1 /////////////////////////////////////////////////////////////////////////////// 2 // weighted_covariance.hpp 3 // 4 // Copyright 2006 Daniel Egloff, Olivier Gygi. 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_COVARIANCE_HPP_DE_01_01_2006 9 #define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_COVARIANCE_HPP_DE_01_01_2006 10 11 #include <vector> 12 #include <limits> 13 #include <numeric> 14 #include <functional> 15 #include <complex> 16 #include <boost/mpl/assert.hpp> 17 #include <boost/mpl/bool.hpp> 18 #include <boost/range.hpp> 19 #include <boost/parameter/keyword.hpp> 20 #include <boost/mpl/placeholders.hpp> 21 #include <boost/numeric/ublas/io.hpp> 22 #include <boost/numeric/ublas/matrix.hpp> 23 #include <boost/type_traits/is_scalar.hpp> 24 #include <boost/type_traits/is_same.hpp> 25 #include <boost/accumulators/framework/accumulator_base.hpp> 26 #include <boost/accumulators/framework/extractor.hpp> 27 #include <boost/accumulators/numeric/functional.hpp> 28 #include <boost/accumulators/framework/parameters/sample.hpp> 29 #include <boost/accumulators/statistics_fwd.hpp> 30 #include <boost/accumulators/statistics/count.hpp> 31 #include <boost/accumulators/statistics/covariance.hpp> // for numeric::outer_product() and type traits 32 #include <boost/accumulators/statistics/weighted_mean.hpp> 33 34 namespace boost { namespace accumulators 35 { 36 37 namespace impl 38 { 39 /////////////////////////////////////////////////////////////////////////////// 40 // weighted_covariance_impl 41 // 42 /** 43 @brief Weighted Covariance Estimator 44 45 An iterative Monte Carlo estimator for the weighted covariance \f$\mathrm{Cov}(X,X')\f$, where \f$X\f$ is a sample 46 and \f$X'\f$ a variate, is given by: 47 48 \f[ 49 \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'), 50 \quad n\ge2,\quad\hat{c}_1 = 0, 51 \f] 52 53 \f$\hat{\mu}_n\f$ and \f$\hat{\mu}_n'\f$ being the weighted means of the samples and variates and 54 \f$\bar{w}_n\f$ the sum of the \f$n\f$ first weights \f$w_i\f$. 55 */ 56 template<typename Sample, typename Weight, typename VariateType, typename VariateTag> 57 struct weighted_covariance_impl 58 : accumulator_base 59 { 60 typedef typename numeric::functional::multiplies<Weight, typename numeric::functional::fdiv<Sample, std::size_t>::result_type>::result_type weighted_sample_type; 61 typedef typename numeric::functional::multiplies<Weight, typename numeric::functional::fdiv<VariateType, std::size_t>::result_type>::result_type weighted_variate_type; 62 // for boost::result_of 63 typedef typename numeric::functional::outer_product<weighted_sample_type, weighted_variate_type>::result_type result_type; 64 65 template<typename Args> weighted_covariance_implboost::accumulators::impl::weighted_covariance_impl66 weighted_covariance_impl(Args const &args) 67 : cov_( 68 numeric::outer_product( 69 numeric::fdiv(args[sample | Sample()], (std::size_t)1) 70 * numeric::one<Weight>::value 71 , numeric::fdiv(args[parameter::keyword<VariateTag>::get() | VariateType()], (std::size_t)1) 72 * numeric::one<Weight>::value 73 ) 74 ) 75 { 76 } 77 78 template<typename Args> operator ()boost::accumulators::impl::weighted_covariance_impl79 void operator ()(Args const &args) 80 { 81 std::size_t cnt = count(args); 82 83 if (cnt > 1) 84 { 85 extractor<tag::weighted_mean_of_variates<VariateType, VariateTag> > const some_weighted_mean_of_variates = {}; 86 87 this->cov_ = this->cov_ * (sum_of_weights(args) - args[weight]) / sum_of_weights(args) 88 + numeric::outer_product( 89 some_weighted_mean_of_variates(args) - args[parameter::keyword<VariateTag>::get()] 90 , weighted_mean(args) - args[sample] 91 ) * args[weight] / (sum_of_weights(args) - args[weight]); 92 } 93 } 94 resultboost::accumulators::impl::weighted_covariance_impl95 result_type result(dont_care) const 96 { 97 return this->cov_; 98 } 99 100 // make this accumulator serializeable 101 template<class Archive> serializeboost::accumulators::impl::weighted_covariance_impl102 void serialize(Archive & ar, const unsigned int file_version) 103 { 104 ar & cov_; 105 } 106 107 private: 108 result_type cov_; 109 }; 110 111 } // namespace impl 112 113 /////////////////////////////////////////////////////////////////////////////// 114 // tag::weighted_covariance 115 // 116 namespace tag 117 { 118 template<typename VariateType, typename VariateTag> 119 struct weighted_covariance 120 : depends_on<count, sum_of_weights, weighted_mean, weighted_mean_of_variates<VariateType, VariateTag> > 121 { 122 typedef accumulators::impl::weighted_covariance_impl<mpl::_1, mpl::_2, VariateType, VariateTag> impl; 123 }; 124 } 125 126 /////////////////////////////////////////////////////////////////////////////// 127 // extract::weighted_covariance 128 // 129 namespace extract 130 { 131 extractor<tag::abstract_covariance> const weighted_covariance = {}; 132 133 BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_covariance) 134 } 135 136 using extract::weighted_covariance; 137 138 }} // namespace boost::accumulators 139 140 #endif 141