#define penalty1_P         10

#define penalty1_N         (penalty1_P + 1)

static double penalty1_x0[penalty1_P] = { 1.0, 2.0, 3.0, 4.0, 5.0,

                                          6.0, 7.0, 8.0, 9.0, 10.0 };

static double penalty1_epsrel = 1.0e-12;

static void

penalty1_checksol(const double x[], const double sumsq,

                  const double epsrel, const char *sname,

                  const char *pname)

{

  const double sumsq_exact = 7.08765146709037993e-05;

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

               sname, pname);

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

}

static int

penalty1_f (const gsl_vector * x, void *params, gsl_vector * f)

{

  const double alpha = 1.0e-5;

  const double sqrt_alpha = sqrt(alpha);

  size_t i;

  double sum = 0.0;

  for (i = 0; i < penalty1_P; ++i)

    {

      double xi = gsl_vector_get(x, i);

      gsl_vector_set(f, i, sqrt_alpha*(xi - 1.0));

      sum += xi * xi;

    }

  gsl_vector_set(f, penalty1_N - 1, sum - 0.25);

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

  return GSL_SUCCESS;

}

static int

penalty1_df (const gsl_vector * x, void *params, gsl_matrix * J)

{

  const double alpha = 1.0e-5;

  const double sqrt_alpha = sqrt(alpha);

  size_t i;

  gsl_matrix_view m = gsl_matrix_submatrix(J, 0, 0, penalty1_P, penalty1_P);

  gsl_vector_view diag = gsl_matrix_diagonal(&m.matrix);

  gsl_matrix_set_zero(&m.matrix);

  gsl_vector_set_all(&diag.vector, sqrt_alpha);

  for (i = 0; i < penalty1_P; ++i)

    {

      double xi = gsl_vector_get(x, i);

      gsl_matrix_set(J, penalty1_N - 1, i, 2.0 * xi);

    }

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

  return GSL_SUCCESS;

}

static int

penalty1_fvv (const gsl_vector * x, const gsl_vector * v,

              void *params, gsl_vector * fvv)

{

  double u;

  gsl_vector_set_zero(fvv);

  gsl_blas_ddot(v, v, &u);

  gsl_vector_set(fvv, penalty1_N - 1, 2.0 * u);

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

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

  return GSL_SUCCESS;

}

static gsl_multifit_nlinear_fdf penalty1_func =

{

  penalty1_f,

  penalty1_df,

  penalty1_fvv,

  penalty1_N,

  penalty1_P,

  NULL,

  0,

  0,

  0

};

static test_fdf_problem penalty1_problem =

{

  "penalty1",

  penalty1_x0,

  NULL,

  NULL,

  &penalty1_epsrel,

  &penalty1_checksol,

  &penalty1_func

};