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Diffstat (limited to 'gsl-1.9/randist/test.c')
-rw-r--r-- | gsl-1.9/randist/test.c | 1968 |
1 files changed, 1968 insertions, 0 deletions
diff --git a/gsl-1.9/randist/test.c b/gsl-1.9/randist/test.c new file mode 100644 index 0000000..540d0eb --- /dev/null +++ b/gsl-1.9/randist/test.c @@ -0,0 +1,1968 @@ +/* randist/test.c + * + * Copyright (C) 1996, 1997, 1998, 1999, 2000 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 2 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> + +#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_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_dirichlet (void); +double test_dirichlet_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_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_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_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); +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 (dirichlet)); + 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 (flat)); + testPDF (FUNC2 (gamma)); + testPDF (FUNC2 (gamma1)); + testPDF (FUNC2 (gamma_int)); + testPDF (FUNC2 (gamma_large)); + 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)); + + 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 (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 = fabs (count - expected) / sqrt (expected); + + status = (sigma > 3); + + gsl_test (status, "%s [%g,%g] (%g observed vs %g expected)", + name, a, b, count / N, p); +} + +#define BINS 100 + +void +testPDF (double (*f) (void), double (*pdf) (double), const char *name) +{ + double count[BINS], p[BINS]; + double a = -5.0, b = +5.0; + double dx = (b - a) / BINS; + int i, j, status = 0, status_i = 0; + + for (i = 0; i < BINS; i++) + count[i] = 0; + + for (i = 0; i < N; i++) + { + double r = f (); + if (r < b && r > a) + { + j = (int) ((r - a) / dx); + count[j]++; + } + } + + for (i = 0; i < BINS; i++) + { + /* Compute an approximation to the integral of p(x) from x to + x+dx using Simpson's rule */ + + double x = a + i * dx; +#define STEPS 100 + double sum = 0; + + if (fabs (x) < 1e-10) /* hit the origin exactly */ + x = 0.0; + + for (j = 1; j < STEPS; j++) + sum += pdf (x + j * dx / STEPS); + + p[i] = 0.5 * (pdf (x) + 2 * sum + pdf (x + dx - 1e-7)) * dx / STEPS; + } + + for (i = 0; i < BINS; i++) + { + double x = a + i * dx; + double d = fabs (count[i] - N * p[i]); + if (p[i] != 0) + { + double s = d / sqrt (N * p[i]); + status_i = (s > 5) && (d > 2); + } + else + { + status_i = (count[i] != 0); + } + 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_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_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); +} + + +/* 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); +} + +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_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_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); +} + + +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); +} |