Added thirdparty: boost library

thirdparty/include/boost/math/statistics/detail/rank.hpp

@@ -0,0 +1,140 @@
+//  (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_DETAIL_RANK_HPP
+#define BOOST_MATH_STATISTICS_DETAIL_RANK_HPP
+
+#include <cstdint>
+#include <vector>
+#include <numeric>
+#include <utility>
+#include <iterator>
+#include <algorithm>
+#include <boost/math/tools/config.hpp>
+
+#ifdef BOOST_MATH_EXEC_COMPATIBLE
+#include <execution>
+#endif
+
+namespace boost { namespace math { namespace statistics { namespace detail {
+
+struct pair_equal
+{
+    template <typename T1, typename T2>
+    bool operator()(const std::pair<T1, T2>& a, const std::pair<T1, T2>& b) const
+    {
+        return a.first == b.first;
+    }
+};
+
+}}}} // Namespaces
+
+#ifndef BOOST_MATH_EXEC_COMPATIBLE
+
+namespace boost { namespace math { namespace statistics { namespace detail {
+
+template <typename ForwardIterator, typename T = typename std::iterator_traits<ForwardIterator>::value_type>
+auto rank(ForwardIterator first, ForwardIterator last) -> std::vector<std::size_t>
+{
+    std::size_t elements = std::distance(first, last);
+
+    std::vector<std::pair<T, std::size_t>> rank_vector(elements);
+    std::size_t i = 0;
+    while (first != last)
+    {
+        rank_vector[i] = std::make_pair(*first, i);
+        ++i;
+        ++first;
+    }
+
+    std::sort(rank_vector.begin(), rank_vector.end());
+
+    // Remove duplicates
+    rank_vector.erase(std::unique(rank_vector.begin(), rank_vector.end(), pair_equal()), rank_vector.end());
+    elements = rank_vector.size();
+
+    std::pair<T, std::size_t> rank;
+    std::vector<std::size_t> result(elements);
+    for (i = 0; i < elements; ++i)
+    {
+        if (rank_vector[i].first != rank.first)
+        {
+            rank = std::make_pair(rank_vector[i].first, i);
+        }
+        result[rank_vector[i].second] = rank.second;
+    }
+
+    return result;
+}
+
+template <typename Container>
+inline auto rank(const Container& c) -> std::vector<std::size_t>
+{
+    return rank(std::begin(c), std::end(c));
+}
+
+}}}} // Namespaces
+
+#else
+
+namespace boost::math::statistics::detail {
+
+template <typename ExecutionPolicy, typename ForwardIterator, typename T = typename std::iterator_traits<ForwardIterator>::value_type>
+auto rank(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last)
+{
+    std::size_t elements = std::distance(first, last);
+
+    std::vector<std::pair<T, std::size_t>> rank_vector(elements);
+    std::size_t i = 0;
+    while (first != last)
+    {
+        rank_vector[i] = std::make_pair(*first, i);
+        ++i;
+        ++first;
+    }
+
+    std::sort(exec, rank_vector.begin(), rank_vector.end());
+
+    // Remove duplicates
+    rank_vector.erase(std::unique(exec, rank_vector.begin(), rank_vector.end(), pair_equal()), rank_vector.end());
+    elements = rank_vector.size();
+
+    std::pair<T, std::size_t> rank;
+    std::vector<std::size_t> result(elements);
+    for (i = 0; i < elements; ++i)
+    {
+        if (rank_vector[i].first != rank.first)
+        {
+            rank = std::make_pair(rank_vector[i].first, i);
+        }
+        result[rank_vector[i].second] = rank.second;
+    }
+
+    return result;
+}
+
+template <typename ExecutionPolicy, typename Container>
+inline auto rank(ExecutionPolicy&& exec, const Container& c)
+{
+    return rank(exec, std::cbegin(c), std::cend(c));
+}
+
+template <typename ForwardIterator, typename T = typename std::iterator_traits<ForwardIterator>::value_type>
+inline auto rank(ForwardIterator first, ForwardIterator last)
+{
+    return rank(std::execution::seq, first, last);
+}
+
+template <typename Container>
+inline auto rank(const Container& c)
+{
+    return rank(std::execution::seq, std::cbegin(c), std::cend(c));
+}
+
+} // Namespaces
+
+#endif // BOOST_MATH_EXEC_COMPATIBLE
+
+#endif // BOOST_MATH_STATISTICS_DETAIL_RANK_HPP

thirdparty/include/boost/math/statistics/detail/single_pass.hpp

@@ -0,0 +1,401 @@
+//  (C) Copyright Nick Thompson 2018
+//  (C) Copyright Matt Borland 2020
+//  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_UNIVARIATE_STATISTICS_DETAIL_SINGLE_PASS_HPP
+#define BOOST_MATH_STATISTICS_UNIVARIATE_STATISTICS_DETAIL_SINGLE_PASS_HPP
+
+#include <boost/math/tools/config.hpp>
+#include <boost/math/tools/assert.hpp>
+#include <tuple>
+#include <iterator>
+#include <type_traits>
+#include <cmath>
+#include <algorithm>
+#include <valarray>
+#include <stdexcept>
+#include <functional>
+#include <vector>
+
+#ifdef BOOST_HAS_THREADS
+#include <future>
+#include <thread>
+#endif
+
+namespace boost { namespace math { namespace statistics { namespace detail {
+
+template<typename ReturnType, typename ForwardIterator>
+ReturnType mean_sequential_impl(ForwardIterator first, ForwardIterator last)
+{
+    const std::size_t elements {static_cast<std::size_t>(std::distance(first, last))};
+    std::valarray<ReturnType> mu {0, 0, 0, 0};
+    std::valarray<ReturnType> temp {0, 0, 0, 0};
+    ReturnType i {1};
+    const ForwardIterator end {std::next(first, elements - (elements % 4))};
+    ForwardIterator it {first};
+
+    while(it != end)
+    {
+        const ReturnType inv {ReturnType(1) / i};
+        temp = {static_cast<ReturnType>(*it++), static_cast<ReturnType>(*it++), static_cast<ReturnType>(*it++), static_cast<ReturnType>(*it++)};
+        temp -= mu;
+        mu += (temp *= inv);
+        i += 1;
+    }
+
+    const ReturnType num1 {ReturnType(elements - (elements % 4))/ReturnType(4)};
+    const ReturnType num2 {num1 + ReturnType(elements % 4)};
+
+    while(it != last)
+    {
+        mu[3] += (*it-mu[3])/i;
+        i += 1;
+        ++it;
+    }
+
+    return (num1 * std::valarray<ReturnType>(mu[std::slice(0,3,1)]).sum() + num2 * mu[3]) / ReturnType(elements);
+}
+
+// Higham, Accuracy and Stability, equation 1.6a and 1.6b:
+// Calculates Mean, M2, and variance
+template<typename ReturnType, typename ForwardIterator>
+ReturnType variance_sequential_impl(ForwardIterator first, ForwardIterator last)
+{
+    using Real = typename std::tuple_element<0, ReturnType>::type;
+
+    Real M = *first;
+    Real Q = 0;
+    Real k = 2;
+    Real M2 = 0;
+    std::size_t n = 1;
+
+    for(auto it = std::next(first); it != last; ++it)
+    {
+        Real tmp = (*it - M) / k;
+        Real delta_1 = *it - M;
+        Q += k*(k-1)*tmp*tmp;
+        M += tmp;
+        k += 1;
+        Real delta_2 = *it - M;
+        M2 += delta_1 * delta_2;
+        ++n;
+    }
+
+    return std::make_tuple(M, M2, Q/(k-1), Real(n));
+}
+
+// https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Higher-order_statistics
+template<typename ReturnType, typename ForwardIterator>
+ReturnType first_four_moments_sequential_impl(ForwardIterator first, ForwardIterator last)
+{
+    using Real = typename std::tuple_element<0, ReturnType>::type;
+    using Size = typename std::tuple_element<4, ReturnType>::type;
+
+    Real M1 = *first;
+    Real M2 = 0;
+    Real M3 = 0;
+    Real M4 = 0;
+    Size n = 2;
+    for (auto it = std::next(first); it != last; ++it)
+    {
+        Real delta21 = *it - M1;
+        Real tmp = delta21/n;
+        M4 = M4 + tmp*(tmp*tmp*delta21*((n-1)*(n*n-3*n+3)) + 6*tmp*M2 - 4*M3);
+        M3 = M3 + tmp*((n-1)*(n-2)*delta21*tmp - 3*M2);
+        M2 = M2 + tmp*(n-1)*delta21;
+        M1 = M1 + tmp;
+        n += 1;
+    }
+
+    return std::make_tuple(M1, M2, M3, M4, n-1);
+}
+
+#ifdef BOOST_HAS_THREADS
+
+// https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Higher-order_statistics
+// EQN 3.1: https://www.osti.gov/servlets/purl/1426900
+template<typename ReturnType, typename ForwardIterator>
+ReturnType first_four_moments_parallel_impl(ForwardIterator first, ForwardIterator last)
+{
+    using Real = typename std::tuple_element<0, ReturnType>::type;
+
+    const auto elements = std::distance(first, last);
+    const unsigned max_concurrency = std::thread::hardware_concurrency() == 0 ? 2u : std::thread::hardware_concurrency();
+    unsigned num_threads = 2u;
+    
+    // Threading is faster for: 10 + 5.13e-3 N/j <= 5.13e-3N => N >= 10^4j/5.13(j-1).
+    const auto parallel_lower_bound = 10e4*max_concurrency/(5.13*(max_concurrency-1));
+    const auto parallel_upper_bound = 10e4*2/5.13; // j = 2
+
+    // https://lemire.me/blog/2020/01/30/cost-of-a-thread-in-c-under-linux/
+    if(elements < parallel_lower_bound)
+    {
+        return detail::first_four_moments_sequential_impl<ReturnType>(first, last);
+    }
+    else if(elements >= parallel_upper_bound)
+    {
+        num_threads = max_concurrency;
+    }
+    else
+    {
+        for(unsigned i = 3; i < max_concurrency; ++i)
+        {
+            if(parallel_lower_bound < 10e4*i/(5.13*(i-1)))
+            {
+                num_threads = i;
+                break;
+            }
+        }
+    }
+
+    std::vector<std::future<ReturnType>> future_manager;
+    const auto elements_per_thread = std::ceil(static_cast<double>(elements) / num_threads);
+
+    auto it = first;
+    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]() -> ReturnType
+        {
+            return first_four_moments_sequential_impl<ReturnType>(it, std::next(it, elements_per_thread));
+        }));
+        it = std::next(it, elements_per_thread);
+    }
+
+    future_manager.emplace_back(std::async(std::launch::async | std::launch::deferred, [it, last]() -> ReturnType
+    {
+        return first_four_moments_sequential_impl<ReturnType>(it, last);
+    }));
+
+    auto temp = future_manager[0].get();
+    Real M1_a = std::get<0>(temp);
+    Real M2_a = std::get<1>(temp);
+    Real M3_a = std::get<2>(temp);
+    Real M4_a = std::get<3>(temp);
+    Real range_a = std::get<4>(temp);
+
+    for(std::size_t i = 1; i < future_manager.size(); ++i)
+    {
+        temp = future_manager[i].get();
+        Real M1_b = std::get<0>(temp);
+        Real M2_b = std::get<1>(temp);
+        Real M3_b = std::get<2>(temp);
+        Real M4_b = std::get<3>(temp);
+        Real range_b = std::get<4>(temp);
+
+        const Real n_ab = range_a + range_b;
+        const Real delta = M1_b - M1_a;
+        
+        M1_a = (range_a * M1_a + range_b * M1_b) / n_ab;
+        M2_a = M2_a + M2_b + delta * delta * (range_a * range_b / n_ab);
+        M3_a = M3_a + M3_b + (delta * delta * delta) * range_a * range_b * (range_a - range_b) / (n_ab * n_ab)    
+               + Real(3) * delta * (range_a * M2_b - range_b * M2_a) / n_ab;
+        M4_a = M4_a + M4_b + (delta * delta * delta * delta) * range_a * range_b * (range_a * range_a - range_a * range_b + range_b * range_b) / (n_ab * n_ab * n_ab)
+               + Real(6) * delta * delta * (range_a * range_a * M2_b + range_b * range_b * M2_a) / (n_ab * n_ab) 
+               + Real(4) * delta * (range_a * M3_b - range_b * M3_a) / n_ab;
+        range_a = n_ab;
+    }
+
+    return std::make_tuple(M1_a, M2_a, M3_a, M4_a, elements);
+}
+
+#endif // BOOST_HAS_THREADS
+
+// Follows equation 1.5 of:
+// https://prod.sandia.gov/techlib-noauth/access-control.cgi/2008/086212.pdf
+template<typename ReturnType, typename ForwardIterator>
+ReturnType skewness_sequential_impl(ForwardIterator first, ForwardIterator last)
+{
+    using std::sqrt;
+    BOOST_MATH_ASSERT_MSG(first != last, "At least one sample is required to compute skewness.");
+    
+    ReturnType M1 = *first;
+    ReturnType M2 = 0;
+    ReturnType M3 = 0;
+    ReturnType n = 2;
+        
+    for (auto it = std::next(first); it != last; ++it)    
+    {
+        ReturnType delta21 = *it - M1;
+        ReturnType tmp = delta21/n;
+        M3 += tmp*((n-1)*(n-2)*delta21*tmp - 3*M2);
+        M2 += tmp*(n-1)*delta21;
+        M1 += tmp;
+        n += 1;
+    }
+   
+    ReturnType var = M2/(n-1);
+    
+    if (var == 0)
+    {
+        // The limit is technically undefined, but the interpretation here is clear:
+        // A constant dataset has no skewness.
+        return ReturnType(0);
+    }
+    
+    ReturnType skew = M3/(M2*sqrt(var));
+    return skew;
+}
+
+template<typename ReturnType, typename ForwardIterator>
+ReturnType gini_coefficient_sequential_impl(ForwardIterator first, ForwardIterator last)
+{
+    ReturnType i = 1;
+    ReturnType num = 0;
+    ReturnType denom = 0;
+
+    for(auto it = first; it != last; ++it)
+    {
+        num += *it*i;
+        denom += *it;
+        ++i;
+    }
+
+    // If the l1 norm is zero, all elements are zero, so every element is the same.
+    if(denom == 0)
+    {
+        return ReturnType(0);
+    }
+    else
+    {
+        return ((2*num)/denom - i)/(i-1);
+    }
+}
+
+template<typename ReturnType, typename ForwardIterator>
+ReturnType gini_range_fraction(ForwardIterator first, ForwardIterator last, std::size_t starting_index)
+{
+    using Real = typename std::tuple_element<0, ReturnType>::type;
+
+    std::size_t i = starting_index + 1;
+    Real num = 0;
+    Real denom = 0;
+
+    for(auto it = first; it != last; ++it)
+    {
+        num += *it*i;
+        denom += *it;
+        ++i;
+    }
+
+    return std::make_tuple(num, denom, i);
+}
+
+#ifdef BOOST_HAS_THREADS
+
+template<typename ReturnType, typename ExecutionPolicy, typename ForwardIterator>
+ReturnType gini_coefficient_parallel_impl(ExecutionPolicy&&, ForwardIterator first, ForwardIterator last)
+{
+    using range_tuple = std::tuple<ReturnType, ReturnType, std::size_t>;
+    
+    const auto elements = std::distance(first, last);
+    const unsigned max_concurrency = std::thread::hardware_concurrency() == 0 ? 2u : std::thread::hardware_concurrency();
+    unsigned num_threads = 2u;
+    
+    // Threading is faster for: 10 + 10.12e-3 N/j <= 10.12e-3N => N >= 10^4j/10.12(j-1).
+    const auto parallel_lower_bound = 10e4*max_concurrency/(10.12*(max_concurrency-1));
+    const auto parallel_upper_bound = 10e4*2/10.12; // j = 2
+
+    // https://lemire.me/blog/2020/01/30/cost-of-a-thread-in-c-under-linux/
+    if(elements < parallel_lower_bound)
+    {
+        return gini_coefficient_sequential_impl<ReturnType>(first, last);
+    }
+    else if(elements >= parallel_upper_bound)
+    {
+        num_threads = max_concurrency;
+    }
+    else
+    {
+        for(unsigned i = 3; i < max_concurrency; ++i)
+        {
+            if(parallel_lower_bound < 10e4*i/(10.12*(i-1)))
+            {
+                num_threads = i;
+                break;
+            }
+        }
+    }
+
+    std::vector<std::future<range_tuple>> future_manager;
+    const auto elements_per_thread = std::ceil(static_cast<double>(elements) / num_threads);
+
+    auto it = first;
+    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, i]() -> range_tuple
+        {
+            return gini_range_fraction<range_tuple>(it, std::next(it, elements_per_thread), i*elements_per_thread);
+        }));
+        it = std::next(it, elements_per_thread);
+    }
+
+    future_manager.emplace_back(std::async(std::launch::async | std::launch::deferred, [it, last, num_threads, elements_per_thread]() -> range_tuple
+    {
+        return gini_range_fraction<range_tuple>(it, last, (num_threads - 1)*elements_per_thread);
+    }));
+
+    ReturnType num = 0;
+    ReturnType denom = 0;
+
+    for(std::size_t i = 0; i < future_manager.size(); ++i)
+    {
+        auto temp = future_manager[i].get();
+        num += std::get<0>(temp);
+        denom += std::get<1>(temp);
+    }
+
+    // If the l1 norm is zero, all elements are zero, so every element is the same.
+    if(denom == 0)
+    {
+        return ReturnType(0);
+    }
+    else
+    {
+        return ((2*num)/denom - elements)/(elements-1);
+    }
+}
+
+#endif // BOOST_HAS_THREADS
+
+template<typename ForwardIterator, typename OutputIterator>
+OutputIterator mode_impl(ForwardIterator first, ForwardIterator last, OutputIterator output)
+{
+    using Z = typename std::iterator_traits<ForwardIterator>::value_type;
+    using Size = typename std::iterator_traits<ForwardIterator>::difference_type;
+
+    std::vector<Z> modes {};
+    modes.reserve(16);
+    Size max_counter {0};
+
+    while(first != last)
+    {
+        Size current_count {0};
+        ForwardIterator end_it {first};
+        while(end_it != last && *end_it == *first)
+        {
+            ++current_count;
+            ++end_it;
+        }
+
+        if(current_count > max_counter)
+        {
+            modes.resize(1);
+            modes[0] = *first;
+            max_counter = current_count;
+        }
+
+        else if(current_count == max_counter)
+        {
+            modes.emplace_back(*first);
+        }
+
+        first = end_it;
+    }
+
+    return std::move(modes.begin(), modes.end(), output);
+}
+}}}}
+
+#endif // BOOST_MATH_STATISTICS_UNIVARIATE_STATISTICS_DETAIL_SINGLE_PASS_HPP