    // Copyright (C) 2006  Davis E. King (davis@dlib.net)
    // License: Boost Software License   See LICENSE.txt for the full license.
    #ifndef DLIB_MATRIx_MATH_FUNCTIONS
    #define DLIB_MATRIx_MATH_FUNCTIONS

    #include "matrix_math_functions_abstract.h"
    #include "matrix_op.h"
    #include "matrix_utilities.h"
    #include "matrix.h"
    #include "../algs.h"
    #include <cmath>
    #include <complex>
    #include <limits>

    namespace dlib
    {

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

        DLIB_DEFINE_FUNCTION_M(op_sqrt, sqrt, std::sqrt, 7)
        DLIB_DEFINE_FUNCTION_M(op_log, log, std::log, 7)
        DLIB_DEFINE_FUNCTION_M(op_log10, log10, std::log10, 7)
        DLIB_DEFINE_FUNCTION_M(op_exp, exp, std::exp, 7)

        DLIB_DEFINE_FUNCTION_M(op_conj, conj, std::conj, 2)

        DLIB_DEFINE_FUNCTION_M(op_ceil, ceil, std::ceil, 7)
        DLIB_DEFINE_FUNCTION_M(op_floor, floor, std::floor, 7)

        DLIB_DEFINE_FUNCTION_M(op_sin, sin, std::sin, 7)
        DLIB_DEFINE_FUNCTION_M(op_cos, cos, std::cos, 7)
        DLIB_DEFINE_FUNCTION_M(op_tan, tan, std::tan, 7)
        DLIB_DEFINE_FUNCTION_M(op_sinh, sinh, std::sinh, 7)
        DLIB_DEFINE_FUNCTION_M(op_cosh, cosh, std::cosh, 7)
        DLIB_DEFINE_FUNCTION_M(op_tanh, tanh, std::tanh, 7)
        DLIB_DEFINE_FUNCTION_M(op_asin, asin, std::asin, 7)
        DLIB_DEFINE_FUNCTION_M(op_acos, acos, std::acos, 7)
        DLIB_DEFINE_FUNCTION_M(op_atan, atan, std::atan, 7)

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

        namespace impl
        {
            template <typename type>
            inline type sigmoid (const type& val)
            {
                return static_cast<type>(1/(1 + std::exp(-val)));
            }

            template <typename type, typename S>
            inline type round_zeros_eps (const type& val, const S& eps)
            {
                // you can only round matrices that contain built in scalar types like double, long, float, etc.
                COMPILE_TIME_ASSERT(is_built_in_scalar_type<type>::value);

                if (val >= eps || val <= -eps)
                    return val;
                else
                    return 0;
            }

            template <typename type>
            inline type round_zeros (const type& val)
            {
                // you can only round matrices that contain built in scalar types like double, long, float, etc.
                COMPILE_TIME_ASSERT(is_built_in_scalar_type<type>::value);

                const type eps = 10*std::numeric_limits<type>::epsilon();
                if (val >= eps || val <= -eps)
                    return val;
                else
                    return 0;
            }

            template <typename type>
            inline type squared (const type& val)
            {
                return val*val;
            }

            template <typename type>
            inline type sign (const type& val)
            {
                if (val >= 0)
                    return +1;
                else
                    return -1;
            }

            template <typename type>
            type cubed (const type& val)
            {
                return val*val*val;
            }

            template <typename type, typename S>
            inline type pow1 (const type& val, const S& s)
            {
                // you can only call pow() on matrices that contain floats, doubles or long doubles.
                COMPILE_TIME_ASSERT((
                        is_same_type<type,float>::value == true ||
                        is_same_type<type,double>::value == true ||
                        is_same_type<type,long double>::value == true
                ));

                return std::pow(val,static_cast<type>(s));
            }

            template <typename type, typename S>
            inline type pow2 (const S& s, const type& val)
            {
                // you can only call pow() on matrices that contain floats, doubles or long doubles.
                COMPILE_TIME_ASSERT((
                        is_same_type<type,float>::value == true ||
                        is_same_type<type,double>::value == true ||
                        is_same_type<type,long double>::value == true
                ));

                return std::pow(static_cast<type>(s),val);
            }

            template <typename type>
            inline type reciprocal (const type& val)
            {
                // you can only compute reciprocal matrices that contain floats, doubles or long doubles.
                COMPILE_TIME_ASSERT((
                        is_same_type<type,float>::value == true ||
                        is_same_type<type,double>::value == true ||
                        is_same_type<type,long double>::value == true  ||
                        is_same_type<type,std::complex<float> >::value == true ||
                        is_same_type<type,std::complex<double> >::value == true ||
                        is_same_type<type,std::complex<long double> >::value == true
                ));

                if (val != static_cast<type>(0))
                    return static_cast<type>((type)1.0/val);
                else
                    return 0;
            }

            template <typename type>
            inline type reciprocal_max (const type& val)
            {
                // you can only compute reciprocal_max matrices that contain floats, doubles or long doubles.
                COMPILE_TIME_ASSERT((
                        is_same_type<type,float>::value == true ||
                        is_same_type<type,double>::value == true ||
                        is_same_type<type,long double>::value == true
                ));

                if (val != static_cast<type>(0))
                    return static_cast<type>((type)1.0/val);
                else
                    return std::numeric_limits<type>::max();
            }

        }

        DLIB_DEFINE_FUNCTION_M(op_sigmoid, sigmoid, impl::sigmoid, 7)
        DLIB_DEFINE_FUNCTION_MS(op_round_zeros, round_zeros, impl::round_zeros_eps, 7)
        DLIB_DEFINE_FUNCTION_M(op_round_zeros2, round_zeros, impl::round_zeros, 7)
        DLIB_DEFINE_FUNCTION_M(op_cubed, cubed, impl::cubed, 7)
        DLIB_DEFINE_FUNCTION_M(op_squared, squared, impl::squared, 6)
        DLIB_DEFINE_FUNCTION_M(op_sign, sign, impl::sign, 6)
        DLIB_DEFINE_FUNCTION_MS(op_pow1, pow, impl::pow1, 7)
        DLIB_DEFINE_FUNCTION_SM(op_pow2, pow, impl::pow2, 7)
        DLIB_DEFINE_FUNCTION_M(op_reciprocal, reciprocal, impl::reciprocal, 6)
        DLIB_DEFINE_FUNCTION_M(op_reciprocal_max, reciprocal_max, impl::reciprocal_max, 6)

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

        template <typename M, typename enabled = void>
        struct op_round : basic_op_m<M>
        {
            op_round( const M& m_) : basic_op_m<M>(m_){}

            const static long cost = M::cost+7;
            typedef typename M::type type;
            typedef const typename M::type const_ret_type;
            const_ret_type apply (long r, long c) const
            {
                return static_cast<type>(std::round(this->m(r,c)));
            }
        };

        template <typename M>
        struct op_round<M,typename enable_if_c<std::numeric_limits<typename M::type>::is_integer>::type >
        : basic_op_m<M>
        {
            op_round( const M& m_) : basic_op_m<M>(m_){}

            const static long cost = M::cost;
            typedef typename M::type type;
            typedef typename M::const_ret_type const_ret_type;
            const_ret_type apply (long r, long c) const
            {
                return this->m(r,c);
            }
        };

        template <
            typename EXP
            >
        const matrix_op<op_round<EXP> > round (
            const matrix_exp<EXP>& m
        )
        {
            // you can only round matrices that contain built in scalar types like double, long, float, etc.
            COMPILE_TIME_ASSERT(is_built_in_scalar_type<typename EXP::type>::value);

            typedef op_round<EXP> op;
            return matrix_op<op>(op(m.ref()));
        }

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

        template <typename M>
        struct op_normalize : basic_op_m<M>
        {
            typedef typename M::type type;

            op_normalize( const M& m_, const type& s_) : basic_op_m<M>(m_), s(s_){}

            const type s;

            const static long cost = M::cost+5;
            typedef const typename M::type const_ret_type;
            const_ret_type apply (long r, long c) const
            {
                return this->m(r,c)*s;
            }
        };

        template <
            typename EXP
            >
        const matrix_op<op_normalize<EXP> > normalize (
            const matrix_exp<EXP>& m
        )
        {
            // you can only compute normalized matrices that contain floats, doubles or long doubles.
            COMPILE_TIME_ASSERT((
                    is_same_type<typename EXP::type,float>::value == true ||
                    is_same_type<typename EXP::type,double>::value == true ||
                    is_same_type<typename EXP::type,long double>::value == true
            ));

            typedef op_normalize<EXP> op;
            typename EXP::type temp = std::sqrt(sum(squared(m)));
            if (temp != 0.0)
                temp = 1.0/temp;

            return matrix_op<op>(op(m.ref(),temp));
        }

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

        template <typename M, typename return_type = typename M::type>
        struct op_abs : basic_op_m<M>
        {
            op_abs( const M& m_) : basic_op_m<M>(m_){}

            const static long cost = M::cost+7;
            typedef typename M::type type;
            typedef const typename M::type const_ret_type;
            const_ret_type apply ( long r, long c) const
            {
                return static_cast<type>(std::abs(this->m(r,c)));
            }
        };

        template <typename M, typename T>
        struct op_abs<M, std::complex<T> > : basic_op_m<M>
        {
            op_abs( const M& m_) : basic_op_m<M>(m_){}

            const static long cost = M::cost;
            typedef T type;
            typedef const T const_ret_type;
            const_ret_type apply ( long r, long c) const
            {
                return static_cast<type>(std::abs(this->m(r,c)));
            }
        };

        template <
            typename EXP
            >
        const matrix_op<op_abs<EXP> > abs (
            const matrix_exp<EXP>& m
        )
        {
            typedef op_abs<EXP> op;
            return matrix_op<op>(op(m.ref()));
        }

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

        template <typename M>
        struct op_complex_matrix : basic_op_m<M>
        {
            op_complex_matrix( const M& m_) : basic_op_m<M>(m_){}

            const static long cost = M::cost+1;
            typedef std::complex<typename M::type> type;
            typedef const std::complex<typename M::type> const_ret_type;
            const_ret_type apply ( long r, long c) const
            {
                return type(this->m(r,c));
            }
        };

        template <
            typename EXP
            >
        const matrix_op<op_complex_matrix<EXP> > complex_matrix (
            const matrix_exp<EXP>& m
        )
        {
            typedef op_complex_matrix<EXP> op;
            return matrix_op<op>(op(m.ref()));
        }

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

        template <typename M1, typename M2>
        struct op_complex_matrix2 : basic_op_mm<M1,M2>
        {
            op_complex_matrix2( const M1& m1_, const M2& m2_) : basic_op_mm<M1,M2>(m1_,m2_){}

            const static long cost = M1::cost+M2::cost+1;
            typedef std::complex<typename M1::type> type;
            typedef const std::complex<typename M1::type> const_ret_type;

            const_ret_type apply ( long r, long c) const
            { return type(this->m1(r,c), this->m2(r,c)); }
        };

        template <
            typename EXP1,
            typename EXP2
            >
        const matrix_op<op_complex_matrix2<EXP1,EXP2> > complex_matrix (
            const matrix_exp<EXP1>& real_part,
            const matrix_exp<EXP2>& imag_part
        )
        {
            COMPILE_TIME_ASSERT((is_same_type<typename EXP1::type,typename EXP2::type>::value == true));
            COMPILE_TIME_ASSERT(EXP1::NR == EXP2::NR || EXP1::NR == 0 || EXP2::NR == 0);
            COMPILE_TIME_ASSERT(EXP1::NC == EXP2::NC || EXP1::NC == 0 || EXP2::NC == 0);

            DLIB_ASSERT(real_part.nr() == imag_part.nr() &&
                   real_part.nc() == imag_part.nc(),
                "\tconst matrix_exp::type complex_matrix(real_part, imag_part)"
                << "\n\tYou can only make a complex matrix from two equally sized matrices"
                << "\n\treal_part.nr(): " << real_part.nr()
                << "\n\treal_part.nc(): " << real_part.nc()
                << "\n\timag_part.nr(): " << imag_part.nr()
                << "\n\timag_part.nc(): " << imag_part.nc()
                );

            typedef op_complex_matrix2<EXP1,EXP2> op;
            return matrix_op<op>(op(real_part.ref(),imag_part.ref()));
        }

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

        template <typename M>
        struct op_norm : basic_op_m<M>
        {
            op_norm( const M& m_) : basic_op_m<M>(m_){}

            const static long cost = M::cost+6;
            typedef typename M::type::value_type type;
            typedef const typename M::type::value_type const_ret_type;
            const_ret_type apply ( long r, long c) const
            { return std::norm(this->m(r,c)); }
        };

        template <
            typename EXP
            >
        const matrix_op<op_norm<EXP> > norm (
            const matrix_exp<EXP>& m
        )
        {
            typedef op_norm<EXP> op;
            return matrix_op<op>(op(m.ref()));
        }

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

        template <typename M>
        struct op_real : basic_op_m<M>
        {
            op_real( const M& m_) : basic_op_m<M>(m_){}

            const static long cost = M::cost;
            typedef typename M::type::value_type type;
            typedef const typename M::type::value_type const_ret_type;
            const_ret_type apply ( long r, long c) const
            { return std::real(this->m(r,c)); }
        };

        template <
            typename EXP
            >
        const matrix_op<op_real<EXP> > real (
            const matrix_exp<EXP>& m
        )
        {
            typedef op_real<EXP> op;
            return matrix_op<op>(op(m.ref()));
        }

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

        template <typename M>
        struct op_imag : basic_op_m<M>
        {
            op_imag( const M& m_) : basic_op_m<M>(m_){}

            const static long cost = M::cost;
            typedef typename M::type::value_type type;
            typedef const typename M::type::value_type const_ret_type;
            const_ret_type apply (long r, long c) const
            { return std::imag(this->m(r,c)); }
        };

        template <
            typename EXP
            >
        const matrix_op<op_imag<EXP> > imag (
            const matrix_exp<EXP>& m
        )
        {
            typedef op_imag<EXP> op;
            return matrix_op<op>(op(m.ref()));
        }

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

        template <typename M>
        struct op_softmax : basic_op_m<M>
        {
            typedef typename M::type type;

            op_softmax(const M& m_, const type& s_, const type& v_) : basic_op_m<M>(m_), s(s_), v(v_){}

            const type s;
            const type v;

            const static long cost = M::cost + 9;
            typedef type const_ret_type;
            const_ret_type apply(long r, long c) const { return std::exp(this->m(r, c) - v) * s; }
        };

        template <
          typename EXP
          >
        const matrix_op<op_softmax<EXP> > soft_max (
            const matrix_exp<EXP>& m
        )
        {
            // you can only compute softmax on matrices that contain floats, doubles or long doubles.
            COMPILE_TIME_ASSERT((
                  is_same_type<typename EXP::type,float>::value == true ||
                  is_same_type<typename EXP::type,double>::value == true ||
                  is_same_type<typename EXP::type,long double>::value == true
            ));
            typedef op_softmax<EXP> op;
            typename EXP::type max_val = max(m);
            typename EXP::type temp = static_cast<typename EXP::type>(1) / sum(exp(m - max_val));
            return matrix_op<op>(op(m.ref(), temp, max_val));
        }

    }

    #endif // DLIB_MATRIx_MATH_FUNCTIONS