Date: 2024-12-02T08:56:57+00:00

Actual source code: epssetup.c
slepc-3.22.2 2024-12-02
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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:    EPS routines related to problem setup
     12: */

     14: #include <slepc/private/epsimpl.h>

     16: /*
     17:    Let the solver choose the ST type that should be used by default,
     18:    otherwise set it to SHIFT.
     19:    This is called at EPSSetFromOptions (before STSetFromOptions)
     20:    and also at EPSSetUp (in case EPSSetFromOptions was not called).
     21: */
     22: PetscErrorCode EPSSetDefaultST(EPS eps)
     23: {
     24:   PetscFunctionBegin;
     25:   PetscTryTypeMethod(eps,setdefaultst);
     26:   if (!((PetscObject)eps->st)->type_name) PetscCall(STSetType(eps->st,STSHIFT));
     27:   PetscFunctionReturn(PETSC_SUCCESS);
     28: }

     30: /*
     31:    This is done by preconditioned eigensolvers that use the PC only.
     32:    It sets STPRECOND with KSPPREONLY.
     33: */
     34: PetscErrorCode EPSSetDefaultST_Precond(EPS eps)
     35: {
     36:   KSP            ksp;

     38:   PetscFunctionBegin;
     39:   if (!((PetscObject)eps->st)->type_name) PetscCall(STSetType(eps->st,STPRECOND));
     40:   PetscCall(STGetKSP(eps->st,&ksp));
     41:   if (!((PetscObject)ksp)->type_name) PetscCall(KSPSetType(ksp,KSPPREONLY));
     42:   PetscFunctionReturn(PETSC_SUCCESS);
     43: }

     45: /*
     46:    This is done by preconditioned eigensolvers that can also use the KSP.
     47:    It sets STPRECOND with the default KSP (GMRES) and maxit=5.
     48: */
     49: PetscErrorCode EPSSetDefaultST_GMRES(EPS eps)
     50: {
     51:   KSP            ksp;

     53:   PetscFunctionBegin;
     54:   if (!((PetscObject)eps->st)->type_name) PetscCall(STSetType(eps->st,STPRECOND));
     55:   PetscCall(STPrecondSetKSPHasMat(eps->st,PETSC_TRUE));
     56:   PetscCall(STGetKSP(eps->st,&ksp));
     57:   if (!((PetscObject)ksp)->type_name) {
     58:     PetscCall(KSPSetType(ksp,KSPGMRES));
     59:     PetscCall(KSPSetTolerances(ksp,PETSC_CURRENT,PETSC_CURRENT,PETSC_CURRENT,5));
     60:   }
     61:   PetscFunctionReturn(PETSC_SUCCESS);
     62: }

     64: #if defined(SLEPC_HAVE_SCALAPACK) || defined(SLEPC_HAVE_ELPA) || defined(SLEPC_HAVE_ELEMENTAL) || defined(SLEPC_HAVE_EVSL)
     65: /*
     66:    This is for direct eigensolvers that work with A and B directly, so
     67:    no need to factorize B.
     68: */
     69: PetscErrorCode EPSSetDefaultST_NoFactor(EPS eps)
     70: {
     71:   KSP            ksp;
     72:   PC             pc;

     74:   PetscFunctionBegin;
     75:   if (!((PetscObject)eps->st)->type_name) PetscCall(STSetType(eps->st,STSHIFT));
     76:   PetscCall(STGetKSP(eps->st,&ksp));
     77:   if (!((PetscObject)ksp)->type_name) PetscCall(KSPSetType(ksp,KSPPREONLY));
     78:   PetscCall(KSPGetPC(ksp,&pc));
     79:   if (!((PetscObject)pc)->type_name) PetscCall(PCSetType(pc,PCNONE));
     80:   PetscFunctionReturn(PETSC_SUCCESS);
     81: }
     82: #endif

     84: /*
     85:    Check that the ST selected by the user is compatible with the EPS solver and options
     86: */
     87: static PetscErrorCode EPSCheckCompatibleST(EPS eps)
     88: {
     89:   PetscBool      precond,shift,sinvert,cayley,lyapii;
     90: #if defined(PETSC_USE_COMPLEX)
     91:   PetscScalar    sigma;
     92: #endif

     94:   PetscFunctionBegin;
     95:   PetscCall(PetscObjectTypeCompare((PetscObject)eps->st,STPRECOND,&precond));
     96:   PetscCall(PetscObjectTypeCompare((PetscObject)eps->st,STSHIFT,&shift));
     97:   PetscCall(PetscObjectTypeCompare((PetscObject)eps->st,STSINVERT,&sinvert));
     98:   PetscCall(PetscObjectTypeCompare((PetscObject)eps->st,STCAYLEY,&cayley));

    100:   /* preconditioned eigensolvers */
    101:   PetscCheck(eps->categ!=EPS_CATEGORY_PRECOND || precond,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"This solver requires ST=PRECOND");
    102:   PetscCheck(eps->categ==EPS_CATEGORY_PRECOND || !precond,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"STPRECOND is intended for preconditioned eigensolvers only");

    104:   /* harmonic extraction */
    105:   PetscCheck(precond || shift || !eps->extraction || eps->extraction==EPS_RITZ,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Cannot use a spectral transformation combined with harmonic extraction");

    107:   /* real shifts in Hermitian problems */
    108: #if defined(PETSC_USE_COMPLEX)
    109:   PetscCall(STGetShift(eps->st,&sigma));
    110:   PetscCheck(!eps->ishermitian || PetscImaginaryPart(sigma)==0.0,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Hermitian problems are not compatible with complex shifts");
    111: #endif

    113:   /* Cayley with PGNHEP */
    114:   PetscCheck(!cayley || eps->problem_type!=EPS_PGNHEP,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Cayley spectral transformation is not compatible with PGNHEP");

    116:   /* make sure that the user does not specify smallest magnitude with shift-and-invert */
    117:   if ((cayley || sinvert) && (eps->categ==EPS_CATEGORY_KRYLOV || eps->categ==EPS_CATEGORY_OTHER)) {
    118:     PetscCall(PetscObjectTypeCompare((PetscObject)eps,EPSLYAPII,&lyapii));
    119:     PetscCheck(lyapii || eps->which==EPS_TARGET_MAGNITUDE || eps->which==EPS_TARGET_REAL || eps->which==EPS_TARGET_IMAGINARY || eps->which==EPS_ALL || eps->which==EPS_WHICH_USER,PetscObjectComm((PetscObject)eps),PETSC_ERR_USER_INPUT,"Shift-and-invert requires a target 'which' (see EPSSetWhichEigenpairs), for instance -st_type sinvert -eps_target 0 -eps_target_magnitude");
    120:   }
    121:   PetscFunctionReturn(PETSC_SUCCESS);
    122: }

    124: /*
    125:    MatEstimateSpectralRange_EPS: estimate the spectral range [left,right] of a
    126:    symmetric/Hermitian matrix A using an auxiliary EPS object
    127: */
    128: PetscErrorCode MatEstimateSpectralRange_EPS(Mat A,PetscReal *left,PetscReal *right)
    129: {
    130:   PetscInt       nconv;
    131:   PetscScalar    eig0;
    132:   PetscReal      tol=1e-3,errest=tol;
    133:   EPS            eps;

    135:   PetscFunctionBegin;
    136:   *left = 0.0; *right = 0.0;
    137:   PetscCall(EPSCreate(PetscObjectComm((PetscObject)A),&eps));
    138:   PetscCall(EPSSetOptionsPrefix(eps,"eps_filter_"));
    139:   PetscCall(EPSSetOperators(eps,A,NULL));
    140:   PetscCall(EPSSetProblemType(eps,EPS_HEP));
    141:   PetscCall(EPSSetTolerances(eps,tol,50));
    142:   PetscCall(EPSSetConvergenceTest(eps,EPS_CONV_ABS));
    143:   PetscCall(EPSSetWhichEigenpairs(eps,EPS_SMALLEST_REAL));
    144:   PetscCall(EPSSolve(eps));
    145:   PetscCall(EPSGetConverged(eps,&nconv));
    146:   if (nconv>0) {
    147:     PetscCall(EPSGetEigenvalue(eps,0,&eig0,NULL));
    148:     PetscCall(EPSGetErrorEstimate(eps,0,&errest));
    149:   } else eig0 = eps->eigr[0];
    150:   *left = PetscRealPart(eig0)-errest;
    151:   PetscCall(EPSSetWhichEigenpairs(eps,EPS_LARGEST_REAL));
    152:   PetscCall(EPSSolve(eps));
    153:   PetscCall(EPSGetConverged(eps,&nconv));
    154:   if (nconv>0) {
    155:     PetscCall(EPSGetEigenvalue(eps,0,&eig0,NULL));
    156:     PetscCall(EPSGetErrorEstimate(eps,0,&errest));
    157:   } else eig0 = eps->eigr[0];
    158:   *right = PetscRealPart(eig0)+errest;
    159:   PetscCall(EPSDestroy(&eps));
    160:   PetscFunctionReturn(PETSC_SUCCESS);
    161: }

    163: /*
    164:    EPSSetUpSort_Basic: configure the EPS sorting criterion according to 'which'
    165: */
    166: PetscErrorCode EPSSetUpSort_Basic(EPS eps)
    167: {
    168:   PetscFunctionBegin;
    169:   switch (eps->which) {
    170:     case EPS_LARGEST_MAGNITUDE:
    171:       eps->sc->comparison    = SlepcCompareLargestMagnitude;
    172:       eps->sc->comparisonctx = NULL;
    173:       break;
    174:     case EPS_SMALLEST_MAGNITUDE:
    175:       eps->sc->comparison    = SlepcCompareSmallestMagnitude;
    176:       eps->sc->comparisonctx = NULL;
    177:       break;
    178:     case EPS_LARGEST_REAL:
    179:       eps->sc->comparison    = SlepcCompareLargestReal;
    180:       eps->sc->comparisonctx = NULL;
    181:       break;
    182:     case EPS_SMALLEST_REAL:
    183:       eps->sc->comparison    = SlepcCompareSmallestReal;
    184:       eps->sc->comparisonctx = NULL;
    185:       break;
    186:     case EPS_LARGEST_IMAGINARY:
    187:       eps->sc->comparison    = SlepcCompareLargestImaginary;
    188:       eps->sc->comparisonctx = NULL;
    189:       break;
    190:     case EPS_SMALLEST_IMAGINARY:
    191:       eps->sc->comparison    = SlepcCompareSmallestImaginary;
    192:       eps->sc->comparisonctx = NULL;
    193:       break;
    194:     case EPS_TARGET_MAGNITUDE:
    195:       eps->sc->comparison    = SlepcCompareTargetMagnitude;
    196:       eps->sc->comparisonctx = &eps->target;
    197:       break;
    198:     case EPS_TARGET_REAL:
    199:       eps->sc->comparison    = SlepcCompareTargetReal;
    200:       eps->sc->comparisonctx = &eps->target;
    201:       break;
    202:     case EPS_TARGET_IMAGINARY:
    203: #if defined(PETSC_USE_COMPLEX)
    204:       eps->sc->comparison    = SlepcCompareTargetImaginary;
    205:       eps->sc->comparisonctx = &eps->target;
    206: #endif
    207:       break;
    208:     case EPS_ALL:
    209:       eps->sc->comparison    = SlepcCompareSmallestReal;
    210:       eps->sc->comparisonctx = NULL;
    211:       break;
    212:     case EPS_WHICH_USER:
    213:       break;
    214:   }
    215:   eps->sc->map    = NULL;
    216:   eps->sc->mapobj = NULL;
    217:   PetscFunctionReturn(PETSC_SUCCESS);
    218: }

    220: /*
    221:    EPSSetUpSort_Default: configure both EPS and DS sorting criterion
    222: */
    223: PetscErrorCode EPSSetUpSort_Default(EPS eps)
    224: {
    225:   SlepcSC        sc;
    226:   PetscBool      istrivial;

    228:   PetscFunctionBegin;
    229:   /* fill sorting criterion context */
    230:   PetscCall(EPSSetUpSort_Basic(eps));
    231:   /* fill sorting criterion for DS */
    232:   PetscCall(DSGetSlepcSC(eps->ds,&sc));
    233:   PetscCall(RGIsTrivial(eps->rg,&istrivial));
    234:   sc->rg            = istrivial? NULL: eps->rg;
    235:   sc->comparison    = eps->sc->comparison;
    236:   sc->comparisonctx = eps->sc->comparisonctx;
    237:   sc->map           = SlepcMap_ST;
    238:   sc->mapobj        = (PetscObject)eps->st;
    239:   PetscFunctionReturn(PETSC_SUCCESS);
    240: }

    242: /*@
    243:    EPSSetDSType - Sets the type of the internal DS object based on the current
    244:    settings of the eigenvalue solver.

    246:    Collective

    248:    Input Parameter:
    249: .  eps - eigenproblem solver context

    251:    Note:
    252:    This function need not be called explicitly, since it will be called at
    253:    both EPSSetFromOptions() and EPSSetUp().

    255:    Level: developer

    257: .seealso: EPSSetFromOptions(), EPSSetUp()
    258: @*/
    259: PetscErrorCode EPSSetDSType(EPS eps)
    260: {
    261:   PetscFunctionBegin;
    263:   PetscTryTypeMethod(eps,setdstype);
    264:   PetscFunctionReturn(PETSC_SUCCESS);
    265: }

    267: /*@
    268:    EPSSetUp - Sets up all the internal data structures necessary for the
    269:    execution of the eigensolver. Then calls STSetUp() for any set-up
    270:    operations associated to the ST object.

    272:    Collective

    274:    Input Parameter:
    275: .  eps   - eigenproblem solver context

    277:    Notes:
    278:    This function need not be called explicitly in most cases, since EPSSolve()
    279:    calls it. It can be useful when one wants to measure the set-up time
    280:    separately from the solve time.

    282:    Level: developer

    284: .seealso: EPSCreate(), EPSSolve(), EPSDestroy(), STSetUp(), EPSSetInitialSpace()
    285: @*/
    286: PetscErrorCode EPSSetUp(EPS eps)
    287: {
    288:   Mat            A,B;
    289:   PetscInt       k,nmat;
    290:   PetscBool      flg;

    292:   PetscFunctionBegin;
    294:   if (eps->state) PetscFunctionReturn(PETSC_SUCCESS);
    295:   PetscCall(PetscLogEventBegin(EPS_SetUp,eps,0,0,0));

    297:   /* reset the convergence flag from the previous solves */
    298:   eps->reason = EPS_CONVERGED_ITERATING;

    300:   /* Set default solver type (EPSSetFromOptions was not called) */
    301:   if (!((PetscObject)eps)->type_name) PetscCall(EPSSetType(eps,EPSKRYLOVSCHUR));
    302:   if (!eps->st) PetscCall(EPSGetST(eps,&eps->st));
    303:   PetscCall(EPSSetDefaultST(eps));

    305:   PetscCall(STSetTransform(eps->st,PETSC_TRUE));
    306:   PetscCall(STSetStructured(eps->st,PETSC_FALSE));
    307:   if (eps->useds && !eps->ds) PetscCall(EPSGetDS(eps,&eps->ds));
    308:   if (eps->useds) PetscCall(EPSSetDSType(eps));
    309:   if (eps->twosided) {
    310:     PetscCheck(!eps->ishermitian || (eps->isgeneralized && !eps->ispositive),PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Two-sided methods are not intended for %s problems",SLEPC_STRING_HERMITIAN);
    311:   }
    312:   if (!eps->rg) PetscCall(EPSGetRG(eps,&eps->rg));
    313:   if (!((PetscObject)eps->rg)->type_name) PetscCall(RGSetType(eps->rg,RGINTERVAL));

    315:   /* Set problem dimensions */
    316:   PetscCall(STGetNumMatrices(eps->st,&nmat));
    317:   PetscCheck(nmat,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONGSTATE,"EPSSetOperators must be called first");
    318:   PetscCall(STMatGetSize(eps->st,&eps->n,NULL));
    319:   PetscCall(STMatGetLocalSize(eps->st,&eps->nloc,NULL));

    321:   /* Set default problem type */
    322:   if (!eps->problem_type) {
    323:     if (nmat==1) PetscCall(EPSSetProblemType(eps,EPS_NHEP));
    324:     else PetscCall(EPSSetProblemType(eps,EPS_GNHEP));
    325:   } else if (nmat==1 && eps->isgeneralized) {
    326:     PetscCall(PetscInfo(eps,"Eigenproblem set as generalized but no matrix B was provided; reverting to a standard eigenproblem\n"));
    327:     eps->isgeneralized = PETSC_FALSE;
    328:     eps->problem_type = eps->ishermitian? EPS_HEP: EPS_NHEP;
    329:   } else PetscCheck(nmat==1 || eps->isgeneralized,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_INCOMP,"Inconsistent EPS state: the problem type does not match the number of matrices");

    331:   if (eps->isstructured) {
    332:     /* make sure the user has set the appropriate matrix */
    333:     PetscCall(STGetMatrix(eps->st,0,&A));
    334:     if (eps->problem_type==EPS_BSE) PetscCall(SlepcCheckMatStruct(A,SLEPC_MAT_STRUCT_BSE,NULL));
    335:   }

    337:   /* safeguard for small problems */
    338:   if (eps->isstructured) {
    339:     if (2*eps->nev > eps->n) eps->nev = eps->n/2;
    340:     if (2*eps->ncv > eps->n) eps->ncv = eps->n/2;
    341:   } else {
    342:     if (eps->nev > eps->n) eps->nev = eps->n;
    343:     if (eps->ncv > eps->n) eps->ncv = eps->n;
    344:   }

    346:   /* check some combinations of eps->which */
    347:   PetscCheck(!eps->ishermitian || (eps->isgeneralized && !eps->ispositive) || (eps->which!=EPS_LARGEST_IMAGINARY && eps->which!=EPS_SMALLEST_IMAGINARY && eps->which!=EPS_TARGET_IMAGINARY),PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Sorting the eigenvalues along the imaginary axis is not allowed when all eigenvalues are real");

    349:   /* initialization of matrix norms */
    350:   if (eps->conv==EPS_CONV_NORM) {
    351:     if (!eps->nrma) {
    352:       PetscCall(STGetMatrix(eps->st,0,&A));
    353:       PetscCall(MatNorm(A,NORM_INFINITY,&eps->nrma));
    354:     }
    355:     if (nmat>1 && !eps->nrmb) {
    356:       PetscCall(STGetMatrix(eps->st,1,&B));
    357:       PetscCall(MatNorm(B,NORM_INFINITY,&eps->nrmb));
    358:     }
    359:   }

    361:   /* call specific solver setup */
    362:   PetscUseTypeMethod(eps,setup);

    364:   /* if purification is set, check that it really makes sense */
    365:   if (eps->purify) {
    366:     if (eps->categ==EPS_CATEGORY_PRECOND || eps->categ==EPS_CATEGORY_CONTOUR) eps->purify = PETSC_FALSE;
    367:     else {
    368:       if (!eps->isgeneralized) eps->purify = PETSC_FALSE;
    369:       else if (!eps->ishermitian && !eps->ispositive) eps->purify = PETSC_FALSE;
    370:       else {
    371:         PetscCall(PetscObjectTypeCompare((PetscObject)eps->st,STCAYLEY,&flg));
    372:         if (flg) eps->purify = PETSC_FALSE;
    373:       }
    374:     }
    375:   }

    377:   /* set tolerance if not yet set */
    378:   if (eps->tol==(PetscReal)PETSC_DETERMINE) eps->tol = SLEPC_DEFAULT_TOL;

    380:   /* set up sorting criterion */
    381:   PetscTryTypeMethod(eps,setupsort);

    383:   /* Build balancing matrix if required */
    384:   if (eps->balance!=EPS_BALANCE_USER) {
    385:     PetscCall(STSetBalanceMatrix(eps->st,NULL));
    386:     if (!eps->ishermitian && (eps->balance==EPS_BALANCE_ONESIDE || eps->balance==EPS_BALANCE_TWOSIDE)) {
    387:       if (!eps->D) PetscCall(BVCreateVec(eps->V,&eps->D));
    388:       PetscCall(EPSBuildBalance_Krylov(eps));
    389:       PetscCall(STSetBalanceMatrix(eps->st,eps->D));
    390:     }
    391:   }

    393:   /* Setup ST */
    394:   PetscCall(STSetUp(eps->st));
    395:   PetscCall(EPSCheckCompatibleST(eps));

    397:   /* process deflation and initial vectors */
    398:   if (eps->nds<0) {
    399:     PetscCheck(!eps->isstructured,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Deflation space is not supported in structured eigenproblems");
    400:     k = -eps->nds;
    401:     PetscCall(BVInsertConstraints(eps->V,&k,eps->defl));
    402:     PetscCall(SlepcBasisDestroy_Private(&eps->nds,&eps->defl));
    403:     eps->nds = k;
    404:     PetscCall(STCheckNullSpace(eps->st,eps->V));
    405:   }
    406:   if (eps->nini<0) {
    407:     k = -eps->nini;
    408:     PetscCheck(k<=eps->ncv,PetscObjectComm((PetscObject)eps),PETSC_ERR_USER_INPUT,"The number of initial vectors is larger than ncv");
    409:     PetscCall(BVInsertVecs(eps->V,0,&k,eps->IS,PETSC_TRUE));
    410:     PetscCall(SlepcBasisDestroy_Private(&eps->nini,&eps->IS));
    411:     eps->nini = k;
    412:   }
    413:   if (eps->twosided && eps->ninil<0) {
    414:     k = -eps->ninil;
    415:     PetscCheck(k<=eps->ncv,PetscObjectComm((PetscObject)eps),PETSC_ERR_USER_INPUT,"The number of left initial vectors is larger than ncv");
    416:     PetscCall(BVInsertVecs(eps->W,0,&k,eps->ISL,PETSC_TRUE));
    417:     PetscCall(SlepcBasisDestroy_Private(&eps->ninil,&eps->ISL));
    418:     eps->ninil = k;
    419:   }

    421:   PetscCall(PetscLogEventEnd(EPS_SetUp,eps,0,0,0));
    422:   eps->state = EPS_STATE_SETUP;
    423:   PetscFunctionReturn(PETSC_SUCCESS);
    424: }

    426: /*@
    427:    EPSSetOperators - Sets the matrices associated with the eigenvalue problem.

    429:    Collective

    431:    Input Parameters:
    432: +  eps - the eigenproblem solver context
    433: .  A  - the matrix associated with the eigensystem
    434: -  B  - the second matrix in the case of generalized eigenproblems

    436:    Notes:
    437:    To specify a standard eigenproblem, use NULL for parameter B.

    439:    It must be called before EPSSetUp(). If it is called again after EPSSetUp() and
    440:    the matrix sizes have changed then the EPS object is reset.

    442:    For structured eigenproblem types such as EPS_BSE (see EPSSetProblemType()), the
    443:    provided matrices must have been created with the corresponding helper function,
    444:    i.e., MatCreateBSE().

    446:    Level: beginner

    448: .seealso: EPSSolve(), EPSSetUp(), EPSReset(), EPSGetST(), STGetMatrix(), EPSSetProblemType()
    449: @*/
    450: PetscErrorCode EPSSetOperators(EPS eps,Mat A,Mat B)
    451: {
    452:   PetscInt       m,n,m0,mloc,nloc,mloc0,nmat;
    453:   Mat            mat[2];

    455:   PetscFunctionBegin;
    459:   PetscCheckSameComm(eps,1,A,2);
    460:   if (B) PetscCheckSameComm(eps,1,B,3);

    462:   /* Check matrix sizes */
    463:   PetscCall(MatGetSize(A,&m,&n));
    464:   PetscCall(MatGetLocalSize(A,&mloc,&nloc));
    465:   PetscCheck(m==n,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"A is a non-square matrix (%" PetscInt_FMT " rows, %" PetscInt_FMT " cols)",m,n);
    466:   PetscCheck(mloc==nloc,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"A does not have equal row and column sizes (%" PetscInt_FMT ", %" PetscInt_FMT ")",mloc,nloc);
    467:   if (B) {
    468:     PetscCall(MatGetSize(B,&m0,&n));
    469:     PetscCall(MatGetLocalSize(B,&mloc0,&nloc));
    470:     PetscCheck(m0==n,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"B is a non-square matrix (%" PetscInt_FMT " rows, %" PetscInt_FMT " cols)",m0,n);
    471:     PetscCheck(mloc0==nloc,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"B does not have equal row and column local sizes (%" PetscInt_FMT ", %" PetscInt_FMT ")",mloc0,nloc);
    472:     PetscCheck(m==m0,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_INCOMP,"Dimensions of A and B do not match (%" PetscInt_FMT ", %" PetscInt_FMT ")",m,m0);
    473:     PetscCheck(mloc==mloc0,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_INCOMP,"Local dimensions of A and B do not match (%" PetscInt_FMT ", %" PetscInt_FMT ")",mloc,mloc0);
    474:   }
    475:   if (eps->state && (n!=eps->n || nloc!=eps->nloc)) PetscCall(EPSReset(eps));
    476:   eps->nrma = 0.0;
    477:   eps->nrmb = 0.0;
    478:   if (!eps->st) PetscCall(EPSGetST(eps,&eps->st));
    479:   mat[0] = A;
    480:   if (B) {
    481:     mat[1] = B;
    482:     nmat = 2;
    483:   } else nmat = 1;
    484:   PetscCall(STSetMatrices(eps->st,nmat,mat));
    485:   eps->state = EPS_STATE_INITIAL;
    486:   PetscFunctionReturn(PETSC_SUCCESS);
    487: }

    489: /*@
    490:    EPSGetOperators - Gets the matrices associated with the eigensystem.

    492:    Collective

    494:    Input Parameter:
    495: .  eps - the EPS context

    497:    Output Parameters:
    498: +  A  - the matrix associated with the eigensystem
    499: -  B  - the second matrix in the case of generalized eigenproblems

    501:    Note:
    502:    Does not increase the reference count of the matrices, so you should not destroy them.

    504:    Level: intermediate

    506: .seealso: EPSSolve(), EPSGetST(), STGetMatrix(), STSetMatrices()
    507: @*/
    508: PetscErrorCode EPSGetOperators(EPS eps,Mat *A,Mat *B)
    509: {
    510:   ST             st;
    511:   PetscInt       k;

    513:   PetscFunctionBegin;
    515:   PetscCall(EPSGetST(eps,&st));
    516:   PetscCall(STGetNumMatrices(st,&k));
    517:   if (A) {
    518:     if (k<1) *A = NULL;
    519:     else PetscCall(STGetMatrix(st,0,A));
    520:   }
    521:   if (B) {
    522:     if (k<2) *B = NULL;
    523:     else PetscCall(STGetMatrix(st,1,B));
    524:   }
    525:   PetscFunctionReturn(PETSC_SUCCESS);
    526: }

    528: /*@
    529:    EPSSetDeflationSpace - Specify a basis of vectors that constitute the deflation
    530:    space.

    532:    Collective

    534:    Input Parameters:
    535: +  eps - the eigenproblem solver context
    536: .  n   - number of vectors
    537: -  v   - set of basis vectors of the deflation space

    539:    Notes:
    540:    When a deflation space is given, the eigensolver seeks the eigensolution
    541:    in the restriction of the problem to the orthogonal complement of this
    542:    space. This can be used for instance in the case that an invariant
    543:    subspace is known beforehand (such as the nullspace of the matrix).

    545:    These vectors do not persist from one EPSSolve() call to the other, so the
    546:    deflation space should be set every time.

    548:    The vectors do not need to be mutually orthonormal, since they are explicitly
    549:    orthonormalized internally.

    551:    Level: intermediate

    553: .seealso: EPSSetInitialSpace()
    554: @*/
    555: PetscErrorCode EPSSetDeflationSpace(EPS eps,PetscInt n,Vec v[])
    556: {
    557:   PetscFunctionBegin;
    560:   PetscCheck(n>=0,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"Argument n cannot be negative");
    561:   if (n>0) {
    562:     PetscAssertPointer(v,3);
    564:   }
    565:   PetscCall(SlepcBasisReference_Private(n,v,&eps->nds,&eps->defl));
    566:   if (n>0) eps->state = EPS_STATE_INITIAL;
    567:   PetscFunctionReturn(PETSC_SUCCESS);
    568: }

    570: /*@
    571:    EPSSetInitialSpace - Specify a basis of vectors that constitute the initial
    572:    space, that is, the subspace from which the solver starts to iterate.

    574:    Collective

    576:    Input Parameters:
    577: +  eps - the eigenproblem solver context
    578: .  n   - number of vectors
    579: -  is  - set of basis vectors of the initial space

    581:    Notes:
    582:    Some solvers start to iterate on a single vector (initial vector). In that case,
    583:    the other vectors are ignored.

    585:    These vectors do not persist from one EPSSolve() call to the other, so the
    586:    initial space should be set every time.

    588:    The vectors do not need to be mutually orthonormal, since they are explicitly
    589:    orthonormalized internally.

    591:    Common usage of this function is when the user can provide a rough approximation
    592:    of the wanted eigenspace. Then, convergence may be faster.

    594:    Level: intermediate

    596: .seealso: EPSSetLeftInitialSpace(), EPSSetDeflationSpace()
    597: @*/
    598: PetscErrorCode EPSSetInitialSpace(EPS eps,PetscInt n,Vec is[])
    599: {
    600:   PetscFunctionBegin;
    603:   PetscCheck(n>=0,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"Argument n cannot be negative");
    604:   if (n>0) {
    605:     PetscAssertPointer(is,3);
    607:   }
    608:   PetscCall(SlepcBasisReference_Private(n,is,&eps->nini,&eps->IS));
    609:   if (n>0) eps->state = EPS_STATE_INITIAL;
    610:   PetscFunctionReturn(PETSC_SUCCESS);
    611: }

    613: /*@
    614:    EPSSetLeftInitialSpace - Specify a basis of vectors that constitute the left
    615:    initial space, used by two-sided solvers to start the left subspace.

    617:    Collective

    619:    Input Parameters:
    620: +  eps - the eigenproblem solver context
    621: .  n   - number of vectors
    622: -  isl - set of basis vectors of the left initial space

    624:    Notes:
    625:    Left initial vectors are used to initiate the left search space in two-sided
    626:    eigensolvers. Users should pass here an approximation of the left eigenspace,
    627:    if available.

    629:    The same comments in EPSSetInitialSpace() are applicable here.

    631:    Level: intermediate

    633: .seealso: EPSSetInitialSpace(), EPSSetTwoSided()
    634: @*/
    635: PetscErrorCode EPSSetLeftInitialSpace(EPS eps,PetscInt n,Vec isl[])
    636: {
    637:   PetscFunctionBegin;
    640:   PetscCheck(n>=0,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"Argument n cannot be negative");
    641:   if (n>0) {
    642:     PetscAssertPointer(isl,3);
    644:   }
    645:   PetscCall(SlepcBasisReference_Private(n,isl,&eps->ninil,&eps->ISL));
    646:   if (n>0) eps->state = EPS_STATE_INITIAL;
    647:   PetscFunctionReturn(PETSC_SUCCESS);
    648: }

    650: /*
    651:   EPSSetDimensions_Default - Set reasonable values for ncv, mpd if not set
    652:   by the user. This is called at setup.
    653:  */
    654: PetscErrorCode EPSSetDimensions_Default(EPS eps,PetscInt nev,PetscInt *ncv,PetscInt *mpd)
    655: {
    656:   PetscBool      krylov;
    657:   PetscInt       n = eps->isstructured? eps->n/2: eps->n;

    659:   PetscFunctionBegin;
    660:   if (*ncv!=PETSC_DETERMINE) { /* ncv set */
    661:     PetscCall(PetscObjectTypeCompareAny((PetscObject)eps,&krylov,EPSKRYLOVSCHUR,EPSARNOLDI,EPSLANCZOS,""));
    662:     if (krylov) {
    663:       PetscCheck(*ncv>=nev+1 || (*ncv==nev && *ncv==n),PetscObjectComm((PetscObject)eps),PETSC_ERR_USER_INPUT,"The value of ncv must be at least nev+1");
    664:     } else {
    665:       PetscCheck(*ncv>=nev,PetscObjectComm((PetscObject)eps),PETSC_ERR_USER_INPUT,"The value of ncv must be at least nev");
    666:     }
    667:   } else if (*mpd!=PETSC_DETERMINE) { /* mpd set */
    668:     *ncv = PetscMin(n,nev+(*mpd));
    669:   } else { /* neither set: defaults depend on nev being small or large */
    670:     if (nev<500) *ncv = PetscMin(n,PetscMax(2*nev,nev+15));
    671:     else {
    672:       *mpd = 500;
    673:       *ncv = PetscMin(n,nev+(*mpd));
    674:     }
    675:   }
    676:   if (*mpd==PETSC_DETERMINE) *mpd = *ncv;
    677:   PetscFunctionReturn(PETSC_SUCCESS);
    678: }

    680: /*@
    681:    EPSAllocateSolution - Allocate memory storage for common variables such
    682:    as eigenvalues and eigenvectors.

    684:    Collective

    686:    Input Parameters:
    687: +  eps   - eigensolver context
    688: -  extra - number of additional positions, used for methods that require a
    689:            working basis slightly larger than ncv

    691:    Developer Notes:
    692:    This is SLEPC_EXTERN because it may be required by user plugin EPS
    693:    implementations.

    695:    Level: developer

    697: .seealso: EPSSetUp()
    698: @*/
    699: PetscErrorCode EPSAllocateSolution(EPS eps,PetscInt extra)
    700: {
    701:   PetscInt       oldsize,requested;
    702:   PetscRandom    rand;
    703:   Vec            t;

    705:   PetscFunctionBegin;
    706:   requested = eps->ncv + extra;

    708:   /* oldsize is zero if this is the first time setup is called */
    709:   PetscCall(BVGetSizes(eps->V,NULL,NULL,&oldsize));

    711:   /* allocate space for eigenvalues and friends */
    712:   if (requested != oldsize || !eps->eigr) {
    713:     PetscCall(PetscFree4(eps->eigr,eps->eigi,eps->errest,eps->perm));
    714:     PetscCall(PetscMalloc4(requested,&eps->eigr,requested,&eps->eigi,requested,&eps->errest,requested,&eps->perm));
    715:   }

    717:   /* workspace for the case of arbitrary selection */
    718:   if (eps->arbitrary) {
    719:     if (eps->rr) PetscCall(PetscFree2(eps->rr,eps->ri));
    720:     PetscCall(PetscMalloc2(requested,&eps->rr,requested,&eps->ri));
    721:   }

    723:   /* allocate V */
    724:   if (!eps->V) PetscCall(EPSGetBV(eps,&eps->V));
    725:   if (!oldsize) {
    726:     if (!((PetscObject)eps->V)->type_name) PetscCall(BVSetType(eps->V,BVMAT));
    727:     PetscCall(STMatCreateVecsEmpty(eps->st,&t,NULL));
    728:     PetscCall(BVSetSizesFromVec(eps->V,t,requested));
    729:     PetscCall(VecDestroy(&t));
    730:   } else PetscCall(BVResize(eps->V,requested,PETSC_FALSE));

    732:   /* allocate W */
    733:   if (eps->twosided) {
    734:     PetscCall(BVGetRandomContext(eps->V,&rand));  /* make sure the random context is available when duplicating */
    735:     PetscCall(BVDestroy(&eps->W));
    736:     PetscCall(BVDuplicate(eps->V,&eps->W));
    737:   }
    738:   PetscFunctionReturn(PETSC_SUCCESS);
    739: }