libcarla/include/system/boost/math/statistics/linear_regression.hpp

/*
 * 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