Actual source code: ks-slice.c
slepc-3.10.1 2018-10-23
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2018, Universitat Politecnica de Valencia, Spain

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

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

     15:    References:

     17:        [1] R.G. Grimes et al., "A shifted block Lanczos algorithm for
     18:            solving sparse symmetric generalized eigenproblems", SIAM J.
     19:            Matrix Anal. Appl. 15(1):228-272, 1994.

     21:        [2] C. Campos and J.E. Roman, "Spectrum slicing strategies based
     22:            on restarted Lanczos methods", Numer. Algor. 60(2):279-295,
     23:            2012.
     24: */

     26: #include <slepc/private/epsimpl.h>
     27: #include "krylovschur.h"

     29: static PetscBool  cited = PETSC_FALSE;
     30: static const char citation[] =
     31:   "@Article{slepc-slice,\n"
     32:   "   author = \"C. Campos and J. E. Roman\",\n"
     33:   "   title = \"Strategies for spectrum slicing based on restarted {Lanczos} methods\",\n"
     34:   "   journal = \"Numer. Algorithms\",\n"
     35:   "   volume = \"60\",\n"
     36:   "   number = \"2\",\n"
     37:   "   pages = \"279--295\",\n"
     38:   "   year = \"2012,\"\n"
     39:   "   doi = \"https://doi.org/10.1007/s11075-012-9564-z\"\n"
     40:   "}\n";

     42: #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 = NULL;
     68:   return(0);
     69: }

     71: PetscErrorCode EPSReset_KrylovSchur_Slice(EPS eps)
     72: {
     73:   PetscErrorCode  ierr;
     74:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;

     77:   if (!ctx->global) return(0);
     78:   /* Destroy auxiliary EPS */
     79:   EPSSliceResetSR(ctx->eps);
     80:   EPSDestroy(&ctx->eps);
     81:   if (ctx->npart>1) {
     82:     PetscSubcommDestroy(&ctx->subc);
     83:     if (ctx->commset) {
     84:       MPI_Comm_free(&ctx->commrank);
     85:       ctx->commset = PETSC_FALSE;
     86:     }
     87:   }
     88:   PetscFree(ctx->subintervals);
     89:   PetscFree(ctx->nconv_loc);
     90:   EPSSliceResetSR(eps);
     91:   PetscFree(ctx->inertias);
     92:   PetscFree(ctx->shifts);
     93:   if (ctx->npart>1) {
     94:     ISDestroy(&ctx->isrow);
     95:     ISDestroy(&ctx->iscol);
     96:     MatDestroyMatrices(1,&ctx->submata);
     97:     MatDestroyMatrices(1,&ctx->submatb);
     98:   }
     99:   return(0);
    100: }

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

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

    130:   /* allocate sr->V and transfer options from eps->V */
    131:   BVDestroy(&sr->V);
    132:   BVCreate(PetscObjectComm((PetscObject)eps),&sr->V);
    133:   PetscLogObjectParent((PetscObject)eps,(PetscObject)sr->V);
    134:   if (!eps->V) { EPSGetBV(eps,&eps->V); }
    135:   if (!((PetscObject)(eps->V))->type_name) {
    136:     BVSetType(sr->V,BVSVEC);
    137:   } else {
    138:     BVGetType(eps->V,&type);
    139:     BVSetType(sr->V,type);
    140:   }
    141:   STMatCreateVecsEmpty(eps->st,&t,NULL);
    142:   BVSetSizesFromVec(sr->V,t,k);
    143:   VecDestroy(&t);
    144:   EPS_SetInnerProduct(eps);
    145:   BVGetMatrix(eps->V,&matrix,NULL);
    146:   BVSetMatrix(sr->V,matrix,PETSC_FALSE);
    147:   BVGetOrthogonalization(eps->V,&orthog_type,&orthog_ref,&eta,&ob_type);
    148:   BVSetOrthogonalization(sr->V,orthog_type,orthog_ref,eta,ob_type);
    149:   return(0);
    150: }

    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=NULL,Br=NULL;
    163:   PetscInt           i;
    164:   PetscReal          h,a,b,zero;
    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:   PetscObjectState   Astate,Bstate=0;
    173:   PetscObjectId      Aid,Bid=0;
    174:   MatSolverType      stype;

    177:   EPSGetOperators(eps,&A,&B);
    178:   if (ctx->npart==1) {
    179:     if (!ctx->eps) { EPSCreate(((PetscObject)eps)->comm,&ctx->eps); }
    180:     EPSSetType(ctx->eps,((PetscObject)eps)->type_name);
    181:     EPSSetOperators(ctx->eps,A,B);
    182:     a = eps->inta; b = eps->intb;
    183:   } else {
    184:     PetscObjectStateGet((PetscObject)A,&Astate);
    185:     PetscObjectGetId((PetscObject)A,&Aid);
    186:     if (B) {
    187:       PetscObjectStateGet((PetscObject)B,&Bstate);
    188:       PetscObjectGetId((PetscObject)B,&Bid);
    189:     }
    190:     if (!ctx->subc) {
    191:       /* Create context for subcommunicators */
    192:       PetscSubcommCreate(PetscObjectComm((PetscObject)eps),&ctx->subc);
    193:       PetscSubcommSetNumber(ctx->subc,ctx->npart);
    194:       PetscSubcommSetType(ctx->subc,PETSC_SUBCOMM_CONTIGUOUS);
    195:       PetscLogObjectMemory((PetscObject)eps,sizeof(PetscSubcomm));

    197:       /* Duplicate matrices */
    198:       MatCreateRedundantMatrix(A,0,PetscSubcommChild(ctx->subc),MAT_INITIAL_MATRIX,&Ar);
    199:       ctx->Astate = Astate;
    200:       ctx->Aid = Aid;
    201:       if (B) {
    202:         MatCreateRedundantMatrix(B,0,PetscSubcommChild(ctx->subc),MAT_INITIAL_MATRIX,&Br);
    203:         ctx->Bstate = Bstate;
    204:         ctx->Bid = Bid;
    205:       }
    206:     } else {
    207:       if (ctx->Astate != Astate || (B && ctx->Bstate != Bstate) || ctx->Aid != Aid || (B && ctx->Bid != Bid)) {
    208:         EPSGetOperators(ctx->eps,&Ar,&Br);
    209:         MatCreateRedundantMatrix(A,0,PetscSubcommChild(ctx->subc),MAT_INITIAL_MATRIX,&Ar);
    210:         ctx->Astate = Astate;
    211:         ctx->Aid = Aid;
    212:         if (B) {
    213:           MatCreateRedundantMatrix(B,0,PetscSubcommChild(ctx->subc),MAT_INITIAL_MATRIX,&Br);
    214:           ctx->Bstate = Bstate;
    215:           ctx->Bid = Bid;
    216:         }
    217:         EPSSetOperators(ctx->eps,Ar,Br);
    218:         MatDestroy(&Ar);
    219:         MatDestroy(&Br);
    220:       }
    221:     }

    223:     /* Determine subintervals */
    224:     if (!ctx->subintset) { /* uniform distribution if no set by user */
    225:       if (!sr->hasEnd) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"Global interval must be bounded for splitting it in uniform subintervals");
    226:       h = (eps->intb-eps->inta)/ctx->npart;
    227:       a = eps->inta+ctx->subc->color*h;
    228:       b = (ctx->subc->color==ctx->npart-1)?eps->intb:eps->inta+(ctx->subc->color+1)*h;
    229:       PetscFree(ctx->subintervals);
    230:       PetscMalloc1(ctx->npart+1,&ctx->subintervals);
    231:       for (i=0;i<ctx->npart;i++) ctx->subintervals[i] = eps->inta+h*i;
    232:       ctx->subintervals[ctx->npart] = eps->intb;
    233:     } else {
    234:       a = ctx->subintervals[ctx->subc->color];
    235:       b = ctx->subintervals[ctx->subc->color+1];
    236:     }

    238:     if (!ctx->eps) {
    239:       /* Create auxiliary EPS */
    240:       EPSCreate(PetscSubcommChild(ctx->subc),&ctx->eps);
    241:       EPSSetOperators(ctx->eps,Ar,Br);
    242:       MatDestroy(&Ar);
    243:       MatDestroy(&Br);
    244:     }

    246:     /* Create subcommunicator grouping processes with same rank */
    247:     if (ctx->commset) { MPI_Comm_free(&ctx->commrank); }
    248:     MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);
    249:     MPI_Comm_split(((PetscObject)eps)->comm,rank,ctx->subc->color,&ctx->commrank);
    250:     ctx->commset = PETSC_TRUE;
    251:   }
    252:   EPSSetType(ctx->eps,((PetscObject)eps)->type_name);

    254:   /* Transfer options for ST, KSP and PC */
    255:   STGetType(eps->st,&sttype);
    256:   STSetType(ctx->eps->st,sttype);
    257:   STGetKSP(eps->st,&ksp);
    258:   KSPGetType(ksp,&ksptype);
    259:   KSPGetPC(ksp,&pc);
    260:   PCGetType(pc,&pctype);
    261:   PCFactorGetMatSolverType(pc,&stype);
    262:   PCFactorGetZeroPivot(pc,&zero);
    263:   STGetKSP(ctx->eps->st,&ksp);
    264:   KSPSetType(ksp,ksptype);
    265:   KSPGetPC(ksp,&pc);
    266:   PCSetType(pc,pctype);
    267:   PCFactorSetZeroPivot(pc,zero);
    268:   if (stype) { PCFactorSetMatSolverType(pc,stype); }

    270:   EPSSetConvergenceTest(ctx->eps,eps->conv);
    271:   EPSSetInterval(ctx->eps,a,b);
    272:   ctx_local = (EPS_KRYLOVSCHUR*)ctx->eps->data;
    273:   ctx_local->npart = ctx->npart;
    274:   ctx_local->detect = ctx->detect;
    275:   ctx_local->global = PETSC_FALSE;
    276:   ctx_local->eps = eps;
    277:   ctx_local->subc = ctx->subc;
    278:   ctx_local->commrank = ctx->commrank;

    280:   EPSSetDimensions(ctx->eps,ctx->nev,ctx->ncv,ctx->mpd);
    281:   EPSKrylovSchurSetLocking(ctx->eps,ctx->lock);

    283:   /* transfer options from eps->V */
    284:   EPSGetBV(ctx->eps,&V);
    285:   if (!eps->V) { EPSGetBV(eps,&eps->V); }
    286:   if (!((PetscObject)(eps->V))->type_name) {
    287:     BVSetType(V,BVSVEC);
    288:   } else {
    289:     BVGetType(eps->V,&type);
    290:     BVSetType(V,type);
    291:   }
    292:   BVGetOrthogonalization(eps->V,&orthog_type,&orthog_ref,&eta,&ob_type);
    293:   BVSetOrthogonalization(V,orthog_type,orthog_ref,eta,ob_type);
    294:   ctx->eps->which = eps->which;
    295:   ctx->eps->max_it = eps->max_it;
    296:   ctx->eps->tol = eps->tol;
    297:   ctx->eps->purify = eps->purify;
    298:   if (eps->tol==PETSC_DEFAULT) eps->tol = SLEPC_DEFAULT_TOL;
    299:   EPSSetProblemType(ctx->eps,eps->problem_type);
    300:   EPSSetUp(ctx->eps);
    301:   ctx->eps->nconv = 0;
    302:   ctx->eps->its   = 0;
    303:   for (i=0;i<ctx->eps->ncv;i++) {
    304:     ctx->eps->eigr[i]   = 0.0;
    305:     ctx->eps->eigi[i]   = 0.0;
    306:     ctx->eps->errest[i] = 0.0;
    307:   }
    308:   return(0);
    309: }

    311: static PetscErrorCode EPSSliceGetInertia(EPS eps,PetscReal shift,PetscInt *inertia,PetscInt *zeros)
    312: {
    314:   KSP            ksp;
    315:   PC             pc;
    316:   Mat            F;
    317:   PetscReal      nzshift;

    320:   if (shift >= PETSC_MAX_REAL) { /* Right-open interval */
    321:     if (inertia) *inertia = eps->n;
    322:   } else if (shift <= PETSC_MIN_REAL) {
    323:     if (inertia) *inertia = 0;
    324:     if (zeros) *zeros = 0;
    325:   } else {
    326:     /* If the shift is zero, perturb it to a very small positive value.
    327:        The goal is that the nonzero pattern is the same in all cases and reuse
    328:        the symbolic factorizations */
    329:     nzshift = (shift==0.0)? 10.0/PETSC_MAX_REAL: shift;
    330:     STSetShift(eps->st,nzshift);
    331:     STSetUp(eps->st);
    332:     STGetKSP(eps->st,&ksp);
    333:     KSPGetPC(ksp,&pc);
    334:     PCFactorGetMatrix(pc,&F);
    335:     MatGetInertia(F,inertia,zeros,NULL);
    336:   }
    337:   return(0);
    338: }

    340: /*
    341:    Dummy backtransform operation
    342:  */
    343: static PetscErrorCode EPSBackTransform_Skip(EPS eps)
    344: {
    346:   return(0);
    347: }

    349: PetscErrorCode EPSSetUp_KrylovSchur_Slice(EPS eps)
    350: {
    351:   PetscErrorCode  ierr;
    352:   PetscBool       issinv;
    353:   EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data,*ctx_glob;
    354:   EPS_SR          sr,sr_loc,sr_glob;
    355:   PetscInt        nEigs,dssz=1,i,zeros=0,off=0,method;
    356:   PetscMPIInt     nproc,rank=0,aux;
    357:   PetscReal       r;
    358:   MPI_Request     req;
    359:   Mat             A,B=NULL;
    360:   SlepcSC         sc;
    361:   PetscInt        flg=0;
    362:   DSParallelType  ptype;

    365:   if (ctx->global) {
    366:     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");
    367:     if (!eps->ishermitian) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Spectrum slicing only available for symmetric/Hermitian eigenproblems");
    368:     if (eps->arbitrary) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Arbitrary selection of eigenpairs cannot be used with spectrum slicing");
    369:     PetscObjectTypeCompareAny((PetscObject)eps->st,&issinv,STSINVERT,STCAYLEY,"");
    370:     if (!issinv) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Shift-and-invert or Cayley ST is needed for spectrum slicing");
    371:     if (eps->tol==PETSC_DEFAULT) eps->tol = SLEPC_DEFAULT_TOL*1e-2;  /* use tighter tolerance */
    372:     if (!eps->max_it) eps->max_it = 100;
    373:     if (ctx->nev==1) ctx->nev = PetscMin(40,eps->n);  /* nev not set, use default value */
    374:     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");
    375:   }
    376:   eps->ops->backtransform = EPSBackTransform_Skip;

    378:   /* create spectrum slicing context and initialize it */
    379:   EPSSliceResetSR(eps);
    380:   PetscNewLog(eps,&sr);
    381:   ctx->sr = sr;
    382:   sr->itsKs = 0;
    383:   sr->nleap = 0;
    384:   sr->nMAXCompl = eps->nev/4;
    385:   sr->iterCompl = eps->max_it/4;
    386:   sr->sPres = NULL;
    387:   sr->nS = 0;

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

    460:     /* compute inertia0 */
    461:     EPSSliceGetInertia(eps,sr->int0,&sr->inertia0,ctx->detect?&zeros:NULL);
    462:     PetscOptionsGetInt(NULL,NULL,"-eps_krylovschur_hiteigenvalue",&flg,NULL);
    463:     if (zeros) { /* error in factorization */
    464:       if (sr->int0==ctx->eps->inta || sr->int0==ctx->eps->intb) SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_USER,"Found singular matrix for the transformed problem in the interval endpoint");
    465:       else if(ctx_glob->subintset && !flg) SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_USER,"Found singular matrix for the transformed problem in an interval endpoint defined by user");
    466:       else {
    467:         if (flg==1) { /* idle subgroup */
    468:           sr->inertia0 = -1;
    469:         } else { /* perturb shift */
    470:           sr->int0 *= (1.0+SLICE_PTOL);
    471:           EPSSliceGetInertia(eps,sr->int0,&sr->inertia0,&zeros);
    472:           if (zeros) SETERRQ1(((PetscObject)eps)->comm,PETSC_ERR_CONV_FAILED,"Inertia computation fails in %g",sr->int1);
    473:         }
    474:       }
    475:     }
    476:     if (ctx->npart>1) {
    477:       /* inertia1 is received from neighbour */
    478:       MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);
    479:       if (!rank) {
    480:         if ( sr->inertia0!=-1 && ((sr->dir>0 && ctx->subc->color>0) || (sr->dir<0 && ctx->subc->color<ctx->npart-1)) ) { /* send inertia0 to neighbour0 */
    481:           MPI_Isend(&(sr->inertia0),1,MPIU_INT,ctx->subc->color-sr->dir,0,ctx->commrank,&req);
    482:           MPI_Isend(&(sr->int0),1,MPIU_REAL,ctx->subc->color-sr->dir,0,ctx->commrank,&req);
    483:         }
    484:         if ((sr->dir>0 && ctx->subc->color<ctx->npart-1)|| (sr->dir<0 && ctx->subc->color>0)) { /* receive inertia1 from neighbour1 */
    485:           MPI_Recv(&(sr->inertia1),1,MPIU_INT,ctx->subc->color+sr->dir,0,ctx->commrank,MPI_STATUS_IGNORE);
    486:           MPI_Recv(&(sr->int1),1,MPIU_REAL,ctx->subc->color+sr->dir,0,ctx->commrank,MPI_STATUS_IGNORE);
    487:         }
    488:         if ( sr->inertia0==-1 && !(sr->dir>0 && ctx->subc->color==ctx->npart-1) && !(sr->dir<0 && ctx->subc->color==0)) {
    489:           sr->inertia0 = sr->inertia1; sr->int0 = sr->int1;
    490:           MPI_Isend(&(sr->inertia0),1,MPIU_INT,ctx->subc->color-sr->dir,0,ctx->commrank,&req);
    491:           MPI_Isend(&(sr->int0),1,MPIU_REAL,ctx->subc->color-sr->dir,0,ctx->commrank,&req);
    492:         }
    493:       }
    494:       if ((sr->dir>0 && ctx->subc->color<ctx->npart-1)||(sr->dir<0 && ctx->subc->color>0)) {
    495:         MPI_Bcast(&sr->inertia1,1,MPIU_INT,0,PetscSubcommChild(ctx->subc));
    496:         MPI_Bcast(&sr->int1,1,MPIU_REAL,0,PetscSubcommChild(ctx->subc));
    497:       } else sr_glob->inertia1 = sr->inertia1;
    498:     }

    500:     /* last process in eps comm computes inertia1 */
    501:     if (ctx->npart==1 || ((sr->dir>0 && ctx->subc->color==ctx->npart-1) || (sr->dir<0 && ctx->subc->color==0))) {
    502:       EPSSliceGetInertia(eps,sr->int1,&sr->inertia1,ctx->detect?&zeros:NULL);
    503:       if (zeros) SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_USER,"Found singular matrix for the transformed problem in an interval endpoint defined by user");
    504:       if (!rank && sr->inertia0==-1) {
    505:         sr->inertia0 = sr->inertia1; sr->int0 = sr->int1;
    506:         MPI_Isend(&(sr->inertia0),1,MPIU_INT,ctx->subc->color-sr->dir,0,ctx->commrank,&req);
    507:         MPI_Isend(&(sr->int0),1,MPIU_REAL,ctx->subc->color-sr->dir,0,ctx->commrank,&req);
    508:       }
    509:       if (sr->hasEnd) {
    510:         sr->dir = -sr->dir; r = sr->int0; sr->int0 = sr->int1; sr->int1 = r;
    511:         i = sr->inertia0; sr->inertia0 = sr->inertia1; sr->inertia1 = i;
    512:       }
    513:     }

    515:     /* number of eigenvalues in interval */
    516:     sr->numEigs = (sr->dir)*(sr->inertia1 - sr->inertia0);
    517:     if (ctx->npart>1) {
    518:       /* memory allocate for subinterval eigenpairs */
    519:       EPSSliceAllocateSolution(eps,1);
    520:     }
    521:     dssz = eps->ncv+1;
    522:     if (sr->numEigs>0) {
    523:       DSGetSlepcSC(eps->ds,&sc);
    524:       sc->rg            = NULL;
    525:       sc->comparison    = SlepcCompareLargestMagnitude;
    526:       sc->comparisonctx = NULL;
    527:       sc->map           = NULL;
    528:       sc->mapobj        = NULL;
    529:     }
    530:     DSGetParallel(ctx->eps->ds,&ptype);
    531:     DSSetParallel(eps->ds,ptype);
    532:     DSGetMethod(ctx->eps->ds,&method);
    533:     DSSetMethod(eps->ds,method);
    534:   }
    535:   DSSetType(eps->ds,DSHEP);
    536:   DSSetCompact(eps->ds,PETSC_TRUE);
    537:   DSAllocate(eps->ds,dssz);
    538:   /* keep state of subcomm matrices to check that the user does not modify them */
    539:   EPSGetOperators(eps,&A,&B);
    540:   PetscObjectStateGet((PetscObject)A,&ctx->Astate);
    541:   PetscObjectGetId((PetscObject)A,&ctx->Aid);
    542:   if (B) {
    543:     PetscObjectStateGet((PetscObject)B,&ctx->Bstate);
    544:     PetscObjectGetId((PetscObject)B,&ctx->Bid);
    545:   } else {
    546:     ctx->Bstate=0;
    547:     ctx->Bid=0;
    548:   }
    549:   return(0);
    550: }

    552: static PetscErrorCode EPSSliceGatherEigenVectors(EPS eps)
    553: {
    554:   PetscErrorCode  ierr;
    555:   Vec             v,vg,v_loc;
    556:   IS              is1,is2;
    557:   VecScatter      vec_sc;
    558:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
    559:   PetscInt        nloc,m0,n0,i,si,idx,*idx1,*idx2,j;
    560:   PetscScalar     *array;
    561:   EPS_SR          sr_loc;
    562:   BV              V_loc;

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

    568:   /* Gather parallel eigenvectors */
    569:   BVGetColumn(eps->V,0,&v);
    570:   VecGetOwnershipRange(v,&n0,&m0);
    571:   BVRestoreColumn(eps->V,0,&v);
    572:   BVGetColumn(ctx->eps->V,0,&v);
    573:   VecGetLocalSize(v,&nloc);
    574:   BVRestoreColumn(ctx->eps->V,0,&v);
    575:   PetscMalloc2(m0-n0,&idx1,m0-n0,&idx2);
    576:   VecCreateMPI(PetscObjectComm((PetscObject)eps),nloc,PETSC_DECIDE,&vg);
    577:   idx = -1;
    578:   for (si=0;si<ctx->npart;si++) {
    579:     j = 0;
    580:     for (i=n0;i<m0;i++) {
    581:       idx1[j]   = i;
    582:       idx2[j++] = i+eps->n*si;
    583:     }
    584:     ISCreateGeneral(PetscObjectComm((PetscObject)eps),(m0-n0),idx1,PETSC_COPY_VALUES,&is1);
    585:     ISCreateGeneral(PetscObjectComm((PetscObject)eps),(m0-n0),idx2,PETSC_COPY_VALUES,&is2);
    586:     BVGetColumn(eps->V,0,&v);
    587:     VecScatterCreate(v,is1,vg,is2,&vec_sc);
    588:     BVRestoreColumn(eps->V,0,&v);
    589:     ISDestroy(&is1);
    590:     ISDestroy(&is2);
    591:     for (i=0;i<ctx->nconv_loc[si];i++) {
    592:       BVGetColumn(eps->V,++idx,&v);
    593:       if (ctx->subc->color==si) {
    594:         BVGetColumn(V_loc,i,&v_loc);
    595:         VecGetArray(v_loc,&array);
    596:         VecPlaceArray(vg,array);
    597:       }
    598:       VecScatterBegin(vec_sc,vg,v,INSERT_VALUES,SCATTER_REVERSE);
    599:       VecScatterEnd(vec_sc,vg,v,INSERT_VALUES,SCATTER_REVERSE);
    600:       if (ctx->subc->color==si) {
    601:         VecResetArray(vg);
    602:         VecRestoreArray(v_loc,&array);
    603:         BVRestoreColumn(V_loc,i,&v_loc);
    604:       }
    605:       BVRestoreColumn(eps->V,idx,&v);
    606:     }
    607:     VecScatterDestroy(&vec_sc);
    608:   }
    609:   PetscFree2(idx1,idx2);
    610:   VecDestroy(&vg);
    611:   return(0);
    612: }

    614: /*
    615:   EPSComputeVectors_Slice - Recover Eigenvectors from subcomunicators
    616:  */
    617: PetscErrorCode EPSComputeVectors_Slice(EPS eps)
    618: {
    619:   PetscErrorCode  ierr;
    620:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;

    623:   if (ctx->global && ctx->npart>1) {
    624:     EPSComputeVectors(ctx->eps);
    625:     EPSSliceGatherEigenVectors(eps);
    626:   }
    627:   return(0);
    628: }

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

    632: static PetscErrorCode EPSSliceGetInertias(EPS eps,PetscInt *n,PetscReal **shifts,PetscInt **inertias)
    633: {
    634:   PetscErrorCode  ierr;
    635:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
    636:   PetscInt        i=0,j,tmpi;
    637:   PetscReal       v,tmpr;
    638:   EPS_shift       s;

    641:   if (!eps->state) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONGSTATE,"Must call EPSSetUp() first");
    642:   if (!ctx->sr) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONGSTATE,"Only available in interval computations, see EPSSetInterval()");
    643:   if (!ctx->sr->s0) {  /* EPSSolve not called yet */
    644:     *n = 2;
    645:   } else {
    646:     *n = 1;
    647:     s = ctx->sr->s0;
    648:     while (s) {
    649:       (*n)++;
    650:       s = s->neighb[1];
    651:     }
    652:   }
    653:   PetscMalloc1(*n,shifts);
    654:   PetscMalloc1(*n,inertias);
    655:   if (!ctx->sr->s0) {  /* EPSSolve not called yet */
    656:     (*shifts)[0]   = ctx->sr->int0;
    657:     (*shifts)[1]   = ctx->sr->int1;
    658:     (*inertias)[0] = ctx->sr->inertia0;
    659:     (*inertias)[1] = ctx->sr->inertia1;
    660:   } else {
    661:     s = ctx->sr->s0;
    662:     while (s) {
    663:       (*shifts)[i]     = s->value;
    664:       (*inertias)[i++] = s->inertia;
    665:       s = s->neighb[1];
    666:     }
    667:     (*shifts)[i]   = ctx->sr->int1;
    668:     (*inertias)[i] = ctx->sr->inertia1;
    669:   }
    670:   /* remove possible duplicate in last position */
    671:   if ((*shifts)[(*n)-1]==(*shifts)[(*n)-2]) (*n)--;
    672:   /* sort result */
    673:   for (i=0;i<*n;i++) {
    674:     v = (*shifts)[i];
    675:     for (j=i+1;j<*n;j++) {
    676:       if (v > (*shifts)[j]) {
    677:         SWAP((*shifts)[i],(*shifts)[j],tmpr);
    678:         SWAP((*inertias)[i],(*inertias)[j],tmpi);
    679:         v = (*shifts)[i];
    680:       }
    681:     }
    682:   }
    683:   return(0);
    684: }

    686: static PetscErrorCode EPSSliceGatherSolution(EPS eps)
    687: {
    688:   PetscErrorCode  ierr;
    689:   PetscMPIInt     rank,nproc;
    690:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
    691:   PetscInt        i,idx,j;
    692:   PetscInt        *perm_loc,off=0,*inertias_loc,ns;
    693:   PetscScalar     *eigr_loc;
    694:   EPS_SR          sr_loc;
    695:   PetscReal       *shifts_loc;
    696:   PetscMPIInt     *disp,*ns_loc,aux;

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

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

    726:   /* Gather eigenvalues (same ranks have fully set of eigenvalues)*/
    727:   eigr_loc = sr_loc->eigr;
    728:   perm_loc = sr_loc->perm;
    729:   MPI_Comm_size(((PetscObject)eps)->comm,&nproc);
    730:   PetscMalloc1(ctx->npart,&disp);
    731:   disp[0] = 0;
    732:   for (i=1;i<ctx->npart;i++) disp[i] = disp[i-1]+ctx->nconv_loc[i-1];
    733:   if (nproc%ctx->npart==0) { /* subcommunicators with the same size */
    734:     PetscMPIIntCast(sr_loc->numEigs,&aux);
    735:     MPI_Allgatherv(eigr_loc,aux,MPIU_SCALAR,eps->eigr,ctx->nconv_loc,disp,MPIU_SCALAR,ctx->commrank); /* eigenvalues */
    736:     MPI_Allgatherv(perm_loc,aux,MPIU_INT,eps->perm,ctx->nconv_loc,disp,MPIU_INT,ctx->commrank); /* perm */
    737:     for (i=1;i<ctx->npart;i++) disp[i] = disp[i-1]+ns_loc[i-1];
    738:     PetscMPIIntCast(ns,&aux);
    739:     MPI_Allgatherv(shifts_loc,aux,MPIU_REAL,ctx->shifts,ns_loc,disp,MPIU_REAL,ctx->commrank); /* shifts */
    740:     MPI_Allgatherv(inertias_loc,aux,MPIU_INT,ctx->inertias,ns_loc,disp,MPIU_INT,ctx->commrank); /* inertias */
    741:     MPI_Allreduce(&sr_loc->itsKs,&eps->its,1,MPIU_INT,MPI_SUM,ctx->commrank);
    742:   } else { /* subcommunicators with different size */
    743:     MPI_Comm_rank(PetscSubcommChild(ctx->subc),&rank);
    744:     if (!rank) {
    745:       PetscMPIIntCast(sr_loc->numEigs,&aux);
    746:       MPI_Allgatherv(eigr_loc,aux,MPIU_SCALAR,eps->eigr,ctx->nconv_loc,disp,MPIU_SCALAR,ctx->commrank); /* eigenvalues */
    747:       MPI_Allgatherv(perm_loc,aux,MPIU_INT,eps->perm,ctx->nconv_loc,disp,MPIU_INT,ctx->commrank); /* perm */
    748:       for (i=1;i<ctx->npart;i++) disp[i] = disp[i-1]+ns_loc[i-1];
    749:       PetscMPIIntCast(ns,&aux);
    750:       MPI_Allgatherv(shifts_loc,aux,MPIU_REAL,ctx->shifts,ns_loc,disp,MPIU_REAL,ctx->commrank); /* shifts */
    751:       MPI_Allgatherv(inertias_loc,aux,MPIU_INT,ctx->inertias,ns_loc,disp,MPIU_INT,ctx->commrank); /* inertias */
    752:       MPI_Allreduce(&sr_loc->itsKs,&eps->its,1,MPIU_INT,MPI_SUM,ctx->commrank);
    753:     }
    754:     PetscMPIIntCast(eps->nconv,&aux);
    755:     MPI_Bcast(eps->eigr,aux,MPIU_SCALAR,0,PetscSubcommChild(ctx->subc));
    756:     MPI_Bcast(eps->perm,aux,MPIU_INT,0,PetscSubcommChild(ctx->subc));
    757:     MPI_Bcast(ctx->shifts,ctx->nshifts,MPIU_REAL,0,PetscSubcommChild(ctx->subc));
    758:     PetscMPIIntCast(ctx->nshifts,&aux);
    759:     MPI_Bcast(ctx->inertias,aux,MPIU_INT,0,PetscSubcommChild(ctx->subc));
    760:     MPI_Bcast(&eps->its,1,MPIU_INT,0,PetscSubcommChild(ctx->subc));
    761:   }
    762:   /* Update global array eps->perm */
    763:   idx = ctx->nconv_loc[0];
    764:   for (i=1;i<ctx->npart;i++) {
    765:     off += ctx->nconv_loc[i-1];
    766:     for (j=0;j<ctx->nconv_loc[i];j++) eps->perm[idx++] += off;
    767:   }

    769:   /* Gather parallel eigenvectors */
    770:   PetscFree(ns_loc);
    771:   PetscFree(disp);
    772:   PetscFree(shifts_loc);
    773:   PetscFree(inertias_loc);
    774:   return(0);
    775: }

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

    789:   sr = ctx->sr;
    790:   PetscNewLog(eps,&s);
    791:   s->value = val;
    792:   s->neighb[0] = neighb0;
    793:   if (neighb0) neighb0->neighb[1] = s;
    794:   s->neighb[1] = neighb1;
    795:   if (neighb1) neighb1->neighb[0] = s;
    796:   s->comp[0] = PETSC_FALSE;
    797:   s->comp[1] = PETSC_FALSE;
    798:   s->index = -1;
    799:   s->neigs = 0;
    800:   s->nconv[0] = s->nconv[1] = 0;
    801:   s->nsch[0] = s->nsch[1]=0;
    802:   /* Inserts in the stack of pending shifts */
    803:   /* If needed, the array is resized */
    804:   if (sr->nPend >= sr->maxPend) {
    805:     sr->maxPend *= 2;
    806:     PetscMalloc1(sr->maxPend,&pending2);
    807:     PetscLogObjectMemory((PetscObject)eps,sizeof(EPS_shift));
    808:     for (i=0;i<sr->nPend;i++) pending2[i] = sr->pending[i];
    809:     PetscFree(sr->pending);
    810:     sr->pending = pending2;
    811:   }
    812:   sr->pending[sr->nPend++]=s;
    813:   return(0);
    814: }

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

    827:   DSGetLeadingDimension(eps->ds,&ld);
    828:   dir = (sr->sPres->neighb[0] == sr->sPrev)?1:-1;
    829:   dir*=sr->dir;
    830:   k = 0;
    831:   for (i=0;i<sr->nS;i++) {
    832:     if (dir*PetscRealPart(sr->S[i])>0.0) {
    833:       sr->S[k] = sr->S[i];
    834:       sr->S[sr->nS+k] = sr->S[sr->nS+i];
    835:       BVGetColumn(sr->Vnext,k,&v);
    836:       BVCopyVec(eps->V,eps->nconv+i,v);
    837:       BVRestoreColumn(sr->Vnext,k,&v);
    838:       k++;
    839:       if (k>=sr->nS/2)break;
    840:     }
    841:   }
    842:   /* Copy to DS */
    843:   DSGetArray(eps->ds,DS_MAT_A,&A);
    844:   PetscMemzero(A,ld*ld*sizeof(PetscScalar));
    845:   for (i=0;i<k;i++) {
    846:     A[i*(1+ld)] = sr->S[i];
    847:     A[k+i*ld] = sr->S[sr->nS+i];
    848:   }
    849:   sr->nS = k;
    850:   DSRestoreArray(eps->ds,DS_MAT_A,&A);
    851:   DSGetDimensions(eps->ds,&nv,NULL,NULL,NULL,NULL);
    852:   DSSetDimensions(eps->ds,nv,0,0,k);
    853:   /* Append u to V */
    854:   BVGetColumn(sr->Vnext,sr->nS,&v);
    855:   BVCopyVec(eps->V,sr->nv,v);
    856:   BVRestoreColumn(sr->Vnext,sr->nS,&v);
    857:   return(0);
    858: }

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

    871:   sr = ctx->sr;
    872:   if (sr->nPend > 0) {
    873:     sr->sPrev = sr->sPres;
    874:     sr->sPres = sr->pending[--sr->nPend];
    875:     sPres = sr->sPres;
    876:     EPSSliceGetInertia(eps,sPres->value,&iner,ctx->detect?&zeros:NULL);
    877:     if (zeros) {
    878:       newShift = sPres->value*(1.0+SLICE_PTOL);
    879:       if (sr->dir*(sPres->neighb[0] && newShift-sPres->neighb[0]->value) < 0) newShift = (sPres->value+sPres->neighb[0]->value)/2;
    880:       else if (sPres->neighb[1] && sr->dir*(sPres->neighb[1]->value-newShift) < 0) newShift = (sPres->value+sPres->neighb[1]->value)/2;
    881:       EPSSliceGetInertia(eps,newShift,&iner,&zeros);
    882:       if (zeros) SETERRQ1(((PetscObject)eps)->comm,PETSC_ERR_CONV_FAILED,"Inertia computation fails in %g",newShift);
    883:       sPres->value = newShift;
    884:     }
    885:     sr->sPres->inertia = iner;
    886:     eps->target = sr->sPres->value;
    887:     eps->reason = EPS_CONVERGED_ITERATING;
    888:     eps->its = 0;
    889:   } else sr->sPres = NULL;
    890:   return(0);
    891: }

    893: /*
    894:    Symmetric KrylovSchur adapted to spectrum slicing:
    895:    Allows searching an specific amount of eigenvalues in the subintervals left and right.
    896:    Returns whether the search has succeeded
    897: */
    898: static PetscErrorCode EPSKrylovSchur_Slice(EPS eps)
    899: {
    900:   PetscErrorCode  ierr;
    901:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
    902:   PetscInt        i,k,l,ld,nv,*iwork,j;
    903:   Mat             U;
    904:   PetscScalar     *Q,*A;
    905:   PetscReal       *a,*b,beta;
    906:   PetscBool       breakdown;
    907:   PetscInt        count0,count1;
    908:   PetscReal       lambda;
    909:   EPS_shift       sPres;
    910:   PetscBool       complIterating;
    911:   PetscBool       sch0,sch1;
    912:   PetscInt        iterCompl=0,n0,n1;
    913:   EPS_SR          sr = ctx->sr;

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

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

    980:     /* Residual */
    981:     EPSKrylovConvergence(eps,PETSC_TRUE,eps->nconv,nv-eps->nconv,beta,1.0,&k);
    982:     /* Checking values obtained for completing */
    983:     for (i=0;i<k;i++) {
    984:       sr->back[i]=eps->eigr[i];
    985:     }
    986:     STBackTransform(eps->st,k,sr->back,eps->eigi);
    987:     count0=count1=0;
    988:     for (i=0;i<k;i++) {
    989:       lambda = PetscRealPart(sr->back[i]);
    990:       if (((sr->dir)*(sPres->value - lambda) > 0) && ((sr->dir)*(lambda - sPres->ext[0]) > 0)) count0++;
    991:       if (((sr->dir)*(lambda - sPres->value) > 0) && ((sr->dir)*(sPres->ext[1] - lambda) > 0)) count1++;
    992:     }
    993:     if (k>eps->nev && eps->ncv-k<5) eps->reason = EPS_CONVERGED_TOL;
    994:     else {
    995:       /* Checks completion */
    996:       if ((!sch0||count0 >= sPres->nsch[0]) && (!sch1 ||count1 >= sPres->nsch[1])) {
    997:         eps->reason = EPS_CONVERGED_TOL;
    998:       } else {
    999:         if (!complIterating && eps->its >= eps->max_it) eps->reason = EPS_DIVERGED_ITS;
    1000:         if (complIterating) {
    1001:           if (--iterCompl <= 0) eps->reason = EPS_DIVERGED_ITS;
    1002:         } else if (k >= eps->nev) {
    1003:           n0 = sPres->nsch[0]-count0;
    1004:           n1 = sPres->nsch[1]-count1;
    1005:           if (sr->iterCompl>0 && ((n0>0 && n0<= sr->nMAXCompl)||(n1>0&&n1<=sr->nMAXCompl))) {
    1006:             /* Iterating for completion*/
    1007:             complIterating = PETSC_TRUE;
    1008:             if (n0 >sr->nMAXCompl)sch0 = PETSC_FALSE;
    1009:             if (n1 >sr->nMAXCompl)sch1 = PETSC_FALSE;
    1010:             iterCompl = sr->iterCompl;
    1011:           } else eps->reason = EPS_CONVERGED_TOL;
    1012:         }
    1013:       }
    1014:     }
    1015:     /* Update l */
    1016:     if (eps->reason == EPS_CONVERGED_ITERATING) l = PetscMax(1,(PetscInt)((nv-k)*ctx->keep));
    1017:     else l = nv-k;
    1018:     if (breakdown) l=0;
    1019:     if (!ctx->lock && l>0 && eps->reason == EPS_CONVERGED_ITERATING) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */

    1021:     if (eps->reason == EPS_CONVERGED_ITERATING) {
    1022:       if (breakdown) {
    1023:         /* Start a new Lanczos factorization */
    1024:         PetscInfo2(eps,"Breakdown in Krylov-Schur method (it=%D norm=%g)\n",eps->its,(double)beta);
    1025:         EPSGetStartVector(eps,k,&breakdown);
    1026:         if (breakdown) {
    1027:           eps->reason = EPS_DIVERGED_BREAKDOWN;
    1028:           PetscInfo(eps,"Unable to generate more start vectors\n");
    1029:         }
    1030:       } else {
    1031:         /* Prepare the Rayleigh quotient for restart */
    1032:         DSGetArrayReal(eps->ds,DS_MAT_T,&a);
    1033:         DSGetArray(eps->ds,DS_MAT_Q,&Q);
    1034:         b = a + ld;
    1035:         for (i=k;i<k+l;i++) {
    1036:           a[i] = PetscRealPart(eps->eigr[i]);
    1037:           b[i] = PetscRealPart(Q[nv-1+i*ld]*beta);
    1038:         }
    1039:         DSRestoreArrayReal(eps->ds,DS_MAT_T,&a);
    1040:         DSRestoreArray(eps->ds,DS_MAT_Q,&Q);
    1041:       }
    1042:     }
    1043:     /* Update the corresponding vectors V(:,idx) = V*Q(:,idx) */
    1044:     DSGetMat(eps->ds,DS_MAT_Q,&U);
    1045:     BVMultInPlace(eps->V,U,eps->nconv,k+l);
    1046:     MatDestroy(&U);

    1048:     /* Normalize u and append it to V */
    1049:     if (eps->reason == EPS_CONVERGED_ITERATING && !breakdown) {
    1050:       BVCopyColumn(eps->V,nv,k+l);
    1051:     }
    1052:     eps->nconv = k;
    1053:     if (eps->reason != EPS_CONVERGED_ITERATING) {
    1054:       /* Store approximated values for next shift */
    1055:       DSGetArray(eps->ds,DS_MAT_Q,&Q);
    1056:       sr->nS = l;
    1057:       for (i=0;i<l;i++) {
    1058:         sr->S[i] = eps->eigr[i+k];/* Diagonal elements */
    1059:         sr->S[i+l] = Q[nv-1+(i+k)*ld]*beta; /* Out of diagonal elements */
    1060:       }
    1061:       DSRestoreArray(eps->ds,DS_MAT_Q,&Q);
    1062:     }
    1063:   }
    1064:   /* Check for completion */
    1065:   for (i=0;i< eps->nconv; i++) {
    1066:     if ((sr->dir)*PetscRealPart(eps->eigr[i])>0) sPres->nconv[1]++;
    1067:     else sPres->nconv[0]++;
    1068:   }
    1069:   sPres->comp[0] = PetscNot(count0 < sPres->nsch[0]);
    1070:   sPres->comp[1] = PetscNot(count1 < sPres->nsch[1]);
    1071:   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()");
    1072:   PetscFree(iwork);
    1073:   return(0);
    1074: }

    1076: /*
    1077:   Obtains value of subsequent shift
    1078: */
    1079: static PetscErrorCode EPSGetNewShiftValue(EPS eps,PetscInt side,PetscReal *newS)
    1080: {
    1081:   PetscReal       lambda,d_prev;
    1082:   PetscInt        i,idxP;
    1083:   EPS_SR          sr;
    1084:   EPS_shift       sPres,s;
    1085:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;

    1088:   sr = ctx->sr;
    1089:   sPres = sr->sPres;
    1090:   if (sPres->neighb[side]) {
    1091:   /* Completing a previous interval */
    1092:     if (!sPres->neighb[side]->neighb[side] && sPres->neighb[side]->nconv[side]==0) { /* One of the ends might be too far from eigenvalues */
    1093:       if (side) *newS = (sPres->value + PetscRealPart(sr->eigr[sr->perm[sr->indexEig-1]]))/2;
    1094:       else *newS = (sPres->value + PetscRealPart(sr->eigr[sr->perm[0]]))/2;
    1095:     } else *newS=(sPres->value + sPres->neighb[side]->value)/2;
    1096:   } else { /* (Only for side=1). Creating a new interval. */
    1097:     if (sPres->neigs==0) {/* No value has been accepted*/
    1098:       if (sPres->neighb[0]) {
    1099:         /* Multiplying by 10 the previous distance */
    1100:         *newS = sPres->value + 10*(sr->dir)*PetscAbsReal(sPres->value - sPres->neighb[0]->value);
    1101:         sr->nleap++;
    1102:         /* Stops when the interval is open and no values are found in the last 5 shifts (there might be infinite eigenvalues) */
    1103:         if (!sr->hasEnd && sr->nleap > 5) SETERRQ(PetscObjectComm((PetscObject)eps),1,"Unable to compute the wanted eigenvalues with open interval");
    1104:       } else { /* First shift */
    1105:         if (eps->nconv != 0) {
    1106:           /* Unaccepted values give information for next shift */
    1107:           idxP=0;/* Number of values left from shift */
    1108:           for (i=0;i<eps->nconv;i++) {
    1109:             lambda = PetscRealPart(eps->eigr[i]);
    1110:             if ((sr->dir)*(lambda - sPres->value) <0) idxP++;
    1111:             else break;
    1112:           }
    1113:           /* Avoiding subtraction of eigenvalues (might be the same).*/
    1114:           if (idxP>0) {
    1115:             d_prev = PetscAbsReal(sPres->value - PetscRealPart(eps->eigr[0]))/(idxP+0.3);
    1116:           } else {
    1117:             d_prev = PetscAbsReal(sPres->value - PetscRealPart(eps->eigr[eps->nconv-1]))/(eps->nconv+0.3);
    1118:           }
    1119:           *newS = sPres->value + ((sr->dir)*d_prev*eps->nev)/2;
    1120:         } else { /* No values found, no information for next shift */
    1121:           SETERRQ(PetscObjectComm((PetscObject)eps),1,"First shift renders no information");
    1122:         }
    1123:       }
    1124:     } else { /* Accepted values found */
    1125:       sr->nleap = 0;
    1126:       /* Average distance of values in previous subinterval */
    1127:       s = sPres->neighb[0];
    1128:       while (s && PetscAbs(s->inertia - sPres->inertia)==0) {
    1129:         s = s->neighb[0];/* Looking for previous shifts with eigenvalues within */
    1130:       }
    1131:       if (s) {
    1132:         d_prev = PetscAbsReal((sPres->value - s->value)/(sPres->inertia - s->inertia));
    1133:       } else { /* First shift. Average distance obtained with values in this shift */
    1134:         /* first shift might be too far from first wanted eigenvalue (no values found outside the interval)*/
    1135:         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)) {
    1136:           d_prev =  PetscAbsReal((PetscRealPart(sr->eigr[sr->indexEig-1]) - PetscRealPart(sr->eigr[0])))/(sPres->neigs+0.3);
    1137:         } else {
    1138:           d_prev = PetscAbsReal(PetscRealPart(sr->eigr[sr->indexEig-1]) - sPres->value)/(sPres->neigs+0.3);
    1139:         }
    1140:       }
    1141:       /* Average distance is used for next shift by adding it to value on the right or to shift */
    1142:       if ((sr->dir)*(PetscRealPart(sr->eigr[sPres->index + sPres->neigs -1]) - sPres->value)>0) {
    1143:         *newS = PetscRealPart(sr->eigr[sPres->index + sPres->neigs -1])+ ((sr->dir)*d_prev*(eps->nev))/2;
    1144:       } else { /* Last accepted value is on the left of shift. Adding to shift */
    1145:         *newS = sPres->value + ((sr->dir)*d_prev*(eps->nev))/2;
    1146:       }
    1147:     }
    1148:     /* End of interval can not be surpassed */
    1149:     if ((sr->dir)*(sr->int1 - *newS) < 0) *newS = sr->int1;
    1150:   }/* of neighb[side]==null */
    1151:   return(0);
    1152: }

    1154: /*
    1155:   Function for sorting an array of real values
    1156: */
    1157: static PetscErrorCode sortRealEigenvalues(PetscScalar *r,PetscInt *perm,PetscInt nr,PetscBool prev,PetscInt dir)
    1158: {
    1159:   PetscReal      re;
    1160:   PetscInt       i,j,tmp;

    1163:   if (!prev) for (i=0;i<nr;i++) perm[i] = i;
    1164:   /* Insertion sort */
    1165:   for (i=1;i<nr;i++) {
    1166:     re = PetscRealPart(r[perm[i]]);
    1167:     j = i-1;
    1168:     while (j>=0 && dir*(re - PetscRealPart(r[perm[j]])) <= 0) {
    1169:       tmp = perm[j]; perm[j] = perm[j+1]; perm[j+1] = tmp; j--;
    1170:     }
    1171:   }
    1172:   return(0);
    1173: }

    1175: /* Stores the pairs obtained since the last shift in the global arrays */
    1176: static PetscErrorCode EPSStoreEigenpairs(EPS eps)
    1177: {
    1178:   PetscErrorCode  ierr;
    1179:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
    1180:   PetscReal       lambda,err,norm;
    1181:   PetscInt        i,count;
    1182:   PetscBool       iscayley;
    1183:   EPS_SR          sr = ctx->sr;
    1184:   EPS_shift       sPres;
    1185:   Vec             v,w;

    1188:   sPres = sr->sPres;
    1189:   sPres->index = sr->indexEig;
    1190:   count = sr->indexEig;
    1191:   /* Back-transform */
    1192:   STBackTransform(eps->st,eps->nconv,eps->eigr,eps->eigi);
    1193:   PetscObjectTypeCompare((PetscObject)eps->st,STCAYLEY,&iscayley);
    1194:   /* Sort eigenvalues */
    1195:   sortRealEigenvalues(eps->eigr,eps->perm,eps->nconv,PETSC_FALSE,sr->dir);
    1196:   /* Values stored in global array */
    1197:   for (i=0;i<eps->nconv;i++) {
    1198:     lambda = PetscRealPart(eps->eigr[eps->perm[i]]);
    1199:     err = eps->errest[eps->perm[i]];

    1201:     if ((sr->dir)*(lambda - sPres->ext[0]) > 0 && (sr->dir)*(sPres->ext[1] - lambda) > 0) {/* Valid value */
    1202:       if (count>=sr->numEigs) SETERRQ(PetscObjectComm((PetscObject)eps),1,"Unexpected error in Spectrum Slicing");
    1203:       sr->eigr[count] = lambda;
    1204:       sr->errest[count] = err;
    1205:       /* Explicit purification */
    1206:       BVGetColumn(eps->V,eps->perm[i],&w);
    1207:       if (eps->purify) {
    1208:         BVGetColumn(sr->V,count,&v);
    1209:         STApply(eps->st,w,v);
    1210:         BVRestoreColumn(sr->V,count,&v);
    1211:       } else {
    1212:         BVInsertVec(sr->V,count,w);
    1213:       }
    1214:       BVRestoreColumn(eps->V,eps->perm[i],&w);
    1215:       BVNormColumn(sr->V,count,NORM_2,&norm);
    1216:       BVScaleColumn(sr->V,count,1.0/norm);
    1217:       count++;
    1218:     }
    1219:   }
    1220:   sPres->neigs = count - sr->indexEig;
    1221:   sr->indexEig = count;
    1222:   /* Global ordering array updating */
    1223:   sortRealEigenvalues(sr->eigr,sr->perm,count,PETSC_TRUE,sr->dir);
    1224:   return(0);
    1225: }

    1227: static PetscErrorCode EPSLookForDeflation(EPS eps)
    1228: {
    1229:   PetscErrorCode  ierr;
    1230:   PetscReal       val;
    1231:   PetscInt        i,count0=0,count1=0;
    1232:   EPS_shift       sPres;
    1233:   PetscInt        ini,fin,k,idx0,idx1;
    1234:   EPS_SR          sr;
    1235:   Vec             v;
    1236:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;

    1239:   sr = ctx->sr;
    1240:   sPres = sr->sPres;

    1242:   if (sPres->neighb[0]) ini = (sr->dir)*(sPres->neighb[0]->inertia - sr->inertia0);
    1243:   else ini = 0;
    1244:   fin = sr->indexEig;
    1245:   /* Selection of ends for searching new values */
    1246:   if (!sPres->neighb[0]) sPres->ext[0] = sr->int0;/* First shift */
    1247:   else sPres->ext[0] = sPres->neighb[0]->value;
    1248:   if (!sPres->neighb[1]) {
    1249:     if (sr->hasEnd) sPres->ext[1] = sr->int1;
    1250:     else sPres->ext[1] = (sr->dir > 0)?PETSC_MAX_REAL:PETSC_MIN_REAL;
    1251:   } else sPres->ext[1] = sPres->neighb[1]->value;
    1252:   /* Selection of values between right and left ends */
    1253:   for (i=ini;i<fin;i++) {
    1254:     val=PetscRealPart(sr->eigr[sr->perm[i]]);
    1255:     /* Values to the right of left shift */
    1256:     if ((sr->dir)*(val - sPres->ext[1]) < 0) {
    1257:       if ((sr->dir)*(val - sPres->value) < 0) count0++;
    1258:       else count1++;
    1259:     } else break;
    1260:   }
    1261:   /* The number of values on each side are found */
    1262:   if (sPres->neighb[0]) {
    1263:     sPres->nsch[0] = (sr->dir)*(sPres->inertia - sPres->neighb[0]->inertia)-count0;
    1264:     if (sPres->nsch[0]<0) SETERRQ(PetscObjectComm((PetscObject)eps),1,"Mismatch between number of values found and information from inertia, consider using EPSKrylovSchurSetDetectZeros()");
    1265:   } else sPres->nsch[0] = 0;

    1267:   if (sPres->neighb[1]) {
    1268:     sPres->nsch[1] = (sr->dir)*(sPres->neighb[1]->inertia - sPres->inertia) - count1;
    1269:     if (sPres->nsch[1]<0) SETERRQ(PetscObjectComm((PetscObject)eps),1,"Mismatch between number of values found and information from inertia, consider using EPSKrylovSchurSetDetectZeros()");
    1270:   } else sPres->nsch[1] = (sr->dir)*(sr->inertia1 - sPres->inertia);

    1272:   /* Completing vector of indexes for deflation */
    1273:   idx0 = ini;
    1274:   idx1 = ini+count0+count1;
    1275:   k=0;
    1276:   for (i=idx0;i<idx1;i++) sr->idxDef[k++]=sr->perm[i];
    1277:   BVDuplicateResize(eps->V,k+eps->ncv+1,&sr->Vnext);
    1278:   BVSetNumConstraints(sr->Vnext,k);
    1279:   for (i=0;i<k;i++) {
    1280:     BVGetColumn(sr->Vnext,-i-1,&v);
    1281:     BVCopyVec(sr->V,sr->idxDef[i],v);
    1282:     BVRestoreColumn(sr->Vnext,-i-1,&v);
    1283:   }

    1285:   /* For rational Krylov */
    1286:   if (sr->nS>0 && (sr->sPrev == sr->sPres->neighb[0] || sr->sPrev == sr->sPres->neighb[1])) {
    1287:     EPSPrepareRational(eps);
    1288:   }
    1289:   eps->nconv = 0;
    1290:   /* Get rid of temporary Vnext */
    1291:   BVDestroy(&eps->V);
    1292:   eps->V = sr->Vnext;
    1293:   sr->Vnext = NULL;
    1294:   return(0);
    1295: }

    1297: PetscErrorCode EPSSolve_KrylovSchur_Slice(EPS eps)
    1298: {
    1299:   PetscErrorCode   ierr;
    1300:   PetscInt         i,lds,ti;
    1301:   PetscReal        newS;
    1302:   EPS_KRYLOVSCHUR  *ctx=(EPS_KRYLOVSCHUR*)eps->data;
    1303:   EPS_SR           sr=ctx->sr;
    1304:   Mat              A,B=NULL;
    1305:   PetscObjectState Astate,Bstate=0;
    1306:   PetscObjectId    Aid,Bid=0;

    1309:   PetscCitationsRegister(citation,&cited);
    1310:   if (ctx->global) {
    1311:     EPSSolve_KrylovSchur_Slice(ctx->eps);
    1312:     ctx->eps->state = EPS_STATE_SOLVED;
    1313:     eps->reason = EPS_CONVERGED_TOL;
    1314:     if (ctx->npart>1) {
    1315:       /* Gather solution from subsolvers */
    1316:       EPSSliceGatherSolution(eps);
    1317:     } else {
    1318:       eps->nconv = sr->numEigs;
    1319:       eps->its   = ctx->eps->its;
    1320:       PetscFree(ctx->inertias);
    1321:       PetscFree(ctx->shifts);
    1322:       EPSSliceGetInertias(ctx->eps,&ctx->nshifts,&ctx->shifts,&ctx->inertias);
    1323:     }
    1324:   } else {
    1325:     if (ctx->npart==1) {
    1326:       sr->eigr   = ctx->eps->eigr;
    1327:       sr->eigi   = ctx->eps->eigi;
    1328:       sr->perm   = ctx->eps->perm;
    1329:       sr->errest = ctx->eps->errest;
    1330:       sr->V      = ctx->eps->V;
    1331:     }
    1332:     /* Check that the user did not modify subcomm matrices */
    1333:     EPSGetOperators(eps,&A,&B);
    1334:     PetscObjectStateGet((PetscObject)A,&Astate);
    1335:     PetscObjectGetId((PetscObject)A,&Aid);
    1336:     if (B) {
    1337:       PetscObjectStateGet((PetscObject)B,&Bstate);
    1338:       PetscObjectGetId((PetscObject)B,&Bid);
    1339:     }
    1340:     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");
    1341:     /* Only with eigenvalues present in the interval ...*/
    1342:     if (sr->numEigs==0) {
    1343:       eps->reason = EPS_CONVERGED_TOL;
    1344:       return(0);
    1345:     }
    1346:     /* Array of pending shifts */
    1347:     sr->maxPend = 100; /* Initial size */
    1348:     sr->nPend = 0;
    1349:     PetscMalloc1(sr->maxPend,&sr->pending);
    1350:     PetscLogObjectMemory((PetscObject)eps,(sr->maxPend)*sizeof(EPS_shift));
    1351:     EPSCreateShift(eps,sr->int0,NULL,NULL);
    1352:     /* extract first shift */
    1353:     sr->sPrev = NULL;
    1354:     sr->sPres = sr->pending[--sr->nPend];
    1355:     sr->sPres->inertia = sr->inertia0;
    1356:     eps->target = sr->sPres->value;
    1357:     sr->s0 = sr->sPres;
    1358:     sr->indexEig = 0;
    1359:     /* Memory reservation for auxiliary variables */
    1360:     lds = PetscMin(eps->mpd,eps->ncv);
    1361:     PetscCalloc1(lds*lds,&sr->S);
    1362:     PetscMalloc1(eps->ncv,&sr->back);
    1363:     PetscLogObjectMemory((PetscObject)eps,(sr->numEigs+2*eps->ncv)*sizeof(PetscScalar));
    1364:     for (i=0;i<sr->numEigs;i++) {
    1365:       sr->eigr[i]   = 0.0;
    1366:       sr->eigi[i]   = 0.0;
    1367:       sr->errest[i] = 0.0;
    1368:       sr->perm[i]   = i;
    1369:     }
    1370:     /* Vectors for deflation */
    1371:     PetscMalloc1(sr->numEigs,&sr->idxDef);
    1372:     PetscLogObjectMemory((PetscObject)eps,sr->numEigs*sizeof(PetscInt));
    1373:     sr->indexEig = 0;
    1374:     /* Main loop */
    1375:     while (sr->sPres) {
    1376:       /* Search for deflation */
    1377:       EPSLookForDeflation(eps);
    1378:       /* KrylovSchur */
    1379:       EPSKrylovSchur_Slice(eps);

    1381:       EPSStoreEigenpairs(eps);
    1382:       /* Select new shift */
    1383:       if (!sr->sPres->comp[1]) {
    1384:         EPSGetNewShiftValue(eps,1,&newS);
    1385:         EPSCreateShift(eps,newS,sr->sPres,sr->sPres->neighb[1]);
    1386:       }
    1387:       if (!sr->sPres->comp[0]) {
    1388:         /* Completing earlier interval */
    1389:         EPSGetNewShiftValue(eps,0,&newS);
    1390:         EPSCreateShift(eps,newS,sr->sPres->neighb[0],sr->sPres);
    1391:       }
    1392:       /* Preparing for a new search of values */
    1393:       EPSExtractShift(eps);
    1394:     }

    1396:     /* Updating eps values prior to exit */
    1397:     PetscFree(sr->S);
    1398:     PetscFree(sr->idxDef);
    1399:     PetscFree(sr->pending);
    1400:     PetscFree(sr->back);
    1401:     BVDuplicateResize(eps->V,eps->ncv+1,&sr->Vnext);
    1402:     BVSetNumConstraints(sr->Vnext,0);
    1403:     BVDestroy(&eps->V);
    1404:     eps->V      = sr->Vnext;
    1405:     eps->nconv  = sr->indexEig;
    1406:     eps->reason = EPS_CONVERGED_TOL;
    1407:     eps->its    = sr->itsKs;
    1408:     eps->nds    = 0;
    1409:     if (sr->dir<0) {
    1410:       for (i=0;i<eps->nconv/2;i++) {
    1411:         ti = sr->perm[i]; sr->perm[i] = sr->perm[eps->nconv-1-i]; sr->perm[eps->nconv-1-i] = ti;
    1412:       }
    1413:     }
    1414:   }
    1415:   return(0);
    1416: }