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#define rat43_N 15
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#define rat43_P 4
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static double rat43_x0a[rat43_P] = { 100.0, 10.0, 1.0, 1.0 };
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static double rat43_x0b[rat43_P] = { 700.0, 5.0, 0.75, 1.3 };
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static double rat43_epsrel = 1.0e-6;
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static double rat43_sigma[rat43_P] = {
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1.6302297817E+01, 2.0828735829E+00,
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1.9566123451E-01, 6.8761936385E-01
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};
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static double rat43_F[rat43_N] = { 16.08, 33.83, 65.80, 97.20, 191.55,
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326.20, 386.87, 520.53, 590.03,
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651.92, 724.93, 699.56, 689.96,
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637.56, 717.41 };
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static void
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rat43_checksol(const double x[], const double sumsq,
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const double epsrel, const char *sname,
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const char *pname)
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{
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size_t i;
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const double sumsq_exact = 8.7864049080E+03;
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const double rat43_x[rat43_P] = { 6.9964151270E+02,
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5.2771253025E+00,
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7.5962938329E-01,
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1.2792483859E+00 };
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gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
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sname, pname);
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for (i = 0; i < rat43_P; ++i)
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{
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gsl_test_rel(x[i], rat43_x[i], epsrel, "%s/%s i=%zu",
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sname, pname, i);
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}
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}
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static int
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rat43_f (const gsl_vector * x, void *params, gsl_vector * f)
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{
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double b[rat43_P];
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size_t i;
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for (i = 0; i < rat43_P; i++)
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{
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b[i] = gsl_vector_get(x, i);
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}
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for (i = 0; i < rat43_N; i++)
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{
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double xi = i + 1.0;
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double e = exp(b[1] - b[2]*xi);
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double yi = b[0] / pow(1.0 + e, 1.0 / b[3]);
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gsl_vector_set (f, i, yi - rat43_F[i]);
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}
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(void)params; /* avoid unused parameter warning */
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return GSL_SUCCESS;
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}
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static int
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rat43_df (const gsl_vector * x, void *params, gsl_matrix * df)
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{
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double b[rat43_P];
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size_t i;
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for (i = 0; i < rat43_P; i++)
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{
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b[i] = gsl_vector_get(x, i);
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}
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for (i = 0; i < rat43_N; i++)
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{
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double xi = i + 1.0;
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double e = exp(b[1] - b[2]*xi);
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double term1 = 1.0 + e;
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double term2 = pow(term1, -1.0 / b[3]);
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gsl_matrix_set (df, i, 0, term2);
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gsl_matrix_set (df, i, 1, -b[0] / b[3] * e * term2 / term1);
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gsl_matrix_set (df, i, 2, b[0] / b[3] * xi * e * term2 / term1);
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gsl_matrix_set (df, i, 3, b[0] / b[3] / b[3] * log(term1) * term2);
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}
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(void)params; /* avoid unused parameter warning */
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return GSL_SUCCESS;
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}
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static gsl_multifit_nlinear_fdf rat43_func =
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{
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rat43_f,
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rat43_df,
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NULL, /* analytic expression too complex */
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rat43_N,
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rat43_P,
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NULL,
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0,
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0,
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0
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};
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static test_fdf_problem rat43a_problem =
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{
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"nist-rat43a",
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rat43_x0a,
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NULL,
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rat43_sigma,
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&rat43_epsrel,
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&rat43_checksol,
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&rat43_func
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};
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static test_fdf_problem rat43b_problem =
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{
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"nist-rat43b",
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rat43_x0b,
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NULL,
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rat43_sigma,
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&rat43_epsrel,
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&rat43_checksol,
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&rat43_func
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};
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