Actual source code: subspace.c
1: /*
3: SLEPc eigensolver: "subspace"
5: Method: Subspace Iteration
7: Algorithm:
9: Subspace iteration with Rayleigh-Ritz projection and locking,
10: based on the SRRIT implementation.
12: References:
14: [1] "Subspace Iteration in SLEPc", SLEPc Technical Report STR-3,
15: available at http://www.grycap.upv.es/slepc.
17: Last update: Feb 2009
19: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
20: SLEPc - Scalable Library for Eigenvalue Problem Computations
21: Copyright (c) 2002-2012, Universitat Politecnica de Valencia, Spain
23: This file is part of SLEPc.
24:
25: SLEPc is free software: you can redistribute it and/or modify it under the
26: terms of version 3 of the GNU Lesser General Public License as published by
27: the Free Software Foundation.
29: SLEPc is distributed in the hope that it will be useful, but WITHOUT ANY
30: WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
31: FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for
32: more details.
34: You should have received a copy of the GNU Lesser General Public License
35: along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
36: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
37: */
39: #include <slepc-private/epsimpl.h> /*I "slepceps.h" I*/
40: #include <slepcblaslapack.h>
42: PetscErrorCode EPSSolve_Subspace(EPS);
44: typedef struct {
45: Vec *AV;
46: } EPS_SUBSPACE;
50: PetscErrorCode EPSSetUp_Subspace(EPS eps)
51: {
53: EPS_SUBSPACE *ctx = (EPS_SUBSPACE*)eps->data;
56: if (eps->ncv) { /* ncv set */
57: if (eps->ncv<eps->nev) SETERRQ(((PetscObject)eps)->comm,1,"The value of ncv must be at least nev");
58: }
59: else if (eps->mpd) { /* mpd set */
60: eps->ncv = PetscMin(eps->n,eps->nev+eps->mpd);
61: }
62: else { /* neither set: defaults depend on nev being small or large */
63: if (eps->nev<500) eps->ncv = PetscMin(eps->n,PetscMax(2*eps->nev,eps->nev+15));
64: else { eps->mpd = 500; eps->ncv = PetscMin(eps->n,eps->nev+eps->mpd); }
65: }
66: if (!eps->mpd) eps->mpd = eps->ncv;
67: if (!eps->max_it) eps->max_it = PetscMax(100,2*eps->n/eps->ncv);
68: if (!eps->which) { EPSDefaultSetWhich(eps); }
69: if (eps->which!=EPS_LARGEST_MAGNITUDE && eps->which!=EPS_TARGET_MAGNITUDE) SETERRQ(((PetscObject)eps)->comm,1,"Wrong value of eps->which");
70: if (!eps->extraction) {
71: EPSSetExtraction(eps,EPS_RITZ);
72: } else if (eps->extraction!=EPS_RITZ) SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_SUP,"Unsupported extraction type");
73: if (eps->arbit_func) SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_SUP,"Arbitrary selection of eigenpairs not supported in this solver");
75: EPSAllocateSolution(eps);
76: VecDuplicateVecs(eps->t,eps->ncv,&ctx->AV);
77: if (eps->ishermitian) {
78: DSSetType(eps->ds,DSHEP);
79: } else {
80: DSSetType(eps->ds,DSNHEP);
81: }
82: DSAllocate(eps->ds,eps->ncv);
83: EPSDefaultGetWork(eps,1);
85: /* dispatch solve method */
86: if (eps->leftvecs) SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_SUP,"Left vectors not supported in this solver");
87: eps->ops->solve = EPSSolve_Subspace;
88: return(0);
89: }
93: /*
94: EPSSubspaceFindGroup - Find a group of nearly equimodular eigenvalues, provided
95: in arrays wr and wi, according to the tolerance grptol. Also the 2-norms
96: of the residuals must be passed in (rsd). Arrays are processed from index
97: l to index m only. The output information is:
99: ngrp - number of entries of the group
100: ctr - (w(l)+w(l+ngrp-1))/2
101: ae - average of wr(l),...,wr(l+ngrp-1)
102: arsd - average of rsd(l),...,rsd(l+ngrp-1)
103: */
104: static PetscErrorCode EPSSubspaceFindGroup(PetscInt l,PetscInt m,PetscScalar *wr,PetscScalar *wi,PetscReal *rsd,PetscReal grptol,PetscInt *ngrp,PetscReal *ctr,PetscReal *ae,PetscReal *arsd)
105: {
106: PetscInt i;
107: PetscReal rmod,rmod1;
110: *ngrp = 0;
111: *ctr = 0;
112: rmod = SlepcAbsEigenvalue(wr[l],wi[l]);
114: for (i=l;i<m;) {
115: rmod1 = SlepcAbsEigenvalue(wr[i],wi[i]);
116: if (PetscAbsReal(rmod-rmod1) > grptol*(rmod+rmod1)) break;
117: *ctr = (rmod+rmod1)/2.0;
118: if (wi[i] != 0.0) {
119: (*ngrp)+=2;
120: i+=2;
121: } else {
122: (*ngrp)++;
123: i++;
124: }
125: }
127: *ae = 0;
128: *arsd = 0;
129: if (*ngrp) {
130: for (i=l;i<l+*ngrp;i++) {
131: (*ae) += PetscRealPart(wr[i]);
132: (*arsd) += rsd[i]*rsd[i];
133: }
134: *ae = *ae / *ngrp;
135: *arsd = PetscSqrtScalar(*arsd / *ngrp);
136: }
137: return(0);
138: }
142: /*
143: EPSSubspaceResidualNorms - Computes the column norms of residual vectors
144: OP*V(1:n,l:m) - V*T(1:m,l:m), where, on entry, OP*V has been computed and
145: stored in AV. ldt is the leading dimension of T. On exit, rsd(l) to
146: rsd(m) contain the computed norms.
147: */
148: static PetscErrorCode EPSSubspaceResidualNorms(Vec *V,Vec *AV,PetscScalar *T,PetscInt l,PetscInt m,PetscInt ldt,Vec w,PetscReal *rsd)
149: {
151: PetscInt i,k;
152: PetscScalar t;
155: for (i=l;i<m;i++) {
156: if (i==m-1 || T[i+1+ldt*i]==0.0) k=i+1;
157: else k=i+2;
158: VecCopy(AV[i],w);
159: SlepcVecMAXPBY(w,1.0,-1.0,k,T+ldt*i,V);
160: VecDot(w,w,&t);
161: rsd[i] = PetscRealPart(t);
162: }
163: for (i=l;i<m;i++) {
164: if (i == m-1) {
165: rsd[i] = PetscSqrtReal(rsd[i]);
166: } else if (T[i+1+(ldt*i)]==0.0) {
167: rsd[i] = PetscSqrtReal(rsd[i]);
168: } else {
169: rsd[i] = PetscSqrtReal((rsd[i]+rsd[i+1])/2.0);
170: rsd[i+1] = rsd[i];
171: i++;
172: }
173: }
174: return(0);
175: }
179: PetscErrorCode EPSSolve_Subspace(EPS eps)
180: {
182: EPS_SUBSPACE *ctx = (EPS_SUBSPACE*)eps->data;
183: PetscInt i,k,ld,ngrp,nogrp,*itrsd,*itrsdold,
184: nxtsrr,idsrr,idort,nxtort,nv,ncv = eps->ncv,its;
185: PetscScalar *T,*U;
186: PetscReal arsd,oarsd,ctr,octr,ae,oae,*rsd,norm,tcond=1.0;
187: PetscBool breakdown;
188: /* Parameters */
189: PetscInt init = 5; /* Number of initial iterations */
190: PetscReal stpfac = 1.5, /* Max num of iter before next SRR step */
191: alpha = 1.0, /* Used to predict convergence of next residual */
192: beta = 1.1, /* Used to predict convergence of next residual */
193: grptol = 1e-8, /* Tolerance for EPSSubspaceFindGroup */
194: cnvtol = 1e-6; /* Convergence criterion for cnv */
195: PetscInt orttol = 2; /* Number of decimal digits whose loss
196: can be tolerated in orthogonalization */
199: its = 0;
200: PetscMalloc(sizeof(PetscReal)*ncv,&rsd);
201: PetscMalloc(sizeof(PetscInt)*ncv,&itrsd);
202: PetscMalloc(sizeof(PetscInt)*ncv,&itrsdold);
203: DSGetLeadingDimension(eps->ds,&ld);
205: for (i=0;i<ncv;i++) {
206: rsd[i] = 0.0;
207: itrsd[i] = -1;
208: }
209:
210: /* Complete the initial basis with random vectors and orthonormalize them */
211: k = eps->nini;
212: while (k<ncv) {
213: SlepcVecSetRandom(eps->V[k],eps->rand);
214: IPOrthogonalize(eps->ip,eps->nds,eps->defl,k,PETSC_NULL,eps->V,eps->V[k],PETSC_NULL,&norm,&breakdown);
215: if (norm>0.0 && !breakdown) {
216: VecScale(eps->V[k],1.0/norm);
217: k++;
218: }
219: }
221: while (eps->its<eps->max_it) {
222: eps->its++;
223: nv = PetscMin(eps->nconv+eps->mpd,ncv);
224: DSSetDimensions(eps->ds,nv,PETSC_IGNORE,eps->nconv,0);
225:
226: /* Find group in previously computed eigenvalues */
227: EPSSubspaceFindGroup(eps->nconv,nv,eps->eigr,eps->eigi,rsd,grptol,&nogrp,&octr,&oae,&oarsd);
229: /* AV(:,idx) = OP * V(:,idx) */
230: for (i=eps->nconv;i<nv;i++) {
231: STApply(eps->OP,eps->V[i],ctx->AV[i]);
232: }
234: /* T(:,idx) = V' * AV(:,idx) */
235: DSGetArray(eps->ds,DS_MAT_A,&T);
236: for (i=eps->nconv;i<nv;i++) {
237: VecMDot(ctx->AV[i],nv,eps->V,T+i*ld);
238: }
239: DSRestoreArray(eps->ds,DS_MAT_A,&T);
240: DSSetState(eps->ds,DS_STATE_RAW);
242: /* Solve projected problem */
243: DSSolve(eps->ds,eps->eigr,eps->eigi);
244: DSSort(eps->ds,eps->eigr,eps->eigi,PETSC_NULL,PETSC_NULL,PETSC_NULL);
245:
246: /* Update vectors V(:,idx) = V * U(:,idx) */
247: DSGetArray(eps->ds,DS_MAT_Q,&U);
248: SlepcUpdateVectors(nv,ctx->AV,eps->nconv,nv,U,ld,PETSC_FALSE);
249: SlepcUpdateVectors(nv,eps->V,eps->nconv,nv,U,ld,PETSC_FALSE);
250: DSRestoreArray(eps->ds,DS_MAT_Q,&U);
251:
252: /* Convergence check */
253: DSGetArray(eps->ds,DS_MAT_A,&T);
254: EPSSubspaceResidualNorms(eps->V,ctx->AV,T,eps->nconv,nv,ld,eps->work[0],rsd);
255: DSRestoreArray(eps->ds,DS_MAT_A,&T);
257: for (i=eps->nconv;i<nv;i++) {
258: itrsdold[i] = itrsd[i];
259: itrsd[i] = its;
260: eps->errest[i] = rsd[i];
261: }
262:
263: for (;;) {
264: /* Find group in currently computed eigenvalues */
265: EPSSubspaceFindGroup(eps->nconv,nv,eps->eigr,eps->eigi,eps->errest,grptol,&ngrp,&ctr,&ae,&arsd);
266: if (ngrp!=nogrp) break;
267: if (ngrp==0) break;
268: if (PetscAbsScalar(ae-oae)>ctr*cnvtol*(itrsd[eps->nconv]-itrsdold[eps->nconv])) break;
269: if (arsd>ctr*eps->tol) break;
270: eps->nconv = eps->nconv + ngrp;
271: if (eps->nconv>=nv) break;
272: }
273:
274: EPSMonitor(eps,eps->its,eps->nconv,eps->eigr,eps->eigi,eps->errest,nv);
275: if (eps->nconv>=eps->nev) break;
276:
277: /* Compute nxtsrr (iteration of next projection step) */
278: nxtsrr = PetscMin(eps->max_it,PetscMax((PetscInt)floor(stpfac*its),init));
279:
280: if (ngrp!=nogrp || ngrp==0 || arsd>=oarsd) {
281: idsrr = nxtsrr - its;
282: } else {
283: idsrr = (PetscInt)floor(alpha+beta*(itrsdold[eps->nconv]-itrsd[eps->nconv])*log(arsd/eps->tol)/log(arsd/oarsd));
284: idsrr = PetscMax(1,idsrr);
285: }
286: nxtsrr = PetscMin(nxtsrr,its+idsrr);
288: /* Compute nxtort (iteration of next orthogonalization step) */
289: DSCond(eps->ds,&tcond);
290: idort = PetscMax(1,(PetscInt)floor(orttol/PetscMax(1,log10(tcond))));
291: nxtort = PetscMin(its+idort,nxtsrr);
293: /* V(:,idx) = AV(:,idx) */
294: for (i=eps->nconv;i<nv;i++) {
295: VecCopy(ctx->AV[i],eps->V[i]);
296: }
297: its++;
299: /* Orthogonalization loop */
300: do {
301: while (its<nxtort) {
302:
303: /* AV(:,idx) = OP * V(:,idx) */
304: for (i=eps->nconv;i<nv;i++) {
305: STApply(eps->OP,eps->V[i],ctx->AV[i]);
306: }
307:
308: /* V(:,idx) = AV(:,idx) with normalization */
309: for (i=eps->nconv;i<nv;i++) {
310: VecCopy(ctx->AV[i],eps->V[i]);
311: VecNorm(eps->V[i],NORM_INFINITY,&norm);
312: VecScale(eps->V[i],1/norm);
313: }
314: its++;
315: }
316: /* Orthonormalize vectors */
317: for (i=eps->nconv;i<nv;i++) {
318: IPOrthogonalize(eps->ip,eps->nds,eps->defl,i,PETSC_NULL,eps->V,eps->V[i],PETSC_NULL,&norm,&breakdown);
319: if (breakdown) {
320: SlepcVecSetRandom(eps->V[i],eps->rand);
321: IPOrthogonalize(eps->ip,eps->nds,eps->defl,i,PETSC_NULL,eps->V,eps->V[i],PETSC_NULL,&norm,&breakdown);
322: }
323: VecScale(eps->V[i],1/norm);
324: }
325: nxtort = PetscMin(its+idort,nxtsrr);
326: } while (its<nxtsrr);
327: }
329: PetscFree(rsd);
330: PetscFree(itrsd);
331: PetscFree(itrsdold);
333: if (eps->nconv == eps->nev) eps->reason = EPS_CONVERGED_TOL;
334: else eps->reason = EPS_DIVERGED_ITS;
335: /* truncate Schur decomposition and change the state to raw so that
336: PSVectors() computes eigenvectors from scratch */
337: DSSetDimensions(eps->ds,eps->nconv,PETSC_IGNORE,0,0);
338: DSSetState(eps->ds,DS_STATE_RAW);
339: return(0);
340: }
344: PetscErrorCode EPSReset_Subspace(EPS eps)
345: {
347: EPS_SUBSPACE *ctx = (EPS_SUBSPACE*)eps->data;
350: VecDestroyVecs(eps->ncv,&ctx->AV);
351: EPSReset_Default(eps);
352: return(0);
353: }
357: PetscErrorCode EPSDestroy_Subspace(EPS eps)
358: {
362: PetscFree(eps->data);
363: return(0);
364: }
366: EXTERN_C_BEGIN
369: PetscErrorCode EPSCreate_Subspace(EPS eps)
370: {
374: PetscNewLog(eps,EPS_SUBSPACE,&eps->data);
375: eps->ops->setup = EPSSetUp_Subspace;
376: eps->ops->destroy = EPSDestroy_Subspace;
377: eps->ops->reset = EPSReset_Subspace;
378: eps->ops->backtransform = EPSBackTransform_Default;
379: eps->ops->computevectors = EPSComputeVectors_Schur;
380: return(0);
381: }
382: EXTERN_C_END