test_longley.c

开放gsl矩阵运算

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};


void 
test_longley ()
{     
  size_t i, j;
  {
    gsl_multifit_linear_workspace * work = 
      gsl_multifit_linear_alloc (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_matrix * cov = gsl_matrix_alloc (longley_p, longley_p);
    gsl_vector_view diag;

    double chisq;

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

    gsl_test_rel (gsl_vector_get(c,0), expected_c[0], 1e-10, "longley gsl_fit_multilinear c0") ;
    gsl_test_rel (gsl_vector_get(c,1), expected_c[1], 1e-10, "longley gsl_fit_multilinear c1") ;
    gsl_test_rel (gsl_vector_get(c,2), expected_c[2], 1e-10, "longley gsl_fit_multilinear c2") ;
    gsl_test_rel (gsl_vector_get(c,3), expected_c[3], 1e-10, "longley gsl_fit_multilinear c3") ;
    gsl_test_rel (gsl_vector_get(c,4), expected_c[4], 1e-10, "longley gsl_fit_multilinear c4") ;
    gsl_test_rel (gsl_vector_get(c,5), expected_c[5], 1e-10, "longley gsl_fit_multilinear c5") ;
    gsl_test_rel (gsl_vector_get(c,6), expected_c[6], 1e-10, "longley gsl_fit_multilinear c6") ;

    diag = gsl_matrix_diagonal (cov);

    gsl_test_rel (gsl_vector_get(&diag.vector,0), pow(expected_sd[0],2.0), 1e-10, "longley gsl_fit_multilinear cov00") ;
    gsl_test_rel (gsl_vector_get(&diag.vector,1), pow(expected_sd[1],2.0), 1e-10, "longley gsl_fit_multilinear cov11") ;
    gsl_test_rel (gsl_vector_get(&diag.vector,2), pow(expected_sd[2],2.0), 1e-10, "longley gsl_fit_multilinear cov22") ;
    gsl_test_rel (gsl_vector_get(&diag.vector,3), pow(expected_sd[3],2.0), 1e-10, "longley gsl_fit_multilinear cov33") ;
    gsl_test_rel (gsl_vector_get(&diag.vector,4), pow(expected_sd[4],2.0), 1e-10, "longley gsl_fit_multilinear cov44") ;
    gsl_test_rel (gsl_vector_get(&diag.vector,5), pow(expected_sd[5],2.0), 1e-10, "longley gsl_fit_multilinear cov55") ;
    gsl_test_rel (gsl_vector_get(&diag.vector,6), pow(expected_sd[6],2.0), 1e-10, "longley gsl_fit_multilinear cov66") ;

    gsl_test_rel (chisq, expected_chisq, 1e-10, "longley gsl_fit_multilinear chisq") ;

    gsl_vector_free(c);
    gsl_matrix_free(cov);
    gsl_multifit_linear_free (work);
  }


  {
    gsl_multifit_linear_workspace * work = 
      gsl_multifit_linear_alloc (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 * w = gsl_vector_alloc (longley_n);
    gsl_vector * c = gsl_vector_alloc (longley_p);
    gsl_matrix * cov = gsl_matrix_alloc (longley_p, longley_p);

    double chisq;

    double expected_c[7] = {  -3482258.63459582,
                              15.0618722713733,
                              -0.358191792925910E-01,
                              -2.02022980381683,
                              -1.03322686717359,
                              -0.511041056535807E-01,
                              1829.15146461355 };

    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 }} ;

    double expected_chisq = 836424.055505915;

    gsl_vector_set_all (w, 1.0);

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

    gsl_test_rel (gsl_vector_get(c,0), expected_c[0], 1e-10, "longley gsl_fit_wmultilinear c0") ;
    gsl_test_rel (gsl_vector_get(c,1), expected_c[1], 1e-10, "longley gsl_fit_wmultilinear c1") ;
    gsl_test_rel (gsl_vector_get(c,2), expected_c[2], 1e-10, "longley gsl_fit_wmultilinear c2") ;
    gsl_test_rel (gsl_vector_get(c,3), expected_c[3], 1e-10, "longley gsl_fit_wmultilinear c3") ;
    gsl_test_rel (gsl_vector_get(c,4), expected_c[4], 1e-10, "longley gsl_fit_wmultilinear c4") ;
    gsl_test_rel (gsl_vector_get(c,5), expected_c[5], 1e-10, "longley gsl_fit_wmultilinear c5") ;
    gsl_test_rel (gsl_vector_get(c,6), expected_c[6], 1e-10, "longley gsl_fit_wmultilinear c6") ;

    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_fit_wmultilinear cov(%d,%d)", i, j) ;
          }
      }

    gsl_test_rel (chisq, expected_chisq, 1e-10, "longley gsl_fit_wmultilinear chisq") ;

    gsl_vector_free(w);
    gsl_vector_free(c);
    gsl_matrix_free(cov);
    gsl_multifit_linear_free (work);
  }
}