Date: 2023-09-05T10:17:53+00:00

Actual source code: epssetup.c
slepc-3.19.2 2023-09-05
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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_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,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: 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:   if (eps->useds && !eps->ds) PetscCall(EPSGetDS(eps,&eps->ds));
    307:   if (eps->useds) PetscCall(EPSSetDSType(eps));
    308:   if (eps->twosided) {
    309:     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);
    310:   }
    311:   if (!eps->rg) PetscCall(EPSGetRG(eps,&eps->rg));
    312:   if (!((PetscObject)eps->rg)->type_name) PetscCall(RGSetType(eps->rg,RGINTERVAL));

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

    320:   /* Set default problem type */
    321:   if (!eps->problem_type) {
    322:     if (nmat==1) PetscCall(EPSSetProblemType(eps,EPS_NHEP));
    323:     else PetscCall(EPSSetProblemType(eps,EPS_GNHEP));
    324:   } else if (nmat==1 && eps->isgeneralized) {
    325:     PetscCall(PetscInfo(eps,"Eigenproblem set as generalized but no matrix B was provided; reverting to a standard eigenproblem\n"));
    326:     eps->isgeneralized = PETSC_FALSE;
    327:     eps->problem_type = eps->ishermitian? EPS_HEP: EPS_NHEP;
    328:   } 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");

    330:   if (eps->nev > eps->n) eps->nev = eps->n;
    331:   if (eps->ncv > eps->n) eps->ncv = eps->n;

    333:   /* check some combinations of eps->which */
    334:   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");

    336:   /* initialization of matrix norms */
    337:   if (eps->conv==EPS_CONV_NORM) {
    338:     if (!eps->nrma) {
    339:       PetscCall(STGetMatrix(eps->st,0,&A));
    340:       PetscCall(MatNorm(A,NORM_INFINITY,&eps->nrma));
    341:     }
    342:     if (nmat>1 && !eps->nrmb) {
    343:       PetscCall(STGetMatrix(eps->st,1,&B));
    344:       PetscCall(MatNorm(B,NORM_INFINITY,&eps->nrmb));
    345:     }
    346:   }

    348:   /* call specific solver setup */
    349:   PetscUseTypeMethod(eps,setup);

    351:   /* if purification is set, check that it really makes sense */
    352:   if (eps->purify) {
    353:     if (eps->categ==EPS_CATEGORY_PRECOND || eps->categ==EPS_CATEGORY_CONTOUR) eps->purify = PETSC_FALSE;
    354:     else {
    355:       if (!eps->isgeneralized) eps->purify = PETSC_FALSE;
    356:       else if (!eps->ishermitian && !eps->ispositive) eps->purify = PETSC_FALSE;
    357:       else {
    358:         PetscCall(PetscObjectTypeCompare((PetscObject)eps->st,STCAYLEY,&flg));
    359:         if (flg) eps->purify = PETSC_FALSE;
    360:       }
    361:     }
    362:   }

    364:   /* set tolerance if not yet set */
    365:   if (eps->tol==(PetscReal)PETSC_DEFAULT) eps->tol = SLEPC_DEFAULT_TOL;

    367:   /* set up sorting criterion */
    368:   PetscTryTypeMethod(eps,setupsort);

    370:   /* Build balancing matrix if required */
    371:   if (eps->balance!=EPS_BALANCE_USER) {
    372:     PetscCall(STSetBalanceMatrix(eps->st,NULL));
    373:     if (!eps->ishermitian && (eps->balance==EPS_BALANCE_ONESIDE || eps->balance==EPS_BALANCE_TWOSIDE)) {
    374:       if (!eps->D) PetscCall(BVCreateVec(eps->V,&eps->D));
    375:       PetscCall(EPSBuildBalance_Krylov(eps));
    376:       PetscCall(STSetBalanceMatrix(eps->st,eps->D));
    377:     }
    378:   }

    380:   /* Setup ST */
    381:   PetscCall(STSetUp(eps->st));
    382:   PetscCall(EPSCheckCompatibleST(eps));

    384:   /* process deflation and initial vectors */
    385:   if (eps->nds<0) {
    386:     k = -eps->nds;
    387:     PetscCall(BVInsertConstraints(eps->V,&k,eps->defl));
    388:     PetscCall(SlepcBasisDestroy_Private(&eps->nds,&eps->defl));
    389:     eps->nds = k;
    390:     PetscCall(STCheckNullSpace(eps->st,eps->V));
    391:   }
    392:   if (eps->nini<0) {
    393:     k = -eps->nini;
    394:     PetscCheck(k<=eps->ncv,PetscObjectComm((PetscObject)eps),PETSC_ERR_USER_INPUT,"The number of initial vectors is larger than ncv");
    395:     PetscCall(BVInsertVecs(eps->V,0,&k,eps->IS,PETSC_TRUE));
    396:     PetscCall(SlepcBasisDestroy_Private(&eps->nini,&eps->IS));
    397:     eps->nini = k;
    398:   }
    399:   if (eps->twosided && eps->ninil<0) {
    400:     k = -eps->ninil;
    401:     PetscCheck(k<=eps->ncv,PetscObjectComm((PetscObject)eps),PETSC_ERR_USER_INPUT,"The number of left initial vectors is larger than ncv");
    402:     PetscCall(BVInsertVecs(eps->W,0,&k,eps->ISL,PETSC_TRUE));
    403:     PetscCall(SlepcBasisDestroy_Private(&eps->ninil,&eps->ISL));
    404:     eps->ninil = k;
    405:   }

    407:   PetscCall(PetscLogEventEnd(EPS_SetUp,eps,0,0,0));
    408:   eps->state = EPS_STATE_SETUP;
    409:   PetscFunctionReturn(PETSC_SUCCESS);
    410: }

    412: /*@
    413:    EPSSetOperators - Sets the matrices associated with the eigenvalue problem.

    415:    Collective

    417:    Input Parameters:
    418: +  eps - the eigenproblem solver context
    419: .  A  - the matrix associated with the eigensystem
    420: -  B  - the second matrix in the case of generalized eigenproblems

    422:    Notes:
    423:    To specify a standard eigenproblem, use NULL for parameter B.

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

    428:    Level: beginner

    430: .seealso: EPSSolve(), EPSSetUp(), EPSReset(), EPSGetST(), STGetMatrix()
    431: @*/
    432: PetscErrorCode EPSSetOperators(EPS eps,Mat A,Mat B)
    433: {
    434:   PetscInt       m,n,m0,mloc,nloc,mloc0,nmat;
    435:   Mat            mat[2];

    437:   PetscFunctionBegin;
    441:   PetscCheckSameComm(eps,1,A,2);
    442:   if (B) PetscCheckSameComm(eps,1,B,3);

    444:   /* Check matrix sizes */
    445:   PetscCall(MatGetSize(A,&m,&n));
    446:   PetscCall(MatGetLocalSize(A,&mloc,&nloc));
    447:   PetscCheck(m==n,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"A is a non-square matrix (%" PetscInt_FMT " rows, %" PetscInt_FMT " cols)",m,n);
    448:   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);
    449:   if (B) {
    450:     PetscCall(MatGetSize(B,&m0,&n));
    451:     PetscCall(MatGetLocalSize(B,&mloc0,&nloc));
    452:     PetscCheck(m0==n,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"B is a non-square matrix (%" PetscInt_FMT " rows, %" PetscInt_FMT " cols)",m0,n);
    453:     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);
    454:     PetscCheck(m==m0,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_INCOMP,"Dimensions of A and B do not match (%" PetscInt_FMT ", %" PetscInt_FMT ")",m,m0);
    455:     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);
    456:   }
    457:   if (eps->state && (n!=eps->n || nloc!=eps->nloc)) PetscCall(EPSReset(eps));
    458:   eps->nrma = 0.0;
    459:   eps->nrmb = 0.0;
    460:   if (!eps->st) PetscCall(EPSGetST(eps,&eps->st));
    461:   mat[0] = A;
    462:   if (B) {
    463:     mat[1] = B;
    464:     nmat = 2;
    465:   } else nmat = 1;
    466:   PetscCall(STSetMatrices(eps->st,nmat,mat));
    467:   eps->state = EPS_STATE_INITIAL;
    468:   PetscFunctionReturn(PETSC_SUCCESS);
    469: }

    471: /*@
    472:    EPSGetOperators - Gets the matrices associated with the eigensystem.

    474:    Collective

    476:    Input Parameter:
    477: .  eps - the EPS context

    479:    Output Parameters:
    480: +  A  - the matrix associated with the eigensystem
    481: -  B  - the second matrix in the case of generalized eigenproblems

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

    486:    Level: intermediate

    488: .seealso: EPSSolve(), EPSGetST(), STGetMatrix(), STSetMatrices()
    489: @*/
    490: PetscErrorCode EPSGetOperators(EPS eps,Mat *A,Mat *B)
    491: {
    492:   ST             st;
    493:   PetscInt       k;

    495:   PetscFunctionBegin;
    497:   PetscCall(EPSGetST(eps,&st));
    498:   PetscCall(STGetNumMatrices(st,&k));
    499:   if (A) {
    500:     if (k<1) *A = NULL;
    501:     else PetscCall(STGetMatrix(st,0,A));
    502:   }
    503:   if (B) {
    504:     if (k<2) *B = NULL;
    505:     else PetscCall(STGetMatrix(st,1,B));
    506:   }
    507:   PetscFunctionReturn(PETSC_SUCCESS);
    508: }

    510: /*@C
    511:    EPSSetDeflationSpace - Specify a basis of vectors that constitute the deflation
    512:    space.

    514:    Collective

    516:    Input Parameters:
    517: +  eps - the eigenproblem solver context
    518: .  n   - number of vectors
    519: -  v   - set of basis vectors of the deflation space

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

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

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

    533:    Level: intermediate

    535: .seealso: EPSSetInitialSpace()
    536: @*/
    537: PetscErrorCode EPSSetDeflationSpace(EPS eps,PetscInt n,Vec v[])
    538: {
    539:   PetscFunctionBegin;
    542:   PetscCheck(n>=0,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"Argument n cannot be negative");
    543:   if (n>0) {
    546:   }
    547:   PetscCall(SlepcBasisReference_Private(n,v,&eps->nds,&eps->defl));
    548:   if (n>0) eps->state = EPS_STATE_INITIAL;
    549:   PetscFunctionReturn(PETSC_SUCCESS);
    550: }

    552: /*@C
    553:    EPSSetInitialSpace - Specify a basis of vectors that constitute the initial
    554:    space, that is, the subspace from which the solver starts to iterate.

    556:    Collective

    558:    Input Parameters:
    559: +  eps - the eigenproblem solver context
    560: .  n   - number of vectors
    561: -  is  - set of basis vectors of the initial space

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

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

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

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

    576:    Level: intermediate

    578: .seealso: EPSSetLeftInitialSpace(), EPSSetDeflationSpace()
    579: @*/
    580: PetscErrorCode EPSSetInitialSpace(EPS eps,PetscInt n,Vec is[])
    581: {
    582:   PetscFunctionBegin;
    585:   PetscCheck(n>=0,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"Argument n cannot be negative");
    586:   if (n>0) {
    589:   }
    590:   PetscCall(SlepcBasisReference_Private(n,is,&eps->nini,&eps->IS));
    591:   if (n>0) eps->state = EPS_STATE_INITIAL;
    592:   PetscFunctionReturn(PETSC_SUCCESS);
    593: }

    595: /*@C
    596:    EPSSetLeftInitialSpace - Specify a basis of vectors that constitute the left
    597:    initial space, used by two-sided solvers to start the left subspace.

    599:    Collective

    601:    Input Parameters:
    602: +  eps - the eigenproblem solver context
    603: .  n   - number of vectors
    604: -  isl - set of basis vectors of the left initial space

    606:    Notes:
    607:    Left initial vectors are used to initiate the left search space in two-sided
    608:    eigensolvers. Users should pass here an approximation of the left eigenspace,
    609:    if available.

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

    613:    Level: intermediate

    615: .seealso: EPSSetInitialSpace(), EPSSetTwoSided()
    616: @*/
    617: PetscErrorCode EPSSetLeftInitialSpace(EPS eps,PetscInt n,Vec isl[])
    618: {
    619:   PetscFunctionBegin;
    622:   PetscCheck(n>=0,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"Argument n cannot be negative");
    623:   if (n>0) {
    626:   }
    627:   PetscCall(SlepcBasisReference_Private(n,isl,&eps->ninil,&eps->ISL));
    628:   if (n>0) eps->state = EPS_STATE_INITIAL;
    629:   PetscFunctionReturn(PETSC_SUCCESS);
    630: }

    632: /*
    633:   EPSSetDimensions_Default - Set reasonable values for ncv, mpd if not set
    634:   by the user. This is called at setup.
    635:  */
    636: PetscErrorCode EPSSetDimensions_Default(EPS eps,PetscInt nev,PetscInt *ncv,PetscInt *mpd)
    637: {
    638:   PetscBool      krylov;

    640:   PetscFunctionBegin;
    641:   if (*ncv!=PETSC_DEFAULT) { /* ncv set */
    642:     PetscCall(PetscObjectTypeCompareAny((PetscObject)eps,&krylov,EPSKRYLOVSCHUR,EPSARNOLDI,EPSLANCZOS,""));
    643:     if (krylov) {
    644:       PetscCheck(*ncv>=nev+1 || (*ncv==nev && *ncv==eps->n),PetscObjectComm((PetscObject)eps),PETSC_ERR_USER_INPUT,"The value of ncv must be at least nev+1");
    645:     } else {
    646:       PetscCheck(*ncv>=nev,PetscObjectComm((PetscObject)eps),PETSC_ERR_USER_INPUT,"The value of ncv must be at least nev");
    647:     }
    648:   } else if (*mpd!=PETSC_DEFAULT) { /* mpd set */
    649:     *ncv = PetscMin(eps->n,nev+(*mpd));
    650:   } else { /* neither set: defaults depend on nev being small or large */
    651:     if (nev<500) *ncv = PetscMin(eps->n,PetscMax(2*nev,nev+15));
    652:     else {
    653:       *mpd = 500;
    654:       *ncv = PetscMin(eps->n,nev+(*mpd));
    655:     }
    656:   }
    657:   if (*mpd==PETSC_DEFAULT) *mpd = *ncv;
    658:   PetscFunctionReturn(PETSC_SUCCESS);
    659: }

    661: /*@
    662:    EPSAllocateSolution - Allocate memory storage for common variables such
    663:    as eigenvalues and eigenvectors.

    665:    Collective

    667:    Input Parameters:
    668: +  eps   - eigensolver context
    669: -  extra - number of additional positions, used for methods that require a
    670:            working basis slightly larger than ncv

    672:    Developer Notes:
    673:    This is SLEPC_EXTERN because it may be required by user plugin EPS
    674:    implementations.

    676:    Level: developer

    678: .seealso: EPSSetUp()
    679: @*/
    680: PetscErrorCode EPSAllocateSolution(EPS eps,PetscInt extra)
    681: {
    682:   PetscInt       oldsize,requested;
    683:   PetscRandom    rand;
    684:   Vec            t;

    686:   PetscFunctionBegin;
    687:   requested = eps->ncv + extra;

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

    692:   /* allocate space for eigenvalues and friends */
    693:   if (requested != oldsize || !eps->eigr) {
    694:     PetscCall(PetscFree4(eps->eigr,eps->eigi,eps->errest,eps->perm));
    695:     PetscCall(PetscMalloc4(requested,&eps->eigr,requested,&eps->eigi,requested,&eps->errest,requested,&eps->perm));
    696:   }

    698:   /* workspace for the case of arbitrary selection */
    699:   if (eps->arbitrary) {
    700:     if (eps->rr) PetscCall(PetscFree2(eps->rr,eps->ri));
    701:     PetscCall(PetscMalloc2(requested,&eps->rr,requested,&eps->ri));
    702:   }

    704:   /* allocate V */
    705:   if (!eps->V) PetscCall(EPSGetBV(eps,&eps->V));
    706:   if (!oldsize) {
    707:     if (!((PetscObject)(eps->V))->type_name) PetscCall(BVSetType(eps->V,BVSVEC));
    708:     PetscCall(STMatCreateVecsEmpty(eps->st,&t,NULL));
    709:     PetscCall(BVSetSizesFromVec(eps->V,t,requested));
    710:     PetscCall(VecDestroy(&t));
    711:   } else PetscCall(BVResize(eps->V,requested,PETSC_FALSE));

    713:   /* allocate W */
    714:   if (eps->twosided) {
    715:     PetscCall(BVGetRandomContext(eps->V,&rand));  /* make sure the random context is available when duplicating */
    716:     PetscCall(BVDestroy(&eps->W));
    717:     PetscCall(BVDuplicate(eps->V,&eps->W));
    718:   }
    719:   PetscFunctionReturn(PETSC_SUCCESS);
    720: }