]>
Commit | Line | Data |
---|---|---|
7c673cae FG |
1 | /////////////////////////////////////////////////////////////////////////////// |
2 | // extended_p_square.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_EXTENDED_SINGLE_HPP_DE_01_01_2006 | |
9 | #define BOOST_ACCUMULATORS_STATISTICS_EXTENDED_SINGLE_HPP_DE_01_01_2006 | |
10 | ||
11 | #include <vector> | |
12 | #include <functional> | |
13 | #include <boost/range/begin.hpp> | |
14 | #include <boost/range/end.hpp> | |
15 | #include <boost/range/iterator_range.hpp> | |
16 | #include <boost/iterator/transform_iterator.hpp> | |
17 | #include <boost/iterator/counting_iterator.hpp> | |
18 | #include <boost/iterator/permutation_iterator.hpp> | |
19 | #include <boost/parameter/keyword.hpp> | |
20 | #include <boost/mpl/placeholders.hpp> | |
21 | #include <boost/accumulators/accumulators_fwd.hpp> | |
22 | #include <boost/accumulators/framework/extractor.hpp> | |
23 | #include <boost/accumulators/numeric/functional.hpp> | |
24 | #include <boost/accumulators/framework/parameters/sample.hpp> | |
25 | #include <boost/accumulators/framework/depends_on.hpp> | |
26 | #include <boost/accumulators/statistics_fwd.hpp> | |
27 | #include <boost/accumulators/statistics/count.hpp> | |
28 | #include <boost/accumulators/statistics/times2_iterator.hpp> | |
29 | ||
30 | namespace boost { namespace accumulators | |
31 | { | |
32 | /////////////////////////////////////////////////////////////////////////////// | |
33 | // probabilities named parameter | |
34 | // | |
35 | BOOST_PARAMETER_NESTED_KEYWORD(tag, extended_p_square_probabilities, probabilities) | |
36 | ||
37 | BOOST_ACCUMULATORS_IGNORE_GLOBAL(extended_p_square_probabilities) | |
38 | ||
39 | namespace impl | |
40 | { | |
41 | /////////////////////////////////////////////////////////////////////////////// | |
42 | // extended_p_square_impl | |
43 | // multiple quantile estimation | |
44 | /** | |
45 | @brief Multiple quantile estimation with the extended \f$P^2\f$ algorithm | |
46 | ||
47 | Extended \f$P^2\f$ algorithm for estimation of several quantiles without storing samples. | |
48 | Assume that \f$m\f$ quantiles \f$\xi_{p_1}, \ldots, \xi_{p_m}\f$ are to be estimated. | |
49 | Instead of storing the whole sample cumulative distribution, the algorithm maintains only | |
50 | \f$m+2\f$ principal markers and \f$m+1\f$ middle markers, whose positions are updated | |
51 | with each sample and whose heights are adjusted (if necessary) using a piecewise-parablic | |
52 | formula. The heights of these central markers are the current estimates of the quantiles | |
53 | and returned as an iterator range. | |
54 | ||
55 | For further details, see | |
56 | ||
57 | K. E. E. Raatikainen, Simultaneous estimation of several quantiles, Simulation, Volume 49, | |
58 | Number 4 (October), 1986, p. 159-164. | |
59 | ||
60 | The extended \f$ P^2 \f$ algorithm generalizes the \f$ P^2 \f$ algorithm of | |
61 | ||
62 | R. Jain and I. Chlamtac, The P^2 algorithm for dynamic calculation of quantiles and | |
63 | histograms without storing observations, Communications of the ACM, | |
64 | Volume 28 (October), Number 10, 1985, p. 1076-1085. | |
65 | ||
66 | @param extended_p_square_probabilities A vector of quantile probabilities. | |
67 | */ | |
68 | template<typename Sample> | |
69 | struct extended_p_square_impl | |
70 | : accumulator_base | |
71 | { | |
72 | typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type; | |
73 | typedef std::vector<float_type> array_type; | |
74 | // for boost::result_of | |
75 | typedef iterator_range< | |
76 | detail::lvalue_index_iterator< | |
77 | permutation_iterator< | |
78 | typename array_type::const_iterator | |
79 | , detail::times2_iterator | |
80 | > | |
81 | > | |
82 | > result_type; | |
83 | ||
84 | template<typename Args> | |
85 | extended_p_square_impl(Args const &args) | |
86 | : probabilities( | |
87 | boost::begin(args[extended_p_square_probabilities]) | |
88 | , boost::end(args[extended_p_square_probabilities]) | |
89 | ) | |
90 | , heights(2 * probabilities.size() + 3) | |
91 | , actual_positions(heights.size()) | |
92 | , desired_positions(heights.size()) | |
93 | , positions_increments(heights.size()) | |
94 | { | |
95 | std::size_t num_quantiles = this->probabilities.size(); | |
96 | std::size_t num_markers = this->heights.size(); | |
97 | ||
98 | for(std::size_t i = 0; i < num_markers; ++i) | |
99 | { | |
100 | this->actual_positions[i] = i + 1; | |
101 | } | |
102 | ||
103 | this->positions_increments[0] = 0.; | |
104 | this->positions_increments[num_markers - 1] = 1.; | |
105 | ||
106 | for(std::size_t i = 0; i < num_quantiles; ++i) | |
107 | { | |
108 | this->positions_increments[2 * i + 2] = probabilities[i]; | |
109 | } | |
110 | ||
111 | for(std::size_t i = 0; i <= num_quantiles; ++i) | |
112 | { | |
113 | this->positions_increments[2 * i + 1] = | |
114 | 0.5 * (this->positions_increments[2 * i] + this->positions_increments[2 * i + 2]); | |
115 | } | |
116 | ||
117 | for(std::size_t i = 0; i < num_markers; ++i) | |
118 | { | |
119 | this->desired_positions[i] = 1. + 2. * (num_quantiles + 1.) * this->positions_increments[i]; | |
120 | } | |
121 | } | |
122 | ||
123 | template<typename Args> | |
124 | void operator ()(Args const &args) | |
125 | { | |
126 | std::size_t cnt = count(args); | |
127 | ||
128 | // m+2 principal markers and m+1 middle markers | |
129 | std::size_t num_markers = 2 * this->probabilities.size() + 3; | |
130 | ||
131 | // first accumulate num_markers samples | |
132 | if(cnt <= num_markers) | |
133 | { | |
134 | this->heights[cnt - 1] = args[sample]; | |
135 | ||
136 | // complete the initialization of heights by sorting | |
137 | if(cnt == num_markers) | |
138 | { | |
139 | std::sort(this->heights.begin(), this->heights.end()); | |
140 | } | |
141 | } | |
142 | else | |
143 | { | |
144 | std::size_t sample_cell = 1; | |
145 | ||
146 | // find cell k = sample_cell such that heights[k-1] <= sample < heights[k] | |
147 | if(args[sample] < this->heights[0]) | |
148 | { | |
149 | this->heights[0] = args[sample]; | |
150 | sample_cell = 1; | |
151 | } | |
152 | else if(args[sample] >= this->heights[num_markers - 1]) | |
153 | { | |
154 | this->heights[num_markers - 1] = args[sample]; | |
155 | sample_cell = num_markers - 1; | |
156 | } | |
157 | else | |
158 | { | |
159 | typedef typename array_type::iterator iterator; | |
160 | iterator it = std::upper_bound( | |
161 | this->heights.begin() | |
162 | , this->heights.end() | |
163 | , args[sample] | |
164 | ); | |
165 | ||
166 | sample_cell = std::distance(this->heights.begin(), it); | |
167 | } | |
168 | ||
169 | // update actual positions of all markers above sample_cell index | |
170 | for(std::size_t i = sample_cell; i < num_markers; ++i) | |
171 | { | |
172 | ++this->actual_positions[i]; | |
173 | } | |
174 | ||
175 | // update desired positions of all markers | |
176 | for(std::size_t i = 0; i < num_markers; ++i) | |
177 | { | |
178 | this->desired_positions[i] += this->positions_increments[i]; | |
179 | } | |
180 | ||
181 | // adjust heights and actual positions of markers 1 to num_markers-2 if necessary | |
182 | for(std::size_t i = 1; i <= num_markers - 2; ++i) | |
183 | { | |
184 | // offset to desired position | |
185 | float_type d = this->desired_positions[i] - this->actual_positions[i]; | |
186 | ||
187 | // offset to next position | |
188 | float_type dp = this->actual_positions[i+1] - this->actual_positions[i]; | |
189 | ||
190 | // offset to previous position | |
191 | float_type dm = this->actual_positions[i-1] - this->actual_positions[i]; | |
192 | ||
193 | // height ds | |
194 | float_type hp = (this->heights[i+1] - this->heights[i]) / dp; | |
195 | float_type hm = (this->heights[i-1] - this->heights[i]) / dm; | |
196 | ||
197 | if((d >= 1 && dp > 1) || (d <= -1 && dm < -1)) | |
198 | { | |
199 | short sign_d = static_cast<short>(d / std::abs(d)); | |
200 | ||
201 | float_type h = this->heights[i] + sign_d / (dp - dm) * ((sign_d - dm)*hp | |
202 | + (dp - sign_d) * hm); | |
203 | ||
204 | // try adjusting heights[i] using p-squared formula | |
205 | if(this->heights[i - 1] < h && h < this->heights[i + 1]) | |
206 | { | |
207 | this->heights[i] = h; | |
208 | } | |
209 | else | |
210 | { | |
211 | // use linear formula | |
212 | if(d > 0) | |
213 | { | |
214 | this->heights[i] += hp; | |
215 | } | |
216 | if(d < 0) | |
217 | { | |
218 | this->heights[i] -= hm; | |
219 | } | |
220 | } | |
221 | this->actual_positions[i] += sign_d; | |
222 | } | |
223 | } | |
224 | } | |
225 | } | |
226 | ||
227 | result_type result(dont_care) const | |
228 | { | |
229 | // for i in [1,probabilities.size()], return heights[i * 2] | |
230 | detail::times2_iterator idx_begin = detail::make_times2_iterator(1); | |
231 | detail::times2_iterator idx_end = detail::make_times2_iterator(this->probabilities.size() + 1); | |
232 | ||
233 | return result_type( | |
234 | make_permutation_iterator(this->heights.begin(), idx_begin) | |
235 | , make_permutation_iterator(this->heights.begin(), idx_end) | |
236 | ); | |
237 | } | |
238 | ||
239 | private: | |
240 | array_type probabilities; // the quantile probabilities | |
241 | array_type heights; // q_i | |
242 | array_type actual_positions; // n_i | |
243 | array_type desired_positions; // d_i | |
244 | array_type positions_increments; // f_i | |
245 | }; | |
246 | ||
247 | } // namespace impl | |
248 | ||
249 | /////////////////////////////////////////////////////////////////////////////// | |
250 | // tag::extended_p_square | |
251 | // | |
252 | namespace tag | |
253 | { | |
254 | struct extended_p_square | |
255 | : depends_on<count> | |
256 | , extended_p_square_probabilities | |
257 | { | |
258 | typedef accumulators::impl::extended_p_square_impl<mpl::_1> impl; | |
259 | ||
260 | #ifdef BOOST_ACCUMULATORS_DOXYGEN_INVOKED | |
261 | /// tag::extended_p_square::probabilities named parameter | |
262 | static boost::parameter::keyword<tag::probabilities> const probabilities; | |
263 | #endif | |
264 | }; | |
265 | } | |
266 | ||
267 | /////////////////////////////////////////////////////////////////////////////// | |
268 | // extract::extended_p_square | |
269 | // | |
270 | namespace extract | |
271 | { | |
272 | extractor<tag::extended_p_square> const extended_p_square = {}; | |
273 | ||
274 | BOOST_ACCUMULATORS_IGNORE_GLOBAL(extended_p_square) | |
275 | } | |
276 | ||
277 | using extract::extended_p_square; | |
278 | ||
279 | // So that extended_p_square can be automatically substituted with | |
280 | // weighted_extended_p_square when the weight parameter is non-void | |
281 | template<> | |
282 | struct as_weighted_feature<tag::extended_p_square> | |
283 | { | |
284 | typedef tag::weighted_extended_p_square type; | |
285 | }; | |
286 | ||
287 | template<> | |
288 | struct feature_of<tag::weighted_extended_p_square> | |
289 | : feature_of<tag::extended_p_square> | |
290 | { | |
291 | }; | |
292 | ||
293 | }} // namespace boost::accumulators | |
294 | ||
295 | #endif |