test_vardim.c

#define vardim_N         7 /* p + 2 */
#define vardim_P         5

static double vardim_x0[vardim_P] = { 0.8, 0.6, 0.4, 0.2, 0.0 };
static double vardim_epsrel = 1.0e-12;

static double vardim_J[vardim_N * vardim_P];

static void
vardim_checksol(const double x[], const double sumsq,
                const double epsrel, const char *sname,
                const char *pname)
{
  size_t i;
  const double sumsq_exact = 0.0;

  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
               sname, pname);

  for (i = 0; i < vardim_P; ++i)
    {
      gsl_test_rel(x[i], 1.0, epsrel, "%s/%s i=%zu",
                   sname, pname, i);
    }
}

static int
vardim_f (const gsl_vector * x, void *params, gsl_vector * f)
{
  size_t i;
  double sum = 0.0;

  for (i = 0; i < vardim_P; ++i)
    {
      double xi = gsl_vector_get(x, i);

      gsl_vector_set(f, i, xi - 1.0);

      sum += (i + 1.0) * (xi - 1.0);
    }

  gsl_vector_set(f, vardim_P, sum);
  gsl_vector_set(f, vardim_P + 1, sum*sum);

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

  return GSL_SUCCESS;
}

static int
vardim_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
           const gsl_vector * u, void * params, gsl_vector * v,
           gsl_matrix * JTJ)
{
  gsl_matrix_view J = gsl_matrix_view_array(vardim_J, vardim_N, vardim_P);
  size_t i;
  double sum = 0.0;
  gsl_matrix_view m = gsl_matrix_submatrix(&J.matrix, 0, 0, vardim_P, vardim_P);

  gsl_matrix_set_identity(&m.matrix);

  for (i = 0; i < vardim_P; ++i)
    {
      double xi = gsl_vector_get(x, i);
      sum += (i + 1.0) * (xi - 1.0);
    }

  for (i = 0; i < vardim_P; ++i)
    {
      gsl_matrix_set(&J.matrix, vardim_P, i, i + 1.0);
      gsl_matrix_set(&J.matrix, vardim_P + 1, i, 2*(i + 1.0)*sum);
    }

  if (v)
    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);

  if (JTJ)
    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);

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

  return GSL_SUCCESS;
}

static int
vardim_fvv (const gsl_vector * x, const gsl_vector * v,
            void *params, gsl_vector * fvv)
{
  size_t i;
  double sum = 0.0;

  gsl_vector_set_zero(fvv);

  for (i = 0; i < vardim_P; ++i)
    {
      double vi = gsl_vector_get(v, i);
      sum += (i + 1.0) * vi;
    }

  gsl_vector_set(fvv, vardim_N - 1, 2.0 * sum * sum);

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

  return GSL_SUCCESS;
}

static gsl_multilarge_nlinear_fdf vardim_func =
{
  vardim_f,
  vardim_df,
  vardim_fvv,
  vardim_N,
  vardim_P,
  NULL,
  0,
  0,
  0,
  0
};

static test_fdf_problem vardim_problem =
{
  "vardim",
  vardim_x0,
  NULL,
  &vardim_epsrel,
  &vardim_checksol,
  &vardim_func
};