Actual source code: rqcg.c

slepc-3.18.2 2023-01-26
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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:    SLEPc eigensolver: "rqcg"

 13:    Method: Rayleigh Quotient Conjugate Gradient

 15:    Algorithm:

 17:        Conjugate Gradient minimization of the Rayleigh quotient with
 18:        periodic Rayleigh-Ritz acceleration.

 20:    References:

 22:        [1] L. Bergamaschi et al., "Parallel preconditioned conjugate gradient
 23:            optimization of the Rayleigh quotient for the solution of sparse
 24:            eigenproblems", Appl. Math. Comput. 175(2):1694-1715, 2006.
 25: */

 27: #include <slepc/private/epsimpl.h>

 29: PetscErrorCode EPSSolve_RQCG(EPS);

 31: typedef struct {
 32:   PetscInt nrest;         /* user-provided reset parameter */
 33:   PetscInt allocsize;     /* number of columns of work BV's allocated at setup */
 34:   BV       AV,W,P,G;
 35: } EPS_RQCG;

 37: PetscErrorCode EPSSetUp_RQCG(EPS eps)
 38: {
 39:   PetscInt       nmat;
 40:   EPS_RQCG       *ctx = (EPS_RQCG*)eps->data;

 42:   EPSCheckHermitianDefinite(eps);
 43:   EPSSetDimensions_Default(eps,eps->nev,&eps->ncv,&eps->mpd);
 44:   if (eps->max_it==PETSC_DEFAULT) eps->max_it = PetscMax(100,2*eps->n/eps->ncv);
 45:   if (!eps->which) eps->which = EPS_SMALLEST_REAL;
 47:   EPSCheckUnsupported(eps,EPS_FEATURE_ARBITRARY | EPS_FEATURE_REGION | EPS_FEATURE_EXTRACTION);
 48:   EPSCheckIgnored(eps,EPS_FEATURE_BALANCE);

 50:   if (!ctx->nrest) ctx->nrest = 20;

 52:   EPSAllocateSolution(eps,0);
 53:   EPS_SetInnerProduct(eps);

 55:   STGetNumMatrices(eps->st,&nmat);
 56:   if (!ctx->allocsize) {
 57:     ctx->allocsize = eps->mpd;
 58:     BVDuplicateResize(eps->V,eps->mpd,&ctx->AV);
 59:     if (nmat>1) BVDuplicate(ctx->AV,&ctx->W);
 60:     BVDuplicate(ctx->AV,&ctx->P);
 61:     BVDuplicate(ctx->AV,&ctx->G);
 62:   } else if (ctx->allocsize!=eps->mpd) {
 63:     ctx->allocsize = eps->mpd;
 64:     BVResize(ctx->AV,eps->mpd,PETSC_FALSE);
 65:     if (nmat>1) BVResize(ctx->W,eps->mpd,PETSC_FALSE);
 66:     BVResize(ctx->P,eps->mpd,PETSC_FALSE);
 67:     BVResize(ctx->G,eps->mpd,PETSC_FALSE);
 68:   }
 69:   DSSetType(eps->ds,DSHEP);
 70:   DSAllocate(eps->ds,eps->ncv);
 71:   EPSSetWorkVecs(eps,1);
 72:   return 0;
 73: }

 75: PetscErrorCode EPSSolve_RQCG(EPS eps)
 76: {
 77:   EPS_RQCG       *ctx = (EPS_RQCG*)eps->data;
 78:   PetscInt       i,j,k,ld,nv,ncv = eps->ncv,kini,nmat;
 79:   PetscScalar    *C,*gamma,g,pap,pbp,pbx,pax,nu,mu,alpha,beta;
 80:   PetscReal      resnorm,a,b,c,d,disc,t;
 81:   PetscBool      reset;
 82:   Mat            A,B,Q,Q1;
 83:   Vec            v,av,bv,p,w=eps->work[0];

 85:   DSGetLeadingDimension(eps->ds,&ld);
 86:   STGetNumMatrices(eps->st,&nmat);
 87:   STGetMatrix(eps->st,0,&A);
 88:   if (nmat>1) STGetMatrix(eps->st,1,&B);
 89:   else B = NULL;
 90:   PetscMalloc1(eps->mpd,&gamma);

 92:   kini = eps->nini;
 93:   while (eps->reason == EPS_CONVERGED_ITERATING) {
 94:     eps->its++;
 95:     nv = PetscMin(eps->nconv+eps->mpd,ncv);
 96:     DSSetDimensions(eps->ds,nv,eps->nconv,0);
 97:     for (;kini<nv;kini++) { /* Generate more initial vectors if necessary */
 98:       BVSetRandomColumn(eps->V,kini);
 99:       BVOrthonormalizeColumn(eps->V,kini,PETSC_TRUE,NULL,NULL);
100:     }
101:     reset = (eps->its>1 && (eps->its-1)%ctx->nrest==0)? PETSC_TRUE: PETSC_FALSE;

103:     if (reset) {
104:       /* Prevent BVDotVec below to use B-product, restored at the end */
105:       BVSetMatrix(eps->V,NULL,PETSC_FALSE);

107:       /* Compute Rayleigh quotient */
108:       BVSetActiveColumns(eps->V,eps->nconv,nv);
109:       BVSetActiveColumns(ctx->AV,0,nv-eps->nconv);
110:       BVMatMult(eps->V,A,ctx->AV);
111:       DSGetArray(eps->ds,DS_MAT_A,&C);
112:       for (i=eps->nconv;i<nv;i++) {
113:         BVSetActiveColumns(eps->V,eps->nconv,i+1);
114:         BVGetColumn(ctx->AV,i-eps->nconv,&av);
115:         BVDotVec(eps->V,av,C+eps->nconv+i*ld);
116:         BVRestoreColumn(ctx->AV,i-eps->nconv,&av);
117:         for (j=eps->nconv;j<i-1;j++) C[i+j*ld] = PetscConj(C[j+i*ld]);
118:       }
119:       DSRestoreArray(eps->ds,DS_MAT_A,&C);
120:       DSSetState(eps->ds,DS_STATE_RAW);

122:       /* Solve projected problem */
123:       DSSolve(eps->ds,eps->eigr,eps->eigi);
124:       DSSort(eps->ds,eps->eigr,eps->eigi,NULL,NULL,NULL);
125:       DSSynchronize(eps->ds,eps->eigr,eps->eigi);

127:       /* Update vectors V(:,idx) = V * Y(:,idx) */
128:       DSGetMat(eps->ds,DS_MAT_Q,&Q);
129:       BVMultInPlace(eps->V,Q,eps->nconv,nv);
130:       MatDenseGetSubMatrix(Q,eps->nconv,PETSC_DECIDE,eps->nconv,PETSC_DECIDE,&Q1);
131:       BVMultInPlace(ctx->AV,Q1,0,nv-eps->nconv);
132:       MatDenseRestoreSubMatrix(Q,&Q1);
133:       DSRestoreMat(eps->ds,DS_MAT_Q,&Q);
134:       if (B) BVSetMatrix(eps->V,B,PETSC_FALSE);
135:     } else {
136:       /* No need to do Rayleigh-Ritz, just take diag(V'*A*V) */
137:       for (i=eps->nconv;i<nv;i++) {
138:         BVGetColumn(eps->V,i,&v);
139:         BVGetColumn(ctx->AV,i-eps->nconv,&av);
140:         MatMult(A,v,av);
141:         VecDot(av,v,eps->eigr+i);
142:         BVRestoreColumn(eps->V,i,&v);
143:         BVRestoreColumn(ctx->AV,i-eps->nconv,&av);
144:       }
145:     }

147:     /* Compute gradient and check convergence */
148:     k = -1;
149:     for (i=eps->nconv;i<nv;i++) {
150:       BVGetColumn(eps->V,i,&v);
151:       BVGetColumn(ctx->AV,i-eps->nconv,&av);
152:       BVGetColumn(ctx->G,i-eps->nconv,&p);
153:       if (B) {
154:         BVGetColumn(ctx->W,i-eps->nconv,&bv);
155:         MatMult(B,v,bv);
156:         VecWAXPY(p,-eps->eigr[i],bv,av);
157:         BVRestoreColumn(ctx->W,i-eps->nconv,&bv);
158:       } else VecWAXPY(p,-eps->eigr[i],v,av);
159:       BVRestoreColumn(eps->V,i,&v);
160:       BVRestoreColumn(ctx->AV,i-eps->nconv,&av);
161:       VecNorm(p,NORM_2,&resnorm);
162:       BVRestoreColumn(ctx->G,i-eps->nconv,&p);
163:       (*eps->converged)(eps,eps->eigr[i],0.0,resnorm,&eps->errest[i],eps->convergedctx);
164:       if (k==-1 && eps->errest[i] >= eps->tol) k = i;
165:     }
166:     if (k==-1) k = nv;
167:     (*eps->stopping)(eps,eps->its,eps->max_it,k,eps->nev,&eps->reason,eps->stoppingctx);

169:     /* The next lines are necessary to avoid DS zeroing eigr */
170:     DSGetArray(eps->ds,DS_MAT_A,&C);
171:     for (i=eps->nconv;i<k;i++) C[i+i*ld] = eps->eigr[i];
172:     DSRestoreArray(eps->ds,DS_MAT_A,&C);

174:     if (eps->reason == EPS_CONVERGED_ITERATING) {

176:       /* Search direction */
177:       for (i=0;i<nv-eps->nconv;i++) {
178:         BVGetColumn(ctx->G,i,&v);
179:         STApply(eps->st,v,w);
180:         VecDot(w,v,&g);
181:         BVRestoreColumn(ctx->G,i,&v);
182:         beta = (!reset && eps->its>1)? g/gamma[i]: 0.0;
183:         gamma[i] = g;
184:         BVGetColumn(ctx->P,i,&v);
185:         VecAXPBY(v,1.0,beta,w);
186:         if (i+eps->nconv>0) {
187:           BVSetActiveColumns(eps->V,0,i+eps->nconv);
188:           BVOrthogonalizeVec(eps->V,v,NULL,NULL,NULL);
189:         }
190:         BVRestoreColumn(ctx->P,i,&v);
191:       }

193:       /* Minimization problem */
194:       for (i=eps->nconv;i<nv;i++) {
195:         BVGetColumn(eps->V,i,&v);
196:         BVGetColumn(ctx->AV,i-eps->nconv,&av);
197:         BVGetColumn(ctx->P,i-eps->nconv,&p);
198:         VecDot(av,v,&nu);
199:         VecDot(av,p,&pax);
200:         MatMult(A,p,w);
201:         VecDot(w,p,&pap);
202:         if (B) {
203:           BVGetColumn(ctx->W,i-eps->nconv,&bv);
204:           VecDot(bv,v,&mu);
205:           VecDot(bv,p,&pbx);
206:           BVRestoreColumn(ctx->W,i-eps->nconv,&bv);
207:           MatMult(B,p,w);
208:           VecDot(w,p,&pbp);
209:         } else {
210:           VecDot(v,v,&mu);
211:           VecDot(v,p,&pbx);
212:           VecDot(p,p,&pbp);
213:         }
214:         BVRestoreColumn(ctx->AV,i-eps->nconv,&av);
215:         a = PetscRealPart(pap*pbx-pax*pbp);
216:         b = PetscRealPart(nu*pbp-mu*pap);
217:         c = PetscRealPart(mu*pax-nu*pbx);
218:         t = PetscMax(PetscMax(PetscAbsReal(a),PetscAbsReal(b)),PetscAbsReal(c));
219:         if (t!=0.0) { a /= t; b /= t; c /= t; }
220:         disc = b*b-4.0*a*c;
221:         d = PetscSqrtReal(PetscAbsReal(disc));
222:         if (b>=0.0 && a!=0.0) alpha = (b+d)/(2.0*a);
223:         else if (b!=d) alpha = 2.0*c/(b-d);
224:         else alpha = 0;
225:         /* Next iterate */
226:         if (alpha!=0.0) VecAXPY(v,alpha,p);
227:         BVRestoreColumn(eps->V,i,&v);
228:         BVRestoreColumn(ctx->P,i-eps->nconv,&p);
229:         BVOrthonormalizeColumn(eps->V,i,PETSC_TRUE,NULL,NULL);
230:       }
231:     }

233:     EPSMonitor(eps,eps->its,k,eps->eigr,eps->eigi,eps->errest,nv);
234:     eps->nconv = k;
235:   }

237:   PetscFree(gamma);
238:   return 0;
239: }

241: static PetscErrorCode EPSRQCGSetReset_RQCG(EPS eps,PetscInt nrest)
242: {
243:   EPS_RQCG *ctx = (EPS_RQCG*)eps->data;

245:   if (nrest==PETSC_DEFAULT) {
246:     ctx->nrest = 0;
247:     eps->state = EPS_STATE_INITIAL;
248:   } else {
250:     ctx->nrest = nrest;
251:   }
252:   return 0;
253: }

255: /*@
256:    EPSRQCGSetReset - Sets the reset parameter of the RQCG iteration. Every
257:    nrest iterations, the solver performs a Rayleigh-Ritz projection step.

259:    Logically Collective on eps

261:    Input Parameters:
262: +  eps - the eigenproblem solver context
263: -  nrest - the number of iterations between resets

265:    Options Database Key:
266: .  -eps_rqcg_reset - Sets the reset parameter

268:    Level: advanced

270: .seealso: EPSRQCGGetReset()
271: @*/
272: PetscErrorCode EPSRQCGSetReset(EPS eps,PetscInt nrest)
273: {
276:   PetscTryMethod(eps,"EPSRQCGSetReset_C",(EPS,PetscInt),(eps,nrest));
277:   return 0;
278: }

280: static PetscErrorCode EPSRQCGGetReset_RQCG(EPS eps,PetscInt *nrest)
281: {
282:   EPS_RQCG *ctx = (EPS_RQCG*)eps->data;

284:   *nrest = ctx->nrest;
285:   return 0;
286: }

288: /*@
289:    EPSRQCGGetReset - Gets the reset parameter used in the RQCG method.

291:    Not Collective

293:    Input Parameter:
294: .  eps - the eigenproblem solver context

296:    Output Parameter:
297: .  nrest - the reset parameter

299:    Level: advanced

301: .seealso: EPSRQCGSetReset()
302: @*/
303: PetscErrorCode EPSRQCGGetReset(EPS eps,PetscInt *nrest)
304: {
307:   PetscUseMethod(eps,"EPSRQCGGetReset_C",(EPS,PetscInt*),(eps,nrest));
308:   return 0;
309: }

311: PetscErrorCode EPSReset_RQCG(EPS eps)
312: {
313:   EPS_RQCG       *ctx = (EPS_RQCG*)eps->data;

315:   BVDestroy(&ctx->AV);
316:   BVDestroy(&ctx->W);
317:   BVDestroy(&ctx->P);
318:   BVDestroy(&ctx->G);
319:   ctx->allocsize = 0;
320:   return 0;
321: }

323: PetscErrorCode EPSSetFromOptions_RQCG(EPS eps,PetscOptionItems *PetscOptionsObject)
324: {
325:   PetscBool      flg;
326:   PetscInt       nrest;

328:   PetscOptionsHeadBegin(PetscOptionsObject,"EPS RQCG Options");

330:     PetscOptionsInt("-eps_rqcg_reset","Reset parameter","EPSRQCGSetReset",20,&nrest,&flg);
331:     if (flg) EPSRQCGSetReset(eps,nrest);

333:   PetscOptionsHeadEnd();
334:   return 0;
335: }

337: PetscErrorCode EPSDestroy_RQCG(EPS eps)
338: {
339:   PetscFree(eps->data);
340:   PetscObjectComposeFunction((PetscObject)eps,"EPSRQCGSetReset_C",NULL);
341:   PetscObjectComposeFunction((PetscObject)eps,"EPSRQCGGetReset_C",NULL);
342:   return 0;
343: }

345: PetscErrorCode EPSView_RQCG(EPS eps,PetscViewer viewer)
346: {
347:   EPS_RQCG       *ctx = (EPS_RQCG*)eps->data;
348:   PetscBool      isascii;

350:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
351:   if (isascii) PetscViewerASCIIPrintf(viewer,"  reset every %" PetscInt_FMT " iterations\n",ctx->nrest);
352:   return 0;
353: }

355: SLEPC_EXTERN PetscErrorCode EPSCreate_RQCG(EPS eps)
356: {
357:   EPS_RQCG       *rqcg;

359:   PetscNew(&rqcg);
360:   eps->data = (void*)rqcg;

362:   eps->useds = PETSC_TRUE;
363:   eps->categ = EPS_CATEGORY_PRECOND;

365:   eps->ops->solve          = EPSSolve_RQCG;
366:   eps->ops->setup          = EPSSetUp_RQCG;
367:   eps->ops->setupsort      = EPSSetUpSort_Default;
368:   eps->ops->setfromoptions = EPSSetFromOptions_RQCG;
369:   eps->ops->destroy        = EPSDestroy_RQCG;
370:   eps->ops->reset          = EPSReset_RQCG;
371:   eps->ops->view           = EPSView_RQCG;
372:   eps->ops->backtransform  = EPSBackTransform_Default;
373:   eps->ops->setdefaultst   = EPSSetDefaultST_GMRES;

375:   PetscObjectComposeFunction((PetscObject)eps,"EPSRQCGSetReset_C",EPSRQCGSetReset_RQCG);
376:   PetscObjectComposeFunction((PetscObject)eps,"EPSRQCGGetReset_C",EPSRQCGGetReset_RQCG);
377:   return 0;
378: }