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- // (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_cumul_dist.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_cumul_dist.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 applying 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;
- }
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