#define helical_N         3

#define helical_P         3

#define helical_NTRIES    4

static double helical_x0[helical_P] = { -1.0, 0.0, 0.0 };

static double helical_x[helical_P] = { 1.0, 0.0, 0.0 };

static double helical_epsrel = 1.0e-12;

static void

helical_checksol(const double x[], const double sumsq,

                 const double epsrel, const char *sname,

                 const char *pname)

{

  size_t i;

  const double sumsq_exact = 0.0;

  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",

               sname, pname);

  for (i = 0; i < helical_P; ++i)

    {

      gsl_test_rel(x[i], helical_x[i], epsrel, "%s/%s i=%zu",

                   sname, pname, i);

    }

}

static int

helical_f (const gsl_vector * x, void *params, gsl_vector * f)

{

  double x1 = gsl_vector_get(x, 0);

  double x2 = gsl_vector_get(x, 1);

  double x3 = gsl_vector_get(x, 2);

  double theta = (x1 >= 0.0) ? 0.0 : 5.0;

  double nx = gsl_hypot(x1, x2);

  gsl_vector_set(f, 0, 10.0 * (x3 - 5.0/M_PI*atan(x2 / x1) - theta));

  gsl_vector_set(f, 1, 10.0*(nx - 1.0));

  gsl_vector_set(f, 2, x3);

  return GSL_SUCCESS;

}

static int

helical_df (const gsl_vector * x, void *params, gsl_matrix * J)

{

  double x1 = gsl_vector_get(x, 0);

  double x2 = gsl_vector_get(x, 1);

  double nx = gsl_hypot(x1, x2);

  double nx_sq = nx * nx;

  double term1 = 50.0 / (M_PI * nx_sq);

  double term2 = 10.0 / nx;

  gsl_matrix_set(J, 0, 0, term1*x2);

  gsl_matrix_set(J, 0, 1, -term1*x1);

  gsl_matrix_set(J, 0, 2, 10.0);

  gsl_matrix_set(J, 1, 0, term2*x1);

  gsl_matrix_set(J, 1, 1, term2*x2);

  gsl_matrix_set(J, 1, 2, 0.0);

  gsl_matrix_set(J, 2, 0, 0.0);

  gsl_matrix_set(J, 2, 1, 0.0);

  gsl_matrix_set(J, 2, 2, 1.0);

  return GSL_SUCCESS;

}

static gsl_multifit_function_fdf helical_func =

{

  &helical_f,

  &helical_df,

  NULL,

  helical_N,

  helical_P,

  NULL,

  0,

  0

};

static test_fdf_problem helical_problem =

{

  "helical",

  helical_x0,

  NULL,

  &helical_epsrel,

  helical_NTRIES,

  &helical_checksol,

  &helical_func

};