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#define helical_N 3
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#define helical_P 3
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static double helical_x0[helical_P] = { -1.0, 0.0, 0.0 };
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static double helical_x[helical_P] = { 1.0, 0.0, 0.0 };
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static double helical_epsrel = 1.0e-12;
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static double helical_J[helical_N * helical_P];
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static void
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helical_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 = 0.0;
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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 < helical_P; ++i)
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{
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gsl_test_rel(x[i], helical_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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helical_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 theta = (x1 >= 0.0) ? 0.0 : 5.0;
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double nx = gsl_hypot(x1, x2);
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gsl_vector_set(f, 0, 10.0 * (x3 - 5.0/M_PI*atan(x2 / x1) - theta));
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gsl_vector_set(f, 1, 10.0*(nx - 1.0));
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gsl_vector_set(f, 2, x3);
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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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helical_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
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const gsl_vector * u, void * params, gsl_vector * v,
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gsl_matrix * JTJ)
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{
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gsl_matrix_view J = gsl_matrix_view_array(helical_J, helical_N, helical_P);
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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 nx = gsl_hypot(x1, x2);
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double nx_sq = nx * nx;
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double term1 = 50.0 / (M_PI * nx_sq);
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double term2 = 10.0 / nx;
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gsl_matrix_set(&J.matrix, 0, 0, term1*x2);
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gsl_matrix_set(&J.matrix, 0, 1, -term1*x1);
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gsl_matrix_set(&J.matrix, 0, 2, 10.0);
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gsl_matrix_set(&J.matrix, 1, 0, term2*x1);
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gsl_matrix_set(&J.matrix, 1, 1, term2*x2);
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gsl_matrix_set(&J.matrix, 1, 2, 0.0);
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gsl_matrix_set(&J.matrix, 2, 0, 0.0);
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gsl_matrix_set(&J.matrix, 2, 1, 0.0);
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gsl_matrix_set(&J.matrix, 2, 2, 1.0);
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if (v)
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gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
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if (JTJ)
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gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
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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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helical_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 v1 = gsl_vector_get(v, 0);
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double v2 = gsl_vector_get(v, 1);
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double term1 = v2*x1 - v1*x2;
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double term2 = v1*x1 + v2*x2;
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double term3 = x1*x1 + x2*x2;
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gsl_vector_set(fvv, 0, 100.0 / M_PI * (term1 / term3) * (term2 / term3));
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gsl_vector_set(fvv, 1, 10.0 * (term1 * term1) / pow(term3, 1.5));
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gsl_vector_set(fvv, 2, 0.0);
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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_multilarge_nlinear_fdf helical_func =
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{
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helical_f,
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helical_df,
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helical_fvv,
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helical_N,
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helical_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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0
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};
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static test_fdf_problem helical_problem =
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{
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"helical",
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helical_x0,
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NULL,
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&helical_epsrel,
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&helical_checksol,
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&helical_func
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};
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