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 
tail_quantile_implboost::accumulators::impl::tail_quantile_impl66         tail_quantile_impl(dont_care) {}
67 
68         template<typename Args>
resultboost::accumulators::impl::tail_quantile_impl69         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(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>
serializeboost::accumulators::impl::tail_quantile_impl104         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 tail_quantile = {};
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