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

   1 ///////////////////////////////////////////////////////////////////////////////
   2 // tail_variate_means.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_TAIL_VARIATE_MEANS_HPP_DE_01_01_2006
   9 #define BOOST_ACCUMULATORS_STATISTICS_TAIL_VARIATE_MEANS_HPP_DE_01_01_2006
  10
  11 #include <numeric>
  12 #include <vector>
  13 #include <limits>
  14 #include <functional>
  15 #include <sstream>
  16 #include <stdexcept>
  17 #include <boost/throw_exception.hpp>
  18 #include <boost/parameter/keyword.hpp>
  19 #include <boost/mpl/placeholders.hpp>
  20 #include <boost/type_traits/is_same.hpp>
  21 #include <boost/accumulators/framework/accumulator_base.hpp>
  22 #include <boost/accumulators/framework/extractor.hpp>
  23 #include <boost/accumulators/numeric/functional.hpp>
  24 #include <boost/accumulators/framework/parameters/sample.hpp>
  25 #include <boost/accumulators/statistics_fwd.hpp>
  26 #include <boost/accumulators/statistics/tail.hpp>
  27 #include <boost/accumulators/statistics/tail_variate.hpp>
  28 #include <boost/accumulators/statistics/tail_mean.hpp>
  29 #include <boost/accumulators/statistics/parameters/quantile_probability.hpp>
  30
  31 #ifdef _MSC_VER
  32 # pragma warning(push)
  33 # pragma warning(disable: 4127) // conditional expression is constant
  34 #endif
  35
  36 namespace boost { namespace accumulators
  37 {
  38
  39 namespace impl
  40 {
  41     /**
  42         @brief Estimation of the absolute and relative tail variate means (for both left and right tails)
  43
  44         For all \f$j\f$-th variates associated to the \f$\lceil n(1-\alpha)\rceil\f$ largest samples (or the
  45         \f$\lceil n(1-\alpha)\rceil\f$ smallest samples in case of the left tail), the absolute tail means
  46         \f$\widehat{ATM}_{n,\alpha}(X, j)\f$ are computed and returned as an iterator range. Alternatively,
  47         the relative tail means \f$\widehat{RTM}_{n,\alpha}(X, j)\f$ are returned, which are the absolute
  48         tail means normalized with the (non-coherent) sample tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$.
  49
  50         \f[
  51             \widehat{ATM}_{n,\alpha}^{\mathrm{right}}(X, j) =
  52                 \frac{1}{\lceil n(1-\alpha) \rceil}
  53                 \sum_{i=\lceil \alpha n \rceil}^n \xi_{j,i}
  54         \f]
  55
  56         \f[
  57             \widehat{ATM}_{n,\alpha}^{\mathrm{left}}(X, j) =
  58                 \frac{1}{\lceil n\alpha \rceil}
  59                 \sum_{i=1}^{\lceil n\alpha \rceil} \xi_{j,i}
  60         \f]
  61
  62         \f[
  63             \widehat{RTM}_{n,\alpha}^{\mathrm{right}}(X, j) =
  64                 \frac{\sum_{i=\lceil n\alpha \rceil}^n \xi_{j,i}}
  65             {\lceil n(1-\alpha)\rceil\widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X)}
  66         \f]
  67
  68         \f[
  69             \widehat{RTM}_{n,\alpha}^{\mathrm{left}}(X, j) =
  70                 \frac{\sum_{i=1}^{\lceil n\alpha \rceil} \xi_{j,i}}
  71             {\lceil n\alpha\rceil\widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X)}
  72         \f]
  73     */
  74
  75     ///////////////////////////////////////////////////////////////////////////////
  76     // tail_variate_means_impl
  77     //  by default: absolute tail_variate_means
  78     template<typename Sample, typename Impl, typename LeftRight, typename VariateTag>
  79     struct tail_variate_means_impl
  80       : accumulator_base
  81     {
  82         typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type;
  83         typedef std::vector<float_type> array_type;
  84         // for boost::result_of
  85         typedef iterator_range<typename array_type::iterator> result_type;
  86
  87         tail_variate_means_impl(dont_care) {}
  88
  89         template<typename Args>
  90         result_type result(Args const &args) const
  91         {
  92             std::size_t cnt = count(args);
  93
  94             std::size_t n = static_cast<std::size_t>(
  95                 std::ceil(
  96                     cnt * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] )
  97                 )
  98             );
  99
 100             std::size_t num_variates = tail_variate(args).begin()->size();
 101
 102             this->tail_means_.clear();
 103             this->tail_means_.resize(num_variates, Sample(0));
 104
 105             // If n is in a valid range, return result, otherwise return NaN or throw exception
 106             if (n < static_cast<std::size_t>(tail(args).size()))
 107             {
 108                 this->tail_means_ = std::accumulate(
 109                     tail_variate(args).begin()
 110                   , tail_variate(args).begin() + n
 111                   , this->tail_means_
 112                   , numeric::plus
 113                 );
 114
 115                 float_type factor = n * ( (is_same<Impl, relative>::value) ? non_coherent_tail_mean(args) : 1. );
 116
 117                 std::transform(
 118                     this->tail_means_.begin()
 119                   , this->tail_means_.end()
 120                   , this->tail_means_.begin()
 121 #ifdef BOOST_NO_CXX98_BINDERS
 122                   , std::bind(std::divides<float_type>(), std::placeholders::_1, factor)
 123 #else
 124                   , std::bind2nd(std::divides<float_type>(), factor)
 125 #endif
 126                 );
 127             }
 128             else
 129             {
 130                 if (std::numeric_limits<float_type>::has_quiet_NaN)
 131                 {
 132                     std::fill(
 133                         this->tail_means_.begin()
 134                       , this->tail_means_.end()
 135                       , std::numeric_limits<float_type>::quiet_NaN()
 136                     );
 137                 }
 138                 else
 139                 {
 140                     std::ostringstream msg;
 141                     msg << "index n = " << n << " is not in valid range [0, " << tail(args).size() << ")";
 142                     boost::throw_exception(std::runtime_error(msg.str()));
 143                 }
 144             }
 145             return make_iterator_range(this->tail_means_);
 146         }
 147
 148     private:
 149
 150         mutable array_type tail_means_;
 151
 152     };
 153
 154 } // namespace impl
 155
 156 ///////////////////////////////////////////////////////////////////////////////
 157 // tag::absolute_tail_variate_means
 158 // tag::relative_tail_variate_means
 159 //
 160 namespace tag
 161 {
 162     template<typename LeftRight, typename VariateType, typename VariateTag>
 163     struct absolute_tail_variate_means
 164       : depends_on<count, non_coherent_tail_mean<LeftRight>, tail_variate<VariateType, VariateTag, LeftRight> >
 165     {
 166         typedef accumulators::impl::tail_variate_means_impl<mpl::_1, absolute, LeftRight, VariateTag> impl;
 167     };
 168     template<typename LeftRight, typename VariateType, typename VariateTag>
 169     struct relative_tail_variate_means
 170       : depends_on<count, non_coherent_tail_mean<LeftRight>, tail_variate<VariateType, VariateTag, LeftRight> >
 171     {
 172         typedef accumulators::impl::tail_variate_means_impl<mpl::_1, relative, LeftRight, VariateTag> impl;
 173     };
 174     struct abstract_absolute_tail_variate_means
 175       : depends_on<>
 176     {
 177     };
 178     struct abstract_relative_tail_variate_means
 179       : depends_on<>
 180     {
 181     };
 182 }
 183
 184 ///////////////////////////////////////////////////////////////////////////////
 185 // extract::tail_variate_means
 186 // extract::relative_tail_variate_means
 187 //
 188 namespace extract
 189 {
 190     extractor<tag::abstract_absolute_tail_variate_means> const tail_variate_means = {};
 191     extractor<tag::abstract_relative_tail_variate_means> const relative_tail_variate_means = {};
 192
 193     BOOST_ACCUMULATORS_IGNORE_GLOBAL(tail_variate_means)
 194     BOOST_ACCUMULATORS_IGNORE_GLOBAL(relative_tail_variate_means)
 195 }
 196
 197 using extract::tail_variate_means;
 198 using extract::relative_tail_variate_means;
 199
 200 // tail_variate_means<LeftRight, VariateType, VariateTag>(absolute) -> absolute_tail_variate_means<LeftRight, VariateType, VariateTag>
 201 template<typename LeftRight, typename VariateType, typename VariateTag>
 202 struct as_feature<tag::tail_variate_means<LeftRight, VariateType, VariateTag>(absolute)>
 203 {
 204     typedef tag::absolute_tail_variate_means<LeftRight, VariateType, VariateTag> type;
 205 };
 206
 207 // tail_variate_means<LeftRight, VariateType, VariateTag>(relative) ->relative_tail_variate_means<LeftRight, VariateType, VariateTag>
 208 template<typename LeftRight, typename VariateType, typename VariateTag>
 209 struct as_feature<tag::tail_variate_means<LeftRight, VariateType, VariateTag>(relative)>
 210 {
 211     typedef tag::relative_tail_variate_means<LeftRight, VariateType, VariateTag> type;
 212 };
 213
 214 // Provides non-templatized extractor
 215 template<typename LeftRight, typename VariateType, typename VariateTag>
 216 struct feature_of<tag::absolute_tail_variate_means<LeftRight, VariateType, VariateTag> >
 217   : feature_of<tag::abstract_absolute_tail_variate_means>
 218 {
 219 };
 220
 221 // Provides non-templatized extractor
 222 template<typename LeftRight, typename VariateType, typename VariateTag>
 223 struct feature_of<tag::relative_tail_variate_means<LeftRight, VariateType, VariateTag> >
 224   : feature_of<tag::abstract_relative_tail_variate_means>
 225 {
 226 };
 227
 228 // So that absolute_tail_means can be automatically substituted
 229 // with absolute_weighted_tail_means when the weight parameter is non-void.
 230 template<typename LeftRight, typename VariateType, typename VariateTag>
 231 struct as_weighted_feature<tag::absolute_tail_variate_means<LeftRight, VariateType, VariateTag> >
 232 {
 233     typedef tag::absolute_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> type;
 234 };
 235
 236 template<typename LeftRight, typename VariateType, typename VariateTag>
 237 struct feature_of<tag::absolute_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> >
 238   : feature_of<tag::absolute_tail_variate_means<LeftRight, VariateType, VariateTag> >
 239 {
 240 };
 241
 242 // So that relative_tail_means can be automatically substituted
 243 // with relative_weighted_tail_means when the weight parameter is non-void.
 244 template<typename LeftRight, typename VariateType, typename VariateTag>
 245 struct as_weighted_feature<tag::relative_tail_variate_means<LeftRight, VariateType, VariateTag> >
 246 {
 247     typedef tag::relative_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> type;
 248 };
 249
 250 template<typename LeftRight, typename VariateType, typename VariateTag>
 251 struct feature_of<tag::relative_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> >
 252   : feature_of<tag::relative_tail_variate_means<LeftRight, VariateType, VariateTag> >
 253 {
 254 };
 255
 256 }} // namespace boost::accumulators
 257
 258 #ifdef _MSC_VER
 259 # pragma warning(pop)
 260 #endif
 261
 262 #endif