Date: 2017-05-17T08:25:43+00:00

Actual source code: subspace.c
slepc-3.7.4 2017-05-17
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      1: /*

      3:    SLEPc eigensolver: "subspace"

      5:    Method: Subspace Iteration

      7:    Algorithm:

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

     12:    References:

     14:        [1] "Subspace Iteration in SLEPc", SLEPc Technical Report STR-3,
     15:            available at http://slepc.upv.es.

     17:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     18:    SLEPc - Scalable Library for Eigenvalue Problem Computations
     19:    Copyright (c) 2002-2016, Universitat Politecnica de Valencia, Spain

     21:    This file is part of SLEPc.

     23:    SLEPc is free software: you can redistribute it and/or modify it under  the
     24:    terms of version 3 of the GNU Lesser General Public License as published by
     25:    the Free Software Foundation.

     27:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
     28:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
     29:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
     30:    more details.

     32:    You  should have received a copy of the GNU Lesser General  Public  License
     33:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
     34:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     35: */

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

     41: PetscErrorCode EPSSetUp_Subspace(EPS eps)
     42: {

     46:   EPSSetDimensions_Default(eps,eps->nev,&eps->ncv,&eps->mpd);
     47:   if (!eps->max_it) eps->max_it = PetscMax(100,2*eps->n/eps->ncv);
     48:   if (!eps->which) { EPSSetWhichEigenpairs_Default(eps); }
     49:   if (eps->which!=EPS_LARGEST_MAGNITUDE && eps->which!=EPS_TARGET_MAGNITUDE) SETERRQ(PetscObjectComm((PetscObject)eps),1,"Wrong value of eps->which");
     50:   if (!eps->extraction) {
     51:     EPSSetExtraction(eps,EPS_RITZ);
     52:   } else if (eps->extraction!=EPS_RITZ) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Unsupported extraction type");
     53:   if (eps->arbitrary) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Arbitrary selection of eigenpairs not supported in this solver");

     55:   EPSAllocateSolution(eps,0);
     56:   EPS_SetInnerProduct(eps);
     57:   if (eps->ishermitian) {
     58:     DSSetType(eps->ds,DSHEP);
     59:   } else {
     60:     DSSetType(eps->ds,DSNHEP);
     61:   }
     62:   DSAllocate(eps->ds,eps->ncv);
     63:   EPSSetWorkVecs(eps,1);

     65:   if (eps->isgeneralized && eps->ishermitian && !eps->ispositive) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Requested method does not work for indefinite problems");
     66:   return(0);
     67: }

     71: /*
     72:    EPSSubspaceFindGroup - Find a group of nearly equimodular eigenvalues, provided
     73:    in arrays wr and wi, according to the tolerance grptol. Also the 2-norms
     74:    of the residuals must be passed in (rsd). Arrays are processed from index
     75:    l to index m only. The output information is:

     77:    ngrp - number of entries of the group
     78:    ctr  - (w(l)+w(l+ngrp-1))/2
     79:    ae   - average of wr(l),...,wr(l+ngrp-1)
     80:    arsd - average of rsd(l),...,rsd(l+ngrp-1)
     81: */
     82: static PetscErrorCode EPSSubspaceFindGroup(PetscInt l,PetscInt m,PetscScalar *wr,PetscScalar *wi,PetscReal *rsd,PetscReal grptol,PetscInt *ngrp,PetscReal *ctr,PetscReal *ae,PetscReal *arsd)
     83: {
     84:   PetscInt  i;
     85:   PetscReal rmod,rmod1;

     88:   *ngrp = 0;
     89:   *ctr = 0;
     90:   rmod = SlepcAbsEigenvalue(wr[l],wi[l]);

     92:   for (i=l;i<m;) {
     93:     rmod1 = SlepcAbsEigenvalue(wr[i],wi[i]);
     94:     if (PetscAbsReal(rmod-rmod1) > grptol*(rmod+rmod1)) break;
     95:     *ctr = (rmod+rmod1)/2.0;
     96:     if (wi[i] != 0.0) {
     97:       (*ngrp)+=2;
     98:       i+=2;
     99:     } else {
    100:       (*ngrp)++;
    101:       i++;
    102:     }
    103:   }

    105:   *ae = 0;
    106:   *arsd = 0;
    107:   if (*ngrp) {
    108:     for (i=l;i<l+*ngrp;i++) {
    109:       (*ae) += PetscRealPart(wr[i]);
    110:       (*arsd) += rsd[i]*rsd[i];
    111:     }
    112:     *ae = *ae / *ngrp;
    113:     *arsd = PetscSqrtScalar(*arsd / *ngrp);
    114:   }
    115:   return(0);
    116: }

    120: /*
    121:    EPSSubspaceResidualNorms - Computes the column norms of residual vectors
    122:    OP*V(1:n,l:m) - V*T(1:m,l:m), where, on entry, OP*V has been computed and
    123:    stored in AV. ldt is the leading dimension of T. On exit, rsd(l) to
    124:    rsd(m) contain the computed norms.
    125: */
    126: static PetscErrorCode EPSSubspaceResidualNorms(BV V,BV AV,PetscScalar *T,PetscInt l,PetscInt m,PetscInt ldt,Vec w,PetscReal *rsd)
    127: {
    129:   PetscInt       i,k;
    130:   PetscScalar    t;

    133:   for (i=l;i<m;i++) {
    134:     if (i==m-1 || T[i+1+ldt*i]==0.0) k=i+1;
    135:     else k=i+2;
    136:     BVSetActiveColumns(V,0,k);
    137:     BVCopyVec(AV,i,w);
    138:     BVMultVec(V,-1.0,1.0,w,T+ldt*i);
    139:     VecDot(w,w,&t);
    140:     rsd[i] = PetscRealPart(t);
    141:   }
    142:   for (i=l;i<m;i++) {
    143:     if (i == m-1) {
    144:       rsd[i] = PetscSqrtReal(rsd[i]);
    145:     } else if (T[i+1+(ldt*i)]==0.0) {
    146:       rsd[i] = PetscSqrtReal(rsd[i]);
    147:     } else {
    148:       rsd[i] = PetscSqrtReal((rsd[i]+rsd[i+1])/2.0);
    149:       rsd[i+1] = rsd[i];
    150:       i++;
    151:     }
    152:   }
    153:   return(0);
    154: }

    158: PetscErrorCode EPSSolve_Subspace(EPS eps)
    159: {
    161:   Vec            v,av,w=eps->work[0];
    162:   Mat            H,Q;
    163:   BV             AV;
    164:   PetscInt       i,k,ld,ngrp,nogrp,*itrsd,*itrsdold;
    165:   PetscInt       nxtsrr,idsrr,idort,nxtort,nv,ncv = eps->ncv,its;
    166:   PetscScalar    *T;
    167:   PetscReal      arsd,oarsd,ctr,octr,ae,oae,*rsd,norm,tcond=1.0;
    168:   PetscBool      breakdown;
    169:   /* Parameters */
    170:   PetscInt       init = 5;        /* Number of initial iterations */
    171:   PetscReal      stpfac = 1.5;    /* Max num of iter before next SRR step */
    172:   PetscReal      alpha = 1.0;     /* Used to predict convergence of next residual */
    173:   PetscReal      beta = 1.1;      /* Used to predict convergence of next residual */
    174:   PetscReal      grptol = 1e-8;   /* Tolerance for EPSSubspaceFindGroup */
    175:   PetscReal      cnvtol = 1e-6;   /* Convergence criterion for cnv */
    176:   PetscInt       orttol = 2;      /* Number of decimal digits whose loss
    177:                                      can be tolerated in orthogonalization */

    180:   its = 0;
    181:   PetscMalloc3(ncv,&rsd,ncv,&itrsd,ncv,&itrsdold);
    182:   DSGetLeadingDimension(eps->ds,&ld);
    183:   BVDuplicate(eps->V,&AV);

    185:   for (i=0;i<ncv;i++) {
    186:     rsd[i] = 0.0;
    187:     itrsd[i] = -1;
    188:   }

    190:   /* Complete the initial basis with random vectors and orthonormalize them */
    191:   k = eps->nini;
    192:   while (k<ncv) {
    193:     BVSetRandomColumn(eps->V,k);
    194:     BVOrthogonalizeColumn(eps->V,k,NULL,&norm,&breakdown);
    195:     if (norm>0.0 && !breakdown) {
    196:       BVScaleColumn(eps->V,k,1.0/norm);
    197:       k++;
    198:     }
    199:   }

    201:   while (eps->reason == EPS_CONVERGED_ITERATING) {
    202:     eps->its++;
    203:     nv = PetscMin(eps->nconv+eps->mpd,ncv);
    204:     DSSetDimensions(eps->ds,nv,0,eps->nconv,0);

    206:     /* Find group in previously computed eigenvalues */
    207:     EPSSubspaceFindGroup(eps->nconv,nv,eps->eigr,eps->eigi,rsd,grptol,&nogrp,&octr,&oae,&oarsd);

    209:     /* AV(:,idx) = OP * V(:,idx) */
    210:     for (i=eps->nconv;i<nv;i++) {
    211:       BVGetColumn(eps->V,i,&v);
    212:       BVGetColumn(AV,i,&av);
    213:       STApply(eps->st,v,av);
    214:       BVRestoreColumn(eps->V,i,&v);
    215:       BVRestoreColumn(AV,i,&av);
    216:     }

    218:     /* T(:,idx) = V' * AV(:,idx) */
    219:     BVSetActiveColumns(eps->V,0,nv);
    220:     BVSetActiveColumns(AV,eps->nconv,nv);
    221:     DSGetMat(eps->ds,DS_MAT_A,&H);
    222:     BVDot(AV,eps->V,H);
    223:     DSRestoreMat(eps->ds,DS_MAT_A,&H);
    224:     DSSetState(eps->ds,DS_STATE_RAW);

    226:     /* Solve projected problem */
    227:     DSSolve(eps->ds,eps->eigr,eps->eigi);
    228:     DSSort(eps->ds,eps->eigr,eps->eigi,NULL,NULL,NULL);

    230:     /* Update vectors V(:,idx) = V * U(:,idx) */
    231:     DSGetMat(eps->ds,DS_MAT_Q,&Q);
    232:     BVSetActiveColumns(AV,0,nv);
    233:     BVMultInPlace(eps->V,Q,eps->nconv,nv);
    234:     BVMultInPlace(AV,Q,eps->nconv,nv);
    235:     MatDestroy(&Q);

    237:     /* Convergence check */
    238:     DSGetArray(eps->ds,DS_MAT_A,&T);
    239:     EPSSubspaceResidualNorms(eps->V,AV,T,eps->nconv,nv,ld,w,rsd);
    240:     DSRestoreArray(eps->ds,DS_MAT_A,&T);

    242:     for (i=eps->nconv;i<nv;i++) {
    243:       itrsdold[i] = itrsd[i];
    244:       itrsd[i] = its;
    245:       eps->errest[i] = rsd[i];
    246:     }

    248:     for (;;) {
    249:       /* Find group in currently computed eigenvalues */
    250:       EPSSubspaceFindGroup(eps->nconv,nv,eps->eigr,eps->eigi,eps->errest,grptol,&ngrp,&ctr,&ae,&arsd);
    251:       if (ngrp!=nogrp) break;
    252:       if (ngrp==0) break;
    253:       if (PetscAbsReal(ae-oae)>ctr*cnvtol*(itrsd[eps->nconv]-itrsdold[eps->nconv])) break;
    254:       if (arsd>ctr*eps->tol) break;
    255:       eps->nconv = eps->nconv + ngrp;
    256:       if (eps->nconv>=nv) break;
    257:     }

    259:     EPSMonitor(eps,eps->its,eps->nconv,eps->eigr,eps->eigi,eps->errest,nv);
    260:     (*eps->stopping)(eps,eps->its,eps->max_it,eps->nconv,eps->nev,&eps->reason,eps->stoppingctx);
    261:     if (eps->reason != EPS_CONVERGED_ITERATING) break;

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

    266:     if (ngrp!=nogrp || ngrp==0 || arsd>=oarsd) {
    267:       idsrr = nxtsrr - its;
    268:     } else {
    269:       idsrr = (PetscInt)PetscFloorReal(alpha+beta*(itrsdold[eps->nconv]-itrsd[eps->nconv])*PetscLogReal(arsd/eps->tol)/PetscLogReal(arsd/oarsd));
    270:       idsrr = PetscMax(1,idsrr);
    271:     }
    272:     nxtsrr = PetscMin(nxtsrr,its+idsrr);

    274:     /* Compute nxtort (iteration of next orthogonalization step) */
    275:     DSCond(eps->ds,&tcond);
    276:     idort = PetscMax(1,(PetscInt)PetscFloorReal(orttol/PetscMax(1,PetscLog10Real(tcond))));
    277:     nxtort = PetscMin(its+idort,nxtsrr);

    279:     /* V(:,idx) = AV(:,idx) */
    280:     BVSetActiveColumns(eps->V,eps->nconv,nv);
    281:     BVSetActiveColumns(AV,eps->nconv,nv);
    282:     BVCopy(AV,eps->V);
    283:     its++;

    285:     /* Orthogonalization loop */
    286:     do {
    287:       while (its<nxtort) {

    289:         /* A(:,idx) = OP*V(:,idx) with normalization */
    290:         for (i=eps->nconv;i<nv;i++) {
    291:           BVGetColumn(eps->V,i,&v);
    292:           STApply(eps->st,v,w);
    293:           VecCopy(w,v);
    294:           BVRestoreColumn(eps->V,i,&v);
    295:           BVNormColumn(eps->V,i,NORM_INFINITY,&norm);
    296:           BVScaleColumn(eps->V,i,1/norm);
    297:         }
    298:         its++;
    299:       }
    300:       /* Orthonormalize vectors */
    301:       for (i=eps->nconv;i<nv;i++) {
    302:         BVOrthogonalizeColumn(eps->V,i,NULL,&norm,&breakdown);
    303:         if (breakdown) {
    304:           BVSetRandomColumn(eps->V,i);
    305:           BVOrthogonalizeColumn(eps->V,i,NULL,&norm,&breakdown);
    306:         }
    307:         BVScaleColumn(eps->V,i,1/norm);
    308:       }
    309:       nxtort = PetscMin(its+idort,nxtsrr);
    310:     } while (its<nxtsrr);
    311:   }

    313:   PetscFree3(rsd,itrsd,itrsdold);
    314:   BVDestroy(&AV);
    315:   /* truncate Schur decomposition and change the state to raw so that
    316:      DSVectors() computes eigenvectors from scratch */
    317:   DSSetDimensions(eps->ds,eps->nconv,0,0,0);
    318:   DSSetState(eps->ds,DS_STATE_RAW);
    319:   return(0);
    320: }

    324: PetscErrorCode EPSDestroy_Subspace(EPS eps)
    325: {

    329:   PetscFree(eps->data);
    330:   return(0);
    331: }

    335: PETSC_EXTERN PetscErrorCode EPSCreate_Subspace(EPS eps)
    336: {
    338:   eps->ops->setup                = EPSSetUp_Subspace;
    339:   eps->ops->solve                = EPSSolve_Subspace;
    340:   eps->ops->destroy              = EPSDestroy_Subspace;
    341:   eps->ops->backtransform        = EPSBackTransform_Default;
    342:   eps->ops->computevectors       = EPSComputeVectors_Schur;
    343:   return(0);
    344: }