Date: 2023-01-26T12:18:34+00:00

Actual source code: krylovschur.c
slepc-3.18.2 2023-01-26
Report Typos and Errors

      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

     15:    Algorithm:

     17:        Single-vector Krylov-Schur method for non-symmetric problems,
     18:        including harmonic extraction.

     20:    References:

     22:        [1] "Krylov-Schur Methods in SLEPc", SLEPc Technical Report STR-7,
     23:            available at https://slepc.upv.es.

     25:        [2] G.W. Stewart, "A Krylov-Schur Algorithm for Large Eigenproblems",
     26:            SIAM J. Matrix Anal. App. 23(3):601-614, 2001.

     28:        [3] "Practical Implementation of Harmonic Krylov-Schur", SLEPc Technical
     29:             Report STR-9, available at https://slepc.upv.es.
     30: */

     32: #include <slepc/private/epsimpl.h>
     33: #include "krylovschur.h"

     35: PetscErrorCode EPSGetArbitraryValues(EPS eps,PetscScalar *rr,PetscScalar *ri)
     36: {
     37:   PetscInt       i,newi,ld,n,l;
     38:   Vec            xr=eps->work[0],xi=eps->work[1];
     39:   PetscScalar    re,im,*Zr,*Zi,*X;

     41:   DSGetLeadingDimension(eps->ds,&ld);
     42:   DSGetDimensions(eps->ds,&n,&l,NULL,NULL);
     43:   for (i=l;i<n;i++) {
     44:     re = eps->eigr[i];
     45:     im = eps->eigi[i];
     46:     STBackTransform(eps->st,1,&re,&im);
     47:     newi = i;
     48:     DSVectors(eps->ds,DS_MAT_X,&newi,NULL);
     49:     DSGetArray(eps->ds,DS_MAT_X,&X);
     50:     Zr = X+i*ld;
     51:     if (newi==i+1) Zi = X+newi*ld;
     52:     else Zi = NULL;
     53:     EPSComputeRitzVector(eps,Zr,Zi,eps->V,xr,xi);
     54:     DSRestoreArray(eps->ds,DS_MAT_X,&X);
     55:     (*eps->arbitrary)(re,im,xr,xi,rr+i,ri+i,eps->arbitraryctx);
     56:   }
     57:   return 0;
     58: }

     60: static PetscErrorCode EPSSetUp_KrylovSchur_Filter(EPS eps)
     61: {
     62:   EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;
     63:   PetscBool       estimaterange=PETSC_TRUE;
     64:   PetscReal       rleft,rright;
     65:   Mat             A;

     67:   EPSCheckHermitianCondition(eps,PETSC_TRUE," with polynomial filter");
     68:   EPSCheckStandardCondition(eps,PETSC_TRUE," with polynomial filter");
     70:   EPSCheckUnsupportedCondition(eps,EPS_FEATURE_ARBITRARY | EPS_FEATURE_REGION | EPS_FEATURE_EXTRACTION,PETSC_TRUE," with polynomial filter");
     71:   if (eps->tol==PETSC_DEFAULT) eps->tol = SLEPC_DEFAULT_TOL*1e-2;  /* use tighter tolerance */
     72:   STFilterSetInterval(eps->st,eps->inta,eps->intb);
     73:   if (!ctx->estimatedrange) {
     74:     STFilterGetRange(eps->st,&rleft,&rright);
     75:     estimaterange = (!rleft && !rright)? PETSC_TRUE: PETSC_FALSE;
     76:   }
     77:   if (estimaterange) { /* user did not set a range */
     78:     STGetMatrix(eps->st,0,&A);
     79:     MatEstimateSpectralRange_EPS(A,&rleft,&rright);
     80:     PetscInfo(eps,"Setting eigenvalue range to [%g,%g]\n",(double)rleft,(double)rright);
     81:     STFilterSetRange(eps->st,rleft,rright);
     82:     ctx->estimatedrange = PETSC_TRUE;
     83:   }
     84:   if (eps->ncv==PETSC_DEFAULT && eps->nev==1) eps->nev = 40;  /* user did not provide nev estimation */
     85:   EPSSetDimensions_Default(eps,eps->nev,&eps->ncv,&eps->mpd);
     87:   if (eps->max_it==PETSC_DEFAULT) eps->max_it = PetscMax(100,2*eps->n/eps->ncv);
     88:   return 0;
     89: }

     91: PetscErrorCode EPSSetUp_KrylovSchur(EPS eps)
     92: {
     93:   PetscReal         eta;
     94:   PetscBool         isfilt=PETSC_FALSE;
     95:   BVOrthogType      otype;
     96:   BVOrthogBlockType obtype;
     97:   EPS_KRYLOVSCHUR   *ctx = (EPS_KRYLOVSCHUR*)eps->data;
     98:   enum { EPS_KS_DEFAULT,EPS_KS_SYMM,EPS_KS_SLICE,EPS_KS_FILTER,EPS_KS_INDEF,EPS_KS_TWOSIDED } variant;

    100:   if (eps->which==EPS_ALL) {  /* default values in case of spectrum slicing or polynomial filter  */
    101:     PetscObjectTypeCompare((PetscObject)eps->st,STFILTER,&isfilt);
    102:     if (isfilt) EPSSetUp_KrylovSchur_Filter(eps);
    103:     else EPSSetUp_KrylovSchur_Slice(eps);
    104:   } else {
    105:     EPSSetDimensions_Default(eps,eps->nev,&eps->ncv,&eps->mpd);
    107:     if (eps->max_it==PETSC_DEFAULT) eps->max_it = PetscMax(100,2*eps->n/eps->ncv);
    108:     if (!eps->which) EPSSetWhichEigenpairs_Default(eps);
    109:   }

    112:   EPSCheckDefiniteCondition(eps,eps->arbitrary," with arbitrary selection of eigenpairs");

    116:   if (!ctx->keep) ctx->keep = 0.5;

    118:   EPSAllocateSolution(eps,1);
    119:   EPS_SetInnerProduct(eps);
    120:   if (eps->arbitrary) EPSSetWorkVecs(eps,2);
    121:   else if (eps->ishermitian && !eps->ispositive) EPSSetWorkVecs(eps,1);

    123:   /* dispatch solve method */
    124:   if (eps->ishermitian) {
    125:     if (eps->which==EPS_ALL) {
    126:       EPSCheckDefiniteCondition(eps,eps->which==EPS_ALL," with spectrum slicing");
    127:       variant = isfilt? EPS_KS_FILTER: EPS_KS_SLICE;
    128:     } else if (eps->isgeneralized && !eps->ispositive) {
    129:       variant = EPS_KS_INDEF;
    130:     } else {
    131:       switch (eps->extraction) {
    132:         case EPS_RITZ:     variant = EPS_KS_SYMM; break;
    133:         case EPS_HARMONIC: variant = EPS_KS_DEFAULT; break;
    134:         default: SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Unsupported extraction type");
    135:       }
    136:     }
    137:   } else if (eps->twosided) {
    138:     variant = EPS_KS_TWOSIDED;
    139:   } else {
    140:     switch (eps->extraction) {
    141:       case EPS_RITZ:     variant = EPS_KS_DEFAULT; break;
    142:       case EPS_HARMONIC: variant = EPS_KS_DEFAULT; break;
    143:       default: SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Unsupported extraction type");
    144:     }
    145:   }
    146:   switch (variant) {
    147:     case EPS_KS_DEFAULT:
    148:       eps->ops->solve = EPSSolve_KrylovSchur_Default;
    149:       eps->ops->computevectors = EPSComputeVectors_Schur;
    150:       DSSetType(eps->ds,DSNHEP);
    151:       DSSetExtraRow(eps->ds,PETSC_TRUE);
    152:       DSAllocate(eps->ds,eps->ncv+1);
    153:       break;
    154:     case EPS_KS_SYMM:
    155:     case EPS_KS_FILTER:
    156:       eps->ops->solve = EPSSolve_KrylovSchur_Default;
    157:       eps->ops->computevectors = EPSComputeVectors_Hermitian;
    158:       DSSetType(eps->ds,DSHEP);
    159:       DSSetCompact(eps->ds,PETSC_TRUE);
    160:       DSSetExtraRow(eps->ds,PETSC_TRUE);
    161:       DSAllocate(eps->ds,eps->ncv+1);
    162:       break;
    163:     case EPS_KS_SLICE:
    164:       eps->ops->solve = EPSSolve_KrylovSchur_Slice;
    165:       eps->ops->computevectors = EPSComputeVectors_Slice;
    166:       break;
    167:     case EPS_KS_INDEF:
    168:       eps->ops->solve = EPSSolve_KrylovSchur_Indefinite;
    169:       eps->ops->computevectors = EPSComputeVectors_Indefinite;
    170:       DSSetType(eps->ds,DSGHIEP);
    171:       DSSetCompact(eps->ds,PETSC_TRUE);
    172:       DSSetExtraRow(eps->ds,PETSC_TRUE);
    173:       DSAllocate(eps->ds,eps->ncv+1);
    174:       /* force reorthogonalization for pseudo-Lanczos */
    175:       BVGetOrthogonalization(eps->V,&otype,NULL,&eta,&obtype);
    176:       BVSetOrthogonalization(eps->V,otype,BV_ORTHOG_REFINE_ALWAYS,eta,obtype);
    177:       break;
    178:     case EPS_KS_TWOSIDED:
    179:       eps->ops->solve = EPSSolve_KrylovSchur_TwoSided;
    180:       eps->ops->computevectors = EPSComputeVectors_Schur;
    181:       DSSetType(eps->ds,DSNHEPTS);
    182:       DSAllocate(eps->ds,eps->ncv+1);
    183:       DSSetExtraRow(eps->ds,PETSC_TRUE);
    184:       break;
    185:     default: SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_PLIB,"Unexpected error");
    186:   }
    187:   return 0;
    188: }

    190: PetscErrorCode EPSSetUpSort_KrylovSchur(EPS eps)
    191: {
    192:   EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;
    193:   SlepcSC         sc;
    194:   PetscBool       isfilt;

    196:   EPSSetUpSort_Default(eps);
    197:   if (eps->which==EPS_ALL) {
    198:     PetscObjectTypeCompare((PetscObject)eps->st,STFILTER,&isfilt);
    199:     if (isfilt) {
    200:       DSGetSlepcSC(eps->ds,&sc);
    201:       sc->rg            = NULL;
    202:       sc->comparison    = SlepcCompareLargestReal;
    203:       sc->comparisonctx = NULL;
    204:       sc->map           = NULL;
    205:       sc->mapobj        = NULL;
    206:     } else {
    207:       if (!ctx->global && ctx->sr->numEigs>0) {
    208:         DSGetSlepcSC(eps->ds,&sc);
    209:         sc->rg            = NULL;
    210:         sc->comparison    = SlepcCompareLargestMagnitude;
    211:         sc->comparisonctx = NULL;
    212:         sc->map           = NULL;
    213:         sc->mapobj        = NULL;
    214:       }
    215:     }
    216:   }
    217:   return 0;
    218: }

    220: PetscErrorCode EPSSolve_KrylovSchur_Default(EPS eps)
    221: {
    222:   EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;
    223:   PetscInt        j,*pj,k,l,nv,ld,nconv;
    224:   Mat             U,Op,H,T;
    225:   PetscScalar     *g;
    226:   PetscReal       beta,gamma=1.0;
    227:   PetscBool       breakdown,harmonic,hermitian;

    229:   DSGetLeadingDimension(eps->ds,&ld);
    230:   harmonic = (eps->extraction==EPS_HARMONIC || eps->extraction==EPS_REFINED_HARMONIC)?PETSC_TRUE:PETSC_FALSE;
    231:   hermitian = (eps->ishermitian && !harmonic)?PETSC_TRUE:PETSC_FALSE;
    232:   if (harmonic) PetscMalloc1(ld,&g);
    233:   if (eps->arbitrary) pj = &j;
    234:   else pj = NULL;

    236:   /* Get the starting Arnoldi vector */
    237:   EPSGetStartVector(eps,0,NULL);
    238:   l = 0;

    240:   /* Restart loop */
    241:   while (eps->reason == EPS_CONVERGED_ITERATING) {
    242:     eps->its++;

    244:     /* Compute an nv-step Arnoldi factorization */
    245:     nv = PetscMin(eps->nconv+eps->mpd,eps->ncv);
    246:     DSSetDimensions(eps->ds,nv,eps->nconv,eps->nconv+l);
    247:     STGetOperator(eps->st,&Op);
    248:     if (hermitian) {
    249:       DSGetMat(eps->ds,DS_MAT_T,&T);
    250:       BVMatLanczos(eps->V,Op,T,eps->nconv+l,&nv,&beta,&breakdown);
    251:       DSRestoreMat(eps->ds,DS_MAT_T,&T);
    252:     } else {
    253:       DSGetMat(eps->ds,DS_MAT_A,&H);
    254:       BVMatArnoldi(eps->V,Op,H,eps->nconv+l,&nv,&beta,&breakdown);
    255:       DSRestoreMat(eps->ds,DS_MAT_A,&H);
    256:     }
    257:     STRestoreOperator(eps->st,&Op);
    258:     DSSetDimensions(eps->ds,nv,eps->nconv,eps->nconv+l);
    259:     DSSetState(eps->ds,l?DS_STATE_RAW:DS_STATE_INTERMEDIATE);
    260:     BVSetActiveColumns(eps->V,eps->nconv,nv);

    262:     /* Compute translation of Krylov decomposition if harmonic extraction used */
    263:     if (PetscUnlikely(harmonic)) DSTranslateHarmonic(eps->ds,eps->target,beta,PETSC_FALSE,g,&gamma);

    265:     /* Solve projected problem */
    266:     DSSolve(eps->ds,eps->eigr,eps->eigi);
    267:     if (PetscUnlikely(eps->arbitrary)) {
    268:       EPSGetArbitraryValues(eps,eps->rr,eps->ri);
    269:       j=1;
    270:     }
    271:     DSSort(eps->ds,eps->eigr,eps->eigi,eps->rr,eps->ri,pj);
    272:     DSUpdateExtraRow(eps->ds);
    273:     DSSynchronize(eps->ds,eps->eigr,eps->eigi);

    275:     /* Check convergence */
    276:     EPSKrylovConvergence(eps,PETSC_FALSE,eps->nconv,nv-eps->nconv,beta,0.0,gamma,&k);
    277:     (*eps->stopping)(eps,eps->its,eps->max_it,k,eps->nev,&eps->reason,eps->stoppingctx);
    278:     nconv = k;

    280:     /* Update l */
    281:     if (eps->reason != EPS_CONVERGED_ITERATING || breakdown || k==nv) l = 0;
    282:     else {
    283:       l = PetscMax(1,(PetscInt)((nv-k)*ctx->keep));
    284:       if (!hermitian) DSGetTruncateSize(eps->ds,k,nv,&l);
    285:     }
    286:     if (!ctx->lock && l>0) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */
    287:     if (l) PetscInfo(eps,"Preparing to restart keeping l=%" PetscInt_FMT " vectors\n",l);

    289:     if (eps->reason == EPS_CONVERGED_ITERATING) {
    290:       if (PetscUnlikely(breakdown || k==nv)) {
    291:         /* Start a new Arnoldi factorization */
    292:         PetscInfo(eps,"Breakdown in Krylov-Schur method (it=%" PetscInt_FMT " norm=%g)\n",eps->its,(double)beta);
    293:         if (k<eps->nev) {
    294:           EPSGetStartVector(eps,k,&breakdown);
    295:           if (breakdown) {
    296:             eps->reason = EPS_DIVERGED_BREAKDOWN;
    297:             PetscInfo(eps,"Unable to generate more start vectors\n");
    298:           }
    299:         }
    300:       } else {
    301:         /* Undo translation of Krylov decomposition */
    302:         if (PetscUnlikely(harmonic)) {
    303:           DSSetDimensions(eps->ds,nv,k,l);
    304:           DSTranslateHarmonic(eps->ds,0.0,beta,PETSC_TRUE,g,&gamma);
    305:           /* gamma u^ = u - U*g~ */
    306:           BVSetActiveColumns(eps->V,0,nv);
    307:           BVMultColumn(eps->V,-1.0,1.0,nv,g);
    308:           BVScaleColumn(eps->V,nv,1.0/gamma);
    309:           BVSetActiveColumns(eps->V,eps->nconv,nv);
    310:           DSSetDimensions(eps->ds,nv,k,nv);
    311:         }
    312:         /* Prepare the Rayleigh quotient for restart */
    313:         DSTruncate(eps->ds,k+l,PETSC_FALSE);
    314:       }
    315:     }
    316:     /* Update the corresponding vectors V(:,idx) = V*Q(:,idx) */
    317:     DSGetMat(eps->ds,DS_MAT_Q,&U);
    318:     BVMultInPlace(eps->V,U,eps->nconv,k+l);
    319:     DSRestoreMat(eps->ds,DS_MAT_Q,&U);

    321:     if (eps->reason == EPS_CONVERGED_ITERATING && !breakdown) BVCopyColumn(eps->V,nv,k+l);
    322:     eps->nconv = k;
    323:     EPSMonitor(eps,eps->its,nconv,eps->eigr,eps->eigi,eps->errest,nv);
    324:   }

    326:   if (harmonic) PetscFree(g);
    327:   DSTruncate(eps->ds,eps->nconv,PETSC_TRUE);
    328:   return 0;
    329: }

    331: static PetscErrorCode EPSKrylovSchurSetRestart_KrylovSchur(EPS eps,PetscReal keep)
    332: {
    333:   EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;

    335:   if (keep==PETSC_DEFAULT) ctx->keep = 0.5;
    336:   else {
    338:     ctx->keep = keep;
    339:   }
    340:   return 0;
    341: }

    343: /*@
    344:    EPSKrylovSchurSetRestart - Sets the restart parameter for the Krylov-Schur
    345:    method, in particular the proportion of basis vectors that must be kept
    346:    after restart.

    348:    Logically Collective on eps

    350:    Input Parameters:
    351: +  eps - the eigenproblem solver context
    352: -  keep - the number of vectors to be kept at restart

    354:    Options Database Key:
    355: .  -eps_krylovschur_restart - Sets the restart parameter

    357:    Notes:
    358:    Allowed values are in the range [0.1,0.9]. The default is 0.5.

    360:    Level: advanced

    362: .seealso: EPSKrylovSchurGetRestart()
    363: @*/
    364: PetscErrorCode EPSKrylovSchurSetRestart(EPS eps,PetscReal keep)
    365: {
    368:   PetscTryMethod(eps,"EPSKrylovSchurSetRestart_C",(EPS,PetscReal),(eps,keep));
    369:   return 0;
    370: }

    372: static PetscErrorCode EPSKrylovSchurGetRestart_KrylovSchur(EPS eps,PetscReal *keep)
    373: {
    374:   EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;

    376:   *keep = ctx->keep;
    377:   return 0;
    378: }

    380: /*@
    381:    EPSKrylovSchurGetRestart - Gets the restart parameter used in the
    382:    Krylov-Schur method.

    384:    Not Collective

    386:    Input Parameter:
    387: .  eps - the eigenproblem solver context

    389:    Output Parameter:
    390: .  keep - the restart parameter

    392:    Level: advanced

    394: .seealso: EPSKrylovSchurSetRestart()
    395: @*/
    396: PetscErrorCode EPSKrylovSchurGetRestart(EPS eps,PetscReal *keep)
    397: {
    400:   PetscUseMethod(eps,"EPSKrylovSchurGetRestart_C",(EPS,PetscReal*),(eps,keep));
    401:   return 0;
    402: }

    404: static PetscErrorCode EPSKrylovSchurSetLocking_KrylovSchur(EPS eps,PetscBool lock)
    405: {
    406:   EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;

    408:   ctx->lock = lock;
    409:   return 0;
    410: }

    412: /*@
    413:    EPSKrylovSchurSetLocking - Choose between locking and non-locking variants of
    414:    the Krylov-Schur method.

    416:    Logically Collective on eps

    418:    Input Parameters:
    419: +  eps  - the eigenproblem solver context
    420: -  lock - true if the locking variant must be selected

    422:    Options Database Key:
    423: .  -eps_krylovschur_locking - Sets the locking flag

    425:    Notes:
    426:    The default is to lock converged eigenpairs when the method restarts.
    427:    This behaviour can be changed so that all directions are kept in the
    428:    working subspace even if already converged to working accuracy (the
    429:    non-locking variant).

    431:    Level: advanced

    433: .seealso: EPSKrylovSchurGetLocking()
    434: @*/
    435: PetscErrorCode EPSKrylovSchurSetLocking(EPS eps,PetscBool lock)
    436: {
    439:   PetscTryMethod(eps,"EPSKrylovSchurSetLocking_C",(EPS,PetscBool),(eps,lock));
    440:   return 0;
    441: }

    443: static PetscErrorCode EPSKrylovSchurGetLocking_KrylovSchur(EPS eps,PetscBool *lock)
    444: {
    445:   EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;

    447:   *lock = ctx->lock;
    448:   return 0;
    449: }

    451: /*@
    452:    EPSKrylovSchurGetLocking - Gets the locking flag used in the Krylov-Schur
    453:    method.

    455:    Not Collective

    457:    Input Parameter:
    458: .  eps - the eigenproblem solver context

    460:    Output Parameter:
    461: .  lock - the locking flag

    463:    Level: advanced

    465: .seealso: EPSKrylovSchurSetLocking()
    466: @*/
    467: PetscErrorCode EPSKrylovSchurGetLocking(EPS eps,PetscBool *lock)
    468: {
    471:   PetscUseMethod(eps,"EPSKrylovSchurGetLocking_C",(EPS,PetscBool*),(eps,lock));
    472:   return 0;
    473: }

    475: static PetscErrorCode EPSKrylovSchurSetPartitions_KrylovSchur(EPS eps,PetscInt npart)
    476: {
    477:   EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;
    478:   PetscMPIInt     size;
    479:   PetscInt        newnpart;

    481:   if (npart == PETSC_DEFAULT || npart == PETSC_DECIDE) {
    482:     newnpart = 1;
    483:   } else {
    484:     MPI_Comm_size(PetscObjectComm((PetscObject)eps),&size);
    486:     newnpart = npart;
    487:   }
    488:   if (ctx->npart!=newnpart) {
    489:     if (ctx->npart>1) {
    490:       PetscSubcommDestroy(&ctx->subc);
    491:       if (ctx->commset) {
    492:         MPI_Comm_free(&ctx->commrank);
    493:         ctx->commset = PETSC_FALSE;
    494:       }
    495:     }
    496:     EPSDestroy(&ctx->eps);
    497:     ctx->npart = newnpart;
    498:     eps->state = EPS_STATE_INITIAL;
    499:   }
    500:   return 0;
    501: }

    503: /*@
    504:    EPSKrylovSchurSetPartitions - Sets the number of partitions for the
    505:    case of doing spectrum slicing for a computational interval with the
    506:    communicator split in several sub-communicators.

    508:    Logically Collective on eps

    510:    Input Parameters:
    511: +  eps   - the eigenproblem solver context
    512: -  npart - number of partitions

    514:    Options Database Key:
    515: .  -eps_krylovschur_partitions <npart> - Sets the number of partitions

    517:    Notes:
    518:    By default, npart=1 so all processes in the communicator participate in
    519:    the processing of the whole interval. If npart>1 then the interval is
    520:    divided into npart subintervals, each of them being processed by a
    521:    subset of processes.

    523:    The interval is split proportionally unless the separation points are
    524:    specified with EPSKrylovSchurSetSubintervals().

    526:    Level: advanced

    528: .seealso: EPSKrylovSchurSetSubintervals(), EPSSetInterval()
    529: @*/
    530: PetscErrorCode EPSKrylovSchurSetPartitions(EPS eps,PetscInt npart)
    531: {
    534:   PetscTryMethod(eps,"EPSKrylovSchurSetPartitions_C",(EPS,PetscInt),(eps,npart));
    535:   return 0;
    536: }

    538: static PetscErrorCode EPSKrylovSchurGetPartitions_KrylovSchur(EPS eps,PetscInt *npart)
    539: {
    540:   EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;

    542:   *npart  = ctx->npart;
    543:   return 0;
    544: }

    546: /*@
    547:    EPSKrylovSchurGetPartitions - Gets the number of partitions of the
    548:    communicator in case of spectrum slicing.

    550:    Not Collective

    552:    Input Parameter:
    553: .  eps - the eigenproblem solver context

    555:    Output Parameter:
    556: .  npart - number of partitions

    558:    Level: advanced

    560: .seealso: EPSKrylovSchurSetPartitions()
    561: @*/
    562: PetscErrorCode EPSKrylovSchurGetPartitions(EPS eps,PetscInt *npart)
    563: {
    566:   PetscUseMethod(eps,"EPSKrylovSchurGetPartitions_C",(EPS,PetscInt*),(eps,npart));
    567:   return 0;
    568: }

    570: static PetscErrorCode EPSKrylovSchurSetDetectZeros_KrylovSchur(EPS eps,PetscBool detect)
    571: {
    572:   EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;

    574:   ctx->detect = detect;
    575:   eps->state  = EPS_STATE_INITIAL;
    576:   return 0;
    577: }

    579: /*@
    580:    EPSKrylovSchurSetDetectZeros - Sets a flag to enforce detection of
    581:    zeros during the factorizations throughout the spectrum slicing computation.

    583:    Logically Collective on eps

    585:    Input Parameters:
    586: +  eps    - the eigenproblem solver context
    587: -  detect - check for zeros

    589:    Options Database Key:
    590: .  -eps_krylovschur_detect_zeros - Check for zeros; this takes an optional
    591:    bool value (0/1/no/yes/true/false)

    593:    Notes:
    594:    A zero in the factorization indicates that a shift coincides with an eigenvalue.

    596:    This flag is turned off by default, and may be necessary in some cases,
    597:    especially when several partitions are being used. This feature currently
    598:    requires an external package for factorizations with support for zero
    599:    detection, e.g. MUMPS.

    601:    Level: advanced

    603: .seealso: EPSKrylovSchurSetPartitions(), EPSSetInterval()
    604: @*/
    605: PetscErrorCode EPSKrylovSchurSetDetectZeros(EPS eps,PetscBool detect)
    606: {
    609:   PetscTryMethod(eps,"EPSKrylovSchurSetDetectZeros_C",(EPS,PetscBool),(eps,detect));
    610:   return 0;
    611: }

    613: static PetscErrorCode EPSKrylovSchurGetDetectZeros_KrylovSchur(EPS eps,PetscBool *detect)
    614: {
    615:   EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;

    617:   *detect = ctx->detect;
    618:   return 0;
    619: }

    621: /*@
    622:    EPSKrylovSchurGetDetectZeros - Gets the flag that enforces zero detection
    623:    in spectrum slicing.

    625:    Not Collective

    627:    Input Parameter:
    628: .  eps - the eigenproblem solver context

    630:    Output Parameter:
    631: .  detect - whether zeros detection is enforced during factorizations

    633:    Level: advanced

    635: .seealso: EPSKrylovSchurSetDetectZeros()
    636: @*/
    637: PetscErrorCode EPSKrylovSchurGetDetectZeros(EPS eps,PetscBool *detect)
    638: {
    641:   PetscUseMethod(eps,"EPSKrylovSchurGetDetectZeros_C",(EPS,PetscBool*),(eps,detect));
    642:   return 0;
    643: }

    645: static PetscErrorCode EPSKrylovSchurSetDimensions_KrylovSchur(EPS eps,PetscInt nev,PetscInt ncv,PetscInt mpd)
    646: {
    647:   EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;

    650:   ctx->nev = nev;
    651:   if (ncv == PETSC_DECIDE || ncv == PETSC_DEFAULT) {
    652:     ctx->ncv = PETSC_DEFAULT;
    653:   } else {
    655:     ctx->ncv = ncv;
    656:   }
    657:   if (mpd == PETSC_DECIDE || mpd == PETSC_DEFAULT) {
    658:     ctx->mpd = PETSC_DEFAULT;
    659:   } else {
    661:     ctx->mpd = mpd;
    662:   }
    663:   eps->state = EPS_STATE_INITIAL;
    664:   return 0;
    665: }

    667: /*@
    668:    EPSKrylovSchurSetDimensions - Sets the dimensions used for each subsolve
    669:    step in case of doing spectrum slicing for a computational interval.
    670:    The meaning of the parameters is the same as in EPSSetDimensions().

    672:    Logically Collective on eps

    674:    Input Parameters:
    675: +  eps - the eigenproblem solver context
    676: .  nev - number of eigenvalues to compute
    677: .  ncv - the maximum dimension of the subspace to be used by the subsolve
    678: -  mpd - the maximum dimension allowed for the projected problem

    680:    Options Database Key:
    681: +  -eps_krylovschur_nev <nev> - Sets the number of eigenvalues
    682: .  -eps_krylovschur_ncv <ncv> - Sets the dimension of the subspace
    683: -  -eps_krylovschur_mpd <mpd> - Sets the maximum projected dimension

    685:    Level: advanced

    687: .seealso: EPSKrylovSchurGetDimensions(), EPSSetDimensions(), EPSSetInterval()
    688: @*/
    689: PetscErrorCode EPSKrylovSchurSetDimensions(EPS eps,PetscInt nev,PetscInt ncv,PetscInt mpd)
    690: {
    695:   PetscTryMethod(eps,"EPSKrylovSchurSetDimensions_C",(EPS,PetscInt,PetscInt,PetscInt),(eps,nev,ncv,mpd));
    696:   return 0;
    697: }

    699: static PetscErrorCode EPSKrylovSchurGetDimensions_KrylovSchur(EPS eps,PetscInt *nev,PetscInt *ncv,PetscInt *mpd)
    700: {
    701:   EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;

    703:   if (nev) *nev = ctx->nev;
    704:   if (ncv) *ncv = ctx->ncv;
    705:   if (mpd) *mpd = ctx->mpd;
    706:   return 0;
    707: }

    709: /*@
    710:    EPSKrylovSchurGetDimensions - Gets the dimensions used for each subsolve
    711:    step in case of doing spectrum slicing for a computational interval.

    713:    Not Collective

    715:    Input Parameter:
    716: .  eps - the eigenproblem solver context

    718:    Output Parameters:
    719: +  nev - number of eigenvalues to compute
    720: .  ncv - the maximum dimension of the subspace to be used by the subsolve
    721: -  mpd - the maximum dimension allowed for the projected problem

    723:    Level: advanced

    725: .seealso: EPSKrylovSchurSetDimensions()
    726: @*/
    727: PetscErrorCode EPSKrylovSchurGetDimensions(EPS eps,PetscInt *nev,PetscInt *ncv,PetscInt *mpd)
    728: {
    730:   PetscUseMethod(eps,"EPSKrylovSchurGetDimensions_C",(EPS,PetscInt*,PetscInt*,PetscInt*),(eps,nev,ncv,mpd));
    731:   return 0;
    732: }

    734: static PetscErrorCode EPSKrylovSchurSetSubintervals_KrylovSchur(EPS eps,PetscReal* subint)
    735: {
    736:   EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;
    737:   PetscInt        i;

    741:   if (ctx->subintervals) PetscFree(ctx->subintervals);
    742:   PetscMalloc1(ctx->npart+1,&ctx->subintervals);
    743:   for (i=0;i<ctx->npart+1;i++) ctx->subintervals[i] = subint[i];
    744:   ctx->subintset = PETSC_TRUE;
    745:   eps->state = EPS_STATE_INITIAL;
    746:   return 0;
    747: }

    749: /*@C
    750:    EPSKrylovSchurSetSubintervals - Sets the points that delimit the
    751:    subintervals to be used in spectrum slicing with several partitions.

    753:    Logically Collective on eps

    755:    Input Parameters:
    756: +  eps    - the eigenproblem solver context
    757: -  subint - array of real values specifying subintervals

    759:    Notes:
    760:    This function must be called after EPSKrylovSchurSetPartitions(). For npart
    761:    partitions, the argument subint must contain npart+1 real values sorted in
    762:    ascending order, subint_0, subint_1, ..., subint_npart, where the first
    763:    and last values must coincide with the interval endpoints set with
    764:    EPSSetInterval().

    766:    The subintervals are then defined by two consecutive points [subint_0,subint_1],
    767:    [subint_1,subint_2], and so on.

    769:    Level: advanced

    771: .seealso: EPSKrylovSchurSetPartitions(), EPSKrylovSchurGetSubintervals(), EPSSetInterval()
    772: @*/
    773: PetscErrorCode EPSKrylovSchurSetSubintervals(EPS eps,PetscReal *subint)
    774: {
    776:   PetscTryMethod(eps,"EPSKrylovSchurSetSubintervals_C",(EPS,PetscReal*),(eps,subint));
    777:   return 0;
    778: }

    780: static PetscErrorCode EPSKrylovSchurGetSubintervals_KrylovSchur(EPS eps,PetscReal **subint)
    781: {
    782:   EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;
    783:   PetscInt        i;

    785:   if (!ctx->subintset) {
    788:   }
    789:   PetscMalloc1(ctx->npart+1,subint);
    790:   for (i=0;i<=ctx->npart;i++) (*subint)[i] = ctx->subintervals[i];
    791:   return 0;
    792: }

    794: /*@C
    795:    EPSKrylovSchurGetSubintervals - Returns the points that delimit the
    796:    subintervals used in spectrum slicing with several partitions.

    798:    Logically Collective on eps

    800:    Input Parameter:
    801: .  eps    - the eigenproblem solver context

    803:    Output Parameter:
    804: .  subint - array of real values specifying subintervals

    806:    Notes:
    807:    If the user passed values with EPSKrylovSchurSetSubintervals(), then the
    808:    same values are returned. Otherwise, the values computed internally are
    809:    obtained.

    811:    This function is only available for spectrum slicing runs.

    813:    The returned array has length npart+1 (see EPSKrylovSchurGetPartitions())
    814:    and should be freed by the user.

    816:    Fortran Notes:
    817:    The calling sequence from Fortran is
    818: .vb
    819:    EPSKrylovSchurGetSubintervals(eps,subint,ierr)
    820:    double precision subint(npart+1) output
    821: .ve

    823:    Level: advanced

    825: .seealso: EPSKrylovSchurSetSubintervals(), EPSKrylovSchurGetPartitions(), EPSSetInterval()
    826: @*/
    827: PetscErrorCode EPSKrylovSchurGetSubintervals(EPS eps,PetscReal **subint)
    828: {
    831:   PetscUseMethod(eps,"EPSKrylovSchurGetSubintervals_C",(EPS,PetscReal**),(eps,subint));
    832:   return 0;
    833: }

    835: static PetscErrorCode EPSKrylovSchurGetInertias_KrylovSchur(EPS eps,PetscInt *n,PetscReal **shifts,PetscInt **inertias)
    836: {
    837:   EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;
    838:   PetscInt        i,numsh;
    839:   EPS_SR          sr = ctx->sr;

    843:   switch (eps->state) {
    844:   case EPS_STATE_INITIAL:
    845:     break;
    846:   case EPS_STATE_SETUP:
    847:     numsh = ctx->npart+1;
    848:     if (n) *n = numsh;
    849:     if (shifts) {
    850:       PetscMalloc1(numsh,shifts);
    851:       (*shifts)[0] = eps->inta;
    852:       if (ctx->npart==1) (*shifts)[1] = eps->intb;
    853:       else for (i=1;i<numsh;i++) (*shifts)[i] = ctx->subintervals[i];
    854:     }
    855:     if (inertias) {
    856:       PetscMalloc1(numsh,inertias);
    857:       (*inertias)[0] = (sr->dir==1)?sr->inertia0:sr->inertia1;
    858:       if (ctx->npart==1) (*inertias)[1] = (sr->dir==1)?sr->inertia1:sr->inertia0;
    859:       else for (i=1;i<numsh;i++) (*inertias)[i] = (*inertias)[i-1]+ctx->nconv_loc[i-1];
    860:     }
    861:     break;
    862:   case EPS_STATE_SOLVED:
    863:   case EPS_STATE_EIGENVECTORS:
    864:     numsh = ctx->nshifts;
    865:     if (n) *n = numsh;
    866:     if (shifts) {
    867:       PetscMalloc1(numsh,shifts);
    868:       for (i=0;i<numsh;i++) (*shifts)[i] = ctx->shifts[i];
    869:     }
    870:     if (inertias) {
    871:       PetscMalloc1(numsh,inertias);
    872:       for (i=0;i<numsh;i++) (*inertias)[i] = ctx->inertias[i];
    873:     }
    874:     break;
    875:   }
    876:   return 0;
    877: }

    879: /*@C
    880:    EPSKrylovSchurGetInertias - Gets the values of the shifts and their
    881:    corresponding inertias in case of doing spectrum slicing for a
    882:    computational interval.

    884:    Not Collective

    886:    Input Parameter:
    887: .  eps - the eigenproblem solver context

    889:    Output Parameters:
    890: +  n        - number of shifts, including the endpoints of the interval
    891: .  shifts   - the values of the shifts used internally in the solver
    892: -  inertias - the values of the inertia in each shift

    894:    Notes:
    895:    If called after EPSSolve(), all shifts used internally by the solver are
    896:    returned (including both endpoints and any intermediate ones). If called
    897:    before EPSSolve() and after EPSSetUp() then only the information of the
    898:    endpoints of subintervals is available.

    900:    This function is only available for spectrum slicing runs.

    902:    The returned arrays should be freed by the user. Can pass NULL in any of
    903:    the two arrays if not required.

    905:    Fortran Notes:
    906:    The calling sequence from Fortran is
    907: .vb
    908:    EPSKrylovSchurGetInertias(eps,n,shifts,inertias,ierr)
    909:    integer n
    910:    double precision shifts(*)
    911:    integer inertias(*)
    912: .ve
    913:    The arrays should be at least of length n. The value of n can be determined
    914:    by an initial call
    915: .vb
    916:    EPSKrylovSchurGetInertias(eps,n,PETSC_NULL_REAL,PETSC_NULL_INTEGER,ierr)
    917: .ve

    919:    Level: advanced

    921: .seealso: EPSSetInterval(), EPSKrylovSchurSetSubintervals()
    922: @*/
    923: PetscErrorCode EPSKrylovSchurGetInertias(EPS eps,PetscInt *n,PetscReal **shifts,PetscInt **inertias)
    924: {
    927:   PetscUseMethod(eps,"EPSKrylovSchurGetInertias_C",(EPS,PetscInt*,PetscReal**,PetscInt**),(eps,n,shifts,inertias));
    928:   return 0;
    929: }

    931: static PetscErrorCode EPSKrylovSchurGetSubcommInfo_KrylovSchur(EPS eps,PetscInt *k,PetscInt *n,Vec *v)
    932: {
    933:   EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;
    934:   EPS_SR          sr = ((EPS_KRYLOVSCHUR*)ctx->eps->data)->sr;

    938:   if (k) *k = (ctx->npart==1)? 0: ctx->subc->color;
    939:   if (n) *n = sr->numEigs;
    940:   if (v) BVCreateVec(sr->V,v);
    941:   return 0;
    942: }

    944: /*@C
    945:    EPSKrylovSchurGetSubcommInfo - Gets information related to the case of
    946:    doing spectrum slicing for a computational interval with multiple
    947:    communicators.

    949:    Collective on the subcommunicator (if v is given)

    951:    Input Parameter:
    952: .  eps - the eigenproblem solver context

    954:    Output Parameters:
    955: +  k - index of the subinterval for the calling process
    956: .  n - number of eigenvalues found in the k-th subinterval
    957: -  v - a vector owned by processes in the subcommunicator with dimensions
    958:        compatible for locally computed eigenvectors (or NULL)

    960:    Notes:
    961:    This function is only available for spectrum slicing runs.

    963:    The returned Vec should be destroyed by the user.

    965:    Level: advanced

    967: .seealso: EPSSetInterval(), EPSKrylovSchurSetPartitions(), EPSKrylovSchurGetSubcommPairs()
    968: @*/
    969: PetscErrorCode EPSKrylovSchurGetSubcommInfo(EPS eps,PetscInt *k,PetscInt *n,Vec *v)
    970: {
    972:   PetscUseMethod(eps,"EPSKrylovSchurGetSubcommInfo_C",(EPS,PetscInt*,PetscInt*,Vec*),(eps,k,n,v));
    973:   return 0;
    974: }

    976: static PetscErrorCode EPSKrylovSchurGetSubcommPairs_KrylovSchur(EPS eps,PetscInt i,PetscScalar *eig,Vec v)
    977: {
    978:   EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;
    979:   EPS_SR          sr = ((EPS_KRYLOVSCHUR*)ctx->eps->data)->sr;

    981:   EPSCheckSolved(eps,1);
    984:   if (eig) *eig = sr->eigr[sr->perm[i]];
    985:   if (v) BVCopyVec(sr->V,sr->perm[i],v);
    986:   return 0;
    987: }

    989: /*@
    990:    EPSKrylovSchurGetSubcommPairs - Gets the i-th eigenpair stored
    991:    internally in the subcommunicator to which the calling process belongs.

    993:    Collective on the subcommunicator (if v is given)

    995:    Input Parameters:
    996: +  eps - the eigenproblem solver context
    997: -  i   - index of the solution

    999:    Output Parameters:
    1000: +  eig - the eigenvalue
    1001: -  v   - the eigenvector

    1003:    Notes:
    1004:    It is allowed to pass NULL for v if the eigenvector is not required.
    1005:    Otherwise, the caller must provide a valid Vec objects, i.e.,
    1006:    it must be created by the calling program with EPSKrylovSchurGetSubcommInfo().

    1008:    The index i should be a value between 0 and n-1, where n is the number of
    1009:    vectors in the local subinterval, see EPSKrylovSchurGetSubcommInfo().

    1011:    Level: advanced

    1013: .seealso: EPSSetInterval(), EPSKrylovSchurSetPartitions(), EPSKrylovSchurGetSubcommInfo(), EPSKrylovSchurGetSubcommMats()
    1014: @*/
    1015: PetscErrorCode EPSKrylovSchurGetSubcommPairs(EPS eps,PetscInt i,PetscScalar *eig,Vec v)
    1016: {
    1019:   PetscUseMethod(eps,"EPSKrylovSchurGetSubcommPairs_C",(EPS,PetscInt,PetscScalar*,Vec),(eps,i,eig,v));
    1020:   return 0;
    1021: }

    1023: static PetscErrorCode EPSKrylovSchurGetSubcommMats_KrylovSchur(EPS eps,Mat *A,Mat *B)
    1024: {
    1025:   EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;

    1029:   EPSGetOperators(ctx->eps,A,B);
    1030:   return 0;
    1031: }

    1033: /*@C
    1034:    EPSKrylovSchurGetSubcommMats - Gets the eigenproblem matrices stored
    1035:    internally in the subcommunicator to which the calling process belongs.

    1037:    Collective on the subcommunicator

    1039:    Input Parameter:
    1040: .  eps - the eigenproblem solver context

    1042:    Output Parameters:
    1043: +  A  - the matrix associated with the eigensystem
    1044: -  B  - the second matrix in the case of generalized eigenproblems

    1046:    Notes:
    1047:    This is the analog of EPSGetOperators(), but returns the matrices distributed
    1048:    differently (in the subcommunicator rather than in the parent communicator).

    1050:    These matrices should not be modified by the user.

    1052:    Level: advanced

    1054: .seealso: EPSSetInterval(), EPSKrylovSchurSetPartitions(), EPSKrylovSchurGetSubcommInfo()
    1055: @*/
    1056: PetscErrorCode EPSKrylovSchurGetSubcommMats(EPS eps,Mat *A,Mat *B)
    1057: {
    1059:   PetscTryMethod(eps,"EPSKrylovSchurGetSubcommMats_C",(EPS,Mat*,Mat*),(eps,A,B));
    1060:   return 0;
    1061: }

    1063: static PetscErrorCode EPSKrylovSchurUpdateSubcommMats_KrylovSchur(EPS eps,PetscScalar a,PetscScalar ap,Mat Au,PetscScalar b,PetscScalar bp, Mat Bu,MatStructure str,PetscBool globalup)
    1064: {
    1065:   EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data,*subctx;
    1066:   Mat             A,B=NULL,Ag,Bg=NULL;
    1067:   PetscBool       reuse=PETSC_TRUE;

    1071:   EPSGetOperators(eps,&Ag,&Bg);
    1072:   EPSGetOperators(ctx->eps,&A,&B);

    1074:   MatScale(A,a);
    1075:   if (Au) MatAXPY(A,ap,Au,str);
    1076:   if (B) MatScale(B,b);
    1077:   if (Bu) MatAXPY(B,bp,Bu,str);
    1078:   EPSSetOperators(ctx->eps,A,B);

    1080:   /* Update stored matrix state */
    1081:   subctx = (EPS_KRYLOVSCHUR*)ctx->eps->data;
    1082:   PetscObjectStateGet((PetscObject)A,&subctx->Astate);
    1083:   if (B) PetscObjectStateGet((PetscObject)B,&subctx->Bstate);

    1085:   /* Update matrices in the parent communicator if requested by user */
    1086:   if (globalup) {
    1087:     if (ctx->npart>1) {
    1088:       if (!ctx->isrow) {
    1089:         MatGetOwnershipIS(Ag,&ctx->isrow,&ctx->iscol);
    1090:         reuse = PETSC_FALSE;
    1091:       }
    1092:       if (str==DIFFERENT_NONZERO_PATTERN || str==UNKNOWN_NONZERO_PATTERN) reuse = PETSC_FALSE;
    1093:       if (ctx->submata && !reuse) MatDestroyMatrices(1,&ctx->submata);
    1094:       MatCreateSubMatrices(A,1,&ctx->isrow,&ctx->iscol,(reuse)?MAT_REUSE_MATRIX:MAT_INITIAL_MATRIX,&ctx->submata);
    1095:       MatCreateMPIMatConcatenateSeqMat(((PetscObject)Ag)->comm,ctx->submata[0],PETSC_DECIDE,MAT_REUSE_MATRIX,&Ag);
    1096:       if (B) {
    1097:         if (ctx->submatb && !reuse) MatDestroyMatrices(1,&ctx->submatb);
    1098:         MatCreateSubMatrices(B,1,&ctx->isrow,&ctx->iscol,(reuse)?MAT_REUSE_MATRIX:MAT_INITIAL_MATRIX,&ctx->submatb);
    1099:         MatCreateMPIMatConcatenateSeqMat(((PetscObject)Bg)->comm,ctx->submatb[0],PETSC_DECIDE,MAT_REUSE_MATRIX,&Bg);
    1100:       }
    1101:     }
    1102:     PetscObjectStateGet((PetscObject)Ag,&ctx->Astate);
    1103:     if (Bg) PetscObjectStateGet((PetscObject)Bg,&ctx->Bstate);
    1104:   }
    1105:   EPSSetOperators(eps,Ag,Bg);
    1106:   return 0;
    1107: }

    1109: /*@
    1110:    EPSKrylovSchurUpdateSubcommMats - Update the eigenproblem matrices stored
    1111:    internally in the subcommunicator to which the calling process belongs.

    1113:    Collective on eps

    1115:    Input Parameters:
    1116: +  eps - the eigenproblem solver context
    1117: .  s   - scalar that multiplies the existing A matrix
    1118: .  a   - scalar used in the axpy operation on A
    1119: .  Au  - matrix used in the axpy operation on A
    1120: .  t   - scalar that multiplies the existing B matrix
    1121: .  b   - scalar used in the axpy operation on B
    1122: .  Bu  - matrix used in the axpy operation on B
    1123: .  str - structure flag
    1124: -  globalup - flag indicating if global matrices must be updated

    1126:    Notes:
    1127:    This function modifies the eigenproblem matrices at the subcommunicator level,
    1128:    and optionally updates the global matrices in the parent communicator. The updates
    1129:    are expressed as A <-- s*A + a*Au,  B <-- t*B + b*Bu.

    1131:    It is possible to update one of the matrices, or both.

    1133:    The matrices Au and Bu must be equal in all subcommunicators.

    1135:    The str flag is passed to the MatAXPY() operations to perform the updates.

    1137:    If globalup is true, communication is carried out to reconstruct the updated
    1138:    matrices in the parent communicator. The user must be warned that if global
    1139:    matrices are not in sync with subcommunicator matrices, the errors computed
    1140:    by EPSComputeError() will be wrong even if the computed solution is correct
    1141:    (the synchronization may be done only once at the end).

    1143:    Level: advanced

    1145: .seealso: EPSSetInterval(), EPSKrylovSchurSetPartitions(), EPSKrylovSchurGetSubcommMats()
    1146: @*/
    1147: PetscErrorCode EPSKrylovSchurUpdateSubcommMats(EPS eps,PetscScalar s,PetscScalar a,Mat Au,PetscScalar t,PetscScalar b,Mat Bu,MatStructure str,PetscBool globalup)
    1148: {
    1158:   PetscTryMethod(eps,"EPSKrylovSchurUpdateSubcommMats_C",(EPS,PetscScalar,PetscScalar,Mat,PetscScalar,PetscScalar,Mat,MatStructure,PetscBool),(eps,s,a,Au,t,b,Bu,str,globalup));
    1159:   return 0;
    1160: }

    1162: PetscErrorCode EPSKrylovSchurGetChildEPS(EPS eps,EPS *childeps)
    1163: {
    1164:   EPS_KRYLOVSCHUR  *ctx=(EPS_KRYLOVSCHUR*)eps->data,*ctx_local;
    1165:   Mat              A,B=NULL,Ar=NULL,Br=NULL;
    1166:   PetscMPIInt      rank;
    1167:   PetscObjectState Astate,Bstate=0;
    1168:   PetscObjectId    Aid,Bid=0;
    1169:   STType           sttype;
    1170:   PetscInt         nmat;
    1171:   const char       *prefix;
    1172:   MPI_Comm         child;

    1174:   EPSGetOperators(eps,&A,&B);
    1175:   if (ctx->npart==1) {
    1176:     if (!ctx->eps) EPSCreate(((PetscObject)eps)->comm,&ctx->eps);
    1177:     EPSGetOptionsPrefix(eps,&prefix);
    1178:     EPSSetOptionsPrefix(ctx->eps,prefix);
    1179:     EPSSetOperators(ctx->eps,A,B);
    1180:   } else {
    1181:     PetscObjectStateGet((PetscObject)A,&Astate);
    1182:     PetscObjectGetId((PetscObject)A,&Aid);
    1183:     if (B) {
    1184:       PetscObjectStateGet((PetscObject)B,&Bstate);
    1185:       PetscObjectGetId((PetscObject)B,&Bid);
    1186:     }
    1187:     if (!ctx->subc) {
    1188:       /* Create context for subcommunicators */
    1189:       PetscSubcommCreate(PetscObjectComm((PetscObject)eps),&ctx->subc);
    1190:       PetscSubcommSetNumber(ctx->subc,ctx->npart);
    1191:       PetscSubcommSetType(ctx->subc,PETSC_SUBCOMM_CONTIGUOUS);
    1192:       PetscSubcommGetChild(ctx->subc,&child);

    1194:       /* Duplicate matrices */
    1195:       MatCreateRedundantMatrix(A,0,child,MAT_INITIAL_MATRIX,&Ar);
    1196:       ctx->Astate = Astate;
    1197:       ctx->Aid = Aid;
    1198:       MatPropagateSymmetryOptions(A,Ar);
    1199:       if (B) {
    1200:         MatCreateRedundantMatrix(B,0,child,MAT_INITIAL_MATRIX,&Br);
    1201:         ctx->Bstate = Bstate;
    1202:         ctx->Bid = Bid;
    1203:         MatPropagateSymmetryOptions(B,Br);
    1204:       }
    1205:     } else {
    1206:       PetscSubcommGetChild(ctx->subc,&child);
    1207:       if (ctx->Astate != Astate || (B && ctx->Bstate != Bstate) || ctx->Aid != Aid || (B && ctx->Bid != Bid)) {
    1208:         STGetNumMatrices(ctx->eps->st,&nmat);
    1209:         if (nmat) EPSGetOperators(ctx->eps,&Ar,&Br);
    1210:         MatCreateRedundantMatrix(A,0,child,MAT_INITIAL_MATRIX,&Ar);
    1211:         ctx->Astate = Astate;
    1212:         ctx->Aid = Aid;
    1213:         MatPropagateSymmetryOptions(A,Ar);
    1214:         if (B) {
    1215:           MatCreateRedundantMatrix(B,0,child,MAT_INITIAL_MATRIX,&Br);
    1216:           ctx->Bstate = Bstate;
    1217:           ctx->Bid = Bid;
    1218:           MatPropagateSymmetryOptions(B,Br);
    1219:         }
    1220:         EPSSetOperators(ctx->eps,Ar,Br);
    1221:         MatDestroy(&Ar);
    1222:         MatDestroy(&Br);
    1223:       }
    1224:     }

    1226:     /* Create auxiliary EPS */
    1227:     if (!ctx->eps) {
    1228:       EPSCreate(child,&ctx->eps);
    1229:       EPSGetOptionsPrefix(eps,&prefix);
    1230:       EPSSetOptionsPrefix(ctx->eps,prefix);
    1231:       EPSSetOperators(ctx->eps,Ar,Br);
    1232:       MatDestroy(&Ar);
    1233:       MatDestroy(&Br);
    1234:     }
    1235:     /* Create subcommunicator grouping processes with same rank */
    1236:     if (!ctx->commset) {
    1237:       MPI_Comm_rank(child,&rank);
    1238:       MPI_Comm_split(((PetscObject)eps)->comm,rank,ctx->subc->color,&ctx->commrank);
    1239:       ctx->commset = PETSC_TRUE;
    1240:     }
    1241:   }
    1242:   EPSSetType(ctx->eps,((PetscObject)eps)->type_name);
    1243:   STGetType(eps->st,&sttype);
    1244:   STSetType(ctx->eps->st,sttype);

    1246:   ctx_local = (EPS_KRYLOVSCHUR*)ctx->eps->data;
    1247:   ctx_local->npart = ctx->npart;
    1248:   ctx_local->global = PETSC_FALSE;
    1249:   ctx_local->eps = eps;
    1250:   ctx_local->subc = ctx->subc;
    1251:   ctx_local->commrank = ctx->commrank;
    1252:   *childeps = ctx->eps;
    1253:   return 0;
    1254: }

    1256: static PetscErrorCode EPSKrylovSchurGetKSP_KrylovSchur(EPS eps,KSP *ksp)
    1257: {
    1258:   EPS_KRYLOVSCHUR *ctx=(EPS_KRYLOVSCHUR*)eps->data;
    1259:   ST              st;
    1260:   PetscBool       isfilt;

    1262:   PetscObjectTypeCompare((PetscObject)eps->st,STFILTER,&isfilt);
    1264:   EPSKrylovSchurGetChildEPS(eps,&ctx->eps);
    1265:   EPSGetST(ctx->eps,&st);
    1266:   STGetOperator(st,NULL);
    1267:   STGetKSP(st,ksp);
    1268:   return 0;
    1269: }

    1271: /*@
    1272:    EPSKrylovSchurGetKSP - Retrieve the linear solver object associated with the
    1273:    internal EPS object in case of doing spectrum slicing for a computational interval.

    1275:    Collective on eps

    1277:    Input Parameter:
    1278: .  eps - the eigenproblem solver context

    1280:    Output Parameter:
    1281: .  ksp - the internal KSP object

    1283:    Notes:
    1284:    When invoked to compute all eigenvalues in an interval with spectrum
    1285:    slicing, EPSKRYLOVSCHUR creates another EPS object internally that is
    1286:    used to compute eigenvalues by chunks near selected shifts. This function
    1287:    allows access to the KSP object associated to this internal EPS object.

    1289:    This function is only available for spectrum slicing runs. In case of
    1290:    having more than one partition, the returned KSP will be different
    1291:    in MPI processes belonging to different partitions. Hence, if required,
    1292:    EPSKrylovSchurSetPartitions() must be called BEFORE this function.

    1294:    Level: advanced

    1296: .seealso: EPSSetInterval(), EPSKrylovSchurSetPartitions()
    1297: @*/
    1298: PetscErrorCode EPSKrylovSchurGetKSP(EPS eps,KSP *ksp)
    1299: {
    1301:   PetscUseMethod(eps,"EPSKrylovSchurGetKSP_C",(EPS,KSP*),(eps,ksp));
    1302:   return 0;
    1303: }

    1305: PetscErrorCode EPSSetFromOptions_KrylovSchur(EPS eps,PetscOptionItems *PetscOptionsObject)
    1306: {
    1307:   EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;
    1308:   PetscBool       flg,lock,b,f1,f2,f3,isfilt;
    1309:   PetscReal       keep;
    1310:   PetscInt        i,j,k;
    1311:   KSP             ksp;

    1313:   PetscOptionsHeadBegin(PetscOptionsObject,"EPS Krylov-Schur Options");

    1315:     PetscOptionsReal("-eps_krylovschur_restart","Proportion of vectors kept after restart","EPSKrylovSchurSetRestart",0.5,&keep,&flg);
    1316:     if (flg) EPSKrylovSchurSetRestart(eps,keep);

    1318:     PetscOptionsBool("-eps_krylovschur_locking","Choose between locking and non-locking variants","EPSKrylovSchurSetLocking",PETSC_TRUE,&lock,&flg);
    1319:     if (flg) EPSKrylovSchurSetLocking(eps,lock);

    1321:     i = ctx->npart;
    1322:     PetscOptionsInt("-eps_krylovschur_partitions","Number of partitions of the communicator for spectrum slicing","EPSKrylovSchurSetPartitions",ctx->npart,&i,&flg);
    1323:     if (flg) EPSKrylovSchurSetPartitions(eps,i);

    1325:     b = ctx->detect;
    1326:     PetscOptionsBool("-eps_krylovschur_detect_zeros","Check zeros during factorizations at subinterval boundaries","EPSKrylovSchurSetDetectZeros",ctx->detect,&b,&flg);
    1327:     if (flg) EPSKrylovSchurSetDetectZeros(eps,b);

    1329:     i = 1;
    1330:     j = k = PETSC_DECIDE;
    1331:     PetscOptionsInt("-eps_krylovschur_nev","Number of eigenvalues to compute in each subsolve (only for spectrum slicing)","EPSKrylovSchurSetDimensions",40,&i,&f1);
    1332:     PetscOptionsInt("-eps_krylovschur_ncv","Number of basis vectors in each subsolve (only for spectrum slicing)","EPSKrylovSchurSetDimensions",80,&j,&f2);
    1333:     PetscOptionsInt("-eps_krylovschur_mpd","Maximum dimension of projected problem in each subsolve (only for spectrum slicing)","EPSKrylovSchurSetDimensions",80,&k,&f3);
    1334:     if (f1 || f2 || f3) EPSKrylovSchurSetDimensions(eps,i,j,k);

    1336:   PetscOptionsHeadEnd();

    1338:   /* set options of child KSP in spectrum slicing */
    1339:   if (eps->which==EPS_ALL) {
    1340:     if (!eps->st) EPSGetST(eps,&eps->st);
    1341:     EPSSetDefaultST(eps);
    1342:     STSetFromOptions(eps->st);  /* need to advance this to check ST type */
    1343:     PetscObjectTypeCompare((PetscObject)eps->st,STFILTER,&isfilt);
    1344:     if (!isfilt) {
    1345:       EPSKrylovSchurGetKSP_KrylovSchur(eps,&ksp);
    1346:       KSPSetFromOptions(ksp);
    1347:     }
    1348:   }
    1349:   return 0;
    1350: }

    1352: PetscErrorCode EPSView_KrylovSchur(EPS eps,PetscViewer viewer)
    1353: {
    1354:   EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;
    1355:   PetscBool       isascii,isfilt;
    1356:   KSP             ksp;
    1357:   PetscViewer     sviewer;

    1359:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    1360:   if (isascii) {
    1361:     PetscViewerASCIIPrintf(viewer,"  %d%% of basis vectors kept after restart\n",(int)(100*ctx->keep));
    1362:     PetscViewerASCIIPrintf(viewer,"  using the %slocking variant\n",ctx->lock?"":"non-");
    1363:     if (eps->which==EPS_ALL) {
    1364:       PetscObjectTypeCompare((PetscObject)eps->st,STFILTER,&isfilt);
    1365:       if (isfilt) PetscViewerASCIIPrintf(viewer,"  using filtering to extract all eigenvalues in an interval\n");
    1366:       else {
    1367:         PetscViewerASCIIPrintf(viewer,"  doing spectrum slicing with nev=%" PetscInt_FMT ", ncv=%" PetscInt_FMT ", mpd=%" PetscInt_FMT "\n",ctx->nev,ctx->ncv,ctx->mpd);
    1368:         if (ctx->npart>1) {
    1369:           PetscViewerASCIIPrintf(viewer,"  multi-communicator spectrum slicing with %" PetscInt_FMT " partitions\n",ctx->npart);
    1370:           if (ctx->detect) PetscViewerASCIIPrintf(viewer,"  detecting zeros when factorizing at subinterval boundaries\n");
    1371:         }
    1372:         /* view child KSP */
    1373:         EPSKrylovSchurGetKSP_KrylovSchur(eps,&ksp);
    1374:         PetscViewerASCIIPushTab(viewer);
    1375:         if (ctx->npart>1 && ctx->subc) {
    1376:           PetscViewerGetSubViewer(viewer,ctx->subc->child,&sviewer);
    1377:           if (!ctx->subc->color) KSPView(ksp,sviewer);
    1378:           PetscViewerFlush(sviewer);
    1379:           PetscViewerRestoreSubViewer(viewer,ctx->subc->child,&sviewer);
    1380:           PetscViewerFlush(viewer);
    1381:           /* extra call needed because of the two calls to PetscViewerASCIIPushSynchronized() in PetscViewerGetSubViewer() */
    1382:           PetscViewerASCIIPopSynchronized(viewer);
    1383:         } else KSPView(ksp,viewer);
    1384:         PetscViewerASCIIPopTab(viewer);
    1385:       }
    1386:     }
    1387:   }
    1388:   return 0;
    1389: }

    1391: PetscErrorCode EPSDestroy_KrylovSchur(EPS eps)
    1392: {
    1393:   PetscBool      isfilt;

    1395:   PetscObjectTypeCompare((PetscObject)eps->st,STFILTER,&isfilt);
    1396:   if (eps->which==EPS_ALL && !isfilt) EPSDestroy_KrylovSchur_Slice(eps);
    1397:   PetscFree(eps->data);
    1398:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurSetRestart_C",NULL);
    1399:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurGetRestart_C",NULL);
    1400:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurSetLocking_C",NULL);
    1401:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurGetLocking_C",NULL);
    1402:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurSetPartitions_C",NULL);
    1403:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurGetPartitions_C",NULL);
    1404:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurSetDetectZeros_C",NULL);
    1405:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurGetDetectZeros_C",NULL);
    1406:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurSetDimensions_C",NULL);
    1407:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurGetDimensions_C",NULL);
    1408:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurSetSubintervals_C",NULL);
    1409:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurGetSubintervals_C",NULL);
    1410:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurGetInertias_C",NULL);
    1411:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurGetSubcommInfo_C",NULL);
    1412:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurGetSubcommPairs_C",NULL);
    1413:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurGetSubcommMats_C",NULL);
    1414:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurUpdateSubcommMats_C",NULL);
    1415:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurGetKSP_C",NULL);
    1416:   return 0;
    1417: }

    1419: PetscErrorCode EPSReset_KrylovSchur(EPS eps)
    1420: {
    1421:   PetscBool      isfilt;

    1423:   PetscObjectTypeCompare((PetscObject)eps->st,STFILTER,&isfilt);
    1424:   if (eps->which==EPS_ALL && !isfilt) EPSReset_KrylovSchur_Slice(eps);
    1425:   return 0;
    1426: }

    1428: PetscErrorCode EPSSetDefaultST_KrylovSchur(EPS eps)
    1429: {
    1430:   if (eps->which==EPS_ALL) {
    1431:     if (!((PetscObject)eps->st)->type_name) STSetType(eps->st,STSINVERT);
    1432:   }
    1433:   return 0;
    1434: }

    1436: SLEPC_EXTERN PetscErrorCode EPSCreate_KrylovSchur(EPS eps)
    1437: {
    1438:   EPS_KRYLOVSCHUR *ctx;

    1440:   PetscNew(&ctx);
    1441:   eps->data   = (void*)ctx;
    1442:   ctx->lock   = PETSC_TRUE;
    1443:   ctx->nev    = 1;
    1444:   ctx->ncv    = PETSC_DEFAULT;
    1445:   ctx->mpd    = PETSC_DEFAULT;
    1446:   ctx->npart  = 1;
    1447:   ctx->detect = PETSC_FALSE;
    1448:   ctx->global = PETSC_TRUE;

    1450:   eps->useds = PETSC_TRUE;

    1452:   /* solve and computevectors determined at setup */
    1453:   eps->ops->setup          = EPSSetUp_KrylovSchur;
    1454:   eps->ops->setupsort      = EPSSetUpSort_KrylovSchur;
    1455:   eps->ops->setfromoptions = EPSSetFromOptions_KrylovSchur;
    1456:   eps->ops->destroy        = EPSDestroy_KrylovSchur;
    1457:   eps->ops->reset          = EPSReset_KrylovSchur;
    1458:   eps->ops->view           = EPSView_KrylovSchur;
    1459:   eps->ops->backtransform  = EPSBackTransform_Default;
    1460:   eps->ops->setdefaultst   = EPSSetDefaultST_KrylovSchur;

    1462:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurSetRestart_C",EPSKrylovSchurSetRestart_KrylovSchur);
    1463:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurGetRestart_C",EPSKrylovSchurGetRestart_KrylovSchur);
    1464:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurSetLocking_C",EPSKrylovSchurSetLocking_KrylovSchur);
    1465:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurGetLocking_C",EPSKrylovSchurGetLocking_KrylovSchur);
    1466:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurSetPartitions_C",EPSKrylovSchurSetPartitions_KrylovSchur);
    1467:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurGetPartitions_C",EPSKrylovSchurGetPartitions_KrylovSchur);
    1468:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurSetDetectZeros_C",EPSKrylovSchurSetDetectZeros_KrylovSchur);
    1469:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurGetDetectZeros_C",EPSKrylovSchurGetDetectZeros_KrylovSchur);
    1470:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurSetDimensions_C",EPSKrylovSchurSetDimensions_KrylovSchur);
    1471:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurGetDimensions_C",EPSKrylovSchurGetDimensions_KrylovSchur);
    1472:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurSetSubintervals_C",EPSKrylovSchurSetSubintervals_KrylovSchur);
    1473:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurGetSubintervals_C",EPSKrylovSchurGetSubintervals_KrylovSchur);
    1474:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurGetInertias_C",EPSKrylovSchurGetInertias_KrylovSchur);
    1475:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurGetSubcommInfo_C",EPSKrylovSchurGetSubcommInfo_KrylovSchur);
    1476:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurGetSubcommPairs_C",EPSKrylovSchurGetSubcommPairs_KrylovSchur);
    1477:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurGetSubcommMats_C",EPSKrylovSchurGetSubcommMats_KrylovSchur);
    1478:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurUpdateSubcommMats_C",EPSKrylovSchurUpdateSubcommMats_KrylovSchur);
    1479:   PetscObjectComposeFunction((PetscObject)eps,"EPSKrylovSchurGetKSP_C",EPSKrylovSchurGetKSP_KrylovSchur);
    1480:   return 0;
    1481: }