310 lines
11 KiB
C++
310 lines
11 KiB
C++
///////////////////////////////////////////////////////////////////////////////
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// extended_p_square.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_EXTENDED_SINGLE_HPP_DE_01_01_2006
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#define BOOST_ACCUMULATORS_STATISTICS_EXTENDED_SINGLE_HPP_DE_01_01_2006
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#include <vector>
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#include <functional>
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#include <boost/range/begin.hpp>
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#include <boost/range/end.hpp>
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#include <boost/range/iterator_range.hpp>
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#include <boost/iterator/transform_iterator.hpp>
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#include <boost/iterator/counting_iterator.hpp>
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#include <boost/iterator/permutation_iterator.hpp>
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#include <boost/parameter/keyword.hpp>
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#include <boost/mpl/placeholders.hpp>
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#include <boost/accumulators/accumulators_fwd.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/times2_iterator.hpp>
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#include <boost/serialization/vector.hpp>
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namespace boost { namespace accumulators
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{
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///////////////////////////////////////////////////////////////////////////////
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// probabilities named parameter
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//
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BOOST_PARAMETER_NESTED_KEYWORD(tag, extended_p_square_probabilities, probabilities)
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BOOST_ACCUMULATORS_IGNORE_GLOBAL(extended_p_square_probabilities)
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namespace impl
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{
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///////////////////////////////////////////////////////////////////////////////
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// extended_p_square_impl
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// multiple quantile estimation
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/**
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@brief Multiple quantile estimation with the extended \f$P^2\f$ algorithm
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Extended \f$P^2\f$ algorithm for estimation of several quantiles without storing samples.
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Assume that \f$m\f$ quantiles \f$\xi_{p_1}, \ldots, \xi_{p_m}\f$ are to be estimated.
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Instead of storing the whole sample cumulative distribution, the algorithm maintains only
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\f$m+2\f$ principal markers and \f$m+1\f$ middle markers, whose positions are updated
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with each sample and whose heights are adjusted (if necessary) using a piecewise-parablic
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formula. The heights of these central markers are the current estimates of the quantiles
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and returned as an iterator range.
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For further details, see
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K. E. E. Raatikainen, Simultaneous estimation of several quantiles, Simulation, Volume 49,
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Number 4 (October), 1986, p. 159-164.
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The extended \f$ P^2 \f$ algorithm generalizes the \f$ P^2 \f$ algorithm of
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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 extended_p_square_probabilities A vector of quantile probabilities.
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*/
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template<typename Sample>
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struct extended_p_square_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 std::vector<float_type> array_type;
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// for boost::result_of
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typedef iterator_range<
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detail::lvalue_index_iterator<
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permutation_iterator<
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typename array_type::const_iterator
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, detail::times2_iterator
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>
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>
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> result_type;
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template<typename Args>
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extended_p_square_impl(Args const &args)
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: probabilities(
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boost::begin(args[extended_p_square_probabilities])
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, boost::end(args[extended_p_square_probabilities])
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)
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, heights(2 * probabilities.size() + 3)
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, actual_positions(heights.size())
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, desired_positions(heights.size())
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, positions_increments(heights.size())
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{
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std::size_t num_quantiles = this->probabilities.size();
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std::size_t num_markers = this->heights.size();
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for(std::size_t i = 0; i < num_markers; ++i)
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{
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this->actual_positions[i] = i + 1;
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}
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this->positions_increments[0] = 0.;
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this->positions_increments[num_markers - 1] = 1.;
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for(std::size_t i = 0; i < num_quantiles; ++i)
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{
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this->positions_increments[2 * i + 2] = probabilities[i];
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}
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for(std::size_t i = 0; i <= num_quantiles; ++i)
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{
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this->positions_increments[2 * i + 1] =
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0.5 * (this->positions_increments[2 * i] + this->positions_increments[2 * i + 2]);
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}
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for(std::size_t i = 0; i < num_markers; ++i)
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{
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this->desired_positions[i] = 1. + 2. * (num_quantiles + 1.) * this->positions_increments[i];
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}
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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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// m+2 principal markers and m+1 middle markers
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std::size_t num_markers = 2 * this->probabilities.size() + 3;
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// first accumulate num_markers samples
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if(cnt <= num_markers)
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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 == num_markers)
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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;
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// find cell k = sample_cell such that heights[k-1] <= sample < heights[k]
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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(args[sample] >= this->heights[num_markers - 1])
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{
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this->heights[num_markers - 1] = args[sample];
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sample_cell = num_markers - 1;
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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 actual positions of all markers above sample_cell index
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for(std::size_t i = sample_cell; i < num_markers; ++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 < num_markers; ++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 num_markers-2 if necessary
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for(std::size_t i = 1; i <= num_markers - 2; ++i)
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{
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// offset to desired position
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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 >= 1 && dp > 1) || (d <= -1 && dm < -1))
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{
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short sign_d = static_cast<short>(d / std::abs(d));
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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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// try adjusting heights[i] using p-squared formula
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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 > 0)
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{
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this->heights[i] += hp;
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}
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if(d < 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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// for i in [1,probabilities.size()], return heights[i * 2]
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detail::times2_iterator idx_begin = detail::make_times2_iterator(1);
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detail::times2_iterator idx_end = detail::make_times2_iterator(this->probabilities.size() + 1);
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return result_type(
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make_permutation_iterator(this->heights.begin(), idx_begin)
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, make_permutation_iterator(this->heights.begin(), idx_end)
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);
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}
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public:
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// make this accumulator serializeable
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// TODO: do we need to split to load/save and verify that the parameters 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 & probabilities;
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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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array_type probabilities; // the quantile probabilities
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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; // d_i
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array_type positions_increments; // f_i
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};
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} // namespace impl
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///////////////////////////////////////////////////////////////////////////////
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// tag::extended_p_square
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//
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namespace tag
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{
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struct extended_p_square
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: depends_on<count>
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, extended_p_square_probabilities
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{
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typedef accumulators::impl::extended_p_square_impl<mpl::_1> impl;
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#ifdef BOOST_ACCUMULATORS_DOXYGEN_INVOKED
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/// tag::extended_p_square::probabilities named parameter
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static boost::parameter::keyword<tag::probabilities> const probabilities;
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#endif
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};
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}
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///////////////////////////////////////////////////////////////////////////////
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// extract::extended_p_square
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//
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namespace extract
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{
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extractor<tag::extended_p_square> const extended_p_square = {};
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BOOST_ACCUMULATORS_IGNORE_GLOBAL(extended_p_square)
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}
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using extract::extended_p_square;
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// So that extended_p_square can be automatically substituted with
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// weighted_extended_p_square when the weight parameter is non-void
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template<>
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struct as_weighted_feature<tag::extended_p_square>
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{
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typedef tag::weighted_extended_p_square type;
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};
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template<>
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struct feature_of<tag::weighted_extended_p_square>
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: feature_of<tag::extended_p_square>
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{
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};
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}} // namespace boost::accumulators
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#endif
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