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#define enso_N 168
#define enso_P 9
static double enso_x0a[enso_P] = { 11.0, 3.0, 0.5, 40.0, -0.7, -1.3, 25.0, -0.3, 1.4 };
static double enso_x0b[enso_P] = { 10.0, 3.0, 0.5, 44.0, -1.5, 0.5, 26.0, -0.1, 1.5 };
static double enso_epsrel = 1.0e-3;
static double enso_J[enso_N * enso_P];
static double enso_sigma[enso_P] = {
1.7488832467E-01, 2.4310052139E-01, 2.4354686618E-01, 9.4408025976E-01, 2.8078369611E-01,
4.8073701119E-01, 4.1612939130E-01, 5.1460022911E-01, 2.5434468893E-01
};
static double enso_F[enso_N] = {
12.90000, 11.30000, 10.60000, 11.20000, 10.90000,
7.500000, 7.700000, 11.70000, 12.90000, 14.30000,
10.90000, 13.70000, 17.10000, 14.00000, 15.30000,
8.500000, 5.700000, 5.500000, 7.600000, 8.600000,
7.300000, 7.600000, 12.70000, 11.00000, 12.70000,
12.90000, 13.00000, 10.90000, 10.400000, 10.200000,
8.000000, 10.90000, 13.60000, 10.500000, 9.200000,
12.40000, 12.70000, 13.30000, 10.100000, 7.800000,
4.800000, 3.000000, 2.500000, 6.300000, 9.700000,
11.60000, 8.600000, 12.40000, 10.500000, 13.30000,
10.400000, 8.100000, 3.700000, 10.70000, 5.100000,
10.400000, 10.90000, 11.70000, 11.40000, 13.70000,
14.10000, 14.00000, 12.50000, 6.300000, 9.600000,
11.70000, 5.000000, 10.80000, 12.70000, 10.80000,
11.80000, 12.60000, 15.70000, 12.60000, 14.80000,
7.800000, 7.100000, 11.20000, 8.100000, 6.400000,
5.200000, 12.00000, 10.200000, 12.70000, 10.200000,
14.70000, 12.20000, 7.100000, 5.700000, 6.700000,
3.900000, 8.500000, 8.300000, 10.80000, 16.70000,
12.60000, 12.50000, 12.50000, 9.800000, 7.200000,
4.100000, 10.60000, 10.100000, 10.100000, 11.90000,
13.60000, 16.30000, 17.60000, 15.50000, 16.00000,
15.20000, 11.20000, 14.30000, 14.50000, 8.500000,
12.00000, 12.70000, 11.30000, 14.50000, 15.10000,
10.400000, 11.50000, 13.40000, 7.500000, 0.6000000,
0.3000000, 5.500000, 5.000000, 4.600000, 8.200000,
9.900000, 9.200000, 12.50000, 10.90000, 9.900000,
8.900000, 7.600000, 9.500000, 8.400000, 10.70000,
13.60000, 13.70000, 13.70000, 16.50000, 16.80000,
17.10000, 15.40000, 9.500000, 6.100000, 10.100000,
9.300000, 5.300000, 11.20000, 16.60000, 15.60000,
12.00000, 11.50000, 8.600000, 13.80000, 8.700000,
8.600000, 8.600000, 8.700000, 12.80000, 13.20000,
14.00000, 13.40000, 14.80000
};
static void
enso_checksol(const double x[], const double sumsq,
const double epsrel, const char *sname,
const char *pname)
{
size_t i;
const double sumsq_exact = 7.8853978668E+02;
const double enso_x[enso_P] = {
1.0510749193E+01, 3.0762128085E+00, 5.3280138227E-01,
4.4311088700E+01, -1.6231428586E+00, 5.2554493756E-01,
2.6887614440E+01, 2.1232288488E-01, 1.4966870418E+00 };
gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
sname, pname);
for (i = 0; i < enso_P; ++i)
{
gsl_test_rel(x[i], enso_x[i], epsrel, "%s/%s i=%zu",
sname, pname, i);
}
}
static int
enso_f (const gsl_vector * x, void *params, gsl_vector * f)
{
double b[enso_P];
size_t i;
for (i = 0; i < enso_P; i++)
{
b[i] = gsl_vector_get(x, i);
}
for (i = 0; i < enso_N; i++)
{
double t = (i + 1.0);
double y;
y = b[0];
y += b[1] * cos(2*M_PI*t/12);
y += b[2] * sin(2*M_PI*t/12);
y += b[4] * cos(2*M_PI*t/b[3]);
y += b[5] * sin(2*M_PI*t/b[3]);
y += b[7] * cos(2*M_PI*t/b[6]);
y += b[8] * sin(2*M_PI*t/b[6]);
gsl_vector_set (f, i, enso_F[i] - y);
}
(void)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static int
enso_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(enso_J, enso_N, enso_P);
double b[enso_P];
size_t i;
for (i = 0; i < enso_P; i++)
{
b[i] = gsl_vector_get(x, i);
}
for (i = 0; i < enso_N; i++)
{
double t = (i + 1.0);
gsl_matrix_set (&J.matrix, i, 0, -1.0);
gsl_matrix_set (&J.matrix, i, 1, -cos(2*M_PI*t/12));
gsl_matrix_set (&J.matrix, i, 2, -sin(2*M_PI*t/12));
gsl_matrix_set (&J.matrix, i, 3,
-b[4]*(2*M_PI*t/(b[3]*b[3]))*sin(2*M_PI*t/b[3])
+b[5]*(2*M_PI*t/(b[3]*b[3]))*cos(2*M_PI*t/b[3]));
gsl_matrix_set (&J.matrix, i, 4, -cos(2*M_PI*t/b[3]));
gsl_matrix_set (&J.matrix, i, 5, -sin(2*M_PI*t/b[3]));
gsl_matrix_set (&J.matrix, i, 6,
-b[7] * (2*M_PI*t/(b[6]*b[6])) * sin(2*M_PI*t/b[6])
+b[8] * (2*M_PI*t/(b[6]*b[6])) * cos(2*M_PI*t/b[6]));
gsl_matrix_set (&J.matrix, i, 7, -cos(2*M_PI*t/b[6]));
gsl_matrix_set (&J.matrix, i, 8, -sin(2*M_PI*t/b[6]));
}
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 gsl_multilarge_nlinear_fdf enso_func =
{
enso_f,
enso_df,
NULL, /* analytic expression too complex */
enso_N,
enso_P,
NULL,
0,
0,
0,
0
};
static test_fdf_problem ensoa_problem =
{
"nist-ENSOa",
enso_x0a,
enso_sigma,
&enso_epsrel,
&enso_checksol,
&enso_func
};
static test_fdf_problem ensob_problem =
{
"nist-ENSOb",
enso_x0b,
enso_sigma,
&enso_epsrel,
&enso_checksol,
&enso_func
};
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