#define exp1_N         45

#define exp1_P         4

static double exp1_x0[exp1_P] = { -1.0, -2.0, 1.0, -1.0 };

static double exp1_epsrel = 1.0e-4;

static double exp1_Y[exp1_N] = {

0.090542, 0.124569, 0.179367, 0.195654, 0.269707,

0.286027, 0.289892, 0.317475, 0.308191, 0.336995,

0.348371, 0.321337, 0.299423, 0.338972, 0.304763,

0.288903, 0.300820, 0.303974, 0.283987, 0.262078,

0.281593, 0.267531, 0.218926, 0.225572, 0.200594,

0.197375, 0.182440, 0.183892, 0.152285, 0.174028,

0.150874, 0.126220, 0.126266, 0.106384, 0.118923,

0.091868, 0.128926, 0.119273, 0.115997, 0.105831,

0.075261, 0.068387, 0.090823, 0.085205, 0.067203

};

static void

exp1_checksol(const double x[], const double sumsq,

              const double epsrel, const char *sname,

              const char *pname)

{

  size_t i;

  const double sumsq_exact = 1.0e-2;

  const double exp1_x[exp1_P] = { -4.0, -5.0, 4.0, -4.0 }; /* approx */

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

               sname, pname);

  for (i = 0; i < exp1_P; ++i)

    {

      gsl_test_rel(x[i], exp1_x[i], epsrel, "%s/%s i=%zu",

                   sname, pname, i);

    }

}

static int

exp1_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);

  size_t i;

  for (i = 0; i < exp1_N; ++i)

    {

      double ti = 0.02*(i + 1.0);

      double yi = exp1_Y[i];

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

      gsl_vector_set(f, i, fi);

    }

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

  return GSL_SUCCESS;

}

static int

exp1_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);

  double x4 = gsl_vector_get(x, 3);

  size_t i;

  for (i = 0; i < exp1_N; ++i)

    {

      double ti = 0.02*(i + 1.0);

      double term1 = exp(x1*ti);

      double term2 = exp(x2*ti);

      gsl_matrix_set(J, i, 0, -x3*ti*term1);

      gsl_matrix_set(J, i, 1, -x4*ti*term2);

      gsl_matrix_set(J, i, 2, -term1);

      gsl_matrix_set(J, i, 3, -term2);

    }

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

  return GSL_SUCCESS;

}

static int

exp1_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 x4 = gsl_vector_get(x, 3);

  double v1 = gsl_vector_get(v, 0);

  double v2 = gsl_vector_get(v, 1);

  double v3 = gsl_vector_get(v, 2);

  double v4 = gsl_vector_get(v, 3);

  size_t i;

  for (i = 0; i < exp1_N; ++i)

    {

      double ti = 0.02*(i + 1.0);

      double term1 = exp(x1*ti);

      double term2 = exp(x2*ti);

      double term3 = 2*v3 + ti*v1*x3;

      double term4 = 2*v4 + ti*v2*x4;

      gsl_vector_set(fvv, i, -ti*(v1*term1*term3 + v2*term2*term4));

    }

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

  return GSL_SUCCESS;

}

static gsl_multifit_nlinear_fdf exp1_func =

{

  exp1_f,

  exp1_df,

  exp1_fvv,

  exp1_N,

  exp1_P,

  NULL,

  0,

  0,

  0

};

static test_fdf_problem exp1_problem =

{

  "expfit1",

  exp1_x0,

  NULL,

  NULL,

  &exp1_epsrel,

  &exp1_checksol,

  &exp1_func

};