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1 | /////////////////////////////////////////////////////////////////////////////// |
2 | // extended_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_EXTENDED_SINGLE_QUANTILE_HPP_DE_01_01_2006 | |
9 | #define BOOST_ACCUMULATORS_STATISTICS_EXTENDED_SINGLE_QUANTILE_HPP_DE_01_01_2006 | |
10 | ||
11 | #include <vector> | |
12 | #include <functional> | |
13 | #include <boost/throw_exception.hpp> | |
14 | #include <boost/range/begin.hpp> | |
15 | #include <boost/range/end.hpp> | |
16 | #include <boost/range/iterator_range.hpp> | |
17 | #include <boost/iterator/transform_iterator.hpp> | |
18 | #include <boost/iterator/counting_iterator.hpp> | |
19 | #include <boost/iterator/permutation_iterator.hpp> | |
20 | #include <boost/parameter/keyword.hpp> | |
21 | #include <boost/mpl/placeholders.hpp> | |
22 | #include <boost/type_traits/is_same.hpp> | |
23 | #include <boost/accumulators/framework/accumulator_base.hpp> | |
24 | #include <boost/accumulators/framework/extractor.hpp> | |
25 | #include <boost/accumulators/numeric/functional.hpp> | |
26 | #include <boost/accumulators/framework/parameters/sample.hpp> | |
27 | #include <boost/accumulators/framework/depends_on.hpp> | |
28 | #include <boost/accumulators/statistics_fwd.hpp> | |
29 | #include <boost/accumulators/statistics/count.hpp> | |
30 | #include <boost/accumulators/statistics/parameters/quantile_probability.hpp> | |
31 | #include <boost/accumulators/statistics/extended_p_square.hpp> | |
32 | #include <boost/accumulators/statistics/weighted_extended_p_square.hpp> | |
33 | #include <boost/accumulators/statistics/times2_iterator.hpp> | |
34 | ||
35 | #ifdef _MSC_VER | |
36 | # pragma warning(push) | |
37 | # pragma warning(disable: 4127) // conditional expression is constant | |
38 | #endif | |
39 | ||
40 | namespace boost { namespace accumulators | |
41 | { | |
42 | ||
43 | namespace impl | |
44 | { | |
45 | /////////////////////////////////////////////////////////////////////////////// | |
46 | // extended_p_square_quantile_impl | |
47 | // single quantile estimation | |
48 | /** | |
49 | @brief Quantile estimation using the extended \f$P^2\f$ algorithm for weighted and unweighted samples | |
50 | ||
51 | Uses the quantile estimates calculated by the extended \f$P^2\f$ algorithm to compute | |
52 | intermediate quantile estimates by means of quadratic interpolation. | |
53 | ||
54 | @param quantile_probability The probability of the quantile to be estimated. | |
55 | */ | |
56 | template<typename Sample, typename Impl1, typename Impl2> // Impl1: weighted/unweighted // Impl2: linear/quadratic | |
57 | struct extended_p_square_quantile_impl | |
58 | : accumulator_base | |
59 | { | |
60 | typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type; | |
61 | typedef std::vector<float_type> array_type; | |
62 | typedef iterator_range< | |
63 | detail::lvalue_index_iterator< | |
64 | permutation_iterator< | |
65 | typename array_type::const_iterator | |
66 | , detail::times2_iterator | |
67 | > | |
68 | > | |
69 | > range_type; | |
70 | // for boost::result_of | |
71 | typedef float_type result_type; | |
72 | ||
73 | template<typename Args> | |
74 | extended_p_square_quantile_impl(Args const &args) | |
75 | : probabilities( | |
76 | boost::begin(args[extended_p_square_probabilities]) | |
77 | , boost::end(args[extended_p_square_probabilities]) | |
78 | ) | |
79 | { | |
80 | } | |
81 | ||
82 | template<typename Args> | |
83 | result_type result(Args const &args) const | |
84 | { | |
85 | typedef | |
86 | typename mpl::if_< | |
87 | is_same<Impl1, weighted> | |
88 | , tag::weighted_extended_p_square | |
89 | , tag::extended_p_square | |
90 | >::type | |
91 | extended_p_square_tag; | |
92 | ||
93 | extractor<extended_p_square_tag> const some_extended_p_square = {}; | |
94 | ||
95 | array_type heights(some_extended_p_square(args).size()); | |
96 | std::copy(some_extended_p_square(args).begin(), some_extended_p_square(args).end(), heights.begin()); | |
97 | ||
98 | this->probability = args[quantile_probability]; | |
99 | ||
100 | typename array_type::const_iterator iter_probs = std::lower_bound(this->probabilities.begin(), this->probabilities.end(), this->probability); | |
101 | std::size_t dist = std::distance(this->probabilities.begin(), iter_probs); | |
102 | typename array_type::const_iterator iter_heights = heights.begin() + dist; | |
103 | ||
104 | // If this->probability is not in a valid range return NaN or throw exception | |
105 | if (this->probability < *this->probabilities.begin() || this->probability > *(this->probabilities.end() - 1)) | |
106 | { | |
107 | if (std::numeric_limits<result_type>::has_quiet_NaN) | |
108 | { | |
109 | return std::numeric_limits<result_type>::quiet_NaN(); | |
110 | } | |
111 | else | |
112 | { | |
113 | std::ostringstream msg; | |
114 | msg << "probability = " << this->probability << " is not in valid range ("; | |
115 | msg << *this->probabilities.begin() << ", " << *(this->probabilities.end() - 1) << ")"; | |
116 | boost::throw_exception(std::runtime_error(msg.str())); | |
117 | return Sample(0); | |
118 | } | |
119 | ||
120 | } | |
121 | ||
122 | if (*iter_probs == this->probability) | |
123 | { | |
124 | return heights[dist]; | |
125 | } | |
126 | else | |
127 | { | |
128 | result_type res; | |
129 | ||
130 | if (is_same<Impl2, linear>::value) | |
131 | { | |
132 | ///////////////////////////////////////////////////////////////////////////////// | |
133 | // LINEAR INTERPOLATION | |
134 | // | |
135 | float_type p1 = *iter_probs; | |
136 | float_type p0 = *(iter_probs - 1); | |
137 | float_type h1 = *iter_heights; | |
138 | float_type h0 = *(iter_heights - 1); | |
139 | ||
140 | float_type a = numeric::fdiv(h1 - h0, p1 - p0); | |
141 | float_type b = h1 - p1 * a; | |
142 | ||
143 | res = a * this->probability + b; | |
144 | } | |
145 | else | |
146 | { | |
147 | ///////////////////////////////////////////////////////////////////////////////// | |
148 | // QUADRATIC INTERPOLATION | |
149 | // | |
150 | float_type p0, p1, p2; | |
151 | float_type h0, h1, h2; | |
152 | ||
153 | if ( (dist == 1 || *iter_probs - this->probability <= this->probability - *(iter_probs - 1) ) && dist != this->probabilities.size() - 1 ) | |
154 | { | |
155 | p0 = *(iter_probs - 1); | |
156 | p1 = *iter_probs; | |
157 | p2 = *(iter_probs + 1); | |
158 | h0 = *(iter_heights - 1); | |
159 | h1 = *iter_heights; | |
160 | h2 = *(iter_heights + 1); | |
161 | } | |
162 | else | |
163 | { | |
164 | p0 = *(iter_probs - 2); | |
165 | p1 = *(iter_probs - 1); | |
166 | p2 = *iter_probs; | |
167 | h0 = *(iter_heights - 2); | |
168 | h1 = *(iter_heights - 1); | |
169 | h2 = *iter_heights; | |
170 | } | |
171 | ||
172 | float_type hp21 = numeric::fdiv(h2 - h1, p2 - p1); | |
173 | float_type hp10 = numeric::fdiv(h1 - h0, p1 - p0); | |
174 | float_type p21 = numeric::fdiv(p2 * p2 - p1 * p1, p2 - p1); | |
175 | float_type p10 = numeric::fdiv(p1 * p1 - p0 * p0, p1 - p0); | |
176 | ||
177 | float_type a = numeric::fdiv(hp21 - hp10, p21 - p10); | |
178 | float_type b = hp21 - a * p21; | |
179 | float_type c = h2 - a * p2 * p2 - b * p2; | |
180 | ||
181 | res = a * this->probability * this-> probability + b * this->probability + c; | |
182 | } | |
183 | ||
184 | return res; | |
185 | } | |
186 | ||
187 | } | |
188 | private: | |
189 | ||
190 | array_type probabilities; | |
191 | mutable float_type probability; | |
192 | ||
193 | }; | |
194 | ||
195 | } // namespace impl | |
196 | ||
197 | /////////////////////////////////////////////////////////////////////////////// | |
198 | // tag::extended_p_square_quantile | |
199 | // | |
200 | namespace tag | |
201 | { | |
202 | struct extended_p_square_quantile | |
203 | : depends_on<extended_p_square> | |
204 | { | |
205 | typedef accumulators::impl::extended_p_square_quantile_impl<mpl::_1, unweighted, linear> impl; | |
206 | }; | |
207 | struct extended_p_square_quantile_quadratic | |
208 | : depends_on<extended_p_square> | |
209 | { | |
210 | typedef accumulators::impl::extended_p_square_quantile_impl<mpl::_1, unweighted, quadratic> impl; | |
211 | }; | |
212 | struct weighted_extended_p_square_quantile | |
213 | : depends_on<weighted_extended_p_square> | |
214 | { | |
215 | typedef accumulators::impl::extended_p_square_quantile_impl<mpl::_1, weighted, linear> impl; | |
216 | }; | |
217 | struct weighted_extended_p_square_quantile_quadratic | |
218 | : depends_on<weighted_extended_p_square> | |
219 | { | |
220 | typedef accumulators::impl::extended_p_square_quantile_impl<mpl::_1, weighted, quadratic> impl; | |
221 | }; | |
222 | } | |
223 | ||
224 | /////////////////////////////////////////////////////////////////////////////// | |
225 | // extract::extended_p_square_quantile | |
226 | // extract::weighted_extended_p_square_quantile | |
227 | // | |
228 | namespace extract | |
229 | { | |
230 | extractor<tag::extended_p_square_quantile> const extended_p_square_quantile = {}; | |
231 | extractor<tag::extended_p_square_quantile_quadratic> const extended_p_square_quantile_quadratic = {}; | |
232 | extractor<tag::weighted_extended_p_square_quantile> const weighted_extended_p_square_quantile = {}; | |
233 | extractor<tag::weighted_extended_p_square_quantile_quadratic> const weighted_extended_p_square_quantile_quadratic = {}; | |
234 | ||
235 | BOOST_ACCUMULATORS_IGNORE_GLOBAL(extended_p_square_quantile) | |
236 | BOOST_ACCUMULATORS_IGNORE_GLOBAL(extended_p_square_quantile_quadratic) | |
237 | BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_extended_p_square_quantile) | |
238 | BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_extended_p_square_quantile_quadratic) | |
239 | } | |
240 | ||
241 | using extract::extended_p_square_quantile; | |
242 | using extract::extended_p_square_quantile_quadratic; | |
243 | using extract::weighted_extended_p_square_quantile; | |
244 | using extract::weighted_extended_p_square_quantile_quadratic; | |
245 | ||
246 | // extended_p_square_quantile(linear) -> extended_p_square_quantile | |
247 | template<> | |
248 | struct as_feature<tag::extended_p_square_quantile(linear)> | |
249 | { | |
250 | typedef tag::extended_p_square_quantile type; | |
251 | }; | |
252 | ||
253 | // extended_p_square_quantile(quadratic) -> extended_p_square_quantile_quadratic | |
254 | template<> | |
255 | struct as_feature<tag::extended_p_square_quantile(quadratic)> | |
256 | { | |
257 | typedef tag::extended_p_square_quantile_quadratic type; | |
258 | }; | |
259 | ||
260 | // weighted_extended_p_square_quantile(linear) -> weighted_extended_p_square_quantile | |
261 | template<> | |
262 | struct as_feature<tag::weighted_extended_p_square_quantile(linear)> | |
263 | { | |
264 | typedef tag::weighted_extended_p_square_quantile type; | |
265 | }; | |
266 | ||
267 | // weighted_extended_p_square_quantile(quadratic) -> weighted_extended_p_square_quantile_quadratic | |
268 | template<> | |
269 | struct as_feature<tag::weighted_extended_p_square_quantile(quadratic)> | |
270 | { | |
271 | typedef tag::weighted_extended_p_square_quantile_quadratic type; | |
272 | }; | |
273 | ||
274 | // for the purposes of feature-based dependency resolution, | |
275 | // extended_p_square_quantile and weighted_extended_p_square_quantile | |
276 | // provide the same feature as quantile | |
277 | template<> | |
278 | struct feature_of<tag::extended_p_square_quantile> | |
279 | : feature_of<tag::quantile> | |
280 | { | |
281 | }; | |
282 | template<> | |
283 | struct feature_of<tag::extended_p_square_quantile_quadratic> | |
284 | : feature_of<tag::quantile> | |
285 | { | |
286 | }; | |
287 | // So that extended_p_square_quantile can be automatically substituted with | |
288 | // weighted_extended_p_square_quantile when the weight parameter is non-void | |
289 | template<> | |
290 | struct as_weighted_feature<tag::extended_p_square_quantile> | |
291 | { | |
292 | typedef tag::weighted_extended_p_square_quantile type; | |
293 | }; | |
294 | ||
295 | template<> | |
296 | struct feature_of<tag::weighted_extended_p_square_quantile> | |
297 | : feature_of<tag::extended_p_square_quantile> | |
298 | { | |
299 | }; | |
300 | ||
301 | // So that extended_p_square_quantile_quadratic can be automatically substituted with | |
302 | // weighted_extended_p_square_quantile_quadratic when the weight parameter is non-void | |
303 | template<> | |
304 | struct as_weighted_feature<tag::extended_p_square_quantile_quadratic> | |
305 | { | |
306 | typedef tag::weighted_extended_p_square_quantile_quadratic type; | |
307 | }; | |
308 | template<> | |
309 | struct feature_of<tag::weighted_extended_p_square_quantile_quadratic> | |
310 | : feature_of<tag::extended_p_square_quantile_quadratic> | |
311 | { | |
312 | }; | |
313 | ||
314 | }} // namespace boost::accumulators | |
315 | ||
316 | #ifdef _MSC_VER | |
317 | # pragma warning(pop) | |
318 | #endif | |
319 | ||
320 | #endif |