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
|
#define wnlin_N 40
#define wnlin_P 3
static double wnlin_x0[wnlin_P] = { 1.0, 0.9, 0.0 };
static double wnlin_epsrel = 1.0e-8;
static double wnlin_J[wnlin_N * wnlin_P];
/* data */
static double wnlin_Y[wnlin_N] = {
6.08035e+00, 5.47552e+00, 5.94654e+00, 5.04920e+00, 4.78568e+00,
3.51748e+00, 2.84671e+00, 3.24634e+00, 3.23395e+00, 3.30385e+00,
2.83439e+00, 2.31891e+00, 2.33858e+00, 2.40559e+00, 2.41856e+00,
1.99966e+00, 1.88127e+00, 1.91477e+00, 1.70415e+00, 1.60316e+00,
1.77937e+00, 1.55302e+00, 1.50903e+00, 1.36364e+00, 1.36873e+00,
1.41954e+00, 1.37778e+00, 1.23573e+00, 1.28524e+00, 1.46327e+00,
1.22315e+00, 1.19330e+00, 1.18717e+00, 8.83172e-01, 1.23424e+00,
1.14683e+00, 1.11091e+00, 1.20396e+00, 1.28722e+00, 1.05801e+00
};
/* weights */
static double wnlin_W[wnlin_N] = {
2.77778e+00, 3.27690e+00, 3.85426e+00, 4.51906e+00, 5.28083e+00,
6.14919e+00, 7.13370e+00, 8.24349e+00, 9.48703e+00, 1.08717e+01,
1.24036e+01, 1.40869e+01, 1.59238e+01, 1.79142e+01, 2.00553e+01,
2.23415e+01, 2.47646e+01, 2.73137e+01, 2.99753e+01, 3.27337e+01,
3.55714e+01, 3.84696e+01, 4.14085e+01, 4.43678e+01, 4.73278e+01,
5.02690e+01, 5.31731e+01, 5.60234e+01, 5.88046e+01, 6.15036e+01,
6.41092e+01, 6.66121e+01, 6.90054e+01, 7.12839e+01, 7.34442e+01,
7.54848e+01, 7.74053e+01, 7.92069e+01, 8.08918e+01, 8.24632e+01
};
static void
wnlin_checksol(const double x[], const double sumsq,
const double epsrel, const char *sname,
const char *pname)
{
size_t i;
const double sumsq_exact = 29.7481259665713758;
const double wnlin_x[wnlin_P] = { 5.17378551196259195,
0.111041758006851149,
1.05282724070446099 };
gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
sname, pname);
for (i = 0; i < wnlin_P; ++i)
{
gsl_test_rel(x[i], wnlin_x[i], epsrel, "%s/%s i=%zu",
sname, pname, i);
}
}
static int
wnlin_f (const gsl_vector *x, void *params, gsl_vector *f)
{
double A = gsl_vector_get (x, 0);
double lambda = gsl_vector_get (x, 1);
double b = gsl_vector_get (x, 2);
size_t i;
/* model Yi = A * exp(-lambda * i) + b */
for (i = 0; i < wnlin_N; i++)
{
double ti = i;
double yi = wnlin_Y[i];
double swi = sqrt(wnlin_W[i]);
double Mi = A * exp (-lambda * ti) + b;
gsl_vector_set (f, i, swi * (Mi - yi));
}
return GSL_SUCCESS;
}
static int
wnlin_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(wnlin_J, wnlin_N, wnlin_P);
double A = gsl_vector_get (x, 0);
double lambda = gsl_vector_get (x, 1);
size_t i;
for (i = 0; i < wnlin_N; i++)
{
gsl_vector_view v = gsl_matrix_row(&J.matrix, i);
double ti = i;
double swi = sqrt(wnlin_W[i]);
double e = exp(-lambda * ti);
gsl_vector_set(&v.vector, 0, e);
gsl_vector_set(&v.vector, 1, -ti * A * e);
gsl_vector_set(&v.vector, 2, 1.0);
gsl_vector_scale(&v.vector, swi);
}
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);
return GSL_SUCCESS;
}
static int
wnlin_fvv (const gsl_vector * x, const gsl_vector * v,
void *params, gsl_vector * fvv)
{
double A = gsl_vector_get (x, 0);
double lambda = gsl_vector_get (x, 1);
double v1 = gsl_vector_get(v, 0);
double v2 = gsl_vector_get(v, 1);
size_t i;
for (i = 0; i < wnlin_N; i++)
{
double ti = i;
double swi = sqrt(wnlin_W[i]);
double fvvi;
fvvi = exp(-ti*lambda)*ti*v2 * (-2*v1 + ti*v2*A);
gsl_vector_set(fvv, i, swi * fvvi);
}
return GSL_SUCCESS;
}
static gsl_multilarge_nlinear_fdf wnlin_func1 =
{
wnlin_f,
wnlin_df,
wnlin_fvv,
wnlin_N,
wnlin_P,
NULL,
0,
0,
0,
0
};
static test_fdf_problem wnlin_problem1 =
{
"wnlin_internal_weights",
wnlin_x0,
NULL,
&wnlin_epsrel,
&wnlin_checksol,
&wnlin_func1
};
|
