Actual source code: krylovschur.c
1: /*
3: SLEPc eigensolver: "krylovschur"
5: Method: Krylov-Schur
7: Algorithm:
9: Single-vector Krylov-Schur method for both symmetric and non-symmetric
10: problems.
12: References:
14: [1] "Krylov-Schur Methods in SLEPc", SLEPc Technical Report STR-7,
15: available at http://www.grycap.upv.es/slepc.
17: [2] G.W. Stewart, "A Krylov-Schur Algorithm for Large Eigenproblems",
18: SIAM J. Matrix Analysis and App., 23(3), pp. 601-614, 2001.
20: Last update: Feb 2009
22: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
23: SLEPc - Scalable Library for Eigenvalue Problem Computations
24: Copyright (c) 2002-2010, Universidad Politecnica de Valencia, Spain
26: This file is part of SLEPc.
27:
28: SLEPc is free software: you can redistribute it and/or modify it under the
29: terms of version 3 of the GNU Lesser General Public License as published by
30: the Free Software Foundation.
32: SLEPc is distributed in the hope that it will be useful, but WITHOUT ANY
33: WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
34: FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for
35: more details.
37: You should have received a copy of the GNU Lesser General Public License
38: along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
39: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
40: */
42: #include private/epsimpl.h
43: #include slepcblaslapack.h
45: PetscErrorCode EPSSolve_KRYLOVSCHUR_DEFAULT(EPS);
51: PetscErrorCode EPSSetUp_KRYLOVSCHUR(EPS eps)
52: {
56: if (eps->ncv) { /* ncv set */
57: if (eps->ncv<eps->nev) SETERRQ(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->ncv>eps->nev+eps->mpd) SETERRQ(1,"The value of ncv must not be larger than nev+mpd");
68: if (!eps->max_it) eps->max_it = PetscMax(100,2*eps->n/eps->ncv);
69: if (!eps->which) eps->which = EPS_LARGEST_MAGNITUDE;
70: if (eps->ishermitian && (eps->which==EPS_LARGEST_IMAGINARY || eps->which==EPS_SMALLEST_IMAGINARY))
71: SETERRQ(1,"Wrong value of eps->which");
73: if (!eps->extraction) {
74: EPSSetExtraction(eps,EPS_RITZ);
75: } else if (eps->extraction!=EPS_RITZ && eps->extraction!=EPS_HARMONIC) {
76: SETERRQ(PETSC_ERR_SUP,"Unsupported extraction type");
77: }
79: EPSAllocateSolution(eps);
80: PetscFree(eps->T);
81: if (!eps->ishermitian || eps->extraction==EPS_HARMONIC) {
82: PetscMalloc(eps->ncv*eps->ncv*sizeof(PetscScalar),&eps->T);
83: }
84: EPSDefaultGetWork(eps,1);
86: /* dispatch solve method */
87: if (eps->leftvecs) SETERRQ(PETSC_ERR_SUP,"Left vectors not supported in this solver");
88: if (eps->ishermitian) {
89: switch (eps->extraction) {
90: case EPS_RITZ: eps->ops->solve = EPSSolve_KRYLOVSCHUR_SYMM; break;
91: case EPS_HARMONIC: eps->ops->solve = EPSSolve_KRYLOVSCHUR_HARMONIC; break;
92: default: SETERRQ(PETSC_ERR_SUP,"Unsupported extraction type");
93: }
94: } else {
95: switch (eps->extraction) {
96: case EPS_RITZ: eps->ops->solve = EPSSolve_KRYLOVSCHUR_DEFAULT; break;
97: case EPS_HARMONIC: eps->ops->solve = EPSSolve_KRYLOVSCHUR_HARMONIC; break;
98: default: SETERRQ(PETSC_ERR_SUP,"Unsupported extraction type");
99: }
100: }
101: return(0);
102: }
106: /*
107: EPSProjectedKSNonsym - Solves the projected eigenproblem in the Krylov-Schur
108: method (non-symmetric case).
110: On input:
111: l is the number of vectors kept in previous restart (0 means first restart)
112: S is the projected matrix (leading dimension is lds)
114: On output:
115: S has (real) Schur form with diagonal blocks sorted appropriately
116: Q contains the corresponding Schur vectors (order n, leading dimension n)
117: */
118: PetscErrorCode EPSProjectedKSNonsym(EPS eps,PetscInt l,PetscScalar *S,PetscInt lds,PetscScalar *Q,PetscInt n)
119: {
121: PetscInt i;
124: if (l==0) {
125: PetscMemzero(Q,n*n*sizeof(PetscScalar));
126: for (i=0;i<n;i++)
127: Q[i*(n+1)] = 1.0;
128: } else {
129: /* Reduce S to Hessenberg form, S <- Q S Q' */
130: EPSDenseHessenberg(n,eps->nconv,S,lds,Q);
131: }
132: /* Reduce S to (quasi-)triangular form, S <- Q S Q' */
133: EPSDenseSchur(n,eps->nconv,S,lds,Q,eps->eigr,eps->eigi);
134: /* Sort the remaining columns of the Schur form */
135: EPSSortDenseSchur(eps,n,eps->nconv,S,lds,Q,eps->eigr,eps->eigi);
136: return(0);
137: }
141: PetscErrorCode EPSSolve_KRYLOVSCHUR_DEFAULT(EPS eps)
142: {
144: PetscInt i,k,l,lwork,nv;
145: Vec u=eps->work[0];
146: PetscScalar *S=eps->T,*Q,*work;
147: PetscReal beta;
148: PetscTruth breakdown;
151: PetscMemzero(S,eps->ncv*eps->ncv*sizeof(PetscScalar));
152: PetscMalloc(eps->ncv*eps->ncv*sizeof(PetscScalar),&Q);
153: lwork = 7*eps->ncv;
154: PetscMalloc(lwork*sizeof(PetscScalar),&work);
156: /* Get the starting Arnoldi vector */
157: EPSGetStartVector(eps,0,eps->V[0],PETSC_NULL);
158: l = 0;
159:
160: /* Restart loop */
161: while (eps->reason == EPS_CONVERGED_ITERATING) {
162: eps->its++;
164: /* Compute an nv-step Arnoldi factorization */
165: nv = PetscMin(eps->nconv+eps->mpd,eps->ncv);
166: EPSBasicArnoldi(eps,PETSC_FALSE,S,eps->ncv,eps->V,eps->nconv+l,&nv,u,&beta,&breakdown);
167: VecScale(u,1.0/beta);
169: /* Solve projected problem */
170: EPSProjectedKSNonsym(eps,l,S,eps->ncv,Q,nv);
172: /* Check convergence */
173: EPSKrylovConvergence(eps,PETSC_FALSE,eps->nconv,nv-eps->nconv,S,eps->ncv,Q,eps->V,nv,beta,1.0,&k,work);
174: if (eps->its >= eps->max_it) eps->reason = EPS_DIVERGED_ITS;
175: if (k >= eps->nev) eps->reason = EPS_CONVERGED_TOL;
176:
177: /* Update l */
178: if (eps->reason != EPS_CONVERGED_ITERATING || breakdown) l = 0;
179: else {
180: l = (nv-k)/2;
181: #if !defined(PETSC_USE_COMPLEX)
182: if (S[(k+l-1)*(eps->ncv+1)+1] != 0.0) {
183: if (k+l<nv-1) l = l+1;
184: else l = l-1;
185: }
186: #endif
187: }
189: if (eps->reason == EPS_CONVERGED_ITERATING) {
190: if (breakdown) {
191: /* Start a new Arnoldi factorization */
192: PetscInfo2(eps,"Breakdown in Krylov-Schur method (it=%i norm=%g)\n",eps->its,beta);
193: EPSGetStartVector(eps,k,eps->V[k],&breakdown);
194: if (breakdown) {
195: eps->reason = EPS_DIVERGED_BREAKDOWN;
196: PetscInfo(eps,"Unable to generate more start vectors\n");
197: }
198: } else {
199: /* Prepare the Rayleigh quotient for restart */
200: for (i=k;i<k+l;i++) {
201: S[i*eps->ncv+k+l] = Q[(i+1)*nv-1]*beta;
202: }
203: }
204: }
205: /* Update the corresponding vectors V(:,idx) = V*Q(:,idx) */
206: SlepcUpdateVectors(nv,eps->V,eps->nconv,k+l,Q,nv,PETSC_FALSE);
208: if (eps->reason == EPS_CONVERGED_ITERATING && !breakdown) {
209: VecCopy(u,eps->V[k+l]);
210: }
211: eps->nconv = k;
213: EPSMonitor(eps,eps->its,eps->nconv,eps->eigr,eps->eigi,eps->errest,nv);
214:
215: }
217: PetscFree(Q);
218: PetscFree(work);
219: return(0);
220: }
225: PetscErrorCode EPSCreate_KRYLOVSCHUR(EPS eps)
226: {
228: eps->data = PETSC_NULL;
229: eps->ops->setup = EPSSetUp_KRYLOVSCHUR;
230: eps->ops->setfromoptions = PETSC_NULL;
231: eps->ops->destroy = EPSDestroy_Default;
232: eps->ops->view = PETSC_NULL;
233: eps->ops->backtransform = EPSBackTransform_Default;
234: eps->ops->computevectors = EPSComputeVectors_Schur;
235: return(0);
236: }