test_rosenbrock.c

#define rosenbrock_N         2
#define rosenbrock_P         2

static double rosenbrock_x0[rosenbrock_P] = { -1.2, 1.0 };
static double rosenbrock_epsrel = 1.0e-12;

static double rosenbrock_J[rosenbrock_N * rosenbrock_P];

static void
rosenbrock_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 < rosenbrock_P; ++i)
    {
      gsl_test_rel(x[i], 1.0, epsrel, "%s/%s i=%zu",
                   sname, pname, i);
    }
}

static int
rosenbrock_f (const gsl_vector * x, void *params, gsl_vector * f)
{
  double x1 = gsl_vector_get(x, 0);
  double x2 = gsl_vector_get(x, 1);

  gsl_vector_set(f, 0, 10.0 * (x2 - x1*x1));
  gsl_vector_set(f, 1, 1.0 - x1);

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

  return GSL_SUCCESS;
}

static int
rosenbrock_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(rosenbrock_J, rosenbrock_N, rosenbrock_P);
  double x1 = gsl_vector_get(x, 0);

  gsl_matrix_set(&J.matrix, 0, 0, -20.0*x1);
  gsl_matrix_set(&J.matrix, 0, 1, 10.0);
  gsl_matrix_set(&J.matrix, 1, 0, -1.0);
  gsl_matrix_set(&J.matrix, 1, 1, 0.0);

  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
rosenbrock_fvv (const gsl_vector * x, const gsl_vector * v,
                void *params, gsl_vector * fvv)
{
  double v1 = gsl_vector_get(v, 0);

  gsl_vector_set(fvv, 0, -20.0 * v1 * v1);
  gsl_vector_set(fvv, 1, 0.0);

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

  return GSL_SUCCESS;
}

static gsl_multilarge_nlinear_fdf rosenbrock_func =
{
  rosenbrock_f,
  rosenbrock_df,
  rosenbrock_fvv,
  rosenbrock_N,
  rosenbrock_P,
  NULL,
  0,
  0,
  0,
  0
};

static test_fdf_problem rosenbrock_problem =
{
  "rosenbrock",
  rosenbrock_x0,
  NULL,
  &rosenbrock_epsrel,
  &rosenbrock_checksol,
  &rosenbrock_func
};