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#define eckerle_N 35
#define eckerle_P 3
static double eckerle_x0a[eckerle_P] = { 1.0, 10.0, 500.0 };
static double eckerle_x0b[eckerle_P] = { 1.5, 5.0, 450.0 };
static double eckerle_epsrel = 1.0e-7;
static double eckerle_J[eckerle_N * eckerle_P];
static double eckerle_sigma[eckerle_P] = {
1.5408051163E-02, 4.6803020753E-02, 4.6800518816E-02
};
static double eckerle_X[eckerle_N] = {
400.000000, 405.000000, 410.000000, 415.000000, 420.000000,
425.000000, 430.000000, 435.000000, 436.500000, 438.000000,
439.500000, 441.000000, 442.500000, 444.000000, 445.500000,
447.000000, 448.500000, 450.000000, 451.500000, 453.000000,
454.500000, 456.000000, 457.500000, 459.000000, 460.500000,
462.000000, 463.500000, 465.000000, 470.000000, 475.000000,
480.000000, 485.000000, 490.000000, 495.000000, 500.000000 };
static double eckerle_F[eckerle_N] = {
0.0001575, 0.0001699, 0.0002350, 0.0003102, 0.0004917,
0.0008710, 0.0017418, 0.0046400, 0.0065895, 0.0097302,
0.0149002, 0.0237310, 0.0401683, 0.0712559, 0.1264458,
0.2073413, 0.2902366, 0.3445623, 0.3698049, 0.3668534,
0.3106727, 0.2078154, 0.1164354, 0.0616764, 0.0337200,
0.0194023, 0.0117831, 0.0074357, 0.0022732, 0.0008800,
0.0004579, 0.0002345, 0.0001586, 0.0001143, 0.0000710 };
static void
eckerle_checksol(const double x[], const double sumsq,
const double epsrel, const char *sname,
const char *pname)
{
size_t i;
const double sumsq_exact = 1.4635887487E-03;
const double eckerle_x[eckerle_P] = { 1.5543827178E+00,
4.0888321754E+00,
4.5154121844E+02 };
double new_x[3];
gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
sname, pname);
/* x1 and x2 are unique up to a sign, but they must be
* the same sign */
if (x[0] < 0.0 && x[1] < 0.0)
{
new_x[0] = -x[0];
new_x[1] = -x[1];
}
else
{
new_x[0] = x[0];
new_x[1] = x[1];
}
new_x[2] = x[2];
for (i = 0; i < eckerle_P; ++i)
{
gsl_test_rel(new_x[i], eckerle_x[i], epsrel, "%s/%s i=%zu",
sname, pname, i);
}
}
static int
eckerle_f (const gsl_vector * x, void *params, gsl_vector * f)
{
double b[eckerle_P];
size_t i;
for (i = 0; i < eckerle_P; i++)
{
b[i] = gsl_vector_get(x, i);
}
for (i = 0; i < eckerle_N; i++)
{
double xi = eckerle_X[i];
double term = xi - b[2];
double yi;
yi = b[0] / b[1] * exp(-0.5 * term * term / b[1] / b[1]);
gsl_vector_set (f, i, yi - eckerle_F[i]);
}
(void)params; /* avoid unused parameter warning */
return GSL_SUCCESS;
}
static int
eckerle_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(eckerle_J, eckerle_N, eckerle_P);
double b[eckerle_P];
size_t i;
for (i = 0; i < eckerle_P; i++)
{
b[i] = gsl_vector_get(x, i);
}
for (i = 0; i < eckerle_N; i++)
{
double xi = eckerle_X[i];
double term1 = xi - b[2];
double term2 = exp(-0.5 * term1 * term1 / (b[1] * b[1]));
gsl_matrix_set (&J.matrix, i, 0, term2 / b[1]);
gsl_matrix_set (&J.matrix, i, 1,
-b[0] * term2 / (b[1] * b[1]) + b[0] / pow(b[1], 4.0) * term2 * term1 * term1);
gsl_matrix_set (&J.matrix, i, 2, b[0] / pow(b[1], 3.0) * 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 gsl_multilarge_nlinear_fdf eckerle_func =
{
eckerle_f,
eckerle_df,
NULL, /* analytic expression too complex */
eckerle_N,
eckerle_P,
NULL,
0,
0,
0,
0
};
static test_fdf_problem eckerlea_problem =
{
"nist-eckerlea",
eckerle_x0a,
eckerle_sigma,
&eckerle_epsrel,
&eckerle_checksol,
&eckerle_func
};
static test_fdf_problem eckerleb_problem =
{
"nist-eckerleb",
eckerle_x0b,
eckerle_sigma,
&eckerle_epsrel,
&eckerle_checksol,
&eckerle_func
};
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