weighted_tail_variate_means.hpp

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///////////////////////////////////////////////////////////////////////////////
// weighted_tail_variate_means.hpp
//
//  Copyright 2006 Daniel Egloff, Olivier Gygi. Distributed under the Boost
//  Software License, Version 1.0. (See accompanying file
//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

#ifndef BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_TAIL_VARIATE_MEANS_HPP_DE_01_01_2006
#define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_TAIL_VARIATE_MEANS_HPP_DE_01_01_2006

#include <numeric>
#include <vector>
#include <limits>
#include <functional>
#include <sstream>
#include <stdexcept>
#include <boost/throw_exception.hpp>
#include <boost/parameter/keyword.hpp>
#include <boost/mpl/placeholders.hpp>
#include <boost/type_traits/is_same.hpp>
#include <boost/accumulators/numeric/functional.hpp>
#include <boost/accumulators/framework/accumulator_base.hpp>
#include <boost/accumulators/framework/extractor.hpp>
#include <boost/accumulators/framework/parameters/sample.hpp>
#include <boost/accumulators/statistics_fwd.hpp>
#include <boost/accumulators/statistics/tail.hpp>
#include <boost/accumulators/statistics/tail_variate.hpp>
#include <boost/accumulators/statistics/tail_variate_means.hpp>
#include <boost/accumulators/statistics/weighted_tail_mean.hpp>
#include <boost/accumulators/statistics/parameters/quantile_probability.hpp>

#ifdef _MSC_VER
# pragma warning(push)
# pragma warning(disable: 4127) // conditional expression is constant
#endif

namespace boost
{
    // for _BinaryOperatrion2 in std::inner_product below
    // mutliplies two values and promotes the result to double
    namespace numeric { namespace functional
    {
        ///////////////////////////////////////////////////////////////////////////////
        // numeric::functional::multiply_and_promote_to_double
        template<typename T, typename U>
        struct multiply_and_promote_to_double
          : multiplies<T, double const>
        {
        };
    }}
}

namespace boost { namespace accumulators
{

namespace impl
{
    /**
        @brief Estimation of the absolute and relative weighted tail variate means (for both left and right tails)

        For all \f$j\f$-th variates associated to the

        \f[
            \lambda = \inf\left\{ l \left| \frac{1}{\bar{w}_n}\sum_{i=1}^{l} w_i \geq \alpha \right. \right\}
        \f]

        smallest samples (left tail) or the weighted mean of the

        \f[
            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\}
        \f]

        largest samples (right tail), the absolute weighted tail means \f$\widehat{ATM}_{n,\alpha}(X, j)\f$
        are computed and returned as an iterator range. Alternatively, the relative weighted tail means
        \f$\widehat{RTM}_{n,\alpha}(X, j)\f$ are returned, which are the absolute weighted tail means
        normalized with the weighted (non-coherent) sample tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$.

        \f[
            \widehat{ATM}_{n,\alpha}^{\mathrm{right}}(X, j) =
                \frac{1}{\sum_{i=\rho}^n w_i}
                \sum_{i=\rho}^n w_i \xi_{j,i}
        \f]

        \f[
            \widehat{ATM}_{n,\alpha}^{\mathrm{left}}(X, j) =
                \frac{1}{\sum_{i=1}^{\lambda}}
                \sum_{i=1}^{\lambda} w_i \xi_{j,i}
        \f]

        \f[
            \widehat{RTM}_{n,\alpha}^{\mathrm{right}}(X, j) =
                \frac{\sum_{i=\rho}^n w_i \xi_{j,i}}
            {\sum_{i=\rho}^n w_i \widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X)}
        \f]

        \f[
            \widehat{RTM}_{n,\alpha}^{\mathrm{left}}(X, j) =
                \frac{\sum_{i=1}^{\lambda} w_i \xi_{j,i}}
            {\sum_{i=1}^{\lambda} w_i \widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X)}
        \f]
    */

    ///////////////////////////////////////////////////////////////////////////////
    // weighted_tail_variate_means_impl
    //  by default: absolute weighted_tail_variate_means
    template<typename Sample, typename Weight, typename Impl, typename LeftRight, typename VariateType>
    struct weighted_tail_variate_means_impl
      : accumulator_base
    {
        typedef typename numeric::functional::average<Weight, Weight>::result_type float_type;
        typedef typename numeric::functional::average<typename numeric::functional::multiplies<VariateType, Weight>::result_type, Weight>::result_type array_type;
        // for boost::result_of
        typedef iterator_range<typename array_type::iterator> result_type;

        weighted_tail_variate_means_impl(dont_care) {}

        template<typename Args>
        result_type result(Args const &args) const
        {
            float_type threshold = sum_of_weights(args)
                             * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] );

            std::size_t n = 0;
            Weight sum = Weight(0);

            while (sum < threshold)
            {
                if (n < static_cast<std::size_t>(tail_weights(args).size()))
                {
                    sum += *(tail_weights(args).begin() + n);
                    n++;
                }
                else
                {
                    if (std::numeric_limits<float_type>::has_quiet_NaN)
                    {
                        std::fill(
                            this->tail_means_.begin()
                          , this->tail_means_.end()
                          , std::numeric_limits<float_type>::quiet_NaN()
                        );
                    }
                    else
                    {
                        std::ostringstream msg;
                        msg << "index n = " << n << " is not in valid range [0, " << tail(args).size() << ")";
                        boost::throw_exception(std::runtime_error(msg.str()));
                    }
                }
            }

            std::size_t num_variates = tail_variate(args).begin()->size();

            this->tail_means_.clear();
            this->tail_means_.resize(num_variates, Sample(0));

            this->tail_means_ = std::inner_product(
                tail_variate(args).begin()
              , tail_variate(args).begin() + n
              , tail_weights(args).begin()
              , this->tail_means_
              , numeric::functional::plus<array_type const, array_type const>()
              , numeric::functional::multiply_and_promote_to_double<VariateType const, Weight const>()
            );

            float_type factor = sum * ( (is_same<Impl, relative>::value) ? non_coherent_weighted_tail_mean(args) : 1. );

            std::transform(
                this->tail_means_.begin()
              , this->tail_means_.end()
              , this->tail_means_.begin()
              , std::bind2nd(numeric::functional::divides<typename array_type::value_type const, float_type const>(), factor)
            );

            return make_iterator_range(this->tail_means_);
        }

    private:

        mutable array_type tail_means_;

    };

} // namespace impl

///////////////////////////////////////////////////////////////////////////////
// tag::absolute_weighted_tail_variate_means
// tag::relative_weighted_tail_variate_means
//
namespace tag
{
    template<typename LeftRight, typename VariateType, typename VariateTag>
    struct absolute_weighted_tail_variate_means
      : depends_on<non_coherent_weighted_tail_mean<LeftRight>, tail_variate<VariateType, VariateTag, LeftRight>, tail_weights<LeftRight> >
    {
        typedef accumulators::impl::weighted_tail_variate_means_impl<mpl::_1, mpl::_2, absolute, LeftRight, VariateType> impl;
    };
    template<typename LeftRight, typename VariateType, typename VariateTag>
    struct relative_weighted_tail_variate_means
      : depends_on<non_coherent_weighted_tail_mean<LeftRight>, tail_variate<VariateType, VariateTag, LeftRight>, tail_weights<LeftRight> >
    {
        typedef accumulators::impl::weighted_tail_variate_means_impl<mpl::_1, mpl::_2, relative, LeftRight, VariateType> impl;
    };
}

///////////////////////////////////////////////////////////////////////////////
// extract::weighted_tail_variate_means
// extract::relative_weighted_tail_variate_means
//
namespace extract
{
    extractor<tag::abstract_absolute_tail_variate_means> const weighted_tail_variate_means = {};
    extractor<tag::abstract_relative_tail_variate_means> const relative_weighted_tail_variate_means = {};
}

using extract::weighted_tail_variate_means;
using extract::relative_weighted_tail_variate_means;

// weighted_tail_variate_means<LeftRight, VariateType, VariateTag>(absolute) -> absolute_weighted_tail_variate_means<LeftRight, VariateType, VariateTag>
template<typename LeftRight, typename VariateType, typename VariateTag>
struct as_feature<tag::weighted_tail_variate_means<LeftRight, VariateType, VariateTag>(absolute)>
{
    typedef tag::absolute_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> type;
};

// weighted_tail_variate_means<LeftRight, VariateType, VariateTag>(relative) -> relative_weighted_tail_variate_means<LeftRight, VariateType, VariateTag>
template<typename LeftRight, typename VariateType, typename VariateTag>
struct as_feature<tag::weighted_tail_variate_means<LeftRight, VariateType, VariateTag>(relative)>
{
    typedef tag::relative_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> type;
};

}} // namespace boost::accumulators

#ifdef _MSC_VER
# pragma warning(pop)
#endif

#endif