Added boost header

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

@@ -0,0 +1,293 @@
+///////////////////////////////////////////////////////////////////////////////
+// extended_p_square.hpp
+//
+//  Copyright 2005 Daniel Egloff. 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_EXTENDED_SINGLE_HPP_DE_01_01_2006
+#define BOOST_ACCUMULATORS_STATISTICS_EXTENDED_SINGLE_HPP_DE_01_01_2006
+
+#include <vector>
+#include <functional>
+#include <boost/range/begin.hpp>
+#include <boost/range/end.hpp>
+#include <boost/range/iterator_range.hpp>
+#include <boost/iterator/transform_iterator.hpp>
+#include <boost/iterator/counting_iterator.hpp>
+#include <boost/iterator/permutation_iterator.hpp>
+#include <boost/parameter/keyword.hpp>
+#include <boost/mpl/placeholders.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/framework/depends_on.hpp>
+#include <boost/accumulators/statistics_fwd.hpp>
+#include <boost/accumulators/statistics/count.hpp>
+#include <boost/accumulators/statistics/times2_iterator.hpp>
+
+namespace boost { namespace accumulators
+{
+///////////////////////////////////////////////////////////////////////////////
+// probabilities named parameter
+//
+BOOST_PARAMETER_NESTED_KEYWORD(tag, extended_p_square_probabilities, probabilities)
+
+namespace impl
+{
+    ///////////////////////////////////////////////////////////////////////////////
+    // extended_p_square_impl
+    //  multiple quantile estimation
+    /**
+        @brief Multiple quantile estimation with the extended \f$P^2\f$ algorithm
+
+        Extended \f$P^2\f$ algorithm for estimation of several quantiles without storing samples.
+        Assume that \f$m\f$ quantiles \f$\xi_{p_1}, \ldots, \xi_{p_m}\f$ are to be estimated.
+        Instead of storing the whole sample cumulative distribution, the algorithm maintains only
+        \f$m+2\f$ principal markers and \f$m+1\f$ middle markers, whose positions are updated
+        with each sample and whose heights are adjusted (if necessary) using a piecewise-parablic
+        formula. The heights of these central markers are the current estimates of the quantiles
+        and returned as an iterator range.
+
+        For further details, see
+
+        K. E. E. Raatikainen, Simultaneous estimation of several quantiles, Simulation, Volume 49,
+        Number 4 (October), 1986, p. 159-164.
+
+        The extended \f$ P^2 \f$ algorithm generalizess the \f$ P^2 \f$ algorithm of
+
+        R. Jain and I. Chlamtac, The P^2 algorithmus for dynamic calculation of quantiles and
+        histograms without storing observations, Communications of the ACM,
+        Volume 28 (October), Number 10, 1985, p. 1076-1085.
+
+        @param extended_p_square_probabilities A vector of quantile probabilities.
+    */
+    template<typename Sample>
+    struct extended_p_square_impl
+      : accumulator_base
+    {
+        typedef typename numeric::functional::average<Sample, std::size_t>::result_type float_type;
+        typedef std::vector<float_type> array_type;
+        // for boost::result_of
+        typedef iterator_range<
+            detail::lvalue_index_iterator<
+                permutation_iterator<
+                    typename array_type::const_iterator
+                  , detail::times2_iterator
+                >
+            >
+        > result_type;
+
+        template<typename Args>
+        extended_p_square_impl(Args const &args)
+          : probabilities(
+                boost::begin(args[extended_p_square_probabilities])
+              , boost::end(args[extended_p_square_probabilities])
+            )
+          , heights(2 * probabilities.size() + 3)
+          , actual_positions(heights.size())
+          , desired_positions(heights.size())
+          , positions_increments(heights.size())
+        {
+            std::size_t num_quantiles = this->probabilities.size();
+            std::size_t num_markers = this->heights.size();
+
+            for(std::size_t i = 0; i < num_markers; ++i)
+            {
+                this->actual_positions[i] = i + 1;
+            }
+
+            this->positions_increments[0] = 0.;
+            this->positions_increments[num_markers - 1] = 1.;
+
+            for(std::size_t i = 0; i < num_quantiles; ++i)
+            {
+                this->positions_increments[2 * i + 2] = probabilities[i];
+            }
+
+            for(std::size_t i = 0; i <= num_quantiles; ++i)
+            {
+                this->positions_increments[2 * i + 1] =
+                    0.5 * (this->positions_increments[2 * i] + this->positions_increments[2 * i + 2]);
+            }
+
+            for(std::size_t i = 0; i < num_markers; ++i)
+            {
+                this->desired_positions[i] = 1. + 2. * (num_quantiles + 1.) * this->positions_increments[i];
+            }
+        }
+
+        template<typename Args>
+        void operator ()(Args const &args)
+        {
+            std::size_t cnt = count(args);
+
+            // m+2 principal markers and m+1 middle markers
+            std::size_t num_markers = 2 * this->probabilities.size() + 3;
+
+            // first accumulate num_markers samples
+            if(cnt <= num_markers)
+            {
+                this->heights[cnt - 1] = args[sample];
+
+                // complete the initialization of heights by sorting
+                if(cnt == num_markers)
+                {
+                    std::sort(this->heights.begin(), this->heights.end());
+                }
+            }
+            else
+            {
+                std::size_t sample_cell = 1;
+
+                // find cell k = sample_cell such that heights[k-1] <= sample < heights[k]
+                if(args[sample] < this->heights[0])
+                {
+                    this->heights[0] = args[sample];
+                    sample_cell = 1;
+                }
+                else if(args[sample] >= this->heights[num_markers - 1])
+                {
+                    this->heights[num_markers - 1] = args[sample];
+                    sample_cell = num_markers - 1;
+                }
+                else
+                {
+                    typedef typename array_type::iterator iterator;
+                    iterator it = std::upper_bound(
+                        this->heights.begin()
+                      , this->heights.end()
+                      , args[sample]
+                    );
+
+                    sample_cell = std::distance(this->heights.begin(), it);
+                }
+
+                // update actual positions of all markers above sample_cell index
+                for(std::size_t i = sample_cell; i < num_markers; ++i)
+                {
+                    ++this->actual_positions[i];
+                }
+
+                // update desired positions of all markers
+                for(std::size_t i = 0; i < num_markers; ++i)
+                {
+                    this->desired_positions[i] += this->positions_increments[i];
+                }
+
+                // adjust heights and actual positions of markers 1 to num_markers-2 if necessary
+                for(std::size_t i = 1; i <= num_markers - 2; ++i)
+                {
+                    // offset to desired position
+                    float_type d = this->desired_positions[i] - this->actual_positions[i];
+
+                    // offset to next position
+                    float_type dp = this->actual_positions[i+1] - this->actual_positions[i];
+
+                    // offset to previous position
+                    float_type dm = this->actual_positions[i-1] - this->actual_positions[i];
+
+                    // height ds
+                    float_type hp = (this->heights[i+1] - this->heights[i]) / dp;
+                    float_type hm = (this->heights[i-1] - this->heights[i]) / dm;
+
+                    if((d >= 1 && dp > 1) || (d <= -1 && dm < -1))
+                    {
+                        short sign_d = static_cast<short>(d / std::abs(d));
+
+                        float_type h = this->heights[i] + sign_d / (dp - dm) * ((sign_d - dm)*hp
+                                     + (dp - sign_d) * hm);
+
+                        // try adjusting heights[i] using p-squared formula
+                        if(this->heights[i - 1] < h && h < this->heights[i + 1])
+                        {
+                            this->heights[i] = h;
+                        }
+                        else
+                        {
+                            // use linear formula
+                            if(d > 0)
+                            {
+                                this->heights[i] += hp;
+                            }
+                            if(d < 0)
+                            {
+                                this->heights[i] -= hm;
+                            }
+                        }
+                        this->actual_positions[i] += sign_d;
+                    }
+                }
+            }
+        }
+
+        result_type result(dont_care) const
+        {
+            // for i in [1,probabilities.size()], return heights[i * 2]
+            detail::times2_iterator idx_begin = detail::make_times2_iterator(1);
+            detail::times2_iterator idx_end = detail::make_times2_iterator(this->probabilities.size() + 1);
+
+            return result_type(
+                make_permutation_iterator(this->heights.begin(), idx_begin)
+              , make_permutation_iterator(this->heights.begin(), idx_end)
+            );
+        }
+
+    private:
+        array_type probabilities;         // the quantile probabilities
+        array_type heights;               // q_i
+        array_type actual_positions;      // n_i
+        array_type desired_positions;     // d_i
+        array_type positions_increments;  // f_i
+    };
+
+} // namespace impl
+
+///////////////////////////////////////////////////////////////////////////////
+// tag::extended_p_square
+//
+namespace tag
+{
+    struct extended_p_square
+      : depends_on<count>
+      , extended_p_square_probabilities
+    {
+        typedef accumulators::impl::extended_p_square_impl<mpl::_1> impl;
+
+        #ifdef BOOST_ACCUMULATORS_DOXYGEN_INVOKED
+        /// tag::extended_p_square::probabilities named paramter
+        static boost::parameter::keyword<tag::probabilities> const probabilities;
+        #endif
+    };
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// extract::extended_p_square
+//
+namespace extract
+{
+    extractor<tag::extended_p_square> const extended_p_square = {};
+
+    BOOST_ACCUMULATORS_IGNORE_GLOBAL(extended_p_square)
+}
+
+using extract::extended_p_square;
+
+// So that extended_p_square can be automatically substituted with
+// weighted_extended_p_square when the weight parameter is non-void
+template<>
+struct as_weighted_feature<tag::extended_p_square>
+{
+    typedef tag::weighted_extended_p_square type;
+};
+
+template<>
+struct feature_of<tag::weighted_extended_p_square>
+  : feature_of<tag::extended_p_square>
+{
+};
+
+}} // namespace boost::accumulators
+
+#endif