    // Copyright (C) 2010  Davis E. King (davis@dlib.net)
    // License: Boost Software License   See LICENSE.txt for the full license.
    #ifndef DLIB_SVm_EPSILON_REGRESSION_TRAINER_H__
    #define DLIB_SVm_EPSILON_REGRESSION_TRAINER_H__

    #include "svr_trainer_abstract.h"
    #include <cmath>
    #include <limits>
    #include "../matrix.h"
    #include "../algs.h"

    #include "function.h"
    #include "kernel.h"
    #include "../optimization/optimization_solve_qp3_using_smo.h"

    namespace dlib
    {

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

        template <
            typename K
            >
        class svr_trainer
        {
        public:
            typedef K kernel_type;
            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;
            typedef decision_function<kernel_type> trained_function_type;

            svr_trainer (
            ) :
                C(1),
                eps_insensitivity(0.1),
                cache_size(200),
                eps(0.001)
            {
            }

            void set_cache_size (
                long cache_size_
            )
            {
                // make sure requires clause is not broken
                DLIB_ASSERT(cache_size_ > 0,
                    "\tvoid svr_trainer::set_cache_size(cache_size_)"
                    << "\n\t invalid inputs were given to this function"
                    << "\n\t cache_size: " << cache_size_
                    );
                cache_size = cache_size_;
            }

            long get_cache_size (
            ) const
            {
                return cache_size;
            }

            void set_epsilon (
                scalar_type eps_
            )
            {
                // make sure requires clause is not broken
                DLIB_ASSERT(eps_ > 0,
                    "\tvoid svr_trainer::set_epsilon(eps_)"
                    << "\n\t invalid inputs were given to this function"
                    << "\n\t eps_: " << eps_
                    );
                eps = eps_;
            }

            const scalar_type get_epsilon (
            ) const
            {
                return eps;
            }

            void set_epsilon_insensitivity (
                scalar_type eps_
            )
            {
                // make sure requires clause is not broken
                DLIB_ASSERT(eps_ > 0,
                    "\tvoid svr_trainer::set_epsilon_insensitivity(eps_)"
                    << "\n\t invalid inputs were given to this function"
                    << "\n\t eps_: " << eps_
                    );
                eps_insensitivity = eps_;
            }

            const scalar_type get_epsilon_insensitivity (
            ) const
            {
                return eps_insensitivity;
            }

            void set_kernel (
                const kernel_type& k
            )
            {
                kernel_function = k;
            }

            const kernel_type& get_kernel (
            ) const
            {
                return kernel_function;
            }

            void set_c (
                scalar_type C_
            )
            {
                // make sure requires clause is not broken
                DLIB_ASSERT(C_ > 0,
                    "\t void svr_trainer::set_c()"
                    << "\n\t C must be greater than 0"
                    << "\n\t C_:    " << C_
                    << "\n\t this: " << this
                    );

                C = C_;
            }

            const scalar_type get_c (
            ) const
            {
                return C;
            }

            template <
                typename in_sample_vector_type,
                typename in_scalar_vector_type
                >
            const decision_function<kernel_type> train (
                const in_sample_vector_type& x,
                const in_scalar_vector_type& y
            ) const
            {
                return do_train(mat(x), mat(y));
            }

            void swap (
                svr_trainer& item
            )
            {
                exchange(kernel_function, item.kernel_function);
                exchange(C,            item.C);
                exchange(eps_insensitivity, item.eps_insensitivity);
                exchange(cache_size,      item.cache_size);
                exchange(eps,             item.eps);
            }

        private:

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

            template <typename M>
            struct op_quad
            {
                explicit op_quad(
                    const M& m_
                ) : m(m_) {}

                const M& m;

                typedef typename M::type type;
                typedef type const_ret_type;
                const static long cost = M::cost + 2;

                inline const_ret_type apply ( long r, long c) const
                {
                    if (r < m.nr())
                    {
                        if (c < m.nc())
                        {
                            return m(r,c);
                        }
                        else
                        {
                            return -m(r,c-m.nc());
                        }
                    }
                    else
                    {
                        if (c < m.nc())
                        {
                            return -m(r-m.nr(),c);
                        }
                        else
                        {
                            return m(r-m.nr(),c-m.nc());
                        }
                    }
                }

                const static long NR = 2*M::NR;
                const static long NC = 2*M::NC;
                typedef typename M::mem_manager_type mem_manager_type;
                typedef typename M::layout_type layout_type;

                long nr () const { return 2*m.nr(); }
                long nc () const { return 2*m.nc(); }

                template <typename U> bool aliases               ( const matrix_exp<U>& item) const
                { return m.aliases(item); }
                template <typename U> bool destructively_aliases ( const matrix_exp<U>& item) const
                { return m.aliases(item); }
            };

            template <
                typename EXP
                >
            const matrix_op<op_quad<EXP> >  make_quad (
                const matrix_exp<EXP>& m
            ) const
            /*!
                ensures
                    - returns the following matrix:
                         m -m
                        -m  m
                    - I.e. returns a matrix that is twice the size of m and just
                      contains copies of m and -m
            !*/
            {
                typedef op_quad<EXP> op;
                return matrix_op<op>(op(m.ref()));
            }

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

            template <
                typename in_sample_vector_type,
                typename in_scalar_vector_type
                >
            const decision_function<kernel_type> do_train (
                const in_sample_vector_type& x,
                const in_scalar_vector_type& y
            ) const
            {
                typedef typename K::scalar_type scalar_type;
                typedef typename decision_function<K>::sample_vector_type sample_vector_type;
                typedef typename decision_function<K>::scalar_vector_type scalar_vector_type;

                // make sure requires clause is not broken
                DLIB_ASSERT(is_learning_problem(x,y) == true,
                    "\tdecision_function svr_trainer::train(x,y)"
                    << "\n\t invalid inputs were given to this function"
                    << "\n\t x.nr(): " << x.nr()
                    << "\n\t y.nr(): " << y.nr()
                    << "\n\t x.nc(): " << x.nc()
                    << "\n\t y.nc(): " << y.nc()
                    );

                scalar_vector_type alpha;

                solve_qp3_using_smo<scalar_vector_type> solver;

                solver(symmetric_matrix_cache<float>(make_quad(kernel_matrix(kernel_function,x)), cache_size),
                       uniform_matrix<scalar_type>(2*x.size(),1, eps_insensitivity) + join_cols(y,-y),
                       join_cols(uniform_matrix<scalar_type>(x.size(),1,1), uniform_matrix<scalar_type>(x.size(),1,-1)),
                       0,
                       C,
                       C,
                       alpha,
                       eps);

                scalar_type b;
                calculate_b(alpha,solver.get_gradient(),C,b);

                alpha = -rowm(alpha,range(0,x.size()-1)) + rowm(alpha,range(x.size(), alpha.size()-1));

                // count the number of support vectors
                const long sv_count = (long)sum(alpha != 0);

                scalar_vector_type sv_alpha;
                sample_vector_type support_vectors;

                // size these column vectors so that they have an entry for each support vector
                sv_alpha.set_size(sv_count);
                support_vectors.set_size(sv_count);

                // load the support vectors and their alpha values into these new column matrices
                long idx = 0;
                for (long i = 0; i < alpha.nr(); ++i)
                {
                    if (alpha(i) != 0)
                    {
                        sv_alpha(idx) = alpha(i);
                        support_vectors(idx) = x(i);
                        ++idx;
                    }
                }

                // now return the decision function
                return decision_function<K> (sv_alpha, -b, kernel_function, support_vectors);
            }

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

            template <
                typename scalar_vector_type
                >
            void calculate_b(
                const scalar_vector_type& alpha,
                const scalar_vector_type& df,
                const scalar_type& C,
                scalar_type& b
            ) const
            {
                using namespace std;
                long num_free = 0;
                scalar_type sum_free = 0;

                scalar_type upper_bound = -numeric_limits<scalar_type>::infinity();
                scalar_type lower_bound = numeric_limits<scalar_type>::infinity();

                find_min_and_max(df, upper_bound, lower_bound);

                for(long i = 0; i < alpha.nr(); ++i)
                {
                    if(i < alpha.nr()/2)
                    {
                        if(alpha(i) == C)
                        {
                            if (df(i) > upper_bound)
                                upper_bound = df(i);
                        }
                        else if(alpha(i) == 0)
                        {
                            if (df(i) < lower_bound)
                                lower_bound = df(i);
                        }
                        else
                        {
                            ++num_free;
                            sum_free += df(i);
                        }
                    }
                    else
                    {
                        if(alpha(i) == C)
                        {
                            if (-df(i) < lower_bound)
                                lower_bound = -df(i);
                        }
                        else if(alpha(i) == 0)
                        {
                            if (-df(i) > upper_bound)
                                upper_bound = -df(i);
                        }
                        else
                        {
                            ++num_free;
                            sum_free -= df(i);
                        }
                    }
                }

                if(num_free > 0)
                    b = sum_free/num_free;
                else
                    b = (upper_bound+lower_bound)/2;
            }

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

            kernel_type kernel_function;
            scalar_type C;
            scalar_type eps_insensitivity;
            long cache_size;
            scalar_type eps;
        }; // end of class svr_trainer

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

        template <typename K>
        void swap (
            svr_trainer<K>& a,
            svr_trainer<K>& b
        ) { a.swap(b); }

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

    }

    #endif // DLIB_SVm_EPSILON_REGRESSION_TRAINER_H__