1185 lines
44 KiB
C++
1185 lines
44 KiB
C++
// (C) Copyright Nick Thompson 2018.
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// (C) Copyright Matt Borland 2020.
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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#ifndef BOOST_MATH_STATISTICS_UNIVARIATE_STATISTICS_HPP
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#define BOOST_MATH_STATISTICS_UNIVARIATE_STATISTICS_HPP
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#include <boost/math/statistics/detail/single_pass.hpp>
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#include <boost/math/tools/config.hpp>
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#include <boost/math/tools/assert.hpp>
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#include <algorithm>
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#include <iterator>
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#include <tuple>
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#include <cmath>
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#include <vector>
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#include <type_traits>
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#include <utility>
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#include <numeric>
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#include <list>
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#ifdef BOOST_MATH_EXEC_COMPATIBLE
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#include <execution>
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namespace boost::math::statistics {
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template<class ExecutionPolicy, class ForwardIterator>
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inline auto mean(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last)
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{
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using Real = typename std::iterator_traits<ForwardIterator>::value_type;
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BOOST_MATH_ASSERT_MSG(first != last, "At least one sample is required to compute the mean.");
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if constexpr (std::is_integral_v<Real>)
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{
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if constexpr (std::is_same_v<std::remove_reference_t<decltype(exec)>, decltype(std::execution::seq)>)
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{
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return detail::mean_sequential_impl<double>(first, last);
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}
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else
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{
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return std::reduce(exec, first, last, 0.0) / std::distance(first, last);
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}
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}
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else
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{
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if constexpr (std::is_same_v<std::remove_reference_t<decltype(exec)>, decltype(std::execution::seq)>)
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{
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return detail::mean_sequential_impl<Real>(first, last);
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}
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else
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{
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return std::reduce(exec, first, last, Real(0.0)) / Real(std::distance(first, last));
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}
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}
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}
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template<class ExecutionPolicy, class Container>
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inline auto mean(ExecutionPolicy&& exec, Container const & v)
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{
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return mean(exec, std::cbegin(v), std::cend(v));
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}
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template<class ForwardIterator>
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inline auto mean(ForwardIterator first, ForwardIterator last)
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{
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return mean(std::execution::seq, first, last);
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}
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template<class Container>
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inline auto mean(Container const & v)
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{
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return mean(std::execution::seq, std::cbegin(v), std::cend(v));
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}
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template<class ExecutionPolicy, class ForwardIterator>
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inline auto variance(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last)
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{
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using Real = typename std::iterator_traits<ForwardIterator>::value_type;
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if constexpr (std::is_integral_v<Real>)
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{
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if constexpr (std::is_same_v<std::remove_reference_t<decltype(exec)>, decltype(std::execution::seq)>)
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{
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return std::get<2>(detail::variance_sequential_impl<std::tuple<double, double, double, double>>(first, last));
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}
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else
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{
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const auto results = detail::first_four_moments_parallel_impl<std::tuple<double, double, double, double, double>>(first, last);
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return std::get<1>(results) / std::get<4>(results);
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}
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}
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else
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{
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if constexpr (std::is_same_v<std::remove_reference_t<decltype(exec)>, decltype(std::execution::seq)>)
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{
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return std::get<2>(detail::variance_sequential_impl<std::tuple<Real, Real, Real, Real>>(first, last));
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}
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else
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{
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const auto results = detail::first_four_moments_parallel_impl<std::tuple<Real, Real, Real, Real, Real>>(first, last);
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return std::get<1>(results) / std::get<4>(results);
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}
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}
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}
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template<class ExecutionPolicy, class Container>
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inline auto variance(ExecutionPolicy&& exec, Container const & v)
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{
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return variance(exec, std::cbegin(v), std::cend(v));
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}
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template<class ForwardIterator>
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inline auto variance(ForwardIterator first, ForwardIterator last)
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{
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return variance(std::execution::seq, first, last);
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}
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template<class Container>
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inline auto variance(Container const & v)
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{
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return variance(std::execution::seq, std::cbegin(v), std::cend(v));
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}
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template<class ExecutionPolicy, class ForwardIterator>
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inline auto sample_variance(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last)
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{
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const auto n = std::distance(first, last);
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BOOST_MATH_ASSERT_MSG(n > 1, "At least two samples are required to compute the sample variance.");
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return n*variance(exec, first, last)/(n-1);
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}
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template<class ExecutionPolicy, class Container>
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inline auto sample_variance(ExecutionPolicy&& exec, Container const & v)
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{
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return sample_variance(exec, std::cbegin(v), std::cend(v));
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}
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template<class ForwardIterator>
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inline auto sample_variance(ForwardIterator first, ForwardIterator last)
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{
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return sample_variance(std::execution::seq, first, last);
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}
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template<class Container>
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inline auto sample_variance(Container const & v)
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{
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return sample_variance(std::execution::seq, std::cbegin(v), std::cend(v));
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}
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template<class ExecutionPolicy, class ForwardIterator>
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inline auto mean_and_sample_variance(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last)
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{
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using Real = typename std::iterator_traits<ForwardIterator>::value_type;
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if constexpr (std::is_integral_v<Real>)
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{
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if constexpr (std::is_same_v<std::remove_reference_t<decltype(exec)>, decltype(std::execution::seq)>)
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{
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const auto results = detail::variance_sequential_impl<std::tuple<double, double, double, double>>(first, last);
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return std::make_pair(std::get<0>(results), std::get<2>(results)*std::get<3>(results)/(std::get<3>(results)-1.0));
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}
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else
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{
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const auto results = detail::first_four_moments_parallel_impl<std::tuple<double, double, double, double, double>>(first, last);
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return std::make_pair(std::get<0>(results), std::get<1>(results) / (std::get<4>(results)-1.0));
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}
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}
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else
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{
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if constexpr (std::is_same_v<std::remove_reference_t<decltype(exec)>, decltype(std::execution::seq)>)
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{
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const auto results = detail::variance_sequential_impl<std::tuple<Real, Real, Real, Real>>(first, last);
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return std::make_pair(std::get<0>(results), std::get<2>(results)*std::get<3>(results)/(std::get<3>(results)-Real(1)));
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}
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else
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{
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const auto results = detail::first_four_moments_parallel_impl<std::tuple<Real, Real, Real, Real, Real>>(first, last);
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return std::make_pair(std::get<0>(results), std::get<1>(results) / (std::get<4>(results)-Real(1)));
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}
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}
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}
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template<class ExecutionPolicy, class Container>
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inline auto mean_and_sample_variance(ExecutionPolicy&& exec, Container const & v)
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{
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return mean_and_sample_variance(exec, std::cbegin(v), std::cend(v));
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}
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template<class ForwardIterator>
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inline auto mean_and_sample_variance(ForwardIterator first, ForwardIterator last)
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{
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return mean_and_sample_variance(std::execution::seq, first, last);
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}
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template<class Container>
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inline auto mean_and_sample_variance(Container const & v)
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{
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return mean_and_sample_variance(std::execution::seq, std::cbegin(v), std::cend(v));
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}
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template<class ExecutionPolicy, class ForwardIterator>
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inline auto first_four_moments(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last)
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{
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using Real = typename std::iterator_traits<ForwardIterator>::value_type;
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if constexpr (std::is_integral_v<Real>)
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{
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if constexpr (std::is_same_v<std::remove_reference_t<decltype(exec)>, decltype(std::execution::seq)>)
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{
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const auto results = detail::first_four_moments_sequential_impl<std::tuple<double, double, double, double, double>>(first, last);
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return std::make_tuple(std::get<0>(results), std::get<1>(results) / std::get<4>(results), std::get<2>(results) / std::get<4>(results),
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std::get<3>(results) / std::get<4>(results));
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}
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else
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{
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const auto results = detail::first_four_moments_parallel_impl<std::tuple<double, double, double, double, double>>(first, last);
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return std::make_tuple(std::get<0>(results), std::get<1>(results) / std::get<4>(results), std::get<2>(results) / std::get<4>(results),
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std::get<3>(results) / std::get<4>(results));
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}
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}
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else
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{
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if constexpr (std::is_same_v<std::remove_reference_t<decltype(exec)>, decltype(std::execution::seq)>)
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{
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const auto results = detail::first_four_moments_sequential_impl<std::tuple<Real, Real, Real, Real, Real>>(first, last);
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return std::make_tuple(std::get<0>(results), std::get<1>(results) / std::get<4>(results), std::get<2>(results) / std::get<4>(results),
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std::get<3>(results) / std::get<4>(results));
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}
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else
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{
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const auto results = detail::first_four_moments_parallel_impl<std::tuple<Real, Real, Real, Real, Real>>(first, last);
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return std::make_tuple(std::get<0>(results), std::get<1>(results) / std::get<4>(results), std::get<2>(results) / std::get<4>(results),
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std::get<3>(results) / std::get<4>(results));
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}
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}
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}
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template<class ExecutionPolicy, class Container>
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inline auto first_four_moments(ExecutionPolicy&& exec, Container const & v)
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{
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return first_four_moments(exec, std::cbegin(v), std::cend(v));
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}
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template<class ForwardIterator>
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inline auto first_four_moments(ForwardIterator first, ForwardIterator last)
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{
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return first_four_moments(std::execution::seq, first, last);
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}
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template<class Container>
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inline auto first_four_moments(Container const & v)
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{
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return first_four_moments(std::execution::seq, std::cbegin(v), std::cend(v));
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}
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// https://prod.sandia.gov/techlib-noauth/access-control.cgi/2008/086212.pdf
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template<class ExecutionPolicy, class ForwardIterator>
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inline auto skewness(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last)
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{
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using Real = typename std::iterator_traits<ForwardIterator>::value_type;
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using std::sqrt;
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if constexpr (std::is_same_v<std::remove_reference_t<decltype(exec)>, decltype(std::execution::seq)>)
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{
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if constexpr (std::is_integral_v<Real>)
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{
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return detail::skewness_sequential_impl<double>(first, last);
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}
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else
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{
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return detail::skewness_sequential_impl<Real>(first, last);
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}
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}
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else
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{
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const auto [M1, M2, M3, M4] = first_four_moments(exec, first, last);
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const auto n = std::distance(first, last);
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const auto var = M2/(n-1);
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if (M2 == 0)
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{
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// The limit is technically undefined, but the interpretation here is clear:
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// A constant dataset has no skewness.
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if constexpr (std::is_integral_v<Real>)
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{
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return double(0);
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}
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else
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{
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return Real(0);
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}
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}
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else
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{
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return M3/(M2*sqrt(var)) / Real(2);
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}
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}
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}
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template<class ExecutionPolicy, class Container>
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inline auto skewness(ExecutionPolicy&& exec, Container & v)
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{
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return skewness(exec, std::cbegin(v), std::cend(v));
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}
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template<class ForwardIterator>
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inline auto skewness(ForwardIterator first, ForwardIterator last)
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{
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return skewness(std::execution::seq, first, last);
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}
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template<class Container>
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inline auto skewness(Container const & v)
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{
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return skewness(std::execution::seq, std::cbegin(v), std::cend(v));
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}
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// Follows equation 1.6 of:
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// https://prod.sandia.gov/techlib-noauth/access-control.cgi/2008/086212.pdf
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template<class ExecutionPolicy, class ForwardIterator>
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inline auto kurtosis(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last)
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{
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const auto [M1, M2, M3, M4] = first_four_moments(exec, first, last);
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if (M2 == 0)
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{
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return M2;
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}
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return M4/(M2*M2);
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}
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template<class ExecutionPolicy, class Container>
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inline auto kurtosis(ExecutionPolicy&& exec, Container const & v)
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{
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return kurtosis(exec, std::cbegin(v), std::cend(v));
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}
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template<class ForwardIterator>
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inline auto kurtosis(ForwardIterator first, ForwardIterator last)
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{
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return kurtosis(std::execution::seq, first, last);
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}
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template<class Container>
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inline auto kurtosis(Container const & v)
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{
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return kurtosis(std::execution::seq, std::cbegin(v), std::cend(v));
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}
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template<class ExecutionPolicy, class ForwardIterator>
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inline auto excess_kurtosis(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last)
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{
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return kurtosis(exec, first, last) - 3;
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}
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template<class ExecutionPolicy, class Container>
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inline auto excess_kurtosis(ExecutionPolicy&& exec, Container const & v)
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{
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return excess_kurtosis(exec, std::cbegin(v), std::cend(v));
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}
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template<class ForwardIterator>
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inline auto excess_kurtosis(ForwardIterator first, ForwardIterator last)
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{
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return excess_kurtosis(std::execution::seq, first, last);
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}
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template<class Container>
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inline auto excess_kurtosis(Container const & v)
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{
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return excess_kurtosis(std::execution::seq, std::cbegin(v), std::cend(v));
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}
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template<class ExecutionPolicy, class RandomAccessIterator>
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auto median(ExecutionPolicy&& exec, RandomAccessIterator first, RandomAccessIterator last)
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{
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const auto num_elems = std::distance(first, last);
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BOOST_MATH_ASSERT_MSG(num_elems > 0, "The median of a zero length vector is undefined.");
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if (num_elems & 1)
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{
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auto middle = first + (num_elems - 1)/2;
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std::nth_element(exec, first, middle, last);
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return *middle;
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}
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else
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{
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auto middle = first + num_elems/2 - 1;
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std::nth_element(exec, first, middle, last);
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std::nth_element(exec, middle, middle+1, last);
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return (*middle + *(middle+1))/2;
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}
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}
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template<class ExecutionPolicy, class RandomAccessContainer>
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inline auto median(ExecutionPolicy&& exec, RandomAccessContainer & v)
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{
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return median(exec, std::begin(v), std::end(v));
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}
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template<class RandomAccessIterator>
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inline auto median(RandomAccessIterator first, RandomAccessIterator last)
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{
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return median(std::execution::seq, first, last);
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}
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template<class RandomAccessContainer>
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inline auto median(RandomAccessContainer & v)
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{
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return median(std::execution::seq, std::begin(v), std::end(v));
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}
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#if 0
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//
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// Parallel gini calculation is curently broken, see:
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// https://github.com/boostorg/math/issues/585
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// We will fix this at a later date, for now just use a serial implementation:
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//
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template<class ExecutionPolicy, class RandomAccessIterator>
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inline auto gini_coefficient(ExecutionPolicy&& exec, RandomAccessIterator first, RandomAccessIterator last)
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{
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using Real = typename std::iterator_traits<RandomAccessIterator>::value_type;
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if(!std::is_sorted(exec, first, last))
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{
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std::sort(exec, first, last);
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}
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if constexpr (std::is_same_v<std::remove_reference_t<decltype(exec)>, decltype(std::execution::seq)>)
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{
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if constexpr (std::is_integral_v<Real>)
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{
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return detail::gini_coefficient_sequential_impl<double>(first, last);
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}
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else
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{
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return detail::gini_coefficient_sequential_impl<Real>(first, last);
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}
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}
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else if constexpr (std::is_integral_v<Real>)
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{
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return detail::gini_coefficient_parallel_impl<double>(exec, first, last);
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}
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else
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{
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return detail::gini_coefficient_parallel_impl<Real>(exec, first, last);
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}
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}
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#else
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template<class ExecutionPolicy, class RandomAccessIterator>
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inline auto gini_coefficient(ExecutionPolicy&& exec, RandomAccessIterator first, RandomAccessIterator last)
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{
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using Real = typename std::iterator_traits<RandomAccessIterator>::value_type;
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if (!std::is_sorted(exec, first, last))
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{
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std::sort(exec, first, last);
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}
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if constexpr (std::is_integral_v<Real>)
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{
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return detail::gini_coefficient_sequential_impl<double>(first, last);
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}
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else
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{
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return detail::gini_coefficient_sequential_impl<Real>(first, last);
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}
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}
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#endif
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template<class ExecutionPolicy, class RandomAccessContainer>
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inline auto gini_coefficient(ExecutionPolicy&& exec, RandomAccessContainer & v)
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{
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return gini_coefficient(exec, std::begin(v), std::end(v));
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}
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template<class RandomAccessIterator>
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inline auto gini_coefficient(RandomAccessIterator first, RandomAccessIterator last)
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{
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return gini_coefficient(std::execution::seq, first, last);
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}
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template<class RandomAccessContainer>
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inline auto gini_coefficient(RandomAccessContainer & v)
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{
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return gini_coefficient(std::execution::seq, std::begin(v), std::end(v));
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}
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template<class ExecutionPolicy, class RandomAccessIterator>
|
|
inline auto sample_gini_coefficient(ExecutionPolicy&& exec, RandomAccessIterator first, RandomAccessIterator last)
|
|
{
|
|
const auto n = std::distance(first, last);
|
|
return n*gini_coefficient(exec, first, last)/(n-1);
|
|
}
|
|
|
|
template<class ExecutionPolicy, class RandomAccessContainer>
|
|
inline auto sample_gini_coefficient(ExecutionPolicy&& exec, RandomAccessContainer & v)
|
|
{
|
|
return sample_gini_coefficient(exec, std::begin(v), std::end(v));
|
|
}
|
|
|
|
template<class RandomAccessIterator>
|
|
inline auto sample_gini_coefficient(RandomAccessIterator first, RandomAccessIterator last)
|
|
{
|
|
return sample_gini_coefficient(std::execution::seq, first, last);
|
|
}
|
|
|
|
template<class RandomAccessContainer>
|
|
inline auto sample_gini_coefficient(RandomAccessContainer & v)
|
|
{
|
|
return sample_gini_coefficient(std::execution::seq, std::begin(v), std::end(v));
|
|
}
|
|
|
|
template<class ExecutionPolicy, class RandomAccessIterator>
|
|
auto median_absolute_deviation(ExecutionPolicy&& exec, RandomAccessIterator first, RandomAccessIterator last,
|
|
typename std::iterator_traits<RandomAccessIterator>::value_type center=std::numeric_limits<typename std::iterator_traits<RandomAccessIterator>::value_type>::quiet_NaN())
|
|
{
|
|
using std::abs;
|
|
using Real = typename std::iterator_traits<RandomAccessIterator>::value_type;
|
|
using std::isnan;
|
|
if (isnan(center))
|
|
{
|
|
center = boost::math::statistics::median(exec, first, last);
|
|
}
|
|
const auto num_elems = std::distance(first, last);
|
|
BOOST_MATH_ASSERT_MSG(num_elems > 0, "The median of a zero-length vector is undefined.");
|
|
auto comparator = [¢er](Real a, Real b) { return abs(a-center) < abs(b-center);};
|
|
if (num_elems & 1)
|
|
{
|
|
auto middle = first + (num_elems - 1)/2;
|
|
std::nth_element(exec, first, middle, last, comparator);
|
|
return abs(*middle);
|
|
}
|
|
else
|
|
{
|
|
auto middle = first + num_elems/2 - 1;
|
|
std::nth_element(exec, first, middle, last, comparator);
|
|
std::nth_element(exec, middle, middle+1, last, comparator);
|
|
return (abs(*middle) + abs(*(middle+1)))/abs(static_cast<Real>(2));
|
|
}
|
|
}
|
|
|
|
template<class ExecutionPolicy, class RandomAccessContainer>
|
|
inline auto median_absolute_deviation(ExecutionPolicy&& exec, RandomAccessContainer & v,
|
|
typename RandomAccessContainer::value_type center=std::numeric_limits<typename RandomAccessContainer::value_type>::quiet_NaN())
|
|
{
|
|
return median_absolute_deviation(exec, std::begin(v), std::end(v), center);
|
|
}
|
|
|
|
template<class RandomAccessIterator>
|
|
inline auto median_absolute_deviation(RandomAccessIterator first, RandomAccessIterator last,
|
|
typename RandomAccessIterator::value_type center=std::numeric_limits<typename RandomAccessIterator::value_type>::quiet_NaN())
|
|
{
|
|
return median_absolute_deviation(std::execution::seq, first, last, center);
|
|
}
|
|
|
|
template<class RandomAccessContainer>
|
|
inline auto median_absolute_deviation(RandomAccessContainer & v,
|
|
typename RandomAccessContainer::value_type center=std::numeric_limits<typename RandomAccessContainer::value_type>::quiet_NaN())
|
|
{
|
|
return median_absolute_deviation(std::execution::seq, std::begin(v), std::end(v), center);
|
|
}
|
|
|
|
template<class ExecutionPolicy, class ForwardIterator>
|
|
auto interquartile_range(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last)
|
|
{
|
|
using Real = typename std::iterator_traits<ForwardIterator>::value_type;
|
|
static_assert(!std::is_integral_v<Real>, "Integer values have not yet been implemented.");
|
|
auto m = std::distance(first,last);
|
|
BOOST_MATH_ASSERT_MSG(m >= 3, "At least 3 samples are required to compute the interquartile range.");
|
|
auto k = m/4;
|
|
auto j = m - (4*k);
|
|
// m = 4k+j.
|
|
// If j = 0 or j = 1, then there are an even number of samples below the median, and an even number above the median.
|
|
// Then we must average adjacent elements to get the quartiles.
|
|
// If j = 2 or j = 3, there are an odd number of samples above and below the median, these elements may be directly extracted to get the quartiles.
|
|
|
|
if (j==2 || j==3)
|
|
{
|
|
auto q1 = first + k;
|
|
auto q3 = first + 3*k + j - 1;
|
|
std::nth_element(exec, first, q1, last);
|
|
Real Q1 = *q1;
|
|
std::nth_element(exec, q1, q3, last);
|
|
Real Q3 = *q3;
|
|
return Q3 - Q1;
|
|
} else {
|
|
// j == 0 or j==1:
|
|
auto q1 = first + k - 1;
|
|
auto q3 = first + 3*k - 1 + j;
|
|
std::nth_element(exec, first, q1, last);
|
|
Real a = *q1;
|
|
std::nth_element(exec, q1, q1 + 1, last);
|
|
Real b = *(q1 + 1);
|
|
Real Q1 = (a+b)/2;
|
|
std::nth_element(exec, q1, q3, last);
|
|
a = *q3;
|
|
std::nth_element(exec, q3, q3 + 1, last);
|
|
b = *(q3 + 1);
|
|
Real Q3 = (a+b)/2;
|
|
return Q3 - Q1;
|
|
}
|
|
}
|
|
|
|
template<class ExecutionPolicy, class RandomAccessContainer>
|
|
inline auto interquartile_range(ExecutionPolicy&& exec, RandomAccessContainer & v)
|
|
{
|
|
return interquartile_range(exec, std::begin(v), std::end(v));
|
|
}
|
|
|
|
template<class RandomAccessIterator>
|
|
inline auto interquartile_range(RandomAccessIterator first, RandomAccessIterator last)
|
|
{
|
|
return interquartile_range(std::execution::seq, first, last);
|
|
}
|
|
|
|
template<class RandomAccessContainer>
|
|
inline auto interquartile_range(RandomAccessContainer & v)
|
|
{
|
|
return interquartile_range(std::execution::seq, std::begin(v), std::end(v));
|
|
}
|
|
|
|
template<class ExecutionPolicy, class ForwardIterator, class OutputIterator>
|
|
inline OutputIterator mode(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, OutputIterator output)
|
|
{
|
|
if(!std::is_sorted(exec, first, last))
|
|
{
|
|
if constexpr (std::is_same_v<typename std::iterator_traits<ForwardIterator>::iterator_category(), std::random_access_iterator_tag>)
|
|
{
|
|
std::sort(exec, first, last);
|
|
}
|
|
else
|
|
{
|
|
BOOST_MATH_ASSERT("Data must be sorted for sequential mode calculation");
|
|
}
|
|
}
|
|
|
|
return detail::mode_impl(first, last, output);
|
|
}
|
|
|
|
template<class ExecutionPolicy, class Container, class OutputIterator>
|
|
inline OutputIterator mode(ExecutionPolicy&& exec, Container & v, OutputIterator output)
|
|
{
|
|
return mode(exec, std::begin(v), std::end(v), output);
|
|
}
|
|
|
|
template<class ForwardIterator, class OutputIterator>
|
|
inline OutputIterator mode(ForwardIterator first, ForwardIterator last, OutputIterator output)
|
|
{
|
|
return mode(std::execution::seq, first, last, output);
|
|
}
|
|
|
|
// Requires enable_if_t to not clash with impl that returns std::list
|
|
// Very ugly. std::is_execution_policy_v returns false for the std::execution objects and decltype of the objects (e.g. std::execution::seq)
|
|
template<class Container, class OutputIterator, std::enable_if_t<!std::is_convertible_v<std::execution::sequenced_policy, Container> &&
|
|
!std::is_convertible_v<std::execution::parallel_unsequenced_policy, Container> &&
|
|
!std::is_convertible_v<std::execution::parallel_policy, Container>
|
|
#if __cpp_lib_execution > 201900
|
|
&& !std::is_convertible_v<std::execution::unsequenced_policy, Container>
|
|
#endif
|
|
, bool> = true>
|
|
inline OutputIterator mode(Container & v, OutputIterator output)
|
|
{
|
|
return mode(std::execution::seq, std::begin(v), std::end(v), output);
|
|
}
|
|
|
|
// std::list is the return type for the proposed STL stats library
|
|
|
|
template<class ExecutionPolicy, class ForwardIterator, class Real = typename std::iterator_traits<ForwardIterator>::value_type>
|
|
inline auto mode(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last)
|
|
{
|
|
std::list<Real> modes;
|
|
mode(exec, first, last, std::inserter(modes, modes.begin()));
|
|
return modes;
|
|
}
|
|
|
|
template<class ExecutionPolicy, class Container>
|
|
inline auto mode(ExecutionPolicy&& exec, Container & v)
|
|
{
|
|
return mode(exec, std::begin(v), std::end(v));
|
|
}
|
|
|
|
template<class ForwardIterator>
|
|
inline auto mode(ForwardIterator first, ForwardIterator last)
|
|
{
|
|
return mode(std::execution::seq, first, last);
|
|
}
|
|
|
|
template<class Container>
|
|
inline auto mode(Container & v)
|
|
{
|
|
return mode(std::execution::seq, std::begin(v), std::end(v));
|
|
}
|
|
|
|
} // Namespace boost::math::statistics
|
|
|
|
#else // Backwards compatible bindings for C++11 or execution is not implemented
|
|
|
|
namespace boost { namespace math { namespace statistics {
|
|
|
|
template<bool B, class T = void>
|
|
using enable_if_t = typename std::enable_if<B, T>::type;
|
|
|
|
template<class ForwardIterator, typename Real = typename std::iterator_traits<ForwardIterator>::value_type,
|
|
enable_if_t<std::is_integral<Real>::value, bool> = true>
|
|
inline double mean(const ForwardIterator first, const ForwardIterator last)
|
|
{
|
|
BOOST_MATH_ASSERT_MSG(first != last, "At least one sample is required to compute the mean.");
|
|
return detail::mean_sequential_impl<double>(first, last);
|
|
}
|
|
|
|
template<class Container, typename Real = typename Container::value_type,
|
|
enable_if_t<std::is_integral<Real>::value, bool> = true>
|
|
inline double mean(const Container& c)
|
|
{
|
|
return mean(std::begin(c), std::end(c));
|
|
}
|
|
|
|
template<class ForwardIterator, typename Real = typename std::iterator_traits<ForwardIterator>::value_type,
|
|
enable_if_t<!std::is_integral<Real>::value, bool> = true>
|
|
inline Real mean(const ForwardIterator first, const ForwardIterator last)
|
|
{
|
|
BOOST_MATH_ASSERT_MSG(first != last, "At least one sample is required to compute the mean.");
|
|
return detail::mean_sequential_impl<Real>(first, last);
|
|
}
|
|
|
|
template<class Container, typename Real = typename Container::value_type,
|
|
enable_if_t<!std::is_integral<Real>::value, bool> = true>
|
|
inline Real mean(const Container& c)
|
|
{
|
|
return mean(std::begin(c), std::end(c));
|
|
}
|
|
|
|
template<class ForwardIterator, typename Real = typename std::iterator_traits<ForwardIterator>::value_type,
|
|
enable_if_t<std::is_integral<Real>::value, bool> = true>
|
|
inline double variance(const ForwardIterator first, const ForwardIterator last)
|
|
{
|
|
return std::get<2>(detail::variance_sequential_impl<std::tuple<double, double, double, double>>(first, last));
|
|
}
|
|
|
|
template<class Container, typename Real = typename Container::value_type,
|
|
enable_if_t<std::is_integral<Real>::value, bool> = true>
|
|
inline double variance(const Container& c)
|
|
{
|
|
return variance(std::begin(c), std::end(c));
|
|
}
|
|
|
|
template<class ForwardIterator, typename Real = typename std::iterator_traits<ForwardIterator>::value_type,
|
|
enable_if_t<!std::is_integral<Real>::value, bool> = true>
|
|
inline Real variance(const ForwardIterator first, const ForwardIterator last)
|
|
{
|
|
return std::get<2>(detail::variance_sequential_impl<std::tuple<Real, Real, Real, Real>>(first, last));
|
|
|
|
}
|
|
|
|
template<class Container, typename Real = typename Container::value_type,
|
|
enable_if_t<!std::is_integral<Real>::value, bool> = true>
|
|
inline Real variance(const Container& c)
|
|
{
|
|
return variance(std::begin(c), std::end(c));
|
|
}
|
|
|
|
template<class ForwardIterator, typename Real = typename std::iterator_traits<ForwardIterator>::value_type,
|
|
enable_if_t<std::is_integral<Real>::value, bool> = true>
|
|
inline double sample_variance(const ForwardIterator first, const ForwardIterator last)
|
|
{
|
|
const auto n = std::distance(first, last);
|
|
BOOST_MATH_ASSERT_MSG(n > 1, "At least two samples are required to compute the sample variance.");
|
|
return n*variance(first, last)/(n-1);
|
|
}
|
|
|
|
template<class Container, typename Real = typename Container::value_type,
|
|
enable_if_t<std::is_integral<Real>::value, bool> = true>
|
|
inline double sample_variance(const Container& c)
|
|
{
|
|
return sample_variance(std::begin(c), std::end(c));
|
|
}
|
|
|
|
template<class ForwardIterator, typename Real = typename std::iterator_traits<ForwardIterator>::value_type,
|
|
enable_if_t<!std::is_integral<Real>::value, bool> = true>
|
|
inline Real sample_variance(const ForwardIterator first, const ForwardIterator last)
|
|
{
|
|
const auto n = std::distance(first, last);
|
|
BOOST_MATH_ASSERT_MSG(n > 1, "At least two samples are required to compute the sample variance.");
|
|
return n*variance(first, last)/(n-1);
|
|
}
|
|
|
|
template<class Container, typename Real = typename Container::value_type,
|
|
enable_if_t<!std::is_integral<Real>::value, bool> = true>
|
|
inline Real sample_variance(const Container& c)
|
|
{
|
|
return sample_variance(std::begin(c), std::end(c));
|
|
}
|
|
|
|
template<class ForwardIterator, typename Real = typename std::iterator_traits<ForwardIterator>::value_type,
|
|
enable_if_t<std::is_integral<Real>::value, bool> = true>
|
|
inline std::pair<double, double> mean_and_sample_variance(const ForwardIterator first, const ForwardIterator last)
|
|
{
|
|
const auto results = detail::variance_sequential_impl<std::tuple<double, double, double, double>>(first, last);
|
|
return std::make_pair(std::get<0>(results), std::get<3>(results)*std::get<2>(results)/(std::get<3>(results)-1.0));
|
|
}
|
|
|
|
template<class Container, typename Real = typename Container::value_type,
|
|
enable_if_t<std::is_integral<Real>::value, bool> = true>
|
|
inline std::pair<double, double> mean_and_sample_variance(const Container& c)
|
|
{
|
|
return mean_and_sample_variance(std::begin(c), std::end(c));
|
|
}
|
|
|
|
template<class ForwardIterator, typename Real = typename std::iterator_traits<ForwardIterator>::value_type,
|
|
enable_if_t<!std::is_integral<Real>::value, bool> = true>
|
|
inline std::pair<Real, Real> mean_and_sample_variance(const ForwardIterator first, const ForwardIterator last)
|
|
{
|
|
const auto results = detail::variance_sequential_impl<std::tuple<Real, Real, Real, Real>>(first, last);
|
|
return std::make_pair(std::get<0>(results), std::get<3>(results)*std::get<2>(results)/(std::get<3>(results)-Real(1)));
|
|
}
|
|
|
|
template<class Container, typename Real = typename Container::value_type,
|
|
enable_if_t<!std::is_integral<Real>::value, bool> = true>
|
|
inline std::pair<Real, Real> mean_and_sample_variance(const Container& c)
|
|
{
|
|
return mean_and_sample_variance(std::begin(c), std::end(c));
|
|
}
|
|
|
|
template<class ForwardIterator, typename Real = typename std::iterator_traits<ForwardIterator>::value_type,
|
|
enable_if_t<std::is_integral<Real>::value, bool> = true>
|
|
inline std::tuple<double, double, double, double> first_four_moments(const ForwardIterator first, const ForwardIterator last)
|
|
{
|
|
const auto results = detail::first_four_moments_sequential_impl<std::tuple<double, double, double, double, double>>(first, last);
|
|
return std::make_tuple(std::get<0>(results), std::get<1>(results) / std::get<4>(results), std::get<2>(results) / std::get<4>(results),
|
|
std::get<3>(results) / std::get<4>(results));
|
|
}
|
|
|
|
template<class Container, typename Real = typename Container::value_type,
|
|
enable_if_t<std::is_integral<Real>::value, bool> = true>
|
|
inline std::tuple<double, double, double, double> first_four_moments(const Container& c)
|
|
{
|
|
return first_four_moments(std::begin(c), std::end(c));
|
|
}
|
|
|
|
template<class ForwardIterator, typename Real = typename std::iterator_traits<ForwardIterator>::value_type,
|
|
enable_if_t<!std::is_integral<Real>::value, bool> = true>
|
|
inline std::tuple<Real, Real, Real, Real> first_four_moments(const ForwardIterator first, const ForwardIterator last)
|
|
{
|
|
const auto results = detail::first_four_moments_sequential_impl<std::tuple<Real, Real, Real, Real, Real>>(first, last);
|
|
return std::make_tuple(std::get<0>(results), std::get<1>(results) / std::get<4>(results), std::get<2>(results) / std::get<4>(results),
|
|
std::get<3>(results) / std::get<4>(results));
|
|
}
|
|
|
|
template<class Container, typename Real = typename Container::value_type,
|
|
enable_if_t<!std::is_integral<Real>::value, bool> = true>
|
|
inline std::tuple<Real, Real, Real, Real> first_four_moments(const Container& c)
|
|
{
|
|
return first_four_moments(std::begin(c), std::end(c));
|
|
}
|
|
|
|
template<class ForwardIterator, typename Real = typename std::iterator_traits<ForwardIterator>::value_type,
|
|
enable_if_t<std::is_integral<Real>::value, bool> = true>
|
|
inline double skewness(const ForwardIterator first, const ForwardIterator last)
|
|
{
|
|
return detail::skewness_sequential_impl<double>(first, last);
|
|
}
|
|
|
|
template<class Container, typename Real = typename Container::value_type,
|
|
enable_if_t<std::is_integral<Real>::value, bool> = true>
|
|
inline double skewness(const Container& c)
|
|
{
|
|
return skewness(std::begin(c), std::end(c));
|
|
}
|
|
|
|
template<class ForwardIterator, typename Real = typename std::iterator_traits<ForwardIterator>::value_type,
|
|
enable_if_t<!std::is_integral<Real>::value, bool> = true>
|
|
inline Real skewness(const ForwardIterator first, const ForwardIterator last)
|
|
{
|
|
return detail::skewness_sequential_impl<Real>(first, last);
|
|
}
|
|
|
|
template<class Container, typename Real = typename Container::value_type,
|
|
enable_if_t<!std::is_integral<Real>::value, bool> = true>
|
|
inline Real skewness(const Container& c)
|
|
{
|
|
return skewness(std::begin(c), std::end(c));
|
|
}
|
|
|
|
template<class ForwardIterator, typename Real = typename std::iterator_traits<ForwardIterator>::value_type,
|
|
enable_if_t<std::is_integral<Real>::value, bool> = true>
|
|
inline double kurtosis(const ForwardIterator first, const ForwardIterator last)
|
|
{
|
|
std::tuple<double, double, double, double> M = first_four_moments(first, last);
|
|
|
|
if(std::get<1>(M) == 0)
|
|
{
|
|
return std::get<1>(M);
|
|
}
|
|
else
|
|
{
|
|
return std::get<3>(M)/(std::get<1>(M)*std::get<1>(M));
|
|
}
|
|
}
|
|
|
|
template<class Container, typename Real = typename Container::value_type,
|
|
enable_if_t<std::is_integral<Real>::value, bool> = true>
|
|
inline double kurtosis(const Container& c)
|
|
{
|
|
return kurtosis(std::begin(c), std::end(c));
|
|
}
|
|
|
|
template<class ForwardIterator, typename Real = typename std::iterator_traits<ForwardIterator>::value_type,
|
|
enable_if_t<!std::is_integral<Real>::value, bool> = true>
|
|
inline Real kurtosis(const ForwardIterator first, const ForwardIterator last)
|
|
{
|
|
std::tuple<Real, Real, Real, Real> M = first_four_moments(first, last);
|
|
|
|
if(std::get<1>(M) == 0)
|
|
{
|
|
return std::get<1>(M);
|
|
}
|
|
else
|
|
{
|
|
return std::get<3>(M)/(std::get<1>(M)*std::get<1>(M));
|
|
}
|
|
}
|
|
|
|
template<class Container, typename Real = typename Container::value_type,
|
|
enable_if_t<!std::is_integral<Real>::value, bool> = true>
|
|
inline Real kurtosis(const Container& c)
|
|
{
|
|
return kurtosis(std::begin(c), std::end(c));
|
|
}
|
|
|
|
template<class ForwardIterator, typename Real = typename std::iterator_traits<ForwardIterator>::value_type,
|
|
enable_if_t<std::is_integral<Real>::value, bool> = true>
|
|
inline double excess_kurtosis(const ForwardIterator first, const ForwardIterator last)
|
|
{
|
|
return kurtosis(first, last) - 3;
|
|
}
|
|
|
|
template<class Container, typename Real = typename Container::value_type,
|
|
enable_if_t<std::is_integral<Real>::value, bool> = true>
|
|
inline double excess_kurtosis(const Container& c)
|
|
{
|
|
return excess_kurtosis(std::begin(c), std::end(c));
|
|
}
|
|
|
|
template<class ForwardIterator, typename Real = typename std::iterator_traits<ForwardIterator>::value_type,
|
|
enable_if_t<!std::is_integral<Real>::value, bool> = true>
|
|
inline Real excess_kurtosis(const ForwardIterator first, const ForwardIterator last)
|
|
{
|
|
return kurtosis(first, last) - 3;
|
|
}
|
|
|
|
template<class Container, typename Real = typename Container::value_type,
|
|
enable_if_t<!std::is_integral<Real>::value, bool> = true>
|
|
inline Real excess_kurtosis(const Container& c)
|
|
{
|
|
return excess_kurtosis(std::begin(c), std::end(c));
|
|
}
|
|
|
|
template<class RandomAccessIterator, typename Real = typename std::iterator_traits<RandomAccessIterator>::value_type>
|
|
Real median(RandomAccessIterator first, RandomAccessIterator last)
|
|
{
|
|
const auto num_elems = std::distance(first, last);
|
|
BOOST_MATH_ASSERT_MSG(num_elems > 0, "The median of a zero length vector is undefined.");
|
|
if (num_elems & 1)
|
|
{
|
|
auto middle = first + (num_elems - 1)/2;
|
|
std::nth_element(first, middle, last);
|
|
return *middle;
|
|
}
|
|
else
|
|
{
|
|
auto middle = first + num_elems/2 - 1;
|
|
std::nth_element(first, middle, last);
|
|
std::nth_element(middle, middle+1, last);
|
|
return (*middle + *(middle+1))/2;
|
|
}
|
|
}
|
|
|
|
template<class RandomAccessContainer, typename Real = typename RandomAccessContainer::value_type>
|
|
inline Real median(RandomAccessContainer& c)
|
|
{
|
|
return median(std::begin(c), std::end(c));
|
|
}
|
|
|
|
template<class RandomAccessIterator, typename Real = typename std::iterator_traits<RandomAccessIterator>::value_type,
|
|
enable_if_t<std::is_integral<Real>::value, bool> = true>
|
|
inline double gini_coefficient(RandomAccessIterator first, RandomAccessIterator last)
|
|
{
|
|
if(!std::is_sorted(first, last))
|
|
{
|
|
std::sort(first, last);
|
|
}
|
|
|
|
return detail::gini_coefficient_sequential_impl<double>(first, last);
|
|
}
|
|
|
|
template<class RandomAccessContainer, typename Real = typename RandomAccessContainer::value_type,
|
|
enable_if_t<std::is_integral<Real>::value, bool> = true>
|
|
inline double gini_coefficient(RandomAccessContainer& c)
|
|
{
|
|
return gini_coefficient(std::begin(c), std::end(c));
|
|
}
|
|
|
|
template<class RandomAccessIterator, typename Real = typename std::iterator_traits<RandomAccessIterator>::value_type,
|
|
enable_if_t<!std::is_integral<Real>::value, bool> = true>
|
|
inline Real gini_coefficient(RandomAccessIterator first, RandomAccessIterator last)
|
|
{
|
|
if(!std::is_sorted(first, last))
|
|
{
|
|
std::sort(first, last);
|
|
}
|
|
|
|
return detail::gini_coefficient_sequential_impl<Real>(first, last);
|
|
}
|
|
|
|
template<class RandomAccessContainer, typename Real = typename RandomAccessContainer::value_type,
|
|
enable_if_t<!std::is_integral<Real>::value, bool> = true>
|
|
inline Real gini_coefficient(RandomAccessContainer& c)
|
|
{
|
|
return gini_coefficient(std::begin(c), std::end(c));
|
|
}
|
|
|
|
template<class RandomAccessIterator, typename Real = typename std::iterator_traits<RandomAccessIterator>::value_type,
|
|
enable_if_t<std::is_integral<Real>::value, bool> = true>
|
|
inline double sample_gini_coefficient(RandomAccessIterator first, RandomAccessIterator last)
|
|
{
|
|
const auto n = std::distance(first, last);
|
|
return n*gini_coefficient(first, last)/(n-1);
|
|
}
|
|
|
|
template<class RandomAccessContainer, typename Real = typename RandomAccessContainer::value_type,
|
|
enable_if_t<std::is_integral<Real>::value, bool> = true>
|
|
inline double sample_gini_coefficient(RandomAccessContainer& c)
|
|
{
|
|
return sample_gini_coefficient(std::begin(c), std::end(c));
|
|
}
|
|
|
|
template<class RandomAccessIterator, typename Real = typename std::iterator_traits<RandomAccessIterator>::value_type,
|
|
enable_if_t<!std::is_integral<Real>::value, bool> = true>
|
|
inline Real sample_gini_coefficient(RandomAccessIterator first, RandomAccessIterator last)
|
|
{
|
|
const auto n = std::distance(first, last);
|
|
return n*gini_coefficient(first, last)/(n-1);
|
|
}
|
|
|
|
template<class RandomAccessContainer, typename Real = typename RandomAccessContainer::value_type,
|
|
enable_if_t<!std::is_integral<Real>::value, bool> = true>
|
|
inline Real sample_gini_coefficient(RandomAccessContainer& c)
|
|
{
|
|
return sample_gini_coefficient(std::begin(c), std::end(c));
|
|
}
|
|
|
|
template<class RandomAccessIterator, typename Real = typename std::iterator_traits<RandomAccessIterator>::value_type>
|
|
Real median_absolute_deviation(RandomAccessIterator first, RandomAccessIterator last,
|
|
typename std::iterator_traits<RandomAccessIterator>::value_type center=std::numeric_limits<typename std::iterator_traits<RandomAccessIterator>::value_type>::quiet_NaN())
|
|
{
|
|
using std::abs;
|
|
using std::isnan;
|
|
if (isnan(center))
|
|
{
|
|
center = boost::math::statistics::median(first, last);
|
|
}
|
|
const auto num_elems = std::distance(first, last);
|
|
BOOST_MATH_ASSERT_MSG(num_elems > 0, "The median of a zero-length vector is undefined.");
|
|
auto comparator = [¢er](Real a, Real b) { return abs(a-center) < abs(b-center);};
|
|
if (num_elems & 1)
|
|
{
|
|
auto middle = first + (num_elems - 1)/2;
|
|
std::nth_element(first, middle, last, comparator);
|
|
return abs(*middle);
|
|
}
|
|
else
|
|
{
|
|
auto middle = first + num_elems/2 - 1;
|
|
std::nth_element(first, middle, last, comparator);
|
|
std::nth_element(middle, middle+1, last, comparator);
|
|
return (abs(*middle) + abs(*(middle+1)))/abs(static_cast<Real>(2));
|
|
}
|
|
}
|
|
|
|
template<class RandomAccessContainer, typename Real = typename RandomAccessContainer::value_type>
|
|
inline Real median_absolute_deviation(RandomAccessContainer& c,
|
|
typename RandomAccessContainer::value_type center=std::numeric_limits<typename RandomAccessContainer::value_type>::quiet_NaN())
|
|
{
|
|
return median_absolute_deviation(std::begin(c), std::end(c), center);
|
|
}
|
|
|
|
template<class ForwardIterator, typename Real = typename std::iterator_traits<ForwardIterator>::value_type>
|
|
Real interquartile_range(ForwardIterator first, ForwardIterator last)
|
|
{
|
|
static_assert(!std::is_integral<Real>::value, "Integer values have not yet been implemented.");
|
|
auto m = std::distance(first,last);
|
|
BOOST_MATH_ASSERT_MSG(m >= 3, "At least 3 samples are required to compute the interquartile range.");
|
|
auto k = m/4;
|
|
auto j = m - (4*k);
|
|
// m = 4k+j.
|
|
// If j = 0 or j = 1, then there are an even number of samples below the median, and an even number above the median.
|
|
// Then we must average adjacent elements to get the quartiles.
|
|
// If j = 2 or j = 3, there are an odd number of samples above and below the median, these elements may be directly extracted to get the quartiles.
|
|
|
|
if (j==2 || j==3)
|
|
{
|
|
auto q1 = first + k;
|
|
auto q3 = first + 3*k + j - 1;
|
|
std::nth_element(first, q1, last);
|
|
Real Q1 = *q1;
|
|
std::nth_element(q1, q3, last);
|
|
Real Q3 = *q3;
|
|
return Q3 - Q1;
|
|
}
|
|
else
|
|
{
|
|
// j == 0 or j==1:
|
|
auto q1 = first + k - 1;
|
|
auto q3 = first + 3*k - 1 + j;
|
|
std::nth_element(first, q1, last);
|
|
Real a = *q1;
|
|
std::nth_element(q1, q1 + 1, last);
|
|
Real b = *(q1 + 1);
|
|
Real Q1 = (a+b)/2;
|
|
std::nth_element(q1, q3, last);
|
|
a = *q3;
|
|
std::nth_element(q3, q3 + 1, last);
|
|
b = *(q3 + 1);
|
|
Real Q3 = (a+b)/2;
|
|
return Q3 - Q1;
|
|
}
|
|
}
|
|
|
|
template<class Container, typename Real = typename Container::value_type>
|
|
Real interquartile_range(Container& c)
|
|
{
|
|
return interquartile_range(std::begin(c), std::end(c));
|
|
}
|
|
|
|
template<class ForwardIterator, class OutputIterator,
|
|
enable_if_t<std::is_same<typename std::iterator_traits<ForwardIterator>::iterator_category(), std::random_access_iterator_tag>::value, bool> = true>
|
|
inline OutputIterator mode(ForwardIterator first, ForwardIterator last, OutputIterator output)
|
|
{
|
|
if(!std::is_sorted(first, last))
|
|
{
|
|
std::sort(first, last);
|
|
}
|
|
|
|
return detail::mode_impl(first, last, output);
|
|
}
|
|
|
|
template<class ForwardIterator, class OutputIterator,
|
|
enable_if_t<!std::is_same<typename std::iterator_traits<ForwardIterator>::iterator_category(), std::random_access_iterator_tag>::value, bool> = true>
|
|
inline OutputIterator mode(ForwardIterator first, ForwardIterator last, OutputIterator output)
|
|
{
|
|
if(!std::is_sorted(first, last))
|
|
{
|
|
BOOST_MATH_ASSERT("Data must be sorted for mode calculation");
|
|
}
|
|
|
|
return detail::mode_impl(first, last, output);
|
|
}
|
|
|
|
template<class Container, class OutputIterator>
|
|
inline OutputIterator mode(Container& c, OutputIterator output)
|
|
{
|
|
return mode(std::begin(c), std::end(c), output);
|
|
}
|
|
|
|
template<class ForwardIterator, typename Real = typename std::iterator_traits<ForwardIterator>::value_type>
|
|
inline std::list<Real> mode(ForwardIterator first, ForwardIterator last)
|
|
{
|
|
std::list<Real> modes;
|
|
mode(first, last, std::inserter(modes, modes.begin()));
|
|
return modes;
|
|
}
|
|
|
|
template<class Container, typename Real = typename Container::value_type>
|
|
inline std::list<Real> mode(Container& c)
|
|
{
|
|
return mode(std::begin(c), std::end(c));
|
|
}
|
|
}}}
|
|
#endif
|
|
#endif // BOOST_MATH_STATISTICS_UNIVARIATE_STATISTICS_HPP
|