Actual source code: krylov.c
1: /*
2: Common subroutines for all Krylov-type solvers.
4: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
5: SLEPc - Scalable Library for Eigenvalue Problem Computations
6: Copyright (c) 2002-2010, Universidad Politecnica de Valencia, Spain
8: This file is part of SLEPc.
9:
10: SLEPc is free software: you can redistribute it and/or modify it under the
11: terms of version 3 of the GNU Lesser General Public License as published by
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15: WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
16: FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for
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22: */
24: #include private/epsimpl.h
25: #include private/slepcimpl.h
26: #include slepcblaslapack.h
30: /*
31: EPSBasicArnoldi - Computes an m-step Arnoldi factorization. The first k
32: columns are assumed to be locked and therefore they are not modified. On
33: exit, the following relation is satisfied:
35: OP * V - V * H = f * e_m^T
37: where the columns of V are the Arnoldi vectors (which are B-orthonormal),
38: H is an upper Hessenberg matrix, f is the residual vector and e_m is
39: the m-th vector of the canonical basis. The vector f is B-orthogonal to
40: the columns of V. On exit, beta contains the B-norm of f and the next
41: Arnoldi vector can be computed as v_{m+1} = f / beta.
42: */
43: PetscErrorCode EPSBasicArnoldi(EPS eps,PetscTruth trans,PetscScalar *H,PetscInt ldh,Vec *V,PetscInt k,PetscInt *M,Vec f,PetscReal *beta,PetscTruth *breakdown)
44: {
46: PetscInt j,m = *M;
47: PetscReal norm;
50:
51: for (j=k;j<m-1;j++) {
52: if (trans) { STApplyTranspose(eps->OP,V[j],V[j+1]); }
53: else { STApply(eps->OP,V[j],V[j+1]); }
54: IPOrthogonalize(eps->ip,eps->nds,eps->DS,j+1,PETSC_NULL,V,V[j+1],H+ldh*j,&norm,breakdown);
55: H[j+1+ldh*j] = norm;
56: if (*breakdown) {
57: *M = j+1;
58: *beta = norm;
59: return(0);
60: } else {
61: VecScale(V[j+1],1/norm);
62: }
63: }
64: if (trans) { STApplyTranspose(eps->OP,V[m-1],f); }
65: else { STApply(eps->OP,V[m-1],f); }
66: IPOrthogonalize(eps->ip,eps->nds,eps->DS,m,PETSC_NULL,V,f,H+ldh*(m-1),beta,PETSC_NULL);
67:
68: return(0);
69: }
73: /*
74: EPSKrylovConvergence - Implements the loop that checks for convergence
75: in Krylov methods.
77: Input Parameters:
78: eps - the eigensolver; some error estimates are updated in eps->errest
79: issym - whether the projected problem is symmetric or not
80: kini - initial value of k (the loop variable)
81: nits - number of iterations of the loop
82: S - Schur form of projected matrix (not referenced if issym)
83: lds - leading dimension of S
84: Q - Schur vectors of projected matrix (eigenvectors if issym)
85: V - set of basis vectors (used only if trueresidual is activated)
86: nv - number of vectors to process (dimension of Q, columns of V)
87: beta - norm of f (the residual vector of the Arnoldi/Lanczos factorization)
88: corrf - correction factor for residual estimates (only in harmonic KS)
90: Output Parameters:
91: kout - the first index where the convergence test failed
93: Workspace:
94: work is workspace to store 5*nv scalars, nv booleans and nv reals (only if !issym)
95: */
96: PetscErrorCode EPSKrylovConvergence(EPS eps,PetscTruth issym,PetscInt kini,PetscInt nits,PetscScalar *S,PetscInt lds,PetscScalar *Q,Vec *V,PetscInt nv,PetscReal beta,PetscReal corrf,PetscInt *kout,PetscScalar *work)
97: {
99: PetscInt k,marker;
100: PetscScalar re,im,*Z = work,*work2 = work;
101: PetscReal resnorm;
102: PetscTruth iscomplex,isshift;
105: if (!issym) { Z = work; work2 = work+2*nv; }
106: PetscTypeCompare((PetscObject)eps->OP,STSHIFT,&isshift);
107: marker = -1;
108: for (k=kini;k<kini+nits;k++) {
109: /* eigenvalue */
110: re = eps->eigr[k];
111: im = eps->eigi[k];
112: if (eps->trueres || isshift) {
113: STBackTransform(eps->OP,1,&re,&im);
114: }
115: iscomplex = PETSC_FALSE;
116: if (!issym && k<nv-1 && S[k+1+k*lds] != 0.0) iscomplex = PETSC_TRUE;
117: /* residual norm */
118: if (issym) {
119: resnorm = beta*PetscAbsScalar(Q[(k-kini+1)*nv-1]);
120: } else {
121: DenseSelectedEvec(S,lds,Q,Z,k,iscomplex,nv,work2);
122: if (iscomplex) resnorm = beta*SlepcAbsEigenvalue(Z[nv-1],Z[2*nv-1]);
123: else resnorm = beta*PetscAbsScalar(Z[nv-1]);
124: }
125: if (eps->trueres) {
126: if (issym) Z = Q+(k-kini)*nv;
127: EPSComputeTrueResidual(eps,re,im,Z,V,nv,&resnorm);
128: }
129: else resnorm *= corrf;
130: /* error estimate */
131: (*eps->conv_func)(eps,re,im,resnorm,&eps->errest[k],eps->conv_ctx);
132: if (marker==-1 && eps->errest[k] >= eps->tol) marker = k;
133: if (iscomplex) { eps->errest[k+1] = eps->errest[k]; k++; }
134: if (marker!=-1 && !eps->trackall) break;
135: }
136: if (marker!=-1) k = marker;
137: *kout = k;
139: return(0);
140: }
144: /*
145: EPSFullLanczos - Computes an m-step Lanczos factorization with full
146: reorthogonalization. At each Lanczos step, the corresponding Lanczos
147: vector is orthogonalized with respect to all previous Lanczos vectors.
148: This is equivalent to computing an m-step Arnoldi factorization and
149: exploting symmetry of the operator.
151: The first k columns are assumed to be locked and therefore they are
152: not modified. On exit, the following relation is satisfied:
154: OP * V - V * T = f * e_m^T
156: where the columns of V are the Lanczos vectors (which are B-orthonormal),
157: T is a real symmetric tridiagonal matrix, f is the residual vector and e_m
158: is the m-th vector of the canonical basis. The tridiagonal is stored as
159: two arrays: alpha contains the diagonal elements, beta the off-diagonal.
160: The vector f is B-orthogonal to the columns of V. On exit, the last element
161: of beta contains the B-norm of f and the next Lanczos vector can be
162: computed as v_{m+1} = f / beta(end).
164: */
165: PetscErrorCode EPSFullLanczos(EPS eps,PetscReal *alpha,PetscReal *beta,Vec *V,PetscInt k,PetscInt *M,Vec f,PetscTruth *breakdown)
166: {
168: PetscInt j,m = *M;
169: PetscReal norm;
170: PetscScalar *hwork,lhwork[100];
173: if (m > 100) {
174: PetscMalloc((eps->nds+m)*sizeof(PetscScalar),&hwork);
175: } else {
176: hwork = lhwork;
177: }
179: for (j=k;j<m-1;j++) {
180: STApply(eps->OP,V[j],V[j+1]);
181: IPOrthogonalize(eps->ip,eps->nds,eps->DS,j+1,PETSC_NULL,V,V[j+1],hwork,&norm,breakdown);
182: alpha[j-k] = PetscRealPart(hwork[j]);
183: beta[j-k] = norm;
184: if (*breakdown) {
185: *M = j+1;
186: if (m > 100) {
187: PetscFree(hwork);
188: }
189: return(0);
190: } else {
191: VecScale(V[j+1],1.0/norm);
192: }
193: }
194: STApply(eps->OP,V[m-1],f);
195: IPOrthogonalize(eps->ip,eps->nds,eps->DS,m,PETSC_NULL,V,f,hwork,&norm,PETSC_NULL);
196: alpha[m-1-k] = PetscRealPart(hwork[m-1]);
197: beta[m-1-k] = norm;
198:
199: if (m > 100) {
200: PetscFree(hwork);
201: }
202: return(0);
203: }