#define lin3_N         50  /* can be anything >= p */

#define lin3_P         10  /* >= 3 */

#define lin3_NTRIES    3

static double lin3_x0[lin3_P] = { 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 };

static double lin3_epsrel = 1.0e-10;

static void

lin3_checksol(const double x[], const double sumsq,

              const double epsrel, const char *sname,

              const char *pname)

{

  size_t i;

  const double n = (double) lin3_N;

  const double sumsq_exact = 0.5 * (n*n + 3*n - 6.0) / (2*n - 3.0);

  const double sum_exact = 3.0 / (2.0*n - 3.0);

  double sum = 0.0;

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

               sname, pname);

  for (i = 1; i < lin3_P - 1; ++i)

    sum += (i + 1.0) * x[i];

  gsl_test_rel(sum, sum_exact, epsrel, "%s/%s coeff sum",

               sname, pname);

}

static int

lin3_f (const gsl_vector * x, void *params, gsl_vector * f)

{

  size_t i, j;

  gsl_vector_set(f, 0, -1.0);

  gsl_vector_set(f, lin3_N - 1, -1.0);

  for (i = 1; i < lin3_N - 1; ++i)

    {

      double fi = 0.0;

      for (j = 1; j < lin3_P - 1; ++j)

        {

          double xj = gsl_vector_get(x, j);

          fi += (j + 1) * xj;

        }

      fi = i * fi - 1.0;

      gsl_vector_set(f, i, fi);

    }

  return GSL_SUCCESS;

}

static int

lin3_df (const gsl_vector * x, void *params, gsl_matrix * J)

{

  size_t i, j;

  gsl_matrix_set_zero(J);

  for (i = 1; i < lin3_N - 1; ++i)

    {

      for (j = 1; j < lin3_P - 1; ++j)

        {

          gsl_matrix_set(J, i, j, i * (j + 1.0));

        }

    }

  return GSL_SUCCESS;

}

static gsl_multifit_function_fdf lin3_func =

{

  &lin3_f,

  &lin3_df,

  NULL,

  lin3_N,

  lin3_P,

  NULL,

  0,

  0

};

static test_fdf_problem lin3_problem =

{

  "linear_rank1zeros",

  lin3_x0,

  NULL,

  &lin3_epsrel,

  lin3_NTRIES,

  &lin3_checksol,

  &lin3_func

};