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
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
|
/*
* vim: ts=4 sw=4 et tw=0 wm=0
*
* libcola - A library providing force-directed network layout using the
* stress-majorization method subject to separation constraints.
*
* Copyright (C) 2006-2008 Monash University
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This library 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
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library in the file LICENSE; if not,
* write to the Free Software Foundation, Inc., 59 Temple Place,
* Suite 330, Boston, MA 02111-1307 USA
*
*/
#include <stdio.h>
#include <cassert>
#include <libcola/conjugate_gradient.h>
#include <gsl/gsl_linalg.h>
using std::valarray;
static valarray<double>
outer_prod(valarray<double> x, valarray<double> y) {
valarray<double> result(x.size()*y.size());
for(int j = 0; j < x.size(); j++) {
for(int i = 0; i < y.size(); i++) {
result[j*y.size() + i] = x[j]*y[i];
}
}
return result;
}
static double
uniform() {
return double(rand())/ RAND_MAX;
}
static void
matrix_times_vector(valarray<double> const &matrix, /* m * n */
valarray<double> const &vec, /* n */
valarray<double> &result) /* m */
{
unsigned n = vec.size();
unsigned m = result.size();
assert(m*n == matrix.size());
const double* mp = &matrix[0];
for (unsigned i = 0; i < m; i++) {
double res = 0;
for (unsigned j = 0; j < n; j++)
res += *mp++ * vec[j];
result[i] = res;
}
}
static double
Linfty(valarray<double> const &vec) {
return std::max(vec.max(), -vec.min());
}
int
main (void)
{
double tolerance = 1e-6;
for(int iters = 0; iters < 100; iters++) {
const unsigned N = unsigned(uniform()*40) + 1;
double A_data[N*N];
printf("%ux%u matrix\n", N,N);
for(int r = 0; r < N; r++) {
for(int c = 0; c <= r; c++) {
A_data[r*N + c] = A_data[c*N + r] = fabs(uniform());
}
}
double * A_c[N];
for(int i = 0; i < N; i++)
A_c[i] = &A_data[N*i];
double b_data[N];
for(int i = 0; i < N; i++)
b_data[i] = uniform()*3;
std::valarray<double> b(b_data, N), xx(0.0, N);
std::valarray<double> A(A_data, N*N);
conjugate_gradient(A, xx, b, N, tolerance, 2*N);
gsl_matrix_view m
= gsl_matrix_view_array (A_data, N, N);
gsl_vector_view bgsl
= gsl_vector_view_array (b_data, N);
gsl_vector *xgsl = gsl_vector_alloc (N);
int s;
gsl_permutation * p = gsl_permutation_alloc (N);
gsl_linalg_LU_decomp (&m.matrix, p, &s);
gsl_linalg_LU_solve (&m.matrix, p, &bgsl.vector, xgsl);
std::valarray<double> gsl_xx(0.0, N);
for(unsigned i = 0; i < xx.size(); i++) {
gsl_xx[i] = gsl_vector_get(xgsl, i);
}
double err = Linfty(xx - gsl_xx);
printf ("|xx-nxgsl|_infty = %g\n", err);
if(err > tolerance) {
#if 0 //dubious value
for(int r = 0; r < N; r++) {
for(int c = 0; c < N; c++) {
printf("%g ", A_data[r*N + c]);
}
printf("\n");
}
#endif
printf("\nx njh-cg = \n");
for(unsigned i = 0; i < xx.size(); i++)
printf("%g ", xx[i]);
printf("\nxgsl = ");
for(unsigned i = 0; i < xx.size(); i++)
printf("%g ", gsl_xx[i]);
printf("\n");
valarray<double> result(0.0,N);
matrix_times_vector(A, xx, result);
result -= b;
printf("\nA xx -b = ");
for(unsigned i = 0; i < xx.size(); i++)
printf("%g ", result[i]);
printf("\n");
matrix_times_vector(A, gsl_xx, result);
result -= b;
printf("\nA gsl_xx -b = ");
for(unsigned i = 0; i < xx.size(); i++)
printf("%g ", result[i]);
printf("\n");
printf("FAILED!!!!!!!!!!!!!!!!!!!!!!!!\n");
exit(1);
}
}
return 0;
}
/*
Local Variables:
mode:c++
c-file-style:"stroustrup"
c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
indent-tabs-mode:nil
fill-column:99
End:
*/
// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=4:softtabstop=4
|
