    // Copyright (C) 2011  Davis E. King (davis@dlib.net)
    // License: Boost Software License   See LICENSE.txt for the full license.
    #ifndef DLIB_BUILD_SEPARABLE_PoLY_FILTERS_H__
    #define DLIB_BUILD_SEPARABLE_PoLY_FILTERS_H__

    #include "../matrix.h"
    #include "surf.h"
    #include "../uintn.h"
    #include <vector>

    namespace dlib
    {

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

        typedef std::pair<matrix<double,0,1>, matrix<double,0,1> > separable_filter_type;
        typedef std::pair<matrix<int32,0,1>, matrix<int32,0,1> > separable_int32_filter_type;

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

        inline std::vector<std::vector<separable_filter_type> > build_separable_poly_filters (
            const long order,
            const long window_size
        )
        /*!
            requires
                - 1 <= order <= 6
                - window_size >= 3 && window_size is odd
            ensures
                - the "first" element is the row_filter, the second is the col_filter.
                - Some filters are not totally separable and that's why they are grouped
                  into vectors of vectors.  The groups are all the parts of a partially
                  separable filter.
        !*/
        {
            long num_filters = 6;
            switch (order)
            {
                case 1: num_filters = 3; break;
                case 2: num_filters = 6; break;
                case 3: num_filters = 10; break;
                case 4: num_filters = 15; break;
                case 5: num_filters = 21; break;
                case 6: num_filters = 28; break;
            }

            matrix<double> X(window_size*window_size,num_filters);
            matrix<double,0,1> G(window_size*window_size,1);
            const double sigma = window_size/4.0;

            long cnt = 0;
            for (double x = -window_size/2; x <= window_size/2; ++x)
            {
                for (double y = -window_size/2; y <= window_size/2; ++y)
                {
                    X(cnt, 0) = 1;
                    X(cnt, 1) = x;
                    X(cnt, 2) = y;

                    if (X.nc() > 5)
                    {
                        X(cnt, 3) = x*x;
                        X(cnt, 4) = x*y;
                        X(cnt, 5) = y*y;
                    }
                    if (X.nc() > 9)
                    {
                        X(cnt, 6) = x*x*x;
                        X(cnt, 7) = y*x*x;
                        X(cnt, 8) = y*y*x;
                        X(cnt, 9) = y*y*y;
                    }
                    if (X.nc() > 14)
                    {
                        X(cnt, 10) = x*x*x*x;
                        X(cnt, 11) = y*x*x*x;
                        X(cnt, 12) = y*y*x*x;
                        X(cnt, 13) = y*y*y*x;
                        X(cnt, 14) = y*y*y*y;
                    }
                    if (X.nc() > 20)
                    {
                        X(cnt, 15) = x*x*x*x*x;
                        X(cnt, 16) = y*x*x*x*x;
                        X(cnt, 17) = y*y*x*x*x;
                        X(cnt, 18) = y*y*y*x*x;
                        X(cnt, 19) = y*y*y*y*x;
                        X(cnt, 20) = y*y*y*y*y;
                    }
                    if (X.nc() > 27)
                    {
                        X(cnt, 21) = x*x*x*x*x*x;
                        X(cnt, 22) = y*x*x*x*x*x;
                        X(cnt, 23) = y*y*x*x*x*x;
                        X(cnt, 24) = y*y*y*x*x*x;
                        X(cnt, 25) = y*y*y*y*x*x;
                        X(cnt, 26) = y*y*y*y*y*x;
                        X(cnt, 27) = y*y*y*y*y*y;
                    }

                    G(cnt) = std::sqrt(gaussian(x,y,sigma));
                    ++cnt;
                }
            }

            X = diagm(G)*X;

            const matrix<double> S = inv(trans(X)*X)*trans(X)*diagm(G);

            matrix<double,0,1> row_filter, col_filter;

            matrix<double> u,v, temp;
            matrix<double,0,1> w;

            std::vector<std::vector<separable_filter_type> > results(num_filters);

            for (long r = 0; r < S.nr(); ++r)
            {
                temp = reshape(rowm(S,r), window_size, window_size);
                svd3(temp,u,w,v);
                const double thresh = max(w)*1e-8;
                for (long i = 0; i < w.size(); ++i)
                {
                    if (w(i) > thresh)
                    {
                        col_filter = std::sqrt(w(i))*colm(u,i);
                        row_filter = std::sqrt(w(i))*colm(v,i);
                        results[r].push_back(std::make_pair(row_filter, col_filter));
                    }
                }
            }

            return results;
        }

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

        inline std::vector<std::vector<separable_int32_filter_type> > build_separable_int32_poly_filters (
            const long order,
            const long window_size,
            const double max_range = 300.0
        )
        /*!
            requires
                - 1 <= order <= 6
                - window_size >= 3 && window_size is odd
                - max_range > 1
            ensures
                - the "first" element is the row_filter, the second is the col_filter.
        !*/
        {
            const std::vector<std::vector<separable_filter_type> >& filters = build_separable_poly_filters(order, window_size);
            std::vector<std::vector<separable_int32_filter_type> > int_filters(filters.size());

            for (unsigned long i = 0; i < filters.size(); ++i)
            {

                double max_val = 0;
                for (unsigned long j = 0; j < filters[i].size(); ++j)
                {
                    const separable_filter_type& filt = filters[i][j];
                    max_val = std::max(max_val, max(abs(filt.first)));
                    max_val = std::max(max_val, max(abs(filt.second)));
                }
                if (max_val == 0)
                    max_val = 1;

                int_filters[i].resize(filters[i].size());
                for (unsigned long j = 0; j < filters[i].size(); ++j)
                {
                    const separable_filter_type& filt = filters[i][j];
                    int_filters[i][j].first  = matrix_cast<int32>(round(filt.first*max_range/max_val));
                    int_filters[i][j].second = matrix_cast<int32>(round(filt.second*max_range/max_val));
                }
            }

            return int_filters;
        }

    }

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

    #endif // DLIB_BUILD_SEPARABLE_PoLY_FILTERS_H__