    // Copyright (C) 2012  Davis E. King (davis@dlib.net)
    // License: Boost Software License   See LICENSE.txt for the full license.
    #ifndef DLIB_RLs_H__
    #define DLIB_RLs_H__

    #include "rls_abstract.h"
    #include "../matrix.h"
    #include "function.h"

    namespace dlib
    {

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

        class rls
        {

        public:

            explicit rls(
                double forget_factor_,
                double C_ = 1000
            )
            {
                // make sure requires clause is not broken
                DLIB_ASSERT(0 < forget_factor_ && forget_factor_ <= 1 &&
                            0 < C_,
                    "\t rls::rls()"
                    << "\n\t invalid arguments were given to this function"
                    << "\n\t forget_factor_: " << forget_factor_
                    << "\n\t C_:   " << C_
                    << "\n\t this: " << this
                    );

                C = C_;
                forget_factor = forget_factor_;
            }

            rls(
            )
            {
                C = 1000;
                forget_factor = 1;
            }

            double get_c(
            ) const
            {
                return C;
            }

            double get_forget_factor(
            ) const
            {
                return forget_factor;
            }

            template <typename EXP>
            void train (
                const matrix_exp<EXP>& x,
                double y
            )
            {
                // make sure requires clause is not broken
                DLIB_ASSERT(is_col_vector(x) &&
                            (get_w().size() == 0 || get_w().size() == x.size()),
                    "\t void rls::train()"
                    << "\n\t invalid arguments were given to this function"
                    << "\n\t is_col_vector(x): " << is_col_vector(x)
                    << "\n\t x.size():         " << x.size()
                    << "\n\t get_w().size():   " << get_w().size()
                    << "\n\t this: " << this
                    );

                if (R.size() == 0)
                {
                    R = identity_matrix<double>(x.size())*C;
                    w.set_size(x.size());
                    w = 0;
                }

                // multiply by forget factor and incorporate x*trans(x) into R.
                const double l = 1.0/forget_factor;
                const double temp = 1 + l*trans(x)*R*x;
                matrix<double,0,1> tmp = R*x;
                R = l*R - l*l*(tmp*trans(tmp))/temp;

                // Since we multiplied by the forget factor, we need to add (1-forget_factor) of the
                // identity matrix back in to keep the regularization alive.
                add_eye_to_inv(R, (1-forget_factor)/C);

                // R should always be symmetric.  This line improves numeric stability of this algorithm.
                R = 0.5*(R + trans(R));

                w = w + R*x*(y - trans(x)*w);

            }

            const matrix<double,0,1>& get_w(
            ) const
            {
                return w;
            }

            template <typename EXP>
            double operator() (
                const matrix_exp<EXP>& x
            ) const
            {
                // make sure requires clause is not broken
                DLIB_ASSERT(is_col_vector(x) && get_w().size() == x.size(),
                    "\t double rls::operator()()"
                    << "\n\t invalid arguments were given to this function"
                    << "\n\t is_col_vector(x): " << is_col_vector(x)
                    << "\n\t x.size():         " << x.size()
                    << "\n\t get_w().size():   " << get_w().size()
                    << "\n\t this: " << this
                    );

                return dot(x,w);
            }

            decision_function<linear_kernel<matrix<double,0,1> > > get_decision_function (
            ) const
            {
                // make sure requires clause is not broken
                DLIB_ASSERT(get_w().size() != 0,
                    "\t decision_function rls::get_decision_function()"
                    << "\n\t invalid arguments were given to this function"
                    << "\n\t get_w().size():   " << get_w().size()
                    << "\n\t this: " << this
                    );

                decision_function<linear_kernel<matrix<double,0,1> > > df;
                df.alpha.set_size(1);
                df.basis_vectors.set_size(1);
                df.b = 0;
                df.alpha = 1;
                df.basis_vectors(0) = w;

                return df;
            }

            friend inline void serialize(const rls& item, std::ostream& out)
            {
                int version = 1;
                serialize(version, out);
                serialize(item.w, out);
                serialize(item.R, out);
                serialize(item.C, out);
                serialize(item.forget_factor, out);
            }

            friend inline void deserialize(rls& item, std::istream& in)
            {
                int version = 0;
                deserialize(version, in);
                if (version != 1)
                    throw dlib::serialization_error("Unknown version number found while deserializing rls object.");

                deserialize(item.w, in);
                deserialize(item.R, in);
                deserialize(item.C, in);
                deserialize(item.forget_factor, in);
            }

        private:

            void add_eye_to_inv(
                matrix<double>& m,
                double C
            )
            /*!
                ensures
                    - Let m == inv(M)
                    - this function returns inv(M + C*identity_matrix<double>(m.nr()))
            !*/
            {
                for (long r = 0; r < m.nr(); ++r)
                {
                    m = m - colm(m,r)*trans(colm(m,r))/(1/C + m(r,r));
                }
            }

            matrix<double,0,1> w;
            matrix<double> R;
            double C;
            double forget_factor;
        };

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

    }

    #endif // DLIB_RLs_H__