333 lines
12 KiB
C++
333 lines
12 KiB
C++
///////////////////////////////////////////////////////////////////////////////
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// extended_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_EXTENDED_SINGLE_QUANTILE_HPP_DE_01_01_2006
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#define BOOST_ACCUMULATORS_STATISTICS_EXTENDED_SINGLE_QUANTILE_HPP_DE_01_01_2006
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#include <vector>
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#include <functional>
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#include <boost/throw_exception.hpp>
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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/type_traits/is_same.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/accumulators/statistics/extended_p_square.hpp>
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#include <boost/accumulators/statistics/weighted_extended_p_square.hpp>
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#include <boost/accumulators/statistics/times2_iterator.hpp>
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#ifdef _MSC_VER
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# pragma warning(push)
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# pragma warning(disable: 4127) // conditional expression is constant
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#endif
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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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// extended_p_square_quantile_impl
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// single quantile estimation
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/**
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@brief Quantile estimation using the extended \f$P^2\f$ algorithm for weighted and unweighted samples
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Uses the quantile estimates calculated by the extended \f$P^2\f$ algorithm to compute
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intermediate quantile estimates by means of quadratic interpolation.
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@param quantile_probability The probability of the quantile to be estimated.
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*/
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template<typename Sample, typename Impl1, typename Impl2> // Impl1: weighted/unweighted // Impl2: linear/quadratic
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struct extended_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 std::vector<float_type> array_type;
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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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> range_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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extended_p_square_quantile_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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, probability()
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{
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}
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template<typename Args>
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result_type result(Args const &args) const
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{
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typedef
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typename mpl::if_<
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is_same<Impl1, weighted>
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, tag::weighted_extended_p_square
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, tag::extended_p_square
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>::type
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extended_p_square_tag;
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extractor<extended_p_square_tag> const some_extended_p_square = {};
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array_type heights(some_extended_p_square(args).size());
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std::copy(some_extended_p_square(args).begin(), some_extended_p_square(args).end(), heights.begin());
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this->probability = args[quantile_probability];
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typename array_type::const_iterator iter_probs = std::lower_bound(this->probabilities.begin(), this->probabilities.end(), this->probability);
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std::size_t dist = std::distance(this->probabilities.begin(), iter_probs);
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typename array_type::const_iterator iter_heights = heights.begin() + dist;
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// If this->probability is not in a valid range return NaN or throw exception
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if (this->probability < *this->probabilities.begin() || this->probability > *(this->probabilities.end() - 1))
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{
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if (std::numeric_limits<result_type>::has_quiet_NaN)
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{
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return std::numeric_limits<result_type>::quiet_NaN();
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}
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else
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{
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std::ostringstream msg;
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msg << "probability = " << this->probability << " is not in valid range (";
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msg << *this->probabilities.begin() << ", " << *(this->probabilities.end() - 1) << ")";
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boost::throw_exception(std::runtime_error(msg.str()));
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return Sample(0);
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}
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}
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if (*iter_probs == this->probability)
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{
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return heights[dist];
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}
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else
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{
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result_type res;
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if (is_same<Impl2, linear>::value)
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{
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/////////////////////////////////////////////////////////////////////////////////
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// LINEAR INTERPOLATION
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//
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float_type p1 = *iter_probs;
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float_type p0 = *(iter_probs - 1);
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float_type h1 = *iter_heights;
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float_type h0 = *(iter_heights - 1);
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float_type a = numeric::fdiv(h1 - h0, p1 - p0);
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float_type b = h1 - p1 * a;
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res = a * this->probability + b;
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}
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else
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{
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/////////////////////////////////////////////////////////////////////////////////
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// QUADRATIC INTERPOLATION
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//
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float_type p0, p1, p2;
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float_type h0, h1, h2;
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if ( (dist == 1 || *iter_probs - this->probability <= this->probability - *(iter_probs - 1) ) && dist != this->probabilities.size() - 1 )
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{
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p0 = *(iter_probs - 1);
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p1 = *iter_probs;
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p2 = *(iter_probs + 1);
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h0 = *(iter_heights - 1);
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h1 = *iter_heights;
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h2 = *(iter_heights + 1);
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}
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else
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{
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p0 = *(iter_probs - 2);
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p1 = *(iter_probs - 1);
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p2 = *iter_probs;
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h0 = *(iter_heights - 2);
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h1 = *(iter_heights - 1);
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h2 = *iter_heights;
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}
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float_type hp21 = numeric::fdiv(h2 - h1, p2 - p1);
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float_type hp10 = numeric::fdiv(h1 - h0, p1 - p0);
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float_type p21 = numeric::fdiv(p2 * p2 - p1 * p1, p2 - p1);
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float_type p10 = numeric::fdiv(p1 * p1 - p0 * p0, p1 - p0);
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float_type a = numeric::fdiv(hp21 - hp10, p21 - p10);
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float_type b = hp21 - a * p21;
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float_type c = h2 - a * p2 * p2 - b * p2;
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res = a * this->probability * this-> probability + b * this->probability + c;
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}
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return res;
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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 & probability;
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}
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private:
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array_type probabilities;
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mutable float_type probability;
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};
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} // namespace impl
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///////////////////////////////////////////////////////////////////////////////
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// tag::extended_p_square_quantile
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//
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namespace tag
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{
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struct extended_p_square_quantile
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: depends_on<extended_p_square>
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{
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typedef accumulators::impl::extended_p_square_quantile_impl<mpl::_1, unweighted, linear> impl;
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};
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struct extended_p_square_quantile_quadratic
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: depends_on<extended_p_square>
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{
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typedef accumulators::impl::extended_p_square_quantile_impl<mpl::_1, unweighted, quadratic> impl;
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};
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struct weighted_extended_p_square_quantile
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: depends_on<weighted_extended_p_square>
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{
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typedef accumulators::impl::extended_p_square_quantile_impl<mpl::_1, weighted, linear> impl;
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};
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struct weighted_extended_p_square_quantile_quadratic
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: depends_on<weighted_extended_p_square>
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{
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typedef accumulators::impl::extended_p_square_quantile_impl<mpl::_1, weighted, quadratic> impl;
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};
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}
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///////////////////////////////////////////////////////////////////////////////
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// extract::extended_p_square_quantile
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// extract::weighted_extended_p_square_quantile
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//
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namespace extract
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{
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extractor<tag::extended_p_square_quantile> const extended_p_square_quantile = {};
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extractor<tag::extended_p_square_quantile_quadratic> const extended_p_square_quantile_quadratic = {};
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extractor<tag::weighted_extended_p_square_quantile> const weighted_extended_p_square_quantile = {};
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extractor<tag::weighted_extended_p_square_quantile_quadratic> const weighted_extended_p_square_quantile_quadratic = {};
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BOOST_ACCUMULATORS_IGNORE_GLOBAL(extended_p_square_quantile)
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BOOST_ACCUMULATORS_IGNORE_GLOBAL(extended_p_square_quantile_quadratic)
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BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_extended_p_square_quantile)
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BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_extended_p_square_quantile_quadratic)
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}
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using extract::extended_p_square_quantile;
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using extract::extended_p_square_quantile_quadratic;
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using extract::weighted_extended_p_square_quantile;
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using extract::weighted_extended_p_square_quantile_quadratic;
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// extended_p_square_quantile(linear) -> extended_p_square_quantile
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template<>
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struct as_feature<tag::extended_p_square_quantile(linear)>
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{
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typedef tag::extended_p_square_quantile type;
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};
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// extended_p_square_quantile(quadratic) -> extended_p_square_quantile_quadratic
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template<>
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struct as_feature<tag::extended_p_square_quantile(quadratic)>
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{
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typedef tag::extended_p_square_quantile_quadratic type;
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};
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// weighted_extended_p_square_quantile(linear) -> weighted_extended_p_square_quantile
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template<>
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struct as_feature<tag::weighted_extended_p_square_quantile(linear)>
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{
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typedef tag::weighted_extended_p_square_quantile type;
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};
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// weighted_extended_p_square_quantile(quadratic) -> weighted_extended_p_square_quantile_quadratic
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template<>
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struct as_feature<tag::weighted_extended_p_square_quantile(quadratic)>
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{
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typedef tag::weighted_extended_p_square_quantile_quadratic type;
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};
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// for the purposes of feature-based dependency resolution,
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// extended_p_square_quantile and weighted_extended_p_square_quantile
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// provide the same feature as quantile
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template<>
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struct feature_of<tag::extended_p_square_quantile>
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: feature_of<tag::quantile>
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{
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};
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template<>
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struct feature_of<tag::extended_p_square_quantile_quadratic>
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: feature_of<tag::quantile>
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{
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};
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// So that extended_p_square_quantile can be automatically substituted with
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// weighted_extended_p_square_quantile when the weight parameter is non-void
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template<>
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struct as_weighted_feature<tag::extended_p_square_quantile>
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{
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typedef tag::weighted_extended_p_square_quantile type;
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};
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template<>
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struct feature_of<tag::weighted_extended_p_square_quantile>
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: feature_of<tag::extended_p_square_quantile>
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{
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};
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// So that extended_p_square_quantile_quadratic can be automatically substituted with
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// weighted_extended_p_square_quantile_quadratic when the weight parameter is non-void
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template<>
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struct as_weighted_feature<tag::extended_p_square_quantile_quadratic>
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{
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typedef tag::weighted_extended_p_square_quantile_quadratic type;
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};
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template<>
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struct feature_of<tag::weighted_extended_p_square_quantile_quadratic>
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: feature_of<tag::extended_p_square_quantile_quadratic>
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{
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};
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}} // namespace boost::accumulators
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#ifdef _MSC_VER
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# pragma warning(pop)
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#endif
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#endif
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