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> |
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 | // |
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 = {}; |
132 | |
133 | BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_covariance) |
134 | } |
135 | |
136 | using extract::weighted_covariance; |
137 | |
138 | }} // namespace boost::accumulators |
139 | |
140 | #endif |
141 | |