Chris@16: ///////////////////////////////////////////////////////////////////////////////
Chris@16: // median.hpp
Chris@16: //
Chris@16: //  Copyright 2006 Eric Niebler, Olivier Gygi. Distributed under the Boost
Chris@16: //  Software License, Version 1.0. (See accompanying file
Chris@16: //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@16: 
Chris@16: #ifndef BOOST_ACCUMULATORS_STATISTICS_MEDIAN_HPP_EAN_28_10_2005
Chris@16: #define BOOST_ACCUMULATORS_STATISTICS_MEDIAN_HPP_EAN_28_10_2005
Chris@16: 
Chris@16: #include <boost/mpl/placeholders.hpp>
Chris@16: #include <boost/range/iterator_range.hpp>
Chris@16: #include <boost/accumulators/framework/accumulator_base.hpp>
Chris@16: #include <boost/accumulators/framework/extractor.hpp>
Chris@16: #include <boost/accumulators/numeric/functional.hpp>
Chris@16: #include <boost/accumulators/framework/parameters/sample.hpp>
Chris@16: #include <boost/accumulators/framework/depends_on.hpp>
Chris@16: #include <boost/accumulators/statistics_fwd.hpp>
Chris@16: #include <boost/accumulators/statistics/count.hpp>
Chris@16: #include <boost/accumulators/statistics/p_square_quantile.hpp>
Chris@16: #include <boost/accumulators/statistics/density.hpp>
Chris@16: #include <boost/accumulators/statistics/p_square_cumul_dist.hpp>
Chris@16: 
Chris@16: namespace boost { namespace accumulators
Chris@16: {
Chris@16: 
Chris@16: namespace impl
Chris@16: {
Chris@16:     ///////////////////////////////////////////////////////////////////////////////
Chris@16:     // median_impl
Chris@16:     //
Chris@16:     /**
Chris@16:         @brief Median estimation based on the \f$P^2\f$ quantile estimator
Chris@16: 
Chris@16:         The \f$P^2\f$ algorithm is invoked with a quantile probability of 0.5.
Chris@16:     */
Chris@16:     template<typename Sample>
Chris@16:     struct median_impl
Chris@16:       : accumulator_base
Chris@16:     {
Chris@16:         // for boost::result_of
Chris@16:         typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type result_type;
Chris@16: 
Chris@16:         median_impl(dont_care) {}
Chris@16: 
Chris@16:         template<typename Args>
Chris@16:         result_type result(Args const &args) const
Chris@16:         {
Chris@16:             return p_square_quantile_for_median(args);
Chris@16:         }
Chris@16:     };
Chris@16:     ///////////////////////////////////////////////////////////////////////////////
Chris@16:     // with_density_median_impl
Chris@16:     //
Chris@16:     /**
Chris@16:         @brief Median estimation based on the density estimator
Chris@16: 
Chris@16:         The algorithm determines the bin in which the \f$0.5*cnt\f$-th sample lies, \f$cnt\f$ being
Chris@16:         the total number of samples. It returns the approximate horizontal position of this sample,
Chris@16:         based on a linear interpolation inside the bin.
Chris@16:     */
Chris@16:     template<typename Sample>
Chris@16:     struct with_density_median_impl
Chris@16:       : accumulator_base
Chris@16:     {
Chris@16:         typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type;
Chris@16:         typedef std::vector<std::pair<float_type, float_type> > histogram_type;
Chris@16:         typedef iterator_range<typename histogram_type::iterator> range_type;
Chris@16:         // for boost::result_of
Chris@16:         typedef float_type result_type;
Chris@16: 
Chris@16:         template<typename Args>
Chris@16:         with_density_median_impl(Args const &args)
Chris@16:           : sum(numeric::fdiv(args[sample | Sample()], (std::size_t)1))
Chris@16:           , is_dirty(true)
Chris@16:         {
Chris@16:         }
Chris@16: 
Chris@16:         void operator ()(dont_care)
Chris@16:         {
Chris@16:             this->is_dirty = true;
Chris@16:         }
Chris@16: 
Chris@16: 
Chris@16:         template<typename Args>
Chris@16:         result_type result(Args const &args) const
Chris@16:         {
Chris@16:             if (this->is_dirty)
Chris@16:             {
Chris@16:                 this->is_dirty = false;
Chris@16: 
Chris@16:                 std::size_t cnt = count(args);
Chris@16:                 range_type histogram = density(args);
Chris@16:                 typename range_type::iterator it = histogram.begin();
Chris@16:                 while (this->sum < 0.5 * cnt)
Chris@16:                 {
Chris@16:                     this->sum += it->second * cnt;
Chris@16:                     ++it;
Chris@16:                 }
Chris@16:                 --it;
Chris@16:                 float_type over = numeric::fdiv(this->sum - 0.5 * cnt, it->second * cnt);
Chris@16:                 this->median = it->first * over + (it + 1)->first * (1. - over);
Chris@16:             }
Chris@16: 
Chris@16:             return this->median;
Chris@16:         }
Chris@16: 
Chris@16:     private:
Chris@16:         mutable float_type sum;
Chris@16:         mutable bool is_dirty;
Chris@16:         mutable float_type median;
Chris@16:     };
Chris@16: 
Chris@16:     ///////////////////////////////////////////////////////////////////////////////
Chris@16:     // with_p_square_cumulative_distribution_median_impl
Chris@16:     //
Chris@16:     /**
Chris@16:         @brief Median estimation based on the \f$P^2\f$ cumulative distribution estimator
Chris@16: 
Chris@16:         The algorithm determines the first (leftmost) bin with a height exceeding 0.5. It
Chris@16:         returns the approximate horizontal position of where the cumulative distribution
Chris@16:         equals 0.5, based on a linear interpolation inside the bin.
Chris@16:     */
Chris@16:     template<typename Sample>
Chris@16:     struct with_p_square_cumulative_distribution_median_impl
Chris@16:       : accumulator_base
Chris@16:     {
Chris@16:         typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type;
Chris@16:         typedef std::vector<std::pair<float_type, float_type> > histogram_type;
Chris@16:         typedef iterator_range<typename histogram_type::iterator> range_type;
Chris@16:         // for boost::result_of
Chris@16:         typedef float_type result_type;
Chris@16: 
Chris@16:         with_p_square_cumulative_distribution_median_impl(dont_care)
Chris@16:           : is_dirty(true)
Chris@16:         {
Chris@16:         }
Chris@16: 
Chris@16:         void operator ()(dont_care)
Chris@16:         {
Chris@16:             this->is_dirty = true;
Chris@16:         }
Chris@16: 
Chris@16:         template<typename Args>
Chris@16:         result_type result(Args const &args) const
Chris@16:         {
Chris@16:             if (this->is_dirty)
Chris@16:             {
Chris@16:                 this->is_dirty = false;
Chris@16: 
Chris@16:                 range_type histogram = p_square_cumulative_distribution(args);
Chris@16:                 typename range_type::iterator it = histogram.begin();
Chris@16:                 while (it->second < 0.5)
Chris@16:                 {
Chris@16:                     ++it;
Chris@16:                 }
Chris@16:                 float_type over = numeric::fdiv(it->second - 0.5, it->second - (it - 1)->second);
Chris@16:                 this->median = it->first * over + (it + 1)->first * ( 1. - over );
Chris@16:             }
Chris@16: 
Chris@16:             return this->median;
Chris@16:         }
Chris@16:     private:
Chris@16: 
Chris@16:         mutable bool is_dirty;
Chris@16:         mutable float_type median;
Chris@16:     };
Chris@16: 
Chris@16: } // namespace impl
Chris@16: 
Chris@16: ///////////////////////////////////////////////////////////////////////////////
Chris@16: // tag::median
Chris@16: // tag::with_densisty_median
Chris@16: // tag::with_p_square_cumulative_distribution_median
Chris@16: //
Chris@16: namespace tag
Chris@16: {
Chris@16:     struct median
Chris@16:       : depends_on<p_square_quantile_for_median>
Chris@16:     {
Chris@16:         /// INTERNAL ONLY
Chris@16:         ///
Chris@16:         typedef accumulators::impl::median_impl<mpl::_1> impl;
Chris@16:     };
Chris@16:     struct with_density_median
Chris@16:       : depends_on<count, density>
Chris@16:     {
Chris@16:         /// INTERNAL ONLY
Chris@16:         ///
Chris@16:         typedef accumulators::impl::with_density_median_impl<mpl::_1> impl;
Chris@16:     };
Chris@16:     struct with_p_square_cumulative_distribution_median
Chris@16:       : depends_on<p_square_cumulative_distribution>
Chris@16:     {
Chris@16:         /// INTERNAL ONLY
Chris@16:         ///
Chris@16:         typedef accumulators::impl::with_p_square_cumulative_distribution_median_impl<mpl::_1> impl;
Chris@16:     };
Chris@16: }
Chris@16: 
Chris@16: ///////////////////////////////////////////////////////////////////////////////
Chris@16: // extract::median
Chris@16: // extract::with_density_median
Chris@16: // extract::with_p_square_cumulative_distribution_median
Chris@16: //
Chris@16: namespace extract
Chris@16: {
Chris@16:     extractor<tag::median> const median = {};
Chris@16:     extractor<tag::with_density_median> const with_density_median = {};
Chris@16:     extractor<tag::with_p_square_cumulative_distribution_median> const with_p_square_cumulative_distribution_median = {};
Chris@16: 
Chris@16:     BOOST_ACCUMULATORS_IGNORE_GLOBAL(median)
Chris@16:     BOOST_ACCUMULATORS_IGNORE_GLOBAL(with_density_median)
Chris@16:     BOOST_ACCUMULATORS_IGNORE_GLOBAL(with_p_square_cumulative_distribution_median)
Chris@16: }
Chris@16: 
Chris@16: using extract::median;
Chris@16: using extract::with_density_median;
Chris@16: using extract::with_p_square_cumulative_distribution_median;
Chris@16: 
Chris@16: // median(with_p_square_quantile) -> median
Chris@16: template<>
Chris@16: struct as_feature<tag::median(with_p_square_quantile)>
Chris@16: {
Chris@16:     typedef tag::median type;
Chris@16: };
Chris@16: 
Chris@16: // median(with_density) -> with_density_median
Chris@16: template<>
Chris@16: struct as_feature<tag::median(with_density)>
Chris@16: {
Chris@16:     typedef tag::with_density_median type;
Chris@16: };
Chris@16: 
Chris@16: // median(with_p_square_cumulative_distribution) -> with_p_square_cumulative_distribution_median
Chris@16: template<>
Chris@16: struct as_feature<tag::median(with_p_square_cumulative_distribution)>
Chris@16: {
Chris@16:     typedef tag::with_p_square_cumulative_distribution_median type;
Chris@16: };
Chris@16: 
Chris@16: // for the purposes of feature-based dependency resolution,
Chris@16: // with_density_median and with_p_square_cumulative_distribution_median
Chris@16: // provide the same feature as median
Chris@16: template<>
Chris@16: struct feature_of<tag::with_density_median>
Chris@16:   : feature_of<tag::median>
Chris@16: {
Chris@16: };
Chris@16: 
Chris@16: template<>
Chris@16: struct feature_of<tag::with_p_square_cumulative_distribution_median>
Chris@16:   : feature_of<tag::median>
Chris@16: {
Chris@16: };
Chris@16: 
Chris@16: // So that median can be automatically substituted with
Chris@16: // weighted_median when the weight parameter is non-void.
Chris@16: template<>
Chris@16: struct as_weighted_feature<tag::median>
Chris@16: {
Chris@16:     typedef tag::weighted_median type;
Chris@16: };
Chris@16: 
Chris@16: template<>
Chris@16: struct feature_of<tag::weighted_median>
Chris@16:   : feature_of<tag::median>
Chris@16: {
Chris@16: };
Chris@16: 
Chris@16: // So that with_density_median can be automatically substituted with
Chris@16: // with_density_weighted_median when the weight parameter is non-void.
Chris@16: template<>
Chris@16: struct as_weighted_feature<tag::with_density_median>
Chris@16: {
Chris@16:     typedef tag::with_density_weighted_median type;
Chris@16: };
Chris@16: 
Chris@16: template<>
Chris@16: struct feature_of<tag::with_density_weighted_median>
Chris@16:   : feature_of<tag::with_density_median>
Chris@16: {
Chris@16: };
Chris@16: 
Chris@16: // So that with_p_square_cumulative_distribution_median can be automatically substituted with
Chris@16: // with_p_square_cumulative_distribution_weighted_median when the weight parameter is non-void.
Chris@16: template<>
Chris@16: struct as_weighted_feature<tag::with_p_square_cumulative_distribution_median>
Chris@16: {
Chris@16:     typedef tag::with_p_square_cumulative_distribution_weighted_median type;
Chris@16: };
Chris@16: 
Chris@16: template<>
Chris@16: struct feature_of<tag::with_p_square_cumulative_distribution_weighted_median>
Chris@16:   : feature_of<tag::with_p_square_cumulative_distribution_median>
Chris@16: {
Chris@16: };
Chris@16: 
Chris@16: }} // namespace boost::accumulators
Chris@16: 
Chris@16: #endif