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/*
* Copyright Nick Thompson, 2019
* Copyright Matt Borland, 2021
* Use, modification and distribution are subject to 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_MATH_STATISTICS_LINEAR_REGRESSION_HPP
#define BOOST_MATH_STATISTICS_LINEAR_REGRESSION_HPP
#include <cmath>
#include <algorithm>
#include <utility>
#include <tuple>
#include <stdexcept>
#include <type_traits>
#include <boost/math/statistics/univariate_statistics.hpp>
#include <boost/math/statistics/bivariate_statistics.hpp>
namespace boost { namespace math { namespace statistics { namespace detail {
template<class ReturnType, class RandomAccessContainer>
ReturnType simple_ordinary_least_squares_impl(RandomAccessContainer const & x,
RandomAccessContainer const & y)
{
using Real = typename std::tuple_element<0, ReturnType>::type;
if (x.size() <= 1)
{
throw std::domain_error("At least 2 samples are required to perform a linear regression.");
}
if (x.size() != y.size())
{
throw std::domain_error("The same number of samples must be in the independent and dependent variable.");
}
std::tuple<Real, Real, Real> temp = boost::math::statistics::means_and_covariance(x, y);
Real mu_x = std::get<0>(temp);
Real mu_y = std::get<1>(temp);
Real cov_xy = std::get<2>(temp);
Real var_x = boost::math::statistics::variance(x);
if (var_x <= 0) {
throw std::domain_error("Independent variable has no variance; this breaks linear regression.");
}
Real c1 = cov_xy/var_x;
Real c0 = mu_y - c1*mu_x;
return std::make_pair(c0, c1);
}
template<class ReturnType, class RandomAccessContainer>
ReturnType simple_ordinary_least_squares_with_R_squared_impl(RandomAccessContainer const & x,
RandomAccessContainer const & y)
{
using Real = typename std::tuple_element<0, ReturnType>::type;
if (x.size() <= 1)
{
throw std::domain_error("At least 2 samples are required to perform a linear regression.");
}
if (x.size() != y.size())
{
throw std::domain_error("The same number of samples must be in the independent and dependent variable.");
}
std::tuple<Real, Real, Real> temp = boost::math::statistics::means_and_covariance(x, y);
Real mu_x = std::get<0>(temp);
Real mu_y = std::get<1>(temp);
Real cov_xy = std::get<2>(temp);
Real var_x = boost::math::statistics::variance(x);
if (var_x <= 0) {
throw std::domain_error("Independent variable has no variance; this breaks linear regression.");
}
Real c1 = cov_xy/var_x;
Real c0 = mu_y - c1*mu_x;
Real squared_residuals = 0;
Real squared_mean_deviation = 0;
for(decltype(y.size()) i = 0; i < y.size(); ++i) {
squared_mean_deviation += (y[i] - mu_y)*(y[i]-mu_y);
Real ei = (c0 + c1*x[i]) - y[i];
squared_residuals += ei*ei;
}
Real Rsquared;
if (squared_mean_deviation == 0) {
// Then y = constant, so the linear regression is perfect.
Rsquared = 1;
} else {
Rsquared = 1 - squared_residuals/squared_mean_deviation;
}
return std::make_tuple(c0, c1, Rsquared);
}
} // namespace detail
template<typename RandomAccessContainer, typename Real = typename RandomAccessContainer::value_type,
typename std::enable_if<std::is_integral<Real>::value, bool>::type = true>
inline auto simple_ordinary_least_squares(RandomAccessContainer const & x, RandomAccessContainer const & y) -> std::pair<double, double>
{
return detail::simple_ordinary_least_squares_impl<std::pair<double, double>>(x, y);
}
template<typename RandomAccessContainer, typename Real = typename RandomAccessContainer::value_type,
typename std::enable_if<!std::is_integral<Real>::value, bool>::type = true>
inline auto simple_ordinary_least_squares(RandomAccessContainer const & x, RandomAccessContainer const & y) -> std::pair<Real, Real>
{
return detail::simple_ordinary_least_squares_impl<std::pair<Real, Real>>(x, y);
}
template<typename RandomAccessContainer, typename Real = typename RandomAccessContainer::value_type,
typename std::enable_if<std::is_integral<Real>::value, bool>::type = true>
inline auto simple_ordinary_least_squares_with_R_squared(RandomAccessContainer const & x, RandomAccessContainer const & y) -> std::tuple<double, double, double>
{
return detail::simple_ordinary_least_squares_with_R_squared_impl<std::tuple<double, double, double>>(x, y);
}
template<typename RandomAccessContainer, typename Real = typename RandomAccessContainer::value_type,
typename std::enable_if<!std::is_integral<Real>::value, bool>::type = true>
inline auto simple_ordinary_least_squares_with_R_squared(RandomAccessContainer const & x, RandomAccessContainer const & y) -> std::tuple<Real, Real, Real>
{
return detail::simple_ordinary_least_squares_with_R_squared_impl<std::tuple<Real, Real, Real>>(x, y);
}
}}} // namespace boost::math::statistics
#endif
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