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1 | /////////////////////////////////////////////////////////////////////////////// |
2 | // weighted_p_square_cumul_dist.hpp | |
3 | // | |
4 | // Copyright 2006 Daniel Egloff, 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_P_SQUARE_CUMUL_DIST_HPP_DE_01_01_2006 | |
9 | #define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_P_SQUARE_CUMUL_DIST_HPP_DE_01_01_2006 | |
10 | ||
11 | #include <vector> | |
12 | #include <functional> | |
13 | #include <boost/parameter/keyword.hpp> | |
14 | #include <boost/mpl/placeholders.hpp> | |
15 | #include <boost/range.hpp> | |
16 | #include <boost/accumulators/framework/accumulator_base.hpp> | |
17 | #include <boost/accumulators/framework/extractor.hpp> | |
18 | #include <boost/accumulators/numeric/functional.hpp> | |
19 | #include <boost/accumulators/framework/parameters/sample.hpp> | |
20 | #include <boost/accumulators/statistics_fwd.hpp> | |
21 | #include <boost/accumulators/statistics/count.hpp> | |
22 | #include <boost/accumulators/statistics/sum.hpp> | |
23 | #include <boost/accumulators/statistics/p_square_cumul_dist.hpp> // for named parameter p_square_cumulative_distribution_num_cells | |
24 | ||
25 | namespace boost { namespace accumulators | |
26 | { | |
27 | ||
28 | namespace impl | |
29 | { | |
30 | /////////////////////////////////////////////////////////////////////////////// | |
31 | // weighted_p_square_cumulative_distribution_impl | |
32 | // cumulative distribution calculation (as histogram) | |
33 | /** | |
34 | @brief Histogram calculation of the cumulative distribution with the \f$P^2\f$ algorithm for weighted samples | |
35 | ||
36 | A histogram of the sample cumulative distribution is computed dynamically without storing samples | |
37 | based on the \f$ P^2 \f$ algorithm for weighted samples. The returned histogram has a specifiable | |
38 | amount (num_cells) equiprobable (and not equal-sized) cells. | |
39 | ||
40 | Note that applying importance sampling results in regions to be more and other regions to be less | |
41 | accurately estimated than without importance sampling, i.e., with unweighted samples. | |
42 | ||
43 | For further details, see | |
44 | ||
45 | R. Jain and I. Chlamtac, The P^2 algorithm for dynamic calculation of quantiles and | |
46 | histograms without storing observations, Communications of the ACM, | |
47 | Volume 28 (October), Number 10, 1985, p. 1076-1085. | |
48 | ||
49 | @param p_square_cumulative_distribution_num_cells | |
50 | */ | |
51 | template<typename Sample, typename Weight> | |
52 | struct weighted_p_square_cumulative_distribution_impl | |
53 | : accumulator_base | |
54 | { | |
55 | typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample; | |
56 | typedef typename numeric::functional::fdiv<weighted_sample, std::size_t>::result_type float_type; | |
57 | typedef std::vector<std::pair<float_type, float_type> > histogram_type; | |
58 | typedef std::vector<float_type> array_type; | |
59 | // for boost::result_of | |
60 | typedef iterator_range<typename histogram_type::iterator> result_type; | |
61 | ||
62 | template<typename Args> | |
63 | weighted_p_square_cumulative_distribution_impl(Args const &args) | |
64 | : num_cells(args[p_square_cumulative_distribution_num_cells]) | |
65 | , heights(num_cells + 1) | |
66 | , actual_positions(num_cells + 1) | |
67 | , desired_positions(num_cells + 1) | |
68 | , histogram(num_cells + 1) | |
69 | , is_dirty(true) | |
70 | { | |
71 | } | |
72 | ||
73 | template<typename Args> | |
74 | void operator ()(Args const &args) | |
75 | { | |
76 | this->is_dirty = true; | |
77 | ||
78 | std::size_t cnt = count(args); | |
79 | std::size_t sample_cell = 1; // k | |
80 | std::size_t b = this->num_cells; | |
81 | ||
82 | // accumulate num_cells + 1 first samples | |
83 | if (cnt <= b + 1) | |
84 | { | |
85 | this->heights[cnt - 1] = args[sample]; | |
86 | this->actual_positions[cnt - 1] = args[weight]; | |
87 | ||
88 | // complete the initialization of heights by sorting | |
89 | if (cnt == b + 1) | |
90 | { | |
91 | //std::sort(this->heights.begin(), this->heights.end()); | |
92 | ||
93 | // TODO: we need to sort the initial samples (in heights) in ascending order and | |
94 | // sort their weights (in actual_positions) the same way. The following lines do | |
95 | // it, but there must be a better and more efficient way of doing this. | |
96 | typename array_type::iterator it_begin, it_end, it_min; | |
97 | ||
98 | it_begin = this->heights.begin(); | |
99 | it_end = this->heights.end(); | |
100 | ||
101 | std::size_t pos = 0; | |
102 | ||
103 | while (it_begin != it_end) | |
104 | { | |
105 | it_min = std::min_element(it_begin, it_end); | |
106 | std::size_t d = std::distance(it_begin, it_min); | |
107 | std::swap(*it_begin, *it_min); | |
108 | std::swap(this->actual_positions[pos], this->actual_positions[pos + d]); | |
109 | ++it_begin; | |
110 | ++pos; | |
111 | } | |
112 | ||
113 | // calculate correct initial actual positions | |
114 | for (std::size_t i = 1; i < b; ++i) | |
115 | { | |
116 | this->actual_positions[i] += this->actual_positions[i - 1]; | |
117 | } | |
118 | } | |
119 | } | |
120 | else | |
121 | { | |
122 | // find cell k such that heights[k-1] <= args[sample] < heights[k] and adjust extreme values | |
123 | if (args[sample] < this->heights[0]) | |
124 | { | |
125 | this->heights[0] = args[sample]; | |
126 | this->actual_positions[0] = args[weight]; | |
127 | sample_cell = 1; | |
128 | } | |
129 | else if (this->heights[b] <= args[sample]) | |
130 | { | |
131 | this->heights[b] = args[sample]; | |
132 | sample_cell = b; | |
133 | } | |
134 | else | |
135 | { | |
136 | typename array_type::iterator it; | |
137 | it = std::upper_bound( | |
138 | this->heights.begin() | |
139 | , this->heights.end() | |
140 | , args[sample] | |
141 | ); | |
142 | ||
143 | sample_cell = std::distance(this->heights.begin(), it); | |
144 | } | |
145 | ||
146 | // increment positions of markers above sample_cell | |
147 | for (std::size_t i = sample_cell; i < b + 1; ++i) | |
148 | { | |
149 | this->actual_positions[i] += args[weight]; | |
150 | } | |
151 | ||
152 | // determine desired marker positions | |
153 | for (std::size_t i = 1; i < b + 1; ++i) | |
154 | { | |
155 | this->desired_positions[i] = this->actual_positions[0] | |
156 | + numeric::fdiv((i-1) * (sum_of_weights(args) - this->actual_positions[0]), b); | |
157 | } | |
158 | ||
159 | // adjust heights of markers 2 to num_cells if necessary | |
160 | for (std::size_t i = 1; i < b; ++i) | |
161 | { | |
162 | // offset to desire position | |
163 | float_type d = this->desired_positions[i] - this->actual_positions[i]; | |
164 | ||
165 | // offset to next position | |
166 | float_type dp = this->actual_positions[i + 1] - this->actual_positions[i]; | |
167 | ||
168 | // offset to previous position | |
169 | float_type dm = this->actual_positions[i - 1] - this->actual_positions[i]; | |
170 | ||
171 | // height ds | |
172 | float_type hp = (this->heights[i + 1] - this->heights[i]) / dp; | |
173 | float_type hm = (this->heights[i - 1] - this->heights[i]) / dm; | |
174 | ||
175 | if ( ( d >= 1. && dp > 1. ) || ( d <= -1. && dm < -1. ) ) | |
176 | { | |
177 | short sign_d = static_cast<short>(d / std::abs(d)); | |
178 | ||
179 | // try adjusting heights[i] using p-squared formula | |
180 | float_type h = this->heights[i] + sign_d / (dp - dm) * ( (sign_d - dm) * hp + (dp - sign_d) * hm ); | |
181 | ||
182 | if ( this->heights[i - 1] < h && h < this->heights[i + 1] ) | |
183 | { | |
184 | this->heights[i] = h; | |
185 | } | |
186 | else | |
187 | { | |
188 | // use linear formula | |
189 | if (d>0) | |
190 | { | |
191 | this->heights[i] += hp; | |
192 | } | |
193 | if (d<0) | |
194 | { | |
195 | this->heights[i] -= hm; | |
196 | } | |
197 | } | |
198 | this->actual_positions[i] += sign_d; | |
199 | } | |
200 | } | |
201 | } | |
202 | } | |
203 | ||
204 | template<typename Args> | |
205 | result_type result(Args const &args) const | |
206 | { | |
207 | if (this->is_dirty) | |
208 | { | |
209 | this->is_dirty = false; | |
210 | ||
211 | // creates a vector of std::pair where each pair i holds | |
212 | // the values heights[i] (x-axis of histogram) and | |
213 | // actual_positions[i] / sum_of_weights (y-axis of histogram) | |
214 | ||
215 | for (std::size_t i = 0; i < this->histogram.size(); ++i) | |
216 | { | |
217 | this->histogram[i] = std::make_pair(this->heights[i], numeric::fdiv(this->actual_positions[i], sum_of_weights(args))); | |
218 | } | |
219 | } | |
220 | ||
221 | return make_iterator_range(this->histogram); | |
222 | } | |
223 | ||
224 | private: | |
225 | std::size_t num_cells; // number of cells b | |
226 | array_type heights; // q_i | |
227 | array_type actual_positions; // n_i | |
228 | array_type desired_positions; // n'_i | |
229 | mutable histogram_type histogram; // histogram | |
230 | mutable bool is_dirty; | |
231 | }; | |
232 | ||
233 | } // namespace detail | |
234 | ||
235 | /////////////////////////////////////////////////////////////////////////////// | |
236 | // tag::weighted_p_square_cumulative_distribution | |
237 | // | |
238 | namespace tag | |
239 | { | |
240 | struct weighted_p_square_cumulative_distribution | |
241 | : depends_on<count, sum_of_weights> | |
242 | , p_square_cumulative_distribution_num_cells | |
243 | { | |
244 | typedef accumulators::impl::weighted_p_square_cumulative_distribution_impl<mpl::_1, mpl::_2> impl; | |
245 | }; | |
246 | } | |
247 | ||
248 | /////////////////////////////////////////////////////////////////////////////// | |
249 | // extract::weighted_p_square_cumulative_distribution | |
250 | // | |
251 | namespace extract | |
252 | { | |
253 | extractor<tag::weighted_p_square_cumulative_distribution> const weighted_p_square_cumulative_distribution = {}; | |
254 | ||
255 | BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_p_square_cumulative_distribution) | |
256 | } | |
257 | ||
258 | using extract::weighted_p_square_cumulative_distribution; | |
259 | ||
260 | }} // namespace boost::accumulators | |
261 | ||
262 | #endif |