/////////////////////////////////////////////////////////////////////////////// | |
// variance.hpp | |
// | |
// Copyright 2005 Daniel Egloff, Eric Niebler. Distributed under the Boost | |
// Software License, Version 1.0. (See accompanying file | |
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) | |
#ifndef BOOST_ACCUMULATORS_STATISTICS_VARIANCE_HPP_EAN_28_10_2005 | |
#define BOOST_ACCUMULATORS_STATISTICS_VARIANCE_HPP_EAN_28_10_2005 | |
#include <boost/mpl/placeholders.hpp> | |
#include <boost/accumulators/framework/accumulator_base.hpp> | |
#include <boost/accumulators/framework/extractor.hpp> | |
#include <boost/accumulators/numeric/functional.hpp> | |
#include <boost/accumulators/framework/parameters/sample.hpp> | |
#include <boost/accumulators/framework/depends_on.hpp> | |
#include <boost/accumulators/statistics_fwd.hpp> | |
#include <boost/accumulators/statistics/count.hpp> | |
#include <boost/accumulators/statistics/sum.hpp> | |
#include <boost/accumulators/statistics/mean.hpp> | |
#include <boost/accumulators/statistics/moment.hpp> | |
namespace boost { namespace accumulators | |
{ | |
namespace impl | |
{ | |
//! Lazy calculation of variance. | |
/*! | |
Default sample variance implementation based on the second moment \f$ M_n^{(2)} \f$ moment<2>, mean and count. | |
\f[ | |
\sigma_n^2 = M_n^{(2)} - \mu_n^2. | |
\f] | |
where | |
\f[ | |
\mu_n = \frac{1}{n} \sum_{i = 1}^n x_i. | |
\f] | |
is the estimate of the sample mean and \f$n\f$ is the number of samples. | |
*/ | |
template<typename Sample, typename MeanFeature> | |
struct lazy_variance_impl | |
: accumulator_base | |
{ | |
// for boost::result_of | |
typedef typename numeric::functional::average<Sample, std::size_t>::result_type result_type; | |
lazy_variance_impl(dont_care) {} | |
template<typename Args> | |
result_type result(Args const &args) const | |
{ | |
extractor<MeanFeature> mean; | |
result_type tmp = mean(args); | |
return accumulators::moment<2>(args) - tmp * tmp; | |
} | |
}; | |
//! Iterative calculation of variance. | |
/*! | |
Iterative calculation of sample variance \f$\sigma_n^2\f$ according to the formula | |
\f[ | |
\sigma_n^2 = \frac{1}{n} \sum_{i = 1}^n (x_i - \mu_n)^2 = \frac{n-1}{n} \sigma_{n-1}^2 + \frac{1}{n-1}(x_n - \mu_n)^2. | |
\f] | |
where | |
\f[ | |
\mu_n = \frac{1}{n} \sum_{i = 1}^n x_i. | |
\f] | |
is the estimate of the sample mean and \f$n\f$ is the number of samples. | |
Note that the sample variance is not defined for \f$n <= 1\f$. | |
A simplification can be obtained by the approximate recursion | |
\f[ | |
\sigma_n^2 \approx \frac{n-1}{n} \sigma_{n-1}^2 + \frac{1}{n}(x_n - \mu_n)^2. | |
\f] | |
because the difference | |
\f[ | |
\left(\frac{1}{n-1} - \frac{1}{n}\right)(x_n - \mu_n)^2 = \frac{1}{n(n-1)}(x_n - \mu_n)^2. | |
\f] | |
converges to zero as \f$n \rightarrow \infty\f$. However, for small \f$ n \f$ the difference | |
can be non-negligible. | |
*/ | |
template<typename Sample, typename MeanFeature, typename Tag> | |
struct variance_impl | |
: accumulator_base | |
{ | |
// for boost::result_of | |
typedef typename numeric::functional::average<Sample, std::size_t>::result_type result_type; | |
template<typename Args> | |
variance_impl(Args const &args) | |
: variance(numeric::average(args[sample | Sample()], numeric::one<std::size_t>::value)) | |
{ | |
} | |
template<typename Args> | |
void operator ()(Args const &args) | |
{ | |
std::size_t cnt = count(args); | |
if(cnt > 1) | |
{ | |
extractor<MeanFeature> mean; | |
result_type tmp = args[parameter::keyword<Tag>::get()] - mean(args); | |
this->variance = | |
numeric::average(this->variance * (cnt - 1), cnt) | |
+ numeric::average(tmp * tmp, cnt - 1); | |
} | |
} | |
result_type result(dont_care) const | |
{ | |
return this->variance; | |
} | |
private: | |
result_type variance; | |
}; | |
} // namespace impl | |
/////////////////////////////////////////////////////////////////////////////// | |
// tag::variance | |
// tag::immediate_variance | |
// | |
namespace tag | |
{ | |
struct lazy_variance | |
: depends_on<moment<2>, mean> | |
{ | |
/// INTERNAL ONLY | |
/// | |
typedef accumulators::impl::lazy_variance_impl<mpl::_1, mean> impl; | |
}; | |
struct variance | |
: depends_on<count, immediate_mean> | |
{ | |
/// INTERNAL ONLY | |
/// | |
typedef accumulators::impl::variance_impl<mpl::_1, mean, sample> impl; | |
}; | |
} | |
/////////////////////////////////////////////////////////////////////////////// | |
// extract::lazy_variance | |
// extract::variance | |
// | |
namespace extract | |
{ | |
extractor<tag::lazy_variance> const lazy_variance = {}; | |
extractor<tag::variance> const variance = {}; | |
BOOST_ACCUMULATORS_IGNORE_GLOBAL(lazy_variance) | |
BOOST_ACCUMULATORS_IGNORE_GLOBAL(variance) | |
} | |
using extract::lazy_variance; | |
using extract::variance; | |
// variance(lazy) -> lazy_variance | |
template<> | |
struct as_feature<tag::variance(lazy)> | |
{ | |
typedef tag::lazy_variance type; | |
}; | |
// variance(immediate) -> variance | |
template<> | |
struct as_feature<tag::variance(immediate)> | |
{ | |
typedef tag::variance type; | |
}; | |
// for the purposes of feature-based dependency resolution, | |
// immediate_variance provides the same feature as variance | |
template<> | |
struct feature_of<tag::lazy_variance> | |
: feature_of<tag::variance> | |
{ | |
}; | |
// So that variance can be automatically substituted with | |
// weighted_variance when the weight parameter is non-void. | |
template<> | |
struct as_weighted_feature<tag::variance> | |
{ | |
typedef tag::weighted_variance type; | |
}; | |
// for the purposes of feature-based dependency resolution, | |
// weighted_variance provides the same feature as variance | |
template<> | |
struct feature_of<tag::weighted_variance> | |
: feature_of<tag::variance> | |
{ | |
}; | |
// So that immediate_variance can be automatically substituted with | |
// immediate_weighted_variance when the weight parameter is non-void. | |
template<> | |
struct as_weighted_feature<tag::lazy_variance> | |
{ | |
typedef tag::lazy_weighted_variance type; | |
}; | |
// for the purposes of feature-based dependency resolution, | |
// immediate_weighted_variance provides the same feature as immediate_variance | |
template<> | |
struct feature_of<tag::lazy_weighted_variance> | |
: feature_of<tag::lazy_variance> | |
{ | |
}; | |
//////////////////////////////////////////////////////////////////////////// | |
//// droppable_accumulator<variance_impl> | |
//// need to specialize droppable lazy variance to cache the result at the | |
//// point the accumulator is dropped. | |
///// INTERNAL ONLY | |
///// | |
//template<typename Sample, typename MeanFeature> | |
//struct droppable_accumulator<impl::variance_impl<Sample, MeanFeature> > | |
// : droppable_accumulator_base< | |
// with_cached_result<impl::variance_impl<Sample, MeanFeature> > | |
// > | |
//{ | |
// template<typename Args> | |
// droppable_accumulator(Args const &args) | |
// : droppable_accumulator::base(args) | |
// { | |
// } | |
//}; | |
}} // namespace boost::accumulators | |
#endif |