#define meyerscal_N         16

#define meyerscal_P         3

#define meyerscal_NTRIES    1

static double meyerscal_x0[meyerscal_P] = { 8.85, 4.0, 2.5 };

static double meyerscal_epsrel = 1.0e-8;

static double meyerscal_Y[meyerscal_N] = {

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

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

3307.,  2872.

};

static void

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

                   const double epsrel, const char *sname,

                   const char *pname)

{

  size_t i;

  const double sumsq_exact = 8.794585517003888e-05;

  const double meyerscal_x[meyerscal_P] = { 2.481778312286695e+00,

                                            6.181346341853554e+00,

                                            3.452236344749865e+00 };

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

               sname, pname);

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

    {

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

                   sname, pname, i);

    }

}

static int

meyerscal_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 < meyerscal_N; ++i)

    {

      double ti = 0.45 + 0.05*(i + 1.0);

      double yi = meyerscal_Y[i];

      double fi = x1 * exp(10.0*x2 / (ti + x3) - 13.0) - 1.0e-3*yi;

      gsl_vector_set(f, i, fi);

    }

  return GSL_SUCCESS;

}

static int

meyerscal_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 < meyerscal_N; ++i)

    {

      double ti = 0.45 + 0.05*(i + 1.0);

      double term1 = ti + x3;

      double term2 = exp(10.0*x2/term1 - 13.0);

      gsl_matrix_set(J, i, 0, term2);

      gsl_matrix_set(J, i, 1, 10.0*x1*term2/term1);

      gsl_matrix_set(J, i, 2, -10.0*x1*x2*term2/(term1*term1));

    }

  return GSL_SUCCESS;

}

static gsl_multifit_function_fdf meyerscal_func =

{

  &meyerscal_f,

  &meyerscal_df,

  NULL,

  meyerscal_N,

  meyerscal_P,

  NULL,

  0,

  0

};

static test_fdf_problem meyerscal_problem =

{

  "meyerscal",

  meyerscal_x0,

  NULL,

  &meyerscal_epsrel,

  meyerscal_NTRIES,

  &meyerscal_checksol,

  &meyerscal_func

};