| /////////////////////////////////////////////////////////////////////////////// |
| // 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 |