#define beale_N         3

#define beale_P         2

static double beale_x0[beale_P] = { 1.0, 1.0 };

static double beale_epsrel = 1.0e-12;

static double beale_Y[beale_N] = { 1.5, 2.25, 2.625 };

static void

beale_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;

  const double beale_x[beale_P] = { 3.0, 0.5 };

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

               sname, pname);

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

    {

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

                   sname, pname, i);

    }

}

static int

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

{

  double x1 = gsl_vector_get(x, 0);

  double x2 = gsl_vector_get(x, 1);

  size_t i;

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

    {

      double yi = beale_Y[i];

      double term = pow(x2, i + 1.0);

      double fi = yi - x1*(1.0 - term);

      gsl_vector_set(f, i, fi);

    }

  (void)params; /* avoid unused parameter warning */

  return GSL_SUCCESS;

}

static int

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

{

  double x1 = gsl_vector_get(x, 0);

  double x2 = gsl_vector_get(x, 1);

  size_t i;

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

    {

      double term = pow(x2, (double) i);

      gsl_matrix_set(J, i, 0, term*x2 - 1.0);

      gsl_matrix_set(J, i, 1, (i + 1.0) * x1 * term);

    }

  (void)params; /* avoid unused parameter warning */

  return GSL_SUCCESS;

}

static int

beale_fvv (const gsl_vector * x, const gsl_vector * v,

           void *params, gsl_vector * fvv)

{

  double x1 = gsl_vector_get(x, 0);

  double x2 = gsl_vector_get(x, 1);

  double v1 = gsl_vector_get(v, 0);

  double v2 = gsl_vector_get(v, 1);

  size_t i;

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

    {

      double term = pow(x2, (double)i - 1.0);

      gsl_vector_set(fvv, i, (i + 1.0) * v2 * term *

                             (i * v2 * x1 + 2.0 * v1 * x2));

    }

  (void)params; /* avoid unused parameter warning */

  return GSL_SUCCESS;

}

static gsl_multifit_nlinear_fdf beale_func =

{

  beale_f,

  beale_df,

  beale_fvv,

  beale_N,

  beale_P,

  NULL,

  0,

  0,

  0

};

static test_fdf_problem beale_problem =

{

  "beale",

  beale_x0,

  NULL,

  NULL,

  &beale_epsrel,

  &beale_checksol,

  &beale_func

};