Date: 2015-09-03T15:04:53+00:00

Actual source code: rqcg.c
slepc-3.6.1 2015-09-03
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      1: /*

      3:    SLEPc eigensolver: "rqcg"

      5:    Method: Rayleigh Quotient Conjugate Gradient

      7:    Algorithm:

      9:        Conjugate Gradient minimization of the Rayleigh quotient with
     10:        periodic Rayleigh-Ritz acceleration.

     12:    References:

     14:        [1] L. Bergamaschi et al., "Parallel preconditioned conjugate gradient
     15:            optimization of the Rayleigh quotient for the solution of sparse
     16:            eigenproblems", Appl. Math. Comput. 175(2):1694-1715, 2006.

     18:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     19:    SLEPc - Scalable Library for Eigenvalue Problem Computations
     20:    Copyright (c) 2002-2015, Universitat Politecnica de Valencia, Spain

     22:    This file is part of SLEPc.

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

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

     33:    You  should have received a copy of the GNU Lesser General  Public  License
     34:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
     35:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     36: */

     38: #include <slepc/private/epsimpl.h>                /*I "slepceps.h" I*/

     40: PetscErrorCode EPSSolve_RQCG(EPS);

     42: typedef struct {
     43:   PetscInt nrest;
     44:   BV       AV,W,P,G;
     45: } EPS_RQCG;

     49: PetscErrorCode EPSSetUp_RQCG(EPS eps)
     50: {
     52:   PetscBool      precond;
     53:   PetscInt       nmat;
     54:   EPS_RQCG       *ctx = (EPS_RQCG*)eps->data;

     57:   if (!eps->ishermitian || (eps->isgeneralized && !eps->ispositive)) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"RQCG only works for Hermitian problems");
     58:   EPSSetDimensions_Default(eps,eps->nev,&eps->ncv,&eps->mpd);
     59:   if (!eps->max_it) eps->max_it = PetscMax(100,2*eps->n/eps->ncv);
     60:   if (!eps->which) eps->which = EPS_SMALLEST_REAL;
     61:   if (eps->which!=EPS_SMALLEST_REAL) SETERRQ(PetscObjectComm((PetscObject)eps),1,"Wrong value of eps->which");
     62:   if (!eps->extraction) {
     63:     EPSSetExtraction(eps,EPS_RITZ);
     64:   } else if (eps->extraction!=EPS_RITZ) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Unsupported extraction type");
     65:   if (eps->arbitrary) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Arbitrary selection of eigenpairs not supported in this solver");
     66:   /* Set STPrecond as the default ST */
     67:   if (!((PetscObject)eps->st)->type_name) {
     68:     STSetType(eps->st,STPRECOND);
     69:   }
     70:   PetscObjectTypeCompare((PetscObject)eps->st,STPRECOND,&precond);
     71:   if (!precond) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"RQCG only works with precond ST");

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

     75:   EPSAllocateSolution(eps,0);
     76:   EPS_SetInnerProduct(eps);
     77:   BVDuplicateResize(eps->V,eps->mpd,&ctx->AV);
     78:   PetscLogObjectParent((PetscObject)eps,(PetscObject)ctx->AV);
     79:   STGetNumMatrices(eps->st,&nmat);
     80:   if (nmat>1) {
     81:     BVDuplicate(ctx->AV,&ctx->W);
     82:     PetscLogObjectParent((PetscObject)eps,(PetscObject)ctx->W);
     83:   }
     84:   BVDuplicate(ctx->AV,&ctx->P);
     85:   PetscLogObjectParent((PetscObject)eps,(PetscObject)ctx->P);
     86:   BVDuplicate(ctx->AV,&ctx->G);
     87:   PetscLogObjectParent((PetscObject)eps,(PetscObject)ctx->G);
     88:   DSSetType(eps->ds,DSHEP);
     89:   DSAllocate(eps->ds,eps->ncv);
     90:   EPSSetWorkVecs(eps,1);
     91:   return(0);
     92: }

     96: /*
     97:    ExtractSubmatrix - Returns B = A(k+1:end,k+1:end).
     98: */
     99: static PetscErrorCode ExtractSubmatrix(Mat A,PetscInt k,Mat *B)
    100: {
    102:   PetscInt       j,m,n;
    103:   PetscScalar    *pA,*pB;

    106:   MatGetSize(A,&m,&n);
    107:   MatCreateSeqDense(PETSC_COMM_SELF,m-k,n-k,NULL,B);
    108:   MatDenseGetArray(A,&pA);
    109:   MatDenseGetArray(*B,&pB);
    110:   for (j=k;j<n;j++) {
    111:     PetscMemcpy(pB+(j-k)*(m-k),pA+j*m+k,(m-k)*sizeof(PetscScalar));
    112:   }
    113:   MatDenseRestoreArray(A,&pA);
    114:   MatDenseRestoreArray(*B,&pB);
    115:   return(0);
    116: }

    120: PetscErrorCode EPSSolve_RQCG(EPS eps)
    121: {
    123:   EPS_RQCG       *ctx = (EPS_RQCG*)eps->data;
    124:   PetscInt       i,j,k,ld,nv,ncv = eps->ncv,kini,nmat;
    125:   PetscScalar    *C,*gamma,g,pap,pbp,pbx,pax,nu,mu,alpha,beta;
    126:   PetscReal      resnorm,norm,a,b,c,disc,t;
    127:   PetscBool      reset,breakdown;
    128:   Mat            A,B,Q,Q1;
    129:   Vec            v,av,bv,p,w=eps->work[0];

    132:   DSGetLeadingDimension(eps->ds,&ld);
    133:   STGetNumMatrices(eps->st,&nmat);
    134:   STGetOperators(eps->st,0,&A);
    135:   if (nmat>1) { STGetOperators(eps->st,1,&B); }
    136:   else B = NULL;
    137:   PetscMalloc1(eps->mpd,&gamma);

    139:   kini = eps->nini;
    140:   while (eps->reason == EPS_CONVERGED_ITERATING) {
    141:     eps->its++;
    142:     nv = PetscMin(eps->nconv+eps->mpd,ncv);
    143:     DSSetDimensions(eps->ds,nv,0,eps->nconv,0);
    144:     /* Generate more initial vectors if necessary */
    145:     while (kini<nv) {
    146:       BVSetRandomColumn(eps->V,kini,eps->rand);
    147:       BVOrthogonalizeColumn(eps->V,kini,NULL,&norm,&breakdown);
    148:       if (norm>0.0 && !breakdown) {
    149:         BVScaleColumn(eps->V,kini,1.0/norm);
    150:         kini++;
    151:       }
    152:     }
    153:     reset = (eps->its>1 && (eps->its-1)%ctx->nrest==0)? PETSC_TRUE: PETSC_FALSE;

    155:     if (reset) {
    156:       /* Prevent BVDotVec below to use B-product, restored a the end */
    157:       BVSetMatrix(eps->V,NULL,PETSC_FALSE);

    159:       /* Compute Rayleigh quotient */
    160:       BVSetActiveColumns(eps->V,eps->nconv,nv);
    161:       BVSetActiveColumns(ctx->AV,0,nv-eps->nconv);
    162:       BVMatMult(eps->V,A,ctx->AV);
    163:       DSGetArray(eps->ds,DS_MAT_A,&C);
    164:       for (i=eps->nconv;i<nv;i++) {
    165:         BVSetActiveColumns(eps->V,eps->nconv,i+1);
    166:         BVGetColumn(ctx->AV,i-eps->nconv,&av);
    167:         BVDotVec(eps->V,av,C+eps->nconv+i*ld);
    168:         BVRestoreColumn(ctx->AV,i-eps->nconv,&av);
    169:         for (j=eps->nconv;j<i-1;j++) C[i+j*ld] = C[j+i*ld];
    170:       }
    171:       DSRestoreArray(eps->ds,DS_MAT_A,&C);
    172:       DSSetState(eps->ds,DS_STATE_RAW);

    174:       /* Solve projected problem */
    175:       DSSolve(eps->ds,eps->eigr,eps->eigi);
    176:       DSSort(eps->ds,eps->eigr,eps->eigi,NULL,NULL,NULL);

    178:       /* Update vectors V(:,idx) = V * Y(:,idx) */
    179:       DSGetMat(eps->ds,DS_MAT_Q,&Q);
    180:       BVMultInPlace(eps->V,Q,eps->nconv,nv);
    181:       ExtractSubmatrix(Q,eps->nconv,&Q1);
    182:       BVMultInPlace(ctx->AV,Q1,0,nv-eps->nconv);
    183:       MatDestroy(&Q);
    184:       MatDestroy(&Q1);
    185:       if (B) { BVSetMatrix(eps->V,B,PETSC_FALSE); }
    186:     } else {
    187:       /* No need to do Rayleigh-Ritz, just take diag(V'*A*V) */
    188:       for (i=eps->nconv;i<nv;i++) {
    189:         BVGetColumn(eps->V,i,&v);
    190:         BVGetColumn(ctx->AV,i-eps->nconv,&av);
    191:         MatMult(A,v,av);
    192:         VecDot(av,v,eps->eigr+i);
    193:         BVRestoreColumn(eps->V,i,&v);
    194:         BVRestoreColumn(ctx->AV,i-eps->nconv,&av);
    195:       }
    196:     }

    198:     /* Compute gradient and check convergence */
    199:     k = -1;
    200:     for (i=eps->nconv;i<nv;i++) {
    201:       BVGetColumn(eps->V,i,&v);
    202:       BVGetColumn(ctx->AV,i-eps->nconv,&av);
    203:       BVGetColumn(ctx->G,i-eps->nconv,&p);
    204:       if (B) {
    205:         BVGetColumn(ctx->W,i-eps->nconv,&bv);
    206:         MatMult(B,v,bv);
    207:         VecWAXPY(p,-eps->eigr[i],bv,av);
    208:         BVRestoreColumn(ctx->W,i-eps->nconv,&bv);
    209:       } else {
    210:         VecWAXPY(p,-eps->eigr[i],v,av);
    211:       }
    212:       BVRestoreColumn(eps->V,i,&v);
    213:       BVRestoreColumn(ctx->AV,i-eps->nconv,&av);
    214:       VecNorm(p,NORM_2,&resnorm);
    215:       BVRestoreColumn(ctx->G,i-eps->nconv,&p);
    216:       (*eps->converged)(eps,eps->eigr[i],0.0,resnorm,&eps->errest[i],eps->convergedctx);
    217:       if (k==-1 && eps->errest[i] >= eps->tol) k = i;
    218:     }
    219:     if (k==-1) k = nv;
    220:     if (eps->its >= eps->max_it) eps->reason = EPS_DIVERGED_ITS;
    221:     if (k >= eps->nev) eps->reason = EPS_CONVERGED_TOL;

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

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

    230:       /* Search direction */
    231:       for (i=0;i<nv-eps->nconv;i++) {
    232:         BVGetColumn(ctx->G,i,&v);
    233:         STMatSolve(eps->st,v,w);
    234:         VecDot(v,w,&g);
    235:         BVRestoreColumn(ctx->G,i,&v);
    236:         beta = (!reset && eps->its>1)? g/gamma[i]: 0.0;
    237:         gamma[i] = g;
    238:         BVGetColumn(ctx->P,i,&v);
    239:         VecAXPBY(v,1.0,beta,w);
    240:         if (i+eps->nconv>0) {
    241:           BVSetActiveColumns(eps->V,0,i+eps->nconv);
    242:           BVOrthogonalizeVec(eps->V,v,NULL,NULL,NULL);
    243:         }
    244:         BVRestoreColumn(ctx->P,i,&v);
    245:       }

    247:       /* Minimization problem */
    248:       for (i=eps->nconv;i<nv;i++) {
    249:         BVGetColumn(eps->V,i,&v);
    250:         BVGetColumn(ctx->AV,i-eps->nconv,&av);
    251:         BVGetColumn(ctx->P,i-eps->nconv,&p);
    252:         VecDot(v,av,&nu);
    253:         VecDot(p,av,&pax);
    254:         MatMult(A,p,w);
    255:         VecDot(p,w,&pap);
    256:         if (B) {
    257:           BVGetColumn(ctx->W,i-eps->nconv,&bv);
    258:           VecDot(v,bv,&mu);
    259:           VecDot(p,bv,&pbx);
    260:           BVRestoreColumn(ctx->W,i-eps->nconv,&bv);
    261:           MatMult(B,p,w);
    262:           VecDot(p,w,&pbp);
    263:         } else {
    264:           VecDot(v,v,&mu);
    265:           VecDot(p,v,&pbx);
    266:           VecDot(p,p,&pbp);
    267:         }
    268:         BVRestoreColumn(ctx->AV,i-eps->nconv,&av);
    269:         a = PetscRealPart(pap*pbx-pax*pbp);
    270:         b = PetscRealPart(nu*pbp-mu*pap);
    271:         c = PetscRealPart(mu*pax-nu*pbx);
    272:         t = PetscMax(PetscMax(PetscAbsReal(a),PetscAbsReal(b)),PetscAbsReal(c));
    273:         if (t!=0.0) { a /= t; b /= t; c /= t; }
    274:         disc = PetscSqrtReal(PetscAbsReal(b*b-4.0*a*c));
    275:         if (b>=0.0 && a!=0.0) alpha = (b+disc)/(2.0*a);
    276:         else if (b!=disc) alpha = 2.0*c/(b-disc);
    277:         else alpha = 0;
    278:         /* Next iterate */
    279:         if (alpha!=0.0) {
    280:           VecAXPY(v,alpha,p);
    281:         }
    282:         BVRestoreColumn(eps->V,i,&v);
    283:         BVRestoreColumn(ctx->P,i-eps->nconv,&p);
    284:         BVOrthogonalizeColumn(eps->V,i,NULL,&norm,&breakdown);
    285:         if (!breakdown && norm!=0.0) {
    286:           BVScaleColumn(eps->V,i,1.0/norm);
    287:         }
    288:       }
    289:     }

    291:     EPSMonitor(eps,eps->its,k,eps->eigr,eps->eigi,eps->errest,nv);
    292:     eps->nconv = k;
    293:   }

    295:   PetscFree(gamma);
    296:   return(0);
    297: }

    301: static PetscErrorCode EPSRQCGSetReset_RQCG(EPS eps,PetscInt nrest)
    302: {
    303:   EPS_RQCG *ctx = (EPS_RQCG*)eps->data;

    306:   ctx->nrest = nrest;
    307:   return(0);
    308: }

    312: /*@
    313:    EPSRQCGSetReset - Sets the reset parameter of the RQCG iteration. Every
    314:    nrest iterations, the solver performs a Rayleigh-Ritz projection step.

    316:    Logically Collective on EPS

    318:    Input Parameters:
    319: +  eps - the eigenproblem solver context
    320: -  nrest - the number of iterations between resets

    322:    Options Database Key:
    323: .  -eps_rqcg_reset - Sets the reset parameter

    325:    Level: advanced

    327: .seealso: EPSRQCGGetReset()
    328: @*/
    329: PetscErrorCode EPSRQCGSetReset(EPS eps,PetscInt nrest)
    330: {

    336:   PetscTryMethod(eps,"EPSRQCGSetReset_C",(EPS,PetscInt),(eps,nrest));
    337:   return(0);
    338: }

    342: static PetscErrorCode EPSRQCGGetReset_RQCG(EPS eps,PetscInt *nrest)
    343: {
    344:   EPS_RQCG *ctx = (EPS_RQCG*)eps->data;

    347:   *nrest = ctx->nrest;
    348:   return(0);
    349: }

    353: /*@
    354:    EPSRQCGGetReset - Gets the reset parameter used in the RQCG method.

    356:    Not Collective

    358:    Input Parameter:
    359: .  eps - the eigenproblem solver context

    361:    Output Parameter:
    362: .  nrest - the reset parameter

    364:    Level: advanced

    366: .seealso: EPSRQCGSetReset()
    367: @*/
    368: PetscErrorCode EPSRQCGGetReset(EPS eps,PetscInt *nrest)
    369: {

    375:   PetscTryMethod(eps,"EPSRQCGGetReset_C",(EPS,PetscInt*),(eps,nrest));
    376:   return(0);
    377: }

    381: PetscErrorCode EPSReset_RQCG(EPS eps)
    382: {
    384:   EPS_RQCG       *ctx = (EPS_RQCG*)eps->data;

    387:   BVDestroy(&ctx->AV);
    388:   BVDestroy(&ctx->W);
    389:   BVDestroy(&ctx->P);
    390:   BVDestroy(&ctx->G);
    391:   ctx->nrest = 0;
    392:   return(0);
    393: }

    397: PetscErrorCode EPSSetFromOptions_RQCG(PetscOptions *PetscOptionsObject,EPS eps)
    398: {
    400:   PetscBool      flg;
    401:   PetscInt       nrest;

    404:   PetscOptionsHead(PetscOptionsObject,"EPS RQCG Options");
    405:   PetscOptionsInt("-eps_rqcg_reset","RQCG reset parameter","EPSRQCGSetReset",20,&nrest,&flg);
    406:   if (flg) {
    407:     EPSRQCGSetReset(eps,nrest);
    408:   }
    409:   PetscOptionsTail();
    410:   return(0);
    411: }

    415: PetscErrorCode EPSDestroy_RQCG(EPS eps)
    416: {

    420:   PetscFree(eps->data);
    421:   PetscObjectComposeFunction((PetscObject)eps,"EPSRQCGSetReset_C",NULL);
    422:   PetscObjectComposeFunction((PetscObject)eps,"EPSRQCGGetReset_C",NULL);
    423:   return(0);
    424: }

    428: PetscErrorCode EPSView_RQCG(EPS eps,PetscViewer viewer)
    429: {
    431:   EPS_RQCG       *ctx = (EPS_RQCG*)eps->data;
    432:   PetscBool      isascii;

    435:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    436:   if (isascii) {
    437:     PetscViewerASCIIPrintf(viewer,"  RQCG: reset every %D iterations\n",ctx->nrest);
    438:   }
    439:   return(0);
    440: }

    444: PETSC_EXTERN PetscErrorCode EPSCreate_RQCG(EPS eps)
    445: {
    446:   EPS_RQCG       *rqcg;

    450:   PetscNewLog(eps,&rqcg);
    451:   eps->data = (void*)rqcg;

    453:   eps->ops->setup          = EPSSetUp_RQCG;
    454:   eps->ops->solve          = EPSSolve_RQCG;
    455:   eps->ops->setfromoptions = EPSSetFromOptions_RQCG;
    456:   eps->ops->destroy        = EPSDestroy_RQCG;
    457:   eps->ops->reset          = EPSReset_RQCG;
    458:   eps->ops->view           = EPSView_RQCG;
    459:   eps->ops->backtransform  = EPSBackTransform_Default;
    460:   STSetType(eps->st,STPRECOND);
    461:   STPrecondSetKSPHasMat(eps->st,PETSC_TRUE);
    462:   PetscObjectComposeFunction((PetscObject)eps,"EPSRQCGSetReset_C",EPSRQCGSetReset_RQCG);
    463:   PetscObjectComposeFunction((PetscObject)eps,"EPSRQCGGetReset_C",EPSRQCGGetReset_RQCG);
    464:   return(0);
    465: }