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1 | /////////////////////////////////////////////////////////////////////////////// |
2 | // weighted_variance.hpp | |
3 | // | |
4 | // Copyright 2005 Daniel Egloff, Eric Niebler. 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_VARIANCE_HPP_EAN_28_10_2005 | |
9 | #define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_VARIANCE_HPP_EAN_28_10_2005 | |
10 | ||
11 | #include <boost/mpl/placeholders.hpp> | |
12 | #include <boost/accumulators/framework/accumulator_base.hpp> | |
13 | #include <boost/accumulators/framework/extractor.hpp> | |
14 | #include <boost/accumulators/numeric/functional.hpp> | |
15 | #include <boost/accumulators/framework/parameters/sample.hpp> | |
16 | #include <boost/accumulators/framework/depends_on.hpp> | |
17 | #include <boost/accumulators/statistics_fwd.hpp> | |
18 | #include <boost/accumulators/statistics/count.hpp> | |
19 | #include <boost/accumulators/statistics/variance.hpp> | |
20 | #include <boost/accumulators/statistics/weighted_sum.hpp> | |
21 | #include <boost/accumulators/statistics/weighted_mean.hpp> | |
22 | #include <boost/accumulators/statistics/weighted_moment.hpp> | |
23 | ||
24 | namespace boost { namespace accumulators | |
25 | { | |
26 | ||
27 | namespace impl | |
28 | { | |
29 | //! Lazy calculation of variance of weighted samples. | |
30 | /*! | |
31 | The default implementation of the variance of weighted samples is based on the second moment | |
32 | \f$\widehat{m}_n^{(2)}\f$ (weighted_moment<2>) and the mean\f$ \hat{\mu}_n\f$ (weighted_mean): | |
33 | \f[ | |
34 | \hat{\sigma}_n^2 = \widehat{m}_n^{(2)}-\hat{\mu}_n^2, | |
35 | \f] | |
36 | where \f$n\f$ is the number of samples. | |
37 | */ | |
38 | template<typename Sample, typename Weight, typename MeanFeature> | |
39 | struct lazy_weighted_variance_impl | |
40 | : accumulator_base | |
41 | { | |
42 | typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample; | |
43 | // for boost::result_of | |
44 | typedef typename numeric::functional::fdiv<weighted_sample, Weight>::result_type result_type; | |
45 | ||
46 | lazy_weighted_variance_impl(dont_care) {} | |
47 | ||
48 | template<typename Args> | |
49 | result_type result(Args const &args) const | |
50 | { | |
51 | extractor<MeanFeature> const some_mean = {}; | |
52 | result_type tmp = some_mean(args); | |
53 | return accumulators::weighted_moment<2>(args) - tmp * tmp; | |
54 | } | |
55 | }; | |
56 | ||
57 | //! Iterative calculation of variance of weighted samples. | |
58 | /*! | |
59 | Iterative calculation of variance of weighted samples: | |
60 | \f[ | |
61 | \hat{\sigma}_n^2 = | |
62 | \frac{\bar{w}_n - w_n}{\bar{w}_n}\hat{\sigma}_{n - 1}^2 | |
63 | + \frac{w_n}{\bar{w}_n - w_n}\left(X_n - \hat{\mu}_n\right)^2 | |
64 | ,\quad n\ge2,\quad\hat{\sigma}_0^2 = 0. | |
65 | \f] | |
66 | where \f$\bar{w}_n\f$ is the sum of the \f$n\f$ weights \f$w_i\f$ and \f$\hat{\mu}_n\f$ | |
67 | the estimate of the mean of the weighted samples. Note that the sample variance is not defined for | |
68 | \f$n <= 1\f$. | |
69 | */ | |
70 | template<typename Sample, typename Weight, typename MeanFeature, typename Tag> | |
71 | struct weighted_variance_impl | |
72 | : accumulator_base | |
73 | { | |
74 | typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample; | |
75 | // for boost::result_of | |
76 | typedef typename numeric::functional::fdiv<weighted_sample, Weight>::result_type result_type; | |
77 | ||
78 | template<typename Args> | |
79 | weighted_variance_impl(Args const &args) | |
80 | : weighted_variance(numeric::fdiv(args[sample | Sample()], numeric::one<Weight>::value)) | |
81 | { | |
82 | } | |
83 | ||
84 | template<typename Args> | |
85 | void operator ()(Args const &args) | |
86 | { | |
87 | std::size_t cnt = count(args); | |
88 | ||
89 | if(cnt > 1) | |
90 | { | |
91 | extractor<MeanFeature> const some_mean = {}; | |
92 | ||
93 | result_type tmp = args[parameter::keyword<Tag>::get()] - some_mean(args); | |
94 | ||
95 | this->weighted_variance = | |
96 | numeric::fdiv(this->weighted_variance * (sum_of_weights(args) - args[weight]), sum_of_weights(args)) | |
97 | + numeric::fdiv(tmp * tmp * args[weight], sum_of_weights(args) - args[weight] ); | |
98 | } | |
99 | } | |
100 | ||
101 | result_type result(dont_care) const | |
102 | { | |
103 | return this->weighted_variance; | |
104 | } | |
105 | ||
106 | private: | |
107 | result_type weighted_variance; | |
108 | }; | |
109 | ||
110 | } // namespace impl | |
111 | ||
112 | /////////////////////////////////////////////////////////////////////////////// | |
113 | // tag::weighted_variance | |
114 | // tag::immediate_weighted_variance | |
115 | // | |
116 | namespace tag | |
117 | { | |
118 | struct lazy_weighted_variance | |
119 | : depends_on<weighted_moment<2>, weighted_mean> | |
120 | { | |
121 | /// INTERNAL ONLY | |
122 | /// | |
123 | typedef accumulators::impl::lazy_weighted_variance_impl<mpl::_1, mpl::_2, weighted_mean> impl; | |
124 | }; | |
125 | ||
126 | struct weighted_variance | |
127 | : depends_on<count, immediate_weighted_mean> | |
128 | { | |
129 | /// INTERNAL ONLY | |
130 | /// | |
131 | typedef accumulators::impl::weighted_variance_impl<mpl::_1, mpl::_2, immediate_weighted_mean, sample> impl; | |
132 | }; | |
133 | } | |
134 | ||
135 | /////////////////////////////////////////////////////////////////////////////// | |
136 | // extract::weighted_variance | |
137 | // extract::immediate_weighted_variance | |
138 | // | |
139 | namespace extract | |
140 | { | |
141 | extractor<tag::lazy_weighted_variance> const lazy_weighted_variance = {}; | |
142 | extractor<tag::weighted_variance> const weighted_variance = {}; | |
143 | ||
144 | BOOST_ACCUMULATORS_IGNORE_GLOBAL(lazy_weighted_variance) | |
145 | BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_variance) | |
146 | } | |
147 | ||
148 | using extract::lazy_weighted_variance; | |
149 | using extract::weighted_variance; | |
150 | ||
151 | // weighted_variance(lazy) -> lazy_weighted_variance | |
152 | template<> | |
153 | struct as_feature<tag::weighted_variance(lazy)> | |
154 | { | |
155 | typedef tag::lazy_weighted_variance type; | |
156 | }; | |
157 | ||
158 | // weighted_variance(immediate) -> weighted_variance | |
159 | template<> | |
160 | struct as_feature<tag::weighted_variance(immediate)> | |
161 | { | |
162 | typedef tag::weighted_variance type; | |
163 | }; | |
164 | ||
165 | //////////////////////////////////////////////////////////////////////////// | |
166 | //// droppable_accumulator<weighted_variance_impl> | |
167 | //// need to specialize droppable lazy weighted_variance to cache the result at the | |
168 | //// point the accumulator is dropped. | |
169 | ///// INTERNAL ONLY | |
170 | ///// | |
171 | //template<typename Sample, typename Weight, typename MeanFeature> | |
172 | //struct droppable_accumulator<impl::weighted_variance_impl<Sample, Weight, MeanFeature> > | |
173 | // : droppable_accumulator_base< | |
174 | // with_cached_result<impl::weighted_variance_impl<Sample, Weight, MeanFeature> > | |
175 | // > | |
176 | //{ | |
177 | // template<typename Args> | |
178 | // droppable_accumulator(Args const &args) | |
179 | // : droppable_accumulator::base(args) | |
180 | // { | |
181 | // } | |
182 | //}; | |
183 | ||
184 | }} // namespace boost::accumulators | |
185 | ||
186 | #endif |