1 | /////////////////////////////////////////////////////////////////////////////// |
2 | // tail_quantile.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_TAIL_QUANTILE_HPP_DE_01_01_2006 |
9 | #define BOOST_ACCUMULATORS_STATISTICS_TAIL_QUANTILE_HPP_DE_01_01_2006 |
10 | |
11 | #include <vector> |
12 | #include <limits> |
13 | #include <functional> |
14 | #include <sstream> |
15 | #include <stdexcept> |
16 | #include <boost/config/no_tr1/cmath.hpp> // For ceil |
17 | #include <boost/throw_exception.hpp> |
18 | #include <boost/parameter/keyword.hpp> |
19 | #include <boost/mpl/placeholders.hpp> |
20 | #include <boost/mpl/if.hpp> |
21 | #include <boost/type_traits/is_same.hpp> |
22 | #include <boost/accumulators/framework/depends_on.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/statistics_fwd.hpp> |
28 | #include <boost/accumulators/statistics/tail.hpp> |
29 | #include <boost/accumulators/statistics/count.hpp> |
30 | #include <boost/accumulators/statistics/parameters/quantile_probability.hpp> |
31 | |
32 | #ifdef _MSC_VER |
33 | # pragma warning(push) |
34 | # pragma warning(disable: 4127) // conditional expression is constant |
35 | #endif |
36 | |
37 | namespace boost { namespace accumulators |
38 | { |
39 | |
40 | namespace impl |
41 | { |
42 | /////////////////////////////////////////////////////////////////////////////// |
43 | // tail_quantile_impl |
44 | // Tail quantile estimation based on order statistics |
45 | /** |
46 | @brief Tail quantile estimation based on order statistics (for both left and right tails) |
47 | |
48 | The estimation of a tail quantile \f$\hat{q}\f$ with level \f$\alpha\f$ based on order statistics requires the |
49 | caching of at least the \f$\lceil n\alpha\rceil\f$ smallest or the \f$\lceil n(1-\alpha)\rceil\f$ largest samples, |
50 | \f$n\f$ being the total number of samples. The largest of the \f$\lceil n\alpha\rceil\f$ smallest samples or the |
51 | smallest of the \f$\lceil n(1-\alpha)\rceil\f$ largest samples provides an estimate for the quantile: |
52 | |
53 | \f[ |
54 | \hat{q}_{n,\alpha} = X_{\lceil \alpha n \rceil:n} |
55 | \f] |
56 | |
57 | @param quantile_probability |
58 | */ |
59 | template<typename Sample, typename LeftRight> |
60 | struct tail_quantile_impl |
61 | : accumulator_base |
62 | { |
63 | // for boost::result_of |
64 | typedef Sample result_type; |
65 | |
66 | tail_quantile_impl(dont_care) {} |
67 | |
68 | template<typename Args> |
69 | result_type result(Args const &args) const |
70 | { |
71 | std::size_t cnt = count(args); |
72 | |
73 | std::size_t n = static_cast<std::size_t>( |
74 | std::ceil( |
75 | cnt * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] ) |
76 | ) |
77 | ); |
78 | |
79 | // If n is in a valid range, return result, otherwise return NaN or throw exception |
80 | if ( n < static_cast<std::size_t>(tail(args).size())) |
81 | { |
82 | // Note that the cached samples of the left are sorted in ascending order, |
83 | // whereas the samples of the right tail are sorted in descending order |
84 | return *(boost::begin(tail(args)) + n - 1); |
85 | } |
86 | else |
87 | { |
88 | if (std::numeric_limits<result_type>::has_quiet_NaN) |
89 | { |
90 | return std::numeric_limits<result_type>::quiet_NaN(); |
91 | } |
92 | else |
93 | { |
94 | std::ostringstream msg; |
95 | msg << "index n = " << n << " is not in valid range [0, " << tail(args).size() << ")" ; |
96 | boost::throw_exception(e: std::runtime_error(msg.str())); |
97 | return Sample(0); |
98 | } |
99 | } |
100 | } |
101 | |
102 | // serialization is done by accumulators it depends on |
103 | template<class Archive> |
104 | void serialize(Archive & ar, const unsigned int file_version) {} |
105 | }; |
106 | } // namespace impl |
107 | |
108 | /////////////////////////////////////////////////////////////////////////////// |
109 | // tag::tail_quantile<> |
110 | // |
111 | namespace tag |
112 | { |
113 | template<typename LeftRight> |
114 | struct tail_quantile |
115 | : depends_on<count, tail<LeftRight> > |
116 | { |
117 | /// INTERNAL ONLY |
118 | /// |
119 | typedef accumulators::impl::tail_quantile_impl<mpl::_1, LeftRight> impl; |
120 | }; |
121 | } |
122 | |
123 | /////////////////////////////////////////////////////////////////////////////// |
124 | // extract::tail_quantile |
125 | // |
126 | namespace extract |
127 | { |
128 | extractor<tag::quantile> const = {}; |
129 | |
130 | BOOST_ACCUMULATORS_IGNORE_GLOBAL(tail_quantile) |
131 | } |
132 | |
133 | using extract::tail_quantile; |
134 | |
135 | // for the purposes of feature-based dependency resolution, |
136 | // tail_quantile<LeftRight> provide the same feature as quantile |
137 | template<typename LeftRight> |
138 | struct feature_of<tag::tail_quantile<LeftRight> > |
139 | : feature_of<tag::quantile> |
140 | { |
141 | }; |
142 | |
143 | // So that tail_quantile can be automatically substituted with |
144 | // weighted_tail_quantile when the weight parameter is non-void. |
145 | template<typename LeftRight> |
146 | struct as_weighted_feature<tag::tail_quantile<LeftRight> > |
147 | { |
148 | typedef tag::weighted_tail_quantile<LeftRight> type; |
149 | }; |
150 | |
151 | template<typename LeftRight> |
152 | struct feature_of<tag::weighted_tail_quantile<LeftRight> > |
153 | : feature_of<tag::tail_quantile<LeftRight> > |
154 | {}; |
155 | |
156 | }} // namespace boost::accumulators |
157 | |
158 | #ifdef _MSC_VER |
159 | # pragma warning(pop) |
160 | #endif |
161 | |
162 | #endif |
163 | |