Added boost header

test/external/boost/accumulators/statistics/tail_mean.hpp

@@ -0,0 +1,246 @@
+///////////////////////////////////////////////////////////////////////////////
+// tail_mean.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_TAIL_MEAN_HPP_DE_01_01_2006
+#define BOOST_ACCUMULATORS_STATISTICS_TAIL_MEAN_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/framework/accumulator_base.hpp>
+#include <boost/accumulators/framework/extractor.hpp>
+#include <boost/accumulators/numeric/functional.hpp>
+#include <boost/accumulators/framework/parameters/sample.hpp>
+#include <boost/accumulators/statistics_fwd.hpp>
+#include <boost/accumulators/statistics/count.hpp>
+#include <boost/accumulators/statistics/tail.hpp>
+#include <boost/accumulators/statistics/tail_quantile.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 { namespace accumulators
+{
+
+namespace impl
+{
+
+    ///////////////////////////////////////////////////////////////////////////////
+    // coherent_tail_mean_impl
+    //
+    /**
+        @brief Estimation of the coherent tail mean based on order statistics (for both left and right tails)
+
+        The coherent tail mean \f$\widehat{CTM}_{n,\alpha}(X)\f$ is equal to the non-coherent tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$
+        plus a correction term that ensures coherence in case of non-continuous distributions.
+
+        \f[
+            \widehat{CTM}_{n,\alpha}^{\mathrm{right}}(X) = \widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X) +
+            \frac{1}{\lceil n(1-\alpha)\rceil}\hat{q}_{n,\alpha}(X)\left(1 - \alpha - \frac{1}{n}\lceil n(1-\alpha)\rceil \right)
+        \f]
+
+        \f[
+            \widehat{CTM}_{n,\alpha}^{\mathrm{left}}(X) = \widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X) +
+            \frac{1}{\lceil n\alpha\rceil}\hat{q}_{n,\alpha}(X)\left(\alpha - \frac{1}{n}\lceil n\alpha\rceil \right)
+        \f]
+    */
+    template<typename Sample, typename LeftRight>
+    struct coherent_tail_mean_impl
+      : accumulator_base
+    {
+        typedef typename numeric::functional::average<Sample, std::size_t>::result_type float_type;
+        // for boost::result_of
+        typedef float_type result_type;
+
+        coherent_tail_mean_impl(dont_care) {}
+
+        template<typename Args>
+        result_type result(Args const &args) const
+        {
+            std::size_t cnt = count(args);
+
+            std::size_t n = static_cast<std::size_t>(
+                std::ceil(
+                    cnt * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] )
+                )
+            );
+
+            extractor<tag::non_coherent_tail_mean<LeftRight> > const some_non_coherent_tail_mean = {};
+
+            return some_non_coherent_tail_mean(args)
+                 + numeric::average(quantile(args), n)
+                 * (
+                     ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability]
+                     - numeric::average(n, count(args))
+                   );
+        }
+    };
+
+    ///////////////////////////////////////////////////////////////////////////////
+    // non_coherent_tail_mean_impl
+    //
+    /**
+        @brief Estimation of the (non-coherent) tail mean based on order statistics (for both left and right tails)
+
+        An estimation of the non-coherent tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$ is given by the mean of the
+        \f$\lceil n\alpha\rceil\f$ smallest samples (left tail) or the mean of the  \f$\lceil n(1-\alpha)\rceil\f$
+        largest samples (right tail), \f$n\f$ being the total number of samples and \f$\alpha\f$ the quantile level:
+
+        \f[
+            \widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X) = \frac{1}{\lceil n(1-\alpha)\rceil} \sum_{i=\lceil \alpha n \rceil}^n X_{i:n}
+        \f]
+
+        \f[
+            \widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X) = \frac{1}{\lceil n\alpha\rceil} \sum_{i=1}^{\lceil \alpha n \rceil} X_{i:n}
+        \f]
+
+        It thus requires the caching of at least the \f$\lceil n\alpha\rceil\f$ smallest or the \f$\lceil n(1-\alpha)\rceil\f$
+        largest samples.
+
+        @param quantile_probability
+    */
+    template<typename Sample, typename LeftRight>
+    struct non_coherent_tail_mean_impl
+      : accumulator_base
+    {
+        typedef typename numeric::functional::average<Sample, std::size_t>::result_type float_type;
+        // for boost::result_of
+        typedef float_type result_type;
+
+        non_coherent_tail_mean_impl(dont_care) {}
+
+        template<typename Args>
+        result_type result(Args const &args) const
+        {
+            std::size_t cnt = count(args);
+
+            std::size_t n = static_cast<std::size_t>(
+                std::ceil(
+                    cnt * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] )
+                )
+            );
+
+            // If n is in a valid range, return result, otherwise return NaN or throw exception
+            if (n <= static_cast<std::size_t>(tail(args).size()))
+                return numeric::average(
+                    std::accumulate(
+                        tail(args).begin()
+                      , tail(args).begin() + n
+                      , Sample(0)
+                    )
+                  , n
+                );
+            else
+            {
+                if (std::numeric_limits<result_type>::has_quiet_NaN)
+                {
+                    return std::numeric_limits<result_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()));
+                    return Sample(0);
+                }
+            }
+        }
+    };
+
+} // namespace impl
+
+
+///////////////////////////////////////////////////////////////////////////////
+// tag::coherent_tail_mean<>
+// tag::non_coherent_tail_mean<>
+//
+namespace tag
+{
+    template<typename LeftRight>
+    struct coherent_tail_mean
+      : depends_on<count, quantile, non_coherent_tail_mean<LeftRight> >
+    {
+        typedef accumulators::impl::coherent_tail_mean_impl<mpl::_1, LeftRight> impl;
+    };
+
+    template<typename LeftRight>
+    struct non_coherent_tail_mean
+      : depends_on<count, tail<LeftRight> >
+    {
+        typedef accumulators::impl::non_coherent_tail_mean_impl<mpl::_1, LeftRight> impl;
+    };
+
+    struct abstract_non_coherent_tail_mean
+      : depends_on<>
+    {
+    };
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// extract::non_coherent_tail_mean;
+// extract::coherent_tail_mean;
+//
+namespace extract
+{
+    extractor<tag::abstract_non_coherent_tail_mean> const non_coherent_tail_mean = {};
+    extractor<tag::tail_mean> const coherent_tail_mean = {};
+
+    BOOST_ACCUMULATORS_IGNORE_GLOBAL(non_coherent_tail_mean)
+    BOOST_ACCUMULATORS_IGNORE_GLOBAL(coherent_tail_mean)
+}
+
+using extract::non_coherent_tail_mean;
+using extract::coherent_tail_mean;
+
+// for the purposes of feature-based dependency resolution,
+// coherent_tail_mean<LeftRight> provides the same feature as tail_mean
+template<typename LeftRight>
+struct feature_of<tag::coherent_tail_mean<LeftRight> >
+  : feature_of<tag::tail_mean>
+{
+};
+
+template<typename LeftRight>
+struct feature_of<tag::non_coherent_tail_mean<LeftRight> >
+  : feature_of<tag::abstract_non_coherent_tail_mean>
+{
+};
+
+// So that non_coherent_tail_mean can be automatically substituted
+// with weighted_non_coherent_tail_mean when the weight parameter is non-void.
+template<typename LeftRight>
+struct as_weighted_feature<tag::non_coherent_tail_mean<LeftRight> >
+{
+    typedef tag::non_coherent_weighted_tail_mean<LeftRight> type;
+};
+
+template<typename LeftRight>
+struct feature_of<tag::non_coherent_weighted_tail_mean<LeftRight> >
+  : feature_of<tag::non_coherent_tail_mean<LeftRight> >
+{};
+
+// NOTE that non_coherent_tail_mean cannot be feature-grouped with tail_mean,
+// which is the base feature for coherent tail means, since (at least for
+// non-continuous distributions) non_coherent_tail_mean is a different measure!
+
+}} // namespace boost::accumulators
+
+#ifdef _MSC_VER
+# pragma warning(pop)
+#endif
+
+#endif