#define powell2_N        2

#define powell2_P        2

static double powell2_x0[powell2_P] = { 3.0, 1.0 };

static double powell2_epsrel = 1.0e-3;

static void

powell2_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 < powell2_P; ++i)

    {

      gsl_test_rel(x[i], 0.0, epsrel, "%s/%s i=%zu",

                   sname, pname, i);

    }

}

static int

powell2_f (const gsl_vector * x, void *params, gsl_vector * f)

{

  double x0 = gsl_vector_get (x, 0);

  double x1 = gsl_vector_get (x, 1);

  gsl_vector_set(f, 0, x0);

  gsl_vector_set(f, 1, 10.0*x0/(x0 + 0.1) + 2.0*x1*x1);

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

  return GSL_SUCCESS;

}

static int

powell2_df (const gsl_vector * x, void *params, gsl_matrix * df)

{

  double x0 = gsl_vector_get (x, 0);

  double x1 = gsl_vector_get (x, 1);

  double term = x0 + 0.1;

  gsl_matrix_set(df, 0, 0, 1.0);

  gsl_matrix_set(df, 0, 1, 0.0);

  gsl_matrix_set(df, 1, 0, 1.0 / (term * term));

  gsl_matrix_set(df, 1, 1, 4.0 * x1);

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

  return GSL_SUCCESS;

}

static int

powell2_fvv (const gsl_vector * x, const gsl_vector * v,

             void *params, gsl_vector * fvv)

{

  double x0 = gsl_vector_get (x, 0);

  double v0 = gsl_vector_get (v, 0);

  double v1 = gsl_vector_get (v, 1);

  double term = x0 + 0.1;

  gsl_vector_set(fvv, 0, 0.0);

  gsl_vector_set(fvv, 1, 4*v1*v1 - (2*v0*v0)/pow(term, 3.0));

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

  return GSL_SUCCESS;

}

static gsl_multifit_nlinear_fdf powell2_func =

{

  powell2_f,

  powell2_df,

  powell2_fvv,

  powell2_N,

  powell2_P,

  NULL,

  0,

  0,

  0

};

static test_fdf_problem powell2_problem =

{

  "powell2",

  powell2_x0,

  NULL,

  NULL,

  &powell2_epsrel,

  &powell2_checksol,

  &powell2_func

};