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

   1 ///////////////////////////////////////////////////////////////////////////////
   2 // covariance.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_COVARIANCE_HPP_DE_01_01_2006
   9 #define BOOST_ACCUMULATORS_STATISTICS_COVARIANCE_HPP_DE_01_01_2006
  10
  11 #include <vector>
  12 #include <limits>
  13 #include <numeric>
  14 #include <functional>
  15 #include <complex>
  16 #include <boost/mpl/assert.hpp>
  17 #include <boost/mpl/bool.hpp>
  18 #include <boost/range.hpp>
  19 #include <boost/parameter/keyword.hpp>
  20 #include <boost/mpl/placeholders.hpp>
  21 #include <boost/numeric/ublas/io.hpp>
  22 #include <boost/numeric/ublas/matrix.hpp>
  23 #include <boost/type_traits/is_scalar.hpp>
  24 #include <boost/type_traits/is_same.hpp>
  25 #include <boost/accumulators/framework/accumulator_base.hpp>
  26 #include <boost/accumulators/framework/extractor.hpp>
  27 #include <boost/accumulators/numeric/functional.hpp>
  28 #include <boost/accumulators/framework/parameters/sample.hpp>
  29 #include <boost/accumulators/statistics_fwd.hpp>
  30 #include <boost/accumulators/statistics/count.hpp>
  31 #include <boost/accumulators/statistics/mean.hpp>
  32
  33 namespace boost { namespace numeric
  34 {
  35     namespace functional
  36     {
  37         struct std_vector_tag;
  38
  39         ///////////////////////////////////////////////////////////////////////////////
  40         // functional::outer_product
  41         template<typename Left, typename Right, typename EnableIf = void>
  42         struct outer_product_base
  43           : functional::multiplies<Left, Right>
  44         {};
  45
  46         template<typename Left, typename Right, typename LeftTag = typename tag<Left>::type, typename RightTag = typename tag<Right>::type>
  47         struct outer_product
  48           : outer_product_base<Left, Right, void>
  49         {};
  50
  51         template<typename Left, typename Right>
  52         struct outer_product<Left, Right, std_vector_tag, std_vector_tag>
  53         {
  54             typedef Left first_argument_type;
  55             typedef Right second_argument_type;
  56             typedef
  57                 ublas::matrix<
  58                     typename functional::multiplies<
  59                         typename Left::value_type
  60                       , typename Right::value_type
  61                     >::result_type
  62                 >
  63             result_type;
  64
  65             result_type
  66             operator ()(Left & left, Right & right) const
  67             {
  68                 std::size_t left_size = left.size();
  69                 std::size_t right_size = right.size();
  70                 result_type result(left_size, right_size);
  71                 for (std::size_t i = 0; i < left_size; ++i)
  72                     for (std::size_t j = 0; j < right_size; ++j)
  73                         result(i,j) = numeric::multiplies(left[i], right[j]);
  74                 return result;
  75             }
  76         };
  77     }
  78
  79     namespace op
  80     {
  81         struct outer_product
  82           : boost::detail::function2<functional::outer_product<_1, _2, functional::tag<_1>, functional::tag<_2> > >
  83         {};
  84     }
  85
  86     namespace
  87     {
  88         op::outer_product const &outer_product = boost::detail::pod_singleton<op::outer_product>::instance;
  89     }
  90
  91 }}
  92
  93 namespace boost { namespace accumulators
  94 {
  95
  96 namespace impl
  97 {
  98     ///////////////////////////////////////////////////////////////////////////////
  99     // covariance_impl
 100     //
 101     /**
 102         @brief Covariance Estimator
 103
 104         An iterative Monte Carlo estimator for the covariance \f$\mathrm{Cov}(X,X')\f$, where \f$X\f$ is a sample
 105         and \f$X'\f$ is a variate, is given by:
 106
 107         \f[
 108             \hat{c}_n = \frac{n-1}{n} \hat{c}_{n-1} + \frac{1}{n-1}(X_n - \hat{\mu}_n)(X_n' - \hat{\mu}_n'),\quad n\ge2,\quad\hat{c}_1 = 0,
 109         \f]
 110
 111         \f$\hat{\mu}_n\f$ and \f$\hat{\mu}_n'\f$ being the means of the samples and variates.
 112     */
 113     template<typename Sample, typename VariateType, typename VariateTag>
 114     struct covariance_impl
 115       : accumulator_base
 116     {
 117         typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type sample_type;
 118         typedef typename numeric::functional::fdiv<VariateType, std::size_t>::result_type variate_type;
 119         // for boost::result_of
 120         typedef typename numeric::functional::outer_product<sample_type, variate_type>::result_type result_type;
 121
 122         template<typename Args>
 123         covariance_impl(Args const &args)
 124           : cov_(
 125                 numeric::outer_product(
 126                     numeric::fdiv(args[sample | Sample()], (std::size_t)1)
 127                   , numeric::fdiv(args[parameter::keyword<VariateTag>::get() | VariateType()], (std::size_t)1)
 128                 )
 129             )
 130         {
 131         }
 132
 133         template<typename Args>
 134         void operator ()(Args const &args)
 135         {
 136             std::size_t cnt = count(args);
 137
 138             if (cnt > 1)
 139             {
 140                 extractor<tag::mean_of_variates<VariateType, VariateTag> > const some_mean_of_variates = {};
 141
 142                 this->cov_ = this->cov_*(cnt-1.)/cnt
 143                            + numeric::outer_product(
 144                                  some_mean_of_variates(args) - args[parameter::keyword<VariateTag>::get()]
 145                                , mean(args) - args[sample]
 146                              ) / (cnt-1.);
 147             }
 148         }
 149
 150         result_type result(dont_care) const
 151         {
 152             return this->cov_;
 153         }
 154
 155     private:
 156         result_type cov_;
 157     };
 158
 159 } // namespace impl
 160
 161 ///////////////////////////////////////////////////////////////////////////////
 162 // tag::covariance
 163 //
 164 namespace tag
 165 {
 166     template<typename VariateType, typename VariateTag>
 167     struct covariance
 168       : depends_on<count, mean, mean_of_variates<VariateType, VariateTag> >
 169     {
 170         typedef accumulators::impl::covariance_impl<mpl::_1, VariateType, VariateTag> impl;
 171     };
 172
 173     struct abstract_covariance
 174       : depends_on<>
 175     {
 176     };
 177 }
 178
 179 ///////////////////////////////////////////////////////////////////////////////
 180 // extract::covariance
 181 //
 182 namespace extract
 183 {
 184     extractor<tag::abstract_covariance> const covariance = {};
 185
 186     BOOST_ACCUMULATORS_IGNORE_GLOBAL(covariance)
 187 }
 188
 189 using extract::covariance;
 190
 191 template<typename VariateType, typename VariateTag>
 192 struct feature_of<tag::covariance<VariateType, VariateTag> >
 193   : feature_of<tag::abstract_covariance>
 194 {
 195 };
 196
 197 // So that covariance can be automatically substituted with
 198 // weighted_covariance when the weight parameter is non-void.
 199 template<typename VariateType, typename VariateTag>
 200 struct as_weighted_feature<tag::covariance<VariateType, VariateTag> >
 201 {
 202     typedef tag::weighted_covariance<VariateType, VariateTag> type;
 203 };
 204
 205 template<typename VariateType, typename VariateTag>
 206 struct feature_of<tag::weighted_covariance<VariateType, VariateTag> >
 207   : feature_of<tag::covariance<VariateType, VariateTag> >
 208 {};
 209
 210 }} // namespace boost::accumulators
 211
 212 #endif