boost/accumulators/statistics/weighted_covariance.hpp

   1 ///////////////////////////////////////////////////////////////////////////////
   2 // weighted_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_WEIGHTED_COVARIANCE_HPP_DE_01_01_2006
   9 #define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_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/covariance.hpp> // for numeric::outer_product() and type traits
  32 #include <boost/accumulators/statistics/weighted_mean.hpp>
  33
  34 namespace boost { namespace accumulators
  35 {
  36
  37 namespace impl
  38 {
  39     ///////////////////////////////////////////////////////////////////////////////
  40     // weighted_covariance_impl
  41     //
  42     /**
  43         @brief Weighted Covariance Estimator
  44
  45         An iterative Monte Carlo estimator for the weighted covariance \f$\mathrm{Cov}(X,X')\f$, where \f$X\f$ is a sample
  46         and \f$X'\f$ a variate, is given by:
  47
  48         \f[
  49             \hat{c}_n = \frac{\bar{w}_n-w_n}{\bar{w}_n} \hat{c}_{n-1} + \frac{w_n}{\bar{w}_n-w_n}(X_n - \hat{\mu}_n)(X_n' - \hat{\mu}_n'),
  50             \quad n\ge2,\quad\hat{c}_1 = 0,
  51         \f]
  52
  53         \f$\hat{\mu}_n\f$ and \f$\hat{\mu}_n'\f$ being the weighted means of the samples and variates and
  54         \f$\bar{w}_n\f$ the sum of the \f$n\f$ first weights \f$w_i\f$.
  55     */
  56     template<typename Sample, typename Weight, typename VariateType, typename VariateTag>
  57     struct weighted_covariance_impl
  58       : accumulator_base
  59     {
  60         typedef typename numeric::functional::multiplies<Weight, typename numeric::functional::average<Sample, std::size_t>::result_type>::result_type weighted_sample_type;
  61         typedef typename numeric::functional::multiplies<Weight, typename numeric::functional::average<VariateType, std::size_t>::result_type>::result_type weighted_variate_type;
  62         // for boost::result_of
  63         typedef typename numeric::functional::outer_product<weighted_sample_type, weighted_variate_type>::result_type result_type;
  64
  65         template<typename Args>
  66         weighted_covariance_impl(Args const &args)
  67           : cov_(
  68                 numeric::outer_product(
  69                     numeric::average(args[sample | Sample()], (std::size_t)1)
  70                       * numeric::one<Weight>::value
  71                   , numeric::average(args[parameter::keyword<VariateTag>::get() | VariateType()], (std::size_t)1)
  72                       * numeric::one<Weight>::value
  73                 )
  74             )
  75         {
  76         }
  77
  78         template<typename Args>
  79         void operator ()(Args const &args)
  80         {
  81             std::size_t cnt = count(args);
  82
  83             if (cnt > 1)
  84             {
  85                 extractor<tag::weighted_mean_of_variates<VariateType, VariateTag> > const some_weighted_mean_of_variates = {};
  86
  87                 this->cov_ = this->cov_ * (sum_of_weights(args) - args[weight]) / sum_of_weights(args)
  88                            + numeric::outer_product(
  89                                  some_weighted_mean_of_variates(args) - args[parameter::keyword<VariateTag>::get()]
  90                                , weighted_mean(args) - args[sample]
  91                              ) * args[weight] / (sum_of_weights(args) - args[weight]);
  92             }
  93         }
  94
  95         result_type result(dont_care) const
  96         {
  97             return this->cov_;
  98         }
  99
 100     private:
 101         result_type cov_;
 102     };
 103
 104 } // namespace impl
 105
 106 ///////////////////////////////////////////////////////////////////////////////
 107 // tag::weighted_covariance
 108 //
 109 namespace tag
 110 {
 111     template<typename VariateType, typename VariateTag>
 112     struct weighted_covariance
 113       : depends_on<count, sum_of_weights, weighted_mean, weighted_mean_of_variates<VariateType, VariateTag> >
 114     {
 115         typedef accumulators::impl::weighted_covariance_impl<mpl::_1, mpl::_2, VariateType, VariateTag> impl;
 116     };
 117 }
 118
 119 ///////////////////////////////////////////////////////////////////////////////
 120 // extract::weighted_covariance
 121 //
 122 namespace extract
 123 {
 124     extractor<tag::abstract_covariance> const weighted_covariance = {};
 125 }
 126
 127 using extract::weighted_covariance;
 128
 129 }} // namespace boost::accumulators
 130
 131 #endif