/* 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 #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #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); }