/* randist/test.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007, 2010 James Theiler, Brian Gough
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 3 of the License, or (at
* your option) any later version.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
#include <config.h>
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_randist.h>
#include <gsl/gsl_rng.h>
#include <gsl/gsl_test.h>
#include <gsl/gsl_ieee_utils.h>
#include <gsl/gsl_integration.h>
#include <gsl/gsl_vector.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_blas.h>
#include <gsl/gsl_linalg.h>
#include <gsl/gsl_cdf.h>
#include <gsl/gsl_statistics.h>
#define N 100000
/* Convient test dimension for multivariant distributions */
#define MULTI_DIM 10
void testMoments (double (*f) (void), const char *name,
double a, double b, double p);
void testPDF (double (*f) (void), double (*pdf) (double), const char *name);
void testDiscretePDF (double (*f) (void), double (*pdf) (unsigned int),
const char *name);
void test_shuffle (void);
void test_choose (void);
double test_beta (void);
double test_beta_pdf (double x);
double test_bernoulli (void);
double test_bernoulli_pdf (unsigned int n);
double test_binomial (void);
double test_binomial_pdf (unsigned int n);
double test_binomial_large (void);
double test_binomial_large_pdf (unsigned int n);
double test_binomial_huge (void);
double test_binomial_huge_pdf (unsigned int n);
double test_binomial_max (void);
double test_binomial_max_pdf (unsigned int n);
double test_binomial0 (void);
double test_binomial0_pdf (unsigned int n);
double test_binomial1 (void);
double test_binomial1_pdf (unsigned int n);
double test_binomial_knuth (void);
double test_binomial_knuth_pdf (unsigned int n);
double test_binomial_large_knuth (void);
double test_binomial_large_knuth_pdf (unsigned int n);
double test_binomial_huge_knuth (void);
double test_binomial_huge_knuth_pdf (unsigned int n);
double test_cauchy (void);
double test_cauchy_pdf (double x);
double test_chisq (void);
double test_chisq_pdf (double x);
double test_chisqnu2 (void);
double test_chisqnu2_pdf (double x);
double test_dirichlet (void);
double test_dirichlet_pdf (double x);
double test_dirichlet_small (void);
double test_dirichlet_small_pdf (double x);
void test_dirichlet_moments (void);
double test_discrete1 (void);
double test_discrete1_pdf (unsigned int n);
double test_discrete2 (void);
double test_discrete2_pdf (unsigned int n);
double test_discrete3 (void);
double test_discrete3_pdf (unsigned int n);
double test_erlang (void);
double test_erlang_pdf (double x);
double test_exponential (void);
double test_exponential_pdf (double x);
double test_exppow0 (void);
double test_exppow0_pdf (double x);
double test_exppow1 (void);
double test_exppow1_pdf (double x);
double test_exppow1a (void);
double test_exppow1a_pdf (double x);
double test_exppow2 (void);
double test_exppow2_pdf (double x);
double test_exppow2a (void);
double test_exppow2a_pdf (double x);
double test_exppow2b (void);
double test_exppow2b_pdf (double x);
double test_fdist (void);
double test_fdist_pdf (double x);
double test_fdist_large (void);
double test_fdist_large_pdf (double x);
double test_flat (void);
double test_flat_pdf (double x);
double test_gamma (void);
double test_gamma_pdf (double x);
double test_gamma1 (void);
double test_gamma1_pdf (double x);
double test_gamma_int (void);
double test_gamma_int_pdf (double x);
double test_gamma_large (void);
double test_gamma_large_pdf (double x);
double test_gamma_vlarge (void);
double test_gamma_vlarge_pdf (double x);
double test_gamma_small (void);
double test_gamma_small_pdf (double x);
double test_gamma_mt (void);
double test_gamma_mt_pdf (double x);
double test_gamma_mt1 (void);
double test_gamma_mt1_pdf (double x);
double test_gamma_mt_int (void);
double test_gamma_mt_int_pdf (double x);
double test_gamma_mt_large (void);
double test_gamma_mt_large_pdf (double x);
double test_gamma_mt_small (void);
double test_gamma_mt_small_pdf (double x);
double test_gamma_knuth_vlarge (void);
double test_gamma_knuth_vlarge_pdf (double x);
double test_gaussian (void);
double test_gaussian_pdf (double x);
double test_gaussian_ratio_method (void);
double test_gaussian_ratio_method_pdf (double x);
double test_gaussian_ziggurat (void);
double test_gaussian_ziggurat_pdf (double x);
double test_gaussian_tail (void);
double test_gaussian_tail_pdf (double x);
double test_gaussian_tail1 (void);
double test_gaussian_tail1_pdf (double x);
double test_gaussian_tail2 (void);
double test_gaussian_tail2_pdf (double x);
double test_ugaussian (void);
double test_ugaussian_pdf (double x);
double test_ugaussian_ratio_method (void);
double test_ugaussian_ratio_method_pdf (double x);
double test_ugaussian_tail (void);
double test_ugaussian_tail_pdf (double x);
double test_bivariate_gaussian1 (void);
double test_bivariate_gaussian1_pdf (double x);
double test_bivariate_gaussian2 (void);
double test_bivariate_gaussian2_pdf (double x);
double test_bivariate_gaussian3 (void);
double test_bivariate_gaussian3_pdf (double x);
double test_bivariate_gaussian4 (void);
double test_bivariate_gaussian4_pdf (double x);
void test_multivariate_gaussian_log_pdf (void);
void test_multivariate_gaussian_pdf (void);
void test_multivariate_gaussian (void);
void test_wishart_log_pdf (void);
void test_wishart_pdf (void);
void test_wishart (void);
double test_gumbel1 (void);
double test_gumbel1_pdf (double x);
double test_gumbel2 (void);
double test_gumbel2_pdf (double x);
double test_geometric (void);
double test_geometric_pdf (unsigned int x);
double test_geometric1 (void);
double test_geometric1_pdf (unsigned int x);
double test_hypergeometric1 (void);
double test_hypergeometric1_pdf (unsigned int x);
double test_hypergeometric2 (void);
double test_hypergeometric2_pdf (unsigned int x);
double test_hypergeometric3 (void);
double test_hypergeometric3_pdf (unsigned int x);
double test_hypergeometric4 (void);
double test_hypergeometric4_pdf (unsigned int x);
double test_hypergeometric5 (void);
double test_hypergeometric5_pdf (unsigned int x);
double test_hypergeometric6 (void);
double test_hypergeometric6_pdf (unsigned int x);
double test_landau (void);
double test_landau_pdf (double x);
double test_levy1 (void);
double test_levy1_pdf (double x);
double test_levy2 (void);
double test_levy2_pdf (double x);
double test_levy1a (void);
double test_levy1a_pdf (double x);
double test_levy2a (void);
double test_levy2a_pdf (double x);
double test_levy_skew1 (void);
double test_levy_skew1_pdf (double x);
double test_levy_skew2 (void);
double test_levy_skew2_pdf (double x);
double test_levy_skew1a (void);
double test_levy_skew1a_pdf (double x);
double test_levy_skew2a (void);
double test_levy_skew2a_pdf (double x);
double test_levy_skew1b (void);
double test_levy_skew1b_pdf (double x);
double test_levy_skew2b (void);
double test_levy_skew2b_pdf (double x);
double test_logistic (void);
double test_logistic_pdf (double x);
double test_lognormal (void);
double test_lognormal_pdf (double x);
double test_logarithmic (void);
double test_logarithmic_pdf (unsigned int n);
double test_multinomial (void);
double test_multinomial_pdf (unsigned int n);
double test_multinomial_large (void);
double test_multinomial_large_pdf (unsigned int n);
void test_multinomial_moments (void);
double test_negative_binomial (void);
double test_negative_binomial_pdf (unsigned int n);
double test_pascal (void);
double test_pascal_pdf (unsigned int n);
double test_pareto (void);
double test_pareto_pdf (double x);
double test_poisson (void);
double test_poisson_pdf (unsigned int x);
double test_poisson_large (void);
double test_poisson_large_pdf (unsigned int x);
double test_dir2d (void);
double test_dir2d_pdf (double x);
double test_dir2d_trig_method (void);
double test_dir2d_trig_method_pdf (double x);
double test_dir3dxy (void);
double test_dir3dxy_pdf (double x);
double test_dir3dyz (void);
double test_dir3dyz_pdf (double x);
double test_dir3dzx (void);
double test_dir3dzx_pdf (double x);
double test_rayleigh (void);
double test_rayleigh_pdf (double x);
double test_rayleigh_tail (void);
double test_rayleigh_tail_pdf (double x);
double test_tdist1 (void);
double test_tdist1_pdf (double x);
double test_tdist2 (void);
double test_tdist2_pdf (double x);
double test_laplace (void);
double test_laplace_pdf (double x);
double test_weibull (void);
double test_weibull_pdf (double x);
double test_weibull1 (void);
double test_weibull1_pdf (double x);
gsl_rng *r_global;
static gsl_ran_discrete_t *g1 = NULL;
static gsl_ran_discrete_t *g2 = NULL;
static gsl_ran_discrete_t *g3 = NULL;
int
main (void)
{
gsl_ieee_env_setup ();
gsl_rng_env_setup ();
r_global = gsl_rng_alloc (gsl_rng_default);
#define FUNC(x) test_ ## x, "test gsl_ran_" #x
#define FUNC2(x) test_ ## x, test_ ## x ## _pdf, "test gsl_ran_" #x
test_shuffle ();
test_choose ();
testMoments (FUNC (ugaussian), 0.0, 100.0, 0.5);
testMoments (FUNC (ugaussian), -1.0, 1.0, 0.6826895);
testMoments (FUNC (ugaussian), 3.0, 3.5, 0.0011172689);
testMoments (FUNC (ugaussian_tail), 3.0, 3.5, 0.0011172689 / 0.0013498981);
testMoments (FUNC (exponential), 0.0, 1.0, 1 - exp (-0.5));
testMoments (FUNC (cauchy), 0.0, 10000.0, 0.5);
testMoments (FUNC (discrete1), -0.5, 0.5, 0.59);
testMoments (FUNC (discrete1), 0.5, 1.5, 0.40);
testMoments (FUNC (discrete1), 1.5, 3.5, 0.01);
testMoments (FUNC (discrete2), -0.5, 0.5, 1.0/45.0 );
testMoments (FUNC (discrete2), 8.5, 9.5, 0 );
testMoments (FUNC (discrete3), -0.5, 0.5, 0.05 );
testMoments (FUNC (discrete3), 0.5, 1.5, 0.05 );
testMoments (FUNC (discrete3), -0.5, 9.5, 0.5 );
test_dirichlet_moments ();
test_multinomial_moments ();
testPDF (FUNC2 (beta));
testPDF (FUNC2 (cauchy));
testPDF (FUNC2 (chisq));
testPDF (FUNC2 (chisqnu2));
testPDF (FUNC2 (dirichlet));
testPDF (FUNC2 (dirichlet_small));
testPDF (FUNC2 (erlang));
testPDF (FUNC2 (exponential));
testPDF (FUNC2 (exppow0));
testPDF (FUNC2 (exppow1));
testPDF (FUNC2 (exppow1a));
testPDF (FUNC2 (exppow2));
testPDF (FUNC2 (exppow2a));
testPDF (FUNC2 (exppow2b));
testPDF (FUNC2 (fdist));
testPDF (FUNC2 (fdist_large));
testPDF (FUNC2 (flat));
testPDF (FUNC2 (gamma));
testPDF (FUNC2 (gamma1));
testPDF (FUNC2 (gamma_int));
testPDF (FUNC2 (gamma_large));
testPDF (FUNC2 (gamma_vlarge));
testPDF (FUNC2 (gamma_knuth_vlarge));
testPDF (FUNC2 (gamma_small));
testPDF (FUNC2 (gamma_mt));
testPDF (FUNC2 (gamma_mt1));
testPDF (FUNC2 (gamma_mt_int));
testPDF (FUNC2 (gamma_mt_large));
testPDF (FUNC2 (gamma_mt_small));
testPDF (FUNC2 (gaussian));
testPDF (FUNC2 (gaussian_ratio_method));
testPDF (FUNC2 (gaussian_ziggurat));
testPDF (FUNC2 (ugaussian));
testPDF (FUNC2 (ugaussian_ratio_method));
testPDF (FUNC2 (gaussian_tail));
testPDF (FUNC2 (gaussian_tail1));
testPDF (FUNC2 (gaussian_tail2));
testPDF (FUNC2 (ugaussian_tail));
testPDF (FUNC2 (bivariate_gaussian1));
testPDF (FUNC2 (bivariate_gaussian2));
testPDF (FUNC2 (bivariate_gaussian3));
testPDF (FUNC2 (bivariate_gaussian4));
test_multivariate_gaussian_log_pdf ();
test_multivariate_gaussian_pdf ();
test_multivariate_gaussian ();
test_wishart_log_pdf ();
test_wishart_pdf ();
test_wishart ();
testPDF (FUNC2 (gumbel1));
testPDF (FUNC2 (gumbel2));
testPDF (FUNC2 (landau));
testPDF (FUNC2 (levy1));
testPDF (FUNC2 (levy2));
testPDF (FUNC2 (levy1a));
testPDF (FUNC2 (levy2a));
testPDF (FUNC2 (levy_skew1));
testPDF (FUNC2 (levy_skew2));
testPDF (FUNC2 (levy_skew1a));
testPDF (FUNC2 (levy_skew2a));
testPDF (FUNC2 (levy_skew1b));
testPDF (FUNC2 (levy_skew2b));
testPDF (FUNC2 (logistic));
testPDF (FUNC2 (lognormal));
testPDF (FUNC2 (pareto));
testPDF (FUNC2 (rayleigh));
testPDF (FUNC2 (rayleigh_tail));
testPDF (FUNC2 (tdist1));
testPDF (FUNC2 (tdist2));
testPDF (FUNC2 (laplace));
testPDF (FUNC2 (weibull));
testPDF (FUNC2 (weibull1));
testPDF (FUNC2 (dir2d));
testPDF (FUNC2 (dir2d_trig_method));
testPDF (FUNC2 (dir3dxy));
testPDF (FUNC2 (dir3dyz));
testPDF (FUNC2 (dir3dzx));
testDiscretePDF (FUNC2 (discrete1));
testDiscretePDF (FUNC2 (discrete2));
testDiscretePDF (FUNC2 (discrete3));
testDiscretePDF (FUNC2 (poisson));
testDiscretePDF (FUNC2 (poisson_large));
testDiscretePDF (FUNC2 (bernoulli));
testDiscretePDF (FUNC2 (binomial));
testDiscretePDF (FUNC2 (binomial0));
testDiscretePDF (FUNC2 (binomial1));
testDiscretePDF (FUNC2 (binomial_knuth));
testDiscretePDF (FUNC2 (binomial_large));
testDiscretePDF (FUNC2 (binomial_large_knuth));
testDiscretePDF (FUNC2 (binomial_huge));
testDiscretePDF (FUNC2 (binomial_huge_knuth));
testDiscretePDF (FUNC2 (binomial_max));
testDiscretePDF (FUNC2 (geometric));
testDiscretePDF (FUNC2 (geometric1));
testDiscretePDF (FUNC2 (hypergeometric1));
testDiscretePDF (FUNC2 (hypergeometric2));
testDiscretePDF (FUNC2 (hypergeometric3));
testDiscretePDF (FUNC2 (hypergeometric4));
testDiscretePDF (FUNC2 (hypergeometric5));
testDiscretePDF (FUNC2 (hypergeometric6));
testDiscretePDF (FUNC2 (logarithmic));
testDiscretePDF (FUNC2 (multinomial));
testDiscretePDF (FUNC2 (multinomial_large));
testDiscretePDF (FUNC2 (negative_binomial));
testDiscretePDF (FUNC2 (pascal));
gsl_rng_free (r_global);
gsl_ran_discrete_free (g1);
gsl_ran_discrete_free (g2);
gsl_ran_discrete_free (g3);
exit (gsl_test_summary ());
}
void
test_shuffle (void)
{
double count[10][10];
int x[10] = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 };
int i, j, status = 0;
for (i = 0; i < 10; i++)
{
for (j = 0; j < 10; j++)
{
count[i][j] = 0;
}
}
for (i = 0; i < N; i++)
{
for (j = 0; j < 10; j++)
x[j] = j;
gsl_ran_shuffle (r_global, x, 10, sizeof (int));
for (j = 0; j < 10; j++)
count[x[j]][j]++;
}
for (i = 0; i < 10; i++)
{
for (j = 0; j < 10; j++)
{
double expected = N / 10.0;
double d = fabs (count[i][j] - expected);
double sigma = d / sqrt (expected);
if (sigma > 5 && d > 1)
{
status = 1;
gsl_test (status,
"gsl_ran_shuffle %d,%d (%g observed vs %g expected)",
i, j, count[i][j] / N, 0.1);
}
}
}
gsl_test (status, "gsl_ran_shuffle on {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}");
}
void
test_choose (void)
{
double count[10];
int x[10] = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 };
int y[3] = { 0, 1, 2 };
int i, j, status = 0;
for (i = 0; i < 10; i++)
{
count[i] = 0;
}
for (i = 0; i < N; i++)
{
for (j = 0; j < 10; j++)
x[j] = j;
gsl_ran_choose (r_global, y, 3, x, 10, sizeof (int));
for (j = 0; j < 3; j++)
count[y[j]]++;
}
for (i = 0; i < 10; i++)
{
double expected = 3.0 * N / 10.0;
double d = fabs (count[i] - expected);
double sigma = d / sqrt (expected);
if (sigma > 5 && d > 1)
{
status = 1;
gsl_test (status,
"gsl_ran_choose %d (%g observed vs %g expected)",
i, count[i] / N, 0.1);
}
}
gsl_test (status, "gsl_ran_choose (3) on {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}");
}
void
testMoments (double (*f) (void), const char *name,
double a, double b, double p)
{
int i;
double count = 0, expected, sigma;
int status;
for (i = 0; i < N; i++)
{
double r = f ();
if (r < b && r > a)
count++;
}
expected = p * N;
sigma = (expected > 0) ? fabs (count - expected) / sqrt (expected) : fabs(count - expected);
status = (sigma > 3);
gsl_test (status, "%s [%g,%g] (%g observed vs %g expected)",
name, a, b, count / N, p);
}
#define BINS 100
typedef double pdf_func(double);
/* Keep track of invalid values during integration */
static int pdf_errors = 0;
static double pdf_errval = 0.0;
double
wrapper_function (double x, void *params)
{
pdf_func * pdf = (pdf_func *)params;
double P = pdf(x);
if (!gsl_finite(P)) {
pdf_errors++;
pdf_errval = P;
P = 0; /* skip invalid value now, but return pdf_errval at the end */
}
return P;
}
double
integrate (pdf_func * pdf, double a, double b)
{
double result, abserr;
size_t n = 1000;
gsl_function f;
gsl_integration_workspace * w = gsl_integration_workspace_alloc (n);
f.function = &wrapper_function;
f.params = (void *)pdf;
pdf_errors = 0;
gsl_integration_qags (&f, a, b, 1e-16, 1e-4, n, w, &result, &abserr);
gsl_integration_workspace_free (w);
if (pdf_errors) return pdf_errval;
return result;
}
void
testPDF (double (*f) (void), double (*pdf) (double), const char *name)
{
double count[BINS], edge[BINS], p[BINS];
double a = -5.0, b = +5.0;
double dx = (b - a) / BINS;
double bin;
double total = 0, mean;
int i, j, status = 0, status_i = 0, attempts = 0;
long int n0 = 0, n = N;
for (i = 0; i < BINS; i++)
{
/* Compute the integral of p(x) from x to x+dx */
double x = a + i * dx;
if (fabs (x) < 1e-10) /* hit the origin exactly */
x = 0.0;
p[i] = integrate (pdf, x, x+dx);
}
for (i = 0; i < BINS; i++)
{
count[i] = 0;
edge[i] = 0;
}
trial:
attempts++;
for (i = n0; i < n; i++)
{
double r = f ();
total += r;
if (r < b && r > a)
{
double u = (r - a) / dx;
double f = modf(u, &bin);
j = (int)bin;
if (f == 0)
edge[j]++;
else
count[j]++;
}
}
/* Sort out where the hits on the edges should go */
for (i = 0; i < BINS; i++)
{
/* If the bin above is empty, its lower edge hits belong in the
lower bin */
if (i + 1 < BINS && count[i+1] == 0) {
count[i] += edge[i+1];
edge[i+1] = 0;
}
count[i] += edge[i];
edge[i] = 0;
}
mean = (total / n);
status = !gsl_finite(mean);
if (status) {
gsl_test (status, "%s, finite mean, observed %g", name, mean);
return;
}
for (i = 0; i < BINS; i++)
{
double x = a + i * dx;
double d = fabs (count[i] - n * p[i]);
if (!gsl_finite(p[i]))
{
status_i = 1;
}
else if (p[i] != 0)
{
double s = d / sqrt (n * p[i]);
status_i = (s > 5) && (d > 2);
}
else
{
status_i = (count[i] != 0);
}
/* Extend the sample if there is an outlier on the first attempt
to avoid spurious failures when running large numbers of tests. */
if (status_i && attempts < 50)
{
n0 = n;
n = 2.0*n;
goto trial;
}
status |= status_i;
if (status_i)
gsl_test (status_i, "%s [%g,%g) (%g/%d=%g observed vs %g expected)",
name, x, x + dx, count[i], n, count[i] / n, p[i]);
}
if (status == 0)
gsl_test (status, "%s, sampling against pdf over range [%g,%g) ",
name, a, b);
}
void
testDiscretePDF (double (*f) (void), double (*pdf) (unsigned int),
const char *name)
{
double count[BINS], p[BINS];
unsigned int i;
int status = 0, status_i = 0;
for (i = 0; i < BINS; i++)
count[i] = 0;
for (i = 0; i < N; i++)
{
int r = (int) (f ());
if (r >= 0 && r < BINS)
count[r]++;
}
for (i = 0; i < BINS; i++)
p[i] = pdf (i);
for (i = 0; i < BINS; i++)
{
double d = fabs (count[i] - N * p[i]);
if (p[i] != 0)
{
double s = d / sqrt (N * p[i]);
status_i = (s > 5) && (d > 1);
}
else
{
status_i = (count[i] != 0);
}
status |= status_i;
if (status_i)
gsl_test (status_i, "%s i=%d (%g observed vs %g expected)",
name, i, count[i] / N, p[i]);
}
if (status == 0)
gsl_test (status, "%s, sampling against pdf over range [%d,%d) ",
name, 0, BINS);
}
double
test_beta (void)
{
return gsl_ran_beta (r_global, 2.0, 3.0);
}
double
test_beta_pdf (double x)
{
return gsl_ran_beta_pdf (x, 2.0, 3.0);
}
double
test_bernoulli (void)
{
return gsl_ran_bernoulli (r_global, 0.3);
}
double
test_bernoulli_pdf (unsigned int n)
{
return gsl_ran_bernoulli_pdf (n, 0.3);
}
double
test_binomial (void)
{
return gsl_ran_binomial (r_global, 0.3, 5);
}
double
test_binomial_pdf (unsigned int n)
{
return gsl_ran_binomial_pdf (n, 0.3, 5);
}
double
test_binomial0 (void)
{
return gsl_ran_binomial (r_global, 0, 8);
}
double
test_binomial0_pdf (unsigned int n)
{
return gsl_ran_binomial_pdf (n, 0, 8);
}
double
test_binomial1 (void)
{
return gsl_ran_binomial (r_global, 1, 8);
}
double
test_binomial1_pdf (unsigned int n)
{
return gsl_ran_binomial_pdf (n, 1, 8);
}
double
test_binomial_knuth (void)
{
return gsl_ran_binomial_knuth (r_global, 0.3, 5);
}
double
test_binomial_knuth_pdf (unsigned int n)
{
return gsl_ran_binomial_pdf (n, 0.3, 5);
}
double
test_binomial_large (void)
{
return gsl_ran_binomial (r_global, 0.3, 55);
}
double
test_binomial_large_pdf (unsigned int n)
{
return gsl_ran_binomial_pdf (n, 0.3, 55);
}
double
test_binomial_large_knuth (void)
{
return gsl_ran_binomial_knuth (r_global, 0.3, 55);
}
double
test_binomial_large_knuth_pdf (unsigned int n)
{
return gsl_ran_binomial_pdf (n, 0.3, 55);
}
double
test_binomial_huge (void)
{
return gsl_ran_binomial (r_global, 0.3, 5500);
}
double
test_binomial_huge_pdf (unsigned int n)
{
return gsl_ran_binomial_pdf (n, 0.3, 5500);
}
double
test_binomial_huge_knuth (void)
{
return gsl_ran_binomial_knuth (r_global, 0.3, 5500);
}
double
test_binomial_huge_knuth_pdf (unsigned int n)
{
return gsl_ran_binomial_pdf (n, 0.3, 5500);
}
double
test_binomial_max (void)
{
return gsl_ran_binomial (r_global, 1e-8, 1<<31);
}
double
test_binomial_max_pdf (unsigned int n)
{
return gsl_ran_binomial_pdf (n, 1e-8, 1<<31);
}
double
test_cauchy (void)
{
return gsl_ran_cauchy (r_global, 2.0);
}
double
test_cauchy_pdf (double x)
{
return gsl_ran_cauchy_pdf (x, 2.0);
}
double
test_chisq (void)
{
return gsl_ran_chisq (r_global, 13.0);
}
double
test_chisq_pdf (double x)
{
return gsl_ran_chisq_pdf (x, 13.0);
}
double
test_chisqnu2 (void)
{
return gsl_ran_chisq (r_global, 2.0);
}
double
test_chisqnu2_pdf (double x)
{
return gsl_ran_chisq_pdf (x, 2.0);
}
double
test_dir2d (void)
{
double x = 0, y = 0, theta;
gsl_ran_dir_2d (r_global, &x, &y);
theta = atan2 (x, y);
return theta;
}
double
test_dir2d_pdf (double x)
{
if (x > -M_PI && x <= M_PI)
{
return 1 / (2 * M_PI);
}
else
{
return 0;
}
}
double
test_dir2d_trig_method (void)
{
double x = 0, y = 0, theta;
gsl_ran_dir_2d_trig_method (r_global, &x, &y);
theta = atan2 (x, y);
return theta;
}
double
test_dir2d_trig_method_pdf (double x)
{
if (x > -M_PI && x <= M_PI)
{
return 1 / (2 * M_PI);
}
else
{
return 0;
}
}
double
test_dir3dxy (void)
{
double x = 0, y = 0, z = 0, theta;
gsl_ran_dir_3d (r_global, &x, &y, &z);
theta = atan2 (x, y);
return theta;
}
double
test_dir3dxy_pdf (double x)
{
if (x > -M_PI && x <= M_PI)
{
return 1 / (2 * M_PI);
}
else
{
return 0;
}
}
double
test_dir3dyz (void)
{
double x = 0, y = 0, z = 0, theta;
gsl_ran_dir_3d (r_global, &x, &y, &z);
theta = atan2 (y, z);
return theta;
}
double
test_dir3dyz_pdf (double x)
{
if (x > -M_PI && x <= M_PI)
{
return 1 / (2 * M_PI);
}
else
{
return 0;
}
}
double
test_dir3dzx (void)
{
double x = 0, y = 0, z = 0, theta;
gsl_ran_dir_3d (r_global, &x, &y, &z);
theta = atan2 (z, x);
return theta;
}
double
test_dir3dzx_pdf (double x)
{
if (x > -M_PI && x <= M_PI)
{
return 1 / (2 * M_PI);
}
else
{
return 0;
}
}
double
test_dirichlet (void)
{
/* This is a bit of a lame test, since when K=2, the Dirichlet distribution
becomes a beta distribution */
size_t K = 2;
double alpha[2] = { 2.5, 5.0 };
double theta[2] = { 0.0, 0.0 };
gsl_ran_dirichlet (r_global, K, alpha, theta);
return theta[0];
}
double
test_dirichlet_pdf (double x)
{
size_t K = 2;
double alpha[2] = { 2.5, 5.0 };
double theta[2];
if (x <= 0.0 || x >= 1.0)
return 0.0; /* Out of range */
theta[0] = x;
theta[1] = 1.0 - x;
return gsl_ran_dirichlet_pdf (K, alpha, theta);
}
double
test_dirichlet_small (void)
{
size_t K = 2;
double alpha[2] = { 2.5e-3, 5.0e-3};
double theta[2] = { 0.0, 0.0 };
gsl_ran_dirichlet (r_global, K, alpha, theta);
return theta[0];
}
double
test_dirichlet_small_pdf (double x)
{
size_t K = 2;
double alpha[2] = { 2.5e-3, 5.0e-3 };
double theta[2];
if (x <= 0.0 || x >= 1.0)
return 0.0; /* Out of range */
theta[0] = x;
theta[1] = 1.0 - x;
return gsl_ran_dirichlet_pdf (K, alpha, theta);
}
/* Check that the observed means of the Dirichlet variables are
within reasonable statistical errors of their correct values. */
#define DIRICHLET_K 10
void
test_dirichlet_moments (void)
{
double alpha[DIRICHLET_K];
double theta[DIRICHLET_K];
double theta_sum[DIRICHLET_K];
double alpha_sum = 0.0;
double mean, obs_mean, sd, sigma;
int status, k, n;
for (k = 0; k < DIRICHLET_K; k++)
{
alpha[k] = gsl_ran_exponential (r_global, 0.1);
alpha_sum += alpha[k];
theta_sum[k] = 0.0;
}
for (n = 0; n < N; n++)
{
gsl_ran_dirichlet (r_global, DIRICHLET_K, alpha, theta);
for (k = 0; k < DIRICHLET_K; k++)
theta_sum[k] += theta[k];
}
for (k = 0; k < DIRICHLET_K; k++)
{
mean = alpha[k] / alpha_sum;
sd =
sqrt ((alpha[k] * (1. - alpha[k] / alpha_sum)) /
(alpha_sum * (alpha_sum + 1.)));
obs_mean = theta_sum[k] / N;
sigma = sqrt ((double) N) * fabs (mean - obs_mean) / sd;
status = (sigma > 3.0);
gsl_test (status,
"test gsl_ran_dirichlet: mean (%g observed vs %g expected)",
obs_mean, mean);
}
}
/* Check that the observed means of the multinomial variables are
within reasonable statistical errors of their correct values. */
void
test_multinomial_moments (void)
{
const unsigned int sum_n = 100;
const double p[MULTI_DIM] ={ 0.2, 0.20, 0.17, 0.14, 0.12,
0.07, 0.05, 0.02, 0.02, 0.01 };
unsigned int x[MULTI_DIM];
double x_sum[MULTI_DIM];
double mean, obs_mean, sd, sigma;
int status, k, n;
for (k = 0; k < MULTI_DIM; k++)
x_sum[k] =0.0;
for (n = 0; n < N; n++)
{
gsl_ran_multinomial (r_global, MULTI_DIM, sum_n, p, x);
for (k = 0; k < MULTI_DIM; k++)
x_sum[k] += x[k];
}
for (k = 0; k < MULTI_DIM; k++)
{
mean = p[k] * sum_n;
sd = p[k] * (1.-p[k]) * sum_n;
obs_mean = x_sum[k] / N;
sigma = sqrt ((double) N) * fabs (mean - obs_mean) / sd;
status = (sigma > 3.0);
gsl_test (status,
"test gsl_ran_multinomial: mean (%g observed vs %g expected)",
obs_mean, mean);
}
}
double
test_discrete1 (void)
{
static double P[3] = { 0.59, 0.4, 0.01 };
if (g1 == NULL)
{
g1 = gsl_ran_discrete_preproc (3, P);
}
return gsl_ran_discrete (r_global, g1);
}
double
test_discrete1_pdf (unsigned int n)
{
return gsl_ran_discrete_pdf ((size_t) n, g1);
}
double
test_discrete2 (void)
{
static double P[10] = { 1, 9, 3, 4, 5, 8, 6, 7, 2, 0 };
if (g2 == NULL)
{
g2 = gsl_ran_discrete_preproc (10, P);
}
return gsl_ran_discrete (r_global, g2);
}
double
test_discrete2_pdf (unsigned int n)
{
return gsl_ran_discrete_pdf ((size_t) n, g2);
}
double
test_discrete3 (void)
{
static double P[20];
if (g3 == NULL)
{ int i;
for (i=0; i<20; ++i) P[i]=1.0/20;
g3 = gsl_ran_discrete_preproc (20, P);
}
return gsl_ran_discrete (r_global, g3);
}
double
test_discrete3_pdf (unsigned int n)
{
return gsl_ran_discrete_pdf ((size_t) n, g3);
}
double
test_erlang (void)
{
return gsl_ran_erlang (r_global, 3.0, 4.0);
}
double
test_erlang_pdf (double x)
{
return gsl_ran_erlang_pdf (x, 3.0, 4.0);
}
double
test_exponential (void)
{
return gsl_ran_exponential (r_global, 2.0);
}
double
test_exponential_pdf (double x)
{
return gsl_ran_exponential_pdf (x, 2.0);
}
double
test_exppow0 (void)
{
return gsl_ran_exppow (r_global, 3.7, 0.3);
}
double
test_exppow0_pdf (double x)
{
return gsl_ran_exppow_pdf (x, 3.7, 0.3);
}
double
test_exppow1 (void)
{
return gsl_ran_exppow (r_global, 3.7, 1.0);
}
double
test_exppow1_pdf (double x)
{
return gsl_ran_exppow_pdf (x, 3.7, 1.0);
}
double
test_exppow1a (void)
{
return gsl_ran_exppow (r_global, 3.7, 1.9);
}
double
test_exppow1a_pdf (double x)
{
return gsl_ran_exppow_pdf (x, 3.7, 1.9);
}
double
test_exppow2 (void)
{
return gsl_ran_exppow (r_global, 3.7, 2.0);
}
double
test_exppow2_pdf (double x)
{
return gsl_ran_exppow_pdf (x, 3.7, 2.0);
}
double
test_exppow2a (void)
{
return gsl_ran_exppow (r_global, 3.7, 3.5);
}
double
test_exppow2a_pdf (double x)
{
return gsl_ran_exppow_pdf (x, 3.7, 3.5);
}
double
test_exppow2b (void)
{
return gsl_ran_exppow (r_global, 3.7, 7.5);
}
double
test_exppow2b_pdf (double x)
{
return gsl_ran_exppow_pdf (x, 3.7, 7.5);
}
double
test_fdist (void)
{
return gsl_ran_fdist (r_global, 3.0, 4.0);
}
double
test_fdist_pdf (double x)
{
return gsl_ran_fdist_pdf (x, 3.0, 4.0);
}
/* Test case for bug #28500: overflow in gsl_ran_fdist_pdf */
double
test_fdist_large (void)
{
return gsl_ran_fdist (r_global, 8.0, 249.0);
}
double
test_fdist_large_pdf (double x)
{
return gsl_ran_fdist_pdf (x, 8.0, 249.0);
}
double
test_flat (void)
{
return gsl_ran_flat (r_global, 3.0, 4.0);
}
double
test_flat_pdf (double x)
{
return gsl_ran_flat_pdf (x, 3.0, 4.0);
}
double
test_gamma (void)
{
return gsl_ran_gamma (r_global, 2.5, 2.17);
}
double
test_gamma_pdf (double x)
{
return gsl_ran_gamma_pdf (x, 2.5, 2.17);
}
double
test_gamma1 (void)
{
return gsl_ran_gamma (r_global, 1.0, 2.17);
}
double
test_gamma1_pdf (double x)
{
return gsl_ran_gamma_pdf (x, 1.0, 2.17);
}
double
test_gamma_int (void)
{
return gsl_ran_gamma (r_global, 10.0, 2.17);
}
double
test_gamma_int_pdf (double x)
{
return gsl_ran_gamma_pdf (x, 10.0, 2.17);
}
double
test_gamma_large (void)
{
return gsl_ran_gamma (r_global, 20.0, 2.17);
}
double
test_gamma_large_pdf (double x)
{
return gsl_ran_gamma_pdf (x, 20.0, 2.17);
}
double
test_gamma_small (void)
{
return gsl_ran_gamma (r_global, 0.92, 2.17);
}
double
test_gamma_small_pdf (double x)
{
return gsl_ran_gamma_pdf (x, 0.92, 2.17);
}
double
test_gamma_vlarge (void)
{
/* Scale the distribution to get it into the range [-5,5] */
double c = 2.71828181565;
double b = 6.32899304917e-10;
double d = 1e4;
return (gsl_ran_gamma (r_global, 4294967296.0, b) - c) * d;
}
double
test_gamma_vlarge_pdf (double x)
{
double c = 2.71828181565;
double b = 6.32899304917e-10;
double d = 1e4;
return gsl_ran_gamma_pdf ((x / d) + c, 4294967296.0, b) / d;
}
double
test_gamma_mt (void)
{
return gsl_ran_gamma_mt (r_global, 2.5, 2.17);
}
double
test_gamma_mt_pdf (double x)
{
return gsl_ran_gamma_pdf (x, 2.5, 2.17);
}
double
test_gamma_mt1 (void)
{
return gsl_ran_gamma_mt (r_global, 1.0, 2.17);
}
double
test_gamma_mt1_pdf (double x)
{
return gsl_ran_gamma_pdf (x, 1.0, 2.17);
}
double
test_gamma_mt_int (void)
{
return gsl_ran_gamma_mt (r_global, 10.0, 2.17);
}
double
test_gamma_mt_int_pdf (double x)
{
return gsl_ran_gamma_pdf (x, 10.0, 2.17);
}
double
test_gamma_mt_large (void)
{
return gsl_ran_gamma_mt (r_global, 20.0, 2.17);
}
double
test_gamma_mt_large_pdf (double x)
{
return gsl_ran_gamma_pdf (x, 20.0, 2.17);
}
double
test_gamma_mt_small (void)
{
return gsl_ran_gamma_mt (r_global, 0.92, 2.17);
}
double
test_gamma_mt_small_pdf (double x)
{
return gsl_ran_gamma_pdf (x, 0.92, 2.17);
}
double
test_gamma_knuth_vlarge (void)
{
/* Scale the distribution to get it into the range [-5,5] */
double c = 2.71828181565;
double b = 6.32899304917e-10;
double d = 1e4;
return (gsl_ran_gamma_knuth (r_global, 4294967296.0, b) - c) * d;
}
double
test_gamma_knuth_vlarge_pdf (double x)
{
double c = 2.71828181565;
double b = 6.32899304917e-10;
double d = 1e4;
return gsl_ran_gamma_pdf ((x / d) + c, 4294967296.0, b) / d;
}
double
test_gaussian (void)
{
return gsl_ran_gaussian (r_global, 3.0);
}
double
test_gaussian_pdf (double x)
{
return gsl_ran_gaussian_pdf (x, 3.0);
}
double
test_gaussian_ratio_method (void)
{
return gsl_ran_gaussian_ratio_method (r_global, 3.0);
}
double
test_gaussian_ratio_method_pdf (double x)
{
return gsl_ran_gaussian_pdf (x, 3.0);
}
double
test_gaussian_ziggurat (void)
{
return gsl_ran_gaussian_ziggurat (r_global, 3.12);
}
double
test_gaussian_ziggurat_pdf (double x)
{
return gsl_ran_gaussian_pdf (x, 3.12);
}
double
test_gaussian_tail (void)
{
return gsl_ran_gaussian_tail (r_global, 1.7, 0.25);
}
double
test_gaussian_tail_pdf (double x)
{
return gsl_ran_gaussian_tail_pdf (x, 1.7, 0.25);
}
double
test_gaussian_tail1 (void)
{
return gsl_ran_gaussian_tail (r_global, -1.7, 5.0);
}
double
test_gaussian_tail1_pdf (double x)
{
return gsl_ran_gaussian_tail_pdf (x, -1.7, 5.0);
}
double
test_gaussian_tail2 (void)
{
return gsl_ran_gaussian_tail (r_global, 0.1, 2.0);
}
double
test_gaussian_tail2_pdf (double x)
{
return gsl_ran_gaussian_tail_pdf (x, 0.1, 2.0);
}
double
test_ugaussian (void)
{
return gsl_ran_ugaussian (r_global);
}
double
test_ugaussian_pdf (double x)
{
return gsl_ran_ugaussian_pdf (x);
}
double
test_ugaussian_ratio_method (void)
{
return gsl_ran_ugaussian_ratio_method (r_global);
}
double
test_ugaussian_ratio_method_pdf (double x)
{
return gsl_ran_ugaussian_pdf (x);
}
double
test_ugaussian_tail (void)
{
return gsl_ran_ugaussian_tail (r_global, 3.0);
}
double
test_ugaussian_tail_pdf (double x)
{
return gsl_ran_ugaussian_tail_pdf (x, 3.0);
}
double
test_bivariate_gaussian1 (void)
{
double x = 0, y = 0;
gsl_ran_bivariate_gaussian (r_global, 3.0, 2.0, 0.3, &x, &y);
return x;
}
double
test_bivariate_gaussian1_pdf (double x)
{
return gsl_ran_gaussian_pdf (x, 3.0);
}
double
test_bivariate_gaussian2 (void)
{
double x = 0, y = 0;
gsl_ran_bivariate_gaussian (r_global, 3.0, 2.0, 0.3, &x, &y);
return y;
}
double
test_bivariate_gaussian2_pdf (double y)
{
int i, n = 10;
double sum = 0;
double a = -10, b = 10, dx = (b - a) / n;
for (i = 0; i < n; i++)
{
double x = a + i * dx;
sum += gsl_ran_bivariate_gaussian_pdf (x, y, 3.0, 2.0, 0.3) * dx;
}
return sum;
}
double
test_bivariate_gaussian3 (void)
{
double x = 0, y = 0;
gsl_ran_bivariate_gaussian (r_global, 3.0, 2.0, 0.3, &x, &y);
return x + y;
}
double
test_bivariate_gaussian3_pdf (double x)
{
double sx = 3.0, sy = 2.0, r = 0.3;
double su = (sx + r * sy);
double sv = sy * sqrt (1 - r * r);
double sigma = sqrt (su * su + sv * sv);
return gsl_ran_gaussian_pdf (x, sigma);
}
double
test_bivariate_gaussian4 (void)
{
double x = 0, y = 0;
gsl_ran_bivariate_gaussian (r_global, 3.0, 2.0, -0.5, &x, &y);
return x + y;
}
double
test_bivariate_gaussian4_pdf (double x)
{
double sx = 3.0, sy = 2.0, r = -0.5;
double su = (sx + r * sy);
double sv = sy * sqrt (1 - r * r);
double sigma = sqrt (su * su + sv * sv);
return gsl_ran_gaussian_pdf (x, sigma);
}
/* Examples from R (GPL): http://www.r-project.org/
* library(mvtnorm); packageVersion("mvtnorm") # 1.0.5
* mu <- c(1, 2)
* Sigma <- matrix(c(4,2, 2,3), ncol=2)
* x <- c(0, 0)
* sprintf("%.15f", dmvnorm(x=x, mean=mu, sigma=Sigma, log=TRUE)) # -3.565097837249263
*/
void
test_multivariate_gaussian_log_pdf (void)
{
size_t d = 2;
const double exp_res = -3.565097837249263;
double obs_res;
gsl_vector * mu = gsl_vector_calloc(d);
gsl_matrix * Sigma = gsl_matrix_calloc(d, d);
gsl_matrix * L = gsl_matrix_calloc(d, d);
gsl_vector * x = gsl_vector_calloc(d);
gsl_vector * work = gsl_vector_calloc(d);
gsl_vector_set(mu, 0, 1);
gsl_vector_set(mu, 1, 2);
gsl_matrix_set(Sigma, 0, 0, 4);
gsl_matrix_set(Sigma, 1, 1, 3);
gsl_matrix_set(Sigma, 0, 1, 2);
gsl_matrix_set(Sigma, 1, 0, 2);
gsl_matrix_memcpy(L, Sigma);
gsl_linalg_cholesky_decomp1(L);
gsl_ran_multivariate_gaussian_log_pdf(x, mu, L, &obs_res, work);
gsl_test_rel(obs_res, exp_res, 1.0e-10, "gsl_ran_multivariate_gaussian_log_pdf");
gsl_vector_free(mu);
gsl_matrix_free(Sigma);
gsl_matrix_free(L);
gsl_vector_free(x);
gsl_vector_free(work);
}
/* Examples from R (GPL): http://www.r-project.org/
* library(mvtnorm); packageVersion("mvtnorm") # 1.0.5
* mu <- c(1, 2)
* Sigma <- matrix(c(4,2, 2,3), ncol=2)
* x <- c(0, 0)
* sprintf("%.15f", dmvnorm(x=x, mean=mu, sigma=Sigma, log=FALSE)) # 0.028294217120391
*/
void
test_multivariate_gaussian_pdf (void)
{
size_t d = 2;
const double exp_res = 0.028294217120391;
double obs_res = 0;
gsl_vector * mu = gsl_vector_calloc(d);
gsl_matrix * Sigma = gsl_matrix_calloc(d, d);
gsl_matrix * L = gsl_matrix_calloc(d, d);
gsl_vector * x = gsl_vector_calloc(d);
gsl_vector * work = gsl_vector_calloc(d);
gsl_vector_set(mu, 0, 1);
gsl_vector_set(mu, 1, 2);
gsl_matrix_set(Sigma, 0, 0, 4);
gsl_matrix_set(Sigma, 1, 1, 3);
gsl_matrix_set(Sigma, 0, 1, 2);
gsl_matrix_set(Sigma, 1, 0, 2);
gsl_matrix_memcpy(L, Sigma);
gsl_linalg_cholesky_decomp1(L);
gsl_ran_multivariate_gaussian_pdf(x, mu, L, &obs_res, work);
gsl_test_rel(obs_res, exp_res, 1.0e-10, "gsl_ran_multivariate_gaussian_pdf");
gsl_vector_free(mu);
gsl_matrix_free(Sigma);
gsl_matrix_free(L);
gsl_vector_free(x);
gsl_vector_free(work);
}
/* Draw N random vectors according to a given MVN(mu,Sigma). Then, check that
* one can't reject the null hypothesis that the sample mean is equal to
* the true mean, using Hotelling's test statistic at 95% confidence level.
* Details in "Applied Multivariate Statistical Analysis" by Johnson & Wichern
* (2001), section 5, page 212.
*/
void
test_multivariate_gaussian (void)
{
size_t d = 2, i = 0;
int status = 0;
double T2 = 0, threshold = 0, alpha = 0.05, pvalue = 0;
gsl_vector * mu = gsl_vector_calloc(d);
gsl_matrix * Sigma = gsl_matrix_calloc(d, d);
gsl_matrix * L = gsl_matrix_calloc(d, d);
gsl_vector * sample = gsl_vector_calloc(d);
gsl_matrix * samples = gsl_matrix_calloc(N, d);
gsl_vector * mu_hat = gsl_vector_calloc(d);
gsl_matrix * Sigma_hat = gsl_matrix_calloc(d, d);
gsl_vector * mu_hat_ctr = gsl_vector_calloc(d);
gsl_matrix * Sigma_hat_inv = gsl_matrix_calloc(d, d);
gsl_vector * tmp = gsl_vector_calloc(d);
/* set the true values of parameters mu and Sigma */
gsl_vector_set(mu, 0, 1);
gsl_vector_set(mu, 1, 2);
gsl_matrix_set(Sigma, 0, 0, 4);
gsl_matrix_set(Sigma, 1, 1, 3);
gsl_matrix_set(Sigma, 0, 1, 2);
gsl_matrix_set(Sigma, 1, 0, 2);
/* draw N random vectors */
gsl_matrix_memcpy(L, Sigma);
gsl_linalg_cholesky_decomp1(L);
for (i = 0; i < N; ++i) {
gsl_ran_multivariate_gaussian(r_global, mu, L, sample);
gsl_matrix_set_row(samples, i, sample);
}
/* compute the maximum-likelihood estimates */
gsl_ran_multivariate_gaussian_mean (samples, mu_hat);
gsl_ran_multivariate_gaussian_vcov (samples, Sigma_hat);
/* compute Hotelling's test statistic:
T^2 = n (hat{mu} - mu)' hat{Sigma}^-1 (hat{mu} - mu) */
gsl_vector_memcpy(mu_hat_ctr, mu_hat);
gsl_vector_sub(mu_hat_ctr, mu);
gsl_matrix_memcpy(Sigma_hat_inv, Sigma_hat);
gsl_linalg_cholesky_decomp1(Sigma_hat_inv);
gsl_linalg_cholesky_invert(Sigma_hat_inv);
gsl_blas_dgemv(CblasNoTrans, 1, Sigma_hat_inv, mu_hat_ctr, 0, tmp);
gsl_blas_ddot(mu_hat_ctr, tmp, &T2);
T2 *= N;
/* test if the null hypothesis (hat{mu} = mu) can be rejected
at the alpha level*/
threshold = (N-1) * d / (double)(N-d) * gsl_cdf_fdist_Pinv(1-alpha, d, N-d);
status = (T2 > threshold);
gsl_test(status,
"test gsl_ran_multivariate_gaussian: T2 %f < %f",
T2, threshold);
pvalue = gsl_cdf_fdist_Q(T2, d, N-d);
status = (pvalue < alpha);
gsl_test(status,
"test gsl_ran_multivariate_gaussian: p value %f > %f",
pvalue, alpha);
gsl_vector_free(mu);
gsl_matrix_free(Sigma);
gsl_matrix_free(L);
gsl_vector_free(sample);
gsl_matrix_free(samples);
gsl_vector_free(mu_hat);
gsl_matrix_free(Sigma_hat);
gsl_vector_free(mu_hat_ctr);
gsl_matrix_free(Sigma_hat_inv);
gsl_vector_free(tmp);
}
/* Examples from R (GPL): http://www.r-project.org/
* R> version$version.string # R version 3.4.1 (2017-06-30)
* R> library(MCMCpack); packageVersion("MCMCpack") # 1.3.9
* R> df <- 3
* R> V <- matrix(data=c(1, 0.3, 0.3, 1), nrow=2, ncol=2)
* R> X <- matrix(data=c(2.213322, 1.453357, 1.453357, 3.285779), nrow=2, ncol=2)
* R> sprintf("%.15f", log(dwish(W=X, v=df, S=V))) # -4.931913612377813
*/
void
test_wishart_log_pdf (void)
{
size_t d = 2;
const double df = 3, exp_res = -4.931913612377813;
double obs_res;
gsl_matrix * V = gsl_matrix_calloc(d, d);
gsl_matrix * L = gsl_matrix_calloc(d, d);
gsl_matrix * X = gsl_matrix_calloc(d, d);
gsl_matrix * L_X = gsl_matrix_calloc(d, d);
gsl_matrix * work = gsl_matrix_calloc(d, d);
gsl_matrix_set(V, 0, 0, 1);
gsl_matrix_set(V, 1, 1, 1);
gsl_matrix_set(V, 0, 1, 0.3);
gsl_matrix_set(V, 1, 0, 0.3);
gsl_matrix_memcpy(L, V);
gsl_linalg_cholesky_decomp1(L);
gsl_matrix_set(X, 0, 0, 2.213322);
gsl_matrix_set(X, 1, 1, 3.285779);
gsl_matrix_set(X, 0, 1, 1.453357);
gsl_matrix_set(X, 1, 0, 1.453357);
gsl_matrix_memcpy(L_X, X);
gsl_linalg_cholesky_decomp1(L_X);
gsl_ran_wishart_log_pdf(X, L_X, df, L, &obs_res, work);
gsl_test_rel(obs_res, exp_res, 1.0e-10, "gsl_ran_wishart_log_pdf");
gsl_matrix_free(V);
gsl_matrix_free(L);
gsl_matrix_free(X);
gsl_matrix_free(L_X);
gsl_matrix_free(work);
}
/* Examples from R (GPL): http://www.r-project.org/
* R> version$version.string # R version 3.4.1 (2017-06-30)
* R> library(MCMCpack); packageVersion("MCMCpack") # 1.3.9
* R> df <- 3
* R> V <- matrix(data=c(1, 0.3, 0.3, 1), nrow=2, ncol=2)
* R> X <- matrix(data=c(2.213322, 1.453357, 1.453357, 3.285779), nrow=2, ncol=2)
* R> sprintf("%.15f", dwish(W=X, v=df, S=V)) # 0.007212687778224
*/
void
test_wishart_pdf (void)
{
size_t d = 2;
const double df = 3, exp_res = 0.007212687778224;
double obs_res;
gsl_matrix * V = gsl_matrix_calloc(d, d);
gsl_matrix * L = gsl_matrix_calloc(d, d);
gsl_matrix * X = gsl_matrix_calloc(d, d);
gsl_matrix * L_X = gsl_matrix_calloc(d, d);
gsl_matrix * work = gsl_matrix_calloc(d, d);
gsl_matrix_set(V, 0, 0, 1);
gsl_matrix_set(V, 1, 1, 1);
gsl_matrix_set(V, 0, 1, 0.3);
gsl_matrix_set(V, 1, 0, 0.3);
gsl_matrix_memcpy(L, V);
gsl_linalg_cholesky_decomp1(L);
gsl_matrix_set(X, 0, 0, 2.213322);
gsl_matrix_set(X, 1, 1, 3.285779);
gsl_matrix_set(X, 0, 1, 1.453357);
gsl_matrix_set(X, 1, 0, 1.453357);
gsl_matrix_memcpy(L_X, X);
gsl_linalg_cholesky_decomp1(L_X);
gsl_ran_wishart_pdf(X, L_X, df, L, &obs_res, work);
gsl_test_rel(obs_res, exp_res, 1.0e-10, "gsl_ran_wishart_pdf");
gsl_matrix_free(V);
gsl_matrix_free(L);
gsl_matrix_free(X);
gsl_matrix_free(L_X);
gsl_matrix_free(work);
}
/* Draw N random "matrices" according to a W_d(df,V) with d=1 and V=1,
* and check that their mean and variance are close enough to those of
* a Chi-squared(df), respectively df and 2df.
*/
void
test_wishart (void)
{
size_t d = 1, i, j;
double df[5] = {1, 3, 5, 7, 9}, mean_wishart, var_wishart;
int status;
gsl_matrix * V = gsl_matrix_calloc(d, d);
gsl_matrix * L = gsl_matrix_calloc(d, d);
gsl_matrix * sample_wishart = gsl_matrix_calloc(d, d);
gsl_matrix * work = gsl_matrix_calloc(d, d);
gsl_vector * samples_wishart = gsl_vector_calloc(N);
gsl_matrix_set(V, 0, 0, 1.0);
gsl_matrix_memcpy(L, V);
gsl_linalg_cholesky_decomp1(L);
for (j = 0; j < 5; ++j) { /* for loop over df */
/* draw N random variables from W(df,V) */
for (i = 0; i < N; ++i) {
status = gsl_ran_wishart(r_global, df[j], L, sample_wishart, work);
gsl_vector_set(samples_wishart, i, gsl_matrix_get(sample_wishart, 0, 0));
}
/* compute their mean and variance */
mean_wishart = gsl_stats_mean(samples_wishart->data,
samples_wishart->stride, N);
var_wishart = gsl_stats_variance_m(samples_wishart->data,
samples_wishart->stride,
N, mean_wishart);
/* check */
gsl_test_rel(mean_wishart, df[j], 1.0e-1, "gsl_ran_wishart, mean");
gsl_test_rel(var_wishart, 2*df[j], 1.0e-1, "gsl_ran_wishart, var");
} /* end of for loop over df */
gsl_matrix_free(V);
gsl_matrix_free(L);
gsl_matrix_free(sample_wishart);
gsl_matrix_free(work);
gsl_vector_free(samples_wishart);
}
double
test_geometric (void)
{
return gsl_ran_geometric (r_global, 0.5);
}
double
test_geometric_pdf (unsigned int n)
{
return gsl_ran_geometric_pdf (n, 0.5);
}
double
test_geometric1 (void)
{
return gsl_ran_geometric (r_global, 1.0);
}
double
test_geometric1_pdf (unsigned int n)
{
return gsl_ran_geometric_pdf (n, 1.0);
}
double
test_hypergeometric1 (void)
{
return gsl_ran_hypergeometric (r_global, 5, 7, 4);
}
double
test_hypergeometric1_pdf (unsigned int n)
{
return gsl_ran_hypergeometric_pdf (n, 5, 7, 4);
}
double
test_hypergeometric2 (void)
{
return gsl_ran_hypergeometric (r_global, 5, 7, 11);
}
double
test_hypergeometric2_pdf (unsigned int n)
{
return gsl_ran_hypergeometric_pdf (n, 5, 7, 11);
}
double
test_hypergeometric3 (void)
{
return gsl_ran_hypergeometric (r_global, 5, 7, 1);
}
double
test_hypergeometric3_pdf (unsigned int n)
{
return gsl_ran_hypergeometric_pdf (n, 5, 7, 1);
}
double
test_hypergeometric4 (void)
{
return gsl_ran_hypergeometric (r_global, 5, 7, 20);
}
double
test_hypergeometric4_pdf (unsigned int n)
{
return gsl_ran_hypergeometric_pdf (n, 5, 7, 20);
}
double
test_hypergeometric5 (void)
{
return gsl_ran_hypergeometric (r_global, 2, 7, 5);
}
double
test_hypergeometric5_pdf (unsigned int n)
{
return gsl_ran_hypergeometric_pdf (n, 2, 7, 5);
}
double
test_hypergeometric6 (void)
{
return gsl_ran_hypergeometric (r_global, 2, 10, 3);
}
double
test_hypergeometric6_pdf (unsigned int n)
{
return gsl_ran_hypergeometric_pdf (n, 2, 10, 3);
}
double
test_gumbel1 (void)
{
return gsl_ran_gumbel1 (r_global, 3.12, 4.56);
}
double
test_gumbel1_pdf (double x)
{
return gsl_ran_gumbel1_pdf (x, 3.12, 4.56);
}
double
test_gumbel2 (void)
{
return gsl_ran_gumbel2 (r_global, 3.12, 4.56);
}
double
test_gumbel2_pdf (double x)
{
return gsl_ran_gumbel2_pdf (x, 3.12, 4.56);
}
double
test_landau (void)
{
return gsl_ran_landau (r_global);
}
double
test_landau_pdf (double x)
{
return gsl_ran_landau_pdf (x);
}
double
test_levy1 (void)
{
return gsl_ran_levy (r_global, 5.0, 1.0);
}
double
test_levy1_pdf (double x)
{
return gsl_ran_cauchy_pdf (x, 5.0);
}
double
test_levy2 (void)
{
return gsl_ran_levy (r_global, 5.0, 2.0);
}
double
test_levy2_pdf (double x)
{
return gsl_ran_gaussian_pdf (x, sqrt (2.0) * 5.0);
}
double
test_levy1a (void)
{
return gsl_ran_levy (r_global, 5.0, 1.01);
}
double
test_levy1a_pdf (double x)
{
return gsl_ran_cauchy_pdf (x, 5.0);
}
double
test_levy2a (void)
{
return gsl_ran_levy (r_global, 5.0, 1.99);
}
double
test_levy2a_pdf (double x)
{
return gsl_ran_gaussian_pdf (x, sqrt (2.0) * 5.0);
}
double
test_levy_skew1 (void)
{
return gsl_ran_levy_skew (r_global, 5.0, 1.0, 0.0);
}
double
test_levy_skew1_pdf (double x)
{
return gsl_ran_cauchy_pdf (x, 5.0);
}
double
test_levy_skew2 (void)
{
return gsl_ran_levy_skew (r_global, 5.0, 2.0, 0.0);
}
double
test_levy_skew2_pdf (double x)
{
return gsl_ran_gaussian_pdf (x, sqrt (2.0) * 5.0);
}
double
test_levy_skew1a (void)
{
return gsl_ran_levy_skew (r_global, 5.0, 1.01, 0.0);
}
double
test_levy_skew1a_pdf (double x)
{
return gsl_ran_cauchy_pdf (x, 5.0);
}
double
test_levy_skew2a (void)
{
return gsl_ran_levy_skew (r_global, 5.0, 1.99, 0.0);
}
double
test_levy_skew2a_pdf (double x)
{
return gsl_ran_gaussian_pdf (x, sqrt (2.0) * 5.0);
}
double
test_levy_skew1b (void)
{
return gsl_ran_levy_skew (r_global, 5.0, 1.01, 0.001);
}
double
test_levy_skew1b_pdf (double x)
{
return gsl_ran_cauchy_pdf (x, 5.0);
}
double
test_levy_skew2b (void)
{
return gsl_ran_levy_skew (r_global, 5.0, 1.99, 0.001);
}
double
test_levy_skew2b_pdf (double x)
{
return gsl_ran_gaussian_pdf (x, sqrt (2.0) * 5.0);
}
double
test_logistic (void)
{
return gsl_ran_logistic (r_global, 3.1);
}
double
test_logistic_pdf (double x)
{
return gsl_ran_logistic_pdf (x, 3.1);
}
double
test_logarithmic (void)
{
return gsl_ran_logarithmic (r_global, 0.4);
}
double
test_logarithmic_pdf (unsigned int n)
{
return gsl_ran_logarithmic_pdf (n, 0.4);
}
double
test_lognormal (void)
{
return gsl_ran_lognormal (r_global, 2.7, 1.3);
}
double
test_lognormal_pdf (double x)
{
return gsl_ran_lognormal_pdf (x, 2.7, 1.3);
}
double
test_multinomial (void)
{
const size_t K = 3;
const unsigned int sum_n = BINS;
unsigned int n[3];
/* Test use of weights instead of probabilities. */
const double p[] = { 2., 7., 1.};
gsl_ran_multinomial ( r_global, K, sum_n, p, n);
return n[0];
}
double
test_multinomial_pdf (unsigned int n_0)
{
/* The margional distribution of just 1 variate is binomial. */
size_t K = 2;
/* Test use of weights instead of probabilities */
double p[] = { 0.4, 1.6};
const unsigned int sum_n = BINS;
unsigned int n[2];
n[0] = n_0;
n[1] =sum_n - n_0;
return gsl_ran_multinomial_pdf (K, p, n);
}
double
test_multinomial_large (void)
{
const unsigned int sum_n = BINS;
unsigned int n[MULTI_DIM];
const double p[MULTI_DIM] = { 0.2, 0.20, 0.17, 0.14, 0.12,
0.07, 0.05, 0.04, 0.01, 0.00 };
gsl_ran_multinomial ( r_global, MULTI_DIM, sum_n, p, n);
return n[0];
}
double
test_multinomial_large_pdf (unsigned int n_0)
{
return test_multinomial_pdf(n_0);
}
double
test_negative_binomial (void)
{
return gsl_ran_negative_binomial (r_global, 0.3, 20.0);
}
double
test_negative_binomial_pdf (unsigned int n)
{
return gsl_ran_negative_binomial_pdf (n, 0.3, 20.0);
}
double
test_pascal (void)
{
return gsl_ran_pascal (r_global, 0.8, 3);
}
double
test_pascal_pdf (unsigned int n)
{
return gsl_ran_pascal_pdf (n, 0.8, 3);
}
double
test_pareto (void)
{
return gsl_ran_pareto (r_global, 1.9, 2.75);
}
double
test_pareto_pdf (double x)
{
return gsl_ran_pareto_pdf (x, 1.9, 2.75);
}
double
test_rayleigh (void)
{
return gsl_ran_rayleigh (r_global, 1.9);
}
double
test_rayleigh_pdf (double x)
{
return gsl_ran_rayleigh_pdf (x, 1.9);
}
double
test_rayleigh_tail (void)
{
return gsl_ran_rayleigh_tail (r_global, 2.7, 1.9);
}
double
test_rayleigh_tail_pdf (double x)
{
return gsl_ran_rayleigh_tail_pdf (x, 2.7, 1.9);
}
double
test_poisson (void)
{
return gsl_ran_poisson (r_global, 5.0);
}
double
test_poisson_pdf (unsigned int n)
{
return gsl_ran_poisson_pdf (n, 5.0);
}
double
test_poisson_large (void)
{
return gsl_ran_poisson (r_global, 30.0);
}
double
test_poisson_large_pdf (unsigned int n)
{
return gsl_ran_poisson_pdf (n, 30.0);
}
double
test_tdist1 (void)
{
return gsl_ran_tdist (r_global, 1.75);
}
double
test_tdist1_pdf (double x)
{
return gsl_ran_tdist_pdf (x, 1.75);
}
double
test_tdist2 (void)
{
return gsl_ran_tdist (r_global, 12.75);
}
double
test_tdist2_pdf (double x)
{
return gsl_ran_tdist_pdf (x, 12.75);
}
double
test_laplace (void)
{
return gsl_ran_laplace (r_global, 2.75);
}
double
test_laplace_pdf (double x)
{
return gsl_ran_laplace_pdf (x, 2.75);
}
double
test_weibull (void)
{
return gsl_ran_weibull (r_global, 3.14, 2.75);
}
double
test_weibull_pdf (double x)
{
return gsl_ran_weibull_pdf (x, 3.14, 2.75);
}
double
test_weibull1 (void)
{
return gsl_ran_weibull (r_global, 2.97, 1.0);
}
double
test_weibull1_pdf (double x)
{
return gsl_ran_weibull_pdf (x, 2.97, 1.0);
}