boost/accumulators/statistics/rolling_variance.hpp
///////////////////////////////////////////////////////////////////////////////
// rolling_variance.hpp
// Copyright (C) 2005 Eric Niebler
// Copyright (C) 2014 Pieter Bastiaan Ober (Integricom).
// 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_ROLLING_VARIANCE_HPP_EAN_15_11_2011
#define BOOST_ACCUMULATORS_STATISTICS_ROLLING_VARIANCE_HPP_EAN_15_11_2011
#include <boost/accumulators/accumulators.hpp>
#include <boost/accumulators/statistics/stats.hpp>
#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/rolling_mean.hpp>
#include <boost/accumulators/statistics/rolling_moment.hpp>
#include <boost/type_traits/is_arithmetic.hpp>
#include <boost/utility/enable_if.hpp>
namespace boost { namespace accumulators
{
namespace impl
{
//! Immediate (lazy) calculation of the rolling variance.
/*!
Calculation of sample variance \f$\sigma_n^2\f$ is done as follows, see also
http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance.
For a rolling window of size \f$N\f$, when \f$n <= N\f$, the variance is computed according to the formula
\f[
\sigma_n^2 = \frac{1}{n-1} \sum_{i = 1}^n (x_i - \mu_n)^2.
\f]
When \f$n > N\f$, the sample variance over the window becomes:
\f[
\sigma_n^2 = \frac{1}{N-1} \sum_{i = n-N+1}^n (x_i - \mu_n)^2.
\f]
*/
///////////////////////////////////////////////////////////////////////////////
// lazy_rolling_variance_impl
//
template<typename Sample>
struct lazy_rolling_variance_impl
: accumulator_base
{
// for boost::result_of
typedef typename numeric::functional::fdiv<Sample, std::size_t,void,void>::result_type result_type;
lazy_rolling_variance_impl(dont_care) {}
template<typename Args>
result_type result(Args const &args) const
{
result_type mean = rolling_mean(args);
size_t nr_samples = rolling_count(args);
if (nr_samples < 2) return result_type();
return nr_samples*(rolling_moment<2>(args) - mean*mean)/(nr_samples-1);
}
};
//! Iterative calculation of the rolling variance.
/*!
Iterative calculation of sample variance \f$\sigma_n^2\f$ is done as follows, see also
http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance.
For a rolling window of size \f$N\f$, for the first \f$N\f$ samples, the variance is computed according to the formula
\f[
\sigma_n^2 = \frac{1}{n-1} \sum_{i = 1}^n (x_i - \mu_n)^2 = \frac{1}{n-1}M_{2,n},
\f]
where the sum of squares \f$M_{2,n}\f$ can be recursively computed as:
\f[
M_{2,n} = \sum_{i = 1}^n (x_i - \mu_n)^2 = M_{2,n-1} + (x_n - \mu_n)(x_n - \mu_{n-1}),
\f]
and the estimate of the sample mean as:
\f[
\mu_n = \frac{1}{n} \sum_{i = 1}^n x_i = \mu_{n-1} + \frac{1}{n}(x_n - \mu_{n-1}).
\f]
For further samples, when the rolling window is fully filled with data, one has to take into account that the oldest
sample \f$x_{n-N}\f$ is dropped from the window. The sample variance over the window now becomes:
\f[
\sigma_n^2 = \frac{1}{N-1} \sum_{i = n-N+1}^n (x_i - \mu_n)^2 = \frac{1}{n-1}M_{2,n},
\f]
where the sum of squares \f$M_{2,n}\f$ now equals:
\f[
M_{2,n} = \sum_{i = n-N+1}^n (x_i - \mu_n)^2 = M_{2,n-1} + (x_n - \mu_n)(x_n - \mu_{n-1}) - (x_{n-N} - \mu_n)(x_{n-N} - \mu_{n-1}),
\f]
and the estimated mean is:
\f[
\mu_n = \frac{1}{N} \sum_{i = n-N+1}^n x_i = \mu_{n-1} + \frac{1}{n}(x_n - x_{n-N}).
\f]
Note that the sample variance is not defined for \f$n <= 1\f$.
*/
///////////////////////////////////////////////////////////////////////////////
// immediate_rolling_variance_impl
//
template<typename Sample>
struct immediate_rolling_variance_impl
: accumulator_base
{
// for boost::result_of
typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type result_type;
template<typename Args>
immediate_rolling_variance_impl(Args const &args)
: previous_mean_(numeric::fdiv(args[sample | Sample()], numeric::one<std::size_t>::value))
, sum_of_squares_(numeric::fdiv(args[sample | Sample()], numeric::one<std::size_t>::value))
{
}
template<typename Args>
void operator()(Args const &args)
{
Sample added_sample = args[sample];
result_type mean = immediate_rolling_mean(args);
sum_of_squares_ += (added_sample-mean)*(added_sample-previous_mean_);
if(is_rolling_window_plus1_full(args))
{
Sample removed_sample = rolling_window_plus1(args).front();
sum_of_squares_ -= (removed_sample-mean)*(removed_sample-previous_mean_);
prevent_underflow(sum_of_squares_);
}
previous_mean_ = mean;
}
template<typename Args>
result_type result(Args const &args) const
{
size_t nr_samples = rolling_count(args);
if (nr_samples < 2) return result_type();
return numeric::fdiv(sum_of_squares_,(nr_samples-1));
}
private:
result_type previous_mean_;
result_type sum_of_squares_;
template<typename T>
void prevent_underflow(T &non_negative_number,typename boost::enable_if<boost::is_arithmetic<T>,T>::type* = 0)
{
if (non_negative_number < T(0)) non_negative_number = T(0);
}
template<typename T>
void prevent_underflow(T &non_arithmetic_quantity,typename boost::disable_if<boost::is_arithmetic<T>,T>::type* = 0)
{
}
};
} // namespace impl
///////////////////////////////////////////////////////////////////////////////
// tag:: lazy_rolling_variance
// tag:: immediate_rolling_variance
// tag:: rolling_variance
//
namespace tag
{
struct lazy_rolling_variance
: depends_on< rolling_count, rolling_mean, rolling_moment<2> >
{
/// INTERNAL ONLY
///
typedef accumulators::impl::lazy_rolling_variance_impl< mpl::_1 > impl;
#ifdef BOOST_ACCUMULATORS_DOXYGEN_INVOKED
/// tag::rolling_window::window_size named parameter
static boost::parameter::keyword<tag::rolling_window_size> const window_size;
#endif
};
struct immediate_rolling_variance
: depends_on< rolling_window_plus1, rolling_count, immediate_rolling_mean>
{
/// INTERNAL ONLY
///
typedef accumulators::impl::immediate_rolling_variance_impl< mpl::_1> impl;
#ifdef BOOST_ACCUMULATORS_DOXYGEN_INVOKED
/// tag::rolling_window::window_size named parameter
static boost::parameter::keyword<tag::rolling_window_size> const window_size;
#endif
};
// make immediate_rolling_variance the default implementation
struct rolling_variance : immediate_rolling_variance {};
} // namespace tag
///////////////////////////////////////////////////////////////////////////////
// extract::lazy_rolling_variance
// extract::immediate_rolling_variance
// extract::rolling_variance
//
namespace extract
{
extractor<tag::lazy_rolling_variance> const lazy_rolling_variance = {};
extractor<tag::immediate_rolling_variance> const immediate_rolling_variance = {};
extractor<tag::rolling_variance> const rolling_variance = {};
BOOST_ACCUMULATORS_IGNORE_GLOBAL(lazy_rolling_variance)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(immediate_rolling_variance)
BOOST_ACCUMULATORS_IGNORE_GLOBAL(rolling_variance)
}
using extract::lazy_rolling_variance;
using extract::immediate_rolling_variance;
using extract::rolling_variance;
// rolling_variance(lazy) -> lazy_rolling_variance
template<>
struct as_feature<tag::rolling_variance(lazy)>
{
typedef tag::lazy_rolling_variance type;
};
// rolling_variance(immediate) -> immediate_rolling_variance
template<>
struct as_feature<tag::rolling_variance(immediate)>
{
typedef tag::immediate_rolling_variance type;
};
// for the purposes of feature-based dependency resolution,
// lazy_rolling_variance provides the same feature as rolling_variance
template<>
struct feature_of<tag::lazy_rolling_variance>
: feature_of<tag::rolling_variance>
{
};
// for the purposes of feature-based dependency resolution,
// immediate_rolling_variance provides the same feature as rolling_variance
template<>
struct feature_of<tag::immediate_rolling_variance>
: feature_of<tag::rolling_variance>
{
};
}} // namespace boost::accumulators
#endif