robot/include/boost/math/statistics/chatterjee_correlation.hpp

//  (C) Copyright Matt Borland 2022.
//  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_CHATTERJEE_CORRELATION_HPP
#define BOOST_MATH_STATISTICS_CHATTERJEE_CORRELATION_HPP

#include <cstdint>
#include <cmath>
#include <algorithm>
#include <iterator>
#include <vector>
#include <limits>
#include <utility>
#include <type_traits>
#include <boost/math/tools/assert.hpp>
#include <boost/math/tools/config.hpp>
#include <boost/math/statistics/detail/rank.hpp>

#ifdef BOOST_MATH_EXEC_COMPATIBLE
#include <execution>
#include <future>
#include <thread>
#endif

namespace boost { namespace math { namespace statistics {

namespace detail {

template <typename BDIter>
std::size_t chatterjee_transform(BDIter begin, BDIter end)
{
    std::size_t sum = 0;

    while(++begin != end)
    {
        if(*begin > *std::prev(begin))
        {
            sum += *begin - *std::prev(begin);
        }
        else
        {
            sum += *std::prev(begin) - *begin;
        }
    }

    return sum;
}

template <typename ReturnType, typename ForwardIterator>
ReturnType chatterjee_correlation_seq_impl(ForwardIterator u_begin, ForwardIterator u_end, ForwardIterator v_begin, ForwardIterator v_end)
{
    using std::abs;
    
    BOOST_MATH_ASSERT_MSG(std::is_sorted(u_begin, u_end), "The x values must be sorted in order to use this functionality");

    const std::vector<std::size_t> rank_vector = rank(v_begin, v_end);

    std::size_t sum = chatterjee_transform(rank_vector.begin(), rank_vector.end());

    ReturnType result = static_cast<ReturnType>(1) - (static_cast<ReturnType>(3 * sum) / static_cast<ReturnType>(rank_vector.size() * rank_vector.size() - 1));

    // If the result is 1 then Y is constant and all the elements must be ties
    if (abs(result - static_cast<ReturnType>(1)) < std::numeric_limits<ReturnType>::epsilon())
    {
        return std::numeric_limits<ReturnType>::quiet_NaN();
    }

    return result;
}

} // Namespace detail

template <typename Container, typename Real = typename Container::value_type, 
          typename ReturnType = typename std::conditional<std::is_integral<Real>::value, double, Real>::type>
inline ReturnType chatterjee_correlation(const Container& u, const Container& v)
{
    return detail::chatterjee_correlation_seq_impl<ReturnType>(std::begin(u), std::end(u), std::begin(v), std::end(v));
}

}}} // Namespace boost::math::statistics

#ifdef BOOST_MATH_EXEC_COMPATIBLE

namespace boost::math::statistics {

namespace detail {

template <typename ReturnType, typename ExecutionPolicy, typename ForwardIterator>
ReturnType chatterjee_correlation_par_impl(ExecutionPolicy&& exec, ForwardIterator u_begin, ForwardIterator u_end,
                                                                   ForwardIterator v_begin, ForwardIterator v_end)
{
    using std::abs;
    BOOST_MATH_ASSERT_MSG(std::is_sorted(std::forward<ExecutionPolicy>(exec), u_begin, u_end), "The x values must be sorted in order to use this functionality");

    auto rank_vector = rank(std::forward<ExecutionPolicy>(exec), v_begin, v_end);

    const auto num_threads = std::thread::hardware_concurrency() == 0 ? 2u : std::thread::hardware_concurrency();
    std::vector<std::future<std::size_t>> future_manager {};
    const auto elements_per_thread = std::ceil(static_cast<double>(rank_vector.size()) / num_threads);

    auto it = rank_vector.begin();
    auto end = rank_vector.end();
    for(std::size_t i {}; i < num_threads - 1; ++i)
    {
        future_manager.emplace_back(std::async(std::launch::async | std::launch::deferred, [it, elements_per_thread]() -> std::size_t
        {
            return chatterjee_transform(it, std::next(it, elements_per_thread));
        }));
        it = std::next(it, elements_per_thread - 1);
    }

    future_manager.emplace_back(std::async(std::launch::async | std::launch::deferred, [it, end]() -> std::size_t
    {
        return chatterjee_transform(it, end);
    }));

    std::size_t sum {};
    for(std::size_t i {}; i < future_manager.size(); ++i)
    {
        sum += future_manager[i].get();
    }
    
    ReturnType result = static_cast<ReturnType>(1) - (static_cast<ReturnType>(3 * sum) / static_cast<ReturnType>(rank_vector.size() * rank_vector.size() - 1));

    // If the result is 1 then Y is constant and all the elements must be ties
    if (abs(result - static_cast<ReturnType>(1)) < std::numeric_limits<ReturnType>::epsilon())
    {
        return std::numeric_limits<ReturnType>::quiet_NaN();
    }

    return result;
}

} // Namespace detail

template <typename ExecutionPolicy, typename Container, typename Real = typename Container::value_type,
          typename ReturnType = std::conditional_t<std::is_integral_v<Real>, double, Real>>
inline ReturnType chatterjee_correlation(ExecutionPolicy&& exec, const Container& u, const Container& v)
{
    if constexpr (std::is_same_v<std::remove_reference_t<decltype(exec)>, decltype(std::execution::seq)>)
    {
        return detail::chatterjee_correlation_seq_impl<ReturnType>(std::cbegin(u), std::cend(u),
                                                                   std::cbegin(v), std::cend(v));
    }
    else
    {
        return detail::chatterjee_correlation_par_impl<ReturnType>(std::forward<ExecutionPolicy>(exec),
                                                                   std::cbegin(u), std::cend(u),
                                                                   std::cbegin(v), std::cend(v));
    }
}

} // Namespace boost::math::statistics

#endif

#endif // BOOST_MATH_STATISTICS_CHATTERJEE_CORRELATION_HPP