    // Copyright (C) 2007  Davis E. King (davis@dlib.net)
    // License: Boost Software License   See LICENSE.txt for the full license.
    #undef DLIB_SVm_KERNEL_ABSTRACT_
    #ifdef DLIB_SVm_KERNEL_ABSTRACT_

    #include <cmath>
    #include <limits>
    #include <sstream>
    #include "../matrix/matrix_abstract.h"
    #include "../algs.h"
    #include "../serialize.h"

    namespace dlib
    {

    // ----------------------------------------------------------------------------------------
    // ----------------------------------------------------------------------------------------
    /*!A                               Kernel_Function_Objects                               */
    // ----------------------------------------------------------------------------------------
    // ----------------------------------------------------------------------------------------

        /*!
            WHAT IS A KERNEL FUNCTION OBJECT?
                In the context of the dlib library documentation a kernel function object
                is an object with an interface with the following properties:
                    - a public typedef named sample_type
                    - a public typedef named scalar_type which should be a float, double, or
                      long double type.
                    - an overloaded operator() that operates on two items of sample_type
                      and returns a scalar_type.
                      (e.g. scalar_type val = kernel_function(sample1,sample2);
                       would be a valid expression)
                    - a public typedef named mem_manager_type that is an implementation of
                      dlib/memory_manager/memory_manager_kernel_abstract.h or
                      dlib/memory_manager_global/memory_manager_global_kernel_abstract.h or
                      dlib/memory_manager_stateless/memory_manager_stateless_kernel_abstract.h
                    - an overloaded == operator that tells you if two kernels are
                      identical or not.

            THREAD SAFETY
                For a kernel function to be threadsafe it means that it must be safe to
                evaluate an expression like val = kernel_function(sample1,sample2)
                simultaneously from multiple threads, even when the threads operate on the same
                object instances (i.e. kernel_function, sample1, and sample2).  The most common
                way to make this safe is to ensure that the kernel function does not mutate any
                data, either in itself or in its arguments.

            For examples of kernel functions see the following objects
            (e.g. the radial_basis_kernel).
        !*/

        template <
            typename T
            >
        struct radial_basis_kernel
        {
            /*!
                REQUIREMENTS ON T
                    T must be a dlib::matrix object

                WHAT THIS OBJECT REPRESENTS
                    This object represents a radial basis function kernel

                THREAD SAFETY
                    This kernel is threadsafe.
            !*/

            typedef typename T::type scalar_type;
            typedef T sample_type;
            typedef typename T::mem_manager_type mem_manager_type;

            const scalar_type gamma;

            radial_basis_kernel(
            );
            /*!
                ensures
                    - #gamma == 0.1
            !*/

            radial_basis_kernel(
                const radial_basis_kernel& k
            );
            /*!
                ensures
                    - #gamma == k.gamma
            !*/

            radial_basis_kernel(
                const scalar_type g
            );
            /*!
                ensures
                    - #gamma == g
            !*/

            scalar_type operator() (
                const sample_type& a,
                const sample_type& b
            ) const;
            /*!
                requires
                    - a.nc() == 1
                    - b.nc() == 1
                    - a.nr() == b.nr()
                ensures
                    - returns exp(-gamma * ||a-b||^2)
            !*/

            radial_basis_kernel& operator= (
                const radial_basis_kernel& k
            );
            /*!
                ensures
                    - #gamma = k.gamma
                    - returns *this
            !*/

            bool operator== (
                const radial_basis_kernel& k
            ) const;
            /*!
                ensures
                    - if (k and *this are identical) then
                        - returns true
                    - else
                        - returns false
            !*/

        };

        template <
            typename T
            >
        void serialize (
            const radial_basis_kernel<T>& item,
            std::ostream& out
        );
        /*!
            provides serialization support for radial_basis_kernel
        !*/

        template <
            typename T
            >
        void deserialize (
            radial_basis_kernel<T>& item,
            std::istream& in
        );
        /*!
            provides deserialization support for radial_basis_kernel
        !*/

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

        template <
            typename T
            >
        struct sigmoid_kernel
        {
            /*!
                REQUIREMENTS ON T
                    T must be a dlib::matrix object

                WHAT THIS OBJECT REPRESENTS
                    This object represents a sigmoid kernel

                THREAD SAFETY
                    This kernel is threadsafe.
            !*/

            typedef typename T::type scalar_type;
            typedef T sample_type;
            typedef typename T::mem_manager_type mem_manager_type;

            const scalar_type gamma;
            const scalar_type coef;

            sigmoid_kernel(
            );
            /*!
                ensures
                    - #gamma == 0.1
                    - #coef == -1.0
            !*/

            sigmoid_kernel(
                const sigmoid_kernel& k
            );
            /*!
                ensures
                    - #gamma == k.gamma
                    - #coef == k.coef
            !*/

            sigmoid_kernel(
                const scalar_type g,
                const scalar_type c
            );
            /*!
                ensures
                    - #gamma == g
                    - #coef == c
            !*/

            scalar_type operator() (
                const sample_type& a,
                const sample_type& b
            ) const;
            /*!
                requires
                    - a.nc() == 1
                    - b.nc() == 1
                    - a.nr() == b.nr()
                ensures
                    - returns tanh(gamma*trans(a)*b + coef)
            !*/

            sigmoid_kernel& operator= (
                const sigmoid_kernel& k
            );
            /*!
                ensures
                    - #gamma = k.gamma
                    - #coef = k.coef
                    - returns *this
            !*/

            bool operator== (
                const sigmoid_kernel& k
            ) const;
            /*!
                ensures
                    - if (k and *this are identical) then
                        - returns true
                    - else
                        - returns false
            !*/
        };

        template <
            typename T
            >
        void serialize (
            const sigmoid_kernel<T>& item,
            std::ostream& out
        );
        /*!
            provides serialization support for sigmoid_kernel
        !*/

        template <
            typename T
            >
        void deserialize (
            sigmoid_kernel<T>& item,
            std::istream& in
        );
        /*!
            provides deserialization support for sigmoid_kernel
        !*/

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

        template <
            typename T
            >
        struct polynomial_kernel
        {
            /*!
                REQUIREMENTS ON T
                    T must be a dlib::matrix object

                WHAT THIS OBJECT REPRESENTS
                    This object represents a polynomial kernel

                THREAD SAFETY
                    This kernel is threadsafe.
            !*/

            typedef typename T::type scalar_type;
            typedef T sample_type;
            typedef typename T::mem_manager_type mem_manager_type;

            const scalar_type gamma;
            const scalar_type coef;
            const scalar_type degree;

            polynomial_kernel(
            );
            /*!
                ensures
                    - #gamma == 1
                    - #coef == 0
                    - #degree == 1
            !*/

            polynomial_kernel(
                const polynomial_kernel& k
            );
            /*!
                ensures
                    - #gamma == k.gamma
                    - #coef == k.coef
                    - #degree == k.degree
            !*/

            polynomial_kernel(
                const scalar_type g,
                const scalar_type c,
                const scalar_type d
            );
            /*!
                ensures
                    - #gamma == g
                    - #coef == c
                    - #degree == d
            !*/

            scalar_type operator() (
                const sample_type& a,
                const sample_type& b
            ) const;
            /*!
                requires
                    - a.nc() == 1
                    - b.nc() == 1
                    - a.nr() == b.nr()
                ensures
                    - returns pow(gamma*trans(a)*b + coef, degree)
            !*/

            polynomial_kernel& operator= (
                const polynomial_kernel& k
            );
            /*!
                ensures
                    - #gamma = k.gamma
                    - #coef = k.coef
                    - #degree = k.degree
                    - returns *this
            !*/

            bool operator== (
                const polynomial_kernel& k
            ) const;
            /*!
                ensures
                    - if (k and *this are identical) then
                        - returns true
                    - else
                        - returns false
            !*/
        };

        template <
            typename T
            >
        void serialize (
            const polynomial_kernel<T>& item,
            std::ostream& out
        );
        /*!
            provides serialization support for polynomial_kernel
        !*/

        template <
            typename T
            >
        void deserialize (
            polynomial_kernel<T>& item,
            std::istream& in
        );
        /*!
            provides deserialization support for polynomial_kernel
        !*/

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

        template <
            typename T
            >
        struct linear_kernel
        {
            /*!
                REQUIREMENTS ON T
                    T must be a dlib::matrix object

                WHAT THIS OBJECT REPRESENTS
                    This object represents a linear function kernel

                THREAD SAFETY
                    This kernel is threadsafe.
            !*/

            typedef typename T::type scalar_type;
            typedef T sample_type;
            typedef typename T::mem_manager_type mem_manager_type;

            scalar_type operator() (
                const sample_type& a,
                const sample_type& b
            ) const;
            /*!
                requires
                    - a.nc() == 1
                    - b.nc() == 1
                    - a.nr() == b.nr()
                ensures
                    - returns trans(a)*b
            !*/

            bool operator== (
                const linear_kernel& k
            ) const;
            /*!
                ensures
                    - returns true
            !*/
        };

        template <
            typename T
            >
        void serialize (
            const linear_kernel<T>& item,
            std::ostream& out
        );
        /*!
            provides serialization support for linear_kernel
        !*/

        template <
            typename T
            >
        void deserialize (
            linear_kernel<T>& item,
            std::istream& in
        );
        /*!
            provides deserialization support for linear_kernel
        !*/

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

        template <
            typename T
            >
        struct histogram_intersection_kernel
        {
            /*!
                REQUIREMENTS ON T
                    T must be a dlib::matrix object

                WHAT THIS OBJECT REPRESENTS
                    This object represents a histogram intersection kernel kernel

                THREAD SAFETY
                    This kernel is threadsafe.
            !*/

            typedef typename T::type scalar_type;
            typedef T sample_type;
            typedef typename T::mem_manager_type mem_manager_type;

            scalar_type operator() (
                const sample_type& a,
                const sample_type& b
            ) const;
            /*!
                requires
                    - is_vector(a)
                    - is_vector(b)
                    - a.size() == b.size()
                    - min(a) >= 0
                    - min(b) >= 0
                ensures
                    - returns sum over all i: std::min(a(i), b(i))
            !*/

            bool operator== (
                const histogram_intersection_kernel& k
            ) const;
            /*!
                ensures
                    - returns true
            !*/
        };

        template <
            typename T
            >
        void serialize (
            const histogram_intersection_kernel<T>& item,
            std::ostream& out
        );
        /*!
            provides serialization support for histogram_intersection_kernel
        !*/

        template <
            typename T
            >
        void deserialize (
            histogram_intersection_kernel<T>& item,
            std::istream& in
        );
        /*!
            provides deserialization support for histogram_intersection_kernel
        !*/

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

        template <
            typename T
            >
        struct offset_kernel
        {
            /*!
                REQUIREMENTS ON T
                    T must be a kernel object (e.g. radial_basis_kernel, polynomial_kernel, etc.)

                WHAT THIS OBJECT REPRESENTS
                    This object represents a kernel with a fixed value offset
                    added to it.

                THREAD SAFETY
                    This kernel is threadsafe.
            !*/

            typedef typename T::scalar_type scalar_type;
            typedef typename T::sample_type sample_type;
            typedef typename T::mem_manager_type mem_manager_type;

            const T kernel;
            const scalar_type offset;

            offset_kernel(
            );
            /*!
                ensures
                    - #offset == 0.01
            !*/

            offset_kernel(
                const offset_kernel& k
            );
            /*!
                ensures
                    - #offset == k.offset
                    - #kernel == k.kernel
            !*/

            offset_kernel(
                const T& k,
                const scalar_type& off
            );
            /*!
                ensures
                    - #kernel == k
                    - #offset == off
            !*/

            scalar_type operator() (
                const sample_type& a,
                const sample_type& b
            ) const;
            /*!
                ensures
                    - returns kernel(a,b) + offset
            !*/

            offset_kernel& operator= (
                const offset_kernel& k
            );
            /*!
                ensures
                    - #offset == k.offset
                    - #kernel == k.kernel
            !*/

            bool operator== (
                const offset_kernel& k
            ) const;
            /*!
                ensures
                    - if (k and *this are identical) then
                        - returns true
                    - else
                        - returns false
            !*/
        };

        template <
            typename T
            >
        void serialize (
            const offset_kernel<T>& item,
            std::ostream& out
        );
        /*!
            provides serialization support for offset_kernel
        !*/

        template <
            typename T
            >
        void deserialize (
            offset_kernel<T>& item,
            std::istream& in
        );
        /*!
            provides deserialization support for offset_kernel
        !*/

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

        template <
            typename kernel_type
            >
        struct kernel_derivative
        {
            /*!
                REQUIREMENTS ON kernel_type
                    kernel_type must be one of the following kernel types:
                        - radial_basis_kernel
                        - polynomial_kernel
                        - sigmoid_kernel
                        - linear_kernel
                        - offset_kernel

                WHAT THIS OBJECT REPRESENTS
                    This is a function object that computes the derivative of a kernel
                    function object.

                THREAD SAFETY
                    It is always safe to use distinct instances of this object in different
                    threads.  However, when a single instance is shared between threads then
                    the following rules apply:
                        Instances of this object are allowed to have a mutable cache which is
                        used by const member functions.  Therefore, it is not safe to use one
                        instance of this object from multiple threads (unless protected by a
                        mutex).
            !*/

            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;

            kernel_derivative(
                const kernel_type& k_
            );
            /*!
                ensures
                    - this object will return derivatives of the kernel object k_
                    - #k == k_
            !*/

            const sample_type operator() (
                const sample_type& x,
                const sample_type& y
            ) const;
            /*!
                ensures
                    - returns the derivative of k with respect to y.
            !*/

            const kernel_type& k;
        };

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

    }

    #endif // DLIB_SVm_KERNEL_ABSTRACT_