#define meyerscal_N         16
#define meyerscal_P         3

static double meyerscal_x0[meyerscal_P] = { 8.85, 4.0, 2.5 };
static double meyerscal_epsrel = 1.0e-6;

static double meyerscal_J[meyerscal_N * meyerscal_P];

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);
    }

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

  return GSL_SUCCESS;
}

static int
meyerscal_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
              const gsl_vector * u, void * params, gsl_vector * v,
              gsl_matrix * JTJ)
{
  gsl_matrix_view J = gsl_matrix_view_array(meyerscal_J, meyerscal_N, meyerscal_P);
  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.matrix, i, 0, term2);
      gsl_matrix_set(&J.matrix, i, 1, 10.0*x1*term2/term1);
      gsl_matrix_set(&J.matrix, i, 2, -10.0*x1*x2*term2/(term1*term1));
    }

  if (v)
    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);

  if (JTJ)
    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);

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

  return GSL_SUCCESS;
}

static int
meyerscal_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 < 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);
      double term3 = v2*term1 - v3*x2;
      double term4 = ti*ti*v1 -
                     v3*x1*(5*x2 + x3) +
                     x3*(5*v2*x1 + v1*x3) +
                     ti*(5*v2*x1 - v3*x1 + 2*v1*x3);

      gsl_vector_set(fvv, i, 20*term2*term3*term4 / pow(term1, 4.0));
    }

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

  return GSL_SUCCESS;
}

static gsl_multilarge_nlinear_fdf meyerscal_func =
{
  meyerscal_f,
  meyerscal_df,
  meyerscal_fvv,
  meyerscal_N,
  meyerscal_P,
  NULL,
  0,
  0,
  0,
  0
};

static test_fdf_problem meyerscal_problem =
{
  "meyerscal",
  meyerscal_x0,
  NULL,
  &meyerscal_epsrel,
  &meyerscal_checksol,
  &meyerscal_func
};
