#define brown3_N         3

#define brown3_P         2

static double brown3_x0[brown3_P] = { 1.0, 1.0 };

static double brown3_epsrel = 1.0e-12;

static void

brown3_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;

  const double brown3_x[brown3_P] = { 1.0e6, 2.0e-6 };

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

               sname, pname);

  for (i = 0; i < brown3_P; ++i)

    {

      gsl_test_rel(x[i], brown3_x[i], epsrel, "%s/%s i=%zu",

                   sname, pname, i);

    }

}

static int

brown3_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 - 1.0e6);

  gsl_vector_set(f, 1, x2 - 2.0e-6);

  gsl_vector_set(f, 2, x1*x2 - 2.0);

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

  return GSL_SUCCESS;

}

static int

brown3_df (const gsl_vector * x, void *params, gsl_matrix * J)

{

  double x1 = gsl_vector_get(x, 0);

  double x2 = gsl_vector_get(x, 1);

  gsl_matrix_set_zero(J);

  gsl_matrix_set(J, 0, 0, 1.0);

  gsl_matrix_set(J, 1, 1, 1.0);

  gsl_matrix_set(J, 2, 0, x2);

  gsl_matrix_set(J, 2, 1, x1);

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

  return GSL_SUCCESS;

}

static int

brown3_fvv (const gsl_vector * x, const gsl_vector * v,

            void *params, gsl_vector * fvv)

{

  double v1 = gsl_vector_get(v, 0);

  double v2 = gsl_vector_get(v, 1);

  gsl_vector_set(fvv, 0, 0.0);

  gsl_vector_set(fvv, 1, 0.0);

  gsl_vector_set(fvv, 2, 2.0 * v1 * v2);

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

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

  return GSL_SUCCESS;

}

static gsl_multifit_nlinear_fdf brown3_func =

{

  brown3_f,

  brown3_df,

  brown3_fvv,

  brown3_N,

  brown3_P,

  NULL,

  0,

  0,

  0

};

static test_fdf_problem brown3_problem =

{

  "brown_badly_scaled",

  brown3_x0,

  NULL,

  NULL,

  &brown3_epsrel,

  &brown3_checksol,

  &brown3_func

};