/////////////////////////////////////////////////////////////////////////////// | |
// 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 |