Chris@16: ///////////////////////////////////////////////////////////////////////////////
Chris@16: // weighted_covariance.hpp
Chris@16: //
Chris@16: //  Copyright 2006 Daniel Egloff, Olivier Gygi. Distributed under the Boost
Chris@16: //  Software License, Version 1.0. (See accompanying file
Chris@16: //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@16: 
Chris@16: #ifndef BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_COVARIANCE_HPP_DE_01_01_2006
Chris@16: #define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_COVARIANCE_HPP_DE_01_01_2006
Chris@16: 
Chris@16: #include <vector>
Chris@16: #include <limits>
Chris@16: #include <numeric>
Chris@16: #include <functional>
Chris@16: #include <complex>
Chris@16: #include <boost/mpl/assert.hpp>
Chris@16: #include <boost/mpl/bool.hpp>
Chris@16: #include <boost/range.hpp>
Chris@16: #include <boost/parameter/keyword.hpp>
Chris@16: #include <boost/mpl/placeholders.hpp>
Chris@16: #include <boost/numeric/ublas/io.hpp>
Chris@16: #include <boost/numeric/ublas/matrix.hpp>
Chris@16: #include <boost/type_traits/is_scalar.hpp>
Chris@16: #include <boost/type_traits/is_same.hpp>
Chris@16: #include <boost/accumulators/framework/accumulator_base.hpp>
Chris@16: #include <boost/accumulators/framework/extractor.hpp>
Chris@16: #include <boost/accumulators/numeric/functional.hpp>
Chris@16: #include <boost/accumulators/framework/parameters/sample.hpp>
Chris@16: #include <boost/accumulators/statistics_fwd.hpp>
Chris@16: #include <boost/accumulators/statistics/count.hpp>
Chris@16: #include <boost/accumulators/statistics/covariance.hpp> // for numeric::outer_product() and type traits
Chris@16: #include <boost/accumulators/statistics/weighted_mean.hpp>
Chris@16: 
Chris@16: namespace boost { namespace accumulators
Chris@16: {
Chris@16: 
Chris@16: namespace impl
Chris@16: {
Chris@16:     ///////////////////////////////////////////////////////////////////////////////
Chris@16:     // weighted_covariance_impl
Chris@16:     //
Chris@16:     /**
Chris@16:         @brief Weighted Covariance Estimator
Chris@16: 
Chris@16:         An iterative Monte Carlo estimator for the weighted covariance \f$\mathrm{Cov}(X,X')\f$, where \f$X\f$ is a sample
Chris@16:         and \f$X'\f$ a variate, is given by:
Chris@16: 
Chris@16:         \f[
Chris@16:             \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'),
Chris@16:             \quad n\ge2,\quad\hat{c}_1 = 0,
Chris@16:         \f]
Chris@16: 
Chris@16:         \f$\hat{\mu}_n\f$ and \f$\hat{\mu}_n'\f$ being the weighted means of the samples and variates and
Chris@16:         \f$\bar{w}_n\f$ the sum of the \f$n\f$ first weights \f$w_i\f$.
Chris@16:     */
Chris@16:     template<typename Sample, typename Weight, typename VariateType, typename VariateTag>
Chris@16:     struct weighted_covariance_impl
Chris@16:       : accumulator_base
Chris@16:     {
Chris@16:         typedef typename numeric::functional::multiplies<Weight, typename numeric::functional::fdiv<Sample, std::size_t>::result_type>::result_type weighted_sample_type;
Chris@16:         typedef typename numeric::functional::multiplies<Weight, typename numeric::functional::fdiv<VariateType, std::size_t>::result_type>::result_type weighted_variate_type;
Chris@16:         // for boost::result_of
Chris@16:         typedef typename numeric::functional::outer_product<weighted_sample_type, weighted_variate_type>::result_type result_type;
Chris@16: 
Chris@16:         template<typename Args>
Chris@16:         weighted_covariance_impl(Args const &args)
Chris@16:           : cov_(
Chris@16:                 numeric::outer_product(
Chris@16:                     numeric::fdiv(args[sample | Sample()], (std::size_t)1)
Chris@16:                       * numeric::one<Weight>::value
Chris@16:                   , numeric::fdiv(args[parameter::keyword<VariateTag>::get() | VariateType()], (std::size_t)1)
Chris@16:                       * numeric::one<Weight>::value
Chris@16:                 )
Chris@16:             )
Chris@16:         {
Chris@16:         }
Chris@16: 
Chris@16:         template<typename Args>
Chris@16:         void operator ()(Args const &args)
Chris@16:         {
Chris@16:             std::size_t cnt = count(args);
Chris@16: 
Chris@16:             if (cnt > 1)
Chris@16:             {
Chris@16:                 extractor<tag::weighted_mean_of_variates<VariateType, VariateTag> > const some_weighted_mean_of_variates = {};
Chris@16: 
Chris@16:                 this->cov_ = this->cov_ * (sum_of_weights(args) - args[weight]) / sum_of_weights(args)
Chris@16:                            + numeric::outer_product(
Chris@16:                                  some_weighted_mean_of_variates(args) - args[parameter::keyword<VariateTag>::get()]
Chris@16:                                , weighted_mean(args) - args[sample]
Chris@16:                              ) * args[weight] / (sum_of_weights(args) - args[weight]);
Chris@16:             }
Chris@16:         }
Chris@16: 
Chris@16:         result_type result(dont_care) const
Chris@16:         {
Chris@16:             return this->cov_;
Chris@16:         }
Chris@16: 
Chris@16:     private:
Chris@16:         result_type cov_;
Chris@16:     };
Chris@16: 
Chris@16: } // namespace impl
Chris@16: 
Chris@16: ///////////////////////////////////////////////////////////////////////////////
Chris@16: // tag::weighted_covariance
Chris@16: //
Chris@16: namespace tag
Chris@16: {
Chris@16:     template<typename VariateType, typename VariateTag>
Chris@16:     struct weighted_covariance
Chris@16:       : depends_on<count, sum_of_weights, weighted_mean, weighted_mean_of_variates<VariateType, VariateTag> >
Chris@16:     {
Chris@16:         typedef accumulators::impl::weighted_covariance_impl<mpl::_1, mpl::_2, VariateType, VariateTag> impl;
Chris@16:     };
Chris@16: }
Chris@16: 
Chris@16: ///////////////////////////////////////////////////////////////////////////////
Chris@16: // extract::weighted_covariance
Chris@16: //
Chris@16: namespace extract
Chris@16: {
Chris@16:     extractor<tag::abstract_covariance> const weighted_covariance = {};
Chris@16: 
Chris@16:     BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_covariance)
Chris@16: }
Chris@16: 
Chris@16: using extract::weighted_covariance;
Chris@16: 
Chris@16: }} // namespace boost::accumulators
Chris@16: 
Chris@16: #endif