third_party/boost/include/boost/accumulators/statistics/weighted_peaks_over_threshold.hpp - webm/webmlive - Git at Google

 ///////////////////////////////////////////////////////////////////////////////
 // weighted_peaks_over_threshold.hpp
 //
 //  Copyright 2006 Daniel Egloff, Olivier Gygi. 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_WEIGHTED_PEAKS_OVER_THRESHOLD_HPP_DE_01_01_2006
 #define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_PEAKS_OVER_THRESHOLD_HPP_DE_01_01_2006

 #include <vector>
 #include <limits>
 #include <numeric>
 #include <functional>
 #include <boost/range.hpp>
 #include <boost/mpl/if.hpp>
 #include <boost/mpl/placeholders.hpp>
 #include <boost/parameter/keyword.hpp>
 #include <boost/tuple/tuple.hpp>
 #include <boost/accumulators/numeric/functional.hpp>
 #include <boost/accumulators/framework/accumulator_base.hpp>
 #include <boost/accumulators/framework/extractor.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/parameters/quantile_probability.hpp>
 #include <boost/accumulators/statistics/peaks_over_threshold.hpp> // for named parameters pot_threshold_value and pot_threshold_probability
 #include <boost/accumulators/statistics/sum.hpp>
 #include <boost/accumulators/statistics/tail_variate.hpp>

 #ifdef _MSC_VER
 # pragma warning(push)
 # pragma warning(disable: 4127) // conditional expression is constant
 #endif

 namespace boost { namespace accumulators
 {

 namespace impl
 {

     ///////////////////////////////////////////////////////////////////////////////
     // weighted_peaks_over_threshold_impl
     //  works with an explicit threshold value and does not depend on order statistics of weighted samples
     /**
         @brief Weighted Peaks over Threshold Method for Weighted Quantile and Weighted Tail Mean Estimation

         @sa peaks_over_threshold_impl

         @param quantile_probability
         @param pot_threshold_value
     */
     template<typename Sample, typename Weight, typename LeftRight>
     struct weighted_peaks_over_threshold_impl
       : accumulator_base
     {
         typedef typename numeric::functional::multiplies<Weight, Sample>::result_type weighted_sample;
         typedef typename numeric::functional::average<weighted_sample, std::size_t>::result_type float_type;
         // for boost::result_of
         typedef boost::tuple<float_type, float_type, float_type> result_type;

         template<typename Args>
         weighted_peaks_over_threshold_impl(Args const &args)
           : sign_((is_same<LeftRight, left>::value) ? -1 : 1)
           , mu_(sign_ * numeric::average(args[sample | Sample()], (std::size_t)1))
           , sigma2_(numeric::average(args[sample | Sample()], (std::size_t)1))
           , w_sum_(numeric::average(args[weight | Weight()], (std::size_t)1))
           , threshold_(sign_ * args[pot_threshold_value])
           , fit_parameters_(boost::make_tuple(0., 0., 0.))
           , is_dirty_(true)
         {
         }

         template<typename Args>
         void operator ()(Args const &args)
         {
             this->is_dirty_ = true;

             if (this->sign_ * args[sample] > this->threshold_)
             {
                 this->mu_ += args[weight] * args[sample];
                 this->sigma2_ += args[weight] * args[sample] * args[sample];
                 this->w_sum_ += args[weight];
             }
         }

         template<typename Args>
         result_type result(Args const &args) const
         {
             if (this->is_dirty_)
             {
                 this->is_dirty_ = false;

                 this->mu_ = this->sign_ * numeric::average(this->mu_, this->w_sum_);
                 this->sigma2_ = numeric::average(this->sigma2_, this->w_sum_);
                 this->sigma2_ -= this->mu_ * this->mu_;

                 float_type threshold_probability = numeric::average(sum_of_weights(args) - this->w_sum_, sum_of_weights(args));

                 float_type tmp = numeric::average(( this->mu_ - this->threshold_ )*( this->mu_ - this->threshold_ ), this->sigma2_);
                 float_type xi_hat = 0.5 * ( 1. - tmp );
                 float_type beta_hat = 0.5 * ( this->mu_ - this->threshold_ ) * ( 1. + tmp );
                 float_type beta_bar = beta_hat * std::pow(1. - threshold_probability, xi_hat);
                 float_type u_bar = this->threshold_ - beta_bar * ( std::pow(1. - threshold_probability, -xi_hat) - 1.)/xi_hat;
                 this->fit_parameters_ = boost::make_tuple(u_bar, beta_bar, xi_hat);
             }

             return this->fit_parameters_;
         }

     private:
         short sign_;                         // for left tail fitting, mirror the extreme values
         mutable float_type mu_;              // mean of samples above threshold
         mutable float_type sigma2_;          // variance of samples above threshold
         mutable float_type w_sum_;           // sum of weights of samples above threshold
         float_type threshold_;
         mutable result_type fit_parameters_; // boost::tuple that stores fit parameters
         mutable bool is_dirty_;
     };

     ///////////////////////////////////////////////////////////////////////////////
     // weighted_peaks_over_threshold_prob_impl
     //  determines threshold from a given threshold probability using order statistics
     /**
         @brief Peaks over Threshold Method for Quantile and Tail Mean Estimation

         @sa weighted_peaks_over_threshold_impl

         @param quantile_probability
         @param pot_threshold_probability
     */
     template<typename Sample, typename Weight, typename LeftRight>
     struct weighted_peaks_over_threshold_prob_impl
       : accumulator_base
     {
         typedef typename numeric::functional::multiplies<Weight, Sample>::result_type weighted_sample;
         typedef typename numeric::functional::average<weighted_sample, std::size_t>::result_type float_type;
         // for boost::result_of
         typedef boost::tuple<float_type, float_type, float_type> result_type;

         template<typename Args>
         weighted_peaks_over_threshold_prob_impl(Args const &args)
           : sign_((is_same<LeftRight, left>::value) ? -1 : 1)
           , mu_(sign_ * numeric::average(args[sample | Sample()], (std::size_t)1))
           , sigma2_(numeric::average(args[sample | Sample()], (std::size_t)1))
           , threshold_probability_(args[pot_threshold_probability])
           , fit_parameters_(boost::make_tuple(0., 0., 0.))
           , is_dirty_(true)
         {
         }

         void operator ()(dont_care)
         {
             this->is_dirty_ = true;
         }

         template<typename Args>
         result_type result(Args const &args) const
         {
             if (this->is_dirty_)
             {
                 this->is_dirty_ = false;

                 float_type threshold = sum_of_weights(args)
                              * ( ( is_same<LeftRight, left>::value ) ? this->threshold_probability_ : 1. - this->threshold_probability_ );

                 std::size_t n = 0;
                 Weight sum = Weight(0);

                 while (sum < threshold)
                 {
                     if (n < static_cast<std::size_t>(tail_weights(args).size()))
                     {
                         mu_ += *(tail_weights(args).begin() + n) * *(tail(args).begin() + n);
                         sigma2_ += *(tail_weights(args).begin() + n) * *(tail(args).begin() + n) * (*(tail(args).begin() + n));
                         sum += *(tail_weights(args).begin() + n);
                         n++;
                     }
                     else
                     {
                         if (std::numeric_limits<float_type>::has_quiet_NaN)
                         {
                             return boost::make_tuple(
                                 std::numeric_limits<float_type>::quiet_NaN()
                               , std::numeric_limits<float_type>::quiet_NaN()
                               , std::numeric_limits<float_type>::quiet_NaN()
                             );
                         }
                         else
                         {
                             std::ostringstream msg;
                             msg << "index n = " << n << " is not in valid range [0, " << tail(args).size() << ")";
                             boost::throw_exception(std::runtime_error(msg.str()));
                             return boost::make_tuple(Sample(0), Sample(0), Sample(0));
                         }
                     }
                 }

                 float_type u = *(tail(args).begin() + n - 1) * this->sign_;


                 this->mu_ = this->sign_ * numeric::average(this->mu_, sum);
                 this->sigma2_ = numeric::average(this->sigma2_, sum);
                 this->sigma2_ -= this->mu_ * this->mu_;

                 if (is_same<LeftRight, left>::value)
                     this->threshold_probability_ = 1. - this->threshold_probability_;

                 float_type tmp = numeric::average(( this->mu_ - u )*( this->mu_ - u ), this->sigma2_);
                 float_type xi_hat = 0.5 * ( 1. - tmp );
                 float_type beta_hat = 0.5 * ( this->mu_ - u ) * ( 1. + tmp );
                 float_type beta_bar = beta_hat * std::pow(1. - threshold_probability_, xi_hat);
                 float_type u_bar = u - beta_bar * ( std::pow(1. - threshold_probability_, -xi_hat) - 1.)/xi_hat;
                 this->fit_parameters_ = boost::make_tuple(u_bar, beta_bar, xi_hat);

             }

             return this->fit_parameters_;
         }

     private:
         short sign_;                                // for left tail fitting, mirror the extreme values
         mutable float_type mu_;                     // mean of samples above threshold u
         mutable float_type sigma2_;                 // variance of samples above threshold u
         mutable float_type threshold_probability_;
         mutable result_type fit_parameters_;        // boost::tuple that stores fit parameters
         mutable bool is_dirty_;
     };

 } // namespace impl

 ///////////////////////////////////////////////////////////////////////////////
 // tag::weighted_peaks_over_threshold
 //
 namespace tag
 {
     template<typename LeftRight>
     struct weighted_peaks_over_threshold
       : depends_on<sum_of_weights>
       , pot_threshold_value
     {
         /// INTERNAL ONLY
         typedef accumulators::impl::weighted_peaks_over_threshold_impl<mpl::_1, mpl::_2, LeftRight> impl;
     };

     template<typename LeftRight>
     struct weighted_peaks_over_threshold_prob
       : depends_on<sum_of_weights, tail_weights<LeftRight> >
       , pot_threshold_probability
     {
         /// INTERNAL ONLY
         typedef accumulators::impl::weighted_peaks_over_threshold_prob_impl<mpl::_1, mpl::_2, LeftRight> impl;
     };
 }

 ///////////////////////////////////////////////////////////////////////////////
 // extract::weighted_peaks_over_threshold
 //
 namespace extract
 {
     extractor<tag::abstract_peaks_over_threshold> const weighted_peaks_over_threshold = {};

     BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_peaks_over_threshold)
 }

 using extract::weighted_peaks_over_threshold;

 // weighted_peaks_over_threshold<LeftRight>(with_threshold_value) -> weighted_peaks_over_threshold<LeftRight>
 template<typename LeftRight>
 struct as_feature<tag::weighted_peaks_over_threshold<LeftRight>(with_threshold_value)>
 {
     typedef tag::weighted_peaks_over_threshold<LeftRight> type;
 };

 // weighted_peaks_over_threshold<LeftRight>(with_threshold_probability) -> weighted_peaks_over_threshold_prob<LeftRight>
 template<typename LeftRight>
 struct as_feature<tag::weighted_peaks_over_threshold<LeftRight>(with_threshold_probability)>
 {
     typedef tag::weighted_peaks_over_threshold_prob<LeftRight> type;
 };

 }} // namespace boost::accumulators

 #ifdef _MSC_VER
 # pragma warning(pop)
 #endif

 #endif
	///////////////////////////////////////////////////////////////////////////////
	// weighted_peaks_over_threshold.hpp
	//
	// Copyright 2006 Daniel Egloff, Olivier Gygi. 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_WEIGHTED_PEAKS_OVER_THRESHOLD_HPP_DE_01_01_2006
	#define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_PEAKS_OVER_THRESHOLD_HPP_DE_01_01_2006

	#include <vector>
	#include <limits>
	#include <numeric>
	#include <functional>
	#include <boost/range.hpp>
	#include <boost/mpl/if.hpp>
	#include <boost/mpl/placeholders.hpp>
	#include <boost/parameter/keyword.hpp>
	#include <boost/tuple/tuple.hpp>
	#include <boost/accumulators/numeric/functional.hpp>
	#include <boost/accumulators/framework/accumulator_base.hpp>
	#include <boost/accumulators/framework/extractor.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/parameters/quantile_probability.hpp>
	#include <boost/accumulators/statistics/peaks_over_threshold.hpp> // for named parameters pot_threshold_value and pot_threshold_probability
	#include <boost/accumulators/statistics/sum.hpp>
	#include <boost/accumulators/statistics/tail_variate.hpp>

	#ifdef _MSC_VER
	# pragma warning(push)
	# pragma warning(disable: 4127) // conditional expression is constant
	#endif

	namespace boost { namespace accumulators
	{

	namespace impl
	{

	///////////////////////////////////////////////////////////////////////////////
	// weighted_peaks_over_threshold_impl
	// works with an explicit threshold value and does not depend on order statistics of weighted samples
	/**
	@brief Weighted Peaks over Threshold Method for Weighted Quantile and Weighted Tail Mean Estimation

	@sa peaks_over_threshold_impl

	@param quantile_probability
	@param pot_threshold_value
	*/
	template<typename Sample, typename Weight, typename LeftRight>
	struct weighted_peaks_over_threshold_impl
	: accumulator_base
	{
	typedef typename numeric::functional::multiplies<Weight, Sample>::result_type weighted_sample;
	typedef typename numeric::functional::average<weighted_sample, std::size_t>::result_type float_type;
	// for boost::result_of
	typedef boost::tuple<float_type, float_type, float_type> result_type;

	template<typename Args>
	weighted_peaks_over_threshold_impl(Args const &args)
	: sign_((is_same<LeftRight, left>::value) ? -1 : 1)
	, mu_(sign_ * numeric::average(args[sample \| Sample()], (std::size_t)1))
	, sigma2_(numeric::average(args[sample \| Sample()], (std::size_t)1))
	, w_sum_(numeric::average(args[weight \| Weight()], (std::size_t)1))
	, threshold_(sign_ * args[pot_threshold_value])
	, fit_parameters_(boost::make_tuple(0., 0., 0.))
	, is_dirty_(true)
	{
	}

	template<typename Args>
	void operator ()(Args const &args)
	{
	this->is_dirty_ = true;

	if (this->sign_ * args[sample] > this->threshold_)
	{
	this->mu_ += args[weight] * args[sample];
	this->sigma2_ += args[weight] * args[sample] * args[sample];
	this->w_sum_ += args[weight];
	}
	}

	template<typename Args>
	result_type result(Args const &args) const
	{
	if (this->is_dirty_)
	{
	this->is_dirty_ = false;

	this->mu_ = this->sign_ * numeric::average(this->mu_, this->w_sum_);
	this->sigma2_ = numeric::average(this->sigma2_, this->w_sum_);
	this->sigma2_ -= this->mu_ * this->mu_;

	float_type threshold_probability = numeric::average(sum_of_weights(args) - this->w_sum_, sum_of_weights(args));

	float_type tmp = numeric::average(( this->mu_ - this->threshold_ )*( this->mu_ - this->threshold_ ), this->sigma2_);
	float_type xi_hat = 0.5 * ( 1. - tmp );
	float_type beta_hat = 0.5 * ( this->mu_ - this->threshold_ ) * ( 1. + tmp );
	float_type beta_bar = beta_hat * std::pow(1. - threshold_probability, xi_hat);
	float_type u_bar = this->threshold_ - beta_bar * ( std::pow(1. - threshold_probability, -xi_hat) - 1.)/xi_hat;
	this->fit_parameters_ = boost::make_tuple(u_bar, beta_bar, xi_hat);
	}

	return this->fit_parameters_;
	}

	private:
	short sign_; // for left tail fitting, mirror the extreme values
	mutable float_type mu_; // mean of samples above threshold
	mutable float_type sigma2_; // variance of samples above threshold
	mutable float_type w_sum_; // sum of weights of samples above threshold
	float_type threshold_;
	mutable result_type fit_parameters_; // boost::tuple that stores fit parameters
	mutable bool is_dirty_;
	};

	///////////////////////////////////////////////////////////////////////////////
	// weighted_peaks_over_threshold_prob_impl
	// determines threshold from a given threshold probability using order statistics
	/**
	@brief Peaks over Threshold Method for Quantile and Tail Mean Estimation

	@sa weighted_peaks_over_threshold_impl

	@param quantile_probability
	@param pot_threshold_probability
	*/
	template<typename Sample, typename Weight, typename LeftRight>
	struct weighted_peaks_over_threshold_prob_impl
	: accumulator_base
	{
	typedef typename numeric::functional::multiplies<Weight, Sample>::result_type weighted_sample;
	typedef typename numeric::functional::average<weighted_sample, std::size_t>::result_type float_type;
	// for boost::result_of
	typedef boost::tuple<float_type, float_type, float_type> result_type;

	template<typename Args>
	weighted_peaks_over_threshold_prob_impl(Args const &args)
	: sign_((is_same<LeftRight, left>::value) ? -1 : 1)
	, mu_(sign_ * numeric::average(args[sample \| Sample()], (std::size_t)1))
	, sigma2_(numeric::average(args[sample \| Sample()], (std::size_t)1))
	, threshold_probability_(args[pot_threshold_probability])
	, fit_parameters_(boost::make_tuple(0., 0., 0.))
	, is_dirty_(true)
	{
	}

	void operator ()(dont_care)
	{
	this->is_dirty_ = true;
	}

	template<typename Args>
	result_type result(Args const &args) const
	{
	if (this->is_dirty_)
	{
	this->is_dirty_ = false;

	float_type threshold = sum_of_weights(args)
	* ( ( is_same<LeftRight, left>::value ) ? this->threshold_probability_ : 1. - this->threshold_probability_ );

	std::size_t n = 0;
	Weight sum = Weight(0);

	while (sum < threshold)
	{
	if (n < static_cast<std::size_t>(tail_weights(args).size()))
	{
	mu_ += (tail_weights(args).begin() + n) *(tail(args).begin() + n);
	sigma2_ += (tail_weights(args).begin() + n) (tail(args).begin() + n) (*(tail(args).begin() + n));
	sum += *(tail_weights(args).begin() + n);
	n++;
	}
	else
	{
	if (std::numeric_limits<float_type>::has_quiet_NaN)
	{
	return boost::make_tuple(
	std::numeric_limits<float_type>::quiet_NaN()
	, std::numeric_limits<float_type>::quiet_NaN()
	, std::numeric_limits<float_type>::quiet_NaN()
	);
	}
	else
	{
	std::ostringstream msg;
	msg << "index n = " << n << " is not in valid range [0, " << tail(args).size() << ")";
	boost::throw_exception(std::runtime_error(msg.str()));
	return boost::make_tuple(Sample(0), Sample(0), Sample(0));
	}
	}
	}

	float_type u = (tail(args).begin() + n - 1) this->sign_;


	this->mu_ = this->sign_ * numeric::average(this->mu_, sum);
	this->sigma2_ = numeric::average(this->sigma2_, sum);
	this->sigma2_ -= this->mu_ * this->mu_;

	if (is_same<LeftRight, left>::value)
	this->threshold_probability_ = 1. - this->threshold_probability_;

	float_type tmp = numeric::average(( this->mu_ - u )*( this->mu_ - u ), this->sigma2_);
	float_type xi_hat = 0.5 * ( 1. - tmp );
	float_type beta_hat = 0.5 * ( this->mu_ - u ) * ( 1. + tmp );
	float_type beta_bar = beta_hat * std::pow(1. - threshold_probability_, xi_hat);
	float_type u_bar = u - beta_bar * ( std::pow(1. - threshold_probability_, -xi_hat) - 1.)/xi_hat;
	this->fit_parameters_ = boost::make_tuple(u_bar, beta_bar, xi_hat);

	}

	return this->fit_parameters_;
	}

	private:
	short sign_; // for left tail fitting, mirror the extreme values
	mutable float_type mu_; // mean of samples above threshold u
	mutable float_type sigma2_; // variance of samples above threshold u
	mutable float_type threshold_probability_;
	mutable result_type fit_parameters_; // boost::tuple that stores fit parameters
	mutable bool is_dirty_;
	};

	} // namespace impl

	///////////////////////////////////////////////////////////////////////////////
	// tag::weighted_peaks_over_threshold
	//
	namespace tag
	{
	template<typename LeftRight>
	struct weighted_peaks_over_threshold
	: depends_on<sum_of_weights>
	, pot_threshold_value
	{
	/// INTERNAL ONLY
	typedef accumulators::impl::weighted_peaks_over_threshold_impl<mpl::_1, mpl::_2, LeftRight> impl;
	};

	template<typename LeftRight>
	struct weighted_peaks_over_threshold_prob
	: depends_on<sum_of_weights, tail_weights<LeftRight> >
	, pot_threshold_probability
	{
	/// INTERNAL ONLY
	typedef accumulators::impl::weighted_peaks_over_threshold_prob_impl<mpl::_1, mpl::_2, LeftRight> impl;
	};
	}

	///////////////////////////////////////////////////////////////////////////////
	// extract::weighted_peaks_over_threshold
	//
	namespace extract
	{
	extractor<tag::abstract_peaks_over_threshold> const weighted_peaks_over_threshold = {};

	BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_peaks_over_threshold)
	}

	using extract::weighted_peaks_over_threshold;

	// weighted_peaks_over_threshold<LeftRight>(with_threshold_value) -> weighted_peaks_over_threshold<LeftRight>
	template<typename LeftRight>
	struct as_feature<tag::weighted_peaks_over_threshold<LeftRight>(with_threshold_value)>
	{
	typedef tag::weighted_peaks_over_threshold<LeftRight> type;
	};

	// weighted_peaks_over_threshold<LeftRight>(with_threshold_probability) -> weighted_peaks_over_threshold_prob<LeftRight>
	template<typename LeftRight>
	struct as_feature<tag::weighted_peaks_over_threshold<LeftRight>(with_threshold_probability)>
	{
	typedef tag::weighted_peaks_over_threshold_prob<LeftRight> type;
	};

	}} // namespace boost::accumulators

	#ifdef _MSC_VER
	# pragma warning(pop)
	#endif

	#endif