1 ///////////////////////////////////////////////////////////////////////////////
2 // weighted_variance.hpp
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)
8 #ifndef BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_VARIANCE_HPP_EAN_28_10_2005
9 #define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_VARIANCE_HPP_EAN_28_10_2005
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>
24 namespace boost { namespace accumulators
29 //! Lazy calculation of variance of weighted samples.
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):
34 \hat{\sigma}_n^2 = \widehat{m}_n^{(2)}-\hat{\mu}_n^2,
36 where \f$n\f$ is the number of samples.
38 template<typename Sample, typename Weight, typename MeanFeature>
39 struct lazy_weighted_variance_impl
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;
46 lazy_weighted_variance_impl(dont_care) {}
48 template<typename Args>
49 result_type result(Args const &args) const
51 extractor<MeanFeature> const some_mean = {};
52 result_type tmp = some_mean(args);
53 return accumulators::weighted_moment<2>(args) - tmp * tmp;
57 //! Iterative calculation of variance of weighted samples.
59 Iterative calculation of variance of weighted samples:
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.
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
70 template<typename Sample, typename Weight, typename MeanFeature, typename Tag>
71 struct weighted_variance_impl
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;
78 template<typename Args>
79 weighted_variance_impl(Args const &args)
80 : weighted_variance(numeric::fdiv(args[sample | Sample()], numeric::one<Weight>::value))
84 template<typename Args>
85 void operator ()(Args const &args)
87 std::size_t cnt = count(args);
91 extractor<MeanFeature> const some_mean = {};
93 result_type tmp = args[parameter::keyword<Tag>::get()] - some_mean(args);
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] );
101 result_type result(dont_care) const
103 return this->weighted_variance;
107 result_type weighted_variance;
112 ///////////////////////////////////////////////////////////////////////////////
113 // tag::weighted_variance
114 // tag::immediate_weighted_variance
118 struct lazy_weighted_variance
119 : depends_on<weighted_moment<2>, weighted_mean>
123 typedef accumulators::impl::lazy_weighted_variance_impl<mpl::_1, mpl::_2, weighted_mean> impl;
126 struct weighted_variance
127 : depends_on<count, immediate_weighted_mean>
131 typedef accumulators::impl::weighted_variance_impl<mpl::_1, mpl::_2, immediate_weighted_mean, sample> impl;
135 ///////////////////////////////////////////////////////////////////////////////
136 // extract::weighted_variance
137 // extract::immediate_weighted_variance
141 extractor<tag::lazy_weighted_variance> const lazy_weighted_variance = {};
142 extractor<tag::weighted_variance> const weighted_variance = {};
144 BOOST_ACCUMULATORS_IGNORE_GLOBAL(lazy_weighted_variance)
145 BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_variance)
148 using extract::lazy_weighted_variance;
149 using extract::weighted_variance;
151 // weighted_variance(lazy) -> lazy_weighted_variance
153 struct as_feature<tag::weighted_variance(lazy)>
155 typedef tag::lazy_weighted_variance type;
158 // weighted_variance(immediate) -> weighted_variance
160 struct as_feature<tag::weighted_variance(immediate)>
162 typedef tag::weighted_variance type;
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.
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> >
177 // template<typename Args>
178 // droppable_accumulator(Args const &args)
179 // : droppable_accumulator::base(args)
184 }} // namespace boost::accumulators