test.c

该文件为c++的数学函数库!是一个非常有用的编程工具.它含有各种数学函数,为科学计算、工程应用等程序编写提供方便！

/* 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., 675 Mass Ave, Cambridge, MA 02139, 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_binomial_tpe (void);
double test_binomial_tpe_pdf (unsigned int n);
double test_binomial_large_tpe (void);
double test_binomial_large_tpe_pdf (unsigned int n);
double test_binomial_huge_tpe (void);
double test_binomial_huge_tpe_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_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_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_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;

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 (fdist));
  testPDF (FUNC2 (flat));
  testPDF (FUNC2 (gamma));
  testPDF (FUNC2 (gamma1));
  testPDF (FUNC2 (gamma_int));
  testPDF (FUNC2 (gamma_large));
  testPDF (FUNC2 (gaussian));
  testPDF (FUNC2 (gaussian_ratio_method));
  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 (binomial_tpe));
  testDiscretePDF (FUNC2 (binomial_large));
  testDiscretePDF (FUNC2 (binomial_large_tpe));
  testDiscretePDF (FUNC2 (binomial_huge));
  testDiscretePDF (FUNC2 (binomial_huge_tpe));
  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));

  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 > 1);
        }
      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);