#define powell1_N        4

#define powell1_P        4

#define powell1_NTRIES   4

static double powell1_x0[powell1_P] = { 3.0, -1.0, 0.0, 1.0 };

static double powell1_epsrel = 1.0e-5;

static void

powell1_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 < powell1_P; ++i)

    {

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

                   sname, pname, i);

    }

}

static int

powell1_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 x4 = gsl_vector_get (x, 3);

  gsl_vector_set(f, 0, x1 + 10.0*x2);

  gsl_vector_set(f, 1, sqrt(5.0) * (x3 - x4));

  gsl_vector_set(f, 2, pow(x2 - 2.0*x3, 2.0));

  gsl_vector_set(f, 3, sqrt(10.0) * pow((x1 - x4), 2.0));

  return GSL_SUCCESS;

}

static int

powell1_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 x3 = gsl_vector_get (x, 2);

  double x4 = gsl_vector_get (x, 3);

  double term1 = x2 - 2.0*x3;

  double term2 = x1 - x4;

  gsl_matrix_set(J, 0, 0, 1.0);

  gsl_matrix_set(J, 0, 1, 10.0);

  gsl_matrix_set(J, 0, 2, 0.0);

  gsl_matrix_set(J, 0, 3, 0.0);

  gsl_matrix_set(J, 1, 0, 0.0);

  gsl_matrix_set(J, 1, 1, 0.0);

  gsl_matrix_set(J, 1, 2, sqrt(5.0));

  gsl_matrix_set(J, 1, 3, -sqrt(5.0));

  gsl_matrix_set(J, 2, 0, 0.0);

  gsl_matrix_set(J, 2, 1, 2.0*term1);

  gsl_matrix_set(J, 2, 2, -4.0*term1);

  gsl_matrix_set(J, 2, 3, 0.0);

  gsl_matrix_set(J, 3, 0, 2.0*sqrt(10.0)*term2);

  gsl_matrix_set(J, 3, 1, 0.0);

  gsl_matrix_set(J, 3, 2, 0.0);

  gsl_matrix_set(J, 3, 3, -2.0*sqrt(10.0)*term2);

  return GSL_SUCCESS;

}

static gsl_multifit_function_fdf powell1_func =

{

  &powell1_f,

  &powell1_df,

  NULL,

  powell1_N,

  powell1_P,

  NULL,

  0,

  0

};

static test_fdf_problem powell1_problem =

{

  "powell_singular",

  powell1_x0,

  NULL,

  &powell1_epsrel,

  powell1_NTRIES,

  &powell1_checksol,

  &powell1_func

};