Chris@16: ///////////////////////////////////////////////////////////////////////////////
Chris@16: // 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_COVARIANCE_HPP_DE_01_01_2006
Chris@16: #define BOOST_ACCUMULATORS_STATISTICS_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/mean.hpp>
Chris@16: 
Chris@16: namespace boost { namespace numeric
Chris@16: {
Chris@16:     namespace functional
Chris@16:     {
Chris@16:         struct std_vector_tag;
Chris@16: 
Chris@16:         ///////////////////////////////////////////////////////////////////////////////
Chris@16:         // functional::outer_product
Chris@16:         template<typename Left, typename Right, typename EnableIf = void>
Chris@16:         struct outer_product_base
Chris@16:           : functional::multiplies<Left, Right>
Chris@16:         {};
Chris@16: 
Chris@16:         template<typename Left, typename Right, typename LeftTag = typename tag<Left>::type, typename RightTag = typename tag<Right>::type>
Chris@16:         struct outer_product
Chris@16:           : outer_product_base<Left, Right, void>
Chris@16:         {};
Chris@16: 
Chris@16:         template<typename Left, typename Right>
Chris@16:         struct outer_product<Left, Right, std_vector_tag, std_vector_tag>
Chris@16:           : std::binary_function<
Chris@16:                 Left
Chris@16:               , Right
Chris@16:               , ublas::matrix<
Chris@16:                     typename functional::multiplies<
Chris@16:                         typename Left::value_type
Chris@16:                       , typename Right::value_type
Chris@16:                     >::result_type
Chris@16:                 >
Chris@16:             >
Chris@16:         {
Chris@16:             typedef
Chris@16:                 ublas::matrix<
Chris@16:                     typename functional::multiplies<
Chris@16:                         typename Left::value_type
Chris@16:                       , typename Right::value_type
Chris@16:                     >::result_type
Chris@16:                 >
Chris@16:             result_type;
Chris@16: 
Chris@16:             result_type
Chris@16:             operator ()(Left & left, Right & right) const
Chris@16:             {
Chris@16:                 std::size_t left_size = left.size();
Chris@16:                 std::size_t right_size = right.size();
Chris@16:                 result_type result(left_size, right_size);
Chris@16:                 for (std::size_t i = 0; i < left_size; ++i)
Chris@16:                     for (std::size_t j = 0; j < right_size; ++j)
Chris@16:                         result(i,j) = numeric::multiplies(left[i], right[j]);
Chris@16:                 return result;
Chris@16:             }
Chris@16:         };
Chris@16:     }
Chris@16: 
Chris@16:     namespace op
Chris@16:     {
Chris@16:         struct outer_product
Chris@16:           : boost::detail::function2<functional::outer_product<_1, _2, functional::tag<_1>, functional::tag<_2> > >
Chris@16:         {};
Chris@16:     }
Chris@16: 
Chris@16:     namespace
Chris@16:     {
Chris@16:         op::outer_product const &outer_product = boost::detail::pod_singleton<op::outer_product>::instance;
Chris@16:     }
Chris@16: 
Chris@16: }}
Chris@16: 
Chris@16: namespace boost { namespace accumulators
Chris@16: {
Chris@16: 
Chris@16: namespace impl
Chris@16: {
Chris@16:     ///////////////////////////////////////////////////////////////////////////////
Chris@16:     // covariance_impl
Chris@16:     //
Chris@16:     /**
Chris@16:         @brief Covariance Estimator
Chris@16: 
Chris@16:         An iterative Monte Carlo estimator for the covariance \f$\mathrm{Cov}(X,X')\f$, where \f$X\f$ is a sample
Chris@16:         and \f$X'\f$ is a variate, is given by:
Chris@16: 
Chris@16:         \f[
Chris@16:             \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,
Chris@16:         \f]
Chris@16: 
Chris@16:         \f$\hat{\mu}_n\f$ and \f$\hat{\mu}_n'\f$ being the means of the samples and variates.
Chris@16:     */
Chris@16:     template<typename Sample, typename VariateType, typename VariateTag>
Chris@16:     struct covariance_impl
Chris@16:       : accumulator_base
Chris@16:     {
Chris@16:         typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type sample_type;
Chris@16:         typedef typename numeric::functional::fdiv<VariateType, std::size_t>::result_type variate_type;
Chris@16:         // for boost::result_of
Chris@16:         typedef typename numeric::functional::outer_product<sample_type, variate_type>::result_type result_type;
Chris@16: 
Chris@16:         template<typename Args>
Chris@16:         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::fdiv(args[parameter::keyword<VariateTag>::get() | VariateType()], (std::size_t)1)
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::mean_of_variates<VariateType, VariateTag> > const some_mean_of_variates = {};
Chris@16: 
Chris@16:                 this->cov_ = this->cov_*(cnt-1.)/cnt
Chris@16:                            + numeric::outer_product(
Chris@16:                                  some_mean_of_variates(args) - args[parameter::keyword<VariateTag>::get()]
Chris@16:                                , mean(args) - args[sample]
Chris@16:                              ) / (cnt-1.);
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::covariance
Chris@16: //
Chris@16: namespace tag
Chris@16: {
Chris@16:     template<typename VariateType, typename VariateTag>
Chris@16:     struct covariance
Chris@16:       : depends_on<count, mean, mean_of_variates<VariateType, VariateTag> >
Chris@16:     {
Chris@16:         typedef accumulators::impl::covariance_impl<mpl::_1, VariateType, VariateTag> impl;
Chris@16:     };
Chris@16: 
Chris@16:     struct abstract_covariance
Chris@16:       : depends_on<>
Chris@16:     {
Chris@16:     };
Chris@16: }
Chris@16: 
Chris@16: ///////////////////////////////////////////////////////////////////////////////
Chris@16: // extract::covariance
Chris@16: //
Chris@16: namespace extract
Chris@16: {
Chris@16:     extractor<tag::abstract_covariance> const covariance = {};
Chris@16: 
Chris@16:     BOOST_ACCUMULATORS_IGNORE_GLOBAL(covariance)
Chris@16: }
Chris@16: 
Chris@16: using extract::covariance;
Chris@16: 
Chris@16: template<typename VariateType, typename VariateTag>
Chris@16: struct feature_of<tag::covariance<VariateType, VariateTag> >
Chris@16:   : feature_of<tag::abstract_covariance>
Chris@16: {
Chris@16: };
Chris@16: 
Chris@16: // So that covariance can be automatically substituted with
Chris@16: // weighted_covariance when the weight parameter is non-void.
Chris@16: template<typename VariateType, typename VariateTag>
Chris@16: struct as_weighted_feature<tag::covariance<VariateType, VariateTag> >
Chris@16: {
Chris@16:     typedef tag::weighted_covariance<VariateType, VariateTag> type;
Chris@16: };
Chris@16: 
Chris@16: template<typename VariateType, typename VariateTag>
Chris@16: struct feature_of<tag::weighted_covariance<VariateType, VariateTag> >
Chris@16:   : feature_of<tag::covariance<VariateType, VariateTag> >
Chris@16: {};
Chris@16: 
Chris@16: }} // namespace boost::accumulators
Chris@16: 
Chris@16: #endif