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
|
#define biggs_N 6 /* >= p */
#define biggs_P 6
/* dogleg method has trouble converging from recommended starting point,
* so we use an x0 which is a little closer to the true solution */
/*static double biggs_x0[biggs_P] = { 1.0, 2.0, 1.0, 1.0, 1.0, 1.0 };*/
static double biggs_x0[biggs_P] = { 1.0, 8.0, 1.0, 2.0, 3.0, 2.0 };
static double biggs_epsrel = 1.0e-9;
static double biggs_J[biggs_N * biggs_P];
static void
biggs_checksol(const double x[], const double sumsq,
const double epsrel, const char *sname,
const char *pname)
{
#if 0
const double sumsq_exact = 0.0;
#endif
const double biggs_x[biggs_P] = { 1.0, 10.0, 1.0, 5.0, 4.0, 3.0 };
const double norm_exact = 12.3288280059380;
gsl_vector_const_view v = gsl_vector_const_view_array(biggs_x, biggs_P);
double norm = gsl_blas_dnrm2(&v.vector);
#if 0
/* some solvers have difficulty reaching sumsq = 0 to sufficient
* decimal places */
gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
sname, pname);
#endif
/*
* the solution vector is not unique due to permutations, so test
* the norm instead of individual elements
*/
gsl_test_rel(norm, norm_exact, epsrel, "%s/%s norm",
sname, pname);
(void)x; /* avoid unused parameter warning */
(void)sumsq; /* avoid unused parameter warning */
}
static int
biggs_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);
double x4 = gsl_vector_get(x, 3);
double x5 = gsl_vector_get(x, 4);
double x6 = gsl_vector_get(x, 5);
size_t i;
for (i = 0; i < biggs_N; ++i)
{
double ti = 0.1 * (i + 1.0);
double yi = exp(-ti) - 5*exp(-10*ti) + 3*exp(-4*ti);
double fi = x3*exp(-ti*x1) - x4*exp(-ti*x2) + x6*exp(-ti*x5) - yi;
gsl_vector_set(f, i, fi);
}
(void)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static int
biggs_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(biggs_J, biggs_N, biggs_P);
double x1 = gsl_vector_get(x, 0);
double x2 = gsl_vector_get(x, 1);
double x3 = gsl_vector_get(x, 2);
double x4 = gsl_vector_get(x, 3);
double x5 = gsl_vector_get(x, 4);
double x6 = gsl_vector_get(x, 5);
size_t i;
for (i = 0; i < biggs_N; ++i)
{
double ti = 0.1 * (i + 1.0);
gsl_matrix_set(&J.matrix, i, 0, -ti*x3*exp(-ti*x1));
gsl_matrix_set(&J.matrix, i, 1, ti*x4*exp(-ti*x2));
gsl_matrix_set(&J.matrix, i, 2, exp(-ti*x1));
gsl_matrix_set(&J.matrix, i, 3, -exp(-ti*x2));
gsl_matrix_set(&J.matrix, i, 4, -ti*x6*exp(-ti*x5));
gsl_matrix_set(&J.matrix, i, 5, exp(-ti*x5));
}
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
biggs_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 x4 = gsl_vector_get(x, 3);
double x5 = gsl_vector_get(x, 4);
double x6 = gsl_vector_get(x, 5);
double v1 = gsl_vector_get(v, 0);
double v2 = gsl_vector_get(v, 1);
double v3 = gsl_vector_get(v, 2);
double v4 = gsl_vector_get(v, 3);
double v5 = gsl_vector_get(v, 4);
double v6 = gsl_vector_get(v, 5);
size_t i;
for (i = 0; i < biggs_N; ++i)
{
double ti = 0.1 * (i + 1.0);
double term1 = exp(-ti * x1);
double term2 = exp(-ti * x2);
double term3 = exp(-ti * x5);
gsl_vector_set(fvv, i, ti * term1 * term2 * term3 *
(v1/(term2*term3)*(-2*v3 + ti*v1*x3) -
v2/(term1*term3)*(-2*v4 + ti*v2*x4) +
v5/(term1*term2)*(-2*v6 + ti*v5*x6)));
}
(void)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static gsl_multilarge_nlinear_fdf biggs_func =
{
biggs_f,
biggs_df,
biggs_fvv,
biggs_N,
biggs_P,
NULL,
0,
0,
0,
0
};
static test_fdf_problem biggs_problem =
{
"biggs",
biggs_x0,
NULL,
&biggs_epsrel,
&biggs_checksol,
&biggs_func
};
|
