Actual source code: subspace.c

slepc-3.21.1 2024-04-26
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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: "subspace"

 13:    Method: Subspace Iteration

 15:    Algorithm:

 17:        Subspace iteration with Rayleigh-Ritz projection and locking,
 18:        based on the SRRIT implementation.

 20:    References:

 22:        [1] "Subspace Iteration in SLEPc", SLEPc Technical Report STR-3,
 23:            available at https://slepc.upv.es.
 24: */

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

 28: typedef struct {
 29:   PetscBool estimatedrange;     /* the filter range was not set by the user */
 30: } EPS_SUBSPACE;

 32: static PetscErrorCode EPSSetUp_Subspace_Filter(EPS eps)
 33: {
 34:   EPS_SUBSPACE   *ctx = (EPS_SUBSPACE*)eps->data;
 35:   PetscBool      estimaterange=PETSC_TRUE;
 36:   PetscReal      rleft,rright;
 37:   Mat            A;

 39:   PetscFunctionBegin;
 40:   EPSCheckHermitianCondition(eps,PETSC_TRUE," with polynomial filter");
 41:   EPSCheckStandardCondition(eps,PETSC_TRUE," with polynomial filter");
 42:   PetscCheck(eps->intb<PETSC_MAX_REAL || eps->inta>PETSC_MIN_REAL,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"The defined computational interval should have at least one of their sides bounded");
 43:   EPSCheckUnsupportedCondition(eps,EPS_FEATURE_ARBITRARY | EPS_FEATURE_REGION | EPS_FEATURE_EXTRACTION,PETSC_TRUE," with polynomial filter");
 44:   PetscCall(STFilterSetInterval(eps->st,eps->inta,eps->intb));
 45:   if (!ctx->estimatedrange) {
 46:     PetscCall(STFilterGetRange(eps->st,&rleft,&rright));
 47:     estimaterange = (!rleft && !rright)? PETSC_TRUE: PETSC_FALSE;
 48:   }
 49:   if (estimaterange) { /* user did not set a range */
 50:     PetscCall(STGetMatrix(eps->st,0,&A));
 51:     PetscCall(MatEstimateSpectralRange_EPS(A,&rleft,&rright));
 52:     PetscCall(PetscInfo(eps,"Setting eigenvalue range to [%g,%g]\n",(double)rleft,(double)rright));
 53:     PetscCall(STFilterSetRange(eps->st,rleft,rright));
 54:     ctx->estimatedrange = PETSC_TRUE;
 55:   }
 56:   if (eps->ncv==PETSC_DEFAULT && eps->nev==1) eps->nev = 40;  /* user did not provide nev estimation */
 57:   PetscCall(EPSSetDimensions_Default(eps,eps->nev,&eps->ncv,&eps->mpd));
 58:   PetscCheck(eps->ncv<=eps->nev+eps->mpd,PetscObjectComm((PetscObject)eps),PETSC_ERR_USER_INPUT,"The value of ncv must not be larger than nev+mpd");
 59:   PetscFunctionReturn(PETSC_SUCCESS);
 60: }

 62: static PetscErrorCode EPSSetUp_Subspace(EPS eps)
 63: {
 64:   PetscBool isfilt;

 66:   PetscFunctionBegin;
 67:   EPSCheckDefinite(eps);
 68:   if (eps->max_it==PETSC_DEFAULT) eps->max_it = PetscMax(100,2*eps->n/eps->ncv);
 69:   if (!eps->which) PetscCall(EPSSetWhichEigenpairs_Default(eps));
 70:   if (eps->which==EPS_ALL) {
 71:     PetscCall(PetscObjectTypeCompare((PetscObject)eps->st,STFILTER,&isfilt));
 72:     PetscCheck(isfilt,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Spectrum slicing not supported in this solver");
 73:     PetscCall(EPSSetUp_Subspace_Filter(eps));
 74:   } else {
 75:     PetscCheck(eps->which==EPS_LARGEST_MAGNITUDE || eps->which==EPS_TARGET_MAGNITUDE,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"This solver supports only largest magnitude or target magnitude eigenvalues");
 76:     PetscCall(EPSSetDimensions_Default(eps,eps->nev,&eps->ncv,&eps->mpd));
 77:   }
 78:   EPSCheckUnsupported(eps,EPS_FEATURE_ARBITRARY | EPS_FEATURE_EXTRACTION | EPS_FEATURE_TWOSIDED);
 79:   PetscCheck(eps->converged==EPSConvergedRelative,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"This solver only supports relative convergence test");

 81:   PetscCall(EPSAllocateSolution(eps,0));
 82:   PetscCall(EPS_SetInnerProduct(eps));
 83:   if (eps->ishermitian) PetscCall(DSSetType(eps->ds,DSHEP));
 84:   else PetscCall(DSSetType(eps->ds,DSNHEP));
 85:   PetscCall(DSAllocate(eps->ds,eps->ncv));
 86:   PetscFunctionReturn(PETSC_SUCCESS);
 87: }

 89: static PetscErrorCode EPSSetUpSort_Subspace(EPS eps)
 90: {
 91:   SlepcSC sc;

 93:   PetscFunctionBegin;
 94:   PetscCall(EPSSetUpSort_Default(eps));
 95:   if (eps->which==EPS_ALL) {
 96:     PetscCall(DSGetSlepcSC(eps->ds,&sc));
 97:     sc->rg            = NULL;
 98:     sc->comparison    = SlepcCompareLargestReal;
 99:     sc->comparisonctx = NULL;
100:     sc->map           = NULL;
101:     sc->mapobj        = NULL;
102:   }
103:   PetscFunctionReturn(PETSC_SUCCESS);
104: }

106: /*
107:    EPSSubspaceFindGroup - Find a group of nearly equimodular eigenvalues, provided
108:    in arrays wr and wi, according to the tolerance grptol. Also the 2-norms
109:    of the residuals must be passed in (rsd). Arrays are processed from index
110:    l to index m only. The output information is:

112:    ngrp - number of entries of the group
113:    ctr  - (w(l)+w(l+ngrp-1))/2
114:    ae   - average of wr(l),...,wr(l+ngrp-1)
115:    arsd - average of rsd(l),...,rsd(l+ngrp-1)
116: */
117: static PetscErrorCode EPSSubspaceFindGroup(PetscInt l,PetscInt m,PetscScalar *wr,PetscScalar *wi,PetscReal *rsd,PetscReal grptol,PetscInt *ngrp,PetscReal *ctr,PetscReal *ae,PetscReal *arsd)
118: {
119:   PetscInt  i;
120:   PetscReal rmod,rmod1;

122:   PetscFunctionBegin;
123:   *ngrp = 0;
124:   *ctr = 0;
125:   rmod = SlepcAbsEigenvalue(wr[l],wi[l]);

127:   for (i=l;i<m;) {
128:     rmod1 = SlepcAbsEigenvalue(wr[i],wi[i]);
129:     if (PetscAbsReal(rmod-rmod1) > grptol*(rmod+rmod1)) break;
130:     *ctr = (rmod+rmod1)/2.0;
131:     if (wi[i] == 0.0) {
132:       (*ngrp)++;
133:       i++;
134:     } else {
135:       (*ngrp)+=2;
136:       i+=2;
137:     }
138:   }

140:   *ae = 0;
141:   *arsd = 0;
142:   if (*ngrp) {
143:     for (i=l;i<l+*ngrp;i++) {
144:       (*ae) += PetscRealPart(wr[i]);
145:       (*arsd) += rsd[i]*rsd[i];
146:     }
147:     *ae = *ae / *ngrp;
148:     *arsd = PetscSqrtReal(*arsd / *ngrp);
149:   }
150:   PetscFunctionReturn(PETSC_SUCCESS);
151: }

153: /*
154:    EPSSubspaceResidualNorms - Computes the column norms of residual vectors
155:    OP*V(1:n,l:m) - V*T(1:m,l:m), where, on entry, OP*V has been computed and
156:    stored in R. On exit, rsd(l) to rsd(m) contain the computed norms.
157: */
158: static PetscErrorCode EPSSubspaceResidualNorms(BV R,BV V,Mat T,PetscInt l,PetscInt m,PetscScalar *eigi,PetscReal *rsd)
159: {
160:   PetscInt       i;

162:   PetscFunctionBegin;
163:   PetscCall(BVMult(R,-1.0,1.0,V,T));
164:   for (i=l;i<m;i++) PetscCall(BVNormColumnBegin(R,i,NORM_2,rsd+i));
165:   for (i=l;i<m;i++) PetscCall(BVNormColumnEnd(R,i,NORM_2,rsd+i));
166: #if !defined(PETSC_USE_COMPLEX)
167:   for (i=l;i<m-1;i++) {
168:     if (eigi[i]!=0.0) {
169:       rsd[i]   = SlepcAbs(rsd[i],rsd[i+1]);
170:       rsd[i+1] = rsd[i];
171:       i++;
172:     }
173:   }
174: #endif
175:   PetscFunctionReturn(PETSC_SUCCESS);
176: }

178: static PetscErrorCode EPSSolve_Subspace(EPS eps)
179: {
180:   Mat            H,Q,S,T,B;
181:   BV             AV,R;
182:   PetscBool      indef;
183:   PetscInt       i,k,ld,ngrp,nogrp,*itrsd,*itrsdold;
184:   PetscInt       nxtsrr,idsrr,idort,nxtort,nv,ncv = eps->ncv,its,ninside;
185:   PetscReal      arsd,oarsd,ctr,octr,ae,oae,*rsd,*orsd,tcond=1.0,gamma;
186:   PetscScalar    *oeigr,*oeigi;
187:   /* Parameters */
188:   PetscInt       init = 5;        /* Number of initial iterations */
189:   PetscReal      stpfac = 1.5;    /* Max num of iter before next SRR step */
190:   PetscReal      alpha = 1.0;     /* Used to predict convergence of next residual */
191:   PetscReal      beta = 1.1;      /* Used to predict convergence of next residual */
192:   PetscReal      grptol = SLEPC_DEFAULT_TOL;   /* Tolerance for EPSSubspaceFindGroup */
193:   PetscReal      cnvtol = 1e-6;   /* Convergence criterion for cnv */
194:   PetscInt       orttol = 2;      /* Number of decimal digits whose loss
195:                                      can be tolerated in orthogonalization */

197:   PetscFunctionBegin;
198:   its = 0;
199:   PetscCall(PetscMalloc6(ncv,&rsd,ncv,&orsd,ncv,&oeigr,ncv,&oeigi,ncv,&itrsd,ncv,&itrsdold));
200:   PetscCall(DSGetLeadingDimension(eps->ds,&ld));
201:   PetscCall(BVDuplicate(eps->V,&AV));
202:   PetscCall(BVDuplicate(eps->V,&R));
203:   PetscCall(STGetOperator(eps->st,&S));

205:   for (i=0;i<ncv;i++) {
206:     rsd[i] = 0.0;
207:     itrsd[i] = -1;
208:   }

210:   /* Complete the initial basis with random vectors and orthonormalize them */
211:   for (k=eps->nini;k<ncv;k++) {
212:     PetscCall(BVSetRandomColumn(eps->V,k));
213:     PetscCall(BVOrthonormalizeColumn(eps->V,k,PETSC_TRUE,NULL,NULL));
214:   }

216:   while (eps->reason == EPS_CONVERGED_ITERATING) {
217:     eps->its++;
218:     nv = PetscMin(eps->nconv+eps->mpd,ncv);
219:     PetscCall(DSSetDimensions(eps->ds,nv,eps->nconv,0));

221:     for (i=eps->nconv;i<nv;i++) {
222:       oeigr[i] = eps->eigr[i];
223:       oeigi[i] = eps->eigi[i];
224:       orsd[i]  = rsd[i];
225:     }

227:     /* AV(:,idx) = OP * V(:,idx) */
228:     PetscCall(BVSetActiveColumns(eps->V,eps->nconv,nv));
229:     PetscCall(BVSetActiveColumns(AV,eps->nconv,nv));
230:     PetscCall(BVMatMult(eps->V,S,AV));

232:     /* T(:,idx) = V' * AV(:,idx) */
233:     PetscCall(BVSetActiveColumns(eps->V,0,nv));
234:     PetscCall(DSGetMat(eps->ds,DS_MAT_A,&H));
235:     PetscCall(BVDot(AV,eps->V,H));
236:     PetscCall(DSRestoreMat(eps->ds,DS_MAT_A,&H));
237:     PetscCall(DSSetState(eps->ds,DS_STATE_RAW));

239:     /* Solve projected problem */
240:     PetscCall(DSSolve(eps->ds,eps->eigr,eps->eigi));
241:     PetscCall(DSSort(eps->ds,eps->eigr,eps->eigi,NULL,NULL,NULL));
242:     PetscCall(DSSynchronize(eps->ds,eps->eigr,eps->eigi));

244:     /* Update vectors V(:,idx) = V * U(:,idx) */
245:     PetscCall(DSGetMat(eps->ds,DS_MAT_Q,&Q));
246:     PetscCall(BVSetActiveColumns(AV,0,nv));
247:     PetscCall(BVSetActiveColumns(R,0,nv));
248:     PetscCall(BVMultInPlace(eps->V,Q,eps->nconv,nv));
249:     PetscCall(BVMultInPlace(AV,Q,eps->nconv,nv));
250:     PetscCall(DSRestoreMat(eps->ds,DS_MAT_Q,&Q));
251:     PetscCall(BVCopy(AV,R));

253:     /* Convergence check */
254:     PetscCall(DSGetMat(eps->ds,DS_MAT_A,&T));
255:     PetscCall(EPSSubspaceResidualNorms(R,eps->V,T,eps->nconv,nv,eps->eigi,rsd));
256:     PetscCall(DSRestoreMat(eps->ds,DS_MAT_A,&T));

258:     if (eps->which==EPS_ALL && eps->its>1) {   /* adjust eigenvalue count */
259:       ninside = 0;
260:       PetscCall(STFilterGetThreshold(eps->st,&gamma));
261:       for (i=eps->nconv;i<nv;i++) {
262:         if (PetscRealPart(eps->eigr[i]) < gamma) break;
263:         ninside++;
264:       }
265:       eps->nev = eps->nconv+ninside;
266:     }
267:     for (i=eps->nconv;i<nv;i++) {
268:       itrsdold[i] = itrsd[i];
269:       itrsd[i] = its;
270:       eps->errest[i] = rsd[i];
271:     }

273:     for (;;) {
274:       /* Find clusters of computed eigenvalues */
275:       PetscCall(EPSSubspaceFindGroup(eps->nconv,nv,eps->eigr,eps->eigi,eps->errest,grptol,&ngrp,&ctr,&ae,&arsd));
276:       PetscCall(EPSSubspaceFindGroup(eps->nconv,nv,oeigr,oeigi,orsd,grptol,&nogrp,&octr,&oae,&oarsd));
277:       if (ngrp!=nogrp) break;
278:       if (ngrp==0) break;
279:       if (PetscAbsReal(ae-oae)>ctr*cnvtol*(itrsd[eps->nconv]-itrsdold[eps->nconv])) break;
280:       if (arsd>ctr*eps->tol) break;
281:       eps->nconv = eps->nconv + ngrp;
282:       if (eps->nconv>=nv) break;
283:     }

285:     PetscCall(EPSMonitor(eps,eps->its,eps->nconv,eps->eigr,eps->eigi,eps->errest,nv));
286:     PetscCall((*eps->stopping)(eps,eps->its,eps->max_it,eps->nconv,eps->nev,&eps->reason,eps->stoppingctx));
287:     if (eps->reason != EPS_CONVERGED_ITERATING) break;

289:     /* Compute nxtsrr (iteration of next projection step) */
290:     nxtsrr = PetscMin(eps->max_it,PetscMax((PetscInt)PetscFloorReal(stpfac*its),init));

292:     if (ngrp!=nogrp || ngrp==0 || arsd>=oarsd) {
293:       idsrr = nxtsrr - its;
294:     } else {
295:       idsrr = (PetscInt)PetscFloorReal(alpha+beta*(itrsdold[eps->nconv]-itrsd[eps->nconv])*PetscLogReal(arsd/eps->tol)/PetscLogReal(arsd/oarsd));
296:       idsrr = PetscMax(1,idsrr);
297:     }
298:     nxtsrr = PetscMin(nxtsrr,its+idsrr);

300:     /* Compute nxtort (iteration of next orthogonalization step) */
301:     PetscCall(DSCond(eps->ds,&tcond));
302:     idort = PetscMax(1,(PetscInt)PetscFloorReal(orttol/PetscMax(1,PetscLog10Real(tcond))));
303:     nxtort = PetscMin(its+idort,nxtsrr);
304:     PetscCall(PetscInfo(eps,"Updated iteration counts: nxtort=%" PetscInt_FMT ", nxtsrr=%" PetscInt_FMT "\n",nxtort,nxtsrr));

306:     /* V(:,idx) = AV(:,idx) */
307:     PetscCall(BVSetActiveColumns(eps->V,eps->nconv,nv));
308:     PetscCall(BVSetActiveColumns(AV,eps->nconv,nv));
309:     PetscCall(BVCopy(AV,eps->V));
310:     its++;

312:     /* Orthogonalization loop */
313:     do {
314:       PetscCall(BVGetMatrix(eps->V,&B,&indef));
315:       PetscCall(BVSetMatrix(eps->V,NULL,PETSC_FALSE));
316:       while (its<nxtort) {
317:         /* A(:,idx) = OP*V(:,idx) with normalization */
318:         PetscCall(BVMatMult(eps->V,S,AV));
319:         PetscCall(BVCopy(AV,eps->V));
320:         PetscCall(BVNormalize(eps->V,NULL));
321:         its++;
322:       }
323:       PetscCall(BVSetMatrix(eps->V,B,indef));
324:       /* Orthonormalize vectors */
325:       PetscCall(BVOrthogonalize(eps->V,NULL));
326:       nxtort = PetscMin(its+idort,nxtsrr);
327:     } while (its<nxtsrr);
328:   }

330:   PetscCall(PetscFree6(rsd,orsd,oeigr,oeigi,itrsd,itrsdold));
331:   PetscCall(BVDestroy(&AV));
332:   PetscCall(BVDestroy(&R));
333:   PetscCall(STRestoreOperator(eps->st,&S));
334:   PetscCall(DSTruncate(eps->ds,eps->nconv,PETSC_TRUE));
335:   PetscFunctionReturn(PETSC_SUCCESS);
336: }

338: static PetscErrorCode EPSDestroy_Subspace(EPS eps)
339: {
340:   PetscFunctionBegin;
341:   PetscCall(PetscFree(eps->data));
342:   PetscFunctionReturn(PETSC_SUCCESS);
343: }

345: SLEPC_EXTERN PetscErrorCode EPSCreate_Subspace(EPS eps)
346: {
347:   EPS_SUBSPACE *ctx;

349:   PetscFunctionBegin;
350:   PetscCall(PetscNew(&ctx));
351:   eps->data  = (void*)ctx;

353:   eps->useds = PETSC_TRUE;
354:   eps->categ = EPS_CATEGORY_OTHER;

356:   eps->ops->solve          = EPSSolve_Subspace;
357:   eps->ops->setup          = EPSSetUp_Subspace;
358:   eps->ops->setupsort      = EPSSetUpSort_Subspace;
359:   eps->ops->destroy        = EPSDestroy_Subspace;
360:   eps->ops->backtransform  = EPSBackTransform_Default;
361:   eps->ops->computevectors = EPSComputeVectors_Schur;
362:   PetscFunctionReturn(PETSC_SUCCESS);
363: }