Actual source code: ks-slice.c
slepc-3.21.1 2024-04-26
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-, 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: {
     46:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
     47:   EPS_SR          sr=ctx->sr;
     48:   EPS_shift       s;

     50:   PetscFunctionBegin;
     51:   if (sr) {
     52:     if (ctx->npart>1) {
     53:       PetscCall(BVDestroy(&sr->V));
     54:       PetscCall(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:         PetscCall(PetscFree(s->neighb[0]));
     62:       }
     63:       PetscCall(PetscFree(s));
     64:     }
     65:     PetscCall(PetscFree(sr));
     66:   }
     67:   ctx->sr = NULL;
     68:   PetscFunctionReturn(PETSC_SUCCESS);
     69: }

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

     75:   PetscFunctionBegin;
     76:   if (!ctx->global) PetscFunctionReturn(PETSC_SUCCESS);
     77:   /* Reset auxiliary EPS */
     78:   PetscCall(EPSSliceResetSR(ctx->eps));
     79:   PetscCall(EPSReset(ctx->eps));
     80:   PetscCall(EPSSliceResetSR(eps));
     81:   PetscCall(PetscFree(ctx->inertias));
     82:   PetscCall(PetscFree(ctx->shifts));
     83:   PetscFunctionReturn(PETSC_SUCCESS);
     84: }

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

     90:   PetscFunctionBegin;
     91:   if (!ctx->global) PetscFunctionReturn(PETSC_SUCCESS);
     92:   /* Destroy auxiliary EPS */
     93:   PetscCall(EPSReset_KrylovSchur_Slice(eps));
     94:   PetscCall(EPSDestroy(&ctx->eps));
     95:   if (ctx->npart>1) {
     96:     PetscCall(PetscSubcommDestroy(&ctx->subc));
     97:     if (ctx->commset) {
     98:       PetscCallMPI(MPI_Comm_free(&ctx->commrank));
     99:       ctx->commset = PETSC_FALSE;
    100:     }
    101:     PetscCall(ISDestroy(&ctx->isrow));
    102:     PetscCall(ISDestroy(&ctx->iscol));
    103:     PetscCall(MatDestroyMatrices(1,&ctx->submata));
    104:     PetscCall(MatDestroyMatrices(1,&ctx->submatb));
    105:   }
    106:   PetscCall(PetscFree(ctx->subintervals));
    107:   PetscCall(PetscFree(ctx->nconv_loc));
    108:   PetscFunctionReturn(PETSC_SUCCESS);
    109: }

    111: /*
    112:   EPSSliceAllocateSolution - Allocate memory storage for common variables such
    113:   as eigenvalues and eigenvectors. The argument extra is used for methods
    114:   that require a working basis slightly larger than ncv.
    115: */
    116: static PetscErrorCode EPSSliceAllocateSolution(EPS eps,PetscInt extra)
    117: {
    118:   EPS_KRYLOVSCHUR    *ctx=(EPS_KRYLOVSCHUR*)eps->data;
    119:   PetscReal          eta;
    120:   PetscInt           k;
    121:   BVType             type;
    122:   BVOrthogType       orthog_type;
    123:   BVOrthogRefineType orthog_ref;
    124:   BVOrthogBlockType  ob_type;
    125:   Mat                matrix;
    126:   Vec                t;
    127:   EPS_SR             sr = ctx->sr;

    129:   PetscFunctionBegin;
    130:   /* allocate space for eigenvalues and friends */
    131:   k = PetscMax(1,sr->numEigs);
    132:   PetscCall(PetscFree4(sr->eigr,sr->eigi,sr->errest,sr->perm));
    133:   PetscCall(PetscMalloc4(k,&sr->eigr,k,&sr->eigi,k,&sr->errest,k,&sr->perm));

    135:   /* allocate sr->V and transfer options from eps->V */
    136:   PetscCall(BVDestroy(&sr->V));
    137:   PetscCall(BVCreate(PetscObjectComm((PetscObject)eps),&sr->V));
    138:   if (!eps->V) PetscCall(EPSGetBV(eps,&eps->V));
    139:   if (!((PetscObject)eps->V)->type_name) PetscCall(BVSetType(sr->V,BVMAT));
    140:   else {
    141:     PetscCall(BVGetType(eps->V,&type));
    142:     PetscCall(BVSetType(sr->V,type));
    143:   }
    144:   PetscCall(STMatCreateVecsEmpty(eps->st,&t,NULL));
    145:   PetscCall(BVSetSizesFromVec(sr->V,t,k));
    146:   PetscCall(VecDestroy(&t));
    147:   PetscCall(EPS_SetInnerProduct(eps));
    148:   PetscCall(BVGetMatrix(eps->V,&matrix,NULL));
    149:   PetscCall(BVSetMatrix(sr->V,matrix,PETSC_FALSE));
    150:   PetscCall(BVGetOrthogonalization(eps->V,&orthog_type,&orthog_ref,&eta,&ob_type));
    151:   PetscCall(BVSetOrthogonalization(sr->V,orthog_type,orthog_ref,eta,ob_type));
    152:   PetscFunctionReturn(PETSC_SUCCESS);
    153: }

    155: static PetscErrorCode EPSSliceGetEPS(EPS eps)
    156: {
    157:   EPS_KRYLOVSCHUR    *ctx=(EPS_KRYLOVSCHUR*)eps->data,*ctx_local;
    158:   BV                 V;
    159:   BVType             type;
    160:   PetscReal          eta;
    161:   BVOrthogType       orthog_type;
    162:   BVOrthogRefineType orthog_ref;
    163:   BVOrthogBlockType  ob_type;
    164:   PetscInt           i;
    165:   PetscReal          h,a,b;
    166:   PetscRandom        rand;
    167:   EPS_SR             sr=ctx->sr;

    169:   PetscFunctionBegin;
    170:   if (!ctx->eps) PetscCall(EPSKrylovSchurGetChildEPS(eps,&ctx->eps));

    172:   /* Determine subintervals */
    173:   if (ctx->npart==1) {
    174:     a = eps->inta; b = eps->intb;
    175:   } else {
    176:     if (!ctx->subintset) { /* uniform distribution if no set by user */
    177:       PetscCheck(sr->hasEnd,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"Global interval must be bounded for splitting it in uniform subintervals");
    178:       h = (eps->intb-eps->inta)/ctx->npart;
    179:       a = eps->inta+ctx->subc->color*h;
    180:       b = (ctx->subc->color==ctx->npart-1)?eps->intb:eps->inta+(ctx->subc->color+1)*h;
    181:       PetscCall(PetscFree(ctx->subintervals));
    182:       PetscCall(PetscMalloc1(ctx->npart+1,&ctx->subintervals));
    183:       for (i=0;i<ctx->npart;i++) ctx->subintervals[i] = eps->inta+h*i;
    184:       ctx->subintervals[ctx->npart] = eps->intb;
    185:     } else {
    186:       a = ctx->subintervals[ctx->subc->color];
    187:       b = ctx->subintervals[ctx->subc->color+1];
    188:     }
    189:   }
    190:   PetscCall(EPSSetInterval(ctx->eps,a,b));
    191:   PetscCall(EPSSetConvergenceTest(ctx->eps,eps->conv));
    192:   PetscCall(EPSSetDimensions(ctx->eps,ctx->nev,ctx->ncv,ctx->mpd));
    193:   PetscCall(EPSKrylovSchurSetLocking(ctx->eps,ctx->lock));

    195:   ctx_local = (EPS_KRYLOVSCHUR*)ctx->eps->data;
    196:   ctx_local->detect = ctx->detect;

    198:   /* transfer options from eps->V */
    199:   PetscCall(EPSGetBV(ctx->eps,&V));
    200:   PetscCall(BVGetRandomContext(V,&rand));  /* make sure the random context is available when duplicating */
    201:   if (!eps->V) PetscCall(EPSGetBV(eps,&eps->V));
    202:   if (!((PetscObject)eps->V)->type_name) PetscCall(BVSetType(V,BVMAT));
    203:   else {
    204:     PetscCall(BVGetType(eps->V,&type));
    205:     PetscCall(BVSetType(V,type));
    206:   }
    207:   PetscCall(BVGetOrthogonalization(eps->V,&orthog_type,&orthog_ref,&eta,&ob_type));
    208:   PetscCall(BVSetOrthogonalization(V,orthog_type,orthog_ref,eta,ob_type));

    210:   ctx->eps->which = eps->which;
    211:   ctx->eps->max_it = eps->max_it;
    212:   ctx->eps->tol = eps->tol;
    213:   ctx->eps->purify = eps->purify;
    214:   if (eps->tol==(PetscReal)PETSC_DEFAULT) eps->tol = SLEPC_DEFAULT_TOL;
    215:   PetscCall(EPSSetProblemType(ctx->eps,eps->problem_type));
    216:   PetscCall(EPSSetUp(ctx->eps));
    217:   ctx->eps->nconv = 0;
    218:   ctx->eps->its   = 0;
    219:   for (i=0;i<ctx->eps->ncv;i++) {
    220:     ctx->eps->eigr[i]   = 0.0;
    221:     ctx->eps->eigi[i]   = 0.0;
    222:     ctx->eps->errest[i] = 0.0;
    223:   }
    224:   PetscFunctionReturn(PETSC_SUCCESS);
    225: }

    227: static PetscErrorCode EPSSliceGetInertia(EPS eps,PetscReal shift,PetscInt *inertia,PetscInt *zeros)
    228: {
    229:   KSP            ksp,kspr;
    230:   PC             pc;
    231:   Mat            F;
    232:   PetscReal      nzshift=shift;
    233:   PetscBool      flg;

    235:   PetscFunctionBegin;
    236:   if (shift >= PETSC_MAX_REAL) { /* Right-open interval */
    237:     if (inertia) *inertia = eps->n;
    238:   } else if (shift <= PETSC_MIN_REAL) {
    239:     if (inertia) *inertia = 0;
    240:     if (zeros) *zeros = 0;
    241:   } else {
    242:     /* If the shift is zero, perturb it to a very small positive value.
    243:        The goal is that the nonzero pattern is the same in all cases and reuse
    244:        the symbolic factorizations */
    245:     nzshift = (shift==0.0)? 10.0/PETSC_MAX_REAL: shift;
    246:     PetscCall(STSetShift(eps->st,nzshift));
    247:     PetscCall(STGetKSP(eps->st,&ksp));
    248:     PetscCall(KSPGetPC(ksp,&pc));
    249:     PetscCall(PetscObjectTypeCompare((PetscObject)pc,PCREDUNDANT,&flg));
    250:     if (flg) {
    251:       PetscCall(PCRedundantGetKSP(pc,&kspr));
    252:       PetscCall(KSPGetPC(kspr,&pc));
    253:     }
    254:     PetscCall(PCFactorGetMatrix(pc,&F));
    255:     PetscCall(MatGetInertia(F,inertia,zeros,NULL));
    256:   }
    257:   if (inertia) PetscCall(PetscInfo(eps,"Computed inertia at shift %g: %" PetscInt_FMT "\n",(double)nzshift,*inertia));
    258:   PetscFunctionReturn(PETSC_SUCCESS);
    259: }

    261: /*
    262:    Dummy backtransform operation
    263:  */
    264: static PetscErrorCode EPSBackTransform_Skip(EPS eps)
    265: {
    266:   PetscFunctionBegin;
    267:   PetscFunctionReturn(PETSC_SUCCESS);
    268: }

    270: PetscErrorCode EPSSetUp_KrylovSchur_Slice(EPS eps)
    271: {
    272:   EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data,*ctx_glob;
    273:   EPS_SR          sr,sr_loc,sr_glob;
    274:   PetscInt        nEigs,dssz=1,i,zeros=0,off=0,method,hiteig=0;
    275:   PetscMPIInt     nproc,rank=0,aux;
    276:   PetscReal       r;
    277:   MPI_Request     req;
    278:   Mat             A,B=NULL;
    279:   DSParallelType  ptype;
    280:   MPI_Comm        child;

    282:   PetscFunctionBegin;
    283:   if (ctx->global) {
    284:     EPSCheckHermitianDefiniteCondition(eps,PETSC_TRUE," with spectrum slicing");
    285:     EPSCheckSinvertCayleyCondition(eps,PETSC_TRUE," with spectrum slicing");
    286:     PetscCheck(eps->inta!=eps->intb,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"This solver does not support computing all eigenvalues unless you provide a computational interval with EPSSetInterval()");
    287:     PetscCheck(eps->intb<PETSC_MAX_REAL || eps->inta>PETSC_MIN_REAL,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"The defined computational interval should have at least one of their sides bounded");
    288:     PetscCheck(eps->nds==0,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Spectrum slicing not supported in combination with deflation space");
    289:     EPSCheckUnsupportedCondition(eps,EPS_FEATURE_ARBITRARY | EPS_FEATURE_REGION | EPS_FEATURE_STOPPING,PETSC_TRUE," with spectrum slicing");
    290:     EPSCheckIgnoredCondition(eps,EPS_FEATURE_BALANCE,PETSC_TRUE," with spectrum slicing");
    291:     if (eps->tol==(PetscReal)PETSC_DEFAULT) {
    292: #if defined(PETSC_USE_REAL_SINGLE)
    293:       eps->tol = SLEPC_DEFAULT_TOL;
    294: #else
    295:       /* use tighter tolerance */
    296:       eps->tol = SLEPC_DEFAULT_TOL*1e-2;
    297: #endif
    298:     }
    299:     if (eps->max_it==PETSC_DEFAULT) eps->max_it = 100;
    300:     if (ctx->nev==1) ctx->nev = PetscMin(40,eps->n);  /* nev not set, use default value */
    301:     PetscCheck(eps->n<=10 || ctx->nev>=10,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"nev cannot be less than 10 in spectrum slicing runs");
    302:   }
    303:   eps->ops->backtransform = EPSBackTransform_Skip;

    305:   /* create spectrum slicing context and initialize it */
    306:   PetscCall(EPSSliceResetSR(eps));
    307:   PetscCall(PetscNew(&sr));
    308:   ctx->sr = sr;
    309:   sr->itsKs = 0;
    310:   sr->nleap = 0;
    311:   sr->nMAXCompl = eps->nev/4;
    312:   sr->iterCompl = eps->max_it/4;
    313:   sr->sPres = NULL;
    314:   sr->nS = 0;

    316:   if (ctx->npart==1 || ctx->global) {
    317:     /* check presence of ends and finding direction */
    318:     if ((eps->inta > PETSC_MIN_REAL && !(ctx->subintervals && ctx->subintervals[0]==ctx->subintervals[1])) || eps->intb >= PETSC_MAX_REAL) {
    319:       sr->int0 = eps->inta;
    320:       sr->int1 = eps->intb;
    321:       sr->dir = 1;
    322:       if (eps->intb >= PETSC_MAX_REAL) { /* Right-open interval */
    323:         sr->hasEnd = PETSC_FALSE;
    324:       } else sr->hasEnd = PETSC_TRUE;
    325:     } else {
    326:       sr->int0 = eps->intb;
    327:       sr->int1 = eps->inta;
    328:       sr->dir = -1;
    329:       sr->hasEnd = PetscNot(eps->inta <= PETSC_MIN_REAL);
    330:     }
    331:   }
    332:   if (ctx->global) {
    333:     PetscCall(EPSSetDimensions_Default(eps,ctx->nev,&ctx->ncv,&ctx->mpd));
    334:     /* create subintervals and initialize auxiliary eps for slicing runs */
    335:     PetscCall(EPSKrylovSchurGetChildEPS(eps,&ctx->eps));
    336:     /* prevent computation of factorization in global eps */
    337:     PetscCall(STSetTransform(eps->st,PETSC_FALSE));
    338:     PetscCall(EPSSliceGetEPS(eps));
    339:     sr_loc = ((EPS_KRYLOVSCHUR*)ctx->eps->data)->sr;
    340:     if (ctx->npart>1) {
    341:       PetscCall(PetscSubcommGetChild(ctx->subc,&child));
    342:       if ((sr->dir>0&&ctx->subc->color==0)||(sr->dir<0&&ctx->subc->color==ctx->npart-1)) sr->inertia0 = sr_loc->inertia0;
    343:       PetscCallMPI(MPI_Comm_rank(child,&rank));
    344:       if (!rank) PetscCallMPI(MPI_Bcast(&sr->inertia0,1,MPIU_INT,(sr->dir>0)?0:ctx->npart-1,ctx->commrank));
    345:       PetscCallMPI(MPI_Bcast(&sr->inertia0,1,MPIU_INT,0,child));
    346:       PetscCall(PetscFree(ctx->nconv_loc));
    347:       PetscCall(PetscMalloc1(ctx->npart,&ctx->nconv_loc));
    348:       PetscCallMPI(MPI_Comm_size(((PetscObject)eps)->comm,&nproc));
    349:       if (sr->dir<0) off = 1;
    350:       if (nproc%ctx->npart==0) { /* subcommunicators with the same size */
    351:         PetscCall(PetscMPIIntCast(sr_loc->numEigs,&aux));
    352:         PetscCallMPI(MPI_Allgather(&aux,1,MPI_INT,ctx->nconv_loc,1,MPI_INT,ctx->commrank));
    353:         PetscCallMPI(MPI_Allgather(sr_loc->dir==sr->dir?&sr_loc->int0:&sr_loc->int1,1,MPIU_REAL,ctx->subintervals+off,1,MPIU_REAL,ctx->commrank));
    354:       } else {
    355:         PetscCallMPI(MPI_Comm_rank(child,&rank));
    356:         if (!rank) {
    357:           PetscCall(PetscMPIIntCast(sr_loc->numEigs,&aux));
    358:           PetscCallMPI(MPI_Allgather(&aux,1,MPI_INT,ctx->nconv_loc,1,MPI_INT,ctx->commrank));
    359:           PetscCallMPI(MPI_Allgather(sr_loc->dir==sr->dir?&sr_loc->int0:&sr_loc->int1,1,MPIU_REAL,ctx->subintervals+off,1,MPIU_REAL,ctx->commrank));
    360:         }
    361:         PetscCall(PetscMPIIntCast(ctx->npart,&aux));
    362:         PetscCallMPI(MPI_Bcast(ctx->nconv_loc,aux,MPI_INT,0,child));
    363:         PetscCallMPI(MPI_Bcast(ctx->subintervals+off,aux,MPIU_REAL,0,child));
    364:       }
    365:       nEigs = 0;
    366:       for (i=0;i<ctx->npart;i++) nEigs += ctx->nconv_loc[i];
    367:     } else {
    368:       nEigs = sr_loc->numEigs;
    369:       sr->inertia0 = sr_loc->inertia0;
    370:       sr->dir = sr_loc->dir;
    371:     }
    372:     sr->inertia1 = sr->inertia0+sr->dir*nEigs;
    373:     sr->numEigs = nEigs;
    374:     eps->nev = nEigs;
    375:     eps->ncv = nEigs;
    376:     eps->mpd = nEigs;
    377:   } else {
    378:     ctx_glob = (EPS_KRYLOVSCHUR*)ctx->eps->data;
    379:     sr_glob = ctx_glob->sr;
    380:     if (ctx->npart>1) {
    381:       sr->dir = sr_glob->dir;
    382:       sr->int0 = (sr->dir==1)?eps->inta:eps->intb;
    383:       sr->int1 = (sr->dir==1)?eps->intb:eps->inta;
    384:       if ((sr->dir>0&&ctx->subc->color==ctx->npart-1)||(sr->dir<0&&ctx->subc->color==0)) sr->hasEnd = sr_glob->hasEnd;
    385:       else sr->hasEnd = PETSC_TRUE;
    386:     }
    387:     /* sets first shift */
    388:     PetscCall(STSetShift(eps->st,(sr->int0==0.0)?10.0/PETSC_MAX_REAL:sr->int0));
    389:     PetscCall(STSetUp(eps->st));

    391:     /* compute inertia0 */
    392:     PetscCall(EPSSliceGetInertia(eps,sr->int0,&sr->inertia0,ctx->detect?&zeros:NULL));
    393:     /* undocumented option to control what to do when an eigenvalue is found:
    394:        - error out if it's the endpoint of the user-provided interval (or sub-interval)
    395:        - if it's an endpoint computed internally:
    396:           + if hiteig=0 error out
    397:           + else if hiteig=1 the subgroup that hit the eigenvalue does nothing
    398:           + otherwise the subgroup that hit the eigenvalue perturbs the shift and recomputes inertia
    399:     */
    400:     PetscCall(PetscOptionsGetInt(NULL,NULL,"-eps_krylovschur_hiteigenvalue",&hiteig,NULL));
    401:     if (zeros) { /* error in factorization */
    402:       PetscCheck(sr->int0!=ctx->eps->inta && sr->int0!=ctx->eps->intb,((PetscObject)eps)->comm,PETSC_ERR_USER,"Found singular matrix for the transformed problem in the interval endpoint");
    403:       PetscCheck(!ctx_glob->subintset || hiteig,((PetscObject)eps)->comm,PETSC_ERR_USER,"Found singular matrix for the transformed problem in an interval endpoint defined by user");
    404:       if (hiteig==1) { /* idle subgroup */
    405:         sr->inertia0 = -1;
    406:       } else { /* perturb shift */
    407:         sr->int0 *= (1.0+SLICE_PTOL);
    408:         PetscCall(EPSSliceGetInertia(eps,sr->int0,&sr->inertia0,&zeros));
    409:         PetscCheck(zeros==0,((PetscObject)eps)->comm,PETSC_ERR_CONV_FAILED,"Inertia computation fails in %g",(double)sr->int1);
    410:       }
    411:     }
    412:     if (ctx->npart>1) {
    413:       PetscCall(PetscSubcommGetChild(ctx->subc,&child));
    414:       /* inertia1 is received from neighbour */
    415:       PetscCallMPI(MPI_Comm_rank(child,&rank));
    416:       if (!rank) {
    417:         if (sr->inertia0!=-1 && ((sr->dir>0 && ctx->subc->color>0) || (sr->dir<0 && ctx->subc->color<ctx->npart-1))) { /* send inertia0 to neighbour0 */
    418:           PetscCallMPI(MPI_Isend(&sr->inertia0,1,MPIU_INT,ctx->subc->color-sr->dir,0,ctx->commrank,&req));
    419:           PetscCallMPI(MPI_Isend(&sr->int0,1,MPIU_REAL,ctx->subc->color-sr->dir,0,ctx->commrank,&req));
    420:         }
    421:         if ((sr->dir>0 && ctx->subc->color<ctx->npart-1)|| (sr->dir<0 && ctx->subc->color>0)) { /* receive inertia1 from neighbour1 */
    422:           PetscCallMPI(MPI_Recv(&sr->inertia1,1,MPIU_INT,ctx->subc->color+sr->dir,0,ctx->commrank,MPI_STATUS_IGNORE));
    423:           PetscCallMPI(MPI_Recv(&sr->int1,1,MPIU_REAL,ctx->subc->color+sr->dir,0,ctx->commrank,MPI_STATUS_IGNORE));
    424:         }
    425:         if (sr->inertia0==-1 && !(sr->dir>0 && ctx->subc->color==ctx->npart-1) && !(sr->dir<0 && ctx->subc->color==0)) {
    426:           sr->inertia0 = sr->inertia1; sr->int0 = sr->int1;
    427:           PetscCallMPI(MPI_Isend(&sr->inertia0,1,MPIU_INT,ctx->subc->color-sr->dir,0,ctx->commrank,&req));
    428:           PetscCallMPI(MPI_Isend(&sr->int0,1,MPIU_REAL,ctx->subc->color-sr->dir,0,ctx->commrank,&req));
    429:         }
    430:       }
    431:       if ((sr->dir>0 && ctx->subc->color<ctx->npart-1)||(sr->dir<0 && ctx->subc->color>0)) {
    432:         PetscCallMPI(MPI_Bcast(&sr->inertia1,1,MPIU_INT,0,child));
    433:         PetscCallMPI(MPI_Bcast(&sr->int1,1,MPIU_REAL,0,child));
    434:       } else sr_glob->inertia1 = sr->inertia1;
    435:     }

    437:     /* last process in eps comm computes inertia1 */
    438:     if (ctx->npart==1 || ((sr->dir>0 && ctx->subc->color==ctx->npart-1) || (sr->dir<0 && ctx->subc->color==0))) {
    439:       PetscCall(EPSSliceGetInertia(eps,sr->int1,&sr->inertia1,ctx->detect?&zeros:NULL));
    440:       PetscCheck(zeros==0,((PetscObject)eps)->comm,PETSC_ERR_USER,"Found singular matrix for the transformed problem in an interval endpoint defined by user");
    441:       if (!rank && sr->inertia0==-1) {
    442:         sr->inertia0 = sr->inertia1; sr->int0 = sr->int1;
    443:         PetscCallMPI(MPI_Isend(&sr->inertia0,1,MPIU_INT,ctx->subc->color-sr->dir,0,ctx->commrank,&req));
    444:         PetscCallMPI(MPI_Isend(&sr->int0,1,MPIU_REAL,ctx->subc->color-sr->dir,0,ctx->commrank,&req));
    445:       }
    446:       if (sr->hasEnd) {
    447:         sr->dir = -sr->dir; r = sr->int0; sr->int0 = sr->int1; sr->int1 = r;
    448:         i = sr->inertia0; sr->inertia0 = sr->inertia1; sr->inertia1 = i;
    449:       }
    450:     }

    452:     /* number of eigenvalues in interval */
    453:     sr->numEigs = (sr->dir)*(sr->inertia1 - sr->inertia0);
    454:     if (ctx->npart>1) {
    455:       /* memory allocate for subinterval eigenpairs */
    456:       PetscCall(EPSSliceAllocateSolution(eps,1));
    457:     }
    458:     dssz = eps->ncv+1;
    459:     PetscCall(DSGetParallel(ctx->eps->ds,&ptype));
    460:     PetscCall(DSSetParallel(eps->ds,ptype));
    461:     PetscCall(DSGetMethod(ctx->eps->ds,&method));
    462:     PetscCall(DSSetMethod(eps->ds,method));
    463:   }
    464:   PetscCall(DSSetType(eps->ds,DSHEP));
    465:   PetscCall(DSSetCompact(eps->ds,PETSC_TRUE));
    466:   PetscCall(DSAllocate(eps->ds,dssz));
    467:   /* keep state of subcomm matrices to check that the user does not modify them */
    468:   PetscCall(EPSGetOperators(eps,&A,&B));
    469:   PetscCall(PetscObjectStateGet((PetscObject)A,&ctx->Astate));
    470:   PetscCall(PetscObjectGetId((PetscObject)A,&ctx->Aid));
    471:   if (B) {
    472:     PetscCall(PetscObjectStateGet((PetscObject)B,&ctx->Bstate));
    473:     PetscCall(PetscObjectGetId((PetscObject)B,&ctx->Bid));
    474:   } else {
    475:     ctx->Bstate=0;
    476:     ctx->Bid=0;
    477:   }
    478:   PetscFunctionReturn(PETSC_SUCCESS);
    479: }

    481: static PetscErrorCode EPSSliceGatherEigenVectors(EPS eps)
    482: {
    483:   Vec             v,vg,v_loc;
    484:   IS              is1,is2;
    485:   VecScatter      vec_sc;
    486:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
    487:   PetscInt        nloc,m0,n0,i,si,idx,*idx1,*idx2,j;
    488:   PetscScalar     *array;
    489:   EPS_SR          sr_loc;
    490:   BV              V_loc;

    492:   PetscFunctionBegin;
    493:   sr_loc = ((EPS_KRYLOVSCHUR*)ctx->eps->data)->sr;
    494:   V_loc = sr_loc->V;

    496:   /* Gather parallel eigenvectors */
    497:   PetscCall(BVGetColumn(eps->V,0,&v));
    498:   PetscCall(VecGetOwnershipRange(v,&n0,&m0));
    499:   PetscCall(BVRestoreColumn(eps->V,0,&v));
    500:   PetscCall(BVGetColumn(ctx->eps->V,0,&v));
    501:   PetscCall(VecGetLocalSize(v,&nloc));
    502:   PetscCall(BVRestoreColumn(ctx->eps->V,0,&v));
    503:   PetscCall(PetscMalloc2(m0-n0,&idx1,m0-n0,&idx2));
    504:   PetscCall(VecCreateMPI(PetscObjectComm((PetscObject)eps),nloc,PETSC_DECIDE,&vg));
    505:   idx = -1;
    506:   for (si=0;si<ctx->npart;si++) {
    507:     j = 0;
    508:     for (i=n0;i<m0;i++) {
    509:       idx1[j]   = i;
    510:       idx2[j++] = i+eps->n*si;
    511:     }
    512:     PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)eps),(m0-n0),idx1,PETSC_COPY_VALUES,&is1));
    513:     PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)eps),(m0-n0),idx2,PETSC_COPY_VALUES,&is2));
    514:     PetscCall(BVGetColumn(eps->V,0,&v));
    515:     PetscCall(VecScatterCreate(v,is1,vg,is2,&vec_sc));
    516:     PetscCall(BVRestoreColumn(eps->V,0,&v));
    517:     PetscCall(ISDestroy(&is1));
    518:     PetscCall(ISDestroy(&is2));
    519:     for (i=0;i<ctx->nconv_loc[si];i++) {
    520:       PetscCall(BVGetColumn(eps->V,++idx,&v));
    521:       if (ctx->subc->color==si) {
    522:         PetscCall(BVGetColumn(V_loc,i,&v_loc));
    523:         PetscCall(VecGetArray(v_loc,&array));
    524:         PetscCall(VecPlaceArray(vg,array));
    525:       }
    526:       PetscCall(VecScatterBegin(vec_sc,vg,v,INSERT_VALUES,SCATTER_REVERSE));
    527:       PetscCall(VecScatterEnd(vec_sc,vg,v,INSERT_VALUES,SCATTER_REVERSE));
    528:       if (ctx->subc->color==si) {
    529:         PetscCall(VecResetArray(vg));
    530:         PetscCall(VecRestoreArray(v_loc,&array));
    531:         PetscCall(BVRestoreColumn(V_loc,i,&v_loc));
    532:       }
    533:       PetscCall(BVRestoreColumn(eps->V,idx,&v));
    534:     }
    535:     PetscCall(VecScatterDestroy(&vec_sc));
    536:   }
    537:   PetscCall(PetscFree2(idx1,idx2));
    538:   PetscCall(VecDestroy(&vg));
    539:   PetscFunctionReturn(PETSC_SUCCESS);
    540: }

    542: /*
    543:   EPSComputeVectors_Slice - Recover Eigenvectors from subcomunicators
    544:  */
    545: PetscErrorCode EPSComputeVectors_Slice(EPS eps)
    546: {
    547:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;

    549:   PetscFunctionBegin;
    550:   if (ctx->global && ctx->npart>1) {
    551:     PetscCall(EPSComputeVectors(ctx->eps));
    552:     PetscCall(EPSSliceGatherEigenVectors(eps));
    553:   }
    554:   PetscFunctionReturn(PETSC_SUCCESS);
    555: }

    557: #define SWAP(a,b,t) do {t=a;a=b;b=t;} while (0)

    559: static PetscErrorCode EPSSliceGetInertias(EPS eps,PetscInt *n,PetscReal **shifts,PetscInt **inertias)
    560: {
    561:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
    562:   PetscInt        i=0,j,tmpi;
    563:   PetscReal       v,tmpr;
    564:   EPS_shift       s;

    566:   PetscFunctionBegin;
    567:   PetscCheck(eps->state,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONGSTATE,"Must call EPSSetUp() first");
    568:   PetscCheck(ctx->sr,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONGSTATE,"Only available in interval computations, see EPSSetInterval()");
    569:   if (!ctx->sr->s0) {  /* EPSSolve not called yet */
    570:     *n = 2;
    571:   } else {
    572:     *n = 1;
    573:     s = ctx->sr->s0;
    574:     while (s) {
    575:       (*n)++;
    576:       s = s->neighb[1];
    577:     }
    578:   }
    579:   PetscCall(PetscMalloc1(*n,shifts));
    580:   PetscCall(PetscMalloc1(*n,inertias));
    581:   if (!ctx->sr->s0) {  /* EPSSolve not called yet */
    582:     (*shifts)[0]   = ctx->sr->int0;
    583:     (*shifts)[1]   = ctx->sr->int1;
    584:     (*inertias)[0] = ctx->sr->inertia0;
    585:     (*inertias)[1] = ctx->sr->inertia1;
    586:   } else {
    587:     s = ctx->sr->s0;
    588:     while (s) {
    589:       (*shifts)[i]     = s->value;
    590:       (*inertias)[i++] = s->inertia;
    591:       s = s->neighb[1];
    592:     }
    593:     (*shifts)[i]   = ctx->sr->int1;
    594:     (*inertias)[i] = ctx->sr->inertia1;
    595:   }
    596:   /* remove possible duplicate in last position */
    597:   if ((*shifts)[(*n)-1]==(*shifts)[(*n)-2]) (*n)--;
    598:   /* sort result */
    599:   for (i=0;i<*n;i++) {
    600:     v = (*shifts)[i];
    601:     for (j=i+1;j<*n;j++) {
    602:       if (v > (*shifts)[j]) {
    603:         SWAP((*shifts)[i],(*shifts)[j],tmpr);
    604:         SWAP((*inertias)[i],(*inertias)[j],tmpi);
    605:         v = (*shifts)[i];
    606:       }
    607:     }
    608:   }
    609:   PetscFunctionReturn(PETSC_SUCCESS);
    610: }

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

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

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

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

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

    701: /*
    702:    Fills the fields of a shift structure
    703: */
    704: static PetscErrorCode EPSCreateShift(EPS eps,PetscReal val,EPS_shift neighb0,EPS_shift neighb1)
    705: {
    706:   EPS_shift       s,*pending2;
    707:   PetscInt        i;
    708:   EPS_SR          sr;
    709:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;

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

    742: /* Prepare for Rational Krylov update */
    743: static PetscErrorCode EPSPrepareRational(EPS eps)
    744: {
    745:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
    746:   PetscInt        dir,i,k,ld,nv;
    747:   PetscScalar     *A;
    748:   EPS_SR          sr = ctx->sr;
    749:   Vec             v;

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

    785: /* Provides next shift to be computed */
    786: static PetscErrorCode EPSExtractShift(EPS eps)
    787: {
    788:   PetscInt        iner,zeros=0;
    789:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
    790:   EPS_SR          sr;
    791:   PetscReal       newShift,diam,ptol;
    792:   EPS_shift       sPres;

    794:   PetscFunctionBegin;
    795:   sr = ctx->sr;
    796:   if (sr->nPend > 0) {
    797:     if (sr->sPres==sr->pending[sr->nPend-1]) {
    798:       eps->reason = EPS_CONVERGED_ITERATING;
    799:       eps->its = 0;
    800:       sr->nPend--;
    801:       sr->sPres->rep = PETSC_TRUE;
    802:       PetscFunctionReturn(PETSC_SUCCESS);
    803:     }
    804:     sr->sPrev = sr->sPres;
    805:     sr->sPres = sr->pending[--sr->nPend];
    806:     sPres = sr->sPres;
    807:     PetscCall(EPSSliceGetInertia(eps,sPres->value,&iner,ctx->detect?&zeros:NULL));
    808:     if (zeros) {
    809:       diam = PetscMin(PetscAbsReal(sPres->neighb[0]->value-sPres->value),PetscAbsReal(sPres->neighb[1]->value-sPres->value));
    810:       ptol = PetscMin(SLICE_PTOL,diam/2);
    811:       newShift = sPres->value*(1.0+ptol);
    812:       if (sr->dir*(sPres->neighb[0] && newShift-sPres->neighb[0]->value) < 0) newShift = (sPres->value+sPres->neighb[0]->value)/2;
    813:       else if (sPres->neighb[1] && sr->dir*(sPres->neighb[1]->value-newShift) < 0) newShift = (sPres->value+sPres->neighb[1]->value)/2;
    814:       PetscCall(EPSSliceGetInertia(eps,newShift,&iner,&zeros));
    815:       PetscCheck(zeros==0,((PetscObject)eps)->comm,PETSC_ERR_CONV_FAILED,"Inertia computation fails in %g",(double)newShift);
    816:       sPres->value = newShift;
    817:     }
    818:     sr->sPres->inertia = iner;
    819:     eps->target = sr->sPres->value;
    820:     eps->reason = EPS_CONVERGED_ITERATING;
    821:     eps->its = 0;
    822:   } else sr->sPres = NULL;
    823:   PetscFunctionReturn(PETSC_SUCCESS);
    824: }

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

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

    881:     /* Solve projected problem and compute residual norm estimates */
    882:     if (eps->its == 1 && l > 0) {/* After rational update */
    883:       PetscCall(DSGetArray(eps->ds,DS_MAT_A,&A));
    884:       PetscCall(DSGetArrayReal(eps->ds,DS_MAT_T,&a));
    885:       b = a + ld;
    886:       k = eps->nconv+l;
    887:       A[k*ld+k-1] = A[(k-1)*ld+k];
    888:       A[k*ld+k] = a[k];
    889:       for (j=k+1; j< nv; j++) {
    890:         A[j*ld+j] = a[j];
    891:         A[j*ld+j-1] = b[j-1] ;
    892:         A[(j-1)*ld+j] = b[j-1];
    893:       }
    894:       PetscCall(DSRestoreArray(eps->ds,DS_MAT_A,&A));
    895:       PetscCall(DSRestoreArrayReal(eps->ds,DS_MAT_T,&a));
    896:       PetscCall(DSSolve(eps->ds,eps->eigr,NULL));
    897:       PetscCall(DSSort(eps->ds,eps->eigr,NULL,NULL,NULL,NULL));
    898:       PetscCall(DSSetCompact(eps->ds,PETSC_TRUE));
    899:     } else { /* Restart */
    900:       PetscCall(DSSolve(eps->ds,eps->eigr,NULL));
    901:       PetscCall(DSSort(eps->ds,eps->eigr,NULL,NULL,NULL,NULL));
    902:     }
    903:     PetscCall(DSSynchronize(eps->ds,eps->eigr,NULL));

    905:     /* Residual */
    906:     PetscCall(EPSKrylovConvergence(eps,PETSC_TRUE,eps->nconv,nv-eps->nconv,beta,0.0,1.0,&k));
    907:     /* Checking values obtained for completing */
    908:     for (i=0;i<k;i++) {
    909:       sr->back[i]=eps->eigr[i];
    910:     }
    911:     PetscCall(STBackTransform(eps->st,k,sr->back,eps->eigi));
    912:     count0=count1=0;
    913:     for (i=0;i<k;i++) {
    914:       lambda = PetscRealPart(sr->back[i]);
    915:       if ((sr->dir*(sPres->value - lambda) > 0) && (sr->dir*(lambda - sPres->ext[0]) > 0)) count0++;
    916:       if ((sr->dir*(lambda - sPres->value) > 0) && (sr->dir*(sPres->ext[1] - lambda) > 0)) count1++;
    917:     }
    918:     if (k>eps->nev && eps->ncv-k<5) eps->reason = EPS_CONVERGED_TOL;
    919:     else {
    920:       /* Checks completion */
    921:       if ((!sch0||count0 >= sPres->nsch[0]) && (!sch1 ||count1 >= sPres->nsch[1])) {
    922:         eps->reason = EPS_CONVERGED_TOL;
    923:       } else {
    924:         if (!complIterating && eps->its >= eps->max_it) eps->reason = EPS_DIVERGED_ITS;
    925:         if (complIterating) {
    926:           if (--iterCompl <= 0) eps->reason = EPS_DIVERGED_ITS;
    927:         } else if (k >= eps->nev) {
    928:           n0 = sPres->nsch[0]-count0;
    929:           n1 = sPres->nsch[1]-count1;
    930:           if (sr->iterCompl>0 && ((n0>0 && n0<= sr->nMAXCompl)||(n1>0&&n1<=sr->nMAXCompl))) {
    931:             /* Iterating for completion*/
    932:             complIterating = PETSC_TRUE;
    933:             if (n0 >sr->nMAXCompl)sch0 = PETSC_FALSE;
    934:             if (n1 >sr->nMAXCompl)sch1 = PETSC_FALSE;
    935:             iterCompl = sr->iterCompl;
    936:           } else eps->reason = EPS_CONVERGED_TOL;
    937:         }
    938:       }
    939:     }
    940:     /* Update l */
    941:     if (eps->reason == EPS_CONVERGED_ITERATING) l = PetscMax(1,(PetscInt)((nv-k)*ctx->keep));
    942:     else l = nv-k;
    943:     if (breakdown) l=0;
    944:     if (!ctx->lock && l>0 && eps->reason == EPS_CONVERGED_ITERATING) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */

    946:     if (eps->reason == EPS_CONVERGED_ITERATING) {
    947:       if (breakdown) {
    948:         /* Start a new Lanczos factorization */
    949:         PetscCall(PetscInfo(eps,"Breakdown in Krylov-Schur method (it=%" PetscInt_FMT " norm=%g)\n",eps->its,(double)beta));
    950:         PetscCall(EPSGetStartVector(eps,k,&breakdown));
    951:         if (breakdown) {
    952:           eps->reason = EPS_DIVERGED_BREAKDOWN;
    953:           PetscCall(PetscInfo(eps,"Unable to generate more start vectors\n"));
    954:         }
    955:       } else {
    956:         /* Prepare the Rayleigh quotient for restart */
    957:         PetscCall(DSGetArrayReal(eps->ds,DS_MAT_T,&a));
    958:         PetscCall(DSGetArray(eps->ds,DS_MAT_Q,&Q));
    959:         b = a + ld;
    960:         for (i=k;i<k+l;i++) {
    961:           a[i] = PetscRealPart(eps->eigr[i]);
    962:           b[i] = PetscRealPart(Q[nv-1+i*ld]*beta);
    963:         }
    964:         PetscCall(DSRestoreArrayReal(eps->ds,DS_MAT_T,&a));
    965:         PetscCall(DSRestoreArray(eps->ds,DS_MAT_Q,&Q));
    966:       }
    967:     }
    968:     /* Update the corresponding vectors V(:,idx) = V*Q(:,idx) */
    969:     PetscCall(DSGetMat(eps->ds,DS_MAT_Q,&U));
    970:     PetscCall(BVMultInPlace(eps->V,U,eps->nconv,k+l));
    971:     PetscCall(DSRestoreMat(eps->ds,DS_MAT_Q,&U));

    973:     /* Normalize u and append it to V */
    974:     if (eps->reason == EPS_CONVERGED_ITERATING && !breakdown) PetscCall(BVCopyColumn(eps->V,nv,k+l));
    975:     eps->nconv = k;
    976:     if (eps->reason != EPS_CONVERGED_ITERATING) {
    977:       /* Store approximated values for next shift */
    978:       PetscCall(DSGetArray(eps->ds,DS_MAT_Q,&Q));
    979:       sr->nS = l;
    980:       for (i=0;i<l;i++) {
    981:         sr->S[i] = eps->eigr[i+k];/* Diagonal elements */
    982:         sr->S[i+l] = Q[nv-1+(i+k)*ld]*beta; /* Out of diagonal elements */
    983:       }
    984:       PetscCall(DSRestoreArray(eps->ds,DS_MAT_Q,&Q));
    985:     }
    986:   }
    987:   /* Check for completion */
    988:   for (i=0;i< eps->nconv; i++) {
    989:     if (sr->dir*PetscRealPart(eps->eigr[i])>0) sPres->nconv[1]++;
    990:     else sPres->nconv[0]++;
    991:   }
    992:   sPres->comp[0] = PetscNot(count0 < sPres->nsch[0]);
    993:   sPres->comp[1] = PetscNot(count1 < sPres->nsch[1]);
    994:   PetscCall(PetscInfo(eps,"Lanczos: %" PetscInt_FMT " evals in [%g,%g]%s and %" PetscInt_FMT " evals in [%g,%g]%s\n",count0,(double)(sr->dir==1?sPres->ext[0]:sPres->value),(double)(sr->dir==1?sPres->value:sPres->ext[0]),sPres->comp[0]?"*":"",count1,(double)(sr->dir==1?sPres->value:sPres->ext[1]),(double)(sr->dir==1?sPres->ext[1]:sPres->value),sPres->comp[1]?"*":""));
    995:   PetscCheck(count0<=sPres->nsch[0] && count1<=sPres->nsch[1],PetscObjectComm((PetscObject)eps),PETSC_ERR_PLIB,"Mismatch between number of values found and information from inertia%s",ctx->detect?"":", consider using EPSKrylovSchurSetDetectZeros()");
    996:   PetscCall(PetscFree(iwork));
    997:   PetscFunctionReturn(PETSC_SUCCESS);
    998: }

    1000: /*
    1001:   Obtains value of subsequent shift
    1002: */
    1003: static PetscErrorCode EPSGetNewShiftValue(EPS eps,PetscInt side,PetscReal *newS)
    1004: {
    1005:   PetscReal       lambda,d_prev;
    1006:   PetscInt        i,idxP;
    1007:   EPS_SR          sr;
    1008:   EPS_shift       sPres,s;
    1009:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;

    1011:   PetscFunctionBegin;
    1012:   sr = ctx->sr;
    1013:   sPres = sr->sPres;
    1014:   if (sPres->neighb[side]) {
    1015:     /* Completing a previous interval */
    1016:     *newS = (sPres->value + sPres->neighb[side]->value)/2;
    1017:     if (PetscAbsReal(sPres->value - *newS)/PetscAbsReal(sPres->value)<=100*PETSC_SQRT_MACHINE_EPSILON) *newS = sPres->value;
    1018:   } else { /* (Only for side=1). Creating a new interval. */
    1019:     if (sPres->neigs==0) {/* No value has been accepted*/
    1020:       if (sPres->neighb[0]) {
    1021:         /* Multiplying by 10 the previous distance */
    1022:         *newS = sPres->value + 10*sr->dir*PetscAbsReal(sPres->value - sPres->neighb[0]->value);
    1023:         sr->nleap++;
    1024:         /* Stops when the interval is open and no values are found in the last 5 shifts (there might be infinite eigenvalues) */
    1025:         PetscCheck(sr->hasEnd || sr->nleap<=5,PetscObjectComm((PetscObject)eps),PETSC_ERR_PLIB,"Unable to compute the wanted eigenvalues with open interval");
    1026:       } else { /* First shift */
    1027:         PetscCheck(eps->nconv!=0,PetscObjectComm((PetscObject)eps),PETSC_ERR_PLIB,"First shift renders no information");
    1028:         /* Unaccepted values give information for next shift */
    1029:         idxP=0;/* Number of values left from shift */
    1030:         for (i=0;i<eps->nconv;i++) {
    1031:           lambda = PetscRealPart(eps->eigr[i]);
    1032:           if (sr->dir*(lambda - sPres->value) <0) idxP++;
    1033:           else break;
    1034:         }
    1035:         /* Avoiding subtraction of eigenvalues (might be the same).*/
    1036:         if (idxP>0) {
    1037:           d_prev = PetscAbsReal(sPres->value - PetscRealPart(eps->eigr[0]))/(idxP+0.3);
    1038:         } else {
    1039:           d_prev = PetscAbsReal(sPres->value - PetscRealPart(eps->eigr[eps->nconv-1]))/(eps->nconv+0.3);
    1040:         }
    1041:         *newS = sPres->value + (sr->dir*d_prev*eps->nev)/2;
    1042:       }
    1043:     } else { /* Accepted values found */
    1044:       sr->nleap = 0;
    1045:       /* Average distance of values in previous subinterval */
    1046:       s = sPres->neighb[0];
    1047:       while (s && PetscAbs(s->inertia - sPres->inertia)==0) {
    1048:         s = s->neighb[0];/* Looking for previous shifts with eigenvalues within */
    1049:       }
    1050:       if (s) {
    1051:         d_prev = PetscAbsReal((sPres->value - s->value)/(sPres->inertia - s->inertia));
    1052:       } else { /* First shift. Average distance obtained with values in this shift */
    1053:         /* first shift might be too far from first wanted eigenvalue (no values found outside the interval)*/
    1054:         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)) {
    1055:           d_prev =  PetscAbsReal((PetscRealPart(sr->eigr[sr->indexEig-1]) - PetscRealPart(sr->eigr[0])))/(sPres->neigs+0.3);
    1056:         } else {
    1057:           d_prev = PetscAbsReal(PetscRealPart(sr->eigr[sr->indexEig-1]) - sPres->value)/(sPres->neigs+0.3);
    1058:         }
    1059:       }
    1060:       /* Average distance is used for next shift by adding it to value on the right or to shift */
    1061:       if (sr->dir*(PetscRealPart(sr->eigr[sPres->index + sPres->neigs -1]) - sPres->value)>0) {
    1062:         *newS = PetscRealPart(sr->eigr[sPres->index + sPres->neigs -1])+ (sr->dir*d_prev*eps->nev)/2;
    1063:       } else { /* Last accepted value is on the left of shift. Adding to shift */
    1064:         *newS = sPres->value + (sr->dir*d_prev*eps->nev)/2;
    1065:       }
    1066:     }
    1067:     /* End of interval can not be surpassed */
    1068:     if (sr->dir*(sr->int1 - *newS) < 0) *newS = sr->int1;
    1069:   }/* of neighb[side]==null */
    1070:   PetscFunctionReturn(PETSC_SUCCESS);
    1071: }

    1073: /*
    1074:   Function for sorting an array of real values
    1075: */
    1076: static PetscErrorCode sortRealEigenvalues(PetscScalar *r,PetscInt *perm,PetscInt nr,PetscBool prev,PetscInt dir)
    1077: {
    1078:   PetscReal re;
    1079:   PetscInt  i,j,tmp;

    1081:   PetscFunctionBegin;
    1082:   if (!prev) for (i=0;i<nr;i++) perm[i] = i;
    1083:   /* Insertion sort */
    1084:   for (i=1;i<nr;i++) {
    1085:     re = PetscRealPart(r[perm[i]]);
    1086:     j = i-1;
    1087:     while (j>=0 && dir*(re - PetscRealPart(r[perm[j]])) <= 0) {
    1088:       tmp = perm[j]; perm[j] = perm[j+1]; perm[j+1] = tmp; j--;
    1089:     }
    1090:   }
    1091:   PetscFunctionReturn(PETSC_SUCCESS);
    1092: }

    1094: /* Stores the pairs obtained since the last shift in the global arrays */
    1095: static PetscErrorCode EPSStoreEigenpairs(EPS eps)
    1096: {
    1097:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
    1098:   PetscReal       lambda,err,norm;
    1099:   PetscInt        i,count;
    1100:   PetscBool       iscayley;
    1101:   EPS_SR          sr = ctx->sr;
    1102:   EPS_shift       sPres;
    1103:   Vec             v,w;

    1105:   PetscFunctionBegin;
    1106:   sPres = sr->sPres;
    1107:   sPres->index = sr->indexEig;
    1108:   count = sr->indexEig;
    1109:   /* Back-transform */
    1110:   PetscCall(STBackTransform(eps->st,eps->nconv,eps->eigr,eps->eigi));
    1111:   PetscCall(PetscObjectTypeCompare((PetscObject)eps->st,STCAYLEY,&iscayley));
    1112:   /* Sort eigenvalues */
    1113:   PetscCall(sortRealEigenvalues(eps->eigr,eps->perm,eps->nconv,PETSC_FALSE,sr->dir));
    1114:   /* Values stored in global array */
    1115:   for (i=0;i<eps->nconv;i++) {
    1116:     lambda = PetscRealPart(eps->eigr[eps->perm[i]]);
    1117:     err = eps->errest[eps->perm[i]];

    1119:     if (sr->dir*(lambda - sPres->ext[0]) > 0 && (sr->dir)*(sPres->ext[1] - lambda) > 0) {/* Valid value */
    1120:       PetscCheck(count<sr->numEigs,PetscObjectComm((PetscObject)eps),PETSC_ERR_PLIB,"Unexpected error in Spectrum Slicing");
    1121:       sr->eigr[count] = lambda;
    1122:       sr->errest[count] = err;
    1123:       /* Explicit purification */
    1124:       PetscCall(BVGetColumn(eps->V,eps->perm[i],&w));
    1125:       if (eps->purify) {
    1126:         PetscCall(BVGetColumn(sr->V,count,&v));
    1127:         PetscCall(STApply(eps->st,w,v));
    1128:         PetscCall(BVRestoreColumn(sr->V,count,&v));
    1129:       } else PetscCall(BVInsertVec(sr->V,count,w));
    1130:       PetscCall(BVRestoreColumn(eps->V,eps->perm[i],&w));
    1131:       PetscCall(BVNormColumn(sr->V,count,NORM_2,&norm));
    1132:       PetscCall(BVScaleColumn(sr->V,count,1.0/norm));
    1133:       count++;
    1134:     }
    1135:   }
    1136:   sPres->neigs = count - sr->indexEig;
    1137:   sr->indexEig = count;
    1138:   /* Global ordering array updating */
    1139:   PetscCall(sortRealEigenvalues(sr->eigr,sr->perm,count,PETSC_TRUE,sr->dir));
    1140:   PetscFunctionReturn(PETSC_SUCCESS);
    1141: }

    1143: static PetscErrorCode EPSLookForDeflation(EPS eps)
    1144: {
    1145:   PetscReal       val;
    1146:   PetscInt        i,count0=0,count1=0;
    1147:   EPS_shift       sPres;
    1148:   PetscInt        ini,fin,k,idx0,idx1;
    1149:   EPS_SR          sr;
    1150:   Vec             v;
    1151:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;

    1153:   PetscFunctionBegin;
    1154:   sr = ctx->sr;
    1155:   sPres = sr->sPres;

    1157:   if (sPres->neighb[0]) ini = (sr->dir)*(sPres->neighb[0]->inertia - sr->inertia0);
    1158:   else ini = 0;
    1159:   fin = sr->indexEig;
    1160:   /* Selection of ends for searching new values */
    1161:   if (!sPres->neighb[0]) sPres->ext[0] = sr->int0;/* First shift */
    1162:   else sPres->ext[0] = sPres->neighb[0]->value;
    1163:   if (!sPres->neighb[1]) {
    1164:     if (sr->hasEnd) sPres->ext[1] = sr->int1;
    1165:     else sPres->ext[1] = (sr->dir > 0)?PETSC_MAX_REAL:PETSC_MIN_REAL;
    1166:   } else sPres->ext[1] = sPres->neighb[1]->value;
    1167:   /* Selection of values between right and left ends */
    1168:   for (i=ini;i<fin;i++) {
    1169:     val=PetscRealPart(sr->eigr[sr->perm[i]]);
    1170:     /* Values to the right of left shift */
    1171:     if (sr->dir*(val - sPres->ext[1]) < 0) {
    1172:       if (sr->dir*(val - sPres->value) < 0) count0++;
    1173:       else count1++;
    1174:     } else break;
    1175:   }
    1176:   /* The number of values on each side are found */
    1177:   if (sPres->neighb[0]) {
    1178:     sPres->nsch[0] = (sr->dir)*(sPres->inertia - sPres->neighb[0]->inertia)-count0;
    1179:     PetscCheck(sPres->nsch[0]>=0,PetscObjectComm((PetscObject)eps),PETSC_ERR_PLIB,"Mismatch between number of values found and information from inertia%s",ctx->detect?"":", consider using EPSKrylovSchurSetDetectZeros()");
    1180:   } else sPres->nsch[0] = 0;

    1182:   if (sPres->neighb[1]) {
    1183:     sPres->nsch[1] = (sr->dir)*(sPres->neighb[1]->inertia - sPres->inertia) - count1;
    1184:     PetscCheck(sPres->nsch[1]>=0,PetscObjectComm((PetscObject)eps),PETSC_ERR_PLIB,"Mismatch between number of values found and information from inertia%s",ctx->detect?"":", consider using EPSKrylovSchurSetDetectZeros()");
    1185:   } else sPres->nsch[1] = (sr->dir)*(sr->inertia1 - sPres->inertia);

    1187:   /* Completing vector of indexes for deflation */
    1188:   idx0 = ini;
    1189:   idx1 = ini+count0+count1;
    1190:   k=0;
    1191:   for (i=idx0;i<idx1;i++) sr->idxDef[k++]=sr->perm[i];
    1192:   PetscCall(BVDuplicateResize(eps->V,k+eps->ncv+1,&sr->Vnext));
    1193:   PetscCall(BVSetNumConstraints(sr->Vnext,k));
    1194:   for (i=0;i<k;i++) {
    1195:     PetscCall(BVGetColumn(sr->Vnext,-i-1,&v));
    1196:     PetscCall(BVCopyVec(sr->V,sr->idxDef[i],v));
    1197:     PetscCall(BVRestoreColumn(sr->Vnext,-i-1,&v));
    1198:   }

    1200:   /* For rational Krylov */
    1201:   if (sr->nS>0 && (sr->sPrev == sr->sPres->neighb[0] || sr->sPrev == sr->sPres->neighb[1])) PetscCall(EPSPrepareRational(eps));
    1202:   eps->nconv = 0;
    1203:   /* Get rid of temporary Vnext */
    1204:   PetscCall(BVDestroy(&eps->V));
    1205:   eps->V = sr->Vnext;
    1206:   sr->Vnext = NULL;
    1207:   PetscFunctionReturn(PETSC_SUCCESS);
    1208: }

    1210: PetscErrorCode EPSSolve_KrylovSchur_Slice(EPS eps)
    1211: {
    1212:   PetscInt         i,lds,ti;
    1213:   PetscReal        newS;
    1214:   EPS_KRYLOVSCHUR  *ctx=(EPS_KRYLOVSCHUR*)eps->data;
    1215:   EPS_SR           sr=ctx->sr;
    1216:   Mat              A,B=NULL;
    1217:   PetscObjectState Astate,Bstate=0;
    1218:   PetscObjectId    Aid,Bid=0;

    1220:   PetscFunctionBegin;
    1221:   PetscCall(PetscCitationsRegister(citation,&cited));
    1222:   if (ctx->global) {
    1223:     PetscCall(EPSSolve_KrylovSchur_Slice(ctx->eps));
    1224:     ctx->eps->state = EPS_STATE_SOLVED;
    1225:     eps->reason = EPS_CONVERGED_TOL;
    1226:     if (ctx->npart>1) {
    1227:       /* Gather solution from subsolvers */
    1228:       PetscCall(EPSSliceGatherSolution(eps));
    1229:     } else {
    1230:       eps->nconv = sr->numEigs;
    1231:       eps->its   = ctx->eps->its;
    1232:       PetscCall(PetscFree(ctx->inertias));
    1233:       PetscCall(PetscFree(ctx->shifts));
    1234:       PetscCall(EPSSliceGetInertias(ctx->eps,&ctx->nshifts,&ctx->shifts,&ctx->inertias));
    1235:     }
    1236:   } else {
    1237:     if (ctx->npart==1) {
    1238:       sr->eigr   = ctx->eps->eigr;
    1239:       sr->eigi   = ctx->eps->eigi;
    1240:       sr->perm   = ctx->eps->perm;
    1241:       sr->errest = ctx->eps->errest;
    1242:       sr->V      = ctx->eps->V;
    1243:     }
    1244:     /* Check that the user did not modify subcomm matrices */
    1245:     PetscCall(EPSGetOperators(eps,&A,&B));
    1246:     PetscCall(PetscObjectStateGet((PetscObject)A,&Astate));
    1247:     PetscCall(PetscObjectGetId((PetscObject)A,&Aid));
    1248:     if (B) {
    1249:       PetscCall(PetscObjectStateGet((PetscObject)B,&Bstate));
    1250:       PetscCall(PetscObjectGetId((PetscObject)B,&Bid));
    1251:     }
    1252:     PetscCheck(Astate==ctx->Astate && (!B || Bstate==ctx->Bstate) && Aid==ctx->Aid && (!B || Bid==ctx->Bid),PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Subcomm matrices have been modified by user");
    1253:     /* Only with eigenvalues present in the interval ...*/
    1254:     if (sr->numEigs==0) {
    1255:       eps->reason = EPS_CONVERGED_TOL;
    1256:       PetscFunctionReturn(PETSC_SUCCESS);
    1257:     }
    1258:     /* Array of pending shifts */
    1259:     sr->maxPend = 100; /* Initial size */
    1260:     sr->nPend = 0;
    1261:     PetscCall(PetscMalloc1(sr->maxPend,&sr->pending));
    1262:     PetscCall(EPSCreateShift(eps,sr->int0,NULL,NULL));
    1263:     /* extract first shift */
    1264:     sr->sPrev = NULL;
    1265:     sr->sPres = sr->pending[--sr->nPend];
    1266:     sr->sPres->inertia = sr->inertia0;
    1267:     eps->target = sr->sPres->value;
    1268:     sr->s0 = sr->sPres;
    1269:     sr->indexEig = 0;
    1270:     /* Memory reservation for auxiliary variables */
    1271:     lds = PetscMin(eps->mpd,eps->ncv);
    1272:     PetscCall(PetscCalloc1(lds*lds,&sr->S));
    1273:     PetscCall(PetscMalloc1(eps->ncv,&sr->back));
    1274:     for (i=0;i<sr->numEigs;i++) {
    1275:       sr->eigr[i]   = 0.0;
    1276:       sr->eigi[i]   = 0.0;
    1277:       sr->errest[i] = 0.0;
    1278:       sr->perm[i]   = i;
    1279:     }
    1280:     /* Vectors for deflation */
    1281:     PetscCall(PetscMalloc1(sr->numEigs,&sr->idxDef));
    1282:     sr->indexEig = 0;
    1283:     /* Main loop */
    1284:     while (sr->sPres) {
    1285:       /* Search for deflation */
    1286:       PetscCall(EPSLookForDeflation(eps));
    1287:       /* KrylovSchur */
    1288:       PetscCall(EPSKrylovSchur_Slice(eps));

    1290:       PetscCall(EPSStoreEigenpairs(eps));
    1291:       /* Select new shift */
    1292:       if (!sr->sPres->comp[1]) {
    1293:         PetscCall(EPSGetNewShiftValue(eps,1,&newS));
    1294:         PetscCall(EPSCreateShift(eps,newS,sr->sPres,sr->sPres->neighb[1]));
    1295:       }
    1296:       if (!sr->sPres->comp[0]) {
    1297:         /* Completing earlier interval */
    1298:         PetscCall(EPSGetNewShiftValue(eps,0,&newS));
    1299:         PetscCall(EPSCreateShift(eps,newS,sr->sPres->neighb[0],sr->sPres));
    1300:       }
    1301:       /* Preparing for a new search of values */
    1302:       PetscCall(EPSExtractShift(eps));
    1303:     }

    1305:     /* Updating eps values prior to exit */
    1306:     PetscCall(PetscFree(sr->S));
    1307:     PetscCall(PetscFree(sr->idxDef));
    1308:     PetscCall(PetscFree(sr->pending));
    1309:     PetscCall(PetscFree(sr->back));
    1310:     PetscCall(BVDuplicateResize(eps->V,eps->ncv+1,&sr->Vnext));
    1311:     PetscCall(BVSetNumConstraints(sr->Vnext,0));
    1312:     PetscCall(BVDestroy(&eps->V));
    1313:     eps->V      = sr->Vnext;
    1314:     eps->nconv  = sr->indexEig;
    1315:     eps->reason = EPS_CONVERGED_TOL;
    1316:     eps->its    = sr->itsKs;
    1317:     eps->nds    = 0;
    1318:     if (sr->dir<0) {
    1319:       for (i=0;i<eps->nconv/2;i++) {
    1320:         ti = sr->perm[i]; sr->perm[i] = sr->perm[eps->nconv-1-i]; sr->perm[eps->nconv-1-i] = ti;
    1321:       }
    1322:     }
    1323:   }
    1324:   PetscFunctionReturn(PETSC_SUCCESS);
    1325: }