#define brown2_N        5

#define brown2_P        5

static double brown2_x0[brown2_P] = { 0.5, 0.5, 0.5, 0.5, 0.5 };

static double brown2_epsrel = 1.0e-12;

static void

brown2_checksol(const double x[], const double sumsq,

              const double epsrel, const char *sname,

              const char *pname)

{

  size_t i;

  double sumsq_exact;

  double alpha;

  const double p = (double) brown2_P;

  double alpha1mp, lhs, lastel;

  if (sumsq < 0.5)

    {

      /* sumsq = 0 case */

      sumsq_exact = 0.0;

      alpha = x[0];

      alpha1mp = pow(alpha, 1.0 - p);

      lhs = p*pow(alpha, p) - (p + 1)/alpha1mp;

      lastel = alpha1mp;

      gsl_test_rel(lhs, -1.0, epsrel, "%s/%s alpha lhs",

                   sname, pname);

    }

  else

    {

      /* sumsq = 1 case */

      sumsq_exact = 1.0;

      alpha = 0.0;

      lastel = p + 1.0;

    }

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

               sname, pname);

  for (i = 1; i < brown2_P - 1; ++i)

    {

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

                   sname, pname, i);

    }

  gsl_test_rel(x[brown2_P - 1], lastel, epsrel, "%s/%s last element",

               sname, pname);

}

static int

brown2_f (const gsl_vector * x, void *params, gsl_vector * f)

{

  size_t i;

  double sum = -(brown2_N + 1.0);

  double prod = 1.0;

  for (i = 0; i < brown2_N; ++i)

    {

      double xi = gsl_vector_get(x, i);

      sum += xi;

      prod *= xi;

    }

  for (i = 0; i < brown2_N - 1; ++i)

    {

      double xi = gsl_vector_get(x, i);

      gsl_vector_set(f, i, xi + sum);

    }

  gsl_vector_set(f, brown2_N - 1, prod - 1.0);

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

  return GSL_SUCCESS;

}

static int

brown2_df (const gsl_vector * x, void *params, gsl_matrix * J)

{

  size_t i, j;

  for (j = 0; j < brown2_P; ++j)

    {

      double prod = 1.0;

      for (i = 0; i < brown2_N - 1; i++)

        {

          double Jij = (i == j) ? 2.0 : 1.0;

          gsl_matrix_set(J, i, j, Jij);

        }

      for (i = 0; i < brown2_N; i++)

        {

          if (i != j)

            prod *= gsl_vector_get(x, i);

        }

      gsl_matrix_set(J, brown2_N - 1, j, prod);

    }

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

  return GSL_SUCCESS;

}

static int

brown2_fvv (const gsl_vector * x, const gsl_vector * v,

            void *params, gsl_vector * fvv)

{

  size_t i, j, k;

  double sum = 0.0;

  gsl_vector_set_zero(fvv);

  for (k = 0; k < brown2_P; ++k)

    {

      double vk = gsl_vector_get(v, k);

      for (i = 0; i < brown2_P; ++i)

        {

          double vi = gsl_vector_get(v, i);

          double delta = (i == k) ? 1.0 : 0.0;

          double prod = 1.0;

          for (j = 0; j < brown2_N; ++j)

            {

              if (j != i && j != k)

                {

                  double xj = gsl_vector_get(x, j);

                  prod *= xj;

                }

            }

          sum += vk * vi * (1.0 - delta) * prod;

        }

    }

  gsl_vector_set(fvv, brown2_N - 1, sum);

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

  return GSL_SUCCESS;

}

static gsl_multifit_nlinear_fdf brown2_func =

{

  brown2_f,

  brown2_df,

  brown2_fvv,

  brown2_N,

  brown2_P,

  NULL,

  0,

  0,

  0

};

static test_fdf_problem brown2_problem =

{

  "brown_almost_linear",

  brown2_x0,

  NULL,

  NULL,

  &brown2_epsrel,

  &brown2_checksol,

  &brown2_func

};