| // (C) Copyright Eric Niebler, Olivier Gygi 2006. |
| // Use, modification and distribution are subject to 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) |
| |
| // Test case for weighted_p_square_cumulative_distribution.hpp |
| |
| #include <cmath> |
| #include <boost/random.hpp> |
| #include <boost/test/unit_test.hpp> |
| #include <boost/test/floating_point_comparison.hpp> |
| #include <boost/accumulators/numeric/functional/vector.hpp> |
| #include <boost/accumulators/numeric/functional/complex.hpp> |
| #include <boost/accumulators/numeric/functional/valarray.hpp> |
| #include <boost/accumulators/accumulators.hpp> |
| #include <boost/accumulators/statistics/stats.hpp> |
| #include <boost/accumulators/statistics/weighted_p_square_cumulative_distribution.hpp> |
| |
| using namespace boost; |
| using namespace unit_test; |
| using namespace boost::accumulators; |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| // erf() not known by VC++ compiler! |
| // my_erf() computes error function by numerically integrating with trapezoidal rule |
| // |
| double my_erf(double const& x, int const& n = 1000) |
| { |
| double sum = 0.; |
| double delta = x/n; |
| for (int i = 1; i < n; ++i) |
| sum += std::exp(-i*i*delta*delta) * delta; |
| sum += 0.5 * delta * (1. + std::exp(-x*x)); |
| return sum * 2. / std::sqrt(3.141592653); |
| } |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| // test_stat |
| // |
| void test_stat() |
| { |
| // tolerance in % |
| double epsilon = 4; |
| |
| typedef accumulator_set<double, stats<tag::weighted_p_square_cumulative_distribution>, double > accumulator_t; |
| |
| accumulator_t acc_upper(p_square_cumulative_distribution_num_cells = 100); |
| accumulator_t acc_lower(p_square_cumulative_distribution_num_cells = 100); |
| |
| // two random number generators |
| double mu_upper = 1.0; |
| double mu_lower = -1.0; |
| boost::lagged_fibonacci607 rng; |
| boost::normal_distribution<> mean_sigma_upper(mu_upper,1); |
| boost::normal_distribution<> mean_sigma_lower(mu_lower,1); |
| boost::variate_generator<boost::lagged_fibonacci607&, boost::normal_distribution<> > normal_upper(rng, mean_sigma_upper); |
| boost::variate_generator<boost::lagged_fibonacci607&, boost::normal_distribution<> > normal_lower(rng, mean_sigma_lower); |
| |
| for (std::size_t i=0; i<100000; ++i) |
| { |
| double sample = normal_upper(); |
| acc_upper(sample, weight = std::exp(-mu_upper * (sample - 0.5 * mu_upper))); |
| } |
| |
| for (std::size_t i=0; i<100000; ++i) |
| { |
| double sample = normal_lower(); |
| acc_lower(sample, weight = std::exp(-mu_lower * (sample - 0.5 * mu_lower))); |
| } |
| |
| typedef iterator_range<std::vector<std::pair<double, double> >::iterator > histogram_type; |
| histogram_type histogram_upper = weighted_p_square_cumulative_distribution(acc_upper); |
| histogram_type histogram_lower = weighted_p_square_cumulative_distribution(acc_lower); |
| |
| // Note that applaying importance sampling results in a region of the distribution |
| // to be estimated more accurately and another region to be estimated less accurately |
| // than without importance sampling, i.e., with unweighted samples |
| |
| for (std::size_t i = 0; i < histogram_upper.size(); ++i) |
| { |
| // problem with small results: epsilon is relative (in percent), not absolute! |
| |
| // check upper region of distribution |
| if ( histogram_upper[i].second > 0.1 ) |
| BOOST_CHECK_CLOSE( 0.5 * (1.0 + my_erf( histogram_upper[i].first / std::sqrt(2.0) )), histogram_upper[i].second, epsilon ); |
| // check lower region of distribution |
| if ( histogram_lower[i].second < -0.1 ) |
| BOOST_CHECK_CLOSE( 0.5 * (1.0 + my_erf( histogram_lower[i].first / std::sqrt(2.0) )), histogram_lower[i].second, epsilon ); |
| } |
| } |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| // init_unit_test_suite |
| // |
| test_suite* init_unit_test_suite( int argc, char* argv[] ) |
| { |
| test_suite *test = BOOST_TEST_SUITE("weighted_p_square_cumulative_distribution test"); |
| |
| test->add(BOOST_TEST_CASE(&test_stat)); |
| |
| return test; |
| } |
| |