boost/accumulators/statistics/covariance.hpp
/////////////////////////////////////////////////////////////////////////////// // covariance.hpp // // Copyright 2006 Daniel Egloff, Olivier Gygi. Distributed under the Boost // Software License, Version 1.0. (See accompanying file // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) #ifndef BOOST_ACCUMULATORS_STATISTICS_COVARIANCE_HPP_DE_01_01_2006 #define BOOST_ACCUMULATORS_STATISTICS_COVARIANCE_HPP_DE_01_01_2006 #include <vector> #include <limits> #include <numeric> #include <functional> #include <complex> #include <boost/mpl/assert.hpp> #include <boost/mpl/bool.hpp> #include <boost/range.hpp> #include <boost/parameter/keyword.hpp> #include <boost/mpl/placeholders.hpp> #include <boost/numeric/ublas/io.hpp> #include <boost/numeric/ublas/matrix.hpp> #include <boost/type_traits/is_scalar.hpp> #include <boost/type_traits/is_same.hpp> #include <boost/accumulators/framework/accumulator_base.hpp> #include <boost/accumulators/framework/extractor.hpp> #include <boost/accumulators/numeric/functional.hpp> #include <boost/accumulators/framework/parameters/sample.hpp> #include <boost/accumulators/statistics_fwd.hpp> #include <boost/accumulators/statistics/count.hpp> #include <boost/accumulators/statistics/mean.hpp> namespace boost { namespace numeric { namespace functional { struct std_vector_tag; /////////////////////////////////////////////////////////////////////////////// // functional::outer_product template<typename Left, typename Right, typename EnableIf = void> struct outer_product_base : functional::multiplies<Left, Right> {}; template<typename Left, typename Right, typename LeftTag = typename tag<Left>::type, typename RightTag = typename tag<Right>::type> struct outer_product : outer_product_base<Left, Right, void> {}; template<typename Left, typename Right> struct outer_product<Left, Right, std_vector_tag, std_vector_tag> : std::binary_function< Left , Right , ublas::matrix< typename functional::multiplies< typename Left::value_type , typename Right::value_type >::result_type > > { typedef ublas::matrix< typename functional::multiplies< typename Left::value_type , typename Right::value_type >::result_type > result_type; result_type operator ()(Left & left, Right & right) const { std::size_t left_size = left.size(); std::size_t right_size = right.size(); result_type result(left_size, right_size); for (std::size_t i = 0; i < left_size; ++i) for (std::size_t j = 0; j < right_size; ++j) result(i,j) = numeric::multiplies(left[i], right[j]); return result; } }; } namespace op { struct outer_product : boost::detail::function2<functional::outer_product<_1, _2, functional::tag<_1>, functional::tag<_2> > > {}; } namespace { op::outer_product const &outer_product = boost::detail::pod_singleton<op::outer_product>::instance; } }} namespace boost { namespace accumulators { namespace impl { /////////////////////////////////////////////////////////////////////////////// // covariance_impl // /** @brief Covariance Estimator An iterative Monte Carlo estimator for the covariance \f$\mathrm{Cov}(X,X')\f$, where \f$X\f$ is a sample and \f$X'\f$ is a variate, is given by: \f[ \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, \f] \f$\hat{\mu}_n\f$ and \f$\hat{\mu}_n'\f$ being the means of the samples and variates. */ template<typename Sample, typename VariateType, typename VariateTag> struct covariance_impl : accumulator_base { typedef typename numeric::functional::average<Sample, std::size_t>::result_type sample_type; typedef typename numeric::functional::average<VariateType, std::size_t>::result_type variate_type; // for boost::result_of typedef typename numeric::functional::outer_product<sample_type, variate_type>::result_type result_type; template<typename Args> covariance_impl(Args const &args) : cov_( numeric::outer_product( numeric::average(args[sample | Sample()], (std::size_t)1) , numeric::average(args[parameter::keyword<VariateTag>::get() | VariateType()], (std::size_t)1) ) ) { } template<typename Args> void operator ()(Args const &args) { std::size_t cnt = count(args); if (cnt > 1) { extractor<tag::mean_of_variates<VariateType, VariateTag> > const some_mean_of_variates = {}; this->cov_ = this->cov_*(cnt-1.)/cnt + numeric::outer_product( some_mean_of_variates(args) - args[parameter::keyword<VariateTag>::get()] , mean(args) - args[sample] ) / (cnt-1.); } } result_type result(dont_care) const { return this->cov_; } private: result_type cov_; }; } // namespace impl /////////////////////////////////////////////////////////////////////////////// // tag::covariance // namespace tag { template<typename VariateType, typename VariateTag> struct covariance : depends_on<count, mean, mean_of_variates<VariateType, VariateTag> > { typedef accumulators::impl::covariance_impl<mpl::_1, VariateType, VariateTag> impl; }; struct abstract_covariance : depends_on<> { }; } /////////////////////////////////////////////////////////////////////////////// // extract::covariance // namespace extract { extractor<tag::abstract_covariance> const covariance = {}; BOOST_ACCUMULATORS_IGNORE_GLOBAL(covariance) } using extract::covariance; template<typename VariateType, typename VariateTag> struct feature_of<tag::covariance<VariateType, VariateTag> > : feature_of<tag::abstract_covariance> { }; // So that covariance can be automatically substituted with // weighted_covariance when the weight parameter is non-void. template<typename VariateType, typename VariateTag> struct as_weighted_feature<tag::covariance<VariateType, VariateTag> > { typedef tag::weighted_covariance<VariateType, VariateTag> type; }; template<typename VariateType, typename VariateTag> struct feature_of<tag::weighted_covariance<VariateType, VariateTag> > : feature_of<tag::covariance<VariateType, VariateTag> > {}; }} // namespace boost::accumulators #endif