text: ///////////////////////////////////////////////////////////////////////////////
  // 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 = {};
  
      BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_tail_variate_means)
      BOOST_ACCUMULATORS_IGNORE_GLOBAL(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
  