1// (C) Copyright Eric Niebler, Olivier Gygi 2006.
2// Use, modification and distribution are subject to the
3// Boost Software License, Version 1.0. (See accompanying file
4// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
5
6// Test case for weighted_p_square_cumul_dist.hpp
7
8#include <cmath>
9#include <boost/random.hpp>
10#include <boost/test/unit_test.hpp>
11#include <boost/test/tools/floating_point_comparison.hpp>
12#include <boost/accumulators/numeric/functional/vector.hpp>
13#include <boost/accumulators/numeric/functional/complex.hpp>
14#include <boost/accumulators/numeric/functional/valarray.hpp>
15#include <boost/accumulators/accumulators.hpp>
16#include <boost/accumulators/statistics/stats.hpp>
17#include <boost/accumulators/statistics/weighted_p_square_cumul_dist.hpp>
18
19using namespace boost;
20using namespace unit_test;
21using namespace boost::accumulators;
22
23///////////////////////////////////////////////////////////////////////////////
24// erf() not known by VC++ compiler!
25// my_erf() computes error function by numerically integrating with trapezoidal rule
26//
27double my_erf(double const& x, int const& n = 1000)
28{
29 double sum = 0.;
30 double delta = x/n;
31 for (int i = 1; i < n; ++i)
32 sum += std::exp(x: -i*i*delta*delta) * delta;
33 sum += 0.5 * delta * (1. + std::exp(x: -x*x));
34 return sum * 2. / std::sqrt(x: 3.141592653);
35}
36
37///////////////////////////////////////////////////////////////////////////////
38// test_stat
39//
40void test_stat()
41{
42 // tolerance in %
43 double epsilon = 4;
44
45 typedef accumulator_set<double, stats<tag::weighted_p_square_cumulative_distribution>, double > accumulator_t;
46
47 accumulator_t acc_upper(p_square_cumulative_distribution_num_cells = 100);
48 accumulator_t acc_lower(p_square_cumulative_distribution_num_cells = 100);
49
50 // two random number generators
51 double mu_upper = 1.0;
52 double mu_lower = -1.0;
53 boost::lagged_fibonacci607 rng;
54 boost::normal_distribution<> mean_sigma_upper(mu_upper,1);
55 boost::normal_distribution<> mean_sigma_lower(mu_lower,1);
56 boost::variate_generator<boost::lagged_fibonacci607&, boost::normal_distribution<> > normal_upper(rng, mean_sigma_upper);
57 boost::variate_generator<boost::lagged_fibonacci607&, boost::normal_distribution<> > normal_lower(rng, mean_sigma_lower);
58
59 for (std::size_t i=0; i<100000; ++i)
60 {
61 double sample = normal_upper();
62 acc_upper(sample, weight = std::exp(x: -mu_upper * (sample - 0.5 * mu_upper)));
63 }
64
65 for (std::size_t i=0; i<100000; ++i)
66 {
67 double sample = normal_lower();
68 acc_lower(sample, weight = std::exp(x: -mu_lower * (sample - 0.5 * mu_lower)));
69 }
70
71 typedef iterator_range<std::vector<std::pair<double, double> >::iterator > histogram_type;
72 histogram_type histogram_upper = weighted_p_square_cumulative_distribution(acc_upper);
73 histogram_type histogram_lower = weighted_p_square_cumulative_distribution(acc_lower);
74
75 // Note that applying importance sampling results in a region of the distribution
76 // to be estimated more accurately and another region to be estimated less accurately
77 // than without importance sampling, i.e., with unweighted samples
78
79 for (std::size_t i = 0; i < histogram_upper.size(); ++i)
80 {
81 // problem with small results: epsilon is relative (in percent), not absolute!
82
83 // check upper region of distribution
84 if ( histogram_upper[i].second > 0.1 )
85 BOOST_CHECK_CLOSE( 0.5 * (1.0 + my_erf( histogram_upper[i].first / std::sqrt(2.0) )), histogram_upper[i].second, epsilon );
86 // check lower region of distribution
87 if ( histogram_lower[i].second < -0.1 )
88 BOOST_CHECK_CLOSE( 0.5 * (1.0 + my_erf( histogram_lower[i].first / std::sqrt(2.0) )), histogram_lower[i].second, epsilon );
89 }
90}
91
92///////////////////////////////////////////////////////////////////////////////
93// init_unit_test_suite
94//
95test_suite* init_unit_test_suite( int argc, char* argv[] )
96{
97 test_suite *test = BOOST_TEST_SUITE("weighted_p_square_cumulative_distribution test");
98
99 test->add(BOOST_TEST_CASE(&test_stat));
100
101 return test;
102}
103
104

source code of boost/libs/accumulators/test/weighted_p_square_cumul_dist.cpp