ceph/src/boost/boost/accumulators/statistics/weighted_peaks_over_threshold.hpp

   1 ///////////////////////////////////////////////////////////////////////////////
   2 // weighted_peaks_over_threshold.hpp
   3 //
   4 //  Copyright 2006 Daniel Egloff, Olivier Gygi. Distributed under the Boost
   5 //  Software License, Version 1.0. (See accompanying file
   6 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
   7
   8 #ifndef BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_PEAKS_OVER_THRESHOLD_HPP_DE_01_01_2006
   9 #define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_PEAKS_OVER_THRESHOLD_HPP_DE_01_01_2006
  10
  11 #include <vector>
  12 #include <limits>
  13 #include <numeric>
  14 #include <functional>
  15 #include <boost/throw_exception.hpp>
  16 #include <boost/range.hpp>
  17 #include <boost/mpl/if.hpp>
  18 #include <boost/mpl/placeholders.hpp>
  19 #include <boost/parameter/keyword.hpp>
  20 #include <boost/tuple/tuple.hpp>
  21 #include <boost/accumulators/numeric/functional.hpp>
  22 #include <boost/accumulators/framework/accumulator_base.hpp>
  23 #include <boost/accumulators/framework/extractor.hpp>
  24 #include <boost/accumulators/framework/parameters/sample.hpp>
  25 #include <boost/accumulators/framework/depends_on.hpp>
  26 #include <boost/accumulators/statistics_fwd.hpp>
  27 #include <boost/accumulators/statistics/parameters/quantile_probability.hpp>
  28 #include <boost/accumulators/statistics/peaks_over_threshold.hpp> // for named parameters pot_threshold_value and pot_threshold_probability
  29 #include <boost/accumulators/statistics/sum.hpp>
  30 #include <boost/accumulators/statistics/tail_variate.hpp>
  31
  32 #ifdef _MSC_VER
  33 # pragma warning(push)
  34 # pragma warning(disable: 4127) // conditional expression is constant
  35 #endif
  36
  37 namespace boost { namespace accumulators
  38 {
  39
  40 namespace impl
  41 {
  42
  43     ///////////////////////////////////////////////////////////////////////////////
  44     // weighted_peaks_over_threshold_impl
  45     //  works with an explicit threshold value and does not depend on order statistics of weighted samples
  46     /**
  47         @brief Weighted Peaks over Threshold Method for Weighted Quantile and Weighted Tail Mean Estimation
  48
  49         @sa peaks_over_threshold_impl
  50
  51         @param quantile_probability
  52         @param pot_threshold_value
  53     */
  54     template<typename Sample, typename Weight, typename LeftRight>
  55     struct weighted_peaks_over_threshold_impl
  56       : accumulator_base
  57     {
  58         typedef typename numeric::functional::multiplies<Weight, Sample>::result_type weighted_sample;
  59         typedef typename numeric::functional::fdiv<weighted_sample, std::size_t>::result_type float_type;
  60         // for boost::result_of
  61         typedef boost::tuple<float_type, float_type, float_type> result_type;
  62
  63         template<typename Args>
  64         weighted_peaks_over_threshold_impl(Args const &args)
  65           : sign_((is_same<LeftRight, left>::value) ? -1 : 1)
  66           , mu_(sign_ * numeric::fdiv(args[sample | Sample()], (std::size_t)1))
  67           , sigma2_(numeric::fdiv(args[sample | Sample()], (std::size_t)1))
  68           , w_sum_(numeric::fdiv(args[weight | Weight()], (std::size_t)1))
  69           , threshold_(sign_ * args[pot_threshold_value])
  70           , fit_parameters_(boost::make_tuple(0., 0., 0.))
  71           , is_dirty_(true)
  72         {
  73         }
  74
  75         template<typename Args>
  76         void operator ()(Args const &args)
  77         {
  78             this->is_dirty_ = true;
  79
  80             if (this->sign_ * args[sample] > this->threshold_)
  81             {
  82                 this->mu_ += args[weight] * args[sample];
  83                 this->sigma2_ += args[weight] * args[sample] * args[sample];
  84                 this->w_sum_ += args[weight];
  85             }
  86         }
  87
  88         template<typename Args>
  89         result_type result(Args const &args) const
  90         {
  91             if (this->is_dirty_)
  92             {
  93                 this->is_dirty_ = false;
  94
  95                 this->mu_ = this->sign_ * numeric::fdiv(this->mu_, this->w_sum_);
  96                 this->sigma2_ = numeric::fdiv(this->sigma2_, this->w_sum_);
  97                 this->sigma2_ -= this->mu_ * this->mu_;
  98
  99                 float_type threshold_probability = numeric::fdiv(sum_of_weights(args) - this->w_sum_, sum_of_weights(args));
 100
 101                 float_type tmp = numeric::fdiv(( this->mu_ - this->threshold_ )*( this->mu_ - this->threshold_ ), this->sigma2_);
 102                 float_type xi_hat = 0.5 * ( 1. - tmp );
 103                 float_type beta_hat = 0.5 * ( this->mu_ - this->threshold_ ) * ( 1. + tmp );
 104                 float_type beta_bar = beta_hat * std::pow(1. - threshold_probability, xi_hat);
 105                 float_type u_bar = this->threshold_ - beta_bar * ( std::pow(1. - threshold_probability, -xi_hat) - 1.)/xi_hat;
 106                 this->fit_parameters_ = boost::make_tuple(u_bar, beta_bar, xi_hat);
 107             }
 108
 109             return this->fit_parameters_;
 110         }
 111
 112     private:
 113         short sign_;                         // for left tail fitting, mirror the extreme values
 114         mutable float_type mu_;              // mean of samples above threshold
 115         mutable float_type sigma2_;          // variance of samples above threshold
 116         mutable float_type w_sum_;           // sum of weights of samples above threshold
 117         float_type threshold_;
 118         mutable result_type fit_parameters_; // boost::tuple that stores fit parameters
 119         mutable bool is_dirty_;
 120     };
 121
 122     ///////////////////////////////////////////////////////////////////////////////
 123     // weighted_peaks_over_threshold_prob_impl
 124     //  determines threshold from a given threshold probability using order statistics
 125     /**
 126         @brief Peaks over Threshold Method for Quantile and Tail Mean Estimation
 127
 128         @sa weighted_peaks_over_threshold_impl
 129
 130         @param quantile_probability
 131         @param pot_threshold_probability
 132     */
 133     template<typename Sample, typename Weight, typename LeftRight>
 134     struct weighted_peaks_over_threshold_prob_impl
 135       : accumulator_base
 136     {
 137         typedef typename numeric::functional::multiplies<Weight, Sample>::result_type weighted_sample;
 138         typedef typename numeric::functional::fdiv<weighted_sample, std::size_t>::result_type float_type;
 139         // for boost::result_of
 140         typedef boost::tuple<float_type, float_type, float_type> result_type;
 141
 142         template<typename Args>
 143         weighted_peaks_over_threshold_prob_impl(Args const &args)
 144           : sign_((is_same<LeftRight, left>::value) ? -1 : 1)
 145           , mu_(sign_ * numeric::fdiv(args[sample | Sample()], (std::size_t)1))
 146           , sigma2_(numeric::fdiv(args[sample | Sample()], (std::size_t)1))
 147           , threshold_probability_(args[pot_threshold_probability])
 148           , fit_parameters_(boost::make_tuple(0., 0., 0.))
 149           , is_dirty_(true)
 150         {
 151         }
 152
 153         void operator ()(dont_care)
 154         {
 155             this->is_dirty_ = true;
 156         }
 157
 158         template<typename Args>
 159         result_type result(Args const &args) const
 160         {
 161             if (this->is_dirty_)
 162             {
 163                 this->is_dirty_ = false;
 164
 165                 float_type threshold = sum_of_weights(args)
 166                              * ( ( is_same<LeftRight, left>::value ) ? this->threshold_probability_ : 1. - this->threshold_probability_ );
 167
 168                 std::size_t n = 0;
 169                 Weight sum = Weight(0);
 170
 171                 while (sum < threshold)
 172                 {
 173                     if (n < static_cast<std::size_t>(tail_weights(args).size()))
 174                     {
 175                         mu_ += *(tail_weights(args).begin() + n) * *(tail(args).begin() + n);
 176                         sigma2_ += *(tail_weights(args).begin() + n) * *(tail(args).begin() + n) * (*(tail(args).begin() + n));
 177                         sum += *(tail_weights(args).begin() + n);
 178                         n++;
 179                     }
 180                     else
 181                     {
 182                         if (std::numeric_limits<float_type>::has_quiet_NaN)
 183                         {
 184                             return boost::make_tuple(
 185                                 std::numeric_limits<float_type>::quiet_NaN()
 186                               , std::numeric_limits<float_type>::quiet_NaN()
 187                               , std::numeric_limits<float_type>::quiet_NaN()
 188                             );
 189                         }
 190                         else
 191                         {
 192                             std::ostringstream msg;
 193                             msg << "index n = " << n << " is not in valid range [0, " << tail(args).size() << ")";
 194                             boost::throw_exception(std::runtime_error(msg.str()));
 195                             return boost::make_tuple(Sample(0), Sample(0), Sample(0));
 196                         }
 197                     }
 198                 }
 199
 200                 float_type u = *(tail(args).begin() + n - 1) * this->sign_;
 201
 202
 203                 this->mu_ = this->sign_ * numeric::fdiv(this->mu_, sum);
 204                 this->sigma2_ = numeric::fdiv(this->sigma2_, sum);
 205                 this->sigma2_ -= this->mu_ * this->mu_;
 206
 207                 if (is_same<LeftRight, left>::value)
 208                     this->threshold_probability_ = 1. - this->threshold_probability_;
 209
 210                 float_type tmp = numeric::fdiv(( this->mu_ - u )*( this->mu_ - u ), this->sigma2_);
 211                 float_type xi_hat = 0.5 * ( 1. - tmp );
 212                 float_type beta_hat = 0.5 * ( this->mu_ - u ) * ( 1. + tmp );
 213                 float_type beta_bar = beta_hat * std::pow(1. - threshold_probability_, xi_hat);
 214                 float_type u_bar = u - beta_bar * ( std::pow(1. - threshold_probability_, -xi_hat) - 1.)/xi_hat;
 215                 this->fit_parameters_ = boost::make_tuple(u_bar, beta_bar, xi_hat);
 216
 217             }
 218
 219             return this->fit_parameters_;
 220         }
 221
 222     private:
 223         short sign_;                                // for left tail fitting, mirror the extreme values
 224         mutable float_type mu_;                     // mean of samples above threshold u
 225         mutable float_type sigma2_;                 // variance of samples above threshold u
 226         mutable float_type threshold_probability_;
 227         mutable result_type fit_parameters_;        // boost::tuple that stores fit parameters
 228         mutable bool is_dirty_;
 229     };
 230
 231 } // namespace impl
 232
 233 ///////////////////////////////////////////////////////////////////////////////
 234 // tag::weighted_peaks_over_threshold
 235 //
 236 namespace tag
 237 {
 238     template<typename LeftRight>
 239     struct weighted_peaks_over_threshold
 240       : depends_on<sum_of_weights>
 241       , pot_threshold_value
 242     {
 243         /// INTERNAL ONLY
 244         typedef accumulators::impl::weighted_peaks_over_threshold_impl<mpl::_1, mpl::_2, LeftRight> impl;
 245     };
 246
 247     template<typename LeftRight>
 248     struct weighted_peaks_over_threshold_prob
 249       : depends_on<sum_of_weights, tail_weights<LeftRight> >
 250       , pot_threshold_probability
 251     {
 252         /// INTERNAL ONLY
 253         typedef accumulators::impl::weighted_peaks_over_threshold_prob_impl<mpl::_1, mpl::_2, LeftRight> impl;
 254     };
 255 }
 256
 257 ///////////////////////////////////////////////////////////////////////////////
 258 // extract::weighted_peaks_over_threshold
 259 //
 260 namespace extract
 261 {
 262     extractor<tag::abstract_peaks_over_threshold> const weighted_peaks_over_threshold = {};
 263
 264     BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_peaks_over_threshold)
 265 }
 266
 267 using extract::weighted_peaks_over_threshold;
 268
 269 // weighted_peaks_over_threshold<LeftRight>(with_threshold_value) -> weighted_peaks_over_threshold<LeftRight>
 270 template<typename LeftRight>
 271 struct as_feature<tag::weighted_peaks_over_threshold<LeftRight>(with_threshold_value)>
 272 {
 273     typedef tag::weighted_peaks_over_threshold<LeftRight> type;
 274 };
 275
 276 // weighted_peaks_over_threshold<LeftRight>(with_threshold_probability) -> weighted_peaks_over_threshold_prob<LeftRight>
 277 template<typename LeftRight>
 278 struct as_feature<tag::weighted_peaks_over_threshold<LeftRight>(with_threshold_probability)>
 279 {
 280     typedef tag::weighted_peaks_over_threshold_prob<LeftRight> type;
 281 };
 282
 283 }} // namespace boost::accumulators
 284
 285 #ifdef _MSC_VER
 286 # pragma warning(pop)
 287 #endif
 288
 289 #endif