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/Src/Dependencies/Boost/boost/accumulators/statistics/weighted_tail_variate_means.hpp

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  1///////////////////////////////////////////////////////////////////////////////
  2// weighted_tail_variate_means.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_TAIL_VARIATE_MEANS_HPP_DE_01_01_2006
  9#define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_TAIL_VARIATE_MEANS_HPP_DE_01_01_2006
 10
 11#include <numeric>
 12#include <vector>
 13#include <limits>
 14#include <functional>
 15#include <sstream>
 16#include <stdexcept>
 17#include <boost/throw_exception.hpp>
 18#include <boost/parameter/keyword.hpp>
 19#include <boost/mpl/placeholders.hpp>
 20#include <boost/type_traits/is_same.hpp>
 21#include <boost/accumulators/numeric/functional.hpp>
 22#include <boost/accumulators/framework/accumulator_base.hpp>
 23#include <boost/accumulators/framework/extractor.hpp>
 24#include <boost/accumulators/framework/parameters/sample.hpp>
 25#include <boost/accumulators/statistics_fwd.hpp>
 26#include <boost/accumulators/statistics/tail.hpp>
 27#include <boost/accumulators/statistics/tail_variate.hpp>
 28#include <boost/accumulators/statistics/tail_variate_means.hpp>
 29#include <boost/accumulators/statistics/weighted_tail_mean.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
 37namespace boost
 38{
 39    // for _BinaryOperatrion2 in std::inner_product below
 40    // mutliplies two values and promotes the result to double
 41    namespace numeric { namespace functional
 42    {
 43        ///////////////////////////////////////////////////////////////////////////////
 44        // numeric::functional::multiply_and_promote_to_double
 45        template<typename T, typename U>
 46        struct multiply_and_promote_to_double
 47          : multiplies<T, double const>
 48        {
 49        };
 50    }}
 51}
 52
 53namespace boost { namespace accumulators
 54{
 55
 56namespace impl
 57{
 58    /**
 59        @brief Estimation of the absolute and relative weighted tail variate means (for both left and right tails)
 60
 61        For all \f$j\f$-th variates associated to the
 62
 63        \f[
 64            \lambda = \inf\left\{ l \left| \frac{1}{\bar{w}_n}\sum_{i=1}^{l} w_i \geq \alpha \right. \right\}
 65        \f]
 66
 67        smallest samples (left tail) or the weighted mean of the
 68
 69        \f[
 70            n + 1 - \rho = n + 1 - \sup\left\{ r \left| \frac{1}{\bar{w}_n}\sum_{i=r}^{n} w_i \geq (1 - \alpha) \right. \right\}
 71        \f]
 72
 73        largest samples (right tail), the absolute weighted tail means \f$\widehat{ATM}_{n,\alpha}(X, j)\f$
 74        are computed and returned as an iterator range. Alternatively, the relative weighted tail means
 75        \f$\widehat{RTM}_{n,\alpha}(X, j)\f$ are returned, which are the absolute weighted tail means
 76        normalized with the weighted (non-coherent) sample tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$.
 77
 78        \f[
 79            \widehat{ATM}_{n,\alpha}^{\mathrm{right}}(X, j) =
 80                \frac{1}{\sum_{i=\rho}^n w_i}
 81                \sum_{i=\rho}^n w_i \xi_{j,i}
 82        \f]
 83
 84        \f[
 85            \widehat{ATM}_{n,\alpha}^{\mathrm{left}}(X, j) =
 86                \frac{1}{\sum_{i=1}^{\lambda}}
 87                \sum_{i=1}^{\lambda} w_i \xi_{j,i}
 88        \f]
 89
 90        \f[
 91            \widehat{RTM}_{n,\alpha}^{\mathrm{right}}(X, j) =
 92                \frac{\sum_{i=\rho}^n w_i \xi_{j,i}}
 93            {\sum_{i=\rho}^n w_i \widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X)}
 94        \f]
 95
 96        \f[
 97            \widehat{RTM}_{n,\alpha}^{\mathrm{left}}(X, j) =
 98                \frac{\sum_{i=1}^{\lambda} w_i \xi_{j,i}}
 99            {\sum_{i=1}^{\lambda} w_i \widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X)}
100        \f]
101    */
102
103    ///////////////////////////////////////////////////////////////////////////////
104    // weighted_tail_variate_means_impl
105    //  by default: absolute weighted_tail_variate_means
106    template<typename Sample, typename Weight, typename Impl, typename LeftRight, typename VariateType>
107    struct weighted_tail_variate_means_impl
108      : accumulator_base
109    {
110        typedef typename numeric::functional::average<Weight, Weight>::result_type float_type;
111        typedef typename numeric::functional::average<typename numeric::functional::multiplies<VariateType, Weight>::result_type, Weight>::result_type array_type;
112        // for boost::result_of
113        typedef iterator_range<typename array_type::iterator> result_type;
114
115        weighted_tail_variate_means_impl(dont_care) {}
116
117        template<typename Args>
118        result_type result(Args const &args) const
119        {
120            float_type threshold = sum_of_weights(args)
121                             * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] );
122
123            std::size_t n = 0;
124            Weight sum = Weight(0);
125
126            while (sum < threshold)
127            {
128                if (n < static_cast<std::size_t>(tail_weights(args).size()))
129                {
130                    sum += *(tail_weights(args).begin() + n);
131                    n++;
132                }
133                else
134                {
135                    if (std::numeric_limits<float_type>::has_quiet_NaN)
136                    {
137                        std::fill(
138                            this->tail_means_.begin()
139                          , this->tail_means_.end()
140                          , std::numeric_limits<float_type>::quiet_NaN()
141                        );
142                    }
143                    else
144                    {
145                        std::ostringstream msg;
146                        msg << "index n = " << n << " is not in valid range [0, " << tail(args).size() << ")";
147                        boost::throw_exception(std::runtime_error(msg.str()));
148                    }
149                }
150            }
151
152            std::size_t num_variates = tail_variate(args).begin()->size();
153
154            this->tail_means_.clear();
155            this->tail_means_.resize(num_variates, Sample(0));
156
157            this->tail_means_ = std::inner_product(
158                tail_variate(args).begin()
159              , tail_variate(args).begin() + n
160              , tail_weights(args).begin()
161              , this->tail_means_
162              , numeric::functional::plus<array_type const, array_type const>()
163              , numeric::functional::multiply_and_promote_to_double<VariateType const, Weight const>()
164            );
165
166            float_type factor = sum * ( (is_same<Impl, relative>::value) ? non_coherent_weighted_tail_mean(args) : 1. );
167
168            std::transform(
169                this->tail_means_.begin()
170              , this->tail_means_.end()
171              , this->tail_means_.begin()
172              , std::bind2nd(numeric::functional::divides<typename array_type::value_type const, float_type const>(), factor)
173            );
174
175            return make_iterator_range(this->tail_means_);
176        }
177
178    private:
179
180        mutable array_type tail_means_;
181
182    };
183
184} // namespace impl
185
186///////////////////////////////////////////////////////////////////////////////
187// tag::absolute_weighted_tail_variate_means
188// tag::relative_weighted_tail_variate_means
189//
190namespace tag
191{
192    template<typename LeftRight, typename VariateType, typename VariateTag>
193    struct absolute_weighted_tail_variate_means
194      : depends_on<non_coherent_weighted_tail_mean<LeftRight>, tail_variate<VariateType, VariateTag, LeftRight>, tail_weights<LeftRight> >
195    {
196        typedef accumulators::impl::weighted_tail_variate_means_impl<mpl::_1, mpl::_2, absolute, LeftRight, VariateType> impl;
197    };
198    template<typename LeftRight, typename VariateType, typename VariateTag>
199    struct relative_weighted_tail_variate_means
200      : depends_on<non_coherent_weighted_tail_mean<LeftRight>, tail_variate<VariateType, VariateTag, LeftRight>, tail_weights<LeftRight> >
201    {
202        typedef accumulators::impl::weighted_tail_variate_means_impl<mpl::_1, mpl::_2, relative, LeftRight, VariateType> impl;
203    };
204}
205
206///////////////////////////////////////////////////////////////////////////////
207// extract::weighted_tail_variate_means
208// extract::relative_weighted_tail_variate_means
209//
210namespace extract
211{
212    extractor<tag::abstract_absolute_tail_variate_means> const weighted_tail_variate_means = {};
213    extractor<tag::abstract_relative_tail_variate_means> const relative_weighted_tail_variate_means = {};
214
215    BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_tail_variate_means)
216    BOOST_ACCUMULATORS_IGNORE_GLOBAL(relative_weighted_tail_variate_means)
217}
218
219using extract::weighted_tail_variate_means;
220using extract::relative_weighted_tail_variate_means;
221
222// weighted_tail_variate_means<LeftRight, VariateType, VariateTag>(absolute) -> absolute_weighted_tail_variate_means<LeftRight, VariateType, VariateTag>
223template<typename LeftRight, typename VariateType, typename VariateTag>
224struct as_feature<tag::weighted_tail_variate_means<LeftRight, VariateType, VariateTag>(absolute)>
225{
226    typedef tag::absolute_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> type;
227};
228
229// weighted_tail_variate_means<LeftRight, VariateType, VariateTag>(relative) -> relative_weighted_tail_variate_means<LeftRight, VariateType, VariateTag>
230template<typename LeftRight, typename VariateType, typename VariateTag>
231struct as_feature<tag::weighted_tail_variate_means<LeftRight, VariateType, VariateTag>(relative)>
232{
233    typedef tag::relative_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> type;
234};
235
236}} // namespace boost::accumulators
237
238#ifdef _MSC_VER
239# pragma warning(pop)
240#endif
241
242#endif