Actual source code: rqcg.c
slepc-3.21.1 2024-04-26
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: PetscCall(EPSSetDimensions_Default(eps,eps->nev,&eps->ncv,&eps->mpd));
45: if (eps->max_it==PETSC_DEFAULT) eps->max_it = PetscMax(100,2*eps->n/eps->ncv);
46: if (!eps->which) eps->which = EPS_SMALLEST_REAL;
47: PetscCheck(eps->which==EPS_SMALLEST_REAL,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"This solver supports only smallest real eigenvalues");
48: EPSCheckUnsupported(eps,EPS_FEATURE_ARBITRARY | EPS_FEATURE_REGION | EPS_FEATURE_EXTRACTION);
49: EPSCheckIgnored(eps,EPS_FEATURE_BALANCE);
51: if (!ctx->nrest) ctx->nrest = 20;
53: PetscCall(EPSAllocateSolution(eps,0));
54: PetscCall(EPS_SetInnerProduct(eps));
56: PetscCall(STGetNumMatrices(eps->st,&nmat));
57: if (!ctx->allocsize) {
58: ctx->allocsize = eps->mpd;
59: PetscCall(BVDuplicateResize(eps->V,eps->mpd,&ctx->AV));
60: if (nmat>1) PetscCall(BVDuplicate(ctx->AV,&ctx->W));
61: PetscCall(BVDuplicate(ctx->AV,&ctx->P));
62: PetscCall(BVDuplicate(ctx->AV,&ctx->G));
63: } else if (ctx->allocsize!=eps->mpd) {
64: ctx->allocsize = eps->mpd;
65: PetscCall(BVResize(ctx->AV,eps->mpd,PETSC_FALSE));
66: if (nmat>1) PetscCall(BVResize(ctx->W,eps->mpd,PETSC_FALSE));
67: PetscCall(BVResize(ctx->P,eps->mpd,PETSC_FALSE));
68: PetscCall(BVResize(ctx->G,eps->mpd,PETSC_FALSE));
69: }
70: PetscCall(DSSetType(eps->ds,DSHEP));
71: PetscCall(DSAllocate(eps->ds,eps->ncv));
72: PetscCall(EPSSetWorkVecs(eps,1));
73: PetscFunctionReturn(PETSC_SUCCESS);
74: }
76: static PetscErrorCode EPSSolve_RQCG(EPS eps)
77: {
78: EPS_RQCG *ctx = (EPS_RQCG*)eps->data;
79: PetscInt i,j,k,ld,nv,ncv = eps->ncv,kini,nmat;
80: PetscScalar *C,*gamma,g,pap,pbp,pbx,pax,nu,mu,alpha,beta;
81: PetscReal resnorm,a,b,c,d,disc,t;
82: PetscBool reset;
83: Mat A,B,Q,Q1;
84: Vec v,av,bv,p,w=eps->work[0];
86: PetscFunctionBegin;
87: PetscCall(DSGetLeadingDimension(eps->ds,&ld));
88: PetscCall(STGetNumMatrices(eps->st,&nmat));
89: PetscCall(STGetMatrix(eps->st,0,&A));
90: if (nmat>1) PetscCall(STGetMatrix(eps->st,1,&B));
91: else B = NULL;
92: PetscCall(PetscMalloc1(eps->mpd,&gamma));
94: kini = eps->nini;
95: while (eps->reason == EPS_CONVERGED_ITERATING) {
96: eps->its++;
97: nv = PetscMin(eps->nconv+eps->mpd,ncv);
98: PetscCall(DSSetDimensions(eps->ds,nv,eps->nconv,0));
99: for (;kini<nv;kini++) { /* Generate more initial vectors if necessary */
100: PetscCall(BVSetRandomColumn(eps->V,kini));
101: PetscCall(BVOrthonormalizeColumn(eps->V,kini,PETSC_TRUE,NULL,NULL));
102: }
103: reset = (eps->its>1 && (eps->its-1)%ctx->nrest==0)? PETSC_TRUE: PETSC_FALSE;
105: if (reset) {
106: /* Prevent BVDotVec below to use B-product, restored at the end */
107: PetscCall(BVSetMatrix(eps->V,NULL,PETSC_FALSE));
109: /* Compute Rayleigh quotient */
110: PetscCall(BVSetActiveColumns(eps->V,eps->nconv,nv));
111: PetscCall(BVSetActiveColumns(ctx->AV,0,nv-eps->nconv));
112: PetscCall(BVMatMult(eps->V,A,ctx->AV));
113: PetscCall(DSGetArray(eps->ds,DS_MAT_A,&C));
114: for (i=eps->nconv;i<nv;i++) {
115: PetscCall(BVSetActiveColumns(eps->V,eps->nconv,i+1));
116: PetscCall(BVGetColumn(ctx->AV,i-eps->nconv,&av));
117: PetscCall(BVDotVec(eps->V,av,C+eps->nconv+i*ld));
118: PetscCall(BVRestoreColumn(ctx->AV,i-eps->nconv,&av));
119: for (j=eps->nconv;j<i-1;j++) C[i+j*ld] = PetscConj(C[j+i*ld]);
120: }
121: PetscCall(DSRestoreArray(eps->ds,DS_MAT_A,&C));
122: PetscCall(DSSetState(eps->ds,DS_STATE_RAW));
124: /* Solve projected problem */
125: PetscCall(DSSolve(eps->ds,eps->eigr,eps->eigi));
126: PetscCall(DSSort(eps->ds,eps->eigr,eps->eigi,NULL,NULL,NULL));
127: PetscCall(DSSynchronize(eps->ds,eps->eigr,eps->eigi));
129: /* Update vectors V(:,idx) = V * Y(:,idx) */
130: PetscCall(DSGetMat(eps->ds,DS_MAT_Q,&Q));
131: PetscCall(BVMultInPlace(eps->V,Q,eps->nconv,nv));
132: PetscCall(MatDenseGetSubMatrix(Q,eps->nconv,PETSC_DECIDE,eps->nconv,PETSC_DECIDE,&Q1));
133: PetscCall(BVMultInPlace(ctx->AV,Q1,0,nv-eps->nconv));
134: PetscCall(MatDenseRestoreSubMatrix(Q,&Q1));
135: PetscCall(DSRestoreMat(eps->ds,DS_MAT_Q,&Q));
136: if (B) PetscCall(BVSetMatrix(eps->V,B,PETSC_FALSE));
137: } else {
138: /* No need to do Rayleigh-Ritz, just take diag(V'*A*V) */
139: for (i=eps->nconv;i<nv;i++) {
140: PetscCall(BVGetColumn(eps->V,i,&v));
141: PetscCall(BVGetColumn(ctx->AV,i-eps->nconv,&av));
142: PetscCall(MatMult(A,v,av));
143: PetscCall(VecDot(av,v,eps->eigr+i));
144: PetscCall(BVRestoreColumn(eps->V,i,&v));
145: PetscCall(BVRestoreColumn(ctx->AV,i-eps->nconv,&av));
146: }
147: }
149: /* Compute gradient and check convergence */
150: k = -1;
151: for (i=eps->nconv;i<nv;i++) {
152: PetscCall(BVGetColumn(eps->V,i,&v));
153: PetscCall(BVGetColumn(ctx->AV,i-eps->nconv,&av));
154: PetscCall(BVGetColumn(ctx->G,i-eps->nconv,&p));
155: if (B) {
156: PetscCall(BVGetColumn(ctx->W,i-eps->nconv,&bv));
157: PetscCall(MatMult(B,v,bv));
158: PetscCall(VecWAXPY(p,-eps->eigr[i],bv,av));
159: PetscCall(BVRestoreColumn(ctx->W,i-eps->nconv,&bv));
160: } else PetscCall(VecWAXPY(p,-eps->eigr[i],v,av));
161: PetscCall(BVRestoreColumn(eps->V,i,&v));
162: PetscCall(BVRestoreColumn(ctx->AV,i-eps->nconv,&av));
163: PetscCall(VecNorm(p,NORM_2,&resnorm));
164: PetscCall(BVRestoreColumn(ctx->G,i-eps->nconv,&p));
165: PetscCall((*eps->converged)(eps,eps->eigr[i],0.0,resnorm,&eps->errest[i],eps->convergedctx));
166: if (k==-1 && eps->errest[i] >= eps->tol) k = i;
167: }
168: if (k==-1) k = nv;
169: PetscCall((*eps->stopping)(eps,eps->its,eps->max_it,k,eps->nev,&eps->reason,eps->stoppingctx));
171: /* The next lines are necessary to avoid DS zeroing eigr */
172: PetscCall(DSGetArray(eps->ds,DS_MAT_A,&C));
173: for (i=eps->nconv;i<k;i++) C[i+i*ld] = eps->eigr[i];
174: PetscCall(DSRestoreArray(eps->ds,DS_MAT_A,&C));
176: if (eps->reason == EPS_CONVERGED_ITERATING) {
178: /* Search direction */
179: for (i=0;i<nv-eps->nconv;i++) {
180: PetscCall(BVGetColumn(ctx->G,i,&v));
181: PetscCall(STApply(eps->st,v,w));
182: PetscCall(VecDot(w,v,&g));
183: PetscCall(BVRestoreColumn(ctx->G,i,&v));
184: beta = (!reset && eps->its>1)? g/gamma[i]: 0.0;
185: gamma[i] = g;
186: PetscCall(BVGetColumn(ctx->P,i,&v));
187: PetscCall(VecAXPBY(v,1.0,beta,w));
188: if (i+eps->nconv>0) {
189: PetscCall(BVSetActiveColumns(eps->V,0,i+eps->nconv));
190: PetscCall(BVOrthogonalizeVec(eps->V,v,NULL,NULL,NULL));
191: }
192: PetscCall(BVRestoreColumn(ctx->P,i,&v));
193: }
195: /* Minimization problem */
196: for (i=eps->nconv;i<nv;i++) {
197: PetscCall(BVGetColumn(eps->V,i,&v));
198: PetscCall(BVGetColumn(ctx->AV,i-eps->nconv,&av));
199: PetscCall(BVGetColumn(ctx->P,i-eps->nconv,&p));
200: PetscCall(VecDot(av,v,&nu));
201: PetscCall(VecDot(av,p,&pax));
202: PetscCall(MatMult(A,p,w));
203: PetscCall(VecDot(w,p,&pap));
204: if (B) {
205: PetscCall(BVGetColumn(ctx->W,i-eps->nconv,&bv));
206: PetscCall(VecDot(bv,v,&mu));
207: PetscCall(VecDot(bv,p,&pbx));
208: PetscCall(BVRestoreColumn(ctx->W,i-eps->nconv,&bv));
209: PetscCall(MatMult(B,p,w));
210: PetscCall(VecDot(w,p,&pbp));
211: } else {
212: PetscCall(VecDot(v,v,&mu));
213: PetscCall(VecDot(v,p,&pbx));
214: PetscCall(VecDot(p,p,&pbp));
215: }
216: PetscCall(BVRestoreColumn(ctx->AV,i-eps->nconv,&av));
217: a = PetscRealPart(pap*pbx-pax*pbp);
218: b = PetscRealPart(nu*pbp-mu*pap);
219: c = PetscRealPart(mu*pax-nu*pbx);
220: t = PetscMax(PetscMax(PetscAbsReal(a),PetscAbsReal(b)),PetscAbsReal(c));
221: if (t!=0.0) { a /= t; b /= t; c /= t; }
222: disc = b*b-4.0*a*c;
223: d = PetscSqrtReal(PetscAbsReal(disc));
224: if (b>=0.0 && a!=0.0) alpha = (b+d)/(2.0*a);
225: else if (b!=d) alpha = 2.0*c/(b-d);
226: else alpha = 0;
227: /* Next iterate */
228: if (alpha!=0.0) PetscCall(VecAXPY(v,alpha,p));
229: PetscCall(BVRestoreColumn(eps->V,i,&v));
230: PetscCall(BVRestoreColumn(ctx->P,i-eps->nconv,&p));
231: PetscCall(BVOrthonormalizeColumn(eps->V,i,PETSC_TRUE,NULL,NULL));
232: }
233: }
235: PetscCall(EPSMonitor(eps,eps->its,k,eps->eigr,eps->eigi,eps->errest,nv));
236: eps->nconv = k;
237: }
239: PetscCall(PetscFree(gamma));
240: PetscFunctionReturn(PETSC_SUCCESS);
241: }
243: static PetscErrorCode EPSRQCGSetReset_RQCG(EPS eps,PetscInt nrest)
244: {
245: EPS_RQCG *ctx = (EPS_RQCG*)eps->data;
247: PetscFunctionBegin;
248: if (nrest==PETSC_DEFAULT) {
249: ctx->nrest = 0;
250: eps->state = EPS_STATE_INITIAL;
251: } else {
252: PetscCheck(nrest>0,PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Reset parameter must be >0");
253: ctx->nrest = nrest;
254: }
255: PetscFunctionReturn(PETSC_SUCCESS);
256: }
258: /*@
259: EPSRQCGSetReset - Sets the reset parameter of the RQCG iteration. Every
260: nrest iterations, the solver performs a Rayleigh-Ritz projection step.
262: Logically Collective
264: Input Parameters:
265: + eps - the eigenproblem solver context
266: - nrest - the number of iterations between resets
268: Options Database Key:
269: . -eps_rqcg_reset - Sets the reset parameter
271: Level: advanced
273: .seealso: EPSRQCGGetReset()
274: @*/
275: PetscErrorCode EPSRQCGSetReset(EPS eps,PetscInt nrest)
276: {
277: PetscFunctionBegin;
280: PetscTryMethod(eps,"EPSRQCGSetReset_C",(EPS,PetscInt),(eps,nrest));
281: PetscFunctionReturn(PETSC_SUCCESS);
282: }
284: static PetscErrorCode EPSRQCGGetReset_RQCG(EPS eps,PetscInt *nrest)
285: {
286: EPS_RQCG *ctx = (EPS_RQCG*)eps->data;
288: PetscFunctionBegin;
289: *nrest = ctx->nrest;
290: PetscFunctionReturn(PETSC_SUCCESS);
291: }
293: /*@
294: EPSRQCGGetReset - Gets the reset parameter used in the RQCG method.
296: Not Collective
298: Input Parameter:
299: . eps - the eigenproblem solver context
301: Output Parameter:
302: . nrest - the reset parameter
304: Level: advanced
306: .seealso: EPSRQCGSetReset()
307: @*/
308: PetscErrorCode EPSRQCGGetReset(EPS eps,PetscInt *nrest)
309: {
310: PetscFunctionBegin;
312: PetscAssertPointer(nrest,2);
313: PetscUseMethod(eps,"EPSRQCGGetReset_C",(EPS,PetscInt*),(eps,nrest));
314: PetscFunctionReturn(PETSC_SUCCESS);
315: }
317: static PetscErrorCode EPSReset_RQCG(EPS eps)
318: {
319: EPS_RQCG *ctx = (EPS_RQCG*)eps->data;
321: PetscFunctionBegin;
322: PetscCall(BVDestroy(&ctx->AV));
323: PetscCall(BVDestroy(&ctx->W));
324: PetscCall(BVDestroy(&ctx->P));
325: PetscCall(BVDestroy(&ctx->G));
326: ctx->allocsize = 0;
327: PetscFunctionReturn(PETSC_SUCCESS);
328: }
330: static PetscErrorCode EPSSetFromOptions_RQCG(EPS eps,PetscOptionItems *PetscOptionsObject)
331: {
332: PetscBool flg;
333: PetscInt nrest;
335: PetscFunctionBegin;
336: PetscOptionsHeadBegin(PetscOptionsObject,"EPS RQCG Options");
338: PetscCall(PetscOptionsInt("-eps_rqcg_reset","Reset parameter","EPSRQCGSetReset",20,&nrest,&flg));
339: if (flg) PetscCall(EPSRQCGSetReset(eps,nrest));
341: PetscOptionsHeadEnd();
342: PetscFunctionReturn(PETSC_SUCCESS);
343: }
345: static PetscErrorCode EPSDestroy_RQCG(EPS eps)
346: {
347: PetscFunctionBegin;
348: PetscCall(PetscFree(eps->data));
349: PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSRQCGSetReset_C",NULL));
350: PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSRQCGGetReset_C",NULL));
351: PetscFunctionReturn(PETSC_SUCCESS);
352: }
354: static PetscErrorCode EPSView_RQCG(EPS eps,PetscViewer viewer)
355: {
356: EPS_RQCG *ctx = (EPS_RQCG*)eps->data;
357: PetscBool isascii;
359: PetscFunctionBegin;
360: PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii));
361: if (isascii) PetscCall(PetscViewerASCIIPrintf(viewer," reset every %" PetscInt_FMT " iterations\n",ctx->nrest));
362: PetscFunctionReturn(PETSC_SUCCESS);
363: }
365: SLEPC_EXTERN PetscErrorCode EPSCreate_RQCG(EPS eps)
366: {
367: EPS_RQCG *rqcg;
369: PetscFunctionBegin;
370: PetscCall(PetscNew(&rqcg));
371: eps->data = (void*)rqcg;
373: eps->useds = PETSC_TRUE;
374: eps->categ = EPS_CATEGORY_PRECOND;
376: eps->ops->solve = EPSSolve_RQCG;
377: eps->ops->setup = EPSSetUp_RQCG;
378: eps->ops->setupsort = EPSSetUpSort_Default;
379: eps->ops->setfromoptions = EPSSetFromOptions_RQCG;
380: eps->ops->destroy = EPSDestroy_RQCG;
381: eps->ops->reset = EPSReset_RQCG;
382: eps->ops->view = EPSView_RQCG;
383: eps->ops->backtransform = EPSBackTransform_Default;
384: eps->ops->setdefaultst = EPSSetDefaultST_GMRES;
386: PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSRQCGSetReset_C",EPSRQCGSetReset_RQCG));
387: PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSRQCGGetReset_C",EPSRQCGGetReset_RQCG));
388: PetscFunctionReturn(PETSC_SUCCESS);
389: }