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#define meyerscal_N 16
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#define meyerscal_P 3
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static double meyerscal_x0[meyerscal_P] = { 8.85, 4.0, 2.5 };
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static double meyerscal_epsrel = 1.0e-6;
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static double meyerscal_Y[meyerscal_N] = {
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34780., 28610., 23650., 19630., 16370., 13720., 11540.,
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9744., 8261., 7030., 6005., 5147., 4427., 3820.,
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3307., 2872.
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};
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static void
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meyerscal_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 = 8.794585517003888e-05;
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const double meyerscal_x[meyerscal_P] = { 2.481778312286695e+00,
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6.181346341853554e+00,
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3.452236344749865e+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 < meyerscal_P; ++i)
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{
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gsl_test_rel(x[i], meyerscal_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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meyerscal_f (const gsl_vector * x, void *params, gsl_vector * f)
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{
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double x1 = gsl_vector_get(x, 0);
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double x2 = gsl_vector_get(x, 1);
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double x3 = gsl_vector_get(x, 2);
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size_t i;
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for (i = 0; i < meyerscal_N; ++i)
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{
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double ti = 0.45 + 0.05*(i + 1.0);
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double yi = meyerscal_Y[i];
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double fi = x1 * exp(10.0*x2 / (ti + x3) - 13.0) - 1.0e-3*yi;
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gsl_vector_set(f, i, fi);
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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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meyerscal_df (const gsl_vector * x, void *params, gsl_matrix * J)
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{
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double x1 = gsl_vector_get(x, 0);
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double x2 = gsl_vector_get(x, 1);
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double x3 = gsl_vector_get(x, 2);
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size_t i;
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for (i = 0; i < meyerscal_N; ++i)
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{
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double ti = 0.45 + 0.05*(i + 1.0);
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double term1 = ti + x3;
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double term2 = exp(10.0*x2/term1 - 13.0);
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gsl_matrix_set(J, i, 0, term2);
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gsl_matrix_set(J, i, 1, 10.0*x1*term2/term1);
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gsl_matrix_set(J, i, 2, -10.0*x1*x2*term2/(term1*term1));
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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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meyerscal_fvv (const gsl_vector * x, const gsl_vector * v,
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void *params, gsl_vector * fvv)
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{
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double x1 = gsl_vector_get(x, 0);
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double x2 = gsl_vector_get(x, 1);
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double x3 = gsl_vector_get(x, 2);
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double v1 = gsl_vector_get(v, 0);
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double v2 = gsl_vector_get(v, 1);
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double v3 = gsl_vector_get(v, 2);
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size_t i;
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for (i = 0; i < meyerscal_N; ++i)
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{
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double ti = 0.45 + 0.05*(i + 1.0);
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double term1 = ti + x3;
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double term2 = exp(10.0*x2/term1 - 13.0);
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double term3 = v2*term1 - v3*x2;
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double term4 = ti*ti*v1 -
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v3*x1*(5*x2 + x3) +
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x3*(5*v2*x1 + v1*x3) +
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ti*(5*v2*x1 - v3*x1 + 2*v1*x3);
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gsl_vector_set(fvv, i, 20*term2*term3*term4 / pow(term1, 4.0));
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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 meyerscal_func =
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{
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meyerscal_f,
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meyerscal_df,
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meyerscal_fvv,
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meyerscal_N,
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meyerscal_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 meyerscal_problem =
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{
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"meyerscal",
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meyerscal_x0,
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NULL,
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NULL,
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&meyerscal_epsrel,
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&meyerscal_checksol,
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&meyerscal_func
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};
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