#define meyer_N         16

#define meyer_P         3

static double meyer_x0[meyer_P] = { 0.02, 4000.0, 250.0 };

static double meyer_epsrel = 1.0e-6;

static double meyer_Y[meyer_N] = {

34780., 28610., 23650., 19630., 16370., 13720., 11540.,

9744.,  8261.,  7030.,  6005., 5147., 4427., 3820.,

3307.,  2872.

};

static void

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

               const double epsrel, const char *sname,

               const char *pname)

{

  size_t i;

  const double sumsq_exact = 8.794585517053883e+01;

  const double meyer_x[meyer_P] = { 5.609636471049458e-03,

                                    6.181346346283188e+03,

                                    3.452236346240292e+02 };

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

               sname, pname);

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

    {

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

                   sname, pname, i);

    }

}

static int

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

{

  double x1 = gsl_vector_get(x, 0);

  double x2 = gsl_vector_get(x, 1);

  double x3 = gsl_vector_get(x, 2);

  size_t i;

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

    {

      double ti = 45.0 + 5.0*(i + 1.0);

      double yi = meyer_Y[i];

      double fi = x1 * exp(x2 / (ti + x3)) - yi;

      gsl_vector_set(f, i, fi);

    }

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

  return GSL_SUCCESS;

}

static int

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

{

  double x1 = gsl_vector_get(x, 0);

  double x2 = gsl_vector_get(x, 1);

  double x3 = gsl_vector_get(x, 2);

  size_t i;

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

    {

      double ti = 45.0 + 5.0*(i + 1.0);

      double term1 = ti + x3;

      double term2 = exp(x2 / term1);

      gsl_matrix_set(J, i, 0, term2);

      gsl_matrix_set(J, i, 1, x1*term2/term1);

      gsl_matrix_set(J, i, 2, -x1*x2*term2/(term1*term1));

    }

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

  return GSL_SUCCESS;

}

static int

meyer_fvv (const gsl_vector * x, const gsl_vector * v,

           void *params, gsl_vector * fvv)

{

  double x1 = gsl_vector_get(x, 0);

  double x2 = gsl_vector_get(x, 1);

  double x3 = gsl_vector_get(x, 2);

  double v1 = gsl_vector_get(v, 0);

  double v2 = gsl_vector_get(v, 1);

  double v3 = gsl_vector_get(v, 2);

  size_t i;

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

    {

      double ti = 45.0 + 5.0*(i + 1.0);

      double term1 = ti + x3;

      double term2 = exp(x2 / term1);

      double term3 = v2*term1 - v3*x2;

      double term4 = 2*ti*ti*v1 - v3*x1*(x2 + 2*x3) +

                     x3*(v2*x1 + 2*v1*x3) +

                     ti*(v2*x1 - 2*v3*x1 + 4*v1*x3);

      gsl_vector_set(fvv, i, term2 * term3 * term4 / pow(term1, 4.0));

    }

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

  return GSL_SUCCESS;

}

static gsl_multifit_nlinear_fdf meyer_func =

{

  meyer_f,

  meyer_df,

  meyer_fvv,

  meyer_N,

  meyer_P,

  NULL,

  0,

  0,

  0

};

static test_fdf_problem meyer_problem =

{

  "meyer",

  meyer_x0,

  NULL,

  NULL,

  &meyer_epsrel,

  &meyer_checksol,

  &meyer_func

};