Actual source code: davidson.c

slepc-3.15.2 2021-09-20
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2021, 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: {
 38:   EPS_DAVIDSON   *data = (EPS_DAVIDSON*)eps->data;
 39:   dvdDashboard   *dvd = &data->ddb;
 40:   dvdBlackboard  b;
 41:   PetscInt       min_size_V,bs,initv,nmat;
 42:   Mat            A,B;
 43:   KSP            ksp;
 44:   PetscBool      ipB,ispositive;
 45:   HarmType_t     harm;
 46:   InitType_t     init;
 47:   PetscScalar    target;

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

 67:   EPSXDSetRestart_XD(eps,data->minv,data->plusk);
 68:   min_size_V = data->minv;
 69:   if (!min_size_V) min_size_V = PetscMin(PetscMax(bs,5),eps->mpd/2);
 70:   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");
 71:   initv = data->initialsize;
 72:   if (eps->mpd < initv) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"The initv has to be less or equal than mpd");

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

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

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

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

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

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

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

179:   /* Setup orthogonalization */
180:   EPS_SetInnerProduct(eps);
181:   if (!(ipB && dvd->B)) {
182:     BVSetMatrix(eps->V,NULL,PETSC_FALSE);
183:   }

185:   /* Configure dvd for a basic GD */
186:   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);
187:   return(0);
188: }

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

198:   PetscCitationsRegister(citation,&cited);
199:   /* Call the starting routines */
200:   EPSDavidsonFLCall(d->startList,d);

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

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

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

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

215:     /* Expand the subspace */
216:     d->updateV(d);

218:     /* Monitor progress */
219:     eps->nconv = d->nconv;
220:     eps->its++;
221:     BVGetActiveColumns(d->eps->V,NULL,&k);
222:     EPSMonitor(eps,eps->its,eps->nconv+d->npreconv,eps->eigr,eps->eigi,eps->errest,PetscMin(k,eps->nev));
223:   }

225:   /* Call the ending routines */
226:   EPSDavidsonFLCall(d->endList,d);
227:   return(0);
228: }

230: PetscErrorCode EPSReset_XD(EPS eps)
231: {
232:   EPS_DAVIDSON   *data = (EPS_DAVIDSON*)eps->data;
233:   dvdDashboard   *dvd = &data->ddb;

237:   /* Call step destructors and destroys the list */
238:   EPSDavidsonFLCall(dvd->destroyList,dvd);
239:   EPSDavidsonFLDestroy(&dvd->destroyList);
240:   EPSDavidsonFLDestroy(&dvd->startList);
241:   EPSDavidsonFLDestroy(&dvd->endList);
242:   return(0);
243: }

245: PetscErrorCode EPSXDSetKrylovStart_XD(EPS eps,PetscBool krylovstart)
246: {
247:   EPS_DAVIDSON *data = (EPS_DAVIDSON*)eps->data;

250:   data->krylovstart = krylovstart;
251:   return(0);
252: }

254: PetscErrorCode EPSXDGetKrylovStart_XD(EPS eps,PetscBool *krylovstart)
255: {
256:   EPS_DAVIDSON *data = (EPS_DAVIDSON*)eps->data;

259:   *krylovstart = data->krylovstart;
260:   return(0);
261: }

263: PetscErrorCode EPSXDSetBlockSize_XD(EPS eps,PetscInt blocksize)
264: {
265:   EPS_DAVIDSON *data = (EPS_DAVIDSON*)eps->data;

268:   if (blocksize == PETSC_DEFAULT || blocksize == PETSC_DECIDE) blocksize = 1;
269:   if (blocksize <= 0) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"Invalid blocksize value");
270:   data->blocksize = blocksize;
271:   return(0);
272: }

274: PetscErrorCode EPSXDGetBlockSize_XD(EPS eps,PetscInt *blocksize)
275: {
276:   EPS_DAVIDSON *data = (EPS_DAVIDSON*)eps->data;

279:   *blocksize = data->blocksize;
280:   return(0);
281: }

283: PetscErrorCode EPSXDSetRestart_XD(EPS eps,PetscInt minv,PetscInt plusk)
284: {
285:   EPS_DAVIDSON *data = (EPS_DAVIDSON*)eps->data;

288:   if (minv == PETSC_DEFAULT || minv == PETSC_DECIDE) minv = 5;
289:   if (minv <= 0) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"Invalid minv value");
290:   if (plusk == PETSC_DEFAULT || plusk == PETSC_DECIDE) plusk = eps->problem_type == EPS_GHIEP?0:1;
291:   if (plusk < 0) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"Invalid plusk value");
292:   data->minv = minv;
293:   data->plusk = plusk;
294:   return(0);
295: }

297: PetscErrorCode EPSXDGetRestart_XD(EPS eps,PetscInt *minv,PetscInt *plusk)
298: {
299:   EPS_DAVIDSON *data = (EPS_DAVIDSON*)eps->data;

302:   if (minv) *minv = data->minv;
303:   if (plusk) *plusk = data->plusk;
304:   return(0);
305: }

307: PetscErrorCode EPSXDGetInitialSize_XD(EPS eps,PetscInt *initialsize)
308: {
309:   EPS_DAVIDSON *data = (EPS_DAVIDSON*)eps->data;

312:   *initialsize = data->initialsize;
313:   return(0);
314: }

316: PetscErrorCode EPSXDSetInitialSize_XD(EPS eps,PetscInt initialsize)
317: {
318:   EPS_DAVIDSON *data = (EPS_DAVIDSON*)eps->data;

321:   if (initialsize == PETSC_DEFAULT || initialsize == PETSC_DECIDE) initialsize = 5;
322:   if (initialsize <= 0) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"Invalid initial size value");
323:   data->initialsize = initialsize;
324:   return(0);
325: }

327: PetscErrorCode EPSXDSetBOrth_XD(EPS eps,PetscBool borth)
328: {
329:   EPS_DAVIDSON *data = (EPS_DAVIDSON*)eps->data;

332:   data->ipB = borth;
333:   return(0);
334: }

336: PetscErrorCode EPSXDGetBOrth_XD(EPS eps,PetscBool *borth)
337: {
338:   EPS_DAVIDSON *data = (EPS_DAVIDSON*)eps->data;

341:   *borth = data->ipB;
342:   return(0);
343: }

345: /*
346:   EPSComputeVectors_XD - Compute eigenvectors from the vectors
347:   provided by the eigensolver. This version is intended for solvers
348:   that provide Schur vectors from the QZ decomposition. Given the partial
349:   Schur decomposition OP*V=V*T, the following steps are performed:
350:       1) compute eigenvectors of (S,T): S*Z=T*Z*D
351:       2) compute eigenvectors of OP: X=V*Z
352:  */
353: PetscErrorCode EPSComputeVectors_XD(EPS eps)
354: {
356:   Mat            X;
357:   PetscBool      symm;

360:   PetscObjectTypeCompare((PetscObject)eps->ds,DSHEP,&symm);
361:   if (symm) return(0);
362:   DSVectors(eps->ds,DS_MAT_X,NULL,NULL);

364:   /* V <- V * X */
365:   DSGetMat(eps->ds,DS_MAT_X,&X);
366:   BVSetActiveColumns(eps->V,0,eps->nconv);
367:   BVMultInPlace(eps->V,X,0,eps->nconv);
368:   MatDestroy(&X);
369:   return(0);
370: }