1///////////////////////////////////////////////////////////////////////////////
2// weighted_p_square_quantile.hpp
3//
4// Copyright 2005 Daniel Egloff. 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_P_SQUARE_QUANTILE_HPP_DE_01_01_2006
9#define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_P_SQUARE_QUANTILE_HPP_DE_01_01_2006
10
11#include <cmath>
12#include <functional>
13#include <boost/array.hpp>
14#include <boost/parameter/keyword.hpp>
15#include <boost/mpl/placeholders.hpp>
16#include <boost/type_traits/is_same.hpp>
17#include <boost/accumulators/framework/accumulator_base.hpp>
18#include <boost/accumulators/framework/extractor.hpp>
19#include <boost/accumulators/numeric/functional.hpp>
20#include <boost/accumulators/framework/parameters/sample.hpp>
21#include <boost/accumulators/statistics_fwd.hpp>
22#include <boost/accumulators/statistics/count.hpp>
23#include <boost/accumulators/statistics/sum.hpp>
24#include <boost/accumulators/statistics/parameters/quantile_probability.hpp>
25
26namespace boost { namespace accumulators
27{
28
29namespace impl {
30 ///////////////////////////////////////////////////////////////////////////////
31 // weighted_p_square_quantile_impl
32 // single quantile estimation with weighted samples
33 /**
34 @brief Single quantile estimation with the \f$P^2\f$ algorithm for weighted samples
35
36 This version of the \f$P^2\f$ algorithm extends the \f$P^2\f$ algorithm to support weighted samples.
37 The \f$P^2\f$ algorithm estimates a quantile dynamically without storing samples. Instead of
38 storing the whole sample cumulative distribution, only five points (markers) are stored. The heights
39 of these markers are the minimum and the maximum of the samples and the current estimates of the
40 \f$(p/2)\f$-, \f$p\f$ - and \f$(1+p)/2\f$ -quantiles. Their positions are equal to the number
41 of samples that are smaller or equal to the markers. Each time a new sample is added, the
42 positions of the markers are updated and if necessary their heights are adjusted using a piecewise-
43 parabolic formula.
44
45 For further details, see
46
47 R. Jain and I. Chlamtac, The P^2 algorithm for dynamic calculation of quantiles and
48 histograms without storing observations, Communications of the ACM,
49 Volume 28 (October), Number 10, 1985, p. 1076-1085.
50
51 @param quantile_probability
52 */
53 template<typename Sample, typename Weight, typename Impl>
54 struct weighted_p_square_quantile_impl
55 : accumulator_base
56 {
57 typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample;
58 typedef typename numeric::functional::fdiv<weighted_sample, std::size_t>::result_type float_type;
59 typedef array<float_type, 5> array_type;
60 // for boost::result_of
61 typedef float_type result_type;
62
63 template<typename Args>
64 weighted_p_square_quantile_impl(Args const &args)
65 : p(is_same<Impl, for_median>::value ? 0.5 : args[quantile_probability | 0.5])
66 , heights()
67 , actual_positions()
68 , desired_positions()
69 {
70 }
71
72 template<typename Args>
73 void operator ()(Args const &args)
74 {
75 std::size_t cnt = count(args);
76
77 // accumulate 5 first samples
78 if (cnt <= 5)
79 {
80 this->heights[cnt - 1] = args[sample];
81
82 // In this initialization phase, actual_positions stores the weights of the
83 // initial samples that are needed at the end of the initialization phase to
84 // compute the correct initial positions of the markers.
85 this->actual_positions[cnt - 1] = args[weight];
86
87 // complete the initialization of heights and actual_positions by sorting
88 if (cnt == 5)
89 {
90 // TODO: we need to sort the initial samples (in heights) in ascending order and
91 // sort their weights (in actual_positions) the same way. The following lines do
92 // it, but there must be a better and more efficient way of doing this.
93 typename array_type::iterator it_begin, it_end, it_min;
94
95 it_begin = this->heights.begin();
96 it_end = this->heights.end();
97
98 std::size_t pos = 0;
99
100 while (it_begin != it_end)
101 {
102 it_min = std::min_element(it_begin, it_end);
103 std::size_t d = std::distance(it_begin, it_min);
104 std::swap(*it_begin, *it_min);
105 std::swap(this->actual_positions[pos], this->actual_positions[pos + d]);
106 ++it_begin;
107 ++pos;
108 }
109
110 // calculate correct initial actual positions
111 for (std::size_t i = 1; i < 5; ++i)
112 {
113 this->actual_positions[i] += this->actual_positions[i - 1];
114 }
115 }
116 }
117 else
118 {
119 std::size_t sample_cell = 1; // k
120
121 // find cell k such that heights[k-1] <= args[sample] < heights[k] and adjust extreme values
122 if (args[sample] < this->heights[0])
123 {
124 this->heights[0] = args[sample];
125 this->actual_positions[0] = args[weight];
126 sample_cell = 1;
127 }
128 else if (this->heights[4] <= args[sample])
129 {
130 this->heights[4] = args[sample];
131 sample_cell = 4;
132 }
133 else
134 {
135 typedef typename array_type::iterator iterator;
136 iterator it = std::upper_bound(
137 this->heights.begin()
138 , this->heights.end()
139 , args[sample]
140 );
141
142 sample_cell = std::distance(this->heights.begin(), it);
143 }
144
145 // increment positions of markers above sample_cell
146 for (std::size_t i = sample_cell; i < 5; ++i)
147 {
148 this->actual_positions[i] += args[weight];
149 }
150
151 // update desired positions for all markers
152 this->desired_positions[0] = this->actual_positions[0];
153 this->desired_positions[1] = (sum_of_weights(args) - this->actual_positions[0])
154 * this->p/2. + this->actual_positions[0];
155 this->desired_positions[2] = (sum_of_weights(args) - this->actual_positions[0])
156 * this->p + this->actual_positions[0];
157 this->desired_positions[3] = (sum_of_weights(args) - this->actual_positions[0])
158 * (1. + this->p)/2. + this->actual_positions[0];
159 this->desired_positions[4] = sum_of_weights(args);
160
161 // adjust height and actual positions of markers 1 to 3 if necessary
162 for (std::size_t i = 1; i <= 3; ++i)
163 {
164 // offset to desired positions
165 float_type d = this->desired_positions[i] - this->actual_positions[i];
166
167 // offset to next position
168 float_type dp = this->actual_positions[i + 1] - this->actual_positions[i];
169
170 // offset to previous position
171 float_type dm = this->actual_positions[i - 1] - this->actual_positions[i];
172
173 // height ds
174 float_type hp = (this->heights[i + 1] - this->heights[i]) / dp;
175 float_type hm = (this->heights[i - 1] - this->heights[i]) / dm;
176
177 if ( ( d >= 1. && dp > 1. ) || ( d <= -1. && dm < -1. ) )
178 {
179 short sign_d = static_cast<short>(d / std::abs(d));
180
181 // try adjusting heights[i] using p-squared formula
182 float_type h = this->heights[i] + sign_d / (dp - dm) * ( (sign_d - dm) * hp + (dp - sign_d) * hm );
183
184 if ( this->heights[i - 1] < h && h < this->heights[i + 1] )
185 {
186 this->heights[i] = h;
187 }
188 else
189 {
190 // use linear formula
191 if (d>0)
192 {
193 this->heights[i] += hp;
194 }
195 if (d<0)
196 {
197 this->heights[i] -= hm;
198 }
199 }
200 this->actual_positions[i] += sign_d;
201 }
202 }
203 }
204 }
205
206 result_type result(dont_care) const
207 {
208 return this->heights[2];
209 }
210
211 // make this accumulator serializeable
212 // TODO split to save/load and check on parameters provided in ctor
213 template<class Archive>
214 void serialize(Archive & ar, const unsigned int file_version)
215 {
216 ar & p;
217 ar & heights;
218 ar & actual_positions;
219 ar & desired_positions;
220 }
221
222 private:
223 float_type p; // the quantile probability p
224 array_type heights; // q_i
225 array_type actual_positions; // n_i
226 array_type desired_positions; // n'_i
227 };
228
229} // namespace impl
230
231///////////////////////////////////////////////////////////////////////////////
232// tag::weighted_p_square_quantile
233//
234namespace tag
235{
236 struct weighted_p_square_quantile
237 : depends_on<count, sum_of_weights>
238 {
239 typedef accumulators::impl::weighted_p_square_quantile_impl<mpl::_1, mpl::_2, regular> impl;
240 };
241 struct weighted_p_square_quantile_for_median
242 : depends_on<count, sum_of_weights>
243 {
244 typedef accumulators::impl::weighted_p_square_quantile_impl<mpl::_1, mpl::_2, for_median> impl;
245 };
246}
247
248///////////////////////////////////////////////////////////////////////////////
249// extract::weighted_p_square_quantile
250// extract::weighted_p_square_quantile_for_median
251//
252namespace extract
253{
254 extractor<tag::weighted_p_square_quantile> const weighted_p_square_quantile = {};
255 extractor<tag::weighted_p_square_quantile_for_median> const weighted_p_square_quantile_for_median = {};
256
257 BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_p_square_quantile)
258 BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_p_square_quantile_for_median)
259}
260
261using extract::weighted_p_square_quantile;
262using extract::weighted_p_square_quantile_for_median;
263
264}} // namespace boost::accumulators
265
266#endif
267

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