Actual source code: rqcg.c
slepc-3.7.4 2017-05-17
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) 2002-2016, 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);
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: (*eps->stopping)(eps,eps->its,eps->max_it,k,eps->nev,&eps->reason,eps->stoppingctx);
222: /* The next lines are necessary to avoid DS zeroing eigr */
223: DSGetArray(eps->ds,DS_MAT_A,&C);
224: for (i=eps->nconv;i<k;i++) C[i+i*ld] = eps->eigr[i];
225: DSRestoreArray(eps->ds,DS_MAT_A,&C);
227: if (eps->reason == EPS_CONVERGED_ITERATING) {
229: /* Search direction */
230: for (i=0;i<nv-eps->nconv;i++) {
231: BVGetColumn(ctx->G,i,&v);
232: STMatSolve(eps->st,v,w);
233: VecDot(v,w,&g);
234: BVRestoreColumn(ctx->G,i,&v);
235: beta = (!reset && eps->its>1)? g/gamma[i]: 0.0;
236: gamma[i] = g;
237: BVGetColumn(ctx->P,i,&v);
238: VecAXPBY(v,1.0,beta,w);
239: if (i+eps->nconv>0) {
240: BVSetActiveColumns(eps->V,0,i+eps->nconv);
241: BVOrthogonalizeVec(eps->V,v,NULL,NULL,NULL);
242: }
243: BVRestoreColumn(ctx->P,i,&v);
244: }
246: /* Minimization problem */
247: for (i=eps->nconv;i<nv;i++) {
248: BVGetColumn(eps->V,i,&v);
249: BVGetColumn(ctx->AV,i-eps->nconv,&av);
250: BVGetColumn(ctx->P,i-eps->nconv,&p);
251: VecDot(v,av,&nu);
252: VecDot(p,av,&pax);
253: MatMult(A,p,w);
254: VecDot(p,w,&pap);
255: if (B) {
256: BVGetColumn(ctx->W,i-eps->nconv,&bv);
257: VecDot(v,bv,&mu);
258: VecDot(p,bv,&pbx);
259: BVRestoreColumn(ctx->W,i-eps->nconv,&bv);
260: MatMult(B,p,w);
261: VecDot(p,w,&pbp);
262: } else {
263: VecDot(v,v,&mu);
264: VecDot(p,v,&pbx);
265: VecDot(p,p,&pbp);
266: }
267: BVRestoreColumn(ctx->AV,i-eps->nconv,&av);
268: a = PetscRealPart(pap*pbx-pax*pbp);
269: b = PetscRealPart(nu*pbp-mu*pap);
270: c = PetscRealPart(mu*pax-nu*pbx);
271: t = PetscMax(PetscMax(PetscAbsReal(a),PetscAbsReal(b)),PetscAbsReal(c));
272: if (t!=0.0) { a /= t; b /= t; c /= t; }
273: disc = PetscSqrtReal(PetscAbsReal(b*b-4.0*a*c));
274: if (b>=0.0 && a!=0.0) alpha = (b+disc)/(2.0*a);
275: else if (b!=disc) alpha = 2.0*c/(b-disc);
276: else alpha = 0;
277: /* Next iterate */
278: if (alpha!=0.0) {
279: VecAXPY(v,alpha,p);
280: }
281: BVRestoreColumn(eps->V,i,&v);
282: BVRestoreColumn(ctx->P,i-eps->nconv,&p);
283: BVOrthogonalizeColumn(eps->V,i,NULL,&norm,&breakdown);
284: if (!breakdown && norm!=0.0) {
285: BVScaleColumn(eps->V,i,1.0/norm);
286: }
287: }
288: }
290: EPSMonitor(eps,eps->its,k,eps->eigr,eps->eigi,eps->errest,nv);
291: eps->nconv = k;
292: }
294: PetscFree(gamma);
295: return(0);
296: }
300: static PetscErrorCode EPSRQCGSetReset_RQCG(EPS eps,PetscInt nrest)
301: {
302: EPS_RQCG *ctx = (EPS_RQCG*)eps->data;
305: ctx->nrest = nrest;
306: return(0);
307: }
311: /*@
312: EPSRQCGSetReset - Sets the reset parameter of the RQCG iteration. Every
313: nrest iterations, the solver performs a Rayleigh-Ritz projection step.
315: Logically Collective on EPS
317: Input Parameters:
318: + eps - the eigenproblem solver context
319: - nrest - the number of iterations between resets
321: Options Database Key:
322: . -eps_rqcg_reset - Sets the reset parameter
324: Level: advanced
326: .seealso: EPSRQCGGetReset()
327: @*/
328: PetscErrorCode EPSRQCGSetReset(EPS eps,PetscInt nrest)
329: {
335: PetscTryMethod(eps,"EPSRQCGSetReset_C",(EPS,PetscInt),(eps,nrest));
336: return(0);
337: }
341: static PetscErrorCode EPSRQCGGetReset_RQCG(EPS eps,PetscInt *nrest)
342: {
343: EPS_RQCG *ctx = (EPS_RQCG*)eps->data;
346: *nrest = ctx->nrest;
347: return(0);
348: }
352: /*@
353: EPSRQCGGetReset - Gets the reset parameter used in the RQCG method.
355: Not Collective
357: Input Parameter:
358: . eps - the eigenproblem solver context
360: Output Parameter:
361: . nrest - the reset parameter
363: Level: advanced
365: .seealso: EPSRQCGSetReset()
366: @*/
367: PetscErrorCode EPSRQCGGetReset(EPS eps,PetscInt *nrest)
368: {
374: PetscUseMethod(eps,"EPSRQCGGetReset_C",(EPS,PetscInt*),(eps,nrest));
375: return(0);
376: }
380: PetscErrorCode EPSReset_RQCG(EPS eps)
381: {
383: EPS_RQCG *ctx = (EPS_RQCG*)eps->data;
386: BVDestroy(&ctx->AV);
387: BVDestroy(&ctx->W);
388: BVDestroy(&ctx->P);
389: BVDestroy(&ctx->G);
390: ctx->nrest = 0;
391: return(0);
392: }
396: PetscErrorCode EPSSetFromOptions_RQCG(PetscOptionItems *PetscOptionsObject,EPS eps)
397: {
399: PetscBool flg;
400: PetscInt nrest;
403: PetscOptionsHead(PetscOptionsObject,"EPS RQCG Options");
404: PetscOptionsInt("-eps_rqcg_reset","RQCG reset parameter","EPSRQCGSetReset",20,&nrest,&flg);
405: if (flg) {
406: EPSRQCGSetReset(eps,nrest);
407: }
408: PetscOptionsTail();
409: return(0);
410: }
414: PetscErrorCode EPSDestroy_RQCG(EPS eps)
415: {
419: PetscFree(eps->data);
420: PetscObjectComposeFunction((PetscObject)eps,"EPSRQCGSetReset_C",NULL);
421: PetscObjectComposeFunction((PetscObject)eps,"EPSRQCGGetReset_C",NULL);
422: return(0);
423: }
427: PetscErrorCode EPSView_RQCG(EPS eps,PetscViewer viewer)
428: {
430: EPS_RQCG *ctx = (EPS_RQCG*)eps->data;
431: PetscBool isascii;
434: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
435: if (isascii) {
436: PetscViewerASCIIPrintf(viewer," RQCG: reset every %D iterations\n",ctx->nrest);
437: }
438: return(0);
439: }
443: PETSC_EXTERN PetscErrorCode EPSCreate_RQCG(EPS eps)
444: {
445: EPS_RQCG *rqcg;
449: PetscNewLog(eps,&rqcg);
450: eps->data = (void*)rqcg;
452: eps->ops->setup = EPSSetUp_RQCG;
453: eps->ops->solve = EPSSolve_RQCG;
454: eps->ops->setfromoptions = EPSSetFromOptions_RQCG;
455: eps->ops->destroy = EPSDestroy_RQCG;
456: eps->ops->reset = EPSReset_RQCG;
457: eps->ops->view = EPSView_RQCG;
458: eps->ops->backtransform = EPSBackTransform_Default;
459: STSetType(eps->st,STPRECOND);
460: STPrecondSetKSPHasMat(eps->st,PETSC_TRUE);
461: PetscObjectComposeFunction((PetscObject)eps,"EPSRQCGSetReset_C",EPSRQCGSetReset_RQCG);
462: PetscObjectComposeFunction((PetscObject)eps,"EPSRQCGGetReset_C",EPSRQCGGetReset_RQCG);
463: return(0);
464: }