Date: 2021-02-01T14:41:57+00:00

Actual source code: rqcg.c
slepc-3.14.2 2021-02-01
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2020, 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: {
     40:   PetscInt       nmat;
     41:   EPS_RQCG       *ctx = (EPS_RQCG*)eps->data;

     44:   EPSCheckHermitianDefinite(eps);
     45:   EPSSetDimensions_Default(eps,eps->nev,&eps->ncv,&eps->mpd);
     46:   if (eps->max_it==PETSC_DEFAULT) eps->max_it = PetscMax(100,2*eps->n/eps->ncv);
     47:   if (!eps->which) eps->which = EPS_SMALLEST_REAL;
     48:   if (eps->which!=EPS_SMALLEST_REAL) SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"This solver supports only smallest real eigenvalues");
     49:   EPSCheckUnsupported(eps,EPS_FEATURE_ARBITRARY | EPS_FEATURE_REGION | EPS_FEATURE_EXTRACTION);
     50:   EPSCheckIgnored(eps,EPS_FEATURE_BALANCE);

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

     54:   EPSAllocateSolution(eps,0);
     55:   EPS_SetInnerProduct(eps);

     57:   STGetNumMatrices(eps->st,&nmat);
     58:   if (!ctx->allocsize) {
     59:     ctx->allocsize = eps->mpd;
     60:     BVDuplicateResize(eps->V,eps->mpd,&ctx->AV);
     61:     PetscLogObjectParent((PetscObject)eps,(PetscObject)ctx->AV);
     62:     if (nmat>1) {
     63:       BVDuplicate(ctx->AV,&ctx->W);
     64:       PetscLogObjectParent((PetscObject)eps,(PetscObject)ctx->W);
     65:     }
     66:     BVDuplicate(ctx->AV,&ctx->P);
     67:     PetscLogObjectParent((PetscObject)eps,(PetscObject)ctx->P);
     68:     BVDuplicate(ctx->AV,&ctx->G);
     69:     PetscLogObjectParent((PetscObject)eps,(PetscObject)ctx->G);
     70:   } else if (ctx->allocsize!=eps->mpd) {
     71:     ctx->allocsize = eps->mpd;
     72:     BVResize(ctx->AV,eps->mpd,PETSC_FALSE);
     73:     if (nmat>1) {
     74:       BVResize(ctx->W,eps->mpd,PETSC_FALSE);
     75:     }
     76:     BVResize(ctx->P,eps->mpd,PETSC_FALSE);
     77:     BVResize(ctx->G,eps->mpd,PETSC_FALSE);
     78:   }
     79:   DSSetType(eps->ds,DSHEP);
     80:   DSAllocate(eps->ds,eps->ncv);
     81:   EPSSetWorkVecs(eps,1);
     82:   return(0);
     83: }

     85: /*
     86:    ExtractSubmatrix - Returns B = A(k+1:end,k+1:end).
     87: */
     88: static PetscErrorCode ExtractSubmatrix(Mat A,PetscInt k,Mat *B)
     89: {
     91:   PetscInt       j,m,n;
     92:   PetscScalar    *pA,*pB;

     95:   MatGetSize(A,&m,&n);
     96:   MatCreateSeqDense(PETSC_COMM_SELF,m-k,n-k,NULL,B);
     97:   MatDenseGetArray(A,&pA);
     98:   MatDenseGetArray(*B,&pB);
     99:   for (j=k;j<n;j++) {
    100:     PetscArraycpy(pB+(j-k)*(m-k),pA+j*m+k,m-k);
    101:   }
    102:   MatDenseRestoreArray(A,&pA);
    103:   MatDenseRestoreArray(*B,&pB);
    104:   return(0);
    105: }

    107: PetscErrorCode EPSSolve_RQCG(EPS eps)
    108: {
    110:   EPS_RQCG       *ctx = (EPS_RQCG*)eps->data;
    111:   PetscInt       i,j,k,ld,nv,ncv = eps->ncv,kini,nmat;
    112:   PetscScalar    *C,*gamma,g,pap,pbp,pbx,pax,nu,mu,alpha,beta;
    113:   PetscReal      resnorm,a,b,c,d,disc,t;
    114:   PetscBool      reset;
    115:   Mat            A,B,Q,Q1;
    116:   Vec            v,av,bv,p,w=eps->work[0];

    119:   DSGetLeadingDimension(eps->ds,&ld);
    120:   STGetNumMatrices(eps->st,&nmat);
    121:   STGetMatrix(eps->st,0,&A);
    122:   if (nmat>1) { STGetMatrix(eps->st,1,&B); }
    123:   else B = NULL;
    124:   PetscMalloc1(eps->mpd,&gamma);

    126:   kini = eps->nini;
    127:   while (eps->reason == EPS_CONVERGED_ITERATING) {
    128:     eps->its++;
    129:     nv = PetscMin(eps->nconv+eps->mpd,ncv);
    130:     DSSetDimensions(eps->ds,nv,0,eps->nconv,0);
    131:     for (;kini<nv;kini++) { /* Generate more initial vectors if necessary */
    132:       BVSetRandomColumn(eps->V,kini);
    133:       BVOrthonormalizeColumn(eps->V,kini,PETSC_TRUE,NULL,NULL);
    134:     }
    135:     reset = (eps->its>1 && (eps->its-1)%ctx->nrest==0)? PETSC_TRUE: PETSC_FALSE;

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

    141:       /* Compute Rayleigh quotient */
    142:       BVSetActiveColumns(eps->V,eps->nconv,nv);
    143:       BVSetActiveColumns(ctx->AV,0,nv-eps->nconv);
    144:       BVMatMult(eps->V,A,ctx->AV);
    145:       DSGetArray(eps->ds,DS_MAT_A,&C);
    146:       for (i=eps->nconv;i<nv;i++) {
    147:         BVSetActiveColumns(eps->V,eps->nconv,i+1);
    148:         BVGetColumn(ctx->AV,i-eps->nconv,&av);
    149:         BVDotVec(eps->V,av,C+eps->nconv+i*ld);
    150:         BVRestoreColumn(ctx->AV,i-eps->nconv,&av);
    151:         for (j=eps->nconv;j<i-1;j++) C[i+j*ld] = PetscConj(C[j+i*ld]);
    152:       }
    153:       DSRestoreArray(eps->ds,DS_MAT_A,&C);
    154:       DSSetState(eps->ds,DS_STATE_RAW);

    156:       /* Solve projected problem */
    157:       DSSolve(eps->ds,eps->eigr,eps->eigi);
    158:       DSSort(eps->ds,eps->eigr,eps->eigi,NULL,NULL,NULL);
    159:       DSSynchronize(eps->ds,eps->eigr,eps->eigi);

    161:       /* Update vectors V(:,idx) = V * Y(:,idx) */
    162:       DSGetMat(eps->ds,DS_MAT_Q,&Q);
    163:       BVMultInPlace(eps->V,Q,eps->nconv,nv);
    164:       ExtractSubmatrix(Q,eps->nconv,&Q1);
    165:       BVMultInPlace(ctx->AV,Q1,0,nv-eps->nconv);
    166:       MatDestroy(&Q);
    167:       MatDestroy(&Q1);
    168:       if (B) { BVSetMatrix(eps->V,B,PETSC_FALSE); }
    169:     } else {
    170:       /* No need to do Rayleigh-Ritz, just take diag(V'*A*V) */
    171:       for (i=eps->nconv;i<nv;i++) {
    172:         BVGetColumn(eps->V,i,&v);
    173:         BVGetColumn(ctx->AV,i-eps->nconv,&av);
    174:         MatMult(A,v,av);
    175:         VecDot(av,v,eps->eigr+i);
    176:         BVRestoreColumn(eps->V,i,&v);
    177:         BVRestoreColumn(ctx->AV,i-eps->nconv,&av);
    178:       }
    179:     }

    181:     /* Compute gradient and check convergence */
    182:     k = -1;
    183:     for (i=eps->nconv;i<nv;i++) {
    184:       BVGetColumn(eps->V,i,&v);
    185:       BVGetColumn(ctx->AV,i-eps->nconv,&av);
    186:       BVGetColumn(ctx->G,i-eps->nconv,&p);
    187:       if (B) {
    188:         BVGetColumn(ctx->W,i-eps->nconv,&bv);
    189:         MatMult(B,v,bv);
    190:         VecWAXPY(p,-eps->eigr[i],bv,av);
    191:         BVRestoreColumn(ctx->W,i-eps->nconv,&bv);
    192:       } else {
    193:         VecWAXPY(p,-eps->eigr[i],v,av);
    194:       }
    195:       BVRestoreColumn(eps->V,i,&v);
    196:       BVRestoreColumn(ctx->AV,i-eps->nconv,&av);
    197:       VecNorm(p,NORM_2,&resnorm);
    198:       BVRestoreColumn(ctx->G,i-eps->nconv,&p);
    199:       (*eps->converged)(eps,eps->eigr[i],0.0,resnorm,&eps->errest[i],eps->convergedctx);
    200:       if (k==-1 && eps->errest[i] >= eps->tol) k = i;
    201:     }
    202:     if (k==-1) k = nv;
    203:     (*eps->stopping)(eps,eps->its,eps->max_it,k,eps->nev,&eps->reason,eps->stoppingctx);

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

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

    212:       /* Search direction */
    213:       for (i=0;i<nv-eps->nconv;i++) {
    214:         BVGetColumn(ctx->G,i,&v);
    215:         STApply(eps->st,v,w);
    216:         VecDot(w,v,&g);
    217:         BVRestoreColumn(ctx->G,i,&v);
    218:         beta = (!reset && eps->its>1)? g/gamma[i]: 0.0;
    219:         gamma[i] = g;
    220:         BVGetColumn(ctx->P,i,&v);
    221:         VecAXPBY(v,1.0,beta,w);
    222:         if (i+eps->nconv>0) {
    223:           BVSetActiveColumns(eps->V,0,i+eps->nconv);
    224:           BVOrthogonalizeVec(eps->V,v,NULL,NULL,NULL);
    225:         }
    226:         BVRestoreColumn(ctx->P,i,&v);
    227:       }

    229:       /* Minimization problem */
    230:       for (i=eps->nconv;i<nv;i++) {
    231:         BVGetColumn(eps->V,i,&v);
    232:         BVGetColumn(ctx->AV,i-eps->nconv,&av);
    233:         BVGetColumn(ctx->P,i-eps->nconv,&p);
    234:         VecDot(av,v,&nu);
    235:         VecDot(av,p,&pax);
    236:         MatMult(A,p,w);
    237:         VecDot(w,p,&pap);
    238:         if (B) {
    239:           BVGetColumn(ctx->W,i-eps->nconv,&bv);
    240:           VecDot(bv,v,&mu);
    241:           VecDot(bv,p,&pbx);
    242:           BVRestoreColumn(ctx->W,i-eps->nconv,&bv);
    243:           MatMult(B,p,w);
    244:           VecDot(w,p,&pbp);
    245:         } else {
    246:           VecDot(v,v,&mu);
    247:           VecDot(v,p,&pbx);
    248:           VecDot(p,p,&pbp);
    249:         }
    250:         BVRestoreColumn(ctx->AV,i-eps->nconv,&av);
    251:         a = PetscRealPart(pap*pbx-pax*pbp);
    252:         b = PetscRealPart(nu*pbp-mu*pap);
    253:         c = PetscRealPart(mu*pax-nu*pbx);
    254:         t = PetscMax(PetscMax(PetscAbsReal(a),PetscAbsReal(b)),PetscAbsReal(c));
    255:         if (t!=0.0) { a /= t; b /= t; c /= t; }
    256:         disc = b*b-4.0*a*c;
    257:         d = PetscSqrtReal(PetscAbsReal(disc));
    258:         if (b>=0.0 && a!=0.0) alpha = (b+d)/(2.0*a);
    259:         else if (b!=d) alpha = 2.0*c/(b-d);
    260:         else alpha = 0;
    261:         /* Next iterate */
    262:         if (alpha!=0.0) {
    263:           VecAXPY(v,alpha,p);
    264:         }
    265:         BVRestoreColumn(eps->V,i,&v);
    266:         BVRestoreColumn(ctx->P,i-eps->nconv,&p);
    267:         BVOrthonormalizeColumn(eps->V,i,PETSC_TRUE,NULL,NULL);
    268:       }
    269:     }

    271:     EPSMonitor(eps,eps->its,k,eps->eigr,eps->eigi,eps->errest,nv);
    272:     eps->nconv = k;
    273:   }

    275:   PetscFree(gamma);
    276:   return(0);
    277: }

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

    284:   if (nrest==PETSC_DEFAULT) {
    285:     ctx->nrest = 0;
    286:     eps->state = EPS_STATE_INITIAL;
    287:   } else {
    288:     if (nrest<=0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Reset parameter must be >0");
    289:     ctx->nrest = nrest;
    290:   }
    291:   return(0);
    292: }

    294: /*@
    295:    EPSRQCGSetReset - Sets the reset parameter of the RQCG iteration. Every
    296:    nrest iterations, the solver performs a Rayleigh-Ritz projection step.

    298:    Logically Collective on eps

    300:    Input Parameters:
    301: +  eps - the eigenproblem solver context
    302: -  nrest - the number of iterations between resets

    304:    Options Database Key:
    305: .  -eps_rqcg_reset - Sets the reset parameter

    307:    Level: advanced

    309: .seealso: EPSRQCGGetReset()
    310: @*/
    311: PetscErrorCode EPSRQCGSetReset(EPS eps,PetscInt nrest)
    312: {

    318:   PetscTryMethod(eps,"EPSRQCGSetReset_C",(EPS,PetscInt),(eps,nrest));
    319:   return(0);
    320: }

    322: static PetscErrorCode EPSRQCGGetReset_RQCG(EPS eps,PetscInt *nrest)
    323: {
    324:   EPS_RQCG *ctx = (EPS_RQCG*)eps->data;

    327:   *nrest = ctx->nrest;
    328:   return(0);
    329: }

    331: /*@
    332:    EPSRQCGGetReset - Gets the reset parameter used in the RQCG method.

    334:    Not Collective

    336:    Input Parameter:
    337: .  eps - the eigenproblem solver context

    339:    Output Parameter:
    340: .  nrest - the reset parameter

    342:    Level: advanced

    344: .seealso: EPSRQCGSetReset()
    345: @*/
    346: PetscErrorCode EPSRQCGGetReset(EPS eps,PetscInt *nrest)
    347: {

    353:   PetscUseMethod(eps,"EPSRQCGGetReset_C",(EPS,PetscInt*),(eps,nrest));
    354:   return(0);
    355: }

    357: PetscErrorCode EPSReset_RQCG(EPS eps)
    358: {
    360:   EPS_RQCG       *ctx = (EPS_RQCG*)eps->data;

    363:   BVDestroy(&ctx->AV);
    364:   BVDestroy(&ctx->W);
    365:   BVDestroy(&ctx->P);
    366:   BVDestroy(&ctx->G);
    367:   ctx->allocsize = 0;
    368:   return(0);
    369: }

    371: PetscErrorCode EPSSetFromOptions_RQCG(PetscOptionItems *PetscOptionsObject,EPS eps)
    372: {
    374:   PetscBool      flg;
    375:   PetscInt       nrest;

    378:   PetscOptionsHead(PetscOptionsObject,"EPS RQCG Options");

    380:     PetscOptionsInt("-eps_rqcg_reset","Reset parameter","EPSRQCGSetReset",20,&nrest,&flg);
    381:     if (flg) { EPSRQCGSetReset(eps,nrest); }

    383:   PetscOptionsTail();
    384:   return(0);
    385: }

    387: PetscErrorCode EPSDestroy_RQCG(EPS eps)
    388: {

    392:   PetscFree(eps->data);
    393:   PetscObjectComposeFunction((PetscObject)eps,"EPSRQCGSetReset_C",NULL);
    394:   PetscObjectComposeFunction((PetscObject)eps,"EPSRQCGGetReset_C",NULL);
    395:   return(0);
    396: }

    398: PetscErrorCode EPSView_RQCG(EPS eps,PetscViewer viewer)
    399: {
    401:   EPS_RQCG       *ctx = (EPS_RQCG*)eps->data;
    402:   PetscBool      isascii;

    405:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    406:   if (isascii) {
    407:     PetscViewerASCIIPrintf(viewer,"  reset every %D iterations\n",ctx->nrest);
    408:   }
    409:   return(0);
    410: }

    412: SLEPC_EXTERN PetscErrorCode EPSCreate_RQCG(EPS eps)
    413: {
    414:   EPS_RQCG       *rqcg;

    418:   PetscNewLog(eps,&rqcg);
    419:   eps->data = (void*)rqcg;

    421:   eps->useds = PETSC_TRUE;
    422:   eps->categ = EPS_CATEGORY_PRECOND;

    424:   eps->ops->solve          = EPSSolve_RQCG;
    425:   eps->ops->setup          = EPSSetUp_RQCG;
    426:   eps->ops->setupsort      = EPSSetUpSort_Default;
    427:   eps->ops->setfromoptions = EPSSetFromOptions_RQCG;
    428:   eps->ops->destroy        = EPSDestroy_RQCG;
    429:   eps->ops->reset          = EPSReset_RQCG;
    430:   eps->ops->view           = EPSView_RQCG;
    431:   eps->ops->backtransform  = EPSBackTransform_Default;
    432:   eps->ops->setdefaultst   = EPSSetDefaultST_GMRES;

    434:   PetscObjectComposeFunction((PetscObject)eps,"EPSRQCGSetReset_C",EPSRQCGSetReset_RQCG);
    435:   PetscObjectComposeFunction((PetscObject)eps,"EPSRQCGGetReset_C",EPSRQCGGetReset_RQCG);
    436:   return(0);
    437: }