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
25namespace boost { namespace accumulators
26{
27
28namespace 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 // make this accumulator serializeable
110 template<class Archive>
111 void serialize(Archive & ar, const unsigned int file_version)
112 {
113 ar & sum;
114 ar & is_dirty;
115 ar & median;
116 }
117
118 private:
119 mutable float_type sum;
120 mutable bool is_dirty;
121 mutable float_type median;
122 };
123
124 ///////////////////////////////////////////////////////////////////////////////
125 // with_p_square_cumulative_distribution_weighted_median_impl
126 //
127 /**
128 @brief Median estimation for weighted samples based on the \f$P^2\f$ cumulative distribution estimator
129
130 The algorithm determines the first (leftmost) bin with a height exceeding 0.5. It
131 returns the approximate horizontal position of where the cumulative distribution
132 equals 0.5, based on a linear interpolation inside the bin.
133 */
134 template<typename Sample, typename Weight>
135 struct with_p_square_cumulative_distribution_weighted_median_impl
136 : accumulator_base
137 {
138 typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample;
139 typedef typename numeric::functional::fdiv<weighted_sample, std::size_t>::result_type float_type;
140 typedef std::vector<std::pair<float_type, float_type> > histogram_type;
141 typedef iterator_range<typename histogram_type::iterator> range_type;
142 // for boost::result_of
143 typedef float_type result_type;
144
145 with_p_square_cumulative_distribution_weighted_median_impl(dont_care)
146 : is_dirty(true)
147 {
148 }
149
150 void operator ()(dont_care)
151 {
152 this->is_dirty = true;
153 }
154
155 template<typename Args>
156 result_type result(Args const &args) const
157 {
158 if (this->is_dirty)
159 {
160 this->is_dirty = false;
161
162 range_type histogram = weighted_p_square_cumulative_distribution(args);
163 typename range_type::iterator it = histogram.begin();
164 while (it->second < 0.5)
165 {
166 ++it;
167 }
168 float_type over = numeric::fdiv(it->second - 0.5, it->second - (it - 1)->second);
169 this->median = it->first * over + (it + 1)->first * ( 1. - over );
170 }
171
172 return this->median;
173 }
174
175 // make this accumulator serializeable
176 template<class Archive>
177 void serialize(Archive & ar, const unsigned int file_version)
178 {
179 ar & is_dirty;
180 ar & median;
181 }
182
183 private:
184 mutable bool is_dirty;
185 mutable float_type median;
186 };
187
188} // namespace impl
189
190///////////////////////////////////////////////////////////////////////////////
191// tag::weighted_median
192// tag::with_density_weighted_median
193// tag::with_p_square_cumulative_distribution_weighted_median
194//
195namespace tag
196{
197 struct weighted_median
198 : depends_on<weighted_p_square_quantile_for_median>
199 {
200 /// INTERNAL ONLY
201 ///
202 typedef accumulators::impl::weighted_median_impl<mpl::_1> impl;
203 };
204 struct with_density_weighted_median
205 : depends_on<count, weighted_density>
206 {
207 /// INTERNAL ONLY
208 ///
209 typedef accumulators::impl::with_density_weighted_median_impl<mpl::_1> impl;
210 };
211 struct with_p_square_cumulative_distribution_weighted_median
212 : depends_on<weighted_p_square_cumulative_distribution>
213 {
214 /// INTERNAL ONLY
215 ///
216 typedef accumulators::impl::with_p_square_cumulative_distribution_weighted_median_impl<mpl::_1, mpl::_2> impl;
217 };
218
219}
220
221///////////////////////////////////////////////////////////////////////////////
222// extract::weighted_median
223//
224namespace extract
225{
226 extractor<tag::median> const weighted_median = {};
227
228 BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_median)
229}
230
231using extract::weighted_median;
232// weighted_median(with_p_square_quantile) -> weighted_median
233template<>
234struct as_feature<tag::weighted_median(with_p_square_quantile)>
235{
236 typedef tag::weighted_median type;
237};
238
239// weighted_median(with_density) -> with_density_weighted_median
240template<>
241struct as_feature<tag::weighted_median(with_density)>
242{
243 typedef tag::with_density_weighted_median type;
244};
245
246// weighted_median(with_p_square_cumulative_distribution) -> with_p_square_cumulative_distribution_weighted_median
247template<>
248struct as_feature<tag::weighted_median(with_p_square_cumulative_distribution)>
249{
250 typedef tag::with_p_square_cumulative_distribution_weighted_median type;
251};
252
253}} // namespace boost::accumulators
254
255#endif
256

source code of boost/libs/accumulators/include/boost/accumulators/statistics/weighted_median.hpp