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
34namespace boost { namespace accumulators
35{
36
37namespace 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>
66 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>
79 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
95 result_type result(dont_care) const
96 {
97 return this->cov_;
98 }
99
100 // make this accumulator serializeable
101 template<class Archive>
102 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//
116namespace 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//
129namespace extract
130{
131 extractor<tag::abstract_covariance> const weighted_covariance = {};
132
133 BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_covariance)
134}
135
136using extract::weighted_covariance;
137
138}} // namespace boost::accumulators
139
140#endif
141

source code of boost/libs/accumulators/include/boost/accumulators/statistics/weighted_covariance.hpp