommDestroy(&ctx->subc);
     98:     if (ctx->commset) {
     99:       MPI_Comm_free(&ctx->commrank);
    100:       ctx->commset = PETSC_FALSE;
    101:     }
    102:   }
    103:   PetscFree(ctx->subintervals);
    104:   PetscFree(ctx->nconv_loc);
    105:   EPSSliceResetSR(eps);
    106:   PetscFree(ctx->inertias);
    107:   PetscFree(ctx->shifts);
    108:   if (ctx->npart>1) {
    109:     ISDestroy(&ctx->isrow);
    110:     ISDestroy(&ctx->iscol);
    111:     MatDestroyMatrices(1,&ctx->submata);
    112:     MatDestroyMatrices(1,&ctx->submatb);
    113:   }
    114:   return(0);
    115: }

    119: /*
    120:   EPSSliceAllocateSolution - Allocate memory storage for common variables such
    121:   as eigenvalues and eigenvectors. The argument extra is used for methods
    122:   that require a working basis slightly larger than ncv.
    123: */
    124: static PetscErrorCode EPSSliceAllocateSolution(EPS eps,PetscInt extra)
    125: {
    126:   PetscErrorCode     ierr;
    127:   EPS_KRYLOVSCHUR    *ctx=(EPS_KRYLOVSCHUR*)eps->data;
    128:   PetscReal          eta;
    129:   PetscInt           k;
    130:   PetscLogDouble     cnt;
    131:   BVType             type;
    132:   BVOrthogType       orthog_type;
    133:   BVOrthogRefineType orthog_ref;
    134:   BVOrthogBlockType  ob_type;
    135:   Mat                matrix;
    136:   Vec                t;
    137:   EPS_SR             sr = ctx->sr;

    140:   /* allocate space for eigenvalues and friends */
    141:   k = PetscMax(1,sr->numEigs);
    142:   PetscFree4(sr->eigr,sr->eigi,sr->errest,sr->perm);
    143:   PetscMalloc4(k,&sr->eigr,k,&sr->eigi,k,&sr->errest,k,&sr->perm);
    144:   cnt = 2*k*sizeof(PetscScalar) + 2*k*sizeof(PetscReal) + k*sizeof(PetscInt);
    145:   PetscLogObjectMemory((PetscObject)eps,cnt);

    147:   /* allocate sr->V and transfer options from eps->V */
    148:   BVDestroy(&sr->V);
    149:   BVCreate(PetscObjectComm((PetscObject)eps),&sr->V);
    150:   PetscLogObjectParent((PetscObject)eps,(PetscObject)sr->V);
    151:   if (!eps->V) { EPSGetBV(eps,&eps->V); }
    152:   if (!((PetscObject)(eps->V))->type_name) {
    153:     BVSetType(sr->V,BVSVEC);
    154:   } else {
    155:     BVGetType(eps->V,&type);
    156:     BVSetType(sr->V,type);
    157:   }
    158:   STMatCreateVecs(eps->st,&t,NULL);
    159:   BVSetSizesFromVec(sr->V,t,k);
    160:   VecDestroy(&t);
    161:   EPS_SetInnerProduct(eps);
    162:   BVGetMatrix(eps->V,&matrix,NULL);
    163:   BVSetMatrix(sr->V,matrix,PETSC_FALSE);
    164:   BVGetOrthogonalization(eps->V,&orthog_type,&orthog_ref,&eta,&ob_type);
    165:   BVSetOrthogonalization(sr->V,orthog_type,orthog_ref,eta,ob_type);
    166:   return(0);
    167: }

    171: static PetscErrorCode EPSSliceGetEPS(EPS eps)
    172: {
    173:   PetscErrorCode     ierr;
    174:   EPS_KRYLOVSCHUR    *ctx=(EPS_KRYLOVSCHUR*)eps->data,*ctx_local;
    175:   BV                 V;
    176:   BVType             type;
    177:   PetscReal          eta;
    178:   BVOrthogType       orthog_type;
    179:   BVOrthogRefineType orthog_ref;
    180:   BVOrthogBlockType  ob_type;
    181:   Mat                A,B=NULL,Ar,Br=NULL;
    182:   PetscInt           i;
    183:   PetscReal          h,a,b;
    184:   PetscMPIInt        rank;
    185:   EPS_SR             sr=ctx->sr;
    186:   PC                 pc;
    187:   PCType             pctype;
    188:   KSP                ksp;
    189:   KSPType            ksptype;
    190:   STType             sttype;
    191:   PetscObjectState   Astate,Bstate=0;
    192:   PetscObjectId      Aid,Bid=0;
    193:   const MatSolverPackage stype;

    196:   EPSGetOperators(eps,&A,&B);
    197:   if (ctx->npart==1) {
    198:     if (!ctx->eps) { EPSCreate(((PetscObject)eps)->comm,&ctx->eps); }
    199:     EPSSetType(ctx->eps,((PetscObject)eps)->type_name);
    200:     EPSSetOperators(ctx->eps,A,B);
    201:     a = eps->inta; b = eps->intb;
    202:   } else {
    203:     PetscObjectStateGet((PetscObject)A,&Astate);
    204:     PetscObjectGetId((PetscObject)A,&Aid);
    205:     if (B) {
    206:       PetscObjectStateGet((PetscObject)B,&Bstate);
    207:       PetscObjectGetId((PetscObject)B,&Bid);
    208:     }
    209:     if (!ctx->subc) {
    210:       /* Create context for subcommunicators */
    211:       PetscSubcommCreate(PetscObjectComm((PetscObject)eps),&ctx->subc);
    212:       PetscSubcommSetNumber(ctx->subc,ctx->npart);
    213:       PetscSubcommSetType(ctx->subc,PETSC_SUBCOMM_CONTIGUOUS);
    214:       PetscLogObjectMemory((PetscObject)eps,sizeof(PetscSubcomm));

    216:       /* Duplicate matrices */
    217:       MatCreateRedundantMatrix(A,0,PetscSubcommChild(ctx->subc),MAT_INITIAL_MATRIX,&Ar);
    218:       ctx->Astate = Astate;
    219:       ctx->Aid = Aid;
    220:       if (B) {
    221:         MatCreateRedundantMatrix(B,0,PetscSubcommChild(ctx->subc),MAT_INITIAL_MATRIX,&Br);
    222:         ctx->Bstate = Bstate;
    223:         ctx->Bid = Bid;
    224:       }
    225:     } else {
    226:       if (ctx->Astate != Astate || (B && ctx->Bstate != Bstate) || ctx->Aid != Aid || (B && ctx->Bid != Bid)) {
    227:         EPSGetOperators(ctx->eps,&Ar,&Br);
    228:         MatCreateRedundantMatrix(A,0,PetscSubcommChild(ctx->subc),MAT_INITIAL_MATRIX,&Ar);
    229:         ctx->Astate = Astate;
    230:         ctx->Aid = Aid;
    231:         if (B) {
    232:           MatCreateRedundantMatrix(B,0,PetscSubcommChild(ctx->subc),MAT_INITIAL_MATRIX,&Br);
    233:           ctx->Bstate = Bstate;
    234:           ctx->Bid = Bid;
    235:         }
    236:         EPSSetOperators(ctx->eps,Ar,Br);
    237:         MatDestroy(&Ar);
    238:         MatDestroy(&Br);
    239:       }
    240:     }

    242:     /* Determine subintervals */
    243:     if (!ctx->subintset) { /* uniform distribution if no set by user */
    244:       if (!sr->hasEnd) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"Global interval must be bounded for splitting it in uniform subintervals");
    245:       h = (eps->intb-eps->inta)/ctx->npart;
    246:       a = eps->inta+ctx->subc->color*h;
    247:       b = (ctx->subc->color==ctx->npart-1)?eps->intb:eps->inta+(ctx->subc->color+1)*h;
    248:       PetscFree(ctx->subintervals);
    249:       PetscMalloc1(ctx->npart+1,&ctx->subintervals);
    250:       for (i=0;i<ctx->npart;i++) ctx->subintervals[i] = eps->inta+h*i;
    251:       ctx->subintervals[ctx->npart] = eps->intb;
    252:     } else {
    253:       a = ctx->subintervals[ctx->subc->color];
    254:       b = ctx->subintervals[ctx->subc->color+1];
    255:     }

    257:     if (!ctx->eps) {
    258:       /* Create auxiliary EPS */
    259:       EPSCreate(PetscSubcommChild(ctx->subc),&ctx->eps);
    260:       EPSSetOperators(ctx->eps,Ar,Br);
    261:       MatDestroy(&Ar);
    262:       MatDestroy(&Br);
    263:     }

    265:     /* Create subcommunicator grouping processes with same rank */
    266:     if (ctx->commset) { MPI_Comm_free(&ctx->commrank); }
    267:     MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);
    268:     MPI_Comm_split(((PetscObject)eps)->comm,rank,ctx->subc->color,&ctx->commrank);
    269:     ctx->commset = PETSC_TRUE;
    270:   }
    271:   EPSSetType(ctx->eps,((PetscObject)eps)->type_name);

    273:   /* Transfer options for ST, KSP and PC */
    274:   STGetType(eps->st,&sttype);
    275:   STSetType(ctx->eps->st,sttype);
    276:   STGetKSP(eps->st,&ksp);
    277:   KSPGetType(ksp,&ksptype);
    278:   KSPGetPC(ksp,&pc);
    279:   PCGetType(pc,&pctype);
    280:   PCFactorGetMatSolverPackage(pc,&stype);
    281:   STGetKSP(ctx->eps->st,&ksp);
    282:   KSPSetType(ksp,ksptype);
    283:   KSPGetPC(ksp,&pc);
    284:   PCSetType(pc,pctype);
    285:   if (stype) { PCFactorSetMatSolverPackage(pc,stype); }

    287:   EPSSetConvergenceTest(ctx->eps,eps->conv);
    288:   EPSSetInterval(ctx->eps,a,b);
    289:   ctx_local = (EPS_KRYLOVSCHUR*)ctx->eps->data;
    290:   ctx_local->npart = ctx->npart;
    291:   ctx_local->detect = ctx->detect;
    292:   ctx_local->global = PETSC_FALSE;
    293:   ctx_local->eps = eps;
    294:   ctx_local->subc = ctx->subc;
    295:   ctx_local->commrank = ctx->commrank;

    297:   EPSSetDimensions(ctx->eps,ctx->nev,ctx->ncv,ctx->mpd);
    298:   EPSKrylovSchurSetLocking(ctx->eps,ctx->lock);

    300:   /* transfer options from eps->V */
    301:   EPSGetBV(ctx->eps,&V);
    302:   if (!eps->V) { EPSGetBV(eps,&eps->V); }
    303:   if (!((PetscObject)(eps->V))->type_name) {
    304:     BVSetType(V,BVSVEC);
    305:   } else {
    306:     BVGetType(eps->V,&type);
    307:     BVSetType(V,type);
    308:   }
    309:   BVGetOrthogonalization(eps->V,&orthog_type,&orthog_ref,&eta,&ob_type);
    310:   BVSetOrthogonalization(V,orthog_type,orthog_ref,eta,ob_type);
    311:   ctx->eps->which = eps->which;
    312:   ctx->eps->max_it = eps->max_it;
    313:   ctx->eps->tol = eps->tol;
    314:   ctx->eps->purify = eps->purify;
    315:   if (eps->tol==PETSC_DEFAULT) eps->tol = SLEPC_DEFAULT_TOL;
    316:   EPSSetProblemType(ctx->eps,eps->problem_type);
    317:   EPSSetUp(ctx->eps);
    318:   ctx->eps->nconv = 0;
    319:   ctx->eps->its   = 0;
    320:   for (i=0;i<ctx->eps->ncv;i++) {
    321:     ctx->eps->eigr[i]   = 0.0;
    322:     ctx->eps->eigi[i]   = 0.0;
    323:     ctx->eps->errest[i] = 0.0;
    324:   }
    325:   return(0);
    326: }

    330: static PetscErrorCode EPSSliceGetInertia(EPS eps,PetscReal shift,PetscInt *inertia,PetscInt *zeros)
    331: {
    333:   KSP            ksp;
    334:   PC             pc;
    335:   Mat            F;
    336:   PetscReal      nzshift;

    339:   if (shift >= PETSC_MAX_REAL) { /* Right-open interval */
    340:     if (inertia) *inertia = eps->n;
    341:   } else if (shift <= PETSC_MIN_REAL) {
    342:     if (inertia) *inertia = 0;
    343:     if (zeros) *zeros = 0;
    344:   } else {
    345:     /* If the shift is zero, perturb it to a very small positive value.
    346:        The goal is that the nonzero pattern is the same in all cases and reuse
    347:        the symbolic factorizations */
    348:     nzshift = (shift==0.0)? 10.0/PETSC_MAX_REAL: shift;
    349:     STSetShift(eps->st,nzshift);
    350:     STSetUp(eps->st);
    351:     STGetKSP(eps->st,&ksp);
    352:     KSPGetPC(ksp,&pc);
    353:     PCFactorGetMatrix(pc,&F);
    354:     MatGetInertia(F,inertia,zeros,NULL);
    355:   }
    356:   return(0);
    357: }

    361: PetscErrorCode EPSSetUp_KrylovSchur_Slice(EPS eps)
    362: {
    363:   PetscErrorCode  ierr;
    364:   PetscBool       issinv;
    365:   EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data,*ctx_glob;
    366:   EPS_SR          sr,sr_loc,sr_glob;
    367:   PetscInt        nEigs,dssz=1,i,zeros=0,off=0;
    368:   PetscMPIInt     nproc,rank,aux;
    369:   PetscReal       r;
    370:   MPI_Request     req;
    371:   Mat             A,B=NULL;

    374:   if (ctx->global) {
    375:     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");
    376:     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");
    377:     if (!eps->ishermitian) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Spectrum slicing only available for symmetric/Hermitian eigenproblems");
    378:     if (eps->arbitrary) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Arbitrary selection of eigenpairs cannot be used with spectrum slicing");
    379:     if (!((PetscObject)(eps->st))->type_name) { /* default to shift-and-invert */
    380:       STSetType(eps->st,STSINVERT);
    381:     }
    382:     PetscObjectTypeCompareAny((PetscObject)eps->st,&issinv,STSINVERT,STCAYLEY,"");
    383:     if (!issinv) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Shift-and-invert or Cayley ST is needed for spectrum slicing");
    384:     if (eps->tol==PETSC_DEFAULT) eps->tol = SLEPC_DEFAULT_TOL*1e-2;  /* use tighter tolerance */
    385:     if (!eps->max_it) eps->max_it = 100;
    386:     if (ctx->nev==1) ctx->nev = PetscMin(40,eps->n);  /* nev not set, use default value */
    387:     if (eps->n>10 && ctx->nev<10) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"nev cannot be less than 10 in spectrum slicing runs");
    388:   }
    389:   eps->ops->backtransform = NULL;

    391:   /* create spectrum slicing context and initialize it */
    392:   EPSSliceResetSR(eps);
    393:   PetscNewLog(eps,&sr);
    394:   ctx->sr = sr;
    395:   sr->itsKs = 0;
    396:   sr->nleap = 0;
    397:   sr->nMAXCompl = eps->nev/4;
    398:   sr->iterCompl = eps->max_it/4;
    399:   sr->sPres = NULL;
    400:   sr->nS = 0;

    402:   if (ctx->npart==1 || ctx->global) {
    403:     /* check presence of ends and finding direction */
    404:     if ((eps->inta > PETSC_MIN_REAL && eps->inta != 0.0) || eps->intb >= PETSC_MAX_REAL) {
    405:       sr->int0 = eps->inta;
    406:       sr->int1 = eps->intb;
    407:       sr->dir = 1;
    408:       if (eps->intb >= PETSC_MAX_REAL) { /* Right-open interval */
    409:         sr->hasEnd = PETSC_FALSE;
    410:       } else sr->hasEnd = PETSC_TRUE;
    411:     } else {
    412:       sr->int0 = eps->intb;
    413:       sr->int1 = eps->inta;
    414:       sr->dir = -1;
    415:       sr->hasEnd = PetscNot(eps->inta <= PETSC_MIN_REAL);
    416:     }
    417:   }
    418:   if (ctx->global) {
    419:     /* prevent computation of factorization in global eps */
    420:     STSetTransform(eps->st,PETSC_FALSE);
    421:     EPSSetDimensions_Default(eps,ctx->nev,&ctx->ncv,&ctx->mpd);
    422:     /* create subintervals and initialize auxiliary eps for slicing runs */
    423:     EPSSliceGetEPS(eps);
    424:     sr_loc = ((EPS_KRYLOVSCHUR*)ctx->eps->data)->sr;
    425:     if (ctx->npart>1) {
    426:       if ((sr->dir>0&&ctx->subc->color==0)||(sr->dir<0&&ctx->subc->color==ctx->npart-1)) sr->inertia0 = sr_loc->inertia0;
    427:       MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);
    428:       if (rank==0) {
    429:         MPI_Bcast(&sr->inertia0,1,MPIU_INT,(sr->dir>0)?0:ctx->npart-1,ctx->commrank);
    430:       }
    431:       MPI_Bcast(&sr->inertia0,1,MPIU_INT,0,PetscSubcommChild(ctx->subc));
    432:       PetscFree(ctx->nconv_loc);
    433:       PetscMalloc1(ctx->npart,&ctx->nconv_loc);
    434:       MPI_Comm_size(((PetscObject)eps)->comm,&nproc);
    435:       if (sr->dir<0) off = 1;
    436:       if (nproc%ctx->npart==0) { /* subcommunicators with the same size */
    437:         PetscMPIIntCast(sr_loc->numEigs,&aux);
    438:         MPI_Allgather(&aux,1,MPI_INT,ctx->nconv_loc,1,MPI_INT,ctx->commrank);
    439:         MPI_Allgather(sr_loc->dir==sr->dir?&sr_loc->int0:&sr_loc->int1,1,MPIU_REAL,ctx->subintervals+off,1,MPIU_REAL,ctx->commrank);
    440:       } else {
    441:         MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);
    442:         if (!rank) {
    443:           PetscMPIIntCast(sr_loc->numEigs,&aux);
    444:           MPI_Allgather(&aux,1,MPI_INT,ctx->nconv_loc,1,MPI_INT,ctx->commrank);
    445:           MPI_Allgather(sr_loc->dir==sr->dir?&sr_loc->int0:&sr_loc->int1,1,MPIU_REAL,ctx->subintervals+off,1,MPIU_REAL,ctx->commrank);
    446:         }
    447:         PetscMPIIntCast(ctx->npart,&aux);
    448:         MPI_Bcast(ctx->nconv_loc,aux,MPI_INT,0,PetscSubcommChild(ctx->subc));
    449:         MPI_Bcast(ctx->subintervals+off,aux,MPIU_REAL,0,PetscSubcommChild(ctx->subc));
    450:       }
    451:       nEigs = 0;
    452:       for (i=0;i<ctx->npart;i++) nEigs += ctx->nconv_loc[i];
    453:     } else {
    454:       nEigs = sr_loc->numEigs;
    455:       sr->inertia0 = sr_loc->inertia0;
    456:     }
    457:     sr->inertia1 = sr->inertia0+sr->dir*nEigs;
    458:     sr->numEigs = nEigs;
    459:     eps->nev = nEigs;
    460:     eps->ncv = nEigs;
    461:     eps->mpd = nEigs;
    462:   } else {
    463:     ctx_glob = (EPS_KRYLOVSCHUR*)ctx->eps->data;
    464:     sr_glob = ctx_glob->sr;
    465:     if (ctx->npart>1) {
    466:       sr->dir = sr_glob->dir;
    467:       sr->int0 = (sr->dir==1)?eps->inta:eps->intb;
    468:       sr->int1 = (sr->dir==1)?eps->intb:eps->inta;
    469:       if ((sr->dir>0&&ctx->subc->color==ctx->npart-1)||(sr->dir<0&&ctx->subc->color==0)) sr->hasEnd = sr_glob->hasEnd;
    470:       else sr->hasEnd = PETSC_TRUE;
    471:     }

    473:     /* compute inertia0 */
    474:     EPSSliceGetInertia(eps,sr->int0,&sr->inertia0,ctx->detect?&zeros:NULL);
    475:     if (zeros) { /* error in factorization */
    476:       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");
    477:       else { /* perturb shift */
    478:         sr->int0 *= (1.0+SLICE_PTOL);
    479:         EPSSliceGetInertia(eps,sr->int0,&sr->inertia0,&zeros);
    480:         if (zeros) SETERRQ1(((PetscObject)eps)->comm,PETSC_ERR_CONV_FAILED,"Inertia computation fails in %g",sr->int1);
    481:       }
    482:     }
    483:     if (ctx->npart>1) {
    484:       /* inertia1 is received from neighbour */
    485:       MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);
    486:       if (!rank) {
    487:         if ((sr->dir>0 && ctx->subc->color>0) || (sr->dir<0 && ctx->subc->color<ctx->npart-1)) { /* send inertia0 to neighbour0 */
    488:           MPI_Isend(&(sr->inertia0),1,MPIU_INT,ctx->subc->color-sr->dir,0,ctx->commrank,&req);
    489:           MPI_Isend(&(sr->int0),1,MPIU_REAL,ctx->subc->color-sr->dir,0,ctx->commrank,&req);
    490:         }
    491:         if ((sr->dir>0 && ctx->subc->color<ctx->npart-1)|| (sr->dir<0 && ctx->subc->color>0)) { /* receive inertia1 from neighbour1 */
    492:           MPI_Recv(&(sr->inertia1),1,MPIU_INT,ctx->subc->color+sr->dir,0,ctx->commrank,MPI_STATUS_IGNORE);
    493:           MPI_Recv(&(sr->int1),1,MPIU_REAL,ctx->subc->color+sr->dir,0,ctx->commrank,MPI_STATUS_IGNORE);
    494:         }
    495:       }
    496:       if ((sr->dir>0 && ctx->subc->color<ctx->npart-1)||(sr->dir<0 && ctx->subc->color>0)) {
    497:         MPI_Bcast(&sr->inertia1,1,MPIU_INT,0,PetscSubcommChild(ctx->subc));
    498:         MPI_Bcast(&sr->int1,1,MPIU_REAL,0,PetscSubcommChild(ctx->subc));
    499:       } else sr_glob->inertia1 = sr->inertia1;
    500:     }

    502:     /* last process in eps comm computes inertia1 */
    503:     if (ctx->npart==1 || ((sr->dir>0 && ctx->subc->color==ctx->npart-1) || (sr->dir<0 && ctx->subc->color==0))) {
    504:       EPSSliceGetInertia(eps,sr->int1,&sr->inertia1,ctx->detect?&zeros:NULL);
    505:       if (zeros) SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_USER,"Found singular matrix for the transformed problem in an interval endpoint defined by user");
    506:       if (sr->hasEnd) {
    507:         sr->dir = -sr->dir; r = sr->int0; sr->int0 = sr->int1; sr->int1 = r;
    508:         i = sr->inertia0; sr->inertia0 = sr->inertia1; sr->inertia1 = i;
    509:       }
    510:     }

    512:     /* number of eigenvalues in interval */
    513:     sr->numEigs = (sr->dir)*(sr->inertia1 - sr->inertia0);
    514:     if (ctx->npart>1) {
    515:       /* memory allocate for subinterval eigenpairs */
    516:       EPSSliceAllocateSolution(eps,1);
    517:     }
    518:     dssz = eps->ncv+1;
    519:   }
    520:   DSSetType(eps->ds,DSHEP);
    521:   DSSetCompact(eps->ds,PETSC_TRUE);
    522:   DSAllocate(eps->ds,dssz);
    523:   /* keep state of subcomm matrices to check that the user does not modify them */
    524:   EPSGetOperators(eps,&A,&B);
    525:   PetscObjectStateGet((PetscObject)A,&ctx->Astate);
    526:   PetscObjectGetId((PetscObject)A,&ctx->Aid);
    527:   if (B) {
    528:     PetscObjectStateGet((PetscObject)B,&ctx->Bstate);
    529:     PetscObjectGetId((PetscObject)B,&ctx->Bid);
    530:   } else {
    531:     ctx->Bstate=0;
    532:     ctx->Bid=0;
    533:   }
    534:   return(0);
    535: }

    539: static PetscErrorCode EPSSliceGatherEigenVectors(EPS eps)
    540: {
    541:   PetscErrorCode  ierr;
    542:   Vec             v,vg,v_loc;
    543:   IS              is1,is2;
    544:   VecScatter      vec_sc;
    545:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
    546:   PetscInt        nloc,m0,n0,i,si,idx,*idx1,*idx2,j;
    547:   PetscScalar     *array;
    548:   EPS_SR          sr_loc;
    549:   BV              V_loc;

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

    555:   /* Gather parallel eigenvectors */
    556:   BVGetColumn(eps->V,0,&v);
    557:   VecGetOwnershipRange(v,&n0,&m0);
    558:   BVRestoreColumn(eps->V,0,&v);
    559:   BVGetColumn(ctx->eps->V,0,&v);
    560:   VecGetLocalSize(v,&nloc);
    561:   BVRestoreColumn(ctx->eps->V,0,&v);
    562:   PetscMalloc2(m0-n0,&idx1,m0-n0,&idx2);
    563:   VecCreateMPI(PetscObjectComm((PetscObject)eps),nloc,PETSC_DECIDE,&vg);
    564:   idx = -1;
    565:   for (si=0;si<ctx->npart;si++) {
    566:     j = 0;
    567:     for (i=n0;i<m0;i++) {
    568:       idx1[j]   = i;
    569:       idx2[j++] = i+eps->n*si;
    570:     }
    571:     ISCreateGeneral(PetscObjectComm((PetscObject)eps),(m0-n0),idx1,PETSC_COPY_VALUES,&is1);
    572:     ISCreateGeneral(PetscObjectComm((PetscObject)eps),(m0-n0),idx2,PETSC_COPY_VALUES,&is2);
    573:     BVGetColumn(eps->V,0,&v);
    574:     VecScatterCreate(v,is1,vg,is2,&vec_sc);
    575:     BVRestoreColumn(eps->V,0,&v);
    576:     ISDestroy(&is1);
    577:     ISDestroy(&is2);
    578:     for (i=0;i<ctx->nconv_loc[si];i++) {
    579:       BVGetColumn(eps->V,++idx,&v);
    580:       if (ctx->subc->color==si) {
    581:         BVGetColumn(V_loc,i,&v_loc);
    582:         VecGetArray(v_loc,&array);
    583:         VecPlaceArray(vg,array);
    584:       }
    585:       VecScatterBegin(vec_sc,vg,v,INSERT_VALUES,SCATTER_REVERSE);
    586:       VecScatterEnd(vec_sc,vg,v,INSERT_VALUES,SCATTER_REVERSE);
    587:       if (ctx->subc->color==si) {
    588:         VecResetArray(vg);
    589:         VecRestoreArray(v_loc,&array);
    590:         BVRestoreColumn(V_loc,i,&v_loc);
    591:       }
    592:       BVRestoreColumn(eps->V,idx,&v);
    593:     }
    594:     VecScatterDestroy(&vec_sc);
    595:   }
    596:   PetscFree2(idx1,idx2);
    597:   VecDestroy(&vg);
    598:   return(0);
    599: }

    603: /*
    604:   EPSComputeVectors_Slice - Recover Eigenvectors from subcomunicators
    605:  */
    606: PetscErrorCode EPSComputeVectors_Slice(EPS eps)
    607: {
    608:   PetscErrorCode  ierr;
    609:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;

    612:   if (ctx->global && ctx->npart>1) {
    613:     EPSComputeVectors(ctx->eps);
    614:     EPSSliceGatherEigenVectors(eps);
    615:   }
    616:   return(0);
    617: }

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

    623: static PetscErrorCode EPSSliceGetInertias(EPS eps,PetscInt *n,PetscReal **shifts,PetscInt **inertias)
    624: {
    625:   PetscErrorCode  ierr;
    626:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
    627:   PetscInt        i=0,j,tmpi;
    628:   PetscReal       v,tmpr;
    629:   EPS_shift       s;

    632:   if (!eps->state) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONGSTATE,"Must call EPSSetUp() first");
    633:   if (!ctx->sr) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONGSTATE,"Only available in interval computations, see EPSSetInterval()");
    634:   if (!ctx->sr->s0) {  /* EPSSolve not called yet */
    635:     *n = 2;
    636:   } else {
    637:     *n = 1;
    638:     s = ctx->sr->s0;
    639:     while (s) {
    640:       (*n)++;
    641:       s = s->neighb[1];
    642:     }
    643:   }
    644:   PetscMalloc1(*n,shifts);
    645:   PetscMalloc1(*n,inertias);
    646:   if (!ctx->sr->s0) {  /* EPSSolve not called yet */
    647:     (*shifts)[0]   = ctx->sr->int0;
    648:     (*shifts)[1]   = ctx->sr->int1;
    649:     (*inertias)[0] = ctx->sr->inertia0;
    650:     (*inertias)[1] = ctx->sr->inertia1;
    651:   } else {
    652:     s = ctx->sr->s0;
    653:     while (s) {
    654:       (*shifts)[i]     = s->value;
    655:       (*inertias)[i++] = s->inertia;
    656:       s = s->neighb[1];
    657:     }
    658:     (*shifts)[i]   = ctx->sr->int1;
    659:     (*inertias)[i] = ctx->sr->inertia1;
    660:   }
    661:   /* remove possible duplicate in last position */
    662:   if ((*shifts)[(*n)-1]==(*shifts)[(*n)-2]) (*n)--;
    663:   /* sort result */
    664:   for (i=0;i<*n;i++) {
    665:     v = (*shifts)[i];
    666:     for (j=i+1;j<*n;j++) {
    667:       if (v > (*shifts)[j]) {
    668:         SWAP((*shifts)[i],(*shifts)[j],tmpr);
    669:         SWAP((*inertias)[i],(*inertias)[j],tmpi);
    670:         v = (*shifts)[i];
    671:       }
    672:     }
    673:   }
    674:   return(0);
    675: }

    679: static PetscErrorCode EPSSliceGatherSolution(EPS eps)
    680: {
    681:   PetscErrorCode  ierr;
    682:   PetscMPIInt     rank,nproc;
    683:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
    684:   PetscInt        i,idx,j;
    685:   PetscInt        *perm_loc,off=0,*inertias_loc,ns;
    686:   PetscScalar     *eigr_loc;
    687:   EPS_SR          sr_loc;
    688:   PetscReal       *shifts_loc;
    689:   PetscMPIInt     *disp,*ns_loc,aux;

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

    696:   /* Gather the shifts used and the inertias computed */
    697:   EPSSliceGetInertias(ctx->eps,&ns,&shifts_loc,&inertias_loc);
    698:   if (ctx->sr->dir>0 && shifts_loc[ns-1]==sr_loc->int1 && ctx->subc->color<ctx->npart-1) ns--;
    699:   if (ctx->sr->dir<0 && shifts_loc[ns-1]==sr_loc->int0 && ctx->subc->color>0) {
    700:     ns--;
    701:     for (i=0;i<ns;i++) {
    702:       inertias_loc[i] = inertias_loc[i+1];
    703:       shifts_loc[i] = shifts_loc[i+1];
    704:     }
    705:   }
    706:   PetscMalloc1(ctx->npart,&ns_loc);
    707:   MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);
    708:   PetscMPIIntCast(ns,&aux);
    709:   if (rank==0) { MPI_Allgather(&aux,1,MPI_INT,ns_loc,1,MPI_INT,ctx->commrank); }
    710:   PetscMPIIntCast(ctx->npart,&aux);
    711:   MPI_Bcast(ns_loc,aux,MPI_INT,0,PetscSubcommChild(ctx->subc));
    712:   ctx->nshifts = 0;
    713:   for (i=0;i<ctx->npart;i++) ctx->nshifts += ns_loc[i];
    714:   PetscFree(ctx->inertias);
    715:   PetscFree(ctx->shifts);
    716:   PetscMalloc1(ctx->nshifts,&ctx->inertias);
    717:   PetscMalloc1(ctx->nshifts,&ctx->shifts);

    719:   /* Gather eigenvalues (same ranks have fully set of eigenvalues)*/
    720:   eigr_loc = sr_loc->eigr;
    721:   perm_loc = sr_loc->perm;
    722:   MPI_Comm_size(((PetscObject)eps)->comm,&nproc);
    723:   PetscMalloc1(ctx->npart,&disp);
    724:   disp[0] = 0;
    725:   for (i=1;i<ctx->npart;i++) disp[i] = disp[i-1]+ctx->nconv_loc[i-1];
    726:   if (nproc%ctx->npart==0) { /* subcommunicators with the same size */
    727:     PetscMPIIntCast(sr_loc->numEigs,&aux);
    728:     MPI_Allgatherv(eigr_loc,aux,MPIU_SCALAR,eps->eigr,ctx->nconv_loc,disp,MPIU_SCALAR,ctx->commrank); /* eigenvalues */
    729:     MPI_Allgatherv(perm_loc,aux,MPIU_INT,eps->perm,ctx->nconv_loc,disp,MPIU_INT,ctx->commrank); /* perm */
    730:     for (i=1;i<ctx->npart;i++) disp[i] = disp[i-1]+ns_loc[i-1];
    731:     PetscMPIIntCast(ns,&aux);
    732:     MPI_Allgatherv(shifts_loc,aux,MPIU_REAL,ctx->shifts,ns_loc,disp,MPIU_REAL,ctx->commrank); /* shifts */
    733:     MPI_Allgatherv(inertias_loc,aux,MPIU_INT,ctx->inertias,ns_loc,disp,MPIU_INT,ctx->commrank); /* inertias */
    734:     MPI_Allreduce(&sr_loc->itsKs,&eps->its,1,MPIU_INT,MPI_SUM,ctx->commrank);
    735:   } else { /* subcommunicators with different size */
    736:     MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);
    737:     if (rank==0) {
    738:       PetscMPIIntCast(sr_loc->numEigs,&aux);
    739:       MPI_Allgatherv(eigr_loc,aux,MPIU_SCALAR,eps->eigr,ctx->nconv_loc,disp,MPIU_SCALAR,ctx->commrank); /* eigenvalues */
    740:       MPI_Allgatherv(perm_loc,aux,MPIU_INT,eps->perm,ctx->nconv_loc,disp,MPIU_INT,ctx->commrank); /* perm */
    741:       for (i=1;i<ctx->npart;i++) disp[i] = disp[i-1]+ns_loc[i-1];
    742:       PetscMPIIntCast(ns,&aux);
    743:       MPI_Allgatherv(shifts_loc,aux,MPIU_REAL,ctx->shifts,ns_loc,disp,MPIU_REAL,ctx->commrank); /* shifts */
    744:       MPI_Allgatherv(inertias_loc,aux,MPIU_INT,ctx->inertias,ns_loc,disp,MPIU_INT,ctx->commrank); /* inertias */
    745:       MPI_Allreduce(&sr_loc->itsKs,&eps->its,1,MPIU_INT,MPI_SUM,ctx->commrank);
    746:     }
    747:     PetscMPIIntCast(eps->nconv,&aux);
    748:     MPI_Bcast(eps->eigr,aux,MPIU_SCALAR,0,PetscSubcommChild(ctx->subc));
    749:     MPI_Bcast(eps->perm,aux,MPIU_INT,0,PetscSubcommChild(ctx->subc));
    750:     MPI_Bcast(ctx->shifts,ctx->nshifts,MPIU_REAL,0,PetscSubcommChild(ctx->subc));
    751:     PetscMPIIntCast(ctx->nshifts,&aux);
    752:     MPI_Bcast(ctx->inertias,aux,MPIU_INT,0,PetscSubcommChild(ctx->subc));
    753:     MPI_Bcast(&eps->its,1,MPIU_INT,0,PetscSubcommChild(ctx->subc));
    754:   }
    755:   /* Update global array eps->perm */
    756:   idx = ctx->nconv_loc[0];
    757:   for (i=1;i<ctx->npart;i++) {
    758:     off += ctx->nconv_loc[i-1];
    759:     for (j=0;j<ctx->nconv_loc[i];j++) eps->perm[idx++] += off;
    760:   }

    762:   /* Gather parallel eigenvectors */
    763:   PetscFree(ns_loc);
    764:   PetscFree(disp);
    765:   PetscFree(shifts_loc);
    766:   PetscFree(inertias_loc);
    767:   return(0);
    768: }

    770: /*
    771:    Fills the fields of a shift structure
    772: */
    775: static PetscErrorCode EPSCreateShift(EPS eps,PetscReal val,EPS_shift neighb0,EPS_shift neighb1)
    776: {
    777:   PetscErrorCode  ierr;
    778:   EPS_shift       s,*pending2;
    779:   PetscInt        i;
    780:   EPS_SR          sr;
    781:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;

    784:   sr = ctx->sr;
    785:   PetscNewLog(eps,&s);
    786:   s->value = val;
    787:   s->neighb[0] = neighb0;
    788:   if (neighb0) neighb0->neighb[1] = s;
    789:   s->neighb[1] = neighb1;
    790:   if (neighb1) neighb1->neighb[0] = s;
    791:   s->comp[0] = PETSC_FALSE;
    792:   s->comp[1] = PETSC_FALSE;
    793:   s->index = -1;
    794:   s->neigs = 0;
    795:   s->nconv[0] = s->nconv[1] = 0;
    796:   s->nsch[0] = s->nsch[1]=0;
    797:   /* Inserts in the stack of pending shifts */
    798:   /* If needed, the array is resized */
    799:   if (sr->nPend >= sr->maxPend) {
    800:     sr->maxPend *= 2;
    801:     PetscMalloc1(sr->maxPend,&pending2);
    802:     PetscLogObjectMemory((PetscObject)eps,sizeof(EPS_shift));
    803:     for (i=0;i<sr->nPend;i++) pending2[i] = sr->pending[i];
    804:     PetscFree(sr->pending);
    805:     sr->pending = pending2;
    806:   }
    807:   sr->pending[sr->nPend++]=s;
    808:   return(0);
    809: }

    811: /* Prepare for Rational Krylov update */
    814: static PetscErrorCode EPSPrepareRational(EPS eps)
    815: {
    816:   EPS_KRYLOVSCHUR  *ctx=(EPS_KRYLOVSCHUR*)eps->data;
    817:   PetscErrorCode   ierr;
    818:   PetscInt         dir,i,k,ld,nv;
    819:   PetscScalar      *A;
    820:   EPS_SR           sr = ctx->sr;
    821:   Vec              v;

    824:   DSGetLeadingDimension(eps->ds,&ld);
    825:   dir = (sr->sPres->neighb[0] == sr->sPrev)?1:-1;
    826:   dir*=sr->dir;
    827:   k = 0;
    828:   for (i=0;i<sr->nS;i++) {
    829:     if (dir*PetscRealPart(sr->S[i])>0.0) {
    830:       sr->S[k] = sr->S[i];
    831:       sr->S[sr->nS+k] = sr->S[sr->nS+i];
    832:       BVGetColumn(sr->Vnext,k,&v);
    833:       BVCopyVec(eps->V,eps->nconv+i,v);
    834:       BVRestoreColumn(sr->Vnext,k,&v);
    835:       k++;
    836:       if (k>=sr->nS/2)break;
    837:     }
    838:   }
    839:   /* Copy to DS */
    840:   DSGetArray(eps->ds,DS_MAT_A,&A);
    841:   PetscMemzero(A,ld*ld*sizeof(PetscScalar));
    842:   for (i=0;i<k;i++) {
    843:     A[i*(1+ld)] = sr->S[i];
    844:     A[k+i*ld] = sr->S[sr->nS+i];
    845:   }
    846:   sr->nS = k;
    847:   DSRestoreArray(eps->ds,DS_MAT_A,&A);
    848:   DSGetDimensions(eps->ds,&nv,NULL,NULL,NULL,NULL);
    849:   DSSetDimensions(eps->ds,nv,0,0,k);
    850:   /* Append u to V */
    851:   BVGetColumn(sr->Vnext,sr->nS,&v);
    852:   BVCopyVec(eps->V,sr->nv,v);
    853:   BVRestoreColumn(sr->Vnext,sr->nS,&v);
    854:   return(0);
    855: }

    857: /* Provides next shift to be computed */
    860: static PetscErrorCode EPSExtractShift(EPS eps)
    861: {
    862:   PetscErrorCode   ierr;
    863:   PetscInt         iner,zeros=0;
    864:   EPS_KRYLOVSCHUR  *ctx=(EPS_KRYLOVSCHUR*)eps->data;
    865:   EPS_SR           sr;
    866:   PetscReal        newShift;
    867:   EPS_shift        sPres;

    870:   sr = ctx->sr;
    871:   if (sr->nPend > 0) {
    872:     sr->sPrev = sr->sPres;
    873:     sr->sPres = sr->pending[--sr->nPend];
    874:     sPres = sr->sPres;
    875:     EPSSliceGetInertia(eps,sPres->value,&iner,ctx->detect?&zeros:NULL);
    876:     if (zeros) {
    877:       newShift = sPres->value*(1.0+SLICE_PTOL);
    878:       if (sr->dir*(sPres->neighb[0] && newShift-sPres->neighb[0]->value) < 0) newShift = (sPres->value+sPres->neighb[0]->value)/2;
    879:       else if (sPres->neighb[1] && sr->dir*(sPres->neighb[1]->value-newShift) < 0) newShift = (sPres->value+sPres->neighb[1]->value)/2;
    880:       EPSSliceGetInertia(eps,newShift,&iner,&zeros);
    881:       if (zeros) SETERRQ1(((PetscObject)eps)->comm,PETSC_ERR_CONV_FAILED,"Inertia computation fails in %g",newShift);
    882:       sPres->value = newShift;
    883:     }
    884:     sr->sPres->inertia = iner;
    885:     eps->target = sr->sPres->value;
    886:     eps->reason = EPS_CONVERGED_ITERATING;
    887:     eps->its = 0;
    888:   } else sr->sPres = NULL;
    889:   return(0);
    890: }

    892: /*
    893:    Symmetric KrylovSchur adapted to spectrum slicing:
    894:    Allows searching an specific amount of eigenvalues in the subintervals left and right.
    895:    Returns whether the search has succeeded
    896: */
    899: static PetscErrorCode EPSKrylovSchur_Slice(EPS eps)
    900: {
    901:   PetscErrorCode  ierr;
    902:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
    903:   PetscInt        i,conv,k,l,ld,nv,*iwork,j,p;
    904:   Mat             U;
    905:   PetscScalar     *Q,*A,rtmp;
    906:   PetscReal       *a,*b,beta;
    907:   PetscBool       breakdown;
    908:   PetscInt        count0,count1;
    909:   PetscReal       lambda;
    910:   EPS_shift       sPres;
    911:   PetscBool       complIterating;
    912:   PetscBool       sch0,sch1;
    913:   PetscInt        iterCompl=0,n0,n1;
    914:   EPS_SR          sr = ctx->sr;

    917:   /* Spectrum slicing data */
    918:   sPres = sr->sPres;
    919:   complIterating =PETSC_FALSE;
    920:   sch1 = sch0 = PETSC_TRUE;
    921:   DSGetLeadingDimension(eps->ds,&ld);
    922:   PetscMalloc1(2*ld,&iwork);
    923:   count0=0;count1=0; /* Found on both sides */
    924:   if (sr->nS > 0 && (sPres->neighb[0] == sr->sPrev || sPres->neighb[1] == sr->sPrev)) {
    925:     /* Rational Krylov */
    926:     DSTranslateRKS(eps->ds,sr->sPrev->value-sPres->value);
    927:     DSGetDimensions(eps->ds,NULL,NULL,NULL,&l,NULL);
    928:     DSSetDimensions(eps->ds,l+1,0,0,0);
    929:     BVSetActiveColumns(eps->V,0,l+1);
    930:     DSGetMat(eps->ds,DS_MAT_Q,&U);
    931:     BVMultInPlace(eps->V,U,0,l+1);
    932:     MatDestroy(&U);
    933:   } else {
    934:     /* Get the starting Lanczos vector */
    935:     EPSGetStartVector(eps,0,NULL);
    936:     l = 0;
    937:   }
    938:   /* Restart loop */
    939:   while (eps->reason == EPS_CONVERGED_ITERATING) {
    940:     eps->its++; sr->itsKs++;
    941:     /* Compute an nv-step Lanczos factorization */
    942:     nv = PetscMin(eps->nconv+eps->mpd,eps->ncv);
    943:     DSGetArrayReal(eps->ds,DS_MAT_T,&a);
    944:     b = a + ld;
    945:     EPSFullLanczos(eps,a,b,eps->nconv+l,&nv,&breakdown);
    946:     sr->nv = nv;
    947:     beta = b[nv-1];
    948:     DSRestoreArrayReal(eps->ds,DS_MAT_T,&a);
    949:     DSSetDimensions(eps->ds,nv,0,eps->nconv,eps->nconv+l);
    950:     if (l==0) {
    951:       DSSetState(eps->ds,DS_STATE_INTERMEDIATE);
    952:     } else {
    953:       DSSetState(eps->ds,DS_STATE_RAW);
    954:     }
    955:     BVSetActiveColumns(eps->V,eps->nconv,nv);

    957:     /* Solve projected problem and compute residual norm estimates */
    958:     if (eps->its == 1 && l > 0) {/* After rational update */
    959:       DSGetArray(eps->ds,DS_MAT_A,&A);
    960:       DSGetArrayReal(eps->ds,DS_MAT_T,&a);
    961:       b = a + ld;
    962:       k = eps->nconv+l;
    963:       A[k*ld+k-1] = A[(k-1)*ld+k];
    964:       A[k*ld+k] = a[k];
    965:       for (j=k+1; j< nv; j++) {
    966:         A[j*ld+j] = a[j];
    967:         A[j*ld+j-1] = b[j-1] ;
    968:         A[(j-1)*ld+j] = b[j-1];
    969:       }
    970:       DSRestoreArray(eps->ds,DS_MAT_A,&A);
    971:       DSRestoreArrayReal(eps->ds,DS_MAT_T,&a);
    972:       DSSolve(eps->ds,eps->eigr,NULL);
    973:       DSSort(eps->ds,eps->eigr,NULL,NULL,NULL,NULL);
    974:       DSSetCompact(eps->ds,PETSC_TRUE);
    975:     } else { /* Restart */
    976:       DSSolve(eps->ds,eps->eigr,NULL);
    977:       DSSort(eps->ds,eps->eigr,NULL,NULL,NULL,NULL);
    978:     }
    979:     /* Residual */
    980:     EPSKrylovConvergence(eps,PETSC_TRUE,eps->nconv,nv-eps->nconv,beta,1.0,&k);

    982:     if (ctx->lock) {
    983:       /* Check convergence */
    984:       DSGetArrayReal(eps->ds,DS_MAT_T,&a);
    985:       b = a + ld;
    986:       conv = 0;
    987:       j = k = eps->nconv;
    988:       for (i=eps->nconv;i<nv;i++) if (eps->errest[i] < eps->tol) conv++;
    989:       for (i=eps->nconv;i<nv;i++) {
    990:         if (eps->errest[i] < eps->tol) {
    991:           iwork[j++]=i;
    992:         } else iwork[conv+k++]=i;
    993:       }
    994:       for (i=eps->nconv;i<nv;i++) {
    995:         a[i]=PetscRealPart(eps->eigr[i]);
    996:         b[i]=eps->errest[i];
    997:       }
    998:       for (i=eps->nconv;i<nv;i++) {
    999:         eps->eigr[i] = a[iwork[i]];
    1000:         eps->errest[i] = b[iwork[i]];
    1001:       }
    1002:       for (i=eps->nconv;i<nv;i++) {
    1003:         a[i]=PetscRealPart(eps->eigr[i]);
    1004:         b[i]=eps->errest[i];
    1005:       }
    1006:       DSRestoreArrayReal(eps->ds,DS_MAT_T,&a);
    1007:       DSGetArray(eps->ds,DS_MAT_Q,&Q);
    1008:       for (i=eps->nconv;i<nv;i++) {
    1009:         p=iwork[i];
    1010:         if (p!=i) {
    1011:           j=i+1;
    1012:           while (iwork[j]!=i) j++;
    1013:           iwork[j]=p;iwork[i]=i;
    1014:           for (k=0;k<nv;k++) {
    1015:             rtmp=Q[k+p*ld];Q[k+p*ld]=Q[k+i*ld];Q[k+i*ld]=rtmp;
    1016:           }
    1017:         }
    1018:       }
    1019:       DSRestoreArray(eps->ds,DS_MAT_Q,&Q);
    1020:       k=eps->nconv+conv;
    1021:     }

    1023:     /* Checking values obtained for completing */
    1024:     for (i=0;i<k;i++) {
    1025:       sr->back[i]=eps->eigr[i];
    1026:     }
    1027:     STBackTransform(eps->st,k,sr->back,eps->eigi);
    1028:     count0=count1=0;
    1029:     for (i=0;i<k;i++) {
    1030:       lambda = PetscRealPart(sr->back[i]);
    1031:       if (((sr->dir)*(sPres->value - lambda) > 0) && ((sr->dir)*(lambda - sPres->ext[0]) > 0)) count0++;
    1032:       if (((sr->dir)*(lambda - sPres->value) > 0) && ((sr->dir)*(sPres->ext[1] - lambda) > 0)) count1++;
    1033:     }
    1034:     if (k>eps->nev && eps->ncv-k<5) eps->reason = EPS_CONVERGED_TOL;
    1035:     else {
    1036:       /* Checks completion */
    1037:       if ((!sch0||count0 >= sPres->nsch[0]) && (!sch1 ||count1 >= sPres->nsch[1])) {
    1038:         eps->reason = EPS_CONVERGED_TOL;
    1039:       } else {
    1040:         if (!complIterating && eps->its >= eps->max_it) eps->reason = EPS_DIVERGED_ITS;
    1041:         if (complIterating) {
    1042:           if (--iterCompl <= 0) eps->reason = EPS_DIVERGED_ITS;
    1043:         } else if (k >= eps->nev) {
    1044:           n0 = sPres->nsch[0]-count0;
    1045:           n1 = sPres->nsch[1]-count1;
    1046:           if (sr->iterCompl>0 && ((n0>0 && n0<= sr->nMAXCompl)||(n1>0&&n1<=sr->nMAXCompl))) {
    1047:             /* Iterating for completion*/
    1048:             complIterating = PETSC_TRUE;
    1049:             if (n0 >sr->nMAXCompl)sch0 = PETSC_FALSE;
    1050:             if (n1 >sr->nMAXCompl)sch1 = PETSC_FALSE;
    1051:             iterCompl = sr->iterCompl;
    1052:           } else eps->reason = EPS_CONVERGED_TOL;
    1053:         }
    1054:       }
    1055:     }
    1056:     /* Update l */
    1057:     if (eps->reason == EPS_CONVERGED_ITERATING) l = PetscMax(1,(PetscInt)((nv-k)*ctx->keep));
    1058:     else l = 0;
    1059:     if (!ctx->lock && l>0) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */
    1060:     if (breakdown) l=0;

    1062:     if (eps->reason == EPS_CONVERGED_ITERATING) {
    1063:       if (breakdown) {
    1064:         /* Start a new Lanczos factorization */
    1065:         PetscInfo2(eps,"Breakdown in Krylov-Schur method (it=%D norm=%g)\n",eps->its,(double)beta);
    1066:         EPSGetStartVector(eps,k,&breakdown);
    1067:         if (breakdown) {
    1068:           eps->reason = EPS_DIVERGED_BREAKDOWN;
    1069:           PetscInfo(eps,"Unable to generate more start vectors\n");
    1070:         }
    1071:       } else {
    1072:         /* Prepare the Rayleigh quotient for restart */
    1073:         DSGetArrayReal(eps->ds,DS_MAT_T,&a);
    1074:         DSGetArray(eps->ds,DS_MAT_Q,&Q);
    1075:         b = a + ld;
    1076:         for (i=k;i<k+l;i++) {
    1077:           a[i] = PetscRealPart(eps->eigr[i]);
    1078:           b[i] = PetscRealPart(Q[nv-1+i*ld]*beta);
    1079:         }
    1080:         DSRestoreArrayReal(eps->ds,DS_MAT_T,&a);
    1081:         DSRestoreArray(eps->ds,DS_MAT_Q,&Q);
    1082:       }
    1083:     }
    1084:     /* Update the corresponding vectors V(:,idx) = V*Q(:,idx) */
    1085:     DSGetMat(eps->ds,DS_MAT_Q,&U);
    1086:     BVMultInPlace(eps->V,U,eps->nconv,k+l);
    1087:     MatDestroy(&U);

    1089:     /* Normalize u and append it to V */
    1090:     if (eps->reason == EPS_CONVERGED_ITERATING && !breakdown) {
    1091:       BVCopyColumn(eps->V,nv,k+l);
    1092:     }
    1093:     eps->nconv = k;
    1094:     if (eps->reason != EPS_CONVERGED_ITERATING) {
    1095:       /* Store approximated values for next shift */
    1096:       DSGetArray(eps->ds,DS_MAT_Q,&Q);
    1097:       sr->nS = l;
    1098:       for (i=0;i<l;i++) {
    1099:         sr->S[i] = eps->eigr[i+k];/* Diagonal elements */
    1100:         sr->S[i+l] = Q[nv-1+(i+k)*ld]*beta; /* Out of diagonal elements */
    1101:       }
    1102:       DSRestoreArray(eps->ds,DS_MAT_Q,&Q);
    1103:     }
    1104:   }
    1105:   /* Check for completion */
    1106:   for (i=0;i< eps->nconv; i++) {
    1107:     if ((sr->dir)*PetscRealPart(eps->eigr[i])>0) sPres->nconv[1]++;
    1108:     else sPres->nconv[0]++;
    1109:   }
    1110:   sPres->comp[0] = PetscNot(count0 < sPres->nsch[0]);
    1111:   sPres->comp[1] = PetscNot(count1 < sPres->nsch[1]);
    1112:   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()");
    1113:   PetscFree(iwork);
    1114:   return(0);
    1115: }

    1117: /*
    1118:   Obtains value of subsequent shift
    1119: */
    1122: static PetscErrorCode EPSGetNewShiftValue(EPS eps,PetscInt side,PetscReal *newS)
    1123: {
    1124:   PetscReal       lambda,d_prev;
    1125:   PetscInt        i,idxP;
    1126:   EPS_SR          sr;
    1127:   EPS_shift       sPres,s;
    1128:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;

    1131:   sr = ctx->sr;
    1132:   sPres = sr->sPres;
    1133:   if (sPres->neighb[side]) {
    1134:   /* Completing a previous interval */
    1135:     if (!sPres->neighb[side]->neighb[side] && sPres->neighb[side]->nconv[side]==0) { /* One of the ends might be too far from eigenvalues */
    1136:       if (side) *newS = (sPres->value + PetscRealPart(sr->eigr[sr->perm[sr->indexEig-1]]))/2;
    1137:       else *newS = (sPres->value + PetscRealPart(sr->eigr[sr->perm[0]]))/2;
    1138:     } else *newS=(sPres->value + sPres->neighb[side]->value)/2;
    1139:   } else { /* (Only for side=1). Creating a new interval. */
    1140:     if (sPres->neigs==0) {/* No value has been accepted*/
    1141:       if (sPres->neighb[0]) {
    1142:         /* Multiplying by 10 the previous distance */
    1143:         *newS = sPres->value + 10*(sr->dir)*PetscAbsReal(sPres->value - sPres->neighb[0]->value);
    1144:         sr->nleap++;
    1145:         /* Stops when the interval is open and no values are found in the last 5 shifts (there might be infinite eigenvalues) */
    1146:         if (!sr->hasEnd && sr->nleap > 5) SETERRQ(PetscObjectComm((PetscObject)eps),1,"Unable to compute the wanted eigenvalues with open interval");
    1147:       } else { /* First shift */
    1148:         if (eps->nconv != 0) {
    1149:           /* Unaccepted values give information for next shift */
    1150:           idxP=0;/* Number of values left from shift */
    1151:           for (i=0;i<eps->nconv;i++) {
    1152:             lambda = PetscRealPart(eps->eigr[i]);
    1153:             if ((sr->dir)*(lambda - sPres->value) <0) idxP++;
    1154:             else break;
    1155:           }
    1156:           /* Avoiding subtraction of eigenvalues (might be the same).*/
    1157:           if (idxP>0) {
    1158:             d_prev = PetscAbsReal(sPres->value - PetscRealPart(eps->eigr[0]))/(idxP+0.3);
    1159:           } else {
    1160:             d_prev = PetscAbsReal(sPres->value - PetscRealPart(eps->eigr[eps->nconv-1]))/(eps->nconv+0.3);
    1161:           }
    1162:           *newS = sPres->value + ((sr->dir)*d_prev*eps->nev)/2;
    1163:         } else { /* No values found, no information for next shift */
    1164:           SETERRQ(PetscObjectComm((PetscObject)eps),1,"First shift renders no information");
    1165:         }
    1166:       }
    1167:     } else { /* Accepted values found */
    1168:       sr->nleap = 0;
    1169:       /* Average distance of values in previous subinterval */
    1170:       s = sPres->neighb[0];
    1171:       while (s && PetscAbs(s->inertia - sPres->inertia)==0) {
    1172:         s = s->neighb[0];/* Looking for previous shifts with eigenvalues within */
    1173:       }
    1174:       if (s) {
    1175:         d_prev = PetscAbsReal((sPres->value - s->value)/(sPres->inertia - s->inertia));
    1176:       } else { /* First shift. Average distance obtained with values in this shift */
    1177:         /* first shift might be too far from first wanted eigenvalue (no values found outside the interval)*/
    1178:         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)) {
    1179:           d_prev =  PetscAbsReal((PetscRealPart(sr->eigr[sr->indexEig-1]) - PetscRealPart(sr->eigr[0])))/(sPres->neigs+0.3);
    1180:         } else {
    1181:           d_prev = PetscAbsReal(PetscRealPart(sr->eigr[sr->indexEig-1]) - sPres->value)/(sPres->neigs+0.3);
    1182:         }
    1183:       }
    1184:       /* Average distance is used for next shift by adding it to value on the right or to shift */
    1185:       if ((sr->dir)*(PetscRealPart(sr->eigr[sPres->index + sPres->neigs -1]) - sPres->value)>0) {
    1186:         *newS = PetscRealPart(sr->eigr[sPres->index + sPres->neigs -1])+ ((sr->dir)*d_prev*(eps->nev))/2;
    1187:       } else { /* Last accepted value is on the left of shift. Adding to shift */
    1188:         *newS = sPres->value + ((sr->dir)*d_prev*(eps->nev))/2;
    1189:       }
    1190:     }
    1191:     /* End of interval can not be surpassed */
    1192:     if ((sr->dir)*(sr->int1 - *newS) < 0) *newS = sr->int1;
    1193:   }/* of neighb[side]==null */
    1194:   return(0);
    1195: }

    1197: /*
    1198:   Function for sorting an array of real values
    1199: */
    1202: static PetscErrorCode sortRealEigenvalues(PetscScalar *r,PetscInt *perm,PetscInt nr,PetscBool prev,PetscInt dir)
    1203: {
    1204:   PetscReal      re;
    1205:   PetscInt       i,j,tmp;

    1208:   if (!prev) for (i=0;i<nr;i++) perm[i] = i;
    1209:   /* Insertion sort */
    1210:   for (i=1;i<nr;i++) {
    1211:     re = PetscRealPart(r[perm[i]]);
    1212:     j = i-1;
    1213:     while (j>=0 && dir*(re - PetscRealPart(r[perm[j]])) <= 0) {
    1214:       tmp = perm[j]; perm[j] = perm[j+1]; perm[j+1] = tmp; j--;
    1215:     }
    1216:   }
    1217:   return(0);
    1218: }

    1220: /* Stores the pairs obtained since the last shift in the global arrays */
    1223: static PetscErrorCode EPSStoreEigenpairs(EPS eps)
    1224: {
    1225:   PetscErrorCode  ierr;
    1226:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
    1227:   PetscReal       lambda,err,norm;
    1228:   PetscInt        i,count;
    1229:   PetscBool       iscayley;
    1230:   EPS_SR          sr = ctx->sr;
    1231:   EPS_shift       sPres;
    1232:   Vec             v,w;

    1235:   sPres = sr->sPres;
    1236:   sPres->index = sr->indexEig;
    1237:   count = sr->indexEig;
    1238:   /* Back-transform */
    1239:   STBackTransform(eps->st,eps->nconv,eps->eigr,eps->eigi);
    1240:   PetscObjectTypeCompare((PetscObject)eps->st,STCAYLEY,&iscayley);
    1241:   /* Sort eigenvalues */
    1242:   sortRealEigenvalues(eps->eigr,eps->perm,eps->nconv,PETSC_FALSE,sr->dir);
    1243:   /* Values stored in global array */
    1244:   for (i=0;i<eps->nconv;i++) {
    1245:     lambda = PetscRealPart(eps->eigr[eps->perm[i]]);
    1246:     err = eps->errest[eps->perm[i]];

    1248:     if ((sr->dir)*(lambda - sPres->ext[0]) > 0 && (sr->dir)*(sPres->ext[1] - lambda) > 0) {/* Valid value */
    1249:       if (count>=sr->numEigs) SETERRQ(PetscObjectComm((PetscObject)eps),1,"Unexpected error in Spectrum Slicing");
    1250:       sr->eigr[count] = lambda;
    1251:       sr->errest[count] = err;
    1252:       /* Explicit purification */
    1253:       if (eps->purify) {
    1254:         BVGetColumn(sr->V,count,&v);
    1255:         BVGetColumn(eps->V,eps->perm[i],&w);
    1256:         STApply(eps->st,w,v);
    1257:         BVRestoreColumn(sr->V,count,&v);
    1258:         BVRestoreColumn(eps->V,eps->perm[i],&w);
    1259:         BVNormColumn(sr->V,count,NORM_2,&norm);
    1260:         BVScaleColumn(sr->V,count,1.0/norm);
    1261:       } else {
    1262:         BVGetColumn(eps->V,eps->perm[i],&w);
    1263:         BVInsertVec(sr->V,count,w);
    1264:         BVRestoreColumn(eps->V,eps->perm[i],&w);
    1265:         BVNormColumn(sr->V,count,NORM_2,&norm);
    1266:         BVScaleColumn(sr->V,count,1.0/norm);
    1267:       }
    1268:       count++;
    1269:     }
    1270:   }
    1271:   sPres->neigs = count - sr->indexEig;
    1272:   sr->indexEig = count;
    1273:   /* Global ordering array updating */
    1274:   sortRealEigenvalues(sr->eigr,sr->perm,count,PETSC_TRUE,sr->dir);
    1275:   return(0);
    1276: }

    1280: static PetscErrorCode EPSLookForDeflation(EPS eps)
    1281: {
    1282:   PetscErrorCode  ierr;
    1283:   PetscReal       val;
    1284:   PetscInt        i,count0=0,count1=0;
    1285:   EPS_shift       sPres;
    1286:   PetscInt        ini,fin,k,idx0,idx1;
    1287:   EPS_SR          sr;
    1288:   Vec             v;
    1289:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;

    1292:   sr = ctx->sr;
    1293:   sPres = sr->sPres;

    1295:   if (sPres->neighb[0]) ini = (sr->dir)*(sPres->neighb[0]->inertia - sr->inertia0);
    1296:   else ini = 0;
    1297:   fin = sr->indexEig;
    1298:   /* Selection of ends for searching new values */
    1299:   if (!sPres->neighb[0]) sPres->ext[0] = sr->int0;/* First shift */
    1300:   else sPres->ext[0] = sPres->neighb[0]->value;
    1301:   if (!sPres->neighb[1]) {
    1302:     if (sr->hasEnd) sPres->ext[1] = sr->int1;
    1303:     else sPres->ext[1] = (sr->dir > 0)?PETSC_MAX_REAL:PETSC_MIN_REAL;
    1304:   } else sPres->ext[1] = sPres->neighb[1]->value;
    1305:   /* Selection of values between right and left ends */
    1306:   for (i=ini;i<fin;i++) {
    1307:     val=PetscRealPart(sr->eigr[sr->perm[i]]);
    1308:     /* Values to the right of left shift */
    1309:     if ((sr->dir)*(val - sPres->ext[1]) < 0) {
    1310:       if ((sr->dir)*(val - sPres->value) < 0) count0++;
    1311:       else count1++;
    1312:     } else break;
    1313:   }
    1314:   /* The number of values on each side are found */
    1315:   if (sPres->neighb[0]) {
    1316:     sPres->nsch[0] = (sr->dir)*(sPres->inertia - sPres->neighb[0]->inertia)-count0;
    1317:     if (sPres->nsch[0]<0)SETERRQ(PetscObjectComm((PetscObject)eps),1,"Mismatch between number of values found and information from inertia, consider using EPSKrylovSchurSetDetectZeros()");
    1318:   } else sPres->nsch[0] = 0;

    1320:   if (sPres->neighb[1]) {
    1321:     sPres->nsch[1] = (sr->dir)*(sPres->neighb[1]->inertia - sPres->inertia) - count1;
    1322:     if (sPres->nsch[1]<0)SETERRQ(PetscObjectComm((PetscObject)eps),1,"Mismatch between number of values found and information from inertia, consider using EPSKrylovSchurSetDetectZeros()");
    1323:   } else sPres->nsch[1] = (sr->dir)*(sr->inertia1 - sPres->inertia);

    1325:   /* Completing vector of indexes for deflation */
    1326:   idx0 = ini;
    1327:   idx1 = ini+count0+count1;
    1328:   k=0;
    1329:   for (i=idx0;i<idx1;i++) sr->idxDef[k++]=sr->perm[i];
    1330:   BVDuplicateResize(eps->V,k+eps->ncv+1,&sr->Vnext);
    1331:   BVSetNumConstraints(sr->Vnext,k);
    1332:   for (i=0;i<k;i++) {
    1333:     BVGetColumn(sr->Vnext,-i-1,&v);
    1334:     BVCopyVec(sr->V,sr->idxDef[i],v);
    1335:     BVRestoreColumn(sr->Vnext,-i-1,&v);
    1336:   }

    1338:   /* For rational Krylov */
    1339:   if (sr->nS>0 && (sr->sPrev == sr->sPres->neighb[0] || sr->sPrev == sr->sPres->neighb[1])) {
    1340:     EPSPrepareRational(eps);
    1341:   }
    1342:   eps->nconv = 0;
    1343:   /* Get rid of temporary Vnext */
    1344:   BVDestroy(&eps->V);
    1345:   eps->V = sr->Vnext;
    1346:   sr->Vnext = NULL;
    1347:   return(0);
    1348: }

    1352: PetscErrorCode EPSSolve_KrylovSchur_Slice(EPS eps)
    1353: {
    1354:   PetscErrorCode   ierr;
    1355:   PetscInt         i,lds;
    1356:   PetscReal        newS;
    1357:   EPS_KRYLOVSCHUR  *ctx=(EPS_KRYLOVSCHUR*)eps->data;
    1358:   EPS_SR           sr=ctx->sr;
    1359:   Mat              A,B=NULL;
    1360:   PetscObjectState Astate,Bstate=0;
    1361:   PetscObjectId    Aid,Bid=0;

    1364:   PetscCitationsRegister(citation,&cited);
    1365:   if (ctx->global) {
    1366:     EPSSolve_KrylovSchur_Slice(ctx->eps);
    1367:     ctx->eps->state = EPS_STATE_SOLVED;
    1368:     eps->reason = EPS_CONVERGED_TOL;
    1369:     if (ctx->npart>1) {
    1370:       /* Gather solution from subsolvers */
    1371:       EPSSliceGatherSolution(eps);
    1372:     } else {
    1373:       eps->nconv = sr->numEigs;
    1374:       eps->its   = ctx->eps->its;
    1375:       PetscFree(ctx->inertias);
    1376:       PetscFree(ctx->shifts);
    1377:       EPSSliceGetInertias(ctx->eps,&ctx->nshifts,&ctx->shifts,&ctx->inertias);
    1378:     }
    1379:   } else {
    1380:     if (ctx->npart==1) {
    1381:       sr->eigr   = ctx->eps->eigr;
    1382:       sr->eigi   = ctx->eps->eigi;
    1383:       sr->perm   = ctx->eps->perm;
    1384:       sr->errest = ctx->eps->errest;
    1385:       sr->V      = ctx->eps->V;
    1386:     }
    1387:     /* Check that the user did not modify subcomm matrices */
    1388:     EPSGetOperators(eps,&A,&B);
    1389:     PetscObjectStateGet((PetscObject)A,&Astate);
    1390:     PetscObjectGetId((PetscObject)A,&Aid);
    1391:     if (B) {
    1392:       PetscObjectStateGet((PetscObject)B,&Bstate);
    1393:       PetscObjectGetId((PetscObject)B,&Bid);
    1394:     }
    1395:     if (Astate!=ctx->Astate || (B && Bstate!=ctx->Bstate) || Aid!=ctx->Aid || (B && Bid!=ctx->Bid)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Subcomm matrices have been modified by user");
    1396:     /* Only with eigenvalues present in the interval ...*/
    1397:     if (sr->numEigs==0) {
    1398:       eps->reason = EPS_CONVERGED_TOL;
    1399:       return(0);
    1400:     }
    1401:     /* Array of pending shifts */
    1402:     sr->maxPend = 100; /* Initial size */
    1403:     sr->nPend = 0;
    1404:     PetscMalloc1(sr->maxPend,&sr->pending);
    1405:     PetscLogObjectMemory((PetscObject)eps,(sr->maxPend)*sizeof(EPS_shift));
    1406:     EPSCreateShift(eps,sr->int0,NULL,NULL);
    1407:     /* extract first shift */
    1408:     sr->sPrev = NULL;
    1409:     sr->sPres = sr->pending[--sr->nPend];
    1410:     sr->sPres->inertia = sr->inertia0;
    1411:     eps->target = sr->sPres->value;
    1412:     sr->s0 = sr->sPres;
    1413:     sr->indexEig = 0;
    1414:     /* Memory reservation for auxiliary variables */
    1415:     lds = PetscMin(eps->mpd,eps->ncv);
    1416:     PetscCalloc1(lds*lds,&sr->S);
    1417:     PetscMalloc1(eps->ncv,&sr->back);
    1418:     PetscLogObjectMemory((PetscObject)eps,(sr->numEigs+2*eps->ncv)*sizeof(PetscScalar));
    1419:     for (i=0;i<sr->numEigs;i++) {
    1420:       sr->eigr[i]   = 0.0;
    1421:       sr->eigi[i]   = 0.0;
    1422:       sr->errest[i] = 0.0;
    1423:       sr->perm[i]   = i;
    1424:     }
    1425:     /* Vectors for deflation */
    1426:     PetscMalloc1(sr->numEigs,&sr->idxDef);
    1427:     PetscLogObjectMemory((PetscObject)eps,sr->numEigs*sizeof(PetscInt));
    1428:     sr->indexEig = 0;
    1429:     /* Main loop */
    1430:     while (sr->sPres) {
    1431:       /* Search for deflation */
    1432:       EPSLookForDeflation(eps);
    1433:       /* KrylovSchur */
    1434:       EPSKrylovSchur_Slice(eps);

    1436:       EPSStoreEigenpairs(eps);
    1437:       /* Select new shift */
    1438:       if (!sr->sPres->comp[1]) {
    1439:         EPSGetNewShiftValue(eps,1,&newS);
    1440:         EPSCreateShift(eps,newS,sr->sPres,sr->sPres->neighb[1]);
    1441:       }
    1442:       if (!sr->sPres->comp[0]) {
    1443:         /* Completing earlier interval */
    1444:         EPSGetNewShiftValue(eps,0,&newS);
    1445:         EPSCreateShift(eps,newS,sr->sPres->neighb[0],sr->sPres);
    1446:       }
    1447:       /* Preparing for a new search of values */
    1448:       EPSExtractShift(eps);
    1449:     }

    1451:     /* Updating eps values prior to exit */
    1452:     PetscFree(sr->S);
    1453:     PetscFree(sr->idxDef);
    1454:     PetscFree(sr->pending);
    1455:     PetscFree(sr->back);
    1456:     BVDuplicateResize(eps->V,eps->ncv+1,&sr->Vnext);
    1457:     BVSetNumConstraints(sr->Vnext,0);
    1458:     BVDestroy(&eps->V);
    1459:     eps->V      = sr->Vnext;
    1460:     eps->nconv  = sr->indexEig;
    1461:     eps->reason = EPS_CONVERGED_TOL;
    1462:     eps->its    = sr->itsKs;
    1463:     eps->nds    = 0;
    1464:   }
    1465:   return(0);
    1466: }