#define kowalik_N         11

#define kowalik_P         4

#define kowalik_NTRIES    4

static double kowalik_x0[kowalik_P] = { 0.25, 0.39, 0.415, 0.39 };

static double kowalik_epsrel = 1.0e-7;

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;

  const double kowalik_x2[kowalik_P] = { -99999.9,   /* inf */

                                         -14.0758834005984603,

                                         -99999.9,   /* -inf */

                                         -99999.9 }; /* -inf */

  const double *kowalik_x;

  double sumsq_exact;

  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 (kowalik_x[i] < -90000.0)

        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);

    }

  return GSL_SUCCESS;

}

static int

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

{

  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, i, 0, -term1 / term2);

      gsl_matrix_set(J, i, 1, -ui*x1/term2);

      gsl_matrix_set(J, i, 2, ui*term1*x1 / (term2*term2));

      gsl_matrix_set(J, i, 3, term1*x1 / (term2*term2));

    }

  return GSL_SUCCESS;

}

static gsl_multifit_function_fdf kowalik_func =

{

  &kowalik_f,

  &kowalik_df,

  NULL,

  kowalik_N,

  kowalik_P,

  NULL,

  0,

  0

};

static test_fdf_problem kowalik_problem =

{

  "kowalik",

  kowalik_x0,

  NULL,

  &kowalik_epsrel,

  kowalik_NTRIES,

  &kowalik_checksol,

  &kowalik_func

};