    // Copyright (C) 2009  Davis E. King (davis@dlib.net)
    // License: Boost Software License   See LICENSE.txt for the full license.
    #ifndef DLIB_SVm_SPARSE_VECTOR
    #define DLIB_SVm_SPARSE_VECTOR

    #include "sparse_vector_abstract.h"
    #include <cmath>
    #include <limits>
    #include "../algs.h"
    #include <vector>
    #include <map>
    #include "../graph_utils/edge_list_graphs.h"
    #include "../matrix.h"

    namespace dlib
    {

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

        template <typename T, typename U>
        typename T::value_type::second_type distance_squared (
            const T& a,
            const U& b
        )
        {
            typedef typename T::value_type::second_type scalar_type;
            typedef typename U::value_type::second_type scalar_typeU;
            // Both T and U must contain the same kinds of elements
            COMPILE_TIME_ASSERT((is_same_type<scalar_type, scalar_typeU>::value));

            typename T::const_iterator ai = a.begin();
            typename U::const_iterator bi = b.begin();

            scalar_type sum = 0, temp = 0;
            while (ai != a.end() && bi != b.end())
            {
                if (ai->first == bi->first)
                {
                    temp = ai->second - bi->second;
                    ++ai;
                    ++bi;
                }
                else if (ai->first < bi->first)
                {
                    temp = ai->second;
                    ++ai;
                }
                else
                {
                    temp = bi->second;
                    ++bi;
                }

                sum += temp*temp;
            }

            while (ai != a.end())
            {
                sum += ai->second*ai->second;
                ++ai;
            }
            while (bi != b.end())
            {
                sum += bi->second*bi->second;
                ++bi;
            }

            return sum;
        }

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

        template <typename T, typename U, typename V, typename W>
        typename T::value_type::second_type distance_squared (
            const V& a_scale,
            const T& a,
            const W& b_scale,
            const U& b
        )
        {
            typedef typename T::value_type::second_type scalar_type;
            typedef typename U::value_type::second_type scalar_typeU;
            // Both T and U must contain the same kinds of elements
            COMPILE_TIME_ASSERT((is_same_type<scalar_type, scalar_typeU>::value));

            typename T::const_iterator ai = a.begin();
            typename U::const_iterator bi = b.begin();

            scalar_type sum = 0, temp = 0;
            while (ai != a.end() && bi != b.end())
            {
                if (ai->first == bi->first)
                {
                    temp = a_scale*ai->second - b_scale*bi->second;
                    ++ai;
                    ++bi;
                }
                else if (ai->first < bi->first)
                {
                    temp = a_scale*ai->second;
                    ++ai;
                }
                else
                {
                    temp = b_scale*bi->second;
                    ++bi;
                }

                sum += temp*temp;
            }

            while (ai != a.end())
            {
                sum += a_scale*a_scale*ai->second*ai->second;
                ++ai;
            }
            while (bi != b.end())
            {
                sum += b_scale*b_scale*bi->second*bi->second;
                ++bi;
            }

            return sum;
        }

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

        template <typename T, typename U>
        typename T::value_type::second_type distance (
            const T& a,
            const U& b
        )
        {
            return std::sqrt(distance_squared(a,b));
        }

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

        template <typename T, typename U, typename V, typename W>
        typename T::value_type::second_type distance (
            const V& a_scale,
            const T& a,
            const W& b_scale,
            const U& b
        )
        {
            return std::sqrt(distance_squared(a_scale,a,b_scale,b));
        }

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

        template <typename T, typename EXP>
        typename enable_if<is_matrix<T> >::type assign (
            T& dest,
            const matrix_exp<EXP>& src
        )
        {
            // make sure requires clause is not broken
            DLIB_ASSERT(is_vector(src),
                        "\t void assign(dest,src)"
                        << "\n\t the src matrix must be a row or column vector"
            );

            dest = src;
        }

        template <typename T, typename EXP>
        typename disable_if<is_matrix<T> >::type assign (
            T& dest,
            const matrix_exp<EXP>& src
        )
        {
            // make sure requires clause is not broken
            DLIB_ASSERT(is_vector(src),
                        "\t void assign(dest,src)"
                        << "\n\t the src matrix must be a row or column vector"
            );

            dest.clear();
            typedef typename T::value_type item_type;
            for (long i = 0; i < src.size(); ++i)
            {
                dest.insert(dest.end(),item_type(i, src(i)));
            }
        }

        template <typename T, typename U>
        typename disable_if_c<is_matrix<T>::value || is_matrix<U>::value>::type assign (
            T& dest,        // sparse
            const U& src    // sparse
        )
        {
            dest.assign(src.begin(), src.end());
        }

        template <typename T, typename U, typename Comp, typename Alloc, typename S>
        typename disable_if<is_matrix<S> >::type assign (
            std::map<T,U,Comp,Alloc>& dest, // sparse
            const S& src                    // sparse
        )
        {
            dest.clear();
            dest.insert(src.begin(), src.end());
        }

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

        template <typename T>
        struct has_unsigned_keys
        {
            static const bool value = is_unsigned_type<typename T::value_type::first_type>::value;
        };

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

        namespace impl
        {
            template <typename T, typename U>
            typename T::value_type::second_type general_dot (
                const T& a,
                const U& b
            )
            {
                typedef typename T::value_type::second_type scalar_type;

                typename T::const_iterator ai = a.begin();
                typename U::const_iterator bi = b.begin();

                scalar_type sum = 0;
                while (ai != a.end() && bi != b.end())
                {
                    if (ai->first == bi->first)
                    {
                        sum += ai->second * bi->second;
                        ++ai;
                        ++bi;
                    }
                    else if (ai->first < bi->first)
                    {
                        ++ai;
                    }
                    else
                    {
                        ++bi;
                    }
                }

                return sum;
            }

            template <typename T, typename U>
            inline typename T::value_type::second_type dot (
                const T& a,
                const U& b
            )
            {
                return general_dot(a,b);
            }

            template <typename T, typename U, typename alloc>
            U dot (
                const std::vector<std::pair<T,U>,alloc>& a,
                const std::vector<std::pair<T,U>,alloc>& b
            )
            {
                // You are getting this error because you are attempting to use sparse sample vectors
                // but you aren't using an unsigned integer as your key type in the sparse vectors.
                COMPILE_TIME_ASSERT(is_unsigned_type<T>::value);

                if (a.size() == 0 || b.size() == 0)
                    return 0;

                // if a is really a dense vector but just represented in a sparse container
                if (a.back().first == a.size()-1)
                {
                    double sum = 0;
                    for (unsigned long i = 0; i < b.size(); ++i)
                    {
                        if (b[i].first >= a.size())
                            break;
                        sum += a[b[i].first].second * b[i].second;
                    }
                    return sum;
                }
                // if b is really a dense vector but just represented in a sparse container
                else if (b.back().first == b.size()-1)
                {
                    double sum = 0;
                    for (unsigned long i = 0; i < a.size(); ++i)
                    {
                        if (a[i].first >= b.size())
                            break;
                        sum += b[a[i].first].second * a[i].second;
                    }
                    return sum;
                }
                else
                {
                    return general_dot(a,b);
                }
            }
        }

        template <typename T>
        inline typename T::value_type::second_type dot (
            const T& a,
            const T& b
        )
        {
            return impl::dot(a,b);
        }

        template <typename T1, typename T2, typename T3, typename T4, typename T5, typename T6>
        inline T4 dot (
            const std::vector<T1,T2>& a,
            const std::map<T3,T4,T5,T6>& b
        )
        {
            return impl::dot(a,b);
        }

        template <typename T1, typename T2, typename T3, typename T4, typename T5, typename T6>
        inline T4 dot (
            const std::map<T3,T4,T5,T6>& a,
            const std::vector<T1,T2>& b
        )
        {
            return impl::dot(a,b);
        }

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

        template <typename T, typename EXP>
        typename T::value_type::second_type dot (
            const T& a,
            const matrix_exp<EXP>& b
        )
        {
            // make sure requires clause is not broken
            DLIB_ASSERT(is_vector(b),
                        "\t scalar_type dot(sparse_vector a, dense_vector b)"
                        << "\n\t 'b' must be a vector to be used in a dot product."
            );

            typedef typename T::value_type::second_type scalar_type;
            typedef typename T::value_type::first_type first_type;

            scalar_type sum = 0;
            for (typename T::const_iterator ai = a.begin();
                 (ai != a.end()) && (ai->first < static_cast<first_type>(b.size()));
                 ++ai)
            {
                sum += ai->second * b(ai->first);
            }

            return sum;
        }

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

        template <typename T, typename EXP>
        typename T::value_type::second_type dot (
            const matrix_exp<EXP>& b,
            const T& a
        )
        {
            return dot(a,b);
        }

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

        template <typename T>
        typename T::value_type::second_type length_squared (
            const T& a
        )
        {
            typedef typename T::value_type::second_type scalar_type;

            typename T::const_iterator i;

            scalar_type sum = 0;

            for (i = a.begin(); i != a.end(); ++i)
            {
                sum += i->second * i->second;
            }

            return sum;
        }

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

        template <typename T>
        typename T::value_type::second_type length (
            const T& a
        )
        {
            return std::sqrt(length_squared(a));
        }

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

        template <typename T, typename U>
        typename disable_if<is_matrix<T>,void>::type scale_by (
            T& a,
            const U& value
        )
        {
            for (typename T::iterator i = a.begin(); i != a.end(); ++i)
            {
                i->second *= value;
            }
        }

        template <typename T, typename U>
        typename enable_if<is_matrix<T>,void>::type scale_by (
            T& a,
            const U& value
        )
        {
            a *= value;
        }

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

        template <typename T>
        typename disable_if<is_matrix<T>,T>::type add (
            const T& a,
            const T& b
        )
        {
            T temp;

            typename T::const_iterator i = a.begin();
            typename T::const_iterator j = b.begin();
            while (i != a.end() && j != b.end())
            {
                if (i->first == j->first)
                {
                    temp.insert(temp.end(), std::make_pair(i->first, i->second + j->second));
                    ++i;
                    ++j;
                }
                else if (i->first < j->first)
                {
                    temp.insert(temp.end(), *i);
                    ++i;
                }
                else
                {
                    temp.insert(temp.end(), *j);
                    ++j;
                }
            }

            while (i != a.end())
            {
                temp.insert(temp.end(), *i);
                ++i;
            }
            while (j != b.end())
            {
                temp.insert(temp.end(), *j);
                ++j;
            }

            return temp;
        }

        template <typename T, typename U>
        typename enable_if_c<is_matrix<T>::value && is_matrix<U>::value, matrix_add_exp<T,U> >::type add (
            const T& a,
            const U& b
        )
        {
            return matrix_add_exp<T,U>(a.ref(),b.ref());
        }

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

        template <typename T>
        typename disable_if<is_matrix<T>,T>::type subtract (
            const T& a,
            const T& b
        )
        {
            T temp;

            typename T::const_iterator i = a.begin();
            typename T::const_iterator j = b.begin();
            while (i != a.end() && j != b.end())
            {
                if (i->first == j->first)
                {
                    temp.insert(temp.end(), std::make_pair(i->first, i->second - j->second));
                    ++i;
                    ++j;
                }
                else if (i->first < j->first)
                {
                    temp.insert(temp.end(), *i);
                    ++i;
                }
                else
                {
                    temp.insert(temp.end(), std::make_pair(j->first, -j->second));
                    ++j;
                }
            }

            while (i != a.end())
            {
                temp.insert(temp.end(), *i);
                ++i;
            }
            while (j != b.end())
            {
                temp.insert(temp.end(), std::make_pair(j->first, -j->second));
                ++j;
            }

            return temp;
        }

        template <typename T, typename U>
        typename enable_if_c<is_matrix<T>::value && is_matrix<U>::value, matrix_subtract_exp<T,U> >::type subtract (
            const T& a,
            const U& b
        )
        {
            return matrix_subtract_exp<T,U>(a.ref(),b.ref());
        }

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

        namespace impl
        {
            template <typename T>
            typename enable_if<is_matrix<typename T::type>,unsigned long>::type max_index_plus_one (
                const T& samples
            )
            {
                if (samples.size() > 0)
                    return samples(0).size();
                else
                    return 0;
            }

            template <typename T>
            typename enable_if<is_built_in_scalar_type<typename T::type>,unsigned long>::type max_index_plus_one (
                const T& sample
            )
            {
                return sample.size();
            }

            // This !is_built_in_scalar_type<typename T::type>::value is here to avoid an inexplicable bug in Vistual Studio 2005
            template <typename T>
            typename enable_if_c<(!is_built_in_scalar_type<typename T::type>::value) && (is_pair<typename T::type::value_type>::value) ,unsigned long>::type
            max_index_plus_one (
                const T& samples
            )
            {
                typedef typename T::type sample_type;
                // You are getting this error because you are attempting to use sparse sample vectors
                // but you aren't using an unsigned integer as your key type in the sparse vectors.
                COMPILE_TIME_ASSERT(has_unsigned_keys<sample_type>::value);

                // these should be sparse samples so look over all them to find the max index.
                unsigned long max_dim = 0;
                for (long i = 0; i < samples.size(); ++i)
                {
                    if (samples(i).size() > 0)
                        max_dim = std::max<unsigned long>(max_dim, (--samples(i).end())->first + 1);
                }

                return max_dim;
            }
        }

        template <typename T>
        typename enable_if<is_pair<typename T::value_type>,unsigned long>::type max_index_plus_one (
            const T& sample
        )
        {
            if (sample.size() > 0)
                return (--sample.end())->first + 1;
            return 0;
        }

        template <typename T>
        typename disable_if_c<is_pair<typename T::value_type>::value ||
                              is_same_type<typename T::value_type,sample_pair>::value ||
                              is_same_type<typename T::value_type,ordered_sample_pair>::value , unsigned long>::type
        max_index_plus_one (
            const T& samples
        )
        {
            return impl::max_index_plus_one(mat(samples));
        }

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

        template <typename T, long NR, long NC, typename MM, typename L, typename EXP>
        inline void add_to (
            matrix<T,NR,NC,MM,L>& dest,
            const matrix_exp<EXP>& src
        )
        {
            // make sure requires clause is not broken
            DLIB_ASSERT(is_vector(dest) && max_index_plus_one(src) <= static_cast<unsigned long>(dest.size()),
                        "\t void add_to(dest,src)"
                        << "\n\t dest must be a vector large enough to hold the src vector."
                        << "\n\t is_vector(dest):         " << is_vector(dest)
                        << "\n\t max_index_plus_one(src): " << max_index_plus_one(src)
                        << "\n\t dest.size():             " << dest.size()
            );

            for (long r = 0; r < src.size(); ++r)
                dest(r) += src(r);
        }

        template <typename T, long NR, long NC, typename MM, typename L, typename EXP>
        inline typename disable_if<is_matrix<EXP> >::type add_to (
            matrix<T,NR,NC,MM,L>& dest,
            const EXP& src
        )
        {
            // make sure requires clause is not broken
            DLIB_ASSERT(is_vector(dest) && max_index_plus_one(src) <= static_cast<unsigned long>(dest.size()),
                        "\t void add_to(dest,src)"
                        << "\n\t dest must be a vector large enough to hold the src vector."
                        << "\n\t is_vector(dest):         " << is_vector(dest)
                        << "\n\t max_index_plus_one(src): " << max_index_plus_one(src)
                        << "\n\t dest.size():             " << dest.size()
            );

            for (typename EXP::const_iterator i = src.begin(); i != src.end(); ++i)
                dest(i->first) += i->second;
        }

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

        template <typename T, long NR, long NC, typename MM, typename L, typename EXP, typename U>
        inline void add_to (
            matrix<T,NR,NC,MM,L>& dest,
            const matrix_exp<EXP>& src,
            const U& C
        )
        {
            // make sure requires clause is not broken
            DLIB_ASSERT(is_vector(dest) && max_index_plus_one(src) <= static_cast<unsigned long>(dest.size()),
                        "\t void add_to(dest,src)"
                        << "\n\t dest must be a vector large enough to hold the src vector."
                        << "\n\t is_vector(dest):         " << is_vector(dest)
                        << "\n\t max_index_plus_one(src): " << max_index_plus_one(src)
                        << "\n\t dest.size():             " << dest.size()
            );

            for (long r = 0; r < src.size(); ++r)
                dest(r) += C*src(r);
        }

        template <typename T, long NR, long NC, typename MM, typename L, typename EXP, typename U>
        inline typename disable_if<is_matrix<EXP> >::type add_to (
            matrix<T,NR,NC,MM,L>& dest,
            const EXP& src,
            const U& C
        )
        {
            // make sure requires clause is not broken
            DLIB_ASSERT(is_vector(dest) && max_index_plus_one(src) <= static_cast<unsigned long>(dest.size()),
                        "\t void add_to(dest,src)"
                        << "\n\t dest must be a vector large enough to hold the src vector."
                        << "\n\t is_vector(dest):         " << is_vector(dest)
                        << "\n\t max_index_plus_one(src): " << max_index_plus_one(src)
                        << "\n\t dest.size():             " << dest.size()
            );

            for (typename EXP::const_iterator i = src.begin(); i != src.end(); ++i)
                dest(i->first) += C*i->second;
        }

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

        template <typename T, long NR, long NC, typename MM, typename L, typename EXP>
        inline void subtract_from (
            matrix<T,NR,NC,MM,L>& dest,
            const matrix_exp<EXP>& src
        )
        {
            // make sure requires clause is not broken
            DLIB_ASSERT(is_vector(dest) && max_index_plus_one(src) <= static_cast<unsigned long>(dest.size()),
                        "\t void subtract_from(dest,src)"
                        << "\n\t dest must be a vector large enough to hold the src vector."
                        << "\n\t is_vector(dest):         " << is_vector(dest)
                        << "\n\t max_index_plus_one(src): " << max_index_plus_one(src)
                        << "\n\t dest.size():             " << dest.size()
            );

            for (long r = 0; r < src.size(); ++r)
                dest(r) -= src(r);
        }

        template <typename T, long NR, long NC, typename MM, typename L, typename EXP>
        inline typename disable_if<is_matrix<EXP> >::type subtract_from (
            matrix<T,NR,NC,MM,L>& dest,
            const EXP& src
        )
        {
            // make sure requires clause is not broken
            DLIB_ASSERT(is_vector(dest) && max_index_plus_one(src) <= static_cast<unsigned long>(dest.size()),
                        "\t void subtract_from(dest,src)"
                        << "\n\t dest must be a vector large enough to hold the src vector."
                        << "\n\t is_vector(dest):         " << is_vector(dest)
                        << "\n\t max_index_plus_one(src): " << max_index_plus_one(src)
                        << "\n\t dest.size():             " << dest.size()
            );

            for (typename EXP::const_iterator i = src.begin(); i != src.end(); ++i)
                dest(i->first) -= i->second;
        }

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

        template <typename T, long NR, long NC, typename MM, typename L, typename EXP, typename U>
        inline void subtract_from (
            matrix<T,NR,NC,MM,L>& dest,
            const matrix_exp<EXP>& src,
            const U& C
        )
        {
            // make sure requires clause is not broken
            DLIB_ASSERT(is_vector(dest) && max_index_plus_one(src) <= static_cast<unsigned long>(dest.size()),
                        "\t void subtract_from(dest,src)"
                        << "\n\t dest must be a vector large enough to hold the src vector."
                        << "\n\t is_vector(dest):         " << is_vector(dest)
                        << "\n\t max_index_plus_one(src): " << max_index_plus_one(src)
                        << "\n\t dest.size():             " << dest.size()
            );

            for (long r = 0; r < src.size(); ++r)
                dest(r) -= C*src(r);
        }

        template <typename T, long NR, long NC, typename MM, typename L, typename EXP, typename U>
        inline typename disable_if<is_matrix<EXP> >::type subtract_from (
            matrix<T,NR,NC,MM,L>& dest,
            const EXP& src,
            const U& C
        )
        {
            // make sure requires clause is not broken
            DLIB_ASSERT(is_vector(dest) && max_index_plus_one(src) <= static_cast<unsigned long>(dest.size()),
                        "\t void subtract_from(dest,src)"
                        << "\n\t dest must be a vector large enough to hold the src vector."
                        << "\n\t is_vector(dest):         " << is_vector(dest)
                        << "\n\t max_index_plus_one(src): " << max_index_plus_one(src)
                        << "\n\t dest.size():             " << dest.size()
            );

            for (typename EXP::const_iterator i = src.begin(); i != src.end(); ++i)
                dest(i->first) -= C*i->second;
        }

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

        template <typename T>
        typename T::value_type::second_type min (
            const T& a
        )
        {
            typedef typename T::value_type::second_type type;

            type temp = 0;
            for (typename T::const_iterator i = a.begin(); i != a.end(); ++i)
            {
                if (temp > i->second)
                    temp = i->second;
            }
            return temp;
        }

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

        template <typename T>
        typename T::value_type::second_type max (
            const T& a
        )
        {
            typedef typename T::value_type::second_type type;

            type temp = 0;
            for (typename T::const_iterator i = a.begin(); i != a.end(); ++i)
            {
                if (temp < i->second)
                    temp = i->second;
            }
            return temp;
        }

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

        namespace impl
        {
            template <typename sparse_vector_type>
            inline matrix<typename sparse_vector_type::value_type::second_type,0,1> sparse_to_dense (
                const sparse_vector_type& vect,
                unsigned long num_dimensions
            )
            {
                // You must use unsigned integral key types in your sparse vectors
                typedef typename sparse_vector_type::value_type::first_type idx_type;
                typedef typename sparse_vector_type::value_type::second_type value_type;
                COMPILE_TIME_ASSERT(is_unsigned_type<idx_type>::value);

                matrix<value_type,0,1> result;

                if (vect.size() == 0)
                    return result;

                result.set_size(num_dimensions);
                result = 0;

                for (typename sparse_vector_type::const_iterator j = vect.begin(); j != vect.end(); ++j)
                {
                    if ((long)(j->first) < result.size())
                    {
                        result(j->first) += j->second;
                    }
                }

                return result;
            }
        }

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

        template <typename idx_type, typename value_type, typename alloc>
        matrix<value_type,0,1> sparse_to_dense (
            const std::vector<std::pair<idx_type,value_type>,alloc>& vect,
            unsigned long num_dimensions
        )
        {
            return impl::sparse_to_dense(vect,num_dimensions);
        }

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

        template <typename idx_type, typename value_type, typename alloc>
        matrix<value_type,0,1> sparse_to_dense (
            const std::vector<std::pair<idx_type,value_type>,alloc>& vect
        )
        {
            return impl::sparse_to_dense(vect, max_index_plus_one(vect));
        }

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

        template <typename T1, typename T2, typename T3, typename T4>
        matrix<T2,0,1> sparse_to_dense (
            const std::map<T1,T2,T3,T4>& vect,
            unsigned long num_dimensions
        )
        {
            return impl::sparse_to_dense(vect,num_dimensions);
        }

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

        template <typename T1, typename T2, typename T3, typename T4>
        matrix<T2,0,1> sparse_to_dense (
            const std::map<T1,T2,T3,T4>& vect
        )
        {
            return impl::sparse_to_dense(vect, max_index_plus_one(vect));
        }

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

        template <typename T>
        typename enable_if<is_matrix<T>,T&>::type sparse_to_dense(
            T& item
        ) { return item; }

        template <typename EXP>
        matrix<typename EXP::type,0,1> sparse_to_dense(
            const matrix_exp<EXP>& item,
            unsigned long num
        )
        {
            typedef typename EXP::type type;
            if (item.size() == (long)num)
                return item;
            else if (item.size() < (long)num)
                return join_cols(item, zeros_matrix<type>((long)num-item.size(),1));
            else
                return colm(item,0,(long)num);
        }

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

        template <typename sample_type, typename alloc>
        std::vector<matrix<typename sample_type::value_type::second_type,0,1> > sparse_to_dense (
            const std::vector<sample_type, alloc>& samples,
            unsigned long num_dimensions
        )
        {
            typedef typename sample_type::value_type pair_type;
            typedef typename pair_type::second_type value_type;

            std::vector< matrix<value_type,0,1> > result;

            // now turn all the samples into dense samples
            result.resize(samples.size());

            for (unsigned long i = 0; i < samples.size(); ++i)
            {
                result[i] = sparse_to_dense(samples[i],num_dimensions);
            }

            return result;
        }

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

        template <typename sample_type, typename alloc>
        std::vector<matrix<typename sample_type::value_type::second_type,0,1> > sparse_to_dense (
            const std::vector<sample_type, alloc>& samples
        )
        {
            return sparse_to_dense(samples, max_index_plus_one(samples));
        }

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

        template <
            typename T
            >
        T make_sparse_vector (
            const T& v
        )
        {
            // You must use unsigned integral key types in your sparse vectors
            typedef typename T::value_type::first_type idx_type;
            typedef typename T::value_type::second_type value_type;
            COMPILE_TIME_ASSERT(is_unsigned_type<idx_type>::value);
            std::map<idx_type,value_type> temp;
            for (typename T::const_iterator i = v.begin(); i != v.end(); ++i)
            {
                temp[i->first] += i->second;
            }

            return T(temp.begin(), temp.end());
        }

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

        template <
            typename T
            >
        void make_sparse_vector_inplace(
            T& vect
        )
        {
            vect = make_sparse_vector(vect);
        }

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

        template <
            typename T,
            typename U,
            typename alloc
            >
        void make_sparse_vector_inplace (
            std::vector<std::pair<T,U>,alloc>& vect
        )
        {
            if (vect.size() > 0)
            {
                std::sort(vect.begin(), vect.end());

                // merge duplicates
                for (unsigned long i = 1; i < vect.size(); ++i)
                {
                    // if we found a duplicate
                    if (vect[i-1].first == vect[i].first)
                    {
                        // now start collapsing and merging the vector
                        unsigned long j = i-1;
                        for (unsigned long k = i; k < vect.size(); ++k)
                        {
                            if (vect[j].first == vect[k].first)
                            {
                                vect[j].second += vect[k].second;
                            }
                            else
                            {
                                ++j;
                                vect[j] = vect[k];
                            }
                        }

                        // we removed elements when we merged so we need to adjust the size.
                        vect.resize(j+1);
                        return;
                    }
                }
            }
        }

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

        template <typename EXP, typename T, long NR, long NC, typename MM, typename L>
        void sparse_matrix_vector_multiply (
            const std::vector<sample_pair>& edges,
            const matrix_exp<EXP>& v,
            matrix<T,NR,NC,MM,L>& result
        )
        {
            // make sure requires clause is not broken
            DLIB_ASSERT(max_index_plus_one(edges) <= (unsigned long)v.size() &&
                        is_col_vector(v),
                        "\t void sparse_matrix_vector_multiply()"
                        << "\n\t Invalid inputs were given to this function"
                        << "\n\t max_index_plus_one(edges): " << max_index_plus_one(edges)
                        << "\n\t v.size():                  " << v.size()
                        << "\n\t is_col_vector(v):          " << is_col_vector(v)
            );

            result.set_size(v.nr(),v.nc());
            result = 0;

            for (unsigned long k = 0; k < edges.size(); ++k)
            {
                const long i = edges[k].index1();
                const long j = edges[k].index2();
                const double d = edges[k].distance();

                result(i) += v(j)*d;
                if (i != j)
                    result(j) += v(i)*d;
            }
        }

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

        template <typename EXP>
        matrix<typename EXP::type,0,1> sparse_matrix_vector_multiply (
            const std::vector<sample_pair>& edges,
            const matrix_exp<EXP>& v
        )
        {
            matrix<typename EXP::type,0,1> result;
            sparse_matrix_vector_multiply(edges,v,result);
            return result;
        }

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

        template <typename EXP, typename T, long NR, long NC, typename MM, typename L>
        void sparse_matrix_vector_multiply (
            const std::vector<ordered_sample_pair>& edges,
            const matrix_exp<EXP>& v,
            matrix<T,NR,NC,MM,L>& result
        )
        {
            // make sure requires clause is not broken
            DLIB_ASSERT(max_index_plus_one(edges) <= (unsigned long)v.size() &&
                        is_col_vector(v),
                        "\t void sparse_matrix_vector_multiply()"
                        << "\n\t Invalid inputs were given to this function"
                        << "\n\t max_index_plus_one(edges): " << max_index_plus_one(edges)
                        << "\n\t v.size():                  " << v.size()
                        << "\n\t is_col_vector(v):          " << is_col_vector(v)
            );

            result.set_size(v.nr(),v.nc());
            result = 0;

            for (unsigned long k = 0; k < edges.size(); ++k)
            {
                const long i = edges[k].index1();
                const long j = edges[k].index2();
                const double d = edges[k].distance();

                result(i) += v(j)*d;
            }
        }

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

        template <typename EXP>
        matrix<typename EXP::type,0,1> sparse_matrix_vector_multiply (
            const std::vector<ordered_sample_pair>& edges,
            const matrix_exp<EXP>& v
        )
        {
            matrix<typename EXP::type,0,1> result;
            sparse_matrix_vector_multiply(edges,v,result);
            return result;
        }

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

        template <
            typename EXP,
            typename sparse_vector_type,
            typename T,
            long NR,
            long NC,
            typename MM,
            typename L
            >
        void sparse_matrix_vector_multiply (
            const matrix_exp<EXP>& m,
            const sparse_vector_type& v,
            matrix<T,NR,NC,MM,L>& result
        )
        {
            // make sure requires clause is not broken
            DLIB_ASSERT(max_index_plus_one(v) <= (unsigned long)m.nc(),
                        "\t void sparse_matrix_vector_multiply()"
                        << "\n\t Invalid inputs were given to this function"
                        << "\n\t max_index_plus_one(v): " << max_index_plus_one(v)
                        << "\n\t m.size():              " << m.size()
            );

            result.set_size(m.nr(),1);
            result = 0;

            for (typename sparse_vector_type::const_iterator i = v.begin(); i != v.end(); ++i)
            {
                for (long r = 0; r < result.nr(); ++r)
                {
                    result(r) += m(r, i->first)*i->second;
                }
            }
        }

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

        template <
            typename EXP,
            typename sparse_vector_type
            >
        matrix<typename EXP::type,0,1> sparse_matrix_vector_multiply (
            const matrix_exp<EXP>& m,
            const sparse_vector_type& v
        )
        {
            matrix<typename EXP::type,0,1> result;
            sparse_matrix_vector_multiply(m,v,result);
            return result;
        }

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

    }

    #endif // DLIB_SVm_SPARSE_VECTOR