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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 | ||
92f5a8d4 TL |
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 | ||
7c673cae FG |
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 weighted_covariance = {}; | |
132 | ||
133 | BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_covariance) | |
134 | } | |
135 | ||
136 | using extract::weighted_covariance; | |
137 | ||
138 | }} // namespace boost::accumulators | |
139 | ||
140 | #endif |