#define roth_N         2

#define roth_P         2

static double roth_x0[roth_P] = { 0.5, -2.0 };

static double roth_epsrel = 1.0e-6;

static void

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

              const double epsrel, const char *sname,

              const char *pname)

{

  size_t i;

  const double sumsq_exact1 = 0.0;

  const double roth_x1[roth_P] = { 5.0, 4.0 };

  const double sumsq_exact2 = 48.9842536792400;

  const double roth_x2[roth_P] = { 11.4127789869021, -0.896805253274477 };

  const double *roth_x;

  double sumsq_exact;

  if (fabs(sumsq) < 0.1)

    {

      sumsq_exact = sumsq_exact1;

      roth_x = roth_x1;

    }

  else

    {

      sumsq_exact = sumsq_exact2;

      roth_x = roth_x2;

    }

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

               sname, pname);

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

    {

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

                   sname, pname, i);

    }

}

static int

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

{

  double x1 = gsl_vector_get(x, 0);

  double x2 = gsl_vector_get(x, 1);

  gsl_vector_set(f, 0, x1 - x2*(2.0 - x2*(5.0 - x2)) - 13.0);

  gsl_vector_set(f, 1, x1 - x2*(14.0 - x2*(1.0 + x2)) - 29.0);

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

  return GSL_SUCCESS;

}

static int

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

{

  double x2 = gsl_vector_get(x, 1);

  gsl_matrix_set(J, 0, 0, 1.0);

  gsl_matrix_set(J, 0, 1, -2.0 + x2*(10.0 - 3.0*x2));

  gsl_matrix_set(J, 1, 0, 1.0);

  gsl_matrix_set(J, 1, 1, -14.0 + x2*(2.0 + 3.0*x2));

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

  return GSL_SUCCESS;

}

static int

roth_fvv (const gsl_vector * x, const gsl_vector * v,

          void *params, gsl_vector * fvv)

{

  double x2 = gsl_vector_get(x, 1);

  double v2 = gsl_vector_get(v, 1);

  gsl_vector_set(fvv, 0, (10.0 - 6.0*x2) * v2 * v2);

  gsl_vector_set(fvv, 1, (2.0 + 6.0*x2) * v2 * v2);

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

  return GSL_SUCCESS;

}

static gsl_multifit_nlinear_fdf roth_func =

{

  roth_f,

  roth_df,

  roth_fvv,

  roth_N,

  roth_P,

  NULL,

  0,

  0,

  0

};

static test_fdf_problem roth_problem =

{

  "roth_freudenstein",

  roth_x0,

  NULL,

  NULL,

  &roth_epsrel,

  &roth_checksol,

  &roth_func

};