1///////////////////////////////////////////////////////////////////////////////
2// 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_COVARIANCE_HPP_DE_01_01_2006
9#define BOOST_ACCUMULATORS_STATISTICS_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/mean.hpp>
32
33namespace boost { namespace numeric
34{
35 namespace functional
36 {
37 struct std_vector_tag;
38
39 ///////////////////////////////////////////////////////////////////////////////
40 // functional::outer_product
41 template<typename Left, typename Right, typename EnableIf = void>
42 struct outer_product_base
43 : functional::multiplies<Left, Right>
44 {};
45
46 template<typename Left, typename Right, typename LeftTag = typename tag<Left>::type, typename RightTag = typename tag<Right>::type>
47 struct outer_product
48 : outer_product_base<Left, Right, void>
49 {};
50
51 template<typename Left, typename Right>
52 struct outer_product<Left, Right, std_vector_tag, std_vector_tag>
53 {
54 typedef Left first_argument_type;
55 typedef Right second_argument_type;
56 typedef
57 ublas::matrix<
58 typename functional::multiplies<
59 typename Left::value_type
60 , typename Right::value_type
61 >::result_type
62 >
63 result_type;
64
65 result_type
66 operator ()(Left & left, Right & right) const
67 {
68 std::size_t left_size = left.size();
69 std::size_t right_size = right.size();
70 result_type result(left_size, right_size);
71 for (std::size_t i = 0; i < left_size; ++i)
72 for (std::size_t j = 0; j < right_size; ++j)
73 result(i,j) = numeric::multiplies(left[i], right[j]);
74 return result;
75 }
76 };
77 }
78
79 namespace op
80 {
81 struct outer_product
82 : boost::detail::function2<functional::outer_product<_1, _2, functional::tag<_1>, functional::tag<_2> > >
83 {};
84 }
85
86 namespace
87 {
88 op::outer_product const &outer_product = boost::detail::pod_singleton<op::outer_product>::instance;
89 }
90
91}}
92
93namespace boost { namespace accumulators
94{
95
96namespace impl
97{
98 ///////////////////////////////////////////////////////////////////////////////
99 // covariance_impl
100 //
101 /**
102 @brief Covariance Estimator
103
104 An iterative Monte Carlo estimator for the covariance \f$\mathrm{Cov}(X,X')\f$, where \f$X\f$ is a sample
105 and \f$X'\f$ is a variate, is given by:
106
107 \f[
108 \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,
109 \f]
110
111 \f$\hat{\mu}_n\f$ and \f$\hat{\mu}_n'\f$ being the means of the samples and variates.
112 */
113 template<typename Sample, typename VariateType, typename VariateTag>
114 struct covariance_impl
115 : accumulator_base
116 {
117 typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type sample_type;
118 typedef typename numeric::functional::fdiv<VariateType, std::size_t>::result_type variate_type;
119 // for boost::result_of
120 typedef typename numeric::functional::outer_product<sample_type, variate_type>::result_type result_type;
121
122 template<typename Args>
123 covariance_impl(Args const &args)
124 : cov_(
125 numeric::outer_product(
126 numeric::fdiv(args[sample | Sample()], (std::size_t)1)
127 , numeric::fdiv(args[parameter::keyword<VariateTag>::get() | VariateType()], (std::size_t)1)
128 )
129 )
130 {
131 }
132
133 template<typename Args>
134 void operator ()(Args const &args)
135 {
136 std::size_t cnt = count(args);
137
138 if (cnt > 1)
139 {
140 extractor<tag::mean_of_variates<VariateType, VariateTag> > const some_mean_of_variates = {};
141
142 this->cov_ = this->cov_*(cnt-1.)/cnt
143 + numeric::outer_product(
144 some_mean_of_variates(args) - args[parameter::keyword<VariateTag>::get()]
145 , mean(args) - args[sample]
146 ) / (cnt-1.);
147 }
148 }
149
150 result_type result(dont_care) const
151 {
152 return this->cov_;
153 }
154
155 // make this accumulator serializeable
156 template<class Archive>
157 void serialize(Archive & ar, const unsigned int file_version)
158 {
159 ar & cov_;
160 }
161
162 private:
163 result_type cov_;
164 };
165
166} // namespace impl
167
168///////////////////////////////////////////////////////////////////////////////
169// tag::covariance
170//
171namespace tag
172{
173 template<typename VariateType, typename VariateTag>
174 struct covariance
175 : depends_on<count, mean, mean_of_variates<VariateType, VariateTag> >
176 {
177 typedef accumulators::impl::covariance_impl<mpl::_1, VariateType, VariateTag> impl;
178 };
179
180 struct abstract_covariance
181 : depends_on<>
182 {
183 };
184}
185
186///////////////////////////////////////////////////////////////////////////////
187// extract::covariance
188//
189namespace extract
190{
191 extractor<tag::abstract_covariance> const covariance = {};
192
193 BOOST_ACCUMULATORS_IGNORE_GLOBAL(covariance)
194}
195
196using extract::covariance;
197
198template<typename VariateType, typename VariateTag>
199struct feature_of<tag::covariance<VariateType, VariateTag> >
200 : feature_of<tag::abstract_covariance>
201{
202};
203
204// So that covariance can be automatically substituted with
205// weighted_covariance when the weight parameter is non-void.
206template<typename VariateType, typename VariateTag>
207struct as_weighted_feature<tag::covariance<VariateType, VariateTag> >
208{
209 typedef tag::weighted_covariance<VariateType, VariateTag> type;
210};
211
212template<typename VariateType, typename VariateTag>
213struct feature_of<tag::weighted_covariance<VariateType, VariateTag> >
214 : feature_of<tag::covariance<VariateType, VariateTag> >
215{};
216
217}} // namespace boost::accumulators
218
219#endif
220

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