///////////////////////////////////////////////////////////////////////////////
// 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
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