Date: 2020-01-13T12:00:18+00:00

Actual source code: davidson.c
slepc-3.12.2 2020-01-13
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2019, 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:    Skeleton of Davidson solver. Actual solvers are GD and JD.
     12: */

     14: #include "davidson.h"

     16: static PetscBool  cited = PETSC_FALSE;
     17: static const char citation[] =
     18:   "@Article{slepc-davidson,\n"
     19:   "   author = \"E. Romero and J. E. Roman\",\n"
     20:   "   title = \"A parallel implementation of {Davidson} methods for large-scale eigenvalue problems in {SLEPc}\",\n"
     21:   "   journal = \"{ACM} Trans. Math. Software\",\n"
     22:   "   volume = \"40\",\n"
     23:   "   number = \"2\",\n"
     24:   "   pages = \"13:1--13:29\",\n"
     25:   "   year = \"2014,\"\n"
     26:   "   doi = \"https://doi.org/10.1145/2543696\"\n"
     27:   "}\n";

     29: PetscErrorCode EPSSetUp_XD(EPS eps)
     30: {
     32:   EPS_DAVIDSON   *data = (EPS_DAVIDSON*)eps->data;
     33:   dvdDashboard   *dvd = &data->ddb;
     34:   dvdBlackboard  b;
     35:   PetscInt       min_size_V,bs,initv,nmat;
     36:   Mat            A,B;
     37:   KSP            ksp;
     38:   PetscBool      ipB,ispositive;
     39:   HarmType_t     harm;
     40:   InitType_t     init;
     41:   PetscScalar    target;

     44:   /* Setup EPS options and get the problem specification */
     45:   bs = data->blocksize;
     46:   if (bs <= 0) bs = 1;
     47:   if (eps->ncv) {
     48:     if (eps->ncv<eps->nev) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"The value of ncv must be at least nev");
     49:   } else if (eps->mpd) eps->ncv = eps->mpd + eps->nev + bs;
     50:   else if (eps->nev<500) eps->ncv = PetscMin(eps->n-bs,PetscMax(2*eps->nev,eps->nev+15))+bs;
     51:   else eps->ncv = PetscMin(eps->n-bs,eps->nev+500)+bs;
     52:   if (!eps->mpd) eps->mpd = eps->ncv;
     53:   if (eps->mpd > eps->ncv) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"The mpd has to be less or equal than ncv");
     54:   if (eps->mpd < 2) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"The mpd has to be greater than 2");
     55:   if (!eps->max_it) eps->max_it = PetscMax(100*eps->ncv,2*eps->n);
     56:   if (!eps->which) eps->which = EPS_LARGEST_MAGNITUDE;
     57:   if (eps->ishermitian && (eps->which==EPS_LARGEST_IMAGINARY || eps->which==EPS_SMALLEST_IMAGINARY)) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Wrong value of eps->which");
     58:   if (!(eps->nev + bs <= eps->ncv)) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"The ncv has to be greater than nev plus blocksize");
     59:   if (eps->trueres) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"-eps_true_residual is temporally disable in this solver.");

     61:   EPSXDSetRestart_XD(eps,data->minv,data->plusk);
     62:   min_size_V = data->minv;
     63:   if (!min_size_V) min_size_V = PetscMin(PetscMax(bs,5),eps->mpd/2);
     64:   if (!(min_size_V+bs <= eps->mpd)) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"The value of minv must be less than mpd minus blocksize");
     65:   initv = data->initialsize;
     66:   if (eps->mpd < initv) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"The initv has to be less or equal than mpd");

     68:   /* Change the default sigma to inf if necessary */
     69:   if (eps->which == EPS_LARGEST_MAGNITUDE || eps->which == EPS_LARGEST_REAL || eps->which == EPS_LARGEST_IMAGINARY) {
     70:     STSetDefaultShift(eps->st,PETSC_MAX_REAL);
     71:   }

     73:   /* Set up preconditioner */
     74:   STSetUp(eps->st);

     76:   /* Setup problem specification in dvd */
     77:   STGetNumMatrices(eps->st,&nmat);
     78:   STGetMatrix(eps->st,0,&A);
     79:   if (nmat>1) { STGetMatrix(eps->st,1,&B); }
     80:   EPSReset_XD(eps);
     81:   PetscMemzero(dvd,sizeof(dvdDashboard));
     82:   dvd->A = A; dvd->B = eps->isgeneralized? B: NULL;
     83:   ispositive = eps->ispositive;
     84:   dvd->sA = DVD_MAT_IMPLICIT | (eps->ishermitian? DVD_MAT_HERMITIAN: 0) | ((ispositive && !eps->isgeneralized) ? DVD_MAT_POS_DEF: 0);
     85:   /* Asume -eps_hermitian means hermitian-definite in generalized problems */
     86:   if (!ispositive && !eps->isgeneralized && eps->ishermitian) ispositive = PETSC_TRUE;
     87:   if (!eps->isgeneralized) dvd->sB = DVD_MAT_IMPLICIT | DVD_MAT_HERMITIAN | DVD_MAT_IDENTITY | DVD_MAT_UNITARY | DVD_MAT_POS_DEF;
     88:   else dvd->sB = DVD_MAT_IMPLICIT | (eps->ishermitian? DVD_MAT_HERMITIAN: 0) | (ispositive? DVD_MAT_POS_DEF: 0);
     89:   ipB = (dvd->B && data->ipB && DVD_IS(dvd->sB,DVD_MAT_HERMITIAN))?PETSC_TRUE:PETSC_FALSE;
     90:   dvd->sEP = ((!eps->isgeneralized || (eps->isgeneralized && ipB))? DVD_EP_STD: 0) | (ispositive? DVD_EP_HERMITIAN: 0) | ((eps->problem_type == EPS_GHIEP && ipB) ? DVD_EP_INDEFINITE : 0);
     91:   if (data->ipB && !ipB) data->ipB = PETSC_FALSE;
     92:   dvd->correctXnorm = (dvd->B && (DVD_IS(dvd->sB,DVD_MAT_HERMITIAN)||DVD_IS(dvd->sEP,DVD_EP_INDEFINITE)))?PETSC_TRUE:PETSC_FALSE;
     93:   dvd->nev        = eps->nev;
     94:   dvd->which      = eps->which;
     95:   dvd->withTarget = PETSC_TRUE;
     96:   switch (eps->which) {
     97:     case EPS_TARGET_MAGNITUDE:
     98:     case EPS_TARGET_IMAGINARY:
     99:       dvd->target[0] = target = eps->target;
    100:       dvd->target[1] = 1.0;
    101:       break;
    102:     case EPS_TARGET_REAL:
    103:       dvd->target[0] = PetscRealPart(target = eps->target);
    104:       dvd->target[1] = 1.0;
    105:       break;
    106:     case EPS_LARGEST_REAL:
    107:     case EPS_LARGEST_MAGNITUDE:
    108:     case EPS_LARGEST_IMAGINARY: /* TODO: think about this case */
    109:       dvd->target[0] = 1.0;
    110:       dvd->target[1] = target = 0.0;
    111:       break;
    112:     case EPS_SMALLEST_MAGNITUDE:
    113:     case EPS_SMALLEST_REAL:
    114:     case EPS_SMALLEST_IMAGINARY: /* TODO: think about this case */
    115:       dvd->target[0] = target = 0.0;
    116:       dvd->target[1] = 1.0;
    117:       break;
    118:     case EPS_WHICH_USER:
    119:       STGetShift(eps->st,&target);
    120:       dvd->target[0] = target;
    121:       dvd->target[1] = 1.0;
    122:       break;
    123:     case EPS_ALL:
    124:       SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Unsupported option: which == EPS_ALL");
    125:       break;
    126:     default:
    127:       SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Unsupported value of option 'which'");
    128:   }
    129:   dvd->tol = (eps->tol==PETSC_DEFAULT)? SLEPC_DEFAULT_TOL: eps->tol;
    130:   dvd->eps = eps;

    132:   /* Setup the extraction technique */
    133:   if (!eps->extraction) {
    134:     if (ipB || ispositive) eps->extraction = EPS_RITZ;
    135:     else {
    136:       switch (eps->which) {
    137:         case EPS_TARGET_REAL:
    138:         case EPS_TARGET_MAGNITUDE:
    139:         case EPS_TARGET_IMAGINARY:
    140:         case EPS_SMALLEST_MAGNITUDE:
    141:         case EPS_SMALLEST_REAL:
    142:         case EPS_SMALLEST_IMAGINARY:
    143:           eps->extraction = EPS_HARMONIC;
    144:           break;
    145:         case EPS_LARGEST_REAL:
    146:         case EPS_LARGEST_MAGNITUDE:
    147:         case EPS_LARGEST_IMAGINARY:
    148:           eps->extraction = EPS_HARMONIC_LARGEST;
    149:           break;
    150:         default:
    151:           eps->extraction = EPS_RITZ;
    152:       }
    153:     }
    154:   }
    155:   switch (eps->extraction) {
    156:     case EPS_RITZ:              harm = DVD_HARM_NONE; break;
    157:     case EPS_HARMONIC:          harm = DVD_HARM_RR; break;
    158:     case EPS_HARMONIC_RELATIVE: harm = DVD_HARM_RRR; break;
    159:     case EPS_HARMONIC_RIGHT:    harm = DVD_HARM_REIGS; break;
    160:     case EPS_HARMONIC_LARGEST:  harm = DVD_HARM_LEIGS; break;
    161:     default: SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Unsupported extraction type");
    162:   }

    164:   /* Setup the type of starting subspace */
    165:   init = data->krylovstart? DVD_INITV_KRYLOV: DVD_INITV_CLASSIC;

    167:   /* Preconfigure dvd */
    168:   STGetKSP(eps->st,&ksp);
    169:   dvd_schm_basic_preconf(dvd,&b,eps->mpd,min_size_V,bs,initv,PetscAbs(eps->nini),data->plusk,harm,ksp,init,eps->trackall,data->ipB,data->doubleexp);

    171:   /* Allocate memory */
    172:   EPSAllocateSolution(eps,0);

    174:   /* Setup orthogonalization */
    175:   EPS_SetInnerProduct(eps);
    176:   if (!(ipB && dvd->B)) {
    177:     BVSetMatrix(eps->V,NULL,PETSC_FALSE);
    178:   }

    180:   /* Configure dvd for a basic GD */
    181:   dvd_schm_basic_conf(dvd,&b,eps->mpd,min_size_V,bs,initv,PetscAbs(eps->nini),data->plusk,harm,dvd->withTarget,target,ksp,data->fix,init,eps->trackall,data->ipB,data->dynamic,data->doubleexp);
    182:   return(0);
    183: }

    185: PetscErrorCode EPSSolve_XD(EPS eps)
    186: {
    187:   EPS_DAVIDSON   *data = (EPS_DAVIDSON*)eps->data;
    188:   dvdDashboard   *d = &data->ddb;
    189:   PetscInt       l,k;

    193:   PetscCitationsRegister(citation,&cited);
    194:   /* Call the starting routines */
    195:   EPSDavidsonFLCall(d->startList,d);

    197:   while (eps->reason == EPS_CONVERGED_ITERATING) {

    199:     /* Initialize V, if it is needed */
    200:     BVGetActiveColumns(d->eps->V,&l,&k);
    201:     if (l == k) { d->initV(d); }

    203:     /* Find the best approximated eigenpairs in V, X */
    204:     d->calcPairs(d);

    206:     /* Test for convergence */
    207:     (*eps->stopping)(eps,eps->its,eps->max_it,eps->nconv,eps->nev,&eps->reason,eps->stoppingctx);
    208:     if (eps->reason != EPS_CONVERGED_ITERATING) break;

    210:     /* Expand the subspace */
    211:     d->updateV(d);

    213:     /* Monitor progress */
    214:     eps->nconv = d->nconv;
    215:     eps->its++;
    216:     BVGetActiveColumns(d->eps->V,NULL,&k);
    217:     EPSMonitor(eps,eps->its,eps->nconv+d->npreconv,eps->eigr,eps->eigi,eps->errest,PetscMin(k,eps->nev));
    218:   }

    220:   /* Call the ending routines */
    221:   EPSDavidsonFLCall(d->endList,d);
    222:   return(0);
    223: }

    225: PetscErrorCode EPSReset_XD(EPS eps)
    226: {
    227:   EPS_DAVIDSON   *data = (EPS_DAVIDSON*)eps->data;
    228:   dvdDashboard   *dvd = &data->ddb;

    232:   /* Call step destructors and destroys the list */
    233:   EPSDavidsonFLCall(dvd->destroyList,dvd);
    234:   EPSDavidsonFLDestroy(&dvd->destroyList);
    235:   EPSDavidsonFLDestroy(&dvd->startList);
    236:   EPSDavidsonFLDestroy(&dvd->endList);
    237:   return(0);
    238: }

    240: PetscErrorCode EPSXDSetKrylovStart_XD(EPS eps,PetscBool krylovstart)
    241: {
    242:   EPS_DAVIDSON *data = (EPS_DAVIDSON*)eps->data;

    245:   data->krylovstart = krylovstart;
    246:   return(0);
    247: }

    249: PetscErrorCode EPSXDGetKrylovStart_XD(EPS eps,PetscBool *krylovstart)
    250: {
    251:   EPS_DAVIDSON *data = (EPS_DAVIDSON*)eps->data;

    254:   *krylovstart = data->krylovstart;
    255:   return(0);
    256: }

    258: PetscErrorCode EPSXDSetBlockSize_XD(EPS eps,PetscInt blocksize)
    259: {
    260:   EPS_DAVIDSON *data = (EPS_DAVIDSON*)eps->data;

    263:   if (blocksize == PETSC_DEFAULT || blocksize == PETSC_DECIDE) blocksize = 1;
    264:   if (blocksize <= 0) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"Invalid blocksize value");
    265:   data->blocksize = blocksize;
    266:   return(0);
    267: }

    269: PetscErrorCode EPSXDGetBlockSize_XD(EPS eps,PetscInt *blocksize)
    270: {
    271:   EPS_DAVIDSON *data = (EPS_DAVIDSON*)eps->data;

    274:   *blocksize = data->blocksize;
    275:   return(0);
    276: }

    278: PetscErrorCode EPSXDSetRestart_XD(EPS eps,PetscInt minv,PetscInt plusk)
    279: {
    280:   EPS_DAVIDSON *data = (EPS_DAVIDSON*)eps->data;

    283:   if (minv == PETSC_DEFAULT || minv == PETSC_DECIDE) minv = 5;
    284:   if (minv <= 0) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"Invalid minv value");
    285:   if (plusk == PETSC_DEFAULT || plusk == PETSC_DECIDE) plusk = eps->problem_type == EPS_GHIEP?0:1;
    286:   if (plusk < 0) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"Invalid plusk value");
    287:   data->minv = minv;
    288:   data->plusk = plusk;
    289:   return(0);
    290: }

    292: PetscErrorCode EPSXDGetRestart_XD(EPS eps,PetscInt *minv,PetscInt *plusk)
    293: {
    294:   EPS_DAVIDSON *data = (EPS_DAVIDSON*)eps->data;

    297:   if (minv) *minv = data->minv;
    298:   if (plusk) *plusk = data->plusk;
    299:   return(0);
    300: }

    302: PetscErrorCode EPSXDGetInitialSize_XD(EPS eps,PetscInt *initialsize)
    303: {
    304:   EPS_DAVIDSON *data = (EPS_DAVIDSON*)eps->data;

    307:   *initialsize = data->initialsize;
    308:   return(0);
    309: }

    311: PetscErrorCode EPSXDSetInitialSize_XD(EPS eps,PetscInt initialsize)
    312: {
    313:   EPS_DAVIDSON *data = (EPS_DAVIDSON*)eps->data;

    316:   if (initialsize == PETSC_DEFAULT || initialsize == PETSC_DECIDE) initialsize = 5;
    317:   if (initialsize <= 0) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"Invalid initial size value");
    318:   data->initialsize = initialsize;
    319:   return(0);
    320: }

    322: PetscErrorCode EPSXDSetBOrth_XD(EPS eps,PetscBool borth)
    323: {
    324:   EPS_DAVIDSON *data = (EPS_DAVIDSON*)eps->data;

    327:   data->ipB = borth;
    328:   return(0);
    329: }

    331: PetscErrorCode EPSXDGetBOrth_XD(EPS eps,PetscBool *borth)
    332: {
    333:   EPS_DAVIDSON *data = (EPS_DAVIDSON*)eps->data;

    336:   *borth = data->ipB;
    337:   return(0);
    338: }

    340: /*
    341:   EPSComputeVectors_XD - Compute eigenvectors from the vectors
    342:   provided by the eigensolver. This version is intended for solvers
    343:   that provide Schur vectors from the QZ decomposition. Given the partial
    344:   Schur decomposition OP*V=V*T, the following steps are performed:
    345:       1) compute eigenvectors of (S,T): S*Z=T*Z*D
    346:       2) compute eigenvectors of OP: X=V*Z
    347:  */
    348: PetscErrorCode EPSComputeVectors_XD(EPS eps)
    349: {
    351:   Mat            X;
    352:   PetscBool      symm;

    355:   PetscObjectTypeCompare((PetscObject)eps->ds,DSHEP,&symm);
    356:   if (symm) return(0);
    357:   DSVectors(eps->ds,DS_MAT_X,NULL,NULL);

    359:   /* V <- V * X */
    360:   DSGetMat(eps->ds,DS_MAT_X,&X);
    361:   BVSetActiveColumns(eps->V,0,eps->nconv);
    362:   BVMultInPlace(eps->V,X,0,eps->nconv);
    363:   MatDestroy(&X);
    364:   return(0);
    365: }