#define vardim_N         7 /* p + 2 */

#define vardim_P         5

#define vardim_NTRIES    4

static double vardim_x0[vardim_P] = { 0.8, 0.6, 0.4, 0.2, 0.0 };

static double vardim_epsrel = 1.0e-12;

static void

vardim_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 < vardim_P; ++i)

    {

      gsl_test_rel(x[i], 1.0, epsrel, "%s/%s i=%zu",

                   sname, pname, i);

    }

}

static int

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

{

  size_t i;

  double sum = 0.0;

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

    {

      double xi = gsl_vector_get(x, i);

      gsl_vector_set(f, i, xi - 1.0);

      sum += (i + 1.0) * (xi - 1.0);

    }

  gsl_vector_set(f, vardim_P, sum);

  gsl_vector_set(f, vardim_P + 1, sum*sum);

  return GSL_SUCCESS;

}

static int

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

{

  size_t i;

  double sum = 0.0;

  gsl_matrix_view m = gsl_matrix_submatrix(J, 0, 0, vardim_P, vardim_P);

  gsl_matrix_set_identity(&m.matrix);

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

    {

      double xi = gsl_vector_get(x, i);

      sum += (i + 1.0) * (xi - 1.0);

    }

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

    {

      gsl_matrix_set(J, vardim_P, i, i + 1.0);

      gsl_matrix_set(J, vardim_P + 1, i, 2*(i + 1.0)*sum);

    }

  return GSL_SUCCESS;

}

static gsl_multifit_function_fdf vardim_func =

{

  &vardim_f,

  &vardim_df,

  NULL,

  vardim_N,

  vardim_P,

  NULL,

  0,

  0

};

static test_fdf_problem vardim_problem =

{

  "vardim",

  vardim_x0,

  NULL,

  &vardim_epsrel,

  vardim_NTRIES,

  &vardim_checksol,

  &vardim_func

};