test_kowalik.c

#define kowalik_N         11
#define kowalik_P         4

static double kowalik_x0[kowalik_P] = { 0.25, 0.39, 0.415, 0.39 };
static double kowalik_epsrel = 1.0e-6;

static double kowalik_J[kowalik_N * kowalik_P];

static double kowalik_Y[kowalik_N] = {
0.1957, 0.1947, 0.1735, 0.1600, 0.0844, 0.0627,
0.0456, 0.0342, 0.0323, 0.0235, 0.0246
};

static double kowalik_U[kowalik_N] = {
4.0000, 2.0000, 1.0000, 0.5000, 0.2500, 0.1670,
0.1250, 0.1000, 0.0833, 0.0714, 0.0625
};

static void
kowalik_checksol(const double x[], const double sumsq,
                 const double epsrel, const char *sname,
                 const char *pname)
{
  size_t i;
  gsl_vector_const_view v = gsl_vector_const_view_array(x, kowalik_P);
  const double norm = gsl_blas_dnrm2(&v.vector);
  const double sumsq_exact1 = 3.075056038492370e-04;
  const double kowalik_x1[kowalik_P] = { 1.928069345723978e-01,
                                         1.912823290344599e-01,
                                         1.230565070690708e-01,
                                         1.360623308065148e-01 };
  const double sumsq_exact2 = 0.00102734304869549252;
  double kowalik_x2[kowalik_P] = { 0.0,   /* inf */
                                   -14.0758834005984603,
                                   0.0,   /* -inf */
                                   0.0 }; /* -inf */
  const double *kowalik_x;
  double sumsq_exact;

  kowalik_x2[0] = GSL_NAN;
  kowalik_x2[2] = GSL_NAN;
  kowalik_x2[3] = GSL_NAN;

  if (norm < 10.0)
    {
      kowalik_x = kowalik_x1;
      sumsq_exact = sumsq_exact1;
    }
  else
    {
      kowalik_x = kowalik_x2;
      sumsq_exact = sumsq_exact2;
    }

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

  for (i = 0; i < kowalik_P; ++i)
    {
      if (!gsl_finite(kowalik_x[i]))
        continue;

      gsl_test_rel(x[i], kowalik_x[i], epsrel, "%s/%s i=%zu",
                   sname, pname, i);
    }
}

static int
kowalik_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);
  double x4 = gsl_vector_get(x, 3);
  size_t i;

  for (i = 0; i < kowalik_N; ++i)
    {
      double yi = kowalik_Y[i];
      double ui = kowalik_U[i];
      double fi = yi - (x1*ui*(ui+x2)) / (x4 + ui*(ui + x3));
      gsl_vector_set(f, i, fi);
    }

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

  return GSL_SUCCESS;
}

static int
kowalik_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(kowalik_J, kowalik_N, kowalik_P);
  double x1 = gsl_vector_get(x, 0);
  double x2 = gsl_vector_get(x, 1);
  double x3 = gsl_vector_get(x, 2);
  double x4 = gsl_vector_get(x, 3);
  size_t i;

  for (i = 0; i < kowalik_N; ++i)
    {
      double ui = kowalik_U[i];
      double term1 = ui*(ui + x2);
      double term2 = ui*(ui + x3) + x4;

      gsl_matrix_set(&J.matrix, i, 0, -term1 / term2);
      gsl_matrix_set(&J.matrix, i, 1, -ui*x1/term2);
      gsl_matrix_set(&J.matrix, i, 2, ui*term1*x1 / (term2*term2));
      gsl_matrix_set(&J.matrix, i, 3, term1*x1 / (term2*term2));
    }

  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
kowalik_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 x3 = gsl_vector_get(x, 2);
  double x4 = gsl_vector_get(x, 3);
  double v1 = gsl_vector_get(v, 0);
  double v2 = gsl_vector_get(v, 1);
  double v3 = gsl_vector_get(v, 2);
  double v4 = gsl_vector_get(v, 3);
  size_t i;

  for (i = 0; i < kowalik_N; ++i)
    {
      double ui = kowalik_U[i];
      double term2 = ui*(ui + x3) + x4;
      double term3 = ui*ui*v1 - ui*v3*x1 - v4*x1 +
                     ui*v1*x3 + v1*x4;
      double term4 = ui*ui*(v3-v2) + v4*x2 +
                     ui*(v4 + v3*x2 - v2*x3) - v2*x4;

      gsl_vector_set(fvv, i, 2.0*ui*term3*term4 / pow(term2, 3.0));
    }

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

  return GSL_SUCCESS;
}

static gsl_multilarge_nlinear_fdf kowalik_func =
{
  kowalik_f,
  kowalik_df,
  kowalik_fvv,
  kowalik_N,
  kowalik_P,
  NULL,
  0,
  0,
  0,
  0
};

static test_fdf_problem kowalik_problem =
{
  "kowalik",
  kowalik_x0,
  NULL,
  &kowalik_epsrel,
  &kowalik_checksol,
  &kowalik_func
};