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random/test/statistic_tests.cpp

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/* statistic_tests.cpp file
*
* Copyright Jens Maurer 2000, 2002
* Distributed under the Boost Software License, Version 1.0. (See
* accompanying file LICENSE_1_0.txt or copy at
* http://www.boost.org/LICENSE_1_0.txt)
*
* $Id$
*
* Revision history
*/
#include <iostream>
#include <iomanip>
#include <string>
#include <functional>
#include <vector>
#include <set>
#include <algorithm>
#include <boost/cstdint.hpp>
#include <boost/random.hpp>
#include <boost/math/special_functions/gamma.hpp>
#include <boost/math/distributions/uniform.hpp>
#include <boost/math/distributions/chi_squared.hpp>
#include <boost/math/distributions/normal.hpp>
#include <boost/math/distributions/triangular.hpp>
#include <boost/math/distributions/cauchy.hpp>
#include <boost/math/distributions/gamma.hpp>
#include <boost/math/distributions/exponential.hpp>
#include <boost/math/distributions/lognormal.hpp>
#include "statistic_tests.hpp"
#include "integrate.hpp"
class test_environment;
class test_base
{
protected:
explicit test_base(test_environment & env) : environment(env) { }
void check_(double val) const;
private:
test_environment & environment;
};
class equidistribution_test : test_base
{
public:
equidistribution_test(test_environment & env, unsigned int classes,
unsigned int high_classes)
: test_base(env), classes(classes),
test_distrib_chi_square(boost::math::chi_squared(classes-1), high_classes)
{ }
template<class RNG>
void run(RNG & rng, int n1, int n2)
{
using namespace boost;
std::cout << "equidistribution: " << std::flush;
equidistribution_experiment equi(classes);
variate_generator<RNG&, uniform_smallint<> > uint_linear(rng, uniform_smallint<>(0, classes-1));
check_(run_experiment(test_distrib_chi_square,
experiment_generator(equi, uint_linear, n1), n2));
check_(run_experiment(test_distrib_chi_square,
experiment_generator(equi, uint_linear, n1), 2*n2));
std::cout << " 2D: " << std::flush;
equidistribution_2d_experiment equi_2d(classes);
unsigned int root = static_cast<unsigned int>(std::sqrt(double(classes)));
assert(root * root == classes);
variate_generator<RNG&, uniform_smallint<> > uint_square(rng, uniform_smallint<>(0, root-1));
check_(run_experiment(test_distrib_chi_square,
experiment_generator(equi_2d, uint_square, n1), n2));
check_(run_experiment(test_distrib_chi_square,
experiment_generator(equi_2d, uint_square, n1), 2*n2));
std::cout << std::endl;
}
private:
unsigned int classes;
distribution_experiment test_distrib_chi_square;
};
class ks_distribution_test : test_base
{
public:
ks_distribution_test(test_environment & env, unsigned int classes)
: test_base(env),
test_distrib_chi_square(kolmogorov_smirnov_probability(5000),
classes)
{ }
template<class RNG>
void run(RNG & rng, int n1, int n2)
{
boost::math::uniform ud(static_cast<double>((rng.min)()), static_cast<double>((rng.max)()));
run(rng, ud, n1, n2);
}
template<class RNG, class Dist>
void run(RNG & rng, const Dist& dist, int n1, int n2)
{
using namespace boost;
std::cout << "KS: " << std::flush;
kolmogorov_experiment ks(n1);
check_(run_experiment(test_distrib_chi_square,
ks_experiment_generator(ks, rng, dist), n2));
check_(run_experiment(test_distrib_chi_square,
ks_experiment_generator(ks, rng, dist), 2*n2));
std::cout << std::endl;
}
private:
distribution_experiment test_distrib_chi_square;
};
class runs_test : test_base
{
public:
runs_test(test_environment & env, unsigned int classes,
unsigned int high_classes)
: test_base(env), classes(classes),
test_distrib_chi_square(boost::math::chi_squared(classes-1), high_classes)
{ }
template<class RNG>
void run(RNG & rng, int n1, int n2)
{
using namespace boost;
std::cout << "runs: up: " << std::flush;
runs_experiment<true> r_up(classes);
check_(run_experiment(test_distrib_chi_square,
experiment_generator(r_up, rng, n1), n2));
check_(run_experiment(test_distrib_chi_square,
experiment_generator(r_up, rng, n1), 2*n2));
std::cout << " down: " << std::flush;
runs_experiment<false> r_down(classes);
check_(run_experiment(test_distrib_chi_square,
experiment_generator(r_down, rng, n1), n2));
check_(run_experiment(test_distrib_chi_square,
experiment_generator(r_down, rng, n1), 2*n2));
std::cout << std::endl;
}
private:
unsigned int classes;
distribution_experiment test_distrib_chi_square;
};
class gap_test : test_base
{
public:
gap_test(test_environment & env, unsigned int classes,
unsigned int high_classes)
: test_base(env), classes(classes),
test_distrib_chi_square(boost::math::chi_squared(classes-1), high_classes)
{ }
template<class RNG>
void run(RNG & rng, int n1, int n2)
{
boost::math::uniform ud(
static_cast<double>((rng.min)()),
static_cast<double>((rng.max)()) +
(std::numeric_limits<typename RNG::result_type>::is_integer? 0.0 : 1.0));
run(rng, ud, n1, n2);
}
template<class RNG, class Dist>
void run(RNG & rng, const Dist& dist, int n1, int n2)
{
using namespace boost;
std::cout << "gaps: " << std::flush;
gap_experiment gap(classes, dist, 0.2, 0.8);
check_(run_experiment(test_distrib_chi_square,
experiment_generator(gap, rng, n1), n2));
check_(run_experiment(test_distrib_chi_square,
experiment_generator(gap, rng, n1), 2*n2));
std::cout << std::endl;
}
private:
unsigned int classes;
distribution_experiment test_distrib_chi_square;
};
class poker_test : test_base
{
public:
poker_test(test_environment & env, unsigned int classes,
unsigned int high_classes)
: test_base(env), classes(classes),
test_distrib_chi_square(boost::math::chi_squared(classes-1), high_classes)
{ }
template<class RNG>
void run(RNG & rng, int n1, int n2)
{
using namespace boost;
std::cout << "poker: " << std::flush;
poker_experiment poker(8, classes);
variate_generator<RNG&, uniform_smallint<> > usmall(rng, uniform_smallint<>(0, 7));
check_(run_experiment(test_distrib_chi_square,
experiment_generator(poker, usmall, n1), n2));
check_(run_experiment(test_distrib_chi_square,
experiment_generator(poker, usmall, n1), 2*n2));
std::cout << std::endl;
}
private:
unsigned int classes;
distribution_experiment test_distrib_chi_square;
};
class coupon_collector_test : test_base
{
public:
coupon_collector_test(test_environment & env, unsigned int classes,
unsigned int high_classes)
: test_base(env), classes(classes),
test_distrib_chi_square(boost::math::chi_squared(classes-1), high_classes)
{ }
template<class RNG>
void run(RNG & rng, int n1, int n2)
{
using namespace boost;
std::cout << "coupon collector: " << std::flush;
coupon_collector_experiment coupon(5, classes);
variate_generator<RNG&, uniform_smallint<> > usmall(rng, uniform_smallint<>(0, 4));
check_(run_experiment(test_distrib_chi_square,
experiment_generator(coupon, usmall, n1), n2));
check_(run_experiment(test_distrib_chi_square,
experiment_generator(coupon, usmall, n1), 2*n2));
std::cout << std::endl;
}
private:
unsigned int classes;
distribution_experiment test_distrib_chi_square;
};
class permutation_test : test_base
{
public:
permutation_test(test_environment & env, unsigned int classes,
unsigned int high_classes)
: test_base(env), classes(classes),
test_distrib_chi_square(boost::math::chi_squared(fac<int>(classes)-1),
high_classes)
{ }
template<class RNG>
void run(RNG & rng, int n1, int n2)
{
using namespace boost;
std::cout << "permutation: " << std::flush;
permutation_experiment perm(classes);
// generator_reference_t<RNG> gen_ref(rng);
RNG& gen_ref(rng);
check_(run_experiment(test_distrib_chi_square,
experiment_generator(perm, gen_ref, n1), n2));
check_(run_experiment(test_distrib_chi_square,
experiment_generator(perm, gen_ref, n1), 2*n2));
std::cout << std::endl;
}
private:
unsigned int classes;
distribution_experiment test_distrib_chi_square;
};
class maximum_test : test_base
{
public:
maximum_test(test_environment & env, unsigned int high_classes)
: test_base(env),
test_distrib_chi_square(kolmogorov_smirnov_probability(1000),
high_classes)
{ }
template<class RNG>
void run(RNG & rng, int n1, int n2)
{
using namespace boost;
std::cout << "maximum-of-t: " << std::flush;
maximum_experiment<RNG> mx(rng, n1, 5);
check_(run_experiment(test_distrib_chi_square, mx, n2));
check_(run_experiment(test_distrib_chi_square, mx, 2*n2));
std::cout << std::endl;
}
private:
distribution_experiment test_distrib_chi_square;
};
class birthday_test : test_base
{
public:
birthday_test(test_environment & env, unsigned int high_classes)
: test_base(env),
test_distrib_chi_square(boost::math::chi_squared(4-1), high_classes)
{ }
template<class RNG>
void run(RNG & rng, int n1, int n2)
{
using namespace boost;
std::cout << "birthday spacing: " << std::flush;
boost::variate_generator<RNG&, boost::uniform_int<> > uni(rng, boost::uniform_int<>(0, (1<<25)-1));
birthday_spacing_experiment bsp(4, 512, (1<<25));
check_(run_experiment(test_distrib_chi_square,
experiment_generator(bsp, uni, n1), n2));
check_(run_experiment(test_distrib_chi_square,
experiment_generator(bsp, uni, n1), 2*n2));
std::cout << std::endl;
}
private:
distribution_experiment test_distrib_chi_square;
};
#ifdef BOOST_MSVC
#pragma warning(disable:4355)
#endif
class test_environment
{
public:
static const int classes = 20;
explicit test_environment(double confid)
: confidence(confid),
confidence_chi_square_quantil(quantile(boost::math::chi_squared(classes-1), confidence)),
test_distrib_chi_square6(boost::math::chi_squared(7-1), classes),
ksdist_test(*this, classes),
equi_test(*this, 100, classes),
rns_test(*this, 7, classes),
gp_test(*this, 7, classes),
pk_test(*this, 5, classes),
cpn_test(*this, 15, classes),
perm_test(*this, 5, classes),
max_test(*this, classes),
bday_test(*this, classes)
{
std::cout << "Confidence level: " << confid
<< "; 1-alpha = " << (1-confid)
<< "; chi_square(" << (classes-1)
<< ", " << confidence_chi_square_quantil
<< ") = "
<< cdf(boost::math::chi_squared(classes-1), confidence_chi_square_quantil)
<< std::endl;
}
bool check_confidence(double val, double chi_square_conf) const
{
std::cout << val;
bool result = (val <= chi_square_conf);
if(!result) {
std::cout << "* [";
double prob = (val > 10*chi_square_conf ? 1 :
cdf(boost::math::chi_squared(classes-1), val));
std::cout << (1-prob) << "]";
}
std::cout << " " << std::flush;
return result;
}
bool check_(double chi_square_value) const
{
return check_confidence(chi_square_value, confidence_chi_square_quantil);
}
template<class RNG>
void run_test(const std::string & name)
{
using namespace boost;
std::cout << "Running tests on " << name << std::endl;
RNG rng(1234567);
ksdist_test.run(rng, 5000, 250);
equi_test.run(rng, 5000, 250);
rns_test.run(rng, 100000, 250);
gp_test.run(rng, 10000, 250);
pk_test.run(rng, 5000, 250);
cpn_test.run(rng, 500, 250);
perm_test.run(rng, 1200, 250);
max_test.run(rng, 1000, 250);
bday_test.run(rng, 1000, 150);
std::cout << std::endl;
}
template<class RNG, class Dist, class ExpectedDist>
void run_test(const std::string & name, const Dist & dist, const ExpectedDist & expected_dist)
{
using namespace boost;
std::cout << "Running tests on " << name << std::endl;
RNG rng;
variate_generator<RNG&, Dist> vgen(rng, dist);
ksdist_test.run(vgen, expected_dist, 5000, 250);
rns_test.run(vgen, 100000, 250);
gp_test.run(vgen, expected_dist, 10000, 250);
perm_test.run(vgen, 1200, 250);
std::cout << std::endl;
}
private:
double confidence;
double confidence_chi_square_quantil;
distribution_experiment test_distrib_chi_square6;
ks_distribution_test ksdist_test;
equidistribution_test equi_test;
runs_test rns_test;
gap_test gp_test;
poker_test pk_test;
coupon_collector_test cpn_test;
permutation_test perm_test;
maximum_test max_test;
birthday_test bday_test;
};
void test_base::check_(double val) const
{
environment.check_(val);
}
class program_args
{
public:
program_args(int argc, char** argv)
{
if(argc > 0) {
names.insert(argv + 1, argv + argc);
}
}
bool check_(const std::string & test_name) const
{
return(names.empty() || names.find(test_name) != names.end());
}
private:
std::set<std::string> names;
};
int main(int argc, char* argv[])
{
program_args args(argc, argv);
test_environment env(0.99);
#define TEST(name) \
if(args.check_(#name)) \
env.run_test<boost::name>(#name)
TEST(minstd_rand0);
TEST(minstd_rand);
TEST(rand48);
TEST(ecuyer1988);
TEST(kreutzer1986);
TEST(taus88);
TEST(hellekalek1995);
TEST(mt11213b);
TEST(mt19937);
TEST(lagged_fibonacci607);
TEST(lagged_fibonacci1279);
TEST(lagged_fibonacci2281);
TEST(lagged_fibonacci3217);
TEST(lagged_fibonacci4423);
TEST(lagged_fibonacci9689);
TEST(lagged_fibonacci19937);
TEST(lagged_fibonacci23209);
TEST(lagged_fibonacci44497);
TEST(ranlux3);
TEST(ranlux4);
#if !defined(BOOST_NO_INT64_T) && !defined(BOOST_NO_INTEGRAL_INT64_T)
TEST(ranlux64_3);
TEST(ranlux64_4);
#endif
TEST(ranlux3_01);
TEST(ranlux4_01);
TEST(ranlux64_3_01);
TEST(ranlux64_4_01);
if(args.check_("normal"))
env.run_test<boost::mt19937>("normal", boost::normal_distribution<>(), boost::math::normal());
if(args.check_("triangle"))
env.run_test<boost::mt19937>("triangle", boost::triangle_distribution<>(0, 1, 3), boost::math::triangular(0, 1, 3));
if(args.check_("cauchy"))
env.run_test<boost::mt19937>("cauchy", boost::cauchy_distribution<>(), boost::math::cauchy());
if(args.check_("gamma"))
env.run_test<boost::mt19937>("gamma", boost::gamma_distribution<>(1), boost::math::gamma_distribution<>(1));
if(args.check_("exponential"))
env.run_test<boost::mt19937>("exponential", boost::exponential_distribution<>(), boost::math::exponential());
if(args.check_("lognormal"))
env.run_test<boost::mt19937>("lognormal", boost::lognormal_distribution<>(1, 1),
boost::math::lognormal(std::log(1.0/std::sqrt(2.0)), std::sqrt(std::log(2.0))));
}
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