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#define biggs_N 20 /* >= p */
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#define biggs_P 6
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/* dogleg method has trouble converging from recommended starting point,
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* so we use an x0 which is a little closer to the true solution */
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/*static double biggs_x0[biggs_P] = { 1.0, 2.0, 1.0, 1.0, 1.0, 1.0 };*/
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static double biggs_x0[biggs_P] = { 1.0, 5.0, 1.0, 2.0, 3.0, 2.0 };
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static double biggs_epsrel = 1.0e-9;
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static void
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biggs_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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const double sumsq_exact = 0.0;
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const double biggs_x[biggs_P] = { 1.0, 10.0, 1.0, 5.0, 4.0, 3.0 };
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size_t i;
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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 < biggs_P; ++i)
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{
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gsl_test_rel(x[i], biggs_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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biggs_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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double x4 = gsl_vector_get(x, 3);
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double x5 = gsl_vector_get(x, 4);
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double x6 = gsl_vector_get(x, 5);
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size_t i;
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for (i = 0; i < biggs_N; ++i)
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{
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double ti = 0.1 * (i + 1.0);
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double yi = exp(-ti) - 5*exp(-10*ti) + 3*exp(-4*ti);
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double fi = x3*exp(-ti*x1) - x4*exp(-ti*x2) + x6*exp(-ti*x5) - 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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biggs_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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double x4 = gsl_vector_get(x, 3);
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double x5 = gsl_vector_get(x, 4);
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double x6 = gsl_vector_get(x, 5);
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size_t i;
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for (i = 0; i < biggs_N; ++i)
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{
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double ti = 0.1 * (i + 1.0);
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gsl_matrix_set(J, i, 0, -ti*x3*exp(-ti*x1));
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gsl_matrix_set(J, i, 1, ti*x4*exp(-ti*x2));
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gsl_matrix_set(J, i, 2, exp(-ti*x1));
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gsl_matrix_set(J, i, 3, -exp(-ti*x2));
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gsl_matrix_set(J, i, 4, -ti*x6*exp(-ti*x5));
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gsl_matrix_set(J, i, 5, exp(-ti*x5));
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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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biggs_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 x4 = gsl_vector_get(x, 3);
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double x5 = gsl_vector_get(x, 4);
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double x6 = gsl_vector_get(x, 5);
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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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double v4 = gsl_vector_get(v, 3);
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double v5 = gsl_vector_get(v, 4);
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double v6 = gsl_vector_get(v, 5);
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size_t i;
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for (i = 0; i < biggs_N; ++i)
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{
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double ti = 0.1 * (i + 1.0);
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double term1 = exp(-ti * x1);
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double term2 = exp(-ti * x2);
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double term3 = exp(-ti * x5);
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gsl_vector_set(fvv, i, ti * term1 * term2 * term3 *
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(v1/(term2*term3)*(-2*v3 + ti*v1*x3) -
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v2/(term1*term3)*(-2*v4 + ti*v2*x4) +
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v5/(term1*term2)*(-2*v6 + ti*v5*x6)));
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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 biggs_func =
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{
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biggs_f,
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biggs_df,
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biggs_fvv,
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biggs_N,
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biggs_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 biggs_problem =
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{
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"biggs",
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biggs_x0,
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NULL,
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NULL,
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&biggs_epsrel,
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&biggs_checksol,
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&biggs_func
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};
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