Date: 2026-01-20T11:35:42+00:00

Actual source code: rqcg.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: "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: static 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: static PetscErrorCode EPSSetUp_RQCG(EPS eps)
     38: {
     39:   PetscInt       nmat;
     40:   EPS_RQCG       *ctx = (EPS_RQCG*)eps->data;

     42:   PetscFunctionBegin;
     43:   EPSCheckHermitianDefinite(eps);
     44:   EPSCheckNotStructured(eps);
     45:   PetscCall(EPSSetDimensions_Default(eps,&eps->nev,&eps->ncv,&eps->mpd));
     46:   if (eps->max_it==PETSC_DETERMINE) eps->max_it = PetscMax(100,2*eps->n/eps->ncv);
     47:   if (!eps->which) eps->which = EPS_SMALLEST_REAL;
     48:   PetscCheck(eps->which==EPS_SMALLEST_REAL,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 | EPS_FEATURE_THRESHOLD);
     50:   EPSCheckIgnored(eps,EPS_FEATURE_BALANCE);

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

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

     57:   PetscCall(STGetNumMatrices(eps->st,&nmat));
     58:   if (!ctx->allocsize) {
     59:     ctx->allocsize = eps->mpd;
     60:     PetscCall(BVDuplicateResize(eps->V,eps->mpd,&ctx->AV));
     61:     if (nmat>1) PetscCall(BVDuplicate(ctx->AV,&ctx->W));
     62:     PetscCall(BVDuplicate(ctx->AV,&ctx->P));
     63:     PetscCall(BVDuplicate(ctx->AV,&ctx->G));
     64:   } else if (ctx->allocsize!=eps->mpd) {
     65:     ctx->allocsize = eps->mpd;
     66:     PetscCall(BVResize(ctx->AV,eps->mpd,PETSC_FALSE));
     67:     if (nmat>1) PetscCall(BVResize(ctx->W,eps->mpd,PETSC_FALSE));
     68:     PetscCall(BVResize(ctx->P,eps->mpd,PETSC_FALSE));
     69:     PetscCall(BVResize(ctx->G,eps->mpd,PETSC_FALSE));
     70:   }
     71:   PetscCall(DSSetType(eps->ds,DSHEP));
     72:   PetscCall(DSAllocate(eps->ds,eps->ncv));
     73:   PetscCall(EPSSetWorkVecs(eps,1));
     74:   PetscFunctionReturn(PETSC_SUCCESS);
     75: }

     77: static PetscErrorCode EPSSolve_RQCG(EPS eps)
     78: {
     79:   EPS_RQCG       *ctx = (EPS_RQCG*)eps->data;
     80:   PetscInt       i,j,k,ld,nv,ncv = eps->ncv,kini,nmat;
     81:   PetscScalar    *C,*gamma,g,pap,pbp,pbx,pax,nu,mu,alpha,beta;
     82:   PetscReal      resnorm,a,b,c,d,disc,t;
     83:   PetscBool      reset;
     84:   Mat            A,B,Q,Q1;
     85:   Vec            v,av,bv,p,w=eps->work[0];

     87:   PetscFunctionBegin;
     88:   PetscCall(DSGetLeadingDimension(eps->ds,&ld));
     89:   PetscCall(STGetNumMatrices(eps->st,&nmat));
     90:   PetscCall(STGetMatrix(eps->st,0,&A));
     91:   if (nmat>1) PetscCall(STGetMatrix(eps->st,1,&B));
     92:   else B = NULL;
     93:   PetscCall(PetscMalloc1(eps->mpd,&gamma));

     95:   kini = eps->nini;
     96:   while (eps->reason == EPS_CONVERGED_ITERATING) {
     97:     eps->its++;
     98:     nv = PetscMin(eps->nconv+eps->mpd,ncv);
     99:     PetscCall(DSSetDimensions(eps->ds,nv,eps->nconv,0));
    100:     for (;kini<nv;kini++) { /* Generate more initial vectors if necessary */
    101:       PetscCall(BVSetRandomColumn(eps->V,kini));
    102:       PetscCall(BVOrthonormalizeColumn(eps->V,kini,PETSC_TRUE,NULL,NULL));
    103:     }
    104:     reset = (eps->its>1 && (eps->its-1)%ctx->nrest==0)? PETSC_TRUE: PETSC_FALSE;

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

    110:       /* Compute Rayleigh quotient */
    111:       PetscCall(BVSetActiveColumns(eps->V,eps->nconv,nv));
    112:       PetscCall(BVSetActiveColumns(ctx->AV,0,nv-eps->nconv));
    113:       PetscCall(BVMatMult(eps->V,A,ctx->AV));
    114:       PetscCall(DSGetArray(eps->ds,DS_MAT_A,&C));
    115:       for (i=eps->nconv;i<nv;i++) {
    116:         PetscCall(BVSetActiveColumns(eps->V,eps->nconv,i+1));
    117:         PetscCall(BVGetColumn(ctx->AV,i-eps->nconv,&av));
    118:         PetscCall(BVDotVec(eps->V,av,C+eps->nconv+i*ld));
    119:         PetscCall(BVRestoreColumn(ctx->AV,i-eps->nconv,&av));
    120:         for (j=eps->nconv;j<i-1;j++) C[i+j*ld] = PetscConj(C[j+i*ld]);
    121:       }
    122:       PetscCall(DSRestoreArray(eps->ds,DS_MAT_A,&C));
    123:       PetscCall(DSSetState(eps->ds,DS_STATE_RAW));

    125:       /* Solve projected problem */
    126:       PetscCall(DSSolve(eps->ds,eps->eigr,eps->eigi));
    127:       PetscCall(DSSort(eps->ds,eps->eigr,eps->eigi,NULL,NULL,NULL));
    128:       PetscCall(DSSynchronize(eps->ds,eps->eigr,eps->eigi));

    130:       /* Update vectors V(:,idx) = V * Y(:,idx) */
    131:       PetscCall(DSGetMat(eps->ds,DS_MAT_Q,&Q));
    132:       PetscCall(BVMultInPlace(eps->V,Q,eps->nconv,nv));
    133:       PetscCall(MatDenseGetSubMatrix(Q,eps->nconv,PETSC_DECIDE,eps->nconv,PETSC_DECIDE,&Q1));
    134:       PetscCall(BVMultInPlace(ctx->AV,Q1,0,nv-eps->nconv));
    135:       PetscCall(MatDenseRestoreSubMatrix(Q,&Q1));
    136:       PetscCall(DSRestoreMat(eps->ds,DS_MAT_Q,&Q));
    137:       if (B) PetscCall(BVSetMatrix(eps->V,B,PETSC_FALSE));
    138:     } else {
    139:       /* No need to do Rayleigh-Ritz, just take diag(V'*A*V) */
    140:       for (i=eps->nconv;i<nv;i++) {
    141:         PetscCall(BVGetColumn(eps->V,i,&v));
    142:         PetscCall(BVGetColumn(ctx->AV,i-eps->nconv,&av));
    143:         PetscCall(MatMult(A,v,av));
    144:         PetscCall(VecDot(av,v,eps->eigr+i));
    145:         PetscCall(BVRestoreColumn(eps->V,i,&v));
    146:         PetscCall(BVRestoreColumn(ctx->AV,i-eps->nconv,&av));
    147:       }
    148:     }

    150:     /* Compute gradient and check convergence */
    151:     k = -1;
    152:     for (i=eps->nconv;i<nv;i++) {
    153:       PetscCall(BVGetColumn(eps->V,i,&v));
    154:       PetscCall(BVGetColumn(ctx->AV,i-eps->nconv,&av));
    155:       PetscCall(BVGetColumn(ctx->G,i-eps->nconv,&p));
    156:       if (B) {
    157:         PetscCall(BVGetColumn(ctx->W,i-eps->nconv,&bv));
    158:         PetscCall(MatMult(B,v,bv));
    159:         PetscCall(VecWAXPY(p,-eps->eigr[i],bv,av));
    160:         PetscCall(BVRestoreColumn(ctx->W,i-eps->nconv,&bv));
    161:       } else PetscCall(VecWAXPY(p,-eps->eigr[i],v,av));
    162:       PetscCall(BVRestoreColumn(eps->V,i,&v));
    163:       PetscCall(BVRestoreColumn(ctx->AV,i-eps->nconv,&av));
    164:       PetscCall(VecNorm(p,NORM_2,&resnorm));
    165:       PetscCall(BVRestoreColumn(ctx->G,i-eps->nconv,&p));
    166:       PetscCall((*eps->converged)(eps,eps->eigr[i],0.0,resnorm,&eps->errest[i],eps->convergedctx));
    167:       if (k==-1 && eps->errest[i] >= eps->tol) k = i;
    168:     }
    169:     if (k==-1) k = nv;
    170:     PetscCall((*eps->stopping)(eps,eps->its,eps->max_it,k,eps->nev,&eps->reason,eps->stoppingctx));

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

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

    179:       /* Search direction */
    180:       for (i=0;i<nv-eps->nconv;i++) {
    181:         PetscCall(BVGetColumn(ctx->G,i,&v));
    182:         PetscCall(STApply(eps->st,v,w));
    183:         PetscCall(VecDot(w,v,&g));
    184:         PetscCall(BVRestoreColumn(ctx->G,i,&v));
    185:         beta = (!reset && eps->its>1)? g/gamma[i]: 0.0;
    186:         gamma[i] = g;
    187:         PetscCall(BVGetColumn(ctx->P,i,&v));
    188:         PetscCall(VecAXPBY(v,1.0,beta,w));
    189:         if (i+eps->nconv>0) {
    190:           PetscCall(BVSetActiveColumns(eps->V,0,i+eps->nconv));
    191:           PetscCall(BVOrthogonalizeVec(eps->V,v,NULL,NULL,NULL));
    192:         }
    193:         PetscCall(BVRestoreColumn(ctx->P,i,&v));
    194:       }

    196:       /* Minimization problem */
    197:       for (i=eps->nconv;i<nv;i++) {
    198:         PetscCall(BVGetColumn(eps->V,i,&v));
    199:         PetscCall(BVGetColumn(ctx->AV,i-eps->nconv,&av));
    200:         PetscCall(BVGetColumn(ctx->P,i-eps->nconv,&p));
    201:         PetscCall(VecDot(av,v,&nu));
    202:         PetscCall(VecDot(av,p,&pax));
    203:         PetscCall(MatMult(A,p,w));
    204:         PetscCall(VecDot(w,p,&pap));
    205:         if (B) {
    206:           PetscCall(BVGetColumn(ctx->W,i-eps->nconv,&bv));
    207:           PetscCall(VecDot(bv,v,&mu));
    208:           PetscCall(VecDot(bv,p,&pbx));
    209:           PetscCall(BVRestoreColumn(ctx->W,i-eps->nconv,&bv));
    210:           PetscCall(MatMult(B,p,w));
    211:           PetscCall(VecDot(w,p,&pbp));
    212:         } else {
    213:           PetscCall(VecDot(v,v,&mu));
    214:           PetscCall(VecDot(v,p,&pbx));
    215:           PetscCall(VecDot(p,p,&pbp));
    216:         }
    217:         PetscCall(BVRestoreColumn(ctx->AV,i-eps->nconv,&av));
    218:         a = PetscRealPart(pap*pbx-pax*pbp);
    219:         b = PetscRealPart(nu*pbp-mu*pap);
    220:         c = PetscRealPart(mu*pax-nu*pbx);
    221:         t = PetscMax(PetscMax(PetscAbsReal(a),PetscAbsReal(b)),PetscAbsReal(c));
    222:         if (t!=0.0) { a /= t; b /= t; c /= t; }
    223:         disc = b*b-4.0*a*c;
    224:         d = PetscSqrtReal(PetscAbsReal(disc));
    225:         if (b>=0.0 && a!=0.0) alpha = (b+d)/(2.0*a);
    226:         else if (b!=d) alpha = 2.0*c/(b-d);
    227:         else alpha = 0;
    228:         /* Next iterate */
    229:         if (alpha!=0.0) PetscCall(VecAXPY(v,alpha,p));
    230:         PetscCall(BVRestoreColumn(eps->V,i,&v));
    231:         PetscCall(BVRestoreColumn(ctx->P,i-eps->nconv,&p));
    232:         PetscCall(BVOrthonormalizeColumn(eps->V,i,PETSC_TRUE,NULL,NULL));
    233:       }
    234:     }

    236:     PetscCall(EPSMonitor(eps,eps->its,k,eps->eigr,eps->eigi,eps->errest,nv));
    237:     eps->nconv = k;
    238:   }

    240:   PetscCall(PetscFree(gamma));
    241:   PetscFunctionReturn(PETSC_SUCCESS);
    242: }

    244: static PetscErrorCode EPSRQCGSetReset_RQCG(EPS eps,PetscInt nrest)
    245: {
    246:   EPS_RQCG *ctx = (EPS_RQCG*)eps->data;

    248:   PetscFunctionBegin;
    249:   if (nrest==PETSC_DEFAULT || nrest==PETSC_DECIDE) {
    250:     ctx->nrest = 0;
    251:     eps->state = EPS_STATE_INITIAL;
    252:   } else {
    253:     PetscCheck(nrest>0,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Reset parameter must be >0");
    254:     ctx->nrest = nrest;
    255:   }
    256:   PetscFunctionReturn(PETSC_SUCCESS);
    257: }

    259: /*@
    260:    EPSRQCGSetReset - Sets the reset parameter of the RQCG iteration.

    262:    Logically Collective

    264:    Input Parameters:
    265: +  eps - the linear eigensolver context
    266: -  nrest - the number of iterations between resets

    268:    Options Database Key:
    269: .  -eps_rqcg_reset \<nrest\> - sets the reset parameter

    271:    Note:
    272:    The meaning of the reset parameter is that every `nrest` iterations the
    273:    solver performs a Rayleigh-Ritz projection step.

    275:    Level: advanced

    277: .seealso: [](ch:eps), `EPSRQCG`, `EPSRQCGGetReset()`
    278: @*/
    279: PetscErrorCode EPSRQCGSetReset(EPS eps,PetscInt nrest)
    280: {
    281:   PetscFunctionBegin;
    284:   PetscTryMethod(eps,"EPSRQCGSetReset_C",(EPS,PetscInt),(eps,nrest));
    285:   PetscFunctionReturn(PETSC_SUCCESS);
    286: }

    288: static PetscErrorCode EPSRQCGGetReset_RQCG(EPS eps,PetscInt *nrest)
    289: {
    290:   EPS_RQCG *ctx = (EPS_RQCG*)eps->data;

    292:   PetscFunctionBegin;
    293:   *nrest = ctx->nrest;
    294:   PetscFunctionReturn(PETSC_SUCCESS);
    295: }

    297: /*@
    298:    EPSRQCGGetReset - Gets the reset parameter used in the RQCG method.

    300:    Not Collective

    302:    Input Parameter:
    303: .  eps - the linear eigensolver context

    305:    Output Parameter:
    306: .  nrest - the reset parameter

    308:    Level: advanced

    310: .seealso: [](ch:eps), `EPSRQCG`, `EPSRQCGSetReset()`
    311: @*/
    312: PetscErrorCode EPSRQCGGetReset(EPS eps,PetscInt *nrest)
    313: {
    314:   PetscFunctionBegin;
    316:   PetscAssertPointer(nrest,2);
    317:   PetscUseMethod(eps,"EPSRQCGGetReset_C",(EPS,PetscInt*),(eps,nrest));
    318:   PetscFunctionReturn(PETSC_SUCCESS);
    319: }

    321: static PetscErrorCode EPSReset_RQCG(EPS eps)
    322: {
    323:   EPS_RQCG       *ctx = (EPS_RQCG*)eps->data;

    325:   PetscFunctionBegin;
    326:   PetscCall(BVDestroy(&ctx->AV));
    327:   PetscCall(BVDestroy(&ctx->W));
    328:   PetscCall(BVDestroy(&ctx->P));
    329:   PetscCall(BVDestroy(&ctx->G));
    330:   ctx->allocsize = 0;
    331:   PetscFunctionReturn(PETSC_SUCCESS);
    332: }

    334: static PetscErrorCode EPSSetFromOptions_RQCG(EPS eps,PetscOptionItems PetscOptionsObject)
    335: {
    336:   PetscBool      flg;
    337:   PetscInt       nrest;

    339:   PetscFunctionBegin;
    340:   PetscOptionsHeadBegin(PetscOptionsObject,"EPS RQCG Options");

    342:     PetscCall(PetscOptionsInt("-eps_rqcg_reset","Reset parameter","EPSRQCGSetReset",20,&nrest,&flg));
    343:     if (flg) PetscCall(EPSRQCGSetReset(eps,nrest));

    345:   PetscOptionsHeadEnd();
    346:   PetscFunctionReturn(PETSC_SUCCESS);
    347: }

    349: static PetscErrorCode EPSDestroy_RQCG(EPS eps)
    350: {
    351:   PetscFunctionBegin;
    352:   PetscCall(PetscFree(eps->data));
    353:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSRQCGSetReset_C",NULL));
    354:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSRQCGGetReset_C",NULL));
    355:   PetscFunctionReturn(PETSC_SUCCESS);
    356: }

    358: static PetscErrorCode EPSView_RQCG(EPS eps,PetscViewer viewer)
    359: {
    360:   EPS_RQCG       *ctx = (EPS_RQCG*)eps->data;
    361:   PetscBool      isascii;

    363:   PetscFunctionBegin;
    364:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii));
    365:   if (isascii) PetscCall(PetscViewerASCIIPrintf(viewer,"  reset every %" PetscInt_FMT " iterations\n",ctx->nrest));
    366:   PetscFunctionReturn(PETSC_SUCCESS);
    367: }

    369: /*MC
    370:    EPSRQCG - EPSRQCG = "rqcg" - The Rayleigh Quotient Conjugate Gradient method.

    372:    Notes:
    373:    This is a preconditioned eigensolver for computing leftmost
    374:    eigenvalues, similar to `EPSLOBPCG`, but usually less competitive.

    376:    The description of the method is in {cite:p}`Ber06`

    378:    The preconditioner is specified via the internal `ST` object and its
    379:    associated `KSP`.

    381:    Level: beginner

    383: .seealso: [](ch:eps), `EPS`, `EPSType`, `EPSSetType()`, `EPSGetST()`
    384: M*/
    385: SLEPC_EXTERN PetscErrorCode EPSCreate_RQCG(EPS eps)
    386: {
    387:   EPS_RQCG       *rqcg;

    389:   PetscFunctionBegin;
    390:   PetscCall(PetscNew(&rqcg));
    391:   eps->data = (void*)rqcg;

    393:   eps->useds = PETSC_TRUE;
    394:   eps->categ = EPS_CATEGORY_PRECOND;

    396:   eps->ops->solve          = EPSSolve_RQCG;
    397:   eps->ops->setup          = EPSSetUp_RQCG;
    398:   eps->ops->setupsort      = EPSSetUpSort_Default;
    399:   eps->ops->setfromoptions = EPSSetFromOptions_RQCG;
    400:   eps->ops->destroy        = EPSDestroy_RQCG;
    401:   eps->ops->reset          = EPSReset_RQCG;
    402:   eps->ops->view           = EPSView_RQCG;
    403:   eps->ops->backtransform  = EPSBackTransform_Default;
    404:   eps->ops->setdefaultst   = EPSSetDefaultST_GMRES;

    406:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSRQCGSetReset_C",EPSRQCGSetReset_RQCG));
    407:   PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSRQCGGetReset_C",EPSRQCGGetReset_RQCG));
    408:   PetscFunctionReturn(PETSC_SUCCESS);
    409: }