1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
|
/* linalg/apply_givens.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001 Gerard Jungman, Brian Gough
* Copyright (C) 2004 Joerg Wensch, modifications for LQ.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or (at
* your option) any later version.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
inline static void
apply_givens_qr (size_t M, size_t N, gsl_matrix * Q, gsl_matrix * R,
size_t i, size_t j, double c, double s)
{
size_t k;
/* Apply rotation to matrix Q, Q' = Q G */
#if USE_BLAS
{
gsl_matrix_view Q0M = gsl_matrix_submatrix(Q,0,0,M,j+1);
gsl_vector_view Qi = gsl_matrix_column(&Q0M.matrix,i);
gsl_vector_view Qj = gsl_matrix_column(&Q0M.matrix,j);
gsl_blas_drot(&Qi.vector, &Qj.vector, c, -s);
}
#else
for (k = 0; k < M; k++)
{
double qki = gsl_matrix_get (Q, k, i);
double qkj = gsl_matrix_get (Q, k, j);
gsl_matrix_set (Q, k, i, qki * c - qkj * s);
gsl_matrix_set (Q, k, j, qki * s + qkj * c);
}
#endif
/* Apply rotation to matrix R, R' = G^T R (note: upper triangular so
zero for column < row) */
#if USE_BLAS
{
k = GSL_MIN(i,j);
gsl_matrix_view R0 = gsl_matrix_submatrix(R, 0, k, j+1, N-k);
gsl_vector_view Ri = gsl_matrix_row(&R0.matrix,i);
gsl_vector_view Rj = gsl_matrix_row(&R0.matrix,j);
gsl_blas_drot(&Ri.vector, &Rj.vector, c, -s);
}
#else
for (k = GSL_MIN (i, j); k < N; k++)
{
double rik = gsl_matrix_get (R, i, k);
double rjk = gsl_matrix_get (R, j, k);
gsl_matrix_set (R, i, k, c * rik - s * rjk);
gsl_matrix_set (R, j, k, s * rik + c * rjk);
}
#endif
}
inline static void
apply_givens_lq (size_t M, size_t N, gsl_matrix * Q, gsl_matrix * L,
size_t i, size_t j, double c, double s)
{
size_t k;
/* Apply rotation to matrix Q, Q' = G Q */
#if USE_BLAS
{
gsl_matrix_view Q0M = gsl_matrix_submatrix(Q,0,0,j+1,M);
gsl_vector_view Qi = gsl_matrix_row(&Q0M.matrix,i);
gsl_vector_view Qj = gsl_matrix_row(&Q0M.matrix,j);
gsl_blas_drot(&Qi.vector, &Qj.vector, c, -s);
}
#else
for (k = 0; k < M; k++)
{
double qik = gsl_matrix_get (Q, i, k);
double qjk = gsl_matrix_get (Q, j, k);
gsl_matrix_set (Q, i, k, qik * c - qjk * s);
gsl_matrix_set (Q, j, k, qik * s + qjk * c);
}
#endif
/* Apply rotation to matrix L, L' = L G^T (note: lower triangular so
zero for column > row) */
#if USE_BLAS
{
k = GSL_MIN(i,j);
gsl_matrix_view L0 = gsl_matrix_submatrix(L, k, 0, N-k, j+1);
gsl_vector_view Li = gsl_matrix_column(&L0.matrix,i);
gsl_vector_view Lj = gsl_matrix_column(&L0.matrix,j);
gsl_blas_drot(&Li.vector, &Lj.vector, c, -s);
}
#else
for (k = GSL_MIN (i, j); k < N; k++)
{
double lki = gsl_matrix_get (L, k, i);
double lkj = gsl_matrix_get (L, k, j);
gsl_matrix_set (L, k, i, c * lki - s * lkj);
gsl_matrix_set (L, k, j, s * lki + c * lkj);
}
#endif
}
inline static void
apply_givens_vec (gsl_vector * v, size_t i, size_t j, double c, double s)
{
/* Apply rotation to vector v' = G^T v */
double vi = gsl_vector_get (v, i);
double vj = gsl_vector_get (v, j);
gsl_vector_set (v, i, c * vi - s * vj);
gsl_vector_set (v, j, s * vi + c * vj);
}
|
