boost/accumulators/statistics/median.hpp
/////////////////////////////////////////////////////////////////////////////// // median.hpp // // Copyright 2006 Eric Niebler, Olivier Gygi. 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) #ifndef BOOST_ACCUMULATORS_STATISTICS_MEDIAN_HPP_EAN_28_10_2005 #define BOOST_ACCUMULATORS_STATISTICS_MEDIAN_HPP_EAN_28_10_2005 #include <boost/mpl/placeholders.hpp> #include <boost/range/iterator_range.hpp> #include <boost/accumulators/framework/accumulator_base.hpp> #include <boost/accumulators/framework/extractor.hpp> #include <boost/accumulators/numeric/functional.hpp> #include <boost/accumulators/framework/parameters/sample.hpp> #include <boost/accumulators/framework/depends_on.hpp> #include <boost/accumulators/statistics_fwd.hpp> #include <boost/accumulators/statistics/count.hpp> #include <boost/accumulators/statistics/p_square_quantile.hpp> #include <boost/accumulators/statistics/density.hpp> #include <boost/accumulators/statistics/p_square_cumul_dist.hpp> namespace boost { namespace accumulators { namespace impl { /////////////////////////////////////////////////////////////////////////////// // median_impl // /** @brief Median estimation based on the \f$P^2\f$ quantile estimator The \f$P^2\f$ algorithm is invoked with a quantile probability of 0.5. */ template<typename Sample> struct median_impl : accumulator_base { // for boost::result_of typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type result_type; median_impl(dont_care) {} template<typename Args> result_type result(Args const &args) const { return p_square_quantile_for_median(args); } }; /////////////////////////////////////////////////////////////////////////////// // with_density_median_impl // /** @brief Median estimation based on the density estimator The algorithm determines the bin in which the \f$0.5*cnt\f$-th sample lies, \f$cnt\f$ being the total number of samples. It returns the approximate horizontal position of this sample, based on a linear interpolation inside the bin. */ template<typename Sample> struct with_density_median_impl : accumulator_base { typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type; typedef std::vector<std::pair<float_type, float_type> > histogram_type; typedef iterator_range<typename histogram_type::iterator> range_type; // for boost::result_of typedef float_type result_type; template<typename Args> with_density_median_impl(Args const &args) : sum(numeric::fdiv(args[sample | Sample()], (std::size_t)1)) , is_dirty(true) { } void operator ()(dont_care) { this->is_dirty = true; } template<typename Args> result_type result(Args const &args) const { if (this->is_dirty) { this->is_dirty = false; std::size_t cnt = count(args); range_type histogram = density(args); typename range_type::iterator it = histogram.begin(); while (this->sum < 0.5 * cnt) { this->sum += it->second * cnt; ++it; } --it; float_type over = numeric::fdiv(this->sum - 0.5 * cnt, it->second * cnt); this->median = it->first * over + (it + 1)->first * (1. - over); } return this->median; } private: mutable float_type sum; mutable bool is_dirty; mutable float_type median; }; /////////////////////////////////////////////////////////////////////////////// // with_p_square_cumulative_distribution_median_impl // /** @brief Median estimation based on the \f$P^2\f$ cumulative distribution estimator The algorithm determines the first (leftmost) bin with a height exceeding 0.5. It returns the approximate horizontal position of where the cumulative distribution equals 0.5, based on a linear interpolation inside the bin. */ template<typename Sample> struct with_p_square_cumulative_distribution_median_impl : accumulator_base { typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type; typedef std::vector<std::pair<float_type, float_type> > histogram_type; typedef iterator_range<typename histogram_type::iterator> range_type; // for boost::result_of typedef float_type result_type; with_p_square_cumulative_distribution_median_impl(dont_care) : is_dirty(true) { } void operator ()(dont_care) { this->is_dirty = true; } template<typename Args> result_type result(Args const &args) const { if (this->is_dirty) { this->is_dirty = false; range_type histogram = p_square_cumulative_distribution(args); typename range_type::iterator it = histogram.begin(); while (it->second < 0.5) { ++it; } float_type over = numeric::fdiv(it->second - 0.5, it->second - (it - 1)->second); this->median = it->first * over + (it + 1)->first * ( 1. - over ); } return this->median; } private: mutable bool is_dirty; mutable float_type median; }; } // namespace impl /////////////////////////////////////////////////////////////////////////////// // tag::median // tag::with_densisty_median // tag::with_p_square_cumulative_distribution_median // namespace tag { struct median : depends_on<p_square_quantile_for_median> { /// INTERNAL ONLY /// typedef accumulators::impl::median_impl<mpl::_1> impl; }; struct with_density_median : depends_on<count, density> { /// INTERNAL ONLY /// typedef accumulators::impl::with_density_median_impl<mpl::_1> impl; }; struct with_p_square_cumulative_distribution_median : depends_on<p_square_cumulative_distribution> { /// INTERNAL ONLY /// typedef accumulators::impl::with_p_square_cumulative_distribution_median_impl<mpl::_1> impl; }; } /////////////////////////////////////////////////////////////////////////////// // extract::median // extract::with_density_median // extract::with_p_square_cumulative_distribution_median // namespace extract { extractor<tag::median> const median = {}; extractor<tag::with_density_median> const with_density_median = {}; extractor<tag::with_p_square_cumulative_distribution_median> const with_p_square_cumulative_distribution_median = {}; BOOST_ACCUMULATORS_IGNORE_GLOBAL(median) BOOST_ACCUMULATORS_IGNORE_GLOBAL(with_density_median) BOOST_ACCUMULATORS_IGNORE_GLOBAL(with_p_square_cumulative_distribution_median) } using extract::median; using extract::with_density_median; using extract::with_p_square_cumulative_distribution_median; // median(with_p_square_quantile) -> median template<> struct as_feature<tag::median(with_p_square_quantile)> { typedef tag::median type; }; // median(with_density) -> with_density_median template<> struct as_feature<tag::median(with_density)> { typedef tag::with_density_median type; }; // median(with_p_square_cumulative_distribution) -> with_p_square_cumulative_distribution_median template<> struct as_feature<tag::median(with_p_square_cumulative_distribution)> { typedef tag::with_p_square_cumulative_distribution_median type; }; // for the purposes of feature-based dependency resolution, // with_density_median and with_p_square_cumulative_distribution_median // provide the same feature as median template<> struct feature_of<tag::with_density_median> : feature_of<tag::median> { }; template<> struct feature_of<tag::with_p_square_cumulative_distribution_median> : feature_of<tag::median> { }; // So that median can be automatically substituted with // weighted_median when the weight parameter is non-void. template<> struct as_weighted_feature<tag::median> { typedef tag::weighted_median type; }; template<> struct feature_of<tag::weighted_median> : feature_of<tag::median> { }; // So that with_density_median can be automatically substituted with // with_density_weighted_median when the weight parameter is non-void. template<> struct as_weighted_feature<tag::with_density_median> { typedef tag::with_density_weighted_median type; }; template<> struct feature_of<tag::with_density_weighted_median> : feature_of<tag::with_density_median> { }; // So that with_p_square_cumulative_distribution_median can be automatically substituted with // with_p_square_cumulative_distribution_weighted_median when the weight parameter is non-void. template<> struct as_weighted_feature<tag::with_p_square_cumulative_distribution_median> { typedef tag::with_p_square_cumulative_distribution_weighted_median type; }; template<> struct feature_of<tag::with_p_square_cumulative_distribution_weighted_median> : feature_of<tag::with_p_square_cumulative_distribution_median> { }; }} // namespace boost::accumulators #endif