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 | : std::binary_function< |
54 | Left |
55 | , Right |
56 | , ublas::matrix< |
57 | typename functional::multiplies< |
58 | typename Left::value_type |
59 | , typename Right::value_type |
60 | >::result_type |
61 | > |
62 | > |
63 | { |
64 | typedef |
65 | ublas::matrix< |
66 | typename functional::multiplies< |
67 | typename Left::value_type |
68 | , typename Right::value_type |
69 | >::result_type |
70 | > |
71 | result_type; |
72 | |
73 | result_type |
74 | operator ()(Left & left, Right & right) const |
75 | { |
76 | std::size_t left_size = left.size(); |
77 | std::size_t right_size = right.size(); |
78 | result_type result(left_size, right_size); |
79 | for (std::size_t i = 0; i < left_size; ++i) |
80 | for (std::size_t j = 0; j < right_size; ++j) |
81 | result(i,j) = numeric::multiplies(left[i], right[j]); |
82 | return result; |
83 | } |
84 | }; |
85 | } |
86 | |
87 | namespace op |
88 | { |
89 | struct outer_product |
90 | : boost::detail::function2<functional::outer_product<_1, _2, functional::tag<_1>, functional::tag<_2> > > |
91 | {}; |
92 | } |
93 | |
94 | namespace |
95 | { |
96 | op::outer_product const &outer_product = boost::detail::pod_singleton<op::outer_product>::instance; |
97 | } |
98 | |
99 | }} |
100 | |
101 | namespace boost { namespace accumulators |
102 | { |
103 | |
104 | namespace impl |
105 | { |
106 | /////////////////////////////////////////////////////////////////////////////// |
107 | // covariance_impl |
108 | // |
109 | /** |
110 | @brief Covariance Estimator |
111 | |
112 | An iterative Monte Carlo estimator for the covariance \f$\mathrm{Cov}(X,X')\f$, where \f$X\f$ is a sample |
113 | and \f$X'\f$ is a variate, is given by: |
114 | |
115 | \f[ |
116 | \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, |
117 | \f] |
118 | |
119 | \f$\hat{\mu}_n\f$ and \f$\hat{\mu}_n'\f$ being the means of the samples and variates. |
120 | */ |
121 | template<typename Sample, typename VariateType, typename VariateTag> |
122 | struct covariance_impl |
123 | : accumulator_base |
124 | { |
125 | typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type sample_type; |
126 | typedef typename numeric::functional::fdiv<VariateType, std::size_t>::result_type variate_type; |
127 | // for boost::result_of |
128 | typedef typename numeric::functional::outer_product<sample_type, variate_type>::result_type result_type; |
129 | |
130 | template<typename Args> |
131 | covariance_impl(Args const &args) |
132 | : cov_( |
133 | numeric::outer_product( |
134 | numeric::fdiv(args[sample | Sample()], (std::size_t)1) |
135 | , numeric::fdiv(args[parameter::keyword<VariateTag>::get() | VariateType()], (std::size_t)1) |
136 | ) |
137 | ) |
138 | { |
139 | } |
140 | |
141 | template<typename Args> |
142 | void operator ()(Args const &args) |
143 | { |
144 | std::size_t cnt = count(args); |
145 | |
146 | if (cnt > 1) |
147 | { |
148 | extractor<tag::mean_of_variates<VariateType, VariateTag> > const some_mean_of_variates = {}; |
149 | |
150 | this->cov_ = this->cov_*(cnt-1.)/cnt |
151 | + numeric::outer_product( |
152 | some_mean_of_variates(args) - args[parameter::keyword<VariateTag>::get()] |
153 | , mean(args) - args[sample] |
154 | ) / (cnt-1.); |
155 | } |
156 | } |
157 | |
158 | result_type result(dont_care) const |
159 | { |
160 | return this->cov_; |
161 | } |
162 | |
163 | private: |
164 | result_type cov_; |
165 | }; |
166 | |
167 | } // namespace impl |
168 | |
169 | /////////////////////////////////////////////////////////////////////////////// |
170 | // tag::covariance |
171 | // |
172 | namespace tag |
173 | { |
174 | template<typename VariateType, typename VariateTag> |
175 | struct covariance |
176 | : depends_on<count, mean, mean_of_variates<VariateType, VariateTag> > |
177 | { |
178 | typedef accumulators::impl::covariance_impl<mpl::_1, VariateType, VariateTag> impl; |
179 | }; |
180 | |
181 | struct abstract_covariance |
182 | : depends_on<> |
183 | { |
184 | }; |
185 | } |
186 | |
187 | /////////////////////////////////////////////////////////////////////////////// |
188 | // extract::covariance |
189 | // |
190 | namespace extract |
191 | { |
192 | extractor<tag::abstract_covariance> const = {}; |
193 | |
194 | BOOST_ACCUMULATORS_IGNORE_GLOBAL(covariance) |
195 | } |
196 | |
197 | using extract::covariance; |
198 | |
199 | template<typename VariateType, typename VariateTag> |
200 | struct feature_of<tag::covariance<VariateType, VariateTag> > |
201 | : feature_of<tag::abstract_covariance> |
202 | { |
203 | }; |
204 | |
205 | // So that covariance can be automatically substituted with |
206 | // weighted_covariance when the weight parameter is non-void. |
207 | template<typename VariateType, typename VariateTag> |
208 | struct as_weighted_feature<tag::covariance<VariateType, VariateTag> > |
209 | { |
210 | typedef tag::weighted_covariance<VariateType, VariateTag> type; |
211 | }; |
212 | |
213 | template<typename VariateType, typename VariateTag> |
214 | struct feature_of<tag::weighted_covariance<VariateType, VariateTag> > |
215 | : feature_of<tag::covariance<VariateType, VariateTag> > |
216 | {}; |
217 | |
218 | }} // namespace boost::accumulators |
219 | |
220 | #endif |
221 | |