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
|
/* linalg/test_ql.c
*
* Copyright (C) 2019 Patrick Alken
*
* 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 3 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.
*/
#include <config.h>
#include <stdlib.h>
#include <gsl/gsl_test.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_ieee_utils.h>
#include <gsl/gsl_permute_vector.h>
#include <gsl/gsl_blas.h>
#include <gsl/gsl_linalg.h>
#include <gsl/gsl_rng.h>
#include <gsl/gsl_permutation.h>
static int
test_QL_decomp_eps(const gsl_matrix * m, const double eps, const char * desc)
{
int s = 0;
const size_t M = m->size1;
const size_t N = m->size2;
size_t i, j;
gsl_matrix * QL = gsl_matrix_alloc(M, N);
gsl_vector * tau = gsl_vector_alloc(N);
gsl_matrix * A = gsl_matrix_alloc(M, N);
gsl_matrix * L = gsl_matrix_alloc(M, N);
gsl_matrix * Q = gsl_matrix_alloc(M, M);
gsl_matrix_memcpy(QL, m);
s += gsl_linalg_QL_decomp(QL, tau);
s += gsl_linalg_QL_unpack(QL, tau, Q, L);
/* compute A = Q L */
gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, 1.0, Q, L, 0.0, A);
for (i = 0; i < M; i++)
{
for (j = 0; j < N; j++)
{
double aij = gsl_matrix_get(A, i, j);
double mij = gsl_matrix_get(m, i, j);
gsl_test_rel(aij, mij, eps, "%s (%3lu,%3lu)[%lu,%lu]: %22.18g %22.18g\n",
desc, M, N, i,j, aij, mij);
}
}
gsl_matrix_free(QL);
gsl_vector_free(tau);
gsl_matrix_free(A);
gsl_matrix_free(Q);
gsl_matrix_free(L);
return s;
}
static int
test_QL_decomp(gsl_rng * r)
{
int s = 0;
size_t M, N;
for (M = 1; M <= 30; ++M)
{
for (N = 1; N <= M; ++N)
{
gsl_matrix * A = gsl_matrix_alloc(M, N);
create_random_matrix(A, r);
s += test_QL_decomp_eps(A, 1.0e5 * GSL_MAX(M, N) * GSL_DBL_EPSILON, "QL_decomp random");
gsl_matrix_free(A);
}
}
s += test_QL_decomp_eps(m53, 1.0e2 * GSL_DBL_EPSILON, "QL_decomp m(5,3)");
s += test_QL_decomp_eps(hilb2, 1.0e2 * GSL_DBL_EPSILON, "QL_decomp hilbert(2)");
s += test_QL_decomp_eps(hilb3, 1.0e2 * GSL_DBL_EPSILON, "QL_decomp hilbert(3)");
s += test_QL_decomp_eps(hilb4, 1.0e2 * GSL_DBL_EPSILON, "QL_decomp hilbert(4)");
s += test_QL_decomp_eps(hilb12, 1.0e2 * GSL_DBL_EPSILON, "QL_decomp hilbert(12)");
s += test_QL_decomp_eps(vander2, 1.0e1 * GSL_DBL_EPSILON, "QL_decomp vander(2)");
s += test_QL_decomp_eps(vander3, 1.0e1 * GSL_DBL_EPSILON, "QL_decomp vander(3)");
s += test_QL_decomp_eps(vander4, 1.0e2 * GSL_DBL_EPSILON, "QL_decomp vander(4)");
return s;
}
|
