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 
33 namespace 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
operator ()boost::numeric::functional::outer_product66             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 
93 namespace boost { namespace accumulators
94 {
95 
96 namespace 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>
covariance_implboost::accumulators::impl::covariance_impl123         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>
operator ()boost::accumulators::impl::covariance_impl134         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 
resultboost::accumulators::impl::covariance_impl150         result_type result(dont_care) const
151         {
152             return this->cov_;
153         }
154 
155         // make this accumulator serializeable
156         template<class Archive>
serializeboost::accumulators::impl::covariance_impl157         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 //
171 namespace 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 //
189 namespace extract
190 {
191     extractor<tag::abstract_covariance> const covariance = {};
192 
193     BOOST_ACCUMULATORS_IGNORE_GLOBAL(covariance)
194 }
195 
196 using extract::covariance;
197 
198 template<typename VariateType, typename VariateTag>
199 struct 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.
206 template<typename VariateType, typename VariateTag>
207 struct as_weighted_feature<tag::covariance<VariateType, VariateTag> >
208 {
209     typedef tag::weighted_covariance<VariateType, VariateTag> type;
210 };
211 
212 template<typename VariateType, typename VariateTag>
213 struct feature_of<tag::weighted_covariance<VariateType, VariateTag> >
214   : feature_of<tag::covariance<VariateType, VariateTag> >
215 {};
216 
217 }} // namespace boost::accumulators
218 
219 #endif
220