    // Copyright (C) 2008  Davis E. King (davis@dlib.net)
    // License: Boost Software License   See LICENSE.txt for the full license.
    #ifndef DLIB_KKMEANs_
    #define DLIB_KKMEANs_

    #include <cmath>
    #include <vector>

    #include "../matrix/matrix_abstract.h"
    #include "../algs.h"
    #include "../serialize.h"
    #include "kernel.h"
    #include "../array.h"
    #include "kcentroid.h"
    #include "kkmeans_abstract.h"
    #include "../noncopyable.h"

    namespace dlib
    {

        template <
            typename kernel_type
            >
        class kkmeans : public noncopyable
        {
        public:
            typedef typename kernel_type::scalar_type scalar_type;
            typedef typename kernel_type::sample_type sample_type;
            typedef typename kernel_type::mem_manager_type mem_manager_type;

            kkmeans (
                const kcentroid<kernel_type>& kc_
            ):
                kc(kc_),
                min_change(0.01)
            {
                set_number_of_centers(1);
            }

            ~kkmeans()
            {
            }

            const kernel_type& get_kernel (
            ) const
            {
                return kc.get_kernel();
            }

            void set_kcentroid (
                const kcentroid<kernel_type>& kc_
            )
            {
                kc = kc_;
                set_number_of_centers(number_of_centers());
            }

            const kcentroid<kernel_type>& get_kcentroid (
                unsigned long i
            ) const
            {
                // make sure requires clause is not broken
                DLIB_ASSERT(i < number_of_centers(),
                    "\tkcentroid kkmeans::get_kcentroid(i)"
                    << "\n\tYou have given an invalid value for i"
                    << "\n\ti:                   " << i
                    << "\n\tnumber_of_centers(): " << number_of_centers()
                    << "\n\tthis:                " << this
                    );

                return *centers[i];
            }

            void set_number_of_centers (
                unsigned long num
            )
            {
                // make sure requires clause is not broken
                DLIB_ASSERT(num > 0,
                    "\tvoid kkmeans::set_number_of_centers()"
                    << "\n\tYou can't set the number of centers to zero"
                    << "\n\tthis: " << this
                    );

                centers.set_max_size(num);
                centers.set_size(num);

                for (unsigned long i = 0; i < centers.size(); ++i)
                {
                    centers[i].reset(new kcentroid<kernel_type>(kc));
                }
            }

            unsigned long number_of_centers (
            ) const
            {
                return centers.size();
            }

            template <typename T, typename U>
            void train (
                const T& samples,
                const U& initial_centers,
                long max_iter = 1000
            )
            {
                do_train(mat(samples),mat(initial_centers),max_iter);
            }

            unsigned long operator() (
                const sample_type& sample
            ) const
            {
                unsigned long label = 0;
                scalar_type best_score = (*centers[0])(sample);

                // figure out which center the given sample is closest too
                for (unsigned long i = 1; i < centers.size(); ++i)
                {
                    scalar_type temp = (*centers[i])(sample);
                    if (temp < best_score)
                    {
                        label = i;
                        best_score = temp;
                    }
                }

                return label;
            }

            void set_min_change (
                scalar_type min_change_
            )
            {
                // make sure requires clause is not broken
                DLIB_ASSERT( 0 <= min_change_ < 1,
                    "\tvoid kkmeans::set_min_change()"
                    << "\n\tInvalid arguments to this function"
                    << "\n\tthis: " << this
                    << "\n\tmin_change_: " << min_change_
                    );
                min_change = min_change_;
            }

            const scalar_type get_min_change (
            ) const
            {
                return min_change;
            }

            void swap (
                kkmeans& item
            )
            {
                centers.swap(item.centers);
                kc.swap(item.kc);
                assignments.swap(item.assignments);
                exchange(min_change, item.min_change);
            }

            friend void serialize(const kkmeans& item, std::ostream& out)
            {
                serialize(item.centers.size(),out);
                for (unsigned long i = 0; i < item.centers.size(); ++i)
                {
                    serialize(*item.centers[i], out);
                }
                serialize(item.kc, out);
                serialize(item.min_change, out);
            }

            friend void deserialize(kkmeans& item, std::istream& in)
            {
                unsigned long num;
                deserialize(num, in);
                item.centers.resize(num);
                for (unsigned long i = 0; i < item.centers.size(); ++i)
                {
                    std::unique_ptr<kcentroid<kernel_type> > temp(new kcentroid<kernel_type>(kernel_type()));
                    deserialize(*temp, in);
                    item.centers[i].swap(temp);
                }

                deserialize(item.kc, in);
                deserialize(item.min_change, in);
            }

        private:

            template <typename matrix_type, typename matrix_type2>
            void do_train (
                const matrix_type& samples,
                const matrix_type2& initial_centers,
                long max_iter = 1000
            )
            {
                COMPILE_TIME_ASSERT((is_same_type<typename matrix_type::type, sample_type>::value));
                COMPILE_TIME_ASSERT((is_same_type<typename matrix_type2::type, sample_type>::value));

                // make sure requires clause is not broken
                DLIB_ASSERT(samples.nc() == 1 && initial_centers.nc() == 1 &&
                             initial_centers.nr() == static_cast<long>(number_of_centers()),
                    "\tvoid kkmeans::train()"
                    << "\n\tInvalid arguments to this function"
                    << "\n\tthis: " << this
                    << "\n\tsamples.nc(): " << samples.nc()
                    << "\n\tinitial_centers.nc(): " << initial_centers.nc()
                    << "\n\tinitial_centers.nr(): " << initial_centers.nr()
                    );

                // clear out the old data and initialize the centers
                for (unsigned long i = 0; i < centers.size(); ++i)
                {
                    centers[i]->clear_dictionary();
                    centers[i]->train(initial_centers(i));
                }

                assignments.resize(samples.size());

                bool assignment_changed = true;

                // loop until the centers stabilize
                long count = 0;
                const unsigned long min_num_change = static_cast<unsigned long>(min_change*samples.size());
                unsigned long num_changed = min_num_change;
                while (assignment_changed && count < max_iter && num_changed >= min_num_change)
                {
                    ++count;
                    assignment_changed = false;
                    num_changed = 0;

                    // loop over all the samples and assign them to their closest centers
                    for (long i = 0; i < samples.size(); ++i)
                    {
                        // find the best center
                        unsigned long best_center = 0;
                        scalar_type best_score = (*centers[0])(samples(i));
                        for (unsigned long c = 1; c < centers.size(); ++c)
                        {
                            scalar_type temp = (*centers[c])(samples(i));
                            if (temp < best_score)
                            {
                                best_score = temp;
                                best_center = c;
                            }
                        }

                        // if the current sample changed centers then make note of that
                        if (assignments[i] != best_center)
                        {
                            assignments[i] = best_center;
                            assignment_changed = true;
                            ++num_changed;
                        }
                    }

                    if (assignment_changed)
                    {
                        // now clear out the old data
                        for (unsigned long i = 0; i < centers.size(); ++i)
                            centers[i]->clear_dictionary();

                        // recalculate the cluster centers
                        for (unsigned long i = 0; i < assignments.size(); ++i)
                            centers[assignments[i]]->train(samples(i));
                    }

                }

            }

            array<std::unique_ptr<kcentroid<kernel_type> > > centers;
            kcentroid<kernel_type> kc;
            scalar_type min_change;

            // temp variables
            array<unsigned long> assignments;
        };

    // ----------------------------------------------------------------------------------------

        template <typename kernel_type>
        void swap(kkmeans<kernel_type>& a, kkmeans<kernel_type>& b)
        { a.swap(b); }

    // ----------------------------------------------------------------------------------------

        struct dlib_pick_initial_centers_data
        {
            dlib_pick_initial_centers_data():idx(0), dist(std::numeric_limits<double>::infinity()){}
            long idx;
            double dist;
            bool operator< (const dlib_pick_initial_centers_data& d) const { return dist < d.dist; }
        };

        template <
            typename vector_type1,
            typename vector_type2,
            typename kernel_type
            >
        void pick_initial_centers(
            long num_centers,
            vector_type1& centers,
            const vector_type2& samples,
            const kernel_type& k,
            double percentile = 0.01
        )
        {
            /*
                This function is basically just a non-randomized version of the kmeans++ algorithm
                described in the paper:
                    kmeans++: The Advantages of Careful Seeding by Arthur and Vassilvitskii

            */

            // make sure requires clause is not broken
            DLIB_ASSERT(num_centers > 1 && 0 <= percentile && percentile < 1 && samples.size() > 1,
                "\tvoid pick_initial_centers()"
                << "\n\tYou passed invalid arguments to this function"
                << "\n\tnum_centers: " << num_centers
                << "\n\tpercentile: " << percentile
                << "\n\tsamples.size(): " << samples.size()
                );

            std::vector<dlib_pick_initial_centers_data> scores(samples.size());
            std::vector<dlib_pick_initial_centers_data> scores_sorted(samples.size());
            centers.clear();

            // pick the first sample as one of the centers
            centers.push_back(samples[0]);

            const long best_idx = static_cast<long>(std::max(0.0,samples.size() - samples.size()*percentile - 1));

            // pick the next center
            for (long i = 0; i < num_centers-1; ++i)
            {
                // Loop over the samples and compare them to the most recent center.  Store
                // the distance from each sample to its closest center in scores.
                const double k_cc = k(centers[i], centers[i]);
                for (unsigned long s = 0; s < samples.size(); ++s)
                {
                    // compute the distance between this sample and the current center
                    const double dist = k_cc + k(samples[s],samples[s]) - 2*k(samples[s], centers[i]);

                    if (dist < scores[s].dist)
                    {
                        scores[s].dist = dist;
                        scores[s].idx = s;
                    }
                }

                scores_sorted = scores;

                // now find the winning center and add it to centers.  It is the one that is
                // far away from all the other centers.
                sort(scores_sorted.begin(), scores_sorted.end());
                centers.push_back(samples[scores_sorted[best_idx].idx]);
            }

        }

    // ----------------------------------------------------------------------------------------

        template <
            typename vector_type1,
            typename vector_type2
            >
        void pick_initial_centers(
            long num_centers,
            vector_type1& centers,
            const vector_type2& samples,
            double percentile = 0.01
        )
        {
            typedef typename vector_type1::value_type sample_type;
            linear_kernel<sample_type> kern;
            pick_initial_centers(num_centers, centers, samples, kern, percentile);
        }

    // ----------------------------------------------------------------------------------------

        template <
            typename array_type,
            typename sample_type,
            typename alloc
            >
        void find_clusters_using_kmeans (
            const array_type& samples,
            std::vector<sample_type, alloc>& centers,
            unsigned long max_iter = 1000
        )
        {
            // make sure requires clause is not broken
            DLIB_ASSERT(samples.size() > 0 && centers.size() > 0,
                "\tvoid find_clusters_using_kmeans()"
                << "\n\tYou passed invalid arguments to this function"
                << "\n\t samples.size(): " << samples.size()
                << "\n\t centers.size(): " << centers.size()
                );

    #ifdef ENABLE_ASSERTS
            {
            const long nr = samples[0].nr();
            const long nc = samples[0].nc();
            for (unsigned long i = 0; i < samples.size(); ++i)
            {
                DLIB_ASSERT(is_vector(samples[i]) && samples[i].nr() == nr && samples[i].nc() == nc,
                    "\tvoid find_clusters_using_kmeans()"
                    << "\n\t You passed invalid arguments to this function"
                    << "\n\t is_vector(samples[i]): " << is_vector(samples[i])
                    << "\n\t samples[i].nr():       " << samples[i].nr()
                    << "\n\t nr:                    " << nr
                    << "\n\t samples[i].nc():       " << samples[i].nc()
                    << "\n\t nc:                    " << nc
                    << "\n\t i:                     " << i
                    );
            }
            }
    #endif

            typedef typename sample_type::type scalar_type;

            sample_type zero(centers[0]);
            set_all_elements(zero, 0);

            std::vector<unsigned long> center_element_count;

            // tells which center a sample belongs to
            std::vector<unsigned long> assignments(samples.size(), samples.size());

            unsigned long iter = 0;
            bool centers_changed = true;
            while (centers_changed && iter < max_iter)
            {
                ++iter;
                centers_changed = false;
                center_element_count.assign(centers.size(), 0);

                // loop over each sample and see which center it is closest to
                for (unsigned long i = 0; i < samples.size(); ++i)
                {
                    // find the best center for sample[i]
                    scalar_type best_dist = std::numeric_limits<scalar_type>::max();
                    unsigned long best_center = 0;
                    for (unsigned long j = 0; j < centers.size(); ++j)
                    {
                        scalar_type dist = length(centers[j] - samples[i]);
                        if (dist < best_dist)
                        {
                            best_dist = dist;
                            best_center = j;
                        }
                    }

                    if (assignments[i] != best_center)
                    {
                        centers_changed = true;
                        assignments[i] = best_center;
                    }

                    center_element_count[best_center] += 1;
                }

                // now update all the centers
                centers.assign(centers.size(), zero);
                for (unsigned long i = 0; i < samples.size(); ++i)
                {
                    centers[assignments[i]] += samples[i];
                }
                for (unsigned long i = 0; i < centers.size(); ++i)
                {
                    if (center_element_count[i] != 0)
                        centers[i] /= center_element_count[i];
                }
            }

        }

    // ----------------------------------------------------------------------------------------

        template <
            typename array_type,
            typename sample_type,
            typename alloc
            >
        void find_clusters_using_angular_kmeans (
            const array_type& samples,
            std::vector<sample_type, alloc>& centers,
            unsigned long max_iter = 1000
        )
        {
            // make sure requires clause is not broken
            DLIB_ASSERT(samples.size() > 0 && centers.size() > 0,
                "\tvoid find_clusters_using_angular_kmeans()"
                << "\n\tYou passed invalid arguments to this function"
                << "\n\t samples.size(): " << samples.size()
                << "\n\t centers.size(): " << centers.size()
                );

    #ifdef ENABLE_ASSERTS
            {
            const long nr = samples[0].nr();
            const long nc = samples[0].nc();
            for (unsigned long i = 0; i < samples.size(); ++i)
            {
                DLIB_ASSERT(is_vector(samples[i]) && samples[i].nr() == nr && samples[i].nc() == nc,
                    "\tvoid find_clusters_using_angular_kmeans()"
                    << "\n\t You passed invalid arguments to this function"
                    << "\n\t is_vector(samples[i]): " << is_vector(samples[i])
                    << "\n\t samples[i].nr():       " << samples[i].nr()
                    << "\n\t nr:                    " << nr
                    << "\n\t samples[i].nc():       " << samples[i].nc()
                    << "\n\t nc:                    " << nc
                    << "\n\t i:                     " << i
                    );
            }
            }
    #endif

            typedef typename sample_type::type scalar_type;

            sample_type zero(centers[0]);
            set_all_elements(zero, 0);

            unsigned long seed = 0;

            // tells which center a sample belongs to
            std::vector<unsigned long> assignments(samples.size(), samples.size());
            std::vector<double> lengths;
            for (unsigned long i = 0; i < samples.size(); ++i)
            {
                lengths.push_back(length(samples[i]));
                // If there are zero vectors in samples then just say their length is 1 so we
                // can avoid a division by zero check later on.  Also, this doesn't matter
                // since zero vectors can be assigned to any cluster randomly as there is no
                // basis for picking one based on angle.
                if (lengths.back() == 0)
                    lengths.back() = 1;
            }

            // We will keep the centers as unit vectors at all times throughout the processing.
            for (unsigned long i = 0; i < centers.size(); ++i)
            {
                double len = length(centers[i]);
                // Avoid having length 0 centers.  If that is the case then pick another center
                // at random.
                while(len == 0)
                {
                    centers[i] = matrix_cast<scalar_type>(gaussian_randm(centers[i].nr(), centers[i].nc(), seed++));
                    len = length(centers[i]);
                }
                centers[i] /= len;
            }

            unsigned long iter = 0;
            bool centers_changed = true;
            while (centers_changed && iter < max_iter)
            {
                ++iter;
                centers_changed = false;

                // loop over each sample and see which center it is closest to
                for (unsigned long i = 0; i < samples.size(); ++i)
                {
                    // find the best center for sample[i]
                    scalar_type best_angle = std::numeric_limits<scalar_type>::max();
                    unsigned long best_center = 0;
                    for (unsigned long j = 0; j < centers.size(); ++j)
                    {
                        scalar_type angle = -dot(centers[j],samples[i])/lengths[i];

                        if (angle < best_angle)
                        {
                            best_angle = angle;
                            best_center = j;
                        }
                    }

                    if (assignments[i] != best_center)
                    {
                        centers_changed = true;
                        assignments[i] = best_center;
                    }
                }

                // now update all the centers
                centers.assign(centers.size(), zero);
                for (unsigned long i = 0; i < samples.size(); ++i)
                {
                    centers[assignments[i]] += samples[i];
                }
                // Now length normalize all the centers.
                for (unsigned long i = 0; i < centers.size(); ++i)
                {
                    double len = length(centers[i]);
                    // Avoid having length 0 centers.  If that is the case then pick another center
                    // at random.
                    while(len == 0)
                    {
                        centers[i] = matrix_cast<scalar_type>(gaussian_randm(centers[i].nr(), centers[i].nc(), seed++));
                        len = length(centers[i]);
                        centers_changed = true;
                    }
                    centers[i] /= len;
                }
            }
        }

    // ----------------------------------------------------------------------------------------

        template <
            typename array_type,
            typename EXP
            >
        unsigned long nearest_center (
            const array_type& centers,
            const matrix_exp<EXP>& sample
        )
        {
            // make sure requires clause is not broken
            DLIB_ASSERT(centers.size() > 0 && sample.size() > 0 && is_vector(sample),
                "\t unsigned long nearest_center()"
                << "\n\t You have given invalid inputs to this function."
                << "\n\t centers.size():    " << centers.size()
                << "\n\t sample.size():     " << sample.size()
                << "\n\t is_vector(sample): " << is_vector(sample)
                );

            double best_dist = length_squared(centers[0] - sample);
            unsigned long best_idx = 0;
            for (unsigned long i = 1; i < centers.size(); ++i)
            {
                const double dist = length_squared(centers[i] - sample);
                if (dist < best_dist)
                {
                    best_dist = dist;
                    best_idx = i;
                }
            }
            return best_idx;
        }

    // ----------------------------------------------------------------------------------------

    }

    #endif // DLIB_KKMEANs_