272 lines
9.8 KiB
C++
272 lines
9.8 KiB
C++
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///////////////////////////////////////////////////////////////////////////////
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// p_square_quantile.hpp
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//
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// Copyright 2005 Daniel Egloff. Distributed under the Boost
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// Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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#ifndef BOOST_ACCUMULATORS_STATISTICS_P_SQUARE_QUANTILE_HPP_DE_01_01_2006
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#define BOOST_ACCUMULATORS_STATISTICS_P_SQUARE_QUANTILE_HPP_DE_01_01_2006
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#include <cmath>
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#include <functional>
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#include <boost/array.hpp>
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#include <boost/mpl/placeholders.hpp>
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#include <boost/type_traits/is_same.hpp>
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#include <boost/parameter/keyword.hpp>
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#include <boost/accumulators/framework/accumulator_base.hpp>
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#include <boost/accumulators/framework/extractor.hpp>
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#include <boost/accumulators/numeric/functional.hpp>
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#include <boost/accumulators/framework/parameters/sample.hpp>
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#include <boost/accumulators/framework/depends_on.hpp>
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#include <boost/accumulators/statistics_fwd.hpp>
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#include <boost/accumulators/statistics/count.hpp>
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#include <boost/accumulators/statistics/parameters/quantile_probability.hpp>
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#include <boost/serialization/boost_array.hpp>
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namespace boost { namespace accumulators
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{
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namespace impl
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{
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///////////////////////////////////////////////////////////////////////////////
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// p_square_quantile_impl
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// single quantile estimation
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/**
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@brief Single quantile estimation with the \f$P^2\f$ algorithm
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The \f$P^2\f$ algorithm estimates a quantile dynamically without storing samples. Instead of
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storing the whole sample cumulative distribution, only five points (markers) are stored. The heights
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of these markers are the minimum and the maximum of the samples and the current estimates of the
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\f$(p/2)\f$-, \f$p\f$- and \f$(1+p)/2\f$-quantiles. Their positions are equal to the number
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of samples that are smaller or equal to the markers. Each time a new samples is recorded, the
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positions of the markers are updated and if necessary their heights are adjusted using a piecewise-
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parabolic formula.
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For further details, see
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R. Jain and I. Chlamtac, The P^2 algorithm for dynamic calculation of quantiles and
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histograms without storing observations, Communications of the ACM,
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Volume 28 (October), Number 10, 1985, p. 1076-1085.
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@param quantile_probability
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*/
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template<typename Sample, typename Impl>
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struct p_square_quantile_impl
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: accumulator_base
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{
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typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type;
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typedef array<float_type, 5> array_type;
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// for boost::result_of
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typedef float_type result_type;
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template<typename Args>
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p_square_quantile_impl(Args const &args)
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: p(is_same<Impl, for_median>::value ? float_type(0.5) : args[quantile_probability | float_type(0.5)])
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, heights()
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, actual_positions()
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, desired_positions()
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, positions_increments()
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{
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for(std::size_t i = 0; i < 5; ++i)
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{
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this->actual_positions[i] = i + float_type(1.);
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}
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this->desired_positions[0] = float_type(1.);
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this->desired_positions[1] = float_type(1.) + float_type(2.) * this->p;
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this->desired_positions[2] = float_type(1.) + float_type(4.) * this->p;
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this->desired_positions[3] = float_type(3.) + float_type(2.) * this->p;
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this->desired_positions[4] = float_type(5.);
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this->positions_increments[0] = float_type(0.);
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this->positions_increments[1] = this->p / float_type(2.);
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this->positions_increments[2] = this->p;
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this->positions_increments[3] = (float_type(1.) + this->p) / float_type(2.);
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this->positions_increments[4] = float_type(1.);
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}
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template<typename Args>
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void operator ()(Args const &args)
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{
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std::size_t cnt = count(args);
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// accumulate 5 first samples
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if(cnt <= 5)
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{
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this->heights[cnt - 1] = args[sample];
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// complete the initialization of heights by sorting
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if(cnt == 5)
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{
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std::sort(this->heights.begin(), this->heights.end());
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}
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}
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else
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{
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std::size_t sample_cell = 1; // k
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// find cell k such that heights[k-1] <= args[sample] < heights[k] and adjust extreme values
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if (args[sample] < this->heights[0])
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{
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this->heights[0] = args[sample];
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sample_cell = 1;
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}
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else if (this->heights[4] <= args[sample])
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{
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this->heights[4] = args[sample];
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sample_cell = 4;
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}
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else
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{
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typedef typename array_type::iterator iterator;
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iterator it = std::upper_bound(
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this->heights.begin()
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, this->heights.end()
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, args[sample]
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);
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sample_cell = std::distance(this->heights.begin(), it);
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}
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// update positions of markers above sample_cell
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for(std::size_t i = sample_cell; i < 5; ++i)
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{
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++this->actual_positions[i];
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}
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// update desired positions of all markers
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for(std::size_t i = 0; i < 5; ++i)
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{
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this->desired_positions[i] += this->positions_increments[i];
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}
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// adjust heights and actual positions of markers 1 to 3 if necessary
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for(std::size_t i = 1; i <= 3; ++i)
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{
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// offset to desired positions
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float_type d = this->desired_positions[i] - this->actual_positions[i];
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// offset to next position
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float_type dp = this->actual_positions[i + 1] - this->actual_positions[i];
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// offset to previous position
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float_type dm = this->actual_positions[i - 1] - this->actual_positions[i];
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// height ds
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float_type hp = (this->heights[i + 1] - this->heights[i]) / dp;
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float_type hm = (this->heights[i - 1] - this->heights[i]) / dm;
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if((d >= float_type(1.) && dp > float_type(1.)) || (d <= float_type(-1.) && dm < float_type(-1.)))
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{
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short sign_d = static_cast<short>(d / std::abs(d));
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// try adjusting heights[i] using p-squared formula
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float_type h = this->heights[i] + sign_d / (dp - dm) * ((sign_d - dm) * hp
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+ (dp - sign_d) * hm);
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if(this->heights[i - 1] < h && h < this->heights[i + 1])
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{
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this->heights[i] = h;
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}
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else
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{
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// use linear formula
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if(d > float_type(0))
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{
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this->heights[i] += hp;
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}
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if(d < float_type(0))
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{
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this->heights[i] -= hm;
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}
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}
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this->actual_positions[i] += sign_d;
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}
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}
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}
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}
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result_type result(dont_care) const
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{
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return this->heights[2];
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}
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// make this accumulator serializeable
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// TODO: do we need to split to load/save and verify that P did not change?
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template<class Archive>
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void serialize(Archive & ar, const unsigned int file_version)
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{
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ar & p;
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ar & heights;
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ar & actual_positions;
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ar & desired_positions;
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ar & positions_increments;
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}
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private:
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float_type p; // the quantile probability p
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array_type heights; // q_i
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array_type actual_positions; // n_i
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array_type desired_positions; // n'_i
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array_type positions_increments; // dn'_i
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};
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} // namespace detail
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///////////////////////////////////////////////////////////////////////////////
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// tag::p_square_quantile
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//
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namespace tag
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{
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struct p_square_quantile
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: depends_on<count>
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{
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/// INTERNAL ONLY
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///
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typedef accumulators::impl::p_square_quantile_impl<mpl::_1, regular> impl;
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};
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struct p_square_quantile_for_median
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: depends_on<count>
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{
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/// INTERNAL ONLY
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///
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typedef accumulators::impl::p_square_quantile_impl<mpl::_1, for_median> impl;
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};
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}
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///////////////////////////////////////////////////////////////////////////////
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// extract::p_square_quantile
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// extract::p_square_quantile_for_median
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//
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namespace extract
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{
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extractor<tag::p_square_quantile> const p_square_quantile = {};
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extractor<tag::p_square_quantile_for_median> const p_square_quantile_for_median = {};
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BOOST_ACCUMULATORS_IGNORE_GLOBAL(p_square_quantile)
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BOOST_ACCUMULATORS_IGNORE_GLOBAL(p_square_quantile_for_median)
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}
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using extract::p_square_quantile;
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using extract::p_square_quantile_for_median;
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// So that p_square_quantile can be automatically substituted with
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// weighted_p_square_quantile when the weight parameter is non-void
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template<>
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struct as_weighted_feature<tag::p_square_quantile>
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{
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typedef tag::weighted_p_square_quantile type;
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};
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template<>
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struct feature_of<tag::weighted_p_square_quantile>
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: feature_of<tag::p_square_quantile>
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{
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};
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}} // namespace boost::accumulators
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#endif
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