#define osborne_N         33

#define osborne_P         5

static double osborne_x0[osborne_P] = { 0.5, 1.5, -1.0, 0.01, 0.02 };

static double osborne_epsrel = 1.0e-8;

static double osborne_Y[osborne_N] = {

0.844, 0.908, 0.932, 0.936, 0.925, 0.908, 0.881,

0.850, 0.818, 0.784, 0.751, 0.718, 0.685, 0.658,

0.628, 0.603, 0.580, 0.558, 0.538, 0.522, 0.506,

0.490, 0.478, 0.467, 0.457, 0.448, 0.438, 0.431,

0.424, 0.420, 0.414, 0.411, 0.406

};

static void

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

                 const double epsrel, const char *sname,

                 const char *pname)

{

  const double sumsq_exact = 5.464894697482687e-05;

  double osborne_x[osborne_P];

  osborne_x[0] = 3.754100521058740e-01;

  osborne_x[1] = GSL_NAN;

  osborne_x[2] = GSL_NAN;

  osborne_x[3] = GSL_NAN;

  osborne_x[4] = GSL_NAN;

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

               sname, pname);

  /* only the first model parameter is uniquely constrained */

  gsl_test_rel(x[0], osborne_x[0], epsrel, "%s/%s i=0",

               sname, pname);

}

static int

osborne_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);

  double x4 = gsl_vector_get(x, 3);

  double x5 = gsl_vector_get(x, 4);

  size_t i;

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

    {

      double ti = 10.0*i;

      double yi = osborne_Y[i];

      double fi = yi - (x1 + x2*exp(-x4*ti) + x3*exp(-x5*ti));

      gsl_vector_set(f, i, fi);

    }

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

  return GSL_SUCCESS;

}

static int

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

{

  double x2 = gsl_vector_get(x, 1);

  double x3 = gsl_vector_get(x, 2);

  double x4 = gsl_vector_get(x, 3);

  double x5 = gsl_vector_get(x, 4);

  size_t i;

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

    {

      double ti = 10.0*i;

      double term1 = exp(-x4*ti);

      double term2 = exp(-x5*ti);

      gsl_matrix_set(J, i, 0, -1.0);

      gsl_matrix_set(J, i, 1, -term1);

      gsl_matrix_set(J, i, 2, -term2);

      gsl_matrix_set(J, i, 3, ti*x2*term1);

      gsl_matrix_set(J, i, 4, ti*x3*term2);

    }

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

  return GSL_SUCCESS;

}

static int

osborne_fvv (const gsl_vector * x, const gsl_vector * v,

             void *params, gsl_vector * fvv)

{

  double x2 = gsl_vector_get(x, 1);

  double x3 = gsl_vector_get(x, 2);

  double x4 = gsl_vector_get(x, 3);

  double x5 = gsl_vector_get(x, 4);

  double v2 = gsl_vector_get(v, 1);

  double v3 = gsl_vector_get(v, 2);

  double v4 = gsl_vector_get(v, 3);

  double v5 = gsl_vector_get(v, 4);

  size_t i;

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

    {

      double ti = 10.0*i;

      double term1 = exp(-x4*ti);

      double term2 = exp(-x5*ti);

      double term3 = -2*v2 + ti*v4*x2;

      double term4 = -2*v3 + ti*v5*x3;

      gsl_vector_set(fvv, i, -term1 * term2 * ti *

                             (v4 / term2 * term3 + v5 / term1 * term4));

    }

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

  return GSL_SUCCESS;

}

static gsl_multifit_nlinear_fdf osborne_func =

{

  osborne_f,

  osborne_df,

  osborne_fvv,

  osborne_N,

  osborne_P,

  NULL,

  0,

  0,

  0

};

static test_fdf_problem osborne_problem =

{

  "osborne",

  osborne_x0,

  NULL,

  NULL,

  &osborne_epsrel,

  &osborne_checksol,

  &osborne_func

};