Date: 2022-08-09T09:05:34+00:00

Actual source code: davidson.c
slepc-3.17.2 2022-08-09
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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:    Skeleton of Davidson solver. Actual solvers are GD and JD.

     13:    References:

     15:        [1] E. Romero and J.E. Roman, "A parallel implementation of Davidson
     16:            methods for large-scale eigenvalue problems in SLEPc", ACM Trans.
     17:            Math. Software 40(2):13, 2014.
     18: */

     20: #include "davidson.h"

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

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

     48:   /* Setup EPS options and get the problem specification */
     49:   bs = data->blocksize;
     50:   if (bs <= 0) bs = 1;
     51:   if (eps->ncv!=PETSC_DEFAULT && eps->ncv!=PETSC_DECIDE) {
     53:   } else if (eps->mpd!=PETSC_DEFAULT && eps->mpd!=PETSC_DECIDE) eps->ncv = eps->mpd + eps->nev + bs;
     54:   else if (eps->n < 10) eps->ncv = eps->n+eps->nev+bs;
     55:   else if (eps->nev < 500) eps->ncv = PetscMax(eps->nev,PetscMin(eps->n-bs,PetscMax(2*eps->nev,eps->nev+15))+bs);
     56:   else eps->ncv = PetscMax(eps->nev,PetscMin(eps->n-bs,eps->nev+500)+bs);
     57:   if (eps->mpd==PETSC_DEFAULT || eps->mpd==PETSC_DECIDE) eps->mpd = PetscMin(eps->n,eps->ncv);
     60:   if (eps->max_it == PETSC_DEFAULT || eps->max_it == PETSC_DECIDE) eps->max_it = PetscMax(100*eps->ncv,2*eps->n);
     61:   if (!eps->which) eps->which = EPS_LARGEST_MAGNITUDE;
     64:   EPSCheckUnsupported(eps,EPS_FEATURE_REGION | EPS_FEATURE_TWOSIDED);

     66:   if (!data->minv) data->minv = (eps->n && eps->n<10)? 1: PetscMin(PetscMax(bs,6),eps->mpd/2);
     67:   min_size_V = data->minv;
     69:   if (data->plusk == PETSC_DEFAULT) {
     70:     if (eps->problem_type == EPS_GHIEP || eps->nev+bs>eps->ncv) data->plusk = 0;
     71:     else data->plusk = 1;
     72:   }
     73:   if (!data->initialsize) data->initialsize = (eps->n && eps->n<10)? 1: 6;
     74:   initv = data->initialsize;

     77:   /* Change the default sigma to inf if necessary */
     78:   if (eps->which == EPS_LARGEST_MAGNITUDE || eps->which == EPS_LARGEST_REAL || eps->which == EPS_LARGEST_IMAGINARY) STSetDefaultShift(eps->st,PETSC_MAX_REAL);

     80:   /* Set up preconditioner */
     81:   STSetUp(eps->st);

     83:   /* Setup problem specification in dvd */
     84:   STGetNumMatrices(eps->st,&nmat);
     85:   STGetMatrix(eps->st,0,&A);
     86:   if (nmat>1) STGetMatrix(eps->st,1,&B);
     87:   EPSReset_XD(eps);
     88:   PetscMemzero(dvd,sizeof(dvdDashboard));
     89:   dvd->A = A; dvd->B = eps->isgeneralized? B: NULL;
     90:   ispositive = eps->ispositive;
     91:   dvd->sA = DVD_MAT_IMPLICIT | (eps->ishermitian? DVD_MAT_HERMITIAN: 0) | ((ispositive && !eps->isgeneralized) ? DVD_MAT_POS_DEF: 0);
     92:   /* Assume -eps_hermitian means hermitian-definite in generalized problems */
     93:   if (!ispositive && !eps->isgeneralized && eps->ishermitian) ispositive = PETSC_TRUE;
     94:   if (!eps->isgeneralized) dvd->sB = DVD_MAT_IMPLICIT | DVD_MAT_HERMITIAN | DVD_MAT_IDENTITY | DVD_MAT_UNITARY | DVD_MAT_POS_DEF;
     95:   else dvd->sB = DVD_MAT_IMPLICIT | (eps->ishermitian? DVD_MAT_HERMITIAN: 0) | (ispositive? DVD_MAT_POS_DEF: 0);
     96:   ipB = (dvd->B && data->ipB && DVD_IS(dvd->sB,DVD_MAT_HERMITIAN))?PETSC_TRUE:PETSC_FALSE;
     97:   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);
     98:   if (data->ipB && !ipB) data->ipB = PETSC_FALSE;
     99:   dvd->correctXnorm = (dvd->B && (DVD_IS(dvd->sB,DVD_MAT_HERMITIAN)||DVD_IS(dvd->sEP,DVD_EP_INDEFINITE)))?PETSC_TRUE:PETSC_FALSE;
    100:   dvd->nev        = eps->nev;
    101:   dvd->which      = eps->which;
    102:   dvd->withTarget = PETSC_TRUE;
    103:   switch (eps->which) {
    104:     case EPS_TARGET_MAGNITUDE:
    105:     case EPS_TARGET_IMAGINARY:
    106:       dvd->target[0] = target = eps->target;
    107:       dvd->target[1] = 1.0;
    108:       break;
    109:     case EPS_TARGET_REAL:
    110:       dvd->target[0] = PetscRealPart(target = eps->target);
    111:       dvd->target[1] = 1.0;
    112:       break;
    113:     case EPS_LARGEST_REAL:
    114:     case EPS_LARGEST_MAGNITUDE:
    115:     case EPS_LARGEST_IMAGINARY: /* TODO: think about this case */
    116:       dvd->target[0] = 1.0;
    117:       dvd->target[1] = target = 0.0;
    118:       break;
    119:     case EPS_SMALLEST_MAGNITUDE:
    120:     case EPS_SMALLEST_REAL:
    121:     case EPS_SMALLEST_IMAGINARY: /* TODO: think about this case */
    122:       dvd->target[0] = target = 0.0;
    123:       dvd->target[1] = 1.0;
    124:       break;
    125:     case EPS_WHICH_USER:
    126:       STGetShift(eps->st,&target);
    127:       dvd->target[0] = target;
    128:       dvd->target[1] = 1.0;
    129:       break;
    130:     case EPS_ALL:
    131:       SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"This solver does not support computing all eigenvalues");
    132:     default:
    133:       SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Unsupported value of option 'which'");
    134:   }
    135:   dvd->tol = SlepcDefaultTol(eps->tol);
    136:   dvd->eps = eps;

    138:   /* Setup the extraction technique */
    139:   if (!eps->extraction) {
    140:     if (ipB || ispositive) eps->extraction = EPS_RITZ;
    141:     else {
    142:       switch (eps->which) {
    143:         case EPS_TARGET_REAL:
    144:         case EPS_TARGET_MAGNITUDE:
    145:         case EPS_TARGET_IMAGINARY:
    146:         case EPS_SMALLEST_MAGNITUDE:
    147:         case EPS_SMALLEST_REAL:
    148:         case EPS_SMALLEST_IMAGINARY:
    149:           eps->extraction = EPS_HARMONIC;
    150:           break;
    151:         case EPS_LARGEST_REAL:
    152:         case EPS_LARGEST_MAGNITUDE:
    153:         case EPS_LARGEST_IMAGINARY:
    154:           eps->extraction = EPS_HARMONIC_LARGEST;
    155:           break;
    156:         default:
    157:           eps->extraction = EPS_RITZ;
    158:       }
    159:     }
    160:   }
    161:   switch (eps->extraction) {
    162:     case EPS_RITZ:              harm = DVD_HARM_NONE; break;
    163:     case EPS_HARMONIC:          harm = DVD_HARM_RR; break;
    164:     case EPS_HARMONIC_RELATIVE: harm = DVD_HARM_RRR; break;
    165:     case EPS_HARMONIC_RIGHT:    harm = DVD_HARM_REIGS; break;
    166:     case EPS_HARMONIC_LARGEST:  harm = DVD_HARM_LEIGS; break;
    167:     default: SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Unsupported extraction type");
    168:   }

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

    173:   /* Preconfigure dvd */
    174:   STGetKSP(eps->st,&ksp);
    175:   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);

    177:   /* Allocate memory */
    178:   EPSAllocateSolution(eps,0);

    180:   /* Setup orthogonalization */
    181:   EPS_SetInnerProduct(eps);
    182:   if (!(ipB && dvd->B)) BVSetMatrix(eps->V,NULL,PETSC_FALSE);

    184:   /* Configure dvd for a basic GD */
    185:   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);
    186:   PetscFunctionReturn(0);
    187: }

    189: PetscErrorCode EPSSolve_XD(EPS eps)
    190: {
    191:   EPS_DAVIDSON   *data = (EPS_DAVIDSON*)eps->data;
    192:   dvdDashboard   *d = &data->ddb;
    193:   PetscInt       l,k;

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

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

    201:     /* Initialize V, if it is needed */
    202:     BVGetActiveColumns(d->eps->V,&l,&k);
    203:     if (PetscUnlikely(l == k)) d->initV(d);

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

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

    212:     /* Expand the subspace */
    213:     d->updateV(d);

    215:     /* Monitor progress */
    216:     eps->nconv = d->nconv;
    217:     eps->its++;
    218:     BVGetActiveColumns(d->eps->V,NULL,&k);
    219:     EPSMonitor(eps,eps->its,eps->nconv+d->npreconv,eps->eigr,eps->eigi,eps->errest,PetscMin(k,eps->nev));
    220:   }

    222:   /* Call the ending routines */
    223:   EPSDavidsonFLCall(d->endList,d);
    224:   PetscFunctionReturn(0);
    225: }

    227: PetscErrorCode EPSReset_XD(EPS eps)
    228: {
    229:   EPS_DAVIDSON   *data = (EPS_DAVIDSON*)eps->data;
    230:   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:   PetscFunctionReturn(0);
    238: }

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

    244:   data->krylovstart = krylovstart;
    245:   PetscFunctionReturn(0);
    246: }

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

    252:   *krylovstart = data->krylovstart;
    253:   PetscFunctionReturn(0);
    254: }

    256: PetscErrorCode EPSXDSetBlockSize_XD(EPS eps,PetscInt blocksize)
    257: {
    258:   EPS_DAVIDSON *data = (EPS_DAVIDSON*)eps->data;

    260:   if (blocksize == PETSC_DEFAULT || blocksize == PETSC_DECIDE) blocksize = 1;
    262:   if (data->blocksize != blocksize) {
    263:     data->blocksize = blocksize;
    264:     eps->state      = EPS_STATE_INITIAL;
    265:   }
    266:   PetscFunctionReturn(0);
    267: }

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

    273:   *blocksize = data->blocksize;
    274:   PetscFunctionReturn(0);
    275: }

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

    281:   if (minv == PETSC_DEFAULT || minv == PETSC_DECIDE) minv = 0;
    283:   if (plusk == PETSC_DEFAULT || plusk == PETSC_DECIDE) plusk = PETSC_DEFAULT;
    285:   if (data->minv != minv || data->plusk != plusk) {
    286:     data->minv  = minv;
    287:     data->plusk = plusk;
    288:     eps->state  = EPS_STATE_INITIAL;
    289:   }
    290:   PetscFunctionReturn(0);
    291: }

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

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

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

    306:   *initialsize = data->initialsize;
    307:   PetscFunctionReturn(0);
    308: }

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

    314:   if (initialsize == PETSC_DEFAULT || initialsize == PETSC_DECIDE) initialsize = 0;
    316:   if (data->initialsize != initialsize) {
    317:     data->initialsize = initialsize;
    318:     eps->state        = EPS_STATE_INITIAL;
    319:   }
    320:   PetscFunctionReturn(0);
    321: }

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

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

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

    335:   *borth = data->ipB;
    336:   PetscFunctionReturn(0);
    337: }

    339: /*
    340:   EPSComputeVectors_XD - Compute eigenvectors from the vectors
    341:   provided by the eigensolver. This version is intended for solvers
    342:   that provide Schur vectors from the QZ decomposition. Given the partial
    343:   Schur decomposition OP*V=V*T, the following steps are performed:
    344:       1) compute eigenvectors of (S,T): S*Z=T*Z*D
    345:       2) compute eigenvectors of OP: X=V*Z
    346:  */
    347: PetscErrorCode EPSComputeVectors_XD(EPS eps)
    348: {
    349:   Mat            X;
    350:   PetscBool      symm;

    352:   PetscObjectTypeCompare((PetscObject)eps->ds,DSHEP,&symm);
    353:   if (symm) PetscFunctionReturn(0);
    354:   DSVectors(eps->ds,DS_MAT_X,NULL,NULL);

    356:   /* V <- V * X */
    357:   DSGetMat(eps->ds,DS_MAT_X,&X);
    358:   BVSetActiveColumns(eps->V,0,eps->nconv);
    359:   BVMultInPlace(eps->V,X,0,eps->nconv);
    360:   MatDestroy(&X);
    361:   PetscFunctionReturn(0);
    362: }