# dlib C++ Library - isotonic_regression.h

    // Copyright (C) 2018  Davis E. King (davis@dlib.net)
    // License: Boost Software License   See LICENSE.txt for the full license.
    #ifndef DLIB_ISOTONIC_ReGRESSION_H_
    #define DLIB_ISOTONIC_ReGRESSION_H_

    #include "isotonic_regression_abstract.h"
    #include <vector>
    #include <utility>
    #include <cstddef>

    namespace dlib
    {
        class isotonic_regression
        {
        public:

            template <
                typename const_iterator,
                typename iterator
                >
            void operator() (
                const_iterator begin,
                const_iterator end,
                iterator obegin
            )
            {
                do_isotonic_regression(begin, end);

                // unpack blocks to output
                for (auto& block : blocks)
                {
                    for (size_t k = 0; k < block.num; ++k)
                        set_val(*obegin++, block.avg);
                }

                blocks.clear();
            }

            void operator() (
                std::vector<double>& vect
            ) { (*this)(vect.begin(), vect.end(), vect.begin()); }

            template <typename T, typename U>
            void operator() (
                std::vector<std::pair<T,U>>& vect
            ) { (*this)(vect.begin(), vect.end(), vect.begin()); }

            template <
                typename const_iterator,
                typename iterator
                >
            void fit_with_linear_output_interpolation (
                const_iterator begin,
                const_iterator end,
                iterator obegin
            )
            {
                do_isotonic_regression(begin, end);

                // Unpack blocks to output, but here instead of producing the step function
                // output we linearly interpolate.  Note that this actually fits the data less
                // than the step-function, but in many applications might be closer to what you
                // really want when using isotonic_regression than the step function.
                for (size_t i = 0; i < blocks.size(); ++i)
                {
                    auto& block = blocks[i];

                    double prev = (blocks.front().avg + block.avg)/2;
                    if (i > 0)
                        prev = (blocks[i-1].avg+block.avg)/2;

                    double next = (blocks.back().avg + block.avg)/2;
                    if (i+1 < blocks.size())
                        next = (blocks[i+1].avg+block.avg)/2;

                    for (size_t k = 0; k < block.num; ++k)
                    {
                        const auto mid = block.num/2.0;
                        if (k < mid)
                        {
                            const double alpha = k/mid;
                            set_val(*obegin++, (1-alpha)*prev + alpha*block.avg);
                        }
                        else
                        {
                            const double alpha = k/mid-1;
                            set_val(*obegin++, alpha*next + (1-alpha)*block.avg);
                        }
                    }
                }

                blocks.clear();
            }

            void fit_with_linear_output_interpolation (
                std::vector<double>& vect
            ) { fit_with_linear_output_interpolation(vect.begin(), vect.end(), vect.begin()); }

            template <typename T, typename U>
            void fit_with_linear_output_interpolation (
                std::vector<std::pair<T,U>>& vect
            ) { fit_with_linear_output_interpolation(vect.begin(), vect.end(), vect.begin()); }

        private:

            template <
                typename const_iterator
                >
            void do_isotonic_regression (
                const_iterator begin,
                const_iterator end
            )
            {
                blocks.clear();

                // Do the actual isotonic regression.  The output is a step-function and is
                // stored in the vector of blocks.
                for (auto i = begin; i != end; ++i)
                {
                    blocks.emplace_back(get_val(*i));
                    while (blocks.size() > 1 && prev_block().avg > current_block().avg)
                    {
                        // merge the last two blocks.
                        prev_block() = prev_block() + current_block();
                        blocks.pop_back();
                    }
                }
            }

            template <typename T>
            static double get_val(const T& v) { return v;}

            template <typename T, typename U>
            static double get_val(const std::pair<T,U>& v) { return v.second;}

            template <typename T>
            static void set_val(T& v, double val) { v = val;}

            template <typename T, typename U>
            static void set_val(std::pair<T,U>& v, double val) { v.second = val;}

            struct block_t
            {
                block_t(double val) : num(1), avg(val) {}
                block_t(size_t n, double val) : num(n), avg(val) {}

                size_t num;
                double avg;

                inline block_t operator+(const block_t& rhs) const
                {
                    return block_t(num+rhs.num,
                        (num*avg + rhs.num*rhs.avg)/(num+rhs.num));
                }
            };

            inline block_t& prev_block() { return blocks[blocks.size()-2]; }
            inline block_t& current_block() { return blocks.back(); }

            std::vector<block_t> blocks;
        };
    }

    #endif // DLIB_ISOTONIC_ReGRESSION_H_