-
Notifications
You must be signed in to change notification settings - Fork 0
/
test_gaussian.c
146 lines (122 loc) · 3.88 KB
/
test_gaussian.c
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
#define gaussian_N 15
#define gaussian_P 3
static double gaussian_x0[gaussian_P] = { 0.4, 1.0, 0.0 };
static double gaussian_epsrel = 1.0e-10;
static double gaussian_J[gaussian_N * gaussian_P];
static double gaussian_Y[gaussian_N] = {
0.0009, 0.0044, 0.0175, 0.0540, 0.1295, 0.2420, 0.3521, 0.3989,
0.3521, 0.2420, 0.1295, 0.0540, 0.0175, 0.0044, 0.0009
};
static void
gaussian_checksol(const double x[], const double sumsq,
const double epsrel, const char *sname,
const char *pname)
{
size_t i;
const double sumsq_exact = 1.12793276961871985e-08;
const double gaussian_x[gaussian_P] = { 0.398956137838762825,
1.00001908448786647,
0.0 };
gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
sname, pname);
for (i = 0; i < gaussian_P; ++i)
{
gsl_test_rel(x[i], gaussian_x[i], epsrel, "%s/%s i=%zu",
sname, pname, i);
}
}
static int
gaussian_f (const gsl_vector * x, void *params, gsl_vector * f)
{
double x1 = gsl_vector_get(x, 0);
double x2 = gsl_vector_get(x, 1);
double x3 = gsl_vector_get(x, 2);
size_t i;
for (i = 0; i < gaussian_N; ++i)
{
double ti = (7.0 - i) / 2.0;
double yi = gaussian_Y[i];
double term = ti - x3;
double fi = x1 * exp(-x2*term*term/2.0) - yi;
gsl_vector_set(f, i, fi);
}
(void)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static int
gaussian_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
const gsl_vector * u, void * params, gsl_vector * v,
gsl_matrix * JTJ)
{
gsl_matrix_view J = gsl_matrix_view_array(gaussian_J, gaussian_N, gaussian_P);
double x1 = gsl_vector_get(x, 0);
double x2 = gsl_vector_get(x, 1);
double x3 = gsl_vector_get(x, 2);
size_t i;
for (i = 0; i < gaussian_N; ++i)
{
double ti = (7.0 - i) / 2.0;
double term1 = ti - x3;
double term2 = exp(-x2*term1*term1/2.0);
gsl_matrix_set(&J.matrix, i, 0, term2);
gsl_matrix_set(&J.matrix, i, 1, -0.5*x1*term2*term1*term1);
gsl_matrix_set(&J.matrix, i, 2, x1*x2*term1*term2);
}
if (v)
gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
if (JTJ)
gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
(void)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static int
gaussian_fvv (const gsl_vector * x, const gsl_vector * v,
void *params, gsl_vector * fvv)
{
double x1 = gsl_vector_get(x, 0);
double x2 = gsl_vector_get(x, 1);
double x3 = gsl_vector_get(x, 2);
double v1 = gsl_vector_get(v, 0);
double v2 = gsl_vector_get(v, 1);
double v3 = gsl_vector_get(v, 2);
size_t i;
for (i = 0; i < gaussian_N; ++i)
{
double ti = (7.0 - i) / 2.0;
double term1 = ti - x3;
double term2 = exp(-x2*term1*term1/2.0);
gsl_vector_set(fvv, i, 0.25 * term2 *
(ti*ti*ti*ti*v2*v2*x1 -
4*ti*ti*ti*v2*x1*(v3*x2 + v2*x3) +
v2*x3*x3*(v2*x1*x3*x3 - 4*v1) +
4*v3*v3*x1*x2*(x2*x3*x3 - 1.0) +
4*v3*x3*(-2*v1*x2 + v2*x1*(x2*x3*x3 - 2.0)) +
ti*ti*(4*v3*v3*x1*x2*x2 + 2*v2*(-2*v1 + 3*x1*x3*(2*v3*x2 + v2*x3))) -
4*ti*(v2*v2*x1*x3*x3*x3 + 2*v3*x2*(-v1 + v3*x1*x2*x3) +
v2*(-2*v1*x3 + v3*x1*(-2.0 + 3*x2*x3*x3)))));
}
(void)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static gsl_multilarge_nlinear_fdf gaussian_func =
{
gaussian_f,
gaussian_df,
gaussian_fvv,
gaussian_N,
gaussian_P,
NULL,
0,
0,
0,
0
};
static test_fdf_problem gaussian_problem =
{
"gaussian",
gaussian_x0,
NULL,
&gaussian_epsrel,
&gaussian_checksol,
&gaussian_func
};