1 /* linalg/apply_givens.c
3 * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2007 Gerard Jungman, Brian Gough
4 * Copyright (C) 2004 Joerg Wensch, modifications for LQ.
6 * This program is free software; you can redistribute it and/or modify
7 * it under the terms of the GNU General Public License as published by
8 * the Free Software Foundation; either version 3 of the License, or (at
9 * your option) any later version.
11 * This program is distributed in the hope that it will be useful, but
12 * WITHOUT ANY WARRANTY; without even the implied warranty of
13 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 * General Public License for more details.
16 * You should have received a copy of the GNU General Public License
17 * along with this program; if not, write to the Free Software
18 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
22 apply_givens_qr (size_t M, size_t N, gsl_matrix * Q, gsl_matrix * R,
23 size_t i, size_t j, double c, double s)
27 /* Apply rotation to matrix Q, Q' = Q G */
31 gsl_matrix_view Q0M = gsl_matrix_submatrix(Q,0,0,M,j+1);
32 gsl_vector_view Qi = gsl_matrix_column(&Q0M.matrix,i);
33 gsl_vector_view Qj = gsl_matrix_column(&Q0M.matrix,j);
34 gsl_blas_drot(&Qi.vector, &Qj.vector, c, -s);
37 for (k = 0; k < M; k++)
39 double qki = gsl_matrix_get (Q, k, i);
40 double qkj = gsl_matrix_get (Q, k, j);
41 gsl_matrix_set (Q, k, i, qki * c - qkj * s);
42 gsl_matrix_set (Q, k, j, qki * s + qkj * c);
46 /* Apply rotation to matrix R, R' = G^T R (note: upper triangular so
47 zero for column < row) */
52 gsl_matrix_view R0 = gsl_matrix_submatrix(R, 0, k, j+1, N-k);
53 gsl_vector_view Ri = gsl_matrix_row(&R0.matrix,i);
54 gsl_vector_view Rj = gsl_matrix_row(&R0.matrix,j);
55 gsl_blas_drot(&Ri.vector, &Rj.vector, c, -s);
58 for (k = GSL_MIN (i, j); k < N; k++)
60 double rik = gsl_matrix_get (R, i, k);
61 double rjk = gsl_matrix_get (R, j, k);
62 gsl_matrix_set (R, i, k, c * rik - s * rjk);
63 gsl_matrix_set (R, j, k, s * rik + c * rjk);
69 apply_givens_lq (size_t M, size_t N, gsl_matrix * Q, gsl_matrix * L,
70 size_t i, size_t j, double c, double s)
74 /* Apply rotation to matrix Q, Q' = G Q */
78 gsl_matrix_view Q0M = gsl_matrix_submatrix(Q,0,0,j+1,M);
79 gsl_vector_view Qi = gsl_matrix_row(&Q0M.matrix,i);
80 gsl_vector_view Qj = gsl_matrix_row(&Q0M.matrix,j);
81 gsl_blas_drot(&Qi.vector, &Qj.vector, c, -s);
84 for (k = 0; k < M; k++)
86 double qik = gsl_matrix_get (Q, i, k);
87 double qjk = gsl_matrix_get (Q, j, k);
88 gsl_matrix_set (Q, i, k, qik * c - qjk * s);
89 gsl_matrix_set (Q, j, k, qik * s + qjk * c);
93 /* Apply rotation to matrix L, L' = L G^T (note: lower triangular so
94 zero for column > row) */
99 gsl_matrix_view L0 = gsl_matrix_submatrix(L, k, 0, N-k, j+1);
100 gsl_vector_view Li = gsl_matrix_column(&L0.matrix,i);
101 gsl_vector_view Lj = gsl_matrix_column(&L0.matrix,j);
102 gsl_blas_drot(&Li.vector, &Lj.vector, c, -s);
105 for (k = GSL_MIN (i, j); k < N; k++)
107 double lki = gsl_matrix_get (L, k, i);
108 double lkj = gsl_matrix_get (L, k, j);
109 gsl_matrix_set (L, k, i, c * lki - s * lkj);
110 gsl_matrix_set (L, k, j, s * lki + c * lkj);
116 apply_givens_vec (gsl_vector * v, size_t i, size_t j, double c, double s)
118 /* Apply rotation to vector v' = G^T v */
120 double vi = gsl_vector_get (v, i);
121 double vj = gsl_vector_get (v, j);
122 gsl_vector_set (v, i, c * vi - s * vj);
123 gsl_vector_set (v, j, s * vi + c * vj);