    // Copyright (C) 2008  Davis E. King (davis@dlib.net)
    // License: Boost Software License   See LICENSE.txt for the full license.
    #ifndef DLIB_OPTIMIZATIOn_H_
    #define DLIB_OPTIMIZATIOn_H_

    #include <cmath>
    #include <limits>
    #include "optimization_abstract.h"
    #include "optimization_search_strategies.h"
    #include "optimization_stop_strategies.h"
    #include "optimization_line_search.h"

    namespace dlib
    {

    // ----------------------------------------------------------------------------------------
    // ----------------------------------------------------------------------------------------
    //                    Functions that transform other functions
    // ----------------------------------------------------------------------------------------
    // ----------------------------------------------------------------------------------------

        template <typename funct>
        class central_differences
        {
        public:
            // You get an error on this line when you pass in a global function to this function.
            // You have to either use a function object or pass a pointer to your global function
            // by taking its address using the & operator.  (This check is here because gcc 4.0
            // has a bug that causes it to silently corrupt return values from functions that
            // invoked through a reference)
            COMPILE_TIME_ASSERT(is_function<funct>::value == false);

            central_differences(const funct& f_, double eps_ = 1e-7) : f(f_), eps(eps_){}

            template <typename T>
            typename T::matrix_type operator()(const T& x) const
            {
                // T must be some sort of dlib matrix
                COMPILE_TIME_ASSERT(is_matrix<T>::value);

                typename T::matrix_type der(x.size());
                typename T::matrix_type e(x);
                for (long i = 0; i < x.size(); ++i)
                {
                    const double old_val = e(i);

                    e(i) += eps;
                    const double delta_plus = f(e);
                    e(i) = old_val - eps;
                    const double delta_minus = f(e);

                    der(i) = (delta_plus - delta_minus)/(2*eps);

                    // and finally restore the old value of this element
                    e(i) = old_val;
                }

                return der;
            }

            template <typename T, typename U>
            typename U::matrix_type operator()(const T& item, const U& x) const
            {
                // U must be some sort of dlib matrix
                COMPILE_TIME_ASSERT(is_matrix<U>::value);

                typename U::matrix_type der(x.size());
                typename U::matrix_type e(x);
                for (long i = 0; i < x.size(); ++i)
                {
                    const double old_val = e(i);

                    e(i) += eps;
                    const double delta_plus = f(item,e);
                    e(i) = old_val - eps;
                    const double delta_minus = f(item,e);

                    der(i) = (delta_plus - delta_minus)/(2*eps);

                    // and finally restore the old value of this element
                    e(i) = old_val;
                }

                return der;
            }

            double operator()(const double& x) const
            {
                return (f(x+eps)-f(x-eps))/(2*eps);
            }

        private:
            const funct& f;
            const double eps;
        };

        template <typename funct>
        const central_differences<funct> derivative(const funct& f) { return central_differences<funct>(f); }
        template <typename funct>
        const central_differences<funct> derivative(const funct& f, double eps)
        {
            // You get an error on this line when you pass in a global function to this function.
            // You have to either use a function object or pass a pointer to your global function
            // by taking its address using the & operator.  (This check is here because gcc 4.0
            // has a bug that causes it to silently corrupt return values from functions that
            // invoked through a reference)
            COMPILE_TIME_ASSERT(is_function<funct>::value == false);

            DLIB_ASSERT (
                eps > 0,
                "\tcentral_differences derivative(f,eps)"
                << "\n\tYou must give an epsilon > 0"
                << "\n\teps:     " << eps
            );
            return central_differences<funct>(f,eps);
        }

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

        template <typename funct>
        class negate_function_object
        {
        public:
            // You get an error on this line when you pass in a global function to this function.
            // You have to either use a function object or pass a pointer to your global function
            // by taking its address using the & operator.  (This check is here because gcc 4.0
            // has a bug that causes it to silently corrupt return values from functions that
            // invoked through a reference)
            COMPILE_TIME_ASSERT(is_function<funct>::value == false);

            negate_function_object(const funct& f_) : f(f_){}

            template <typename T>
            double operator()(const T& x) const
            {
                return -f(x);
            }

        private:
            const funct& f;
        };

        template <typename funct>
        const negate_function_object<funct> negate_function(const funct& f) { return negate_function_object<funct>(f); }

    // ----------------------------------------------------------------------------------------
    // ----------------------------------------------------------------------------------------
    //                    Functions that perform unconstrained optimization
    // ----------------------------------------------------------------------------------------
    // ----------------------------------------------------------------------------------------

        template <
            typename search_strategy_type,
            typename stop_strategy_type,
            typename funct,
            typename funct_der,
            typename T
            >
        double find_min (
            search_strategy_type search_strategy,
            stop_strategy_type stop_strategy,
            const funct& f,
            const funct_der& der,
            T& x,
            double min_f
        )
        {
            // You get an error on this line when you pass in a global function to this function.
            // You have to either use a function object or pass a pointer to your global function
            // by taking its address using the & operator.  (This check is here because gcc 4.0
            // has a bug that causes it to silently corrupt return values from functions that
            // invoked through a reference)
            COMPILE_TIME_ASSERT(is_function<funct>::value == false);
            COMPILE_TIME_ASSERT(is_function<funct_der>::value == false);

            COMPILE_TIME_ASSERT(is_matrix<T>::value);
            DLIB_ASSERT (
                is_col_vector(x),
                "\tdouble find_min()"
                << "\n\tYou have to supply column vectors to this function"
                << "\n\tx.nc():    " << x.nc()
            );

            T g, s;

            double f_value = f(x);
            g = der(x);

            DLIB_ASSERT(is_finite(f_value), "The objective function generated non-finite outputs");
            DLIB_ASSERT(is_finite(g), "The objective function generated non-finite outputs");

            while(stop_strategy.should_continue_search(x, f_value, g) && f_value > min_f)
            {
                s = search_strategy.get_next_direction(x, f_value, g);

                double alpha = line_search(
                            make_line_search_function(f,x,s, f_value),
                            f_value,
                            make_line_search_function(der,x,s, g),
                            dot(g,s), // compute initial gradient for the line search
                            search_strategy.get_wolfe_rho(), search_strategy.get_wolfe_sigma(), min_f,
                            search_strategy.get_max_line_search_iterations());

                // Take the search step indicated by the above line search
                x += alpha*s;

                DLIB_ASSERT(is_finite(f_value), "The objective function generated non-finite outputs");
                DLIB_ASSERT(is_finite(g), "The objective function generated non-finite outputs");
            }

            return f_value;
        }

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

        template <
            typename search_strategy_type,
            typename stop_strategy_type,
            typename funct,
            typename funct_der,
            typename T
            >
        double find_max (
            search_strategy_type search_strategy,
            stop_strategy_type stop_strategy,
            const funct& f,
            const funct_der& der,
            T& x,
            double max_f
        )
        {
            // You get an error on this line when you pass in a global function to this function.
            // You have to either use a function object or pass a pointer to your global function
            // by taking its address using the & operator.  (This check is here because gcc 4.0
            // has a bug that causes it to silently corrupt return values from functions that
            // invoked through a reference)
            COMPILE_TIME_ASSERT(is_function<funct>::value == false);
            COMPILE_TIME_ASSERT(is_function<funct_der>::value == false);

            COMPILE_TIME_ASSERT(is_matrix<T>::value);
            DLIB_ASSERT (
                is_col_vector(x),
                "\tdouble find_max()"
                << "\n\tYou have to supply column vectors to this function"
                << "\n\tx.nc():    " << x.nc()
            );

            T g, s;

            // This function is basically just a copy of find_min() but with - put in the right places
            // to flip things around so that it ends up looking for the max rather than the min.

            double f_value = -f(x);
            g = -der(x);

            DLIB_ASSERT(is_finite(f_value), "The objective function generated non-finite outputs");
            DLIB_ASSERT(is_finite(g), "The objective function generated non-finite outputs");

            while(stop_strategy.should_continue_search(x, f_value, g) && f_value > -max_f)
            {
                s = search_strategy.get_next_direction(x, f_value, g);

                double alpha = line_search(
                            negate_function(make_line_search_function(f,x,s, f_value)),
                            f_value,
                            negate_function(make_line_search_function(der,x,s, g)),
                            dot(g,s), // compute initial gradient for the line search
                            search_strategy.get_wolfe_rho(), search_strategy.get_wolfe_sigma(), -max_f,
                            search_strategy.get_max_line_search_iterations()
                            );

                // Take the search step indicated by the above line search
                x += alpha*s;

                // Don't forget to negate these outputs from the line search since they are
                // from the unnegated versions of f() and der()
                g *= -1;
                f_value *= -1;

                DLIB_ASSERT(is_finite(f_value), "The objective function generated non-finite outputs");
                DLIB_ASSERT(is_finite(g), "The objective function generated non-finite outputs");
            }

            return -f_value;
        }

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

        template <
            typename search_strategy_type,
            typename stop_strategy_type,
            typename funct,
            typename T
            >
        double find_min_using_approximate_derivatives (
            search_strategy_type search_strategy,
            stop_strategy_type stop_strategy,
            const funct& f,
            T& x,
            double min_f,
            double derivative_eps = 1e-7
        )
        {
            // You get an error on this line when you pass in a global function to this function.
            // You have to either use a function object or pass a pointer to your global function
            // by taking its address using the & operator.  (This check is here because gcc 4.0
            // has a bug that causes it to silently corrupt return values from functions that
            // invoked through a reference)
            COMPILE_TIME_ASSERT(is_function<funct>::value == false);

            COMPILE_TIME_ASSERT(is_matrix<T>::value);
            DLIB_ASSERT (
                is_col_vector(x) && derivative_eps > 0,
                "\tdouble find_min_using_approximate_derivatives()"
                << "\n\tYou have to supply column vectors to this function"
                << "\n\tx.nc():         " << x.nc()
                << "\n\tderivative_eps: " << derivative_eps
            );

            T g, s;

            double f_value = f(x);
            g = derivative(f,derivative_eps)(x);

            DLIB_ASSERT(is_finite(f_value), "The objective function generated non-finite outputs");
            DLIB_ASSERT(is_finite(g), "The objective function generated non-finite outputs");

            while(stop_strategy.should_continue_search(x, f_value, g) && f_value > min_f)
            {
                s = search_strategy.get_next_direction(x, f_value, g);

                double alpha = line_search(
                            make_line_search_function(f,x,s,f_value),
                            f_value,
                            derivative(make_line_search_function(f,x,s),derivative_eps),
                            dot(g,s),  // Sometimes the following line is a better way of determining the initial gradient.
                            //derivative(make_line_search_function(f,x,s),derivative_eps)(0),
                            search_strategy.get_wolfe_rho(), search_strategy.get_wolfe_sigma(), min_f,
                            search_strategy.get_max_line_search_iterations()
                            );

                // Take the search step indicated by the above line search
                x += alpha*s;

                g = derivative(f,derivative_eps)(x);

                DLIB_ASSERT(is_finite(f_value), "The objective function generated non-finite outputs");
                DLIB_ASSERT(is_finite(g), "The objective function generated non-finite outputs");
            }

            return f_value;
        }

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

        template <
            typename search_strategy_type,
            typename stop_strategy_type,
            typename funct,
            typename T
            >
        double find_max_using_approximate_derivatives (
            search_strategy_type search_strategy,
            stop_strategy_type stop_strategy,
            const funct& f,
            T& x,
            double max_f,
            double derivative_eps = 1e-7
        )
        {
            // You get an error on this line when you pass in a global function to this function.
            // You have to either use a function object or pass a pointer to your global function
            // by taking its address using the & operator.  (This check is here because gcc 4.0
            // has a bug that causes it to silently corrupt return values from functions that
            // invoked through a reference)
            COMPILE_TIME_ASSERT(is_function<funct>::value == false);

            COMPILE_TIME_ASSERT(is_matrix<T>::value);
            DLIB_ASSERT (
                is_col_vector(x) && derivative_eps > 0,
                "\tdouble find_max_using_approximate_derivatives()"
                << "\n\tYou have to supply column vectors to this function"
                << "\n\tx.nc():         " << x.nc()
                << "\n\tderivative_eps: " << derivative_eps
            );

            // Just negate the necessary things and call the find_min version of this function.
            return -find_min_using_approximate_derivatives(
                search_strategy,
                stop_strategy,
                negate_function(f),
                x,
                -max_f,
                derivative_eps
            );
        }

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

    }

    #endif // DLIB_OPTIMIZATIOn_H_