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！

/* cdf/test.c
 * 
 * Copyright (C) 2002 Jason H Stover.
 * 
 * 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., 59 Temple Place, Suite 330, Boston, MA  02111-1307, USA.
 */

#include <config.h>
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_cdf.h>
#include <gsl/gsl_test.h>
#include <gsl/gsl_ieee_utils.h>

#define TEST(func, args, value, tol) { double res = func args ; gsl_test_rel (res, value, tol, #func #args); } ;

#define TEST_TOL0  (2.0*GSL_DBL_EPSILON)
#define TEST_TOL1  (16.0*GSL_DBL_EPSILON)
#define TEST_TOL2  (256.0*GSL_DBL_EPSILON)
#define TEST_TOL3  (2048.0*GSL_DBL_EPSILON)
#define TEST_TOL4  (16384.0*GSL_DBL_EPSILON)
#define TEST_TOL5  (131072.0*GSL_DBL_EPSILON)
#define TEST_TOL6  (1048576.0*GSL_DBL_EPSILON)

void test_ugaussian (void);
void test_ugaussianinv (void);
void test_exponential (void);
void test_exponentialinv (void);
void test_tdist (void);
void test_fdist (void);
void test_gamma (void);
void test_chisq (void);
void test_beta (void);
void test_gammainv (void);
void test_chisqinv (void);
void test_tdistinv (void);

#include "test_auto.c"

int
main (void)
{
  gsl_ieee_env_setup ();
  
  /* Tests for gaussian cumulative distribution function 
     Function values computed with PARI, 28 digits precision */
  
  test_ugaussian ();
  test_exponential ();
  test_tdist (); 
  test_fdist (); 
  test_gamma ();
  test_chisq (); 
  test_beta (); 

  test_ugaussianinv ();
  test_exponentialinv ();
  test_gammainv (); 
  test_chisqinv (); 
  test_tdistinv (); 

  test_auto_beta ();
  test_auto_fdist ();
  test_auto_cauchy ();
  test_auto_gaussian ();
  test_auto_laplace ();
  test_auto_rayleigh ();
  test_auto_flat ();
  test_auto_lognormal ();
  test_auto_gamma ();
  test_auto_chisq ();
  test_auto_tdist ();
  test_auto_gumbel1 ();
  test_auto_gumbel2 ();
  test_auto_weibull ();
  test_auto_pareto ();
  test_auto_logistic ();
  test_auto_gammalarge ();
  
  exit (gsl_test_summary ());
}

void test_ugaussian (void)
{
  TEST (gsl_cdf_ugaussian_P, (0.0), 0.5, TEST_TOL0);
  TEST (gsl_cdf_ugaussian_P, (1e-32), 0.5, TEST_TOL0);
  TEST (gsl_cdf_ugaussian_P, (1e-16), 0.5000000000000000398942280401, TEST_TOL0);
  TEST (gsl_cdf_ugaussian_P, (1e-8), 0.5000000039894228040143267129, TEST_TOL0);
  TEST (gsl_cdf_ugaussian_P, (0.5), 0.6914624612740131036377046105, TEST_TOL0);
  TEST (gsl_cdf_ugaussian_P, (0.7), 0.7580363477769269852506495717, TEST_TOL0);
  TEST (gsl_cdf_ugaussian_P, (5.0), 0.9999997133484281208060883262, TEST_TOL0);
  TEST (gsl_cdf_ugaussian_P, (10.0), 0.9999999999999999999999923801, TEST_TOL0);
  TEST (gsl_cdf_ugaussian_P, (30.0), 1.000000000000000000000000000, TEST_TOL0);
  TEST (gsl_cdf_ugaussian_P, (40.0), 1.000000000000000000000000000, TEST_TOL0);
  TEST (gsl_cdf_ugaussian_P, (1e10), 1.000000000000000000000000000, TEST_TOL0);

  TEST (gsl_cdf_ugaussian_P, (-1e-32), 0.5, TEST_TOL0);
  TEST (gsl_cdf_ugaussian_P, (-1e-16), 0.4999999999999999601057719598, TEST_TOL0);
  TEST (gsl_cdf_ugaussian_P, (-1e-8), 0.4999999960105771959856732870, TEST_TOL0);
  TEST (gsl_cdf_ugaussian_P, (-0.5), 0.3085375387259868963622953894, TEST_TOL0);
  TEST (gsl_cdf_ugaussian_P, (-0.7), 0.2419636522230730147493504282, TEST_TOL0);
  TEST (gsl_cdf_ugaussian_P, (-5.0), 0.0000002866515718791939116737523329, TEST_TOL1);
  TEST (gsl_cdf_ugaussian_P, (-10.0), 7.619853024160526065973343257e-24, TEST_TOL3);
  TEST (gsl_cdf_ugaussian_P, (-30.0), 4.906713927148187059533809288e-198, TEST_TOL3);
  TEST (gsl_cdf_ugaussian_P, (-40.0), 3.655893540915029703748985850e-350, TEST_TOL3);
  TEST (gsl_cdf_ugaussian_P, (-1e10), 0.0, 0.0);

  TEST (gsl_cdf_ugaussian_Q, (0.0), 0.5, TEST_TOL0);
  TEST (gsl_cdf_ugaussian_Q, (1e-32), 0.5, TEST_TOL0);
  TEST (gsl_cdf_ugaussian_Q, (1e-16), 0.4999999999999999601057719598, TEST_TOL0);
  TEST (gsl_cdf_ugaussian_Q, (1e-8), 0.4999999960105771959856732870, TEST_TOL0);
  TEST (gsl_cdf_ugaussian_Q, (0.5), 0.3085375387259868963622953894, TEST_TOL0);
  TEST (gsl_cdf_ugaussian_Q, (0.7), 0.2419636522230730147493504282, TEST_TOL0);
  TEST (gsl_cdf_ugaussian_Q, (5.0), 0.0000002866515718791939116737523329, TEST_TOL3);
  TEST (gsl_cdf_ugaussian_Q, (10.0), 7.619853024160526065973343257e-24, TEST_TOL3);
  TEST (gsl_cdf_ugaussian_Q, (30.0), 4.906713927148187059533809288e-198, TEST_TOL3);
  TEST (gsl_cdf_ugaussian_Q, (40.0), 3.655893540915029703748985850e-350, TEST_TOL3);
  TEST (gsl_cdf_ugaussian_Q, (1e10), 0.0, 0.0);

  TEST (gsl_cdf_ugaussian_Q, (-1e-32), 0.5, TEST_TOL0);
  TEST (gsl_cdf_ugaussian_Q, (-1e-16), 0.5000000000000000398942280401, TEST_TOL0);
  TEST (gsl_cdf_ugaussian_Q, (-1e-8), 0.5000000039894228040143267129, TEST_TOL0);
  TEST (gsl_cdf_ugaussian_Q, (-0.5), 0.6914624612740131036377046105, TEST_TOL0);
  TEST (gsl_cdf_ugaussian_Q, (-0.7), 0.7580363477769269852506495717, TEST_TOL0);
  TEST (gsl_cdf_ugaussian_Q, (-5.0), 0.9999997133484281208060883262, TEST_TOL0);
  TEST (gsl_cdf_ugaussian_Q, (-10.0), 0.9999999999999999999999923801, TEST_TOL0);
  TEST (gsl_cdf_ugaussian_Q, (-30.0), 1.000000000000000000000000000, TEST_TOL0);
  TEST (gsl_cdf_ugaussian_Q, (-40.0), 1.000000000000000000000000000, TEST_TOL0);
  TEST (gsl_cdf_ugaussian_Q, (-1e10), 1.000000000000000000000000000, TEST_TOL0);
}
  /* Test values from Abramowitz & Stegun, Handbook of Mathematical
     Functions, Table 26.1.  Error term is given by dx = dP / Z(x) */

void test_ugaussianinv (void) {
  TEST (gsl_cdf_ugaussian_Pinv, (0.9999997133), 5.0, 1e-4);
  TEST (gsl_cdf_ugaussian_Pinv, (0.9999683288), 4.0, 1e-6);
  TEST (gsl_cdf_ugaussian_Pinv, (0.9986501020), 3.0, 1e-8);
  TEST (gsl_cdf_ugaussian_Pinv, (0.977249868051821), 2.0, 1e-14);
  TEST (gsl_cdf_ugaussian_Pinv, (0.841344746068543), 1.0, TEST_TOL3);
  TEST (gsl_cdf_ugaussian_Pinv, (0.691462461274013), 0.5, TEST_TOL2);
  TEST (gsl_cdf_ugaussian_Pinv, (0.655421741610324), 0.4, TEST_TOL1);
  TEST (gsl_cdf_ugaussian_Pinv, (0.617911422188953), 0.3, TEST_TOL1);
  TEST (gsl_cdf_ugaussian_Pinv, (0.579259709439103), 0.2, TEST_TOL1);
  TEST (gsl_cdf_ugaussian_Pinv, (0.539827837277029), 0.1, TEST_TOL1);
  TEST (gsl_cdf_ugaussian_Pinv, (0.5), 0.0, TEST_TOL0);
  TEST (gsl_cdf_ugaussian_Pinv, (4.60172162722971e-1), -0.1, TEST_TOL1);
  TEST (gsl_cdf_ugaussian_Pinv, (4.20740290560897e-1), -0.2, TEST_TOL1);
  TEST (gsl_cdf_ugaussian_Pinv, (3.82088577811047e-1), -0.3, TEST_TOL1);
  TEST (gsl_cdf_ugaussian_Pinv, (3.44578258389676e-1), -0.4, TEST_TOL1);
  TEST (gsl_cdf_ugaussian_Pinv, (3.08537538725987e-1), -0.5, TEST_TOL2);
  TEST (gsl_cdf_ugaussian_Pinv, (1.58655253931457e-1), -1.0, TEST_TOL3);
  TEST (gsl_cdf_ugaussian_Pinv, (2.2750131948179e-2), -2.0, 1e-14);
  TEST (gsl_cdf_ugaussian_Pinv, (1.349898e-3), -3.0, 1e-8);
  TEST (gsl_cdf_ugaussian_Pinv, (3.16712e-5), -4.0, 1e-6);
  TEST (gsl_cdf_ugaussian_Pinv, (2.86648e-7), -5.0, 1e-4);

  TEST (gsl_cdf_ugaussian_Pinv, (7.61985302416052e-24), -10.0, 1e-4);

  TEST (gsl_cdf_ugaussian_Qinv, (7.61985302416052e-24), 10.0, 1e-4);

  TEST (gsl_cdf_ugaussian_Qinv, (2.86648e-7), 5.0, 1e-4);
  TEST (gsl_cdf_ugaussian_Qinv, (3.16712e-5), 4.0, 1e-6);
  TEST (gsl_cdf_ugaussian_Qinv, (1.349898e-3), 3.0, 1e-8);
  TEST (gsl_cdf_ugaussian_Qinv, (2.2750131948179e-2), 2.0, 1e-14);
  TEST (gsl_cdf_ugaussian_Qinv, (1.58655253931457e-1), 1.0, TEST_TOL3);
  TEST (gsl_cdf_ugaussian_Qinv, (3.08537538725987e-1), 0.5, TEST_TOL2);
  TEST (gsl_cdf_ugaussian_Qinv, (3.44578258389676e-1), 0.4, TEST_TOL1);
  TEST (gsl_cdf_ugaussian_Qinv, (3.82088577811047e-1), 0.3, TEST_TOL1);
  TEST (gsl_cdf_ugaussian_Qinv, (4.20740290560897e-1), 0.2, TEST_TOL1);
  TEST (gsl_cdf_ugaussian_Qinv, (4.60172162722971e-1), 0.1, TEST_TOL1);
  TEST (gsl_cdf_ugaussian_Qinv, (0.5), 0.0, TEST_TOL0);
  TEST (gsl_cdf_ugaussian_Qinv, (0.539827837277029), -0.1, TEST_TOL1);
  TEST (gsl_cdf_ugaussian_Qinv, (0.579259709439103), -0.2, TEST_TOL1);
  TEST (gsl_cdf_ugaussian_Qinv, (0.617911422188953), -0.3, TEST_TOL1);
  TEST (gsl_cdf_ugaussian_Qinv, (0.655421741610324), -0.4, TEST_TOL1);
  TEST (gsl_cdf_ugaussian_Qinv, (0.691462461274013), -0.5, TEST_TOL2);
  TEST (gsl_cdf_ugaussian_Qinv, (0.841344746068543), -1.0, TEST_TOL3);
  TEST (gsl_cdf_ugaussian_Qinv, (0.977249868051821), -2.0, 1e-14);
  TEST (gsl_cdf_ugaussian_Qinv, (0.9986501020), -3.0, 1e-8);
  TEST (gsl_cdf_ugaussian_Qinv, (0.9999683288), -4.0, 1e-6);
  TEST (gsl_cdf_ugaussian_Qinv, (0.9999997133), -5.0, 1e-4);
}


  /* Tests for exponential cumulative distribution function
     Function values computed with PARI, 28 digits precision */

void test_exponential (void)
{
  TEST (gsl_cdf_exponential_P, (0.1, 0.7), 1.33122100249818372e-1, TEST_TOL0);
  TEST (gsl_cdf_exponential_P, (1e-32, 0.7), 1.42857142857142857e-32, TEST_TOL0);
  TEST (gsl_cdf_exponential_P, (1000.0, 0.7), 1.0, TEST_TOL6);

  TEST (gsl_cdf_exponential_Q, (0.1, 0.7), 8.66877899750181628e-1, TEST_TOL0);
  TEST (gsl_cdf_exponential_Q, (1e-32, 0.7), 1.0, TEST_TOL0);
  TEST (gsl_cdf_exponential_Q, (1000.0, 0.7), 0.0, TEST_TOL6);
}

void test_exponentialinv (void) {
  TEST (gsl_cdf_exponential_Pinv, (0.13, 0.7), 9.74834471334553546e-2, TEST_TOL0);
  TEST (gsl_cdf_exponential_Pinv, (1.42e-32, 0.7), 9.94000000000000000e-33, TEST_TOL0);

  TEST (gsl_cdf_exponential_Qinv, (0.86, 0.7), 1.05576022814208545e-1, TEST_TOL0);
  TEST (gsl_cdf_exponential_Qinv, (0.99999, 0.7), 7.00003500023333508e-6, TEST_TOL6);
}

  /* Tests for student's T distribution */