#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_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;

  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 (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));

    }

  (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_multifit_nlinear_fdf kowalik_func =

{

  kowalik_f,

  kowalik_df,

  kowalik_fvv,

  kowalik_N,

  kowalik_P,

  NULL,

  0,

  0,

  0

};

static test_fdf_problem kowalik_problem =

{

  "kowalik",

  kowalik_x0,

  NULL,

  NULL,

  &kowalik_epsrel,

  &kowalik_checksol,

  &kowalik_func

};