boost/accumulators/statistics/weighted_variance.hpp

   1 ///////////////////////////////////////////////////////////////////////////////
   2 // weighted_variance.hpp
   3 //
   4 //  Copyright 2005 Daniel Egloff, Eric Niebler. 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_VARIANCE_HPP_EAN_28_10_2005
   9 #define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_VARIANCE_HPP_EAN_28_10_2005
  10
  11 #include <boost/mpl/placeholders.hpp>
  12 #include <boost/accumulators/framework/accumulator_base.hpp>
  13 #include <boost/accumulators/framework/extractor.hpp>
  14 #include <boost/accumulators/numeric/functional.hpp>
  15 #include <boost/accumulators/framework/parameters/sample.hpp>
  16 #include <boost/accumulators/framework/depends_on.hpp>
  17 #include <boost/accumulators/statistics_fwd.hpp>
  18 #include <boost/accumulators/statistics/count.hpp>
  19 #include <boost/accumulators/statistics/variance.hpp>
  20 #include <boost/accumulators/statistics/weighted_sum.hpp>
  21 #include <boost/accumulators/statistics/weighted_mean.hpp>
  22 #include <boost/accumulators/statistics/weighted_moment.hpp>
  23
  24 namespace boost { namespace accumulators
  25 {
  26
  27 namespace impl
  28 {
  29     //! Lazy calculation of variance of weighted samples.
  30     /*!
  31         The default implementation of the variance of weighted samples is based on the second moment
  32         \f$\widehat{m}_n^{(2)}\f$ (weighted_moment<2>) and the mean\f$ \hat{\mu}_n\f$ (weighted_mean):
  33         \f[
  34             \hat{\sigma}_n^2 = \widehat{m}_n^{(2)}-\hat{\mu}_n^2,
  35         \f]
  36         where \f$n\f$ is the number of samples.
  37     */
  38     template<typename Sample, typename Weight, typename MeanFeature>
  39     struct lazy_weighted_variance_impl
  40       : accumulator_base
  41     {
  42         typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample;
  43         // for boost::result_of
  44         typedef typename numeric::functional::average<weighted_sample, Weight>::result_type result_type;
  45
  46         lazy_weighted_variance_impl(dont_care) {}
  47
  48         template<typename Args>
  49         result_type result(Args const &args) const
  50         {
  51             extractor<MeanFeature> const some_mean = {};
  52             result_type tmp = some_mean(args);
  53             return weighted_moment<2>(args) - tmp * tmp;
  54         }
  55     };
  56
  57     //! Iterative calculation of variance of weighted samples.
  58     /*!
  59         Iterative calculation of variance of weighted samples:
  60         \f[
  61             \hat{\sigma}_n^2 =
  62                 \frac{\bar{w}_n - w_n}{\bar{w}_n}\hat{\sigma}_{n - 1}^2
  63               + \frac{w_n}{\bar{w}_n - w_n}\left(X_n - \hat{\mu}_n\right)^2
  64             ,\quad n\ge2,\quad\hat{\sigma}_0^2 = 0.
  65         \f]
  66         where \f$\bar{w}_n\f$ is the sum of the \f$n\f$ weights \f$w_i\f$ and \f$\hat{\mu}_n\f$
  67         the estimate of the mean of the weighted smaples. Note that the sample variance is not defined for
  68         \f$n <= 1\f$.
  69     */
  70     template<typename Sample, typename Weight, typename MeanFeature, typename Tag>
  71     struct weighted_variance_impl
  72       : accumulator_base
  73     {
  74         typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample;
  75         // for boost::result_of
  76         typedef typename numeric::functional::average<weighted_sample, Weight>::result_type result_type;
  77
  78         template<typename Args>
  79         weighted_variance_impl(Args const &args)
  80           : weighted_variance(numeric::average(args[sample | Sample()], numeric::one<Weight>::value))
  81         {
  82         }
  83
  84         template<typename Args>
  85         void operator ()(Args const &args)
  86         {
  87             std::size_t cnt = count(args);
  88
  89             if(cnt > 1)
  90             {
  91                 extractor<MeanFeature> const some_mean = {};
  92
  93                 result_type tmp = args[parameter::keyword<Tag>::get()] - some_mean(args);
  94
  95                 this->weighted_variance =
  96                     numeric::average(this->weighted_variance * (sum_of_weights(args) - args[weight]), sum_of_weights(args))
  97                   + numeric::average(tmp * tmp * args[weight], sum_of_weights(args) - args[weight] );
  98             }
  99         }
 100
 101         result_type result(dont_care) const
 102         {
 103             return this->weighted_variance;
 104         }
 105
 106     private:
 107         result_type weighted_variance;
 108     };
 109
 110 } // namespace impl
 111
 112 ///////////////////////////////////////////////////////////////////////////////
 113 // tag::weighted_variance
 114 // tag::immediate_weighted_variance
 115 //
 116 namespace tag
 117 {
 118     struct lazy_weighted_variance
 119       : depends_on<weighted_moment<2>, weighted_mean>
 120     {
 121         /// INTERNAL ONLY
 122         ///
 123         typedef accumulators::impl::lazy_weighted_variance_impl<mpl::_1, mpl::_2, weighted_mean> impl;
 124     };
 125
 126     struct weighted_variance
 127       : depends_on<count, immediate_weighted_mean>
 128     {
 129         /// INTERNAL ONLY
 130         ///
 131         typedef accumulators::impl::weighted_variance_impl<mpl::_1, mpl::_2, immediate_weighted_mean, sample> impl;
 132     };
 133 }
 134
 135 ///////////////////////////////////////////////////////////////////////////////
 136 // extract::weighted_variance
 137 // extract::immediate_weighted_variance
 138 //
 139 namespace extract
 140 {
 141     extractor<tag::lazy_weighted_variance> const lazy_weighted_variance = {};
 142     extractor<tag::weighted_variance> const weighted_variance = {};
 143 }
 144
 145 using extract::lazy_weighted_variance;
 146 using extract::weighted_variance;
 147
 148 // weighted_variance(lazy) -> lazy_weighted_variance
 149 template<>
 150 struct as_feature<tag::weighted_variance(lazy)>
 151 {
 152     typedef tag::lazy_weighted_variance type;
 153 };
 154
 155 // weighted_variance(immediate) -> weighted_variance
 156 template<>
 157 struct as_feature<tag::weighted_variance(immediate)>
 158 {
 159     typedef tag::weighted_variance type;
 160 };
 161
 162 ////////////////////////////////////////////////////////////////////////////
 163 //// droppable_accumulator<weighted_variance_impl>
 164 ////  need to specialize droppable lazy weighted_variance to cache the result at the
 165 ////  point the accumulator is dropped.
 166 ///// INTERNAL ONLY
 167 /////
 168 //template<typename Sample, typename Weight, typename MeanFeature>
 169 //struct droppable_accumulator<impl::weighted_variance_impl<Sample, Weight, MeanFeature> >
 170 //  : droppable_accumulator_base<
 171 //        with_cached_result<impl::weighted_variance_impl<Sample, Weight, MeanFeature> >
 172 //    >
 173 //{
 174 //    template<typename Args>
 175 //    droppable_accumulator(Args const &args)
 176 //      : droppable_accumulator::base(args)
 177 //    {
 178 //    }
 179 //};
 180
 181 }} // namespace boost::accumulators
 182
 183 #endif