#define brown1_N         20

#define brown1_P         4

static double brown1_x0[brown1_P] = { 25, 5, -5, -1 };

static double brown1_epsrel = 1.0e-5;

static void

brown1_checksol(const double x[], const double sumsq,

                const double epsrel, const char *sname,

                const char *pname)

{

  size_t i;

  const double sumsq_exact = 8.582220162635628e+04;

  const double brown1_x[brown1_P] = {

    -1.159443990239263e+01, 1.320363005221244e+01,

    -4.034395456782477e-01, 2.367789088597534e-01 };

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

               sname, pname);

  for (i = 0; i < brown1_P; ++i)

    {

      gsl_test_rel(x[i], brown1_x[i], epsrel, "%s/%s i=%zu",

                   sname, pname, i);

    }

}

static int

brown1_f (const gsl_vector * x, void *params, gsl_vector * f)

{

  double x0 = gsl_vector_get (x, 0);

  double x1 = gsl_vector_get (x, 1);

  double x2 = gsl_vector_get (x, 2);

  double x3 = gsl_vector_get (x, 3);

  size_t i;

  for (i = 0; i < brown1_N; i++)

    {

      double ti = 0.2 * (i + 1);

      double ui = x0 + x1 * ti - exp (ti);

      double vi = x2 + x3 * sin (ti) - cos (ti);

      gsl_vector_set (f, i, ui * ui + vi * vi);

    }

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

  return GSL_SUCCESS;

}

static int

brown1_df (const gsl_vector * x, void *params, gsl_matrix * df)

{

  double x0 = gsl_vector_get (x, 0);

  double x1 = gsl_vector_get (x, 1);

  double x2 = gsl_vector_get (x, 2);

  double x3 = gsl_vector_get (x, 3);

  size_t i;

  for (i = 0; i < brown1_N; i++)

    {

      double ti = 0.2 * (i + 1);

      double ui = x0 + x1 * ti - exp (ti);

      double vi = x2 + x3 * sin (ti) - cos (ti);

      gsl_matrix_set (df, i, 0, 2 * ui);

      gsl_matrix_set (df, i, 1, 2 * ui * ti);

      gsl_matrix_set (df, i, 2, 2 * vi);

      gsl_matrix_set (df, i, 3, 2 * vi * sin (ti));

    }

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

  return GSL_SUCCESS;

}

static int

brown1_fvv (const gsl_vector * x, const gsl_vector * v,

            void *params, gsl_vector * fvv)

{

  double v0 = gsl_vector_get (v, 0);

  double v1 = gsl_vector_get (v, 1);

  double v2 = gsl_vector_get (v, 2);

  double v3 = gsl_vector_get (v, 3);

  size_t i;

  for (i = 0; i < brown1_N; i++)

    {

      double ti = 0.2 * (i + 1);

      double term1 = v0 + ti*v1;

      double term2 = v3*sin(ti);

      gsl_vector_set (fvv, i, 2.0 * (term1*term1 + v2*v2 +

                                     term2 * (2*v2 + term2)));

    }

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

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

  return GSL_SUCCESS;

}

static gsl_multifit_nlinear_fdf brown1_func =

{

  brown1_f,

  brown1_df,

  brown1_fvv,

  brown1_N,

  brown1_P,

  NULL,

  0,

  0,

  0

};

static test_fdf_problem brown1_problem =

{

  "brown_dennis",

  brown1_x0,

  NULL,

  NULL,

  &brown1_epsrel,

  &brown1_checksol,

  &brown1_func

};