Actual source code: rqcg.c
slepc-3.14.0 2020-09-30
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: }