Actual source code: subspace.c

      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_DETERMINE && 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:   EPSCheckNotStructured(eps);
     69:   if (eps->max_it==PETSC_DETERMINE) eps->max_it = PetscMax(100,2*eps->n/eps->ncv);
     70:   if (!eps->which) PetscCall(EPSSetWhichEigenpairs_Default(eps));
     71:   if (eps->which==EPS_ALL) {
     72:     if (eps->nev==0) eps->nev = 1;
     73:     PetscCall(PetscObjectTypeCompare((PetscObject)eps->st,STFILTER,&isfilt));
     74:     PetscCheck(isfilt,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Spectrum slicing not supported in this solver");
     75:     PetscCall(EPSSetUp_Subspace_Filter(eps));
     76:   } else {
     77:     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");
     78:     PetscCall(EPSSetDimensions_Default(eps,&eps->nev,&eps->ncv,&eps->mpd));
     79:   }
     80:   EPSCheckUnsupported(eps,EPS_FEATURE_ARBITRARY | EPS_FEATURE_EXTRACTION | EPS_FEATURE_THRESHOLD | EPS_FEATURE_TWOSIDED);
     81:   PetscCheck(eps->converged==EPSConvergedRelative,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"This solver only supports relative convergence test");

     83:   PetscCall(EPSAllocateSolution(eps,0));
     84:   PetscCall(EPS_SetInnerProduct(eps));
     85:   if (eps->ishermitian) PetscCall(DSSetType(eps->ds,DSHEP));
     86:   else PetscCall(DSSetType(eps->ds,DSNHEP));
     87:   PetscCall(DSAllocate(eps->ds,eps->ncv));
     88:   PetscFunctionReturn(PETSC_SUCCESS);
     89: }

     91: static PetscErrorCode EPSSetUpSort_Subspace(EPS eps)
     92: {
     93:   SlepcSC sc;

     95:   PetscFunctionBegin;
     96:   PetscCall(EPSSetUpSort_Default(eps));
     97:   if (eps->which==EPS_ALL) {
     98:     PetscCall(DSGetSlepcSC(eps->ds,&sc));
     99:     sc->rg            = NULL;
    100:     sc->comparison    = SlepcCompareLargestReal;
    101:     sc->comparisonctx = NULL;
    102:     sc->map           = NULL;
    103:     sc->mapobj        = NULL;
    104:   }
    105:   PetscFunctionReturn(PETSC_SUCCESS);
    106: }

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

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

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

    129:   for (i=l;i<m;) {
    130:     rmod1 = SlepcAbsEigenvalue(wr[i],wi[i]);
    131:     if (PetscAbsReal(rmod-rmod1) > grptol*(rmod+rmod1)) break;
    132:     *ctr = (rmod+rmod1)/2.0;
    133:     if (wi[i] == 0.0) {
    134:       (*ngrp)++;
    135:       i++;
    136:     } else {
    137:       (*ngrp)+=2;
    138:       i+=2;
    139:     }
    140:   }

    142:   *ae = 0;
    143:   *arsd = 0;
    144:   if (*ngrp) {
    145:     for (i=l;i<l+*ngrp;i++) {
    146:       (*ae) += PetscRealPart(wr[i]);
    147:       (*arsd) += rsd[i]*rsd[i];
    148:     }
    149:     *ae = *ae / *ngrp;
    150:     *arsd = PetscSqrtReal(*arsd / *ngrp);
    151:   }
    152:   PetscFunctionReturn(PETSC_SUCCESS);
    153: }

    155: /*
    156:    EPSSubspaceResidualNorms - Computes the column norms of residual vectors
    157:    OP*V(1:n,l:m) - V*T(1:m,l:m), where, on entry, OP*V has been computed and
    158:    stored in R. On exit, rsd(l) to rsd(m) contain the computed norms.
    159: */
    160: static PetscErrorCode EPSSubspaceResidualNorms(BV R,BV V,Mat T,PetscInt l,PetscInt m,PetscScalar *eigi,PetscReal *rsd)
    161: {
    162:   PetscInt       i;

    164:   PetscFunctionBegin;
    165:   PetscCall(BVMult(R,-1.0,1.0,V,T));
    166:   for (i=l;i<m;i++) PetscCall(BVNormColumnBegin(R,i,NORM_2,rsd+i));
    167:   for (i=l;i<m;i++) PetscCall(BVNormColumnEnd(R,i,NORM_2,rsd+i));
    168: #if !defined(PETSC_USE_COMPLEX)
    169:   for (i=l;i<m-1;i++) {
    170:     if (eigi[i]!=0.0) {
    171:       rsd[i]   = SlepcAbs(rsd[i],rsd[i+1]);
    172:       rsd[i+1] = rsd[i];
    173:       i++;
    174:     }
    175:   }
    176: #endif
    177:   PetscFunctionReturn(PETSC_SUCCESS);
    178: }

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

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

    207:   for (i=0;i<ncv;i++) {
    208:     rsd[i] = 0.0;
    209:     itrsd[i] = -1;
    210:   }

    212:   /* Complete the initial basis with random vectors and orthonormalize them */
    213:   for (k=eps->nini;k<ncv;k++) {
    214:     PetscCall(BVSetRandomColumn(eps->V,k));
    215:     PetscCall(BVOrthonormalizeColumn(eps->V,k,PETSC_TRUE,NULL,NULL));
    216:   }

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

    223:     for (i=eps->nconv;i<nv;i++) {
    224:       oeigr[i] = eps->eigr[i];
    225:       oeigi[i] = eps->eigi[i];
    226:       orsd[i]  = rsd[i];
    227:     }

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

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

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

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

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

    260:     if (eps->which==EPS_ALL && eps->its>1) {   /* adjust eigenvalue count */
    261:       ninside = 0;
    262:       PetscCall(STFilterGetThreshold(eps->st,&gamma));
    263:       for (i=eps->nconv;i<nv;i++) {
    264:         if (PetscRealPart(eps->eigr[i]) < gamma) break;
    265:         ninside++;
    266:       }
    267:       eps->nev = eps->nconv+ninside;
    268:     }
    269:     for (i=eps->nconv;i<nv;i++) {
    270:       itrsdold[i] = itrsd[i];
    271:       itrsd[i] = its;
    272:       eps->errest[i] = rsd[i];
    273:     }

    275:     for (;;) {
    276:       /* Find clusters of computed eigenvalues */
    277:       PetscCall(EPSSubspaceFindGroup(eps->nconv,nv,eps->eigr,eps->eigi,eps->errest,grptol,&ngrp,&ctr,&ae,&arsd));
    278:       PetscCall(EPSSubspaceFindGroup(eps->nconv,nv,oeigr,oeigi,orsd,grptol,&nogrp,&octr,&oae,&oarsd));
    279:       if (ngrp!=nogrp) break;
    280:       if (ngrp==0) break;
    281:       if (PetscAbsReal(ae-oae)>ctr*cnvtol*(itrsd[eps->nconv]-itrsdold[eps->nconv])) break;
    282:       if (arsd>ctr*eps->tol) break;
    283:       eps->nconv = eps->nconv + ngrp;
    284:       if (eps->nconv>=nv) break;
    285:     }

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

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

    294:     if (ngrp!=nogrp || ngrp==0 || arsd>=oarsd) {
    295:       idsrr = nxtsrr - its;
    296:     } else {
    297:       idsrr = (PetscInt)PetscFloorReal(alpha+beta*(itrsdold[eps->nconv]-itrsd[eps->nconv])*PetscLogReal(arsd/eps->tol)/PetscLogReal(arsd/oarsd));
    298:       idsrr = PetscMax(1,idsrr);
    299:     }
    300:     nxtsrr = PetscMin(nxtsrr,its+idsrr);

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

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

    314:     /* Orthogonalization loop */
    315:     do {
    316:       PetscCall(BVGetMatrix(eps->V,&B,&indef));
    317:       PetscCall(BVSetMatrix(eps->V,NULL,PETSC_FALSE));
    318:       while (its<nxtort) {
    319:         /* A(:,idx) = OP*V(:,idx) with normalization */
    320:         PetscCall(BVMatMult(eps->V,S,AV));
    321:         PetscCall(BVCopy(AV,eps->V));
    322:         PetscCall(BVNormalize(eps->V,NULL));
    323:         its++;
    324:       }
    325:       PetscCall(BVSetMatrix(eps->V,B,indef));
    326:       /* Orthonormalize vectors */
    327:       PetscCall(BVOrthogonalize(eps->V,NULL));
    328:       nxtort = PetscMin(its+idort,nxtsrr);
    329:     } while (its<nxtsrr);
    330:   }

    332:   PetscCall(PetscFree6(rsd,orsd,oeigr,oeigi,itrsd,itrsdold));
    333:   PetscCall(BVDestroy(&AV));
    334:   PetscCall(BVDestroy(&R));
    335:   PetscCall(STRestoreOperator(eps->st,&S));
    336:   PetscCall(DSTruncate(eps->ds,eps->nconv,PETSC_TRUE));
    337:   PetscFunctionReturn(PETSC_SUCCESS);
    338: }

    340: static PetscErrorCode EPSDestroy_Subspace(EPS eps)
    341: {
    342:   PetscFunctionBegin;
    343:   PetscCall(PetscFree(eps->data));
    344:   PetscFunctionReturn(PETSC_SUCCESS);
    345: }

    347: /*MC
    348:    EPSSUBSPACE - EPSSUBSPACE = "subspace" - The simple subspace iteration method.

    350:    Notes:
    351:    This solver is very basic and is not recommended in general, since it
    352:    will not be competitive with respect to other solvers.

    354:    The implemented method is subspace iteration with Rayleigh-Ritz projection and
    355:    locking, based on the SRRIT code {cite:p}`Bai97`.

    357:    Level: beginner

    359: .seealso: [](ch:eps), `EPS`, `EPSType`, `EPSSetType()`
    360: M*/
    361: SLEPC_EXTERN PetscErrorCode EPSCreate_Subspace(EPS eps)
    362: {
    363:   EPS_SUBSPACE *ctx;

    365:   PetscFunctionBegin;
    366:   PetscCall(PetscNew(&ctx));
    367:   eps->data  = (void*)ctx;

    369:   eps->useds = PETSC_TRUE;
    370:   eps->categ = EPS_CATEGORY_OTHER;

    372:   eps->ops->solve          = EPSSolve_Subspace;
    373:   eps->ops->setup          = EPSSetUp_Subspace;
    374:   eps->ops->setupsort      = EPSSetUpSort_Subspace;
    375:   eps->ops->destroy        = EPSDestroy_Subspace;
    376:   eps->ops->backtransform  = EPSBackTransform_Default;
    377:   eps->ops->computevectors = EPSComputeVectors_Schur;
    378:   PetscFunctionReturn(PETSC_SUCCESS);
    379: }