Date: 2018-10-23T10:31:02+00:00

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

      6:    This file is part of SLEPc.
      7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
      8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      9: */
     10: /*
     11:    EPS routines related to problem setup
     12: */

     14: #include <slepc/private/epsimpl.h>       /*I "slepceps.h" I*/

     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: {

     27:   if (eps->ops->setdefaultst) { (*eps->ops->setdefaultst)(eps); }
     28:   if (!((PetscObject)eps->st)->type_name) {
     29:     STSetType(eps->st,STSHIFT);
     30:   }
     31:   return(0);
     32: }

     34: /*
     35:    This is done by preconditioned eigensolvers that use the PC only.
     36:    It sets STPRECOND with KSPPREONLY.
     37: */
     38: PetscErrorCode EPSSetDefaultST_Precond(EPS eps)
     39: {
     41:   KSP            ksp;

     44:   if (!((PetscObject)eps->st)->type_name) {
     45:     STSetType(eps->st,STPRECOND);
     46:     STPrecondSetKSPHasMat(eps->st,PETSC_TRUE);
     47:   }
     48:   STGetKSP(eps->st,&ksp);
     49:   if (!((PetscObject)ksp)->type_name) {
     50:     KSPSetType(ksp,KSPPREONLY);
     51:   }
     52:   return(0);
     53: }

     55: /*
     56:    This is done by preconditioned eigensolvers that can also use the KSP.
     57:    It sets STPRECOND with the default KSP (GMRES).
     58: */
     59: PetscErrorCode EPSSetDefaultST_GMRES(EPS eps)
     60: {
     62:   KSP            ksp;

     65:   if (!((PetscObject)eps->st)->type_name) {
     66:     STSetType(eps->st,STPRECOND);
     67:     STPrecondSetKSPHasMat(eps->st,PETSC_TRUE);
     68:   }
     69:   STGetKSP(eps->st,&ksp);
     70:   KSPSetTolerances(ksp,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,5);
     71:   return(0);
     72: }

     74: /*@
     75:    EPSSetUp - Sets up all the internal data structures necessary for the
     76:    execution of the eigensolver. Then calls STSetUp() for any set-up
     77:    operations associated to the ST object.

     79:    Collective on EPS

     81:    Input Parameter:
     82: .  eps   - eigenproblem solver context

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

     89:    Level: developer

     91: .seealso: EPSCreate(), EPSSolve(), EPSDestroy(), STSetUp(), EPSSetInitialSpace()
     92: @*/
     93: PetscErrorCode EPSSetUp(EPS eps)
     94: {
     96:   Mat            A,B;
     97:   SlepcSC        sc;
     98:   PetscInt       k,nmat;
     99:   PetscBool      flg,istrivial,precond;
    100: #if defined(PETSC_USE_COMPLEX)
    101:   PetscScalar    sigma;
    102: #endif

    106:   if (eps->state) return(0);
    107:   PetscLogEventBegin(EPS_SetUp,eps,0,0,0);

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

    112:   /* Set default solver type (EPSSetFromOptions was not called) */
    113:   if (!((PetscObject)eps)->type_name) {
    114:     EPSSetType(eps,EPSKRYLOVSCHUR);
    115:   }
    116:   if (!eps->st) { EPSGetST(eps,&eps->st); }
    117:   EPSSetDefaultST(eps);

    119:   PetscObjectTypeCompare((PetscObject)eps->st,STPRECOND,&precond);
    120:   if (eps->categ==EPS_CATEGORY_PRECOND && !precond) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"This solver requires ST=PRECOND");
    121:   if (eps->categ!=EPS_CATEGORY_PRECOND && precond) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"STPRECOND is intended for preconditioned eigensolvers only");

    123:   STSetTransform(eps->st,PETSC_TRUE);
    124:   if (eps->useds && !eps->ds) { EPSGetDS(eps,&eps->ds); }
    125:   if (!eps->rg) { EPSGetRG(eps,&eps->rg); }
    126:   if (!((PetscObject)eps->rg)->type_name) {
    127:     RGSetType(eps->rg,RGINTERVAL);
    128:   }

    130:   /* Set problem dimensions */
    131:   STGetNumMatrices(eps->st,&nmat);
    132:   if (!nmat) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONGSTATE,"EPSSetOperators must be called first");
    133:   STMatGetSize(eps->st,&eps->n,NULL);
    134:   STMatGetLocalSize(eps->st,&eps->nloc,NULL);

    136:   /* Set default problem type */
    137:   if (!eps->problem_type) {
    138:     if (nmat==1) {
    139:       EPSSetProblemType(eps,EPS_NHEP);
    140:     } else {
    141:       EPSSetProblemType(eps,EPS_GNHEP);
    142:     }
    143:   } else if (nmat==1 && eps->isgeneralized) {
    144:     PetscInfo(eps,"Eigenproblem set as generalized but no matrix B was provided; reverting to a standard eigenproblem\n");
    145:     eps->isgeneralized = PETSC_FALSE;
    146:     eps->problem_type = eps->ishermitian? EPS_HEP: EPS_NHEP;
    147:   } else if (nmat>1 && !eps->isgeneralized) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_INCOMP,"Inconsistent EPS state");

    149:   if (eps->nev > eps->n) eps->nev = eps->n;
    150:   if (eps->ncv > eps->n) eps->ncv = eps->n;

    152:   /* initialization of matrix norms */
    153:   if (eps->conv==EPS_CONV_NORM) {
    154:     if (!eps->nrma) {
    155:       STGetMatrix(eps->st,0,&A);
    156:       MatNorm(A,NORM_INFINITY,&eps->nrma);
    157:     }
    158:     if (nmat>1 && !eps->nrmb) {
    159:       STGetMatrix(eps->st,1,&B);
    160:       MatNorm(B,NORM_INFINITY,&eps->nrmb);
    161:     }
    162:   }

    164:   /* call specific solver setup */
    165:   (*eps->ops->setup)(eps);

    167:   /* if purification is set, check that it really makes sense */
    168:   if (eps->purify) {
    169:     if (eps->categ==EPS_CATEGORY_PRECOND || eps->categ==EPS_CATEGORY_CONTOUR) eps->purify = PETSC_FALSE;
    170:     else {
    171:       if (!eps->isgeneralized) eps->purify = PETSC_FALSE;
    172:       else if (!eps->ishermitian && !eps->ispositive) eps->purify = PETSC_FALSE;
    173:       else {
    174:         PetscObjectTypeCompare((PetscObject)eps->st,STCAYLEY,&flg);
    175:         if (flg) eps->purify = PETSC_FALSE;
    176:       }
    177:     }
    178:   }

    180:   /* check extraction */
    181:   PetscObjectTypeCompareAny((PetscObject)eps->st,&flg,STPRECOND,STSHIFT,"");
    182:   if (!flg && eps->extraction && eps->extraction!=EPS_RITZ) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Cannot use a spectral transformation combined with harmonic extraction");

    184:   /* set tolerance if not yet set */
    185:   if (eps->tol==PETSC_DEFAULT) eps->tol = SLEPC_DEFAULT_TOL;

    187:   /* fill sorting criterion context */
    188:   switch (eps->which) {
    189:     case EPS_LARGEST_MAGNITUDE:
    190:       eps->sc->comparison    = SlepcCompareLargestMagnitude;
    191:       eps->sc->comparisonctx = NULL;
    192:       break;
    193:     case EPS_SMALLEST_MAGNITUDE:
    194:       eps->sc->comparison    = SlepcCompareSmallestMagnitude;
    195:       eps->sc->comparisonctx = NULL;
    196:       break;
    197:     case EPS_LARGEST_REAL:
    198:       eps->sc->comparison    = SlepcCompareLargestReal;
    199:       eps->sc->comparisonctx = NULL;
    200:       break;
    201:     case EPS_SMALLEST_REAL:
    202:       eps->sc->comparison    = SlepcCompareSmallestReal;
    203:       eps->sc->comparisonctx = NULL;
    204:       break;
    205:     case EPS_LARGEST_IMAGINARY:
    206:       eps->sc->comparison    = SlepcCompareLargestImaginary;
    207:       eps->sc->comparisonctx = NULL;
    208:       break;
    209:     case EPS_SMALLEST_IMAGINARY:
    210:       eps->sc->comparison    = SlepcCompareSmallestImaginary;
    211:       eps->sc->comparisonctx = NULL;
    212:       break;
    213:     case EPS_TARGET_MAGNITUDE:
    214:       eps->sc->comparison    = SlepcCompareTargetMagnitude;
    215:       eps->sc->comparisonctx = &eps->target;
    216:       break;
    217:     case EPS_TARGET_REAL:
    218:       eps->sc->comparison    = SlepcCompareTargetReal;
    219:       eps->sc->comparisonctx = &eps->target;
    220:       break;
    221:     case EPS_TARGET_IMAGINARY:
    222: #if defined(PETSC_USE_COMPLEX)
    223:       eps->sc->comparison    = SlepcCompareTargetImaginary;
    224:       eps->sc->comparisonctx = &eps->target;
    225: #endif
    226:       break;
    227:     case EPS_ALL:
    228:       eps->sc->comparison    = SlepcCompareSmallestReal;
    229:       eps->sc->comparisonctx = NULL;
    230:       break;
    231:     case EPS_WHICH_USER:
    232:       break;
    233:   }
    234:   eps->sc->map    = NULL;
    235:   eps->sc->mapobj = NULL;

    237:   if (eps->useds) {
    238:     /* fill sorting criterion for DS */
    239:     DSGetSlepcSC(eps->ds,&sc);
    240:     RGIsTrivial(eps->rg,&istrivial);
    241:     if (eps->which!=EPS_ALL) {
    242:       sc->rg            = istrivial? NULL: eps->rg;
    243:       sc->comparison    = eps->sc->comparison;
    244:       sc->comparisonctx = eps->sc->comparisonctx;
    245:       sc->map           = SlepcMap_ST;
    246:       sc->mapobj        = (PetscObject)eps->st;
    247:     }
    248:   }

    250:   /* Build balancing matrix if required */
    251:   if (!eps->ishermitian && (eps->balance==EPS_BALANCE_ONESIDE || eps->balance==EPS_BALANCE_TWOSIDE)) {
    252:     if (!eps->D) {
    253:       BVCreateVec(eps->V,&eps->D);
    254:       PetscLogObjectParent((PetscObject)eps,(PetscObject)eps->D);
    255:     } else {
    256:       VecSet(eps->D,1.0);
    257:     }
    258:     EPSBuildBalance_Krylov(eps);
    259:     STSetBalanceMatrix(eps->st,eps->D);
    260:   }

    262:   /* Setup ST */
    263:   STSetUp(eps->st);

    265: #if defined(PETSC_USE_COMPLEX)
    266:   STGetShift(eps->st,&sigma);
    267:   if (eps->ishermitian && PetscImaginaryPart(sigma) != 0.0) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Hermitian problems are not compatible with complex shifts");
    268: #endif
    269:   PetscObjectTypeCompare((PetscObject)eps->st,STCAYLEY,&flg);
    270:   if (flg && eps->problem_type == EPS_PGNHEP) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Cayley spectral transformation is not compatible with PGNHEP");
    271:   PetscObjectTypeCompareAny((PetscObject)eps->st,&flg,STSINVERT,STCAYLEY,"");
    272:   if (flg && (eps->categ==EPS_CATEGORY_KRYLOV || eps->categ==EPS_CATEGORY_OTHER) && (eps->which!=EPS_TARGET_MAGNITUDE && eps->which!=EPS_TARGET_REAL && eps->which!=EPS_TARGET_IMAGINARY && eps->which!=EPS_ALL && eps->which!=EPS_WHICH_USER)) SETERRQ(PetscObjectComm((PetscObject)eps),1,"Shift-and-invert requires a target 'which' (see EPSSetWhichEigenpairs), for instance -st_type sinvert -eps_target 0 -eps_target_magnitude");

    274:   /* process deflation and initial vectors */
    275:   if (eps->nds<0) {
    276:     k = -eps->nds;
    277:     BVInsertConstraints(eps->V,&k,eps->defl);
    278:     SlepcBasisDestroy_Private(&eps->nds,&eps->defl);
    279:     eps->nds = k;
    280:     STCheckNullSpace(eps->st,eps->V);
    281:   }
    282:   if (eps->nini<0) {
    283:     k = -eps->nini;
    284:     if (k>eps->ncv) SETERRQ(PetscObjectComm((PetscObject)eps),1,"The number of initial vectors is larger than ncv");
    285:     BVInsertVecs(eps->V,0,&k,eps->IS,PETSC_TRUE);
    286:     SlepcBasisDestroy_Private(&eps->nini,&eps->IS);
    287:     eps->nini = k;
    288:   }

    290:   PetscLogEventEnd(EPS_SetUp,eps,0,0,0);
    291:   eps->state = EPS_STATE_SETUP;
    292:   return(0);
    293: }

    295: /*@
    296:    EPSSetOperators - Sets the matrices associated with the eigenvalue problem.

    298:    Collective on EPS and Mat

    300:    Input Parameters:
    301: +  eps - the eigenproblem solver context
    302: .  A  - the matrix associated with the eigensystem
    303: -  B  - the second matrix in the case of generalized eigenproblems

    305:    Notes:
    306:    To specify a standard eigenproblem, use NULL for parameter B.

    308:    It must be called before EPSSetUp(). If it is called again after EPSSetUp() then
    309:    the EPS object is reset.

    311:    Level: beginner

    313: .seealso: EPSSolve(), EPSSetUp(), EPSReset(), EPSGetST(), STGetMatrix()
    314: @*/
    315: PetscErrorCode EPSSetOperators(EPS eps,Mat A,Mat B)
    316: {
    318:   PetscInt       m,n,m0,nmat;
    319:   Mat            mat[2];

    328:   /* Check for square matrices */
    329:   MatGetSize(A,&m,&n);
    330:   if (m!=n) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"A is a non-square matrix");
    331:   if (B) {
    332:     MatGetSize(B,&m0,&n);
    333:     if (m0!=n) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"B is a non-square matrix");
    334:     if (m!=m0) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_INCOMP,"Dimensions of A and B do not match");
    335:   }
    336:   if (eps->state && n!=eps->n) { EPSReset(eps); }
    337:   eps->nrma = 0.0;
    338:   eps->nrmb = 0.0;
    339:   if (!eps->st) { EPSGetST(eps,&eps->st); }
    340:   mat[0] = A;
    341:   if (B) {
    342:     mat[1] = B;
    343:     nmat = 2;
    344:   } else nmat = 1;
    345:   STSetMatrices(eps->st,nmat,mat);
    346:   eps->state = EPS_STATE_INITIAL;
    347:   return(0);
    348: }

    350: /*@
    351:    EPSGetOperators - Gets the matrices associated with the eigensystem.

    353:    Collective on EPS and Mat

    355:    Input Parameter:
    356: .  eps - the EPS context

    358:    Output Parameters:
    359: +  A  - the matrix associated with the eigensystem
    360: -  B  - the second matrix in the case of generalized eigenproblems

    362:    Level: intermediate

    364: .seealso: EPSSolve(), EPSGetST(), STGetMatrix(), STSetMatrices()
    365: @*/
    366: PetscErrorCode EPSGetOperators(EPS eps,Mat *A,Mat *B)
    367: {
    369:   ST             st;
    370:   PetscInt       k;

    374:   EPSGetST(eps,&st);
    375:   if (A) { STGetMatrix(st,0,A); }
    376:   if (B) {
    377:     STGetNumMatrices(st,&k);
    378:     if (k==1) B = NULL;
    379:     else {
    380:       STGetMatrix(st,1,B);
    381:     }
    382:   }
    383:   return(0);
    384: }

    386: /*@
    387:    EPSSetDeflationSpace - Specify a basis of vectors that constitute the deflation
    388:    space.

    390:    Collective on EPS and Vec

    392:    Input Parameter:
    393: +  eps - the eigenproblem solver context
    394: .  n   - number of vectors
    395: -  v   - set of basis vectors of the deflation space

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

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

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

    409:    Level: intermediate

    411: .seealso: EPSSetInitialSpace()
    412: @*/
    413: PetscErrorCode EPSSetDeflationSpace(EPS eps,PetscInt n,Vec *v)
    414: {

    420:   if (n<0) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"Argument n out of range");
    421:   SlepcBasisReference_Private(n,v,&eps->nds,&eps->defl);
    422:   if (n>0) eps->state = EPS_STATE_INITIAL;
    423:   return(0);
    424: }

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

    430:    Collective on EPS and Vec

    432:    Input Parameter:
    433: +  eps - the eigenproblem solver context
    434: .  n   - number of vectors
    435: -  is  - set of basis vectors of the initial space

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

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

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

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

    450:    Level: intermediate

    452: .seealso: EPSSetDeflationSpace()
    453: @*/
    454: PetscErrorCode EPSSetInitialSpace(EPS eps,PetscInt n,Vec *is)
    455: {

    461:   if (n<0) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"Argument n cannot be negative");
    462:   SlepcBasisReference_Private(n,is,&eps->nini,&eps->IS);
    463:   if (n>0) eps->state = EPS_STATE_INITIAL;
    464:   return(0);
    465: }

    467: /*
    468:   EPSSetDimensions_Default - Set reasonable values for ncv, mpd if not set
    469:   by the user. This is called at setup.
    470:  */
    471: PetscErrorCode EPSSetDimensions_Default(EPS eps,PetscInt nev,PetscInt *ncv,PetscInt *mpd)
    472: {
    474:   PetscBool      krylov;

    477:   if (*ncv) { /* ncv set */
    478:     PetscObjectTypeCompareAny((PetscObject)eps,&krylov,EPSKRYLOVSCHUR,EPSARNOLDI,EPSLANCZOS,"");
    479:     if (krylov) {
    480:       if (*ncv<nev+1 && !(*ncv==nev && *ncv==eps->n)) SETERRQ(PetscObjectComm((PetscObject)eps),1,"The value of ncv must be at least nev+1");
    481:     } else {
    482:       if (*ncv<nev) SETERRQ(PetscObjectComm((PetscObject)eps),1,"The value of ncv must be at least nev");
    483:     }
    484:   } else if (*mpd) { /* mpd set */
    485:     *ncv = PetscMin(eps->n,nev+(*mpd));
    486:   } else { /* neither set: defaults depend on nev being small or large */
    487:     if (nev<500) *ncv = PetscMin(eps->n,PetscMax(2*nev,nev+15));
    488:     else {
    489:       *mpd = 500;
    490:       *ncv = PetscMin(eps->n,nev+(*mpd));
    491:     }
    492:   }
    493:   if (!*mpd) *mpd = *ncv;
    494:   return(0);
    495: }

    497: /*@
    498:    EPSAllocateSolution - Allocate memory storage for common variables such
    499:    as eigenvalues and eigenvectors.

    501:    Collective on EPS

    503:    Input Parameters:
    504: +  eps   - eigensolver context
    505: -  extra - number of additional positions, used for methods that require a
    506:            working basis slightly larger than ncv

    508:    Developers Note:
    509:    This is PETSC_EXTERN because it may be required by user plugin EPS
    510:    implementations.

    512:    Level: developer
    513: @*/
    514: PetscErrorCode EPSAllocateSolution(EPS eps,PetscInt extra)
    515: {
    517:   PetscInt       oldsize,newc,requested;
    518:   PetscLogDouble cnt;
    519:   Vec            t;

    522:   requested = eps->ncv + extra;

    524:   /* oldsize is zero if this is the first time setup is called */
    525:   BVGetSizes(eps->V,NULL,NULL,&oldsize);
    526:   newc = PetscMax(0,requested-oldsize);

    528:   /* allocate space for eigenvalues and friends */
    529:   if (requested != oldsize || !eps->eigr) {
    530:     PetscFree4(eps->eigr,eps->eigi,eps->errest,eps->perm);
    531:     PetscMalloc4(requested,&eps->eigr,requested,&eps->eigi,requested,&eps->errest,requested,&eps->perm);
    532:     cnt = 2*newc*sizeof(PetscScalar) + 2*newc*sizeof(PetscReal) + newc*sizeof(PetscInt);
    533:     PetscLogObjectMemory((PetscObject)eps,cnt);
    534:   }

    536:   /* workspace for the case of arbitrary selection */
    537:   if (eps->arbitrary) {
    538:     if (eps->rr) {
    539:       PetscFree2(eps->rr,eps->ri);
    540:     }
    541:     PetscMalloc2(requested,&eps->rr,requested,&eps->ri);
    542:     PetscLogObjectMemory((PetscObject)eps,2*newc*sizeof(PetscScalar));
    543:   }

    545:   /* allocate V */
    546:   if (!eps->V) { EPSGetBV(eps,&eps->V); }
    547:   if (!oldsize) {
    548:     if (!((PetscObject)(eps->V))->type_name) {
    549:       BVSetType(eps->V,BVSVEC);
    550:     }
    551:     STMatCreateVecsEmpty(eps->st,&t,NULL);
    552:     BVSetSizesFromVec(eps->V,t,requested);
    553:     VecDestroy(&t);
    554:   } else {
    555:     BVResize(eps->V,requested,PETSC_FALSE);
    556:   }
    557:   return(0);
    558: }