size_t pontius_n = 40;

size_t pontius_p = 3;

double pontius_x[] = { 150000, 300000, 450000, 600000, 750000, 900000,

1050000, 1200000, 1350000, 1500000, 1650000, 1800000, 1950000, 2100000,

2250000, 2400000, 2550000, 2700000, 2850000, 3000000, 150000, 300000,

450000, 600000, 750000, 900000, 1050000, 1200000, 1350000, 1500000,

1650000, 1800000, 1950000, 2100000, 2250000, 2400000, 2550000, 2700000,

2850000, 3000000 };

double pontius_y[] = { .11019, .21956, .32949, .43899, .54803, .65694,

.76562, .87487, .98292, 1.09146, 1.20001, 1.30822, 1.41599, 1.52399,

1.63194, 1.73947, 1.84646, 1.95392, 2.06128, 2.16844, .11052, .22018,

.32939, .43886, .54798, .65739, .76596, .87474, .98300, 1.09150,

1.20004, 1.30818, 1.41613, 1.52408, 1.63159, 1.73965, 1.84696,

1.95445, 2.06177, 2.16829 };

static int

test_pontius_results(const char *str,

                     const gsl_vector *c, const gsl_vector *expected_c,

                     const gsl_vector *cov_diag, const gsl_vector *expected_sd,

                     const double chisq, const double chisq_res,

                     const double expected_chisq)

{

  size_t i;

  /* test coefficient vector */

  for (i = 0; i < pontius_p; ++i)

    {

      gsl_test_rel (gsl_vector_get(c,i),

                    gsl_vector_get(expected_c, i),

                    1.0e-10,

                    "%s c[%zu]", str, i) ;

      if (cov_diag && expected_sd)

        {

          gsl_test_rel (sqrt(gsl_vector_get(cov_diag, i)),

                        gsl_vector_get(expected_sd, i),

                        1e-10,

                        "%s cov[%zu,%zu]", str, i, i);

        }

    }

  gsl_test_rel (chisq, expected_chisq, 1.0e-10, "%s chisq", str);

  gsl_test_rel (chisq_res, expected_chisq, 1.0e-10, "%s chisq residuals", str);

  return GSL_SUCCESS;

}

void

test_pontius ()

{

  size_t i, j;

  gsl_multifit_linear_workspace * work = 

    gsl_multifit_linear_alloc (pontius_n, pontius_p);

  gsl_multifit_robust_workspace * work_rob = 

    gsl_multifit_robust_alloc (gsl_multifit_robust_ols, pontius_n, pontius_p);

  gsl_matrix * X = gsl_matrix_alloc (pontius_n, pontius_p);

  gsl_vector_view y = gsl_vector_view_array (pontius_y, pontius_n);

  gsl_vector * c = gsl_vector_alloc (pontius_p);

  gsl_vector * r = gsl_vector_alloc (pontius_n);

  gsl_matrix * cov = gsl_matrix_alloc (pontius_p, pontius_p);

  double chisq, chisq_res;

  double expected_c[3] = { 0.673565789473684E-03,

                           0.732059160401003E-06,

                          -0.316081871345029E-14};

  double expected_sd[3] = { 0.107938612033077E-03,

                            0.157817399981659E-09,

                            0.486652849992036E-16 };

  double expected_chisq = 0.155761768796992E-05;

  gsl_vector_view diag = gsl_matrix_diagonal (cov);

  gsl_vector_view exp_c = gsl_vector_view_array(expected_c, pontius_p);

  gsl_vector_view exp_sd = gsl_vector_view_array(expected_sd, pontius_p);

  for (i = 0 ; i < pontius_n; i++) 

    {

      for (j = 0; j < pontius_p; j++) 

        {

          gsl_matrix_set(X, i, j, pow(pontius_x[i], j));

        }

    }

  /* test unweighted least squares */

  gsl_multifit_linear (X, &y.vector, c, cov, &chisq, work);

  gsl_multifit_linear_residuals(X, &y.vector, c, r);

  gsl_blas_ddot(r, r, &chisq_res);

  test_pontius_results("pontius gsl_multifit_linear",

                       c, &exp_c.vector,

                       &diag.vector, &exp_sd.vector,

                       chisq, chisq_res, expected_chisq);

  /* test robust least squares */

  gsl_multifit_robust (X, &y.vector, c, cov, work_rob);

  test_pontius_results("pontius gsl_multifit_robust",

                       c, &exp_c.vector,

                       &diag.vector, &exp_sd.vector,

                       1.0, 1.0, 1.0);

  /* test weighted least squares */

  {

    gsl_vector * w = gsl_vector_alloc (pontius_n);

    double expected_cov[3][3] ={ 

      {2.76754385964916e-01 , -3.59649122807024e-07,   9.74658869395731e-14},

      {-3.59649122807024e-07,   5.91630591630603e-13,  -1.77210703526497e-19},

      {9.74658869395731e-14,  -1.77210703526497e-19,   5.62573661988878e-26} };

    gsl_vector_set_all (w, 1.0);

    gsl_multifit_wlinear (X, w, &y.vector, c, cov, &chisq, work);

    gsl_multifit_linear_residuals(X, &y.vector, c, r);

    gsl_blas_ddot(r, r, &chisq_res);

    test_pontius_results("pontius gsl_multifit_wlinear",

                         c, &exp_c.vector,

                         NULL, NULL,

                         chisq, chisq_res, expected_chisq);

    for (i = 0; i < pontius_p; i++) 

      {

        for (j = 0; j < pontius_p; j++)

          {

            gsl_test_rel (gsl_matrix_get(cov,i,j), expected_cov[i][j], 1e-10, 

                          "pontius gsl_multifit_wlinear cov(%d,%d)", i, j) ;

          }

      }

    gsl_vector_free(w);

  }

  gsl_vector_free(c);

  gsl_vector_free(r);

  gsl_matrix_free(cov);

  gsl_matrix_free(X);

  gsl_multifit_linear_free (work);

  gsl_multifit_robust_free (work_rob);

}