| /////////////////////////////////////////////////////////////////////////////// |
| // p_square_quantile.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_P_SQUARE_QUANTILE_HPP_DE_01_01_2006 |
| #define BOOST_ACCUMULATORS_STATISTICS_P_SQUARE_QUANTILE_HPP_DE_01_01_2006 |
| |
| #include <cmath> |
| #include <functional> |
| #include <boost/array.hpp> |
| #include <boost/mpl/placeholders.hpp> |
| #include <boost/type_traits/is_same.hpp> |
| #include <boost/parameter/keyword.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/parameters/quantile_probability.hpp> |
| |
| namespace boost { namespace accumulators |
| { |
| |
| namespace impl |
| { |
| /////////////////////////////////////////////////////////////////////////////// |
| // p_square_quantile_impl |
| // single quantile estimation |
| /** |
| @brief Single quantile estimation with the \f$P^2\f$ algorithm |
| |
| The \f$P^2\f$ algorithm estimates a quantile dynamically without storing samples. Instead of |
| storing the whole sample cumulative distribution, only five points (markers) are stored. The heights |
| of these markers are the minimum and the maximum of the samples and the current estimates of the |
| \f$(p/2)\f$-, \f$p\f$- and \f$(1+p)/2\f$-quantiles. Their positions are equal to the number |
| of samples that are smaller or equal to the markers. Each time a new samples is recorded, the |
| positions of the markers are updated and if necessary their heights are adjusted using a piecewise- |
| parabolic formula. |
| |
| For further details, see |
| |
| R. Jain and I. Chlamtac, The P^2 algorithmus fordynamic calculation of quantiles and |
| histograms without storing observations, Communications of the ACM, |
| Volume 28 (October), Number 10, 1985, p. 1076-1085. |
| |
| @param quantile_probability |
| */ |
| template<typename Sample, typename Impl> |
| struct p_square_quantile_impl |
| : accumulator_base |
| { |
| typedef typename numeric::functional::average<Sample, std::size_t>::result_type float_type; |
| typedef array<float_type, 5> array_type; |
| // for boost::result_of |
| typedef float_type result_type; |
| |
| template<typename Args> |
| p_square_quantile_impl(Args const &args) |
| : p(is_same<Impl, for_median>::value ? 0.5 : args[quantile_probability | 0.5]) |
| , heights() |
| , actual_positions() |
| , desired_positions() |
| , positions_increments() |
| { |
| for(std::size_t i = 0; i < 5; ++i) |
| { |
| this->actual_positions[i] = i + 1; |
| } |
| |
| this->desired_positions[0] = 1.; |
| this->desired_positions[1] = 1. + 2. * this->p; |
| this->desired_positions[2] = 1. + 4. * this->p; |
| this->desired_positions[3] = 3. + 2. * this->p; |
| this->desired_positions[4] = 5.; |
| |
| this->positions_increments[0] = 0.; |
| this->positions_increments[1] = this->p / 2.; |
| this->positions_increments[2] = this->p; |
| this->positions_increments[3] = (1. + this->p) / 2.; |
| this->positions_increments[4] = 1.; |
| } |
| |
| template<typename Args> |
| void operator ()(Args const &args) |
| { |
| std::size_t cnt = count(args); |
| |
| // accumulate 5 first samples |
| if(cnt <= 5) |
| { |
| this->heights[cnt - 1] = args[sample]; |
| |
| // complete the initialization of heights by sorting |
| if(cnt == 5) |
| { |
| std::sort(this->heights.begin(), this->heights.end()); |
| } |
| } |
| else |
| { |
| std::size_t sample_cell = 1; // k |
| |
| // find cell k such that heights[k-1] <= args[sample] < heights[k] and ajust extreme values |
| if (args[sample] < this->heights[0]) |
| { |
| this->heights[0] = args[sample]; |
| sample_cell = 1; |
| } |
| else if (this->heights[4] <= args[sample]) |
| { |
| this->heights[4] = args[sample]; |
| sample_cell = 4; |
| } |
| 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 positions of markers above sample_cell |
| for(std::size_t i = sample_cell; i < 5; ++i) |
| { |
| ++this->actual_positions[i]; |
| } |
| |
| // update desired positions of all markers |
| for(std::size_t i = 0; i < 5; ++i) |
| { |
| this->desired_positions[i] += this->positions_increments[i]; |
| } |
| |
| // adjust heights and actual positions of markers 1 to 3 if necessary |
| for(std::size_t i = 1; i <= 3; ++i) |
| { |
| // offset to desired positions |
| 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)); |
| |
| // try adjusting heights[i] using p-squared formula |
| float_type h = this->heights[i] + sign_d / (dp - dm) * ((sign_d - dm) * hp |
| + (dp - sign_d) * hm); |
| |
| 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 |
| { |
| return this->heights[2]; |
| } |
| |
| private: |
| float_type p; // the quantile probability p |
| array_type heights; // q_i |
| array_type actual_positions; // n_i |
| array_type desired_positions; // n'_i |
| array_type positions_increments; // dn'_i |
| }; |
| |
| } // namespace detail |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| // tag::p_square_quantile |
| // |
| namespace tag |
| { |
| struct p_square_quantile |
| : depends_on<count> |
| { |
| /// INTERNAL ONLY |
| /// |
| typedef accumulators::impl::p_square_quantile_impl<mpl::_1, regular> impl; |
| }; |
| struct p_square_quantile_for_median |
| : depends_on<count> |
| { |
| /// INTERNAL ONLY |
| /// |
| typedef accumulators::impl::p_square_quantile_impl<mpl::_1, for_median> impl; |
| }; |
| } |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| // extract::p_square_quantile |
| // extract::p_square_quantile_for_median |
| // |
| namespace extract |
| { |
| extractor<tag::p_square_quantile> const p_square_quantile = {}; |
| extractor<tag::p_square_quantile_for_median> const p_square_quantile_for_median = {}; |
| |
| BOOST_ACCUMULATORS_IGNORE_GLOBAL(p_square_quantile) |
| BOOST_ACCUMULATORS_IGNORE_GLOBAL(p_square_quantile_for_median) |
| } |
| |
| using extract::p_square_quantile; |
| using extract::p_square_quantile_for_median; |
| |
| // So that p_square_quantile can be automatically substituted with |
| // weighted_p_square_quantile when the weight parameter is non-void |
| template<> |
| struct as_weighted_feature<tag::p_square_quantile> |
| { |
| typedef tag::weighted_p_square_quantile type; |
| }; |
| |
| template<> |
| struct feature_of<tag::weighted_p_square_quantile> |
| : feature_of<tag::p_square_quantile> |
| { |
| }; |
| |
| }} // namespace boost::accumulators |
| |
| #endif |