boost/accumulators/statistics/weighted_median.hpp

   1 ///////////////////////////////////////////////////////////////////////////////
   2 // weighted_median.hpp
   3 //
   4 //  Copyright 2006 Eric Niebler, Olivier Gygi. Distributed under the Boost
   5 //  Software License, Version 1.0. (See accompanying file
   6 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
   7
   8 #ifndef BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_MEDIAN_HPP_EAN_28_10_2005
   9 #define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_MEDIAN_HPP_EAN_28_10_2005
  10
  11 #include <boost/mpl/placeholders.hpp>
  12 #include <boost/range/iterator_range.hpp>
  13 #include <boost/accumulators/framework/accumulator_base.hpp>
  14 #include <boost/accumulators/framework/extractor.hpp>
  15 #include <boost/accumulators/numeric/functional.hpp>
  16 #include <boost/accumulators/framework/parameters/sample.hpp>
  17 #include <boost/accumulators/framework/depends_on.hpp>
  18 #include <boost/accumulators/statistics_fwd.hpp>
  19 #include <boost/accumulators/statistics/count.hpp>
  20 #include <boost/accumulators/statistics/median.hpp>
  21 #include <boost/accumulators/statistics/weighted_p_square_quantile.hpp>
  22 #include <boost/accumulators/statistics/weighted_density.hpp>
  23 #include <boost/accumulators/statistics/weighted_p_square_cumul_dist.hpp>
  24
  25 namespace boost { namespace accumulators
  26 {
  27
  28 namespace impl
  29 {
  30     ///////////////////////////////////////////////////////////////////////////////
  31     // weighted_median_impl
  32     //
  33     /**
  34         @brief Median estimation for weighted samples based on the \f$P^2\f$ quantile estimator
  35
  36         The \f$P^2\f$ algorithm for weighted samples is invoked with a quantile probability of 0.5.
  37     */
  38     template<typename Sample>
  39     struct weighted_median_impl
  40       : accumulator_base
  41     {
  42         // for boost::result_of
  43         typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type result_type;
  44
  45         weighted_median_impl(dont_care) {}
  46
  47         template<typename Args>
  48         result_type result(Args const &args) const
  49         {
  50             return weighted_p_square_quantile_for_median(args);
  51         }
  52     };
  53
  54     ///////////////////////////////////////////////////////////////////////////////
  55     // with_density_weighted_median_impl
  56     //
  57     /**
  58         @brief Median estimation for weighted samples based on the density estimator
  59
  60         The algorithm determines the bin in which the \f$0.5*cnt\f$-th sample lies, \f$cnt\f$ being
  61         the total number of samples. It returns the approximate horizontal position of this sample,
  62         based on a linear interpolation inside the bin.
  63     */
  64     template<typename Sample>
  65     struct with_density_weighted_median_impl
  66       : accumulator_base
  67     {
  68         typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type;
  69         typedef std::vector<std::pair<float_type, float_type> > histogram_type;
  70         typedef iterator_range<typename histogram_type::iterator> range_type;
  71         // for boost::result_of
  72         typedef float_type result_type;
  73
  74         template<typename Args>
  75         with_density_weighted_median_impl(Args const &args)
  76           : sum(numeric::fdiv(args[sample | Sample()], (std::size_t)1))
  77           , is_dirty(true)
  78         {
  79         }
  80
  81         void operator ()(dont_care)
  82         {
  83             this->is_dirty = true;
  84         }
  85
  86         template<typename Args>
  87         result_type result(Args const &args) const
  88         {
  89             if (this->is_dirty)
  90             {
  91                 this->is_dirty = false;
  92
  93                 std::size_t cnt = count(args);
  94                 range_type histogram = weighted_density(args);
  95                 typename range_type::iterator it = histogram.begin();
  96                 while (this->sum < 0.5 * cnt)
  97                 {
  98                     this->sum += it->second * cnt;
  99                     ++it;
 100                 }
 101                 --it;
 102                 float_type over = numeric::fdiv(this->sum - 0.5 * cnt, it->second * cnt);
 103                 this->median = it->first * over + (it + 1)->first * ( 1. - over );
 104             }
 105
 106             return this->median;
 107         }
 108
 109     private:
 110         mutable float_type sum;
 111         mutable bool is_dirty;
 112         mutable float_type median;
 113     };
 114
 115     ///////////////////////////////////////////////////////////////////////////////
 116     // with_p_square_cumulative_distribution_weighted_median_impl
 117     //
 118     /**
 119         @brief Median estimation for weighted samples based on the \f$P^2\f$ cumulative distribution estimator
 120
 121         The algorithm determines the first (leftmost) bin with a height exceeding 0.5. It
 122         returns the approximate horizontal position of where the cumulative distribution
 123         equals 0.5, based on a linear interpolation inside the bin.
 124     */
 125     template<typename Sample, typename Weight>
 126     struct with_p_square_cumulative_distribution_weighted_median_impl
 127       : accumulator_base
 128     {
 129         typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample;
 130         typedef typename numeric::functional::fdiv<weighted_sample, std::size_t>::result_type float_type;
 131         typedef std::vector<std::pair<float_type, float_type> > histogram_type;
 132         typedef iterator_range<typename histogram_type::iterator> range_type;
 133         // for boost::result_of
 134         typedef float_type result_type;
 135
 136         with_p_square_cumulative_distribution_weighted_median_impl(dont_care)
 137           : is_dirty(true)
 138         {
 139         }
 140
 141         void operator ()(dont_care)
 142         {
 143             this->is_dirty = true;
 144         }
 145
 146         template<typename Args>
 147         result_type result(Args const &args) const
 148         {
 149             if (this->is_dirty)
 150             {
 151                 this->is_dirty = false;
 152
 153                 range_type histogram = weighted_p_square_cumulative_distribution(args);
 154                 typename range_type::iterator it = histogram.begin();
 155                 while (it->second < 0.5)
 156                 {
 157                     ++it;
 158                 }
 159                 float_type over = numeric::fdiv(it->second - 0.5, it->second - (it - 1)->second);
 160                 this->median = it->first * over + (it + 1)->first * ( 1. - over );
 161             }
 162
 163             return this->median;
 164         }
 165     private:
 166         mutable bool is_dirty;
 167         mutable float_type median;
 168     };
 169
 170 } // namespace impl
 171
 172 ///////////////////////////////////////////////////////////////////////////////
 173 // tag::weighted_median
 174 // tag::with_density_weighted_median
 175 // tag::with_p_square_cumulative_distribution_weighted_median
 176 //
 177 namespace tag
 178 {
 179     struct weighted_median
 180       : depends_on<weighted_p_square_quantile_for_median>
 181     {
 182         /// INTERNAL ONLY
 183         ///
 184         typedef accumulators::impl::weighted_median_impl<mpl::_1> impl;
 185     };
 186     struct with_density_weighted_median
 187       : depends_on<count, weighted_density>
 188     {
 189         /// INTERNAL ONLY
 190         ///
 191         typedef accumulators::impl::with_density_weighted_median_impl<mpl::_1> impl;
 192     };
 193     struct with_p_square_cumulative_distribution_weighted_median
 194       : depends_on<weighted_p_square_cumulative_distribution>
 195     {
 196         /// INTERNAL ONLY
 197         ///
 198         typedef accumulators::impl::with_p_square_cumulative_distribution_weighted_median_impl<mpl::_1, mpl::_2> impl;
 199     };
 200
 201 }
 202
 203 ///////////////////////////////////////////////////////////////////////////////
 204 // extract::weighted_median
 205 //
 206 namespace extract
 207 {
 208     extractor<tag::median> const weighted_median = {};
 209
 210     BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_median)
 211 }
 212
 213 using extract::weighted_median;
 214 // weighted_median(with_p_square_quantile) -> weighted_median
 215 template<>
 216 struct as_feature<tag::weighted_median(with_p_square_quantile)>
 217 {
 218     typedef tag::weighted_median type;
 219 };
 220
 221 // weighted_median(with_density) -> with_density_weighted_median
 222 template<>
 223 struct as_feature<tag::weighted_median(with_density)>
 224 {
 225     typedef tag::with_density_weighted_median type;
 226 };
 227
 228 // weighted_median(with_p_square_cumulative_distribution) -> with_p_square_cumulative_distribution_weighted_median
 229 template<>
 230 struct as_feature<tag::weighted_median(with_p_square_cumulative_distribution)>
 231 {
 232     typedef tag::with_p_square_cumulative_distribution_weighted_median type;
 233 };
 234
 235 }} // namespace boost::accumulators
 236
 237 #endif