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size_t longley_n = 16;
size_t longley_p = 7;
double longley_x [] = {
1, 83.0, 234289, 2356, 1590, 107608, 1947,
1, 88.5, 259426, 2325, 1456, 108632, 1948,
1, 88.2, 258054, 3682, 1616, 109773, 1949,
1, 89.5, 284599, 3351, 1650, 110929, 1950,
1, 96.2, 328975, 2099, 3099, 112075, 1951,
1, 98.1, 346999, 1932, 3594, 113270, 1952,
1, 99.0, 365385, 1870, 3547, 115094, 1953,
1, 100.0, 363112, 3578, 3350, 116219, 1954,
1, 101.2, 397469, 2904, 3048, 117388, 1955,
1, 104.6, 419180, 2822, 2857, 118734, 1956,
1, 108.4, 442769, 2936, 2798, 120445, 1957,
1, 110.8, 444546, 4681, 2637, 121950, 1958,
1, 112.6, 482704, 3813, 2552, 123366, 1959,
1, 114.2, 502601, 3931, 2514, 125368, 1960,
1, 115.7, 518173, 4806, 2572, 127852, 1961,
1, 116.9, 554894, 4007, 2827, 130081, 1962 } ;
double longley_y[] = {60323, 61122, 60171, 61187, 63221, 63639, 64989, 63761,
66019, 67857, 68169, 66513, 68655, 69564, 69331, 70551};
static int
test_longley_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 < longley_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_longley ()
{
gsl_multifit_linear_workspace * work =
gsl_multifit_linear_alloc (longley_n, longley_p);
gsl_multifit_robust_workspace * work_rob =
gsl_multifit_robust_alloc (gsl_multifit_robust_ols, longley_n, longley_p);
gsl_matrix_view X = gsl_matrix_view_array (longley_x, longley_n, longley_p);
gsl_vector_view y = gsl_vector_view_array (longley_y, longley_n);
gsl_vector * c = gsl_vector_alloc (longley_p);
gsl_vector * r = gsl_vector_alloc (longley_n);
gsl_matrix * cov = gsl_matrix_alloc (longley_p, longley_p);
double chisq, chisq_res;
double expected_c[7] = { -3482258.63459582,
15.0618722713733,
-0.358191792925910E-01,
-2.02022980381683,
-1.03322686717359,
-0.511041056535807E-01,
1829.15146461355 };
double expected_sd[7] = { 890420.383607373,
84.9149257747669,
0.334910077722432E-01,
0.488399681651699,
0.214274163161675,
0.226073200069370,
455.478499142212 } ;
double expected_chisq = 836424.055505915;
gsl_vector_view diag = gsl_matrix_diagonal (cov);
gsl_vector_view exp_c = gsl_vector_view_array(expected_c, longley_p);
gsl_vector_view exp_sd = gsl_vector_view_array(expected_sd, longley_p);
/* test unweighted least squares */
gsl_multifit_linear (&X.matrix, &y.vector, c, cov, &chisq, work);
gsl_multifit_linear_residuals(&X.matrix, &y.vector, c, r);
gsl_blas_ddot(r, r, &chisq_res);
test_longley_results("longley 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.matrix, &y.vector, c, cov, work_rob);
test_longley_results("longley gsl_multifit_robust",
c, &exp_c.vector,
&diag.vector, &exp_sd.vector,
1.0, 1.0, 1.0);
/* test weighted least squares */
{
size_t i, j;
gsl_vector * w = gsl_vector_alloc (longley_n);
double expected_cov[7][7] = { { 8531122.56783558,
-166.727799925578, 0.261873708176346, 3.91188317230983,
1.1285582054705, -0.889550869422687, -4362.58709870581},
{-166.727799925578, 0.0775861253030891, -1.98725210399982e-05,
-0.000247667096727256, -6.82911920718824e-05, 0.000136160797527761,
0.0775255245956248},
{0.261873708176346, -1.98725210399982e-05, 1.20690316701888e-08,
1.66429546772984e-07, 3.61843600487847e-08, -6.78805814483582e-08,
-0.00013158719037715},
{3.91188317230983, -0.000247667096727256, 1.66429546772984e-07,
2.56665052544717e-06, 6.96541409215597e-07, -9.00858307771567e-07,
-0.00197260370663974},
{1.1285582054705, -6.82911920718824e-05, 3.61843600487847e-08,
6.96541409215597e-07, 4.94032602583969e-07, -9.8469143760973e-08,
-0.000576921112208274},
{-0.889550869422687, 0.000136160797527761, -6.78805814483582e-08,
-9.00858307771567e-07, -9.8469143760973e-08, 5.49938542664952e-07,
0.000430074434198215},
{-4362.58709870581, 0.0775255245956248, -0.00013158719037715,
-0.00197260370663974, -0.000576921112208274, 0.000430074434198215,
2.23229587481535 }} ;
gsl_vector_set_all (w, 1.0);
gsl_multifit_wlinear (&X.matrix, w, &y.vector, c, cov, &chisq, work);
gsl_multifit_linear_residuals(&X.matrix, &y.vector, c, r);
gsl_blas_ddot(r, r, &chisq_res);
test_longley_results("longley gsl_multifit_wlinear",
c, &exp_c.vector,
NULL, NULL,
chisq, chisq_res, expected_chisq);
for (i = 0; i < longley_p; i++)
{
for (j = 0; j < longley_p; j++)
{
gsl_test_rel (gsl_matrix_get(cov,i,j), expected_cov[i][j], 1e-7,
"longley 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_multifit_linear_free (work);
gsl_multifit_robust_free (work_rob);
} /* test_longley() */
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