#define box_N         10 /* can be >= p */

#define box_P         3

/* dogleg method fails with recommended starting point, so use

 * a slightly easier x0 */

/*static double box_x0[box_P] = { 0.0, 10.0, 20.0 };*/

static double box_x0[box_P] = { 5.0, 10.0, 2.0 };

static double box_epsrel = 1.0e-12;

static void

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

              const double epsrel, const char *sname,

              const char *pname)

{

  const double sumsq_exact = 0.0;

  const double eps = 1.0e-6;

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

               sname, pname);

  /* there are 3 possible solution vectors */

  if (fabs(x[2] - 1.0) < eps)

    {

      /* case 1: x* = [ 1; 10; 1 ] */

      gsl_test_rel(x[0], 1.0, epsrel, "%s/%s i=0",

                   sname, pname);

      gsl_test_rel(x[1], 10.0, epsrel, "%s/%s i=1",

                   sname, pname);

      gsl_test_rel(x[2], 1.0, epsrel, "%s/%s i=2",

                   sname, pname);

    }

  else if (fabs(x[2] + 1.0) < eps)

    {

      /* case 2: x* = [ 10; 1; -1 ] */

      gsl_test_rel(x[0], 10.0, epsrel, "%s/%s i=0",

                   sname, pname);

      gsl_test_rel(x[1], 1.0, epsrel, "%s/%s i=1",

                   sname, pname);

      gsl_test_rel(x[2], -1.0, epsrel, "%s/%s i=2",

                   sname, pname);

    }

  else

    {

      /* case 3: x* = [ a; a; 0 ] for any a */

      gsl_test_rel(x[0], x[1], epsrel, "%s/%s i=0,1",

                   sname, pname);

      gsl_test_rel(x[2], 0.0, epsrel, "%s/%s i=2",

                   sname, pname);

    }

}

static int

box_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 < box_N; ++i)

    {

      double ti = (i + 1.0) / 10.0;

      double fi = exp(-x1*ti) - exp(-x2*ti) - x3*(exp(-ti) - exp(-10.0*ti));

      gsl_vector_set(f, i, fi);

    }

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

  return GSL_SUCCESS;

}

static int

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

{

  double x1 = gsl_vector_get(x, 0);

  double x2 = gsl_vector_get(x, 1);

  size_t i;

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

    {

      double ti = (i + 1.0) / 10.0;

      double term1 = exp(-x1*ti);

      double term2 = exp(-x2*ti);

      double term3 = exp(-10.0*ti) - exp(-ti);

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

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

      gsl_matrix_set(J, i, 2, term3);

    }

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

  return GSL_SUCCESS;

}

static int

box_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 v1 = gsl_vector_get(v, 0);

  double v2 = gsl_vector_get(v, 1);

  size_t i;

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

    {

      double ti = (i + 1.0) / 10.0;

      double term1 = exp(-x1*ti);

      double term2 = exp(-x2*ti);

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

    }

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

  return GSL_SUCCESS;

}

static gsl_multifit_nlinear_fdf box_func =

{

  box_f,

  box_df,

  box_fvv,

  box_N,

  box_P,

  NULL,

  0,

  0,

  0

};

static test_fdf_problem box_problem =

{

  "box3d",

  box_x0,

  NULL,

  NULL,

  &box_epsrel,

  &box_checksol,

  &box_func

};