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/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
19 using namespace boost;
20 using namespace unit_test;
21 using 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 //
my_erf(double const & x,int const & n=1000)27 double 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(-i*i*delta*delta) * delta;
33 sum += 0.5 * delta * (1. + std::exp(-x*x));
34 return sum * 2. / std::sqrt(3.141592653);
35 }
36
37 ///////////////////////////////////////////////////////////////////////////////
38 // test_stat
39 //
test_stat()40 void 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(-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(-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 //
init_unit_test_suite(int argc,char * argv[])95 test_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