    // Copyright (C) 2009  Davis E. King (davis@dlib.net)
    // License: Boost Software License   See LICENSE.txt for the full license.
    // This code was adapted from code from the JAMA part of NIST's TNT library.
    //    See: http://math.nist.gov/tnt/
    #ifndef DLIB_MATRIX_CHOLESKY_DECOMPOSITION_H
    #define DLIB_MATRIX_CHOLESKY_DECOMPOSITION_H

    #include "matrix.h"
    #include "matrix_utilities.h"
    #include "matrix_subexp.h"
    #include <cmath>

    #ifdef DLIB_USE_LAPACK
    #include "lapack/potrf.h"
    #endif

    #include "matrix_trsm.h"

    namespace dlib
    {

        template <
            typename matrix_exp_type
            >
        class cholesky_decomposition
        {

        public:

            const static long NR = matrix_exp_type::NR;
            const static long NC = matrix_exp_type::NC;
            typedef typename matrix_exp_type::type type;
            typedef typename matrix_exp_type::mem_manager_type mem_manager_type;
            typedef typename matrix_exp_type::layout_type layout_type;

            typedef matrix<type,0,0,mem_manager_type,layout_type>  matrix_type;
            typedef matrix<type,NR,1,mem_manager_type,layout_type> column_vector_type;

            // You have supplied an invalid type of matrix_exp_type.  You have
            // to use this object with matrices that contain float or double type data.
            COMPILE_TIME_ASSERT((is_same_type<float, type>::value ||
                                 is_same_type<double, type>::value ));

            template <typename EXP>
            cholesky_decomposition(
                const matrix_exp<EXP>& A
            );

            bool is_spd(
            ) const;

            const matrix_type& get_l(
            ) const;

            template <typename EXP>
            const typename EXP::matrix_type solve (
                const matrix_exp<EXP>& B
            ) const;

        private:

            matrix_type L_;     // lower triangular factor
            bool isspd;         // true if matrix to be factored was SPD
        };

    // ----------------------------------------------------------------------------------------
    // ----------------------------------------------------------------------------------------
    //                                      Member functions
    // ----------------------------------------------------------------------------------------
    // ----------------------------------------------------------------------------------------

        template <typename matrix_exp_type>
        bool cholesky_decomposition<matrix_exp_type>::
        is_spd(
        ) const
        {
            return isspd;
        }

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

        template <typename matrix_exp_type>
        const typename cholesky_decomposition<matrix_exp_type>::matrix_type& cholesky_decomposition<matrix_exp_type>::
        get_l(
        ) const
        {
            return L_;
        }

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

        template <typename matrix_exp_type>
        template <typename EXP>
        cholesky_decomposition<matrix_exp_type>::
        cholesky_decomposition(
            const matrix_exp<EXP>& A_
        )
        {
            using std::sqrt;
            COMPILE_TIME_ASSERT((is_same_type<type, typename EXP::type>::value));

            // make sure requires clause is not broken
            DLIB_ASSERT(A_.nr() == A_.nc() && A_.size() > 0,
                "\tcholesky_decomposition::cholesky_decomposition(A_)"
                << "\n\tYou can only use this on square matrices"
                << "\n\tA_.nr():   " << A_.nr()
                << "\n\tA_.nc():   " << A_.nc()
                << "\n\tA_.size(): " << A_.size()
                << "\n\tthis:      " << this
                );

    #ifdef DLIB_USE_LAPACK
            L_ = A_;
            const type eps = max(abs(diag(L_)))*std::sqrt(std::numeric_limits<type>::epsilon())/100;

            // check if the matrix is actually symmetric
            bool is_symmetric = true;
            for (long r = 0; r < L_.nr() && is_symmetric; ++r)
            {
                for (long c = r+1; c < L_.nc() && is_symmetric; ++c)
                {
                    // this is approximately doing: is_symmetric = is_symmetric && ( L_(k,j) == L_(j,k))
                    is_symmetric = is_symmetric && (std::abs(L_(r,c) - L_(c,r)) < eps );
                }
            }

            // now compute the actual cholesky decomposition
            int info = lapack::potrf('L', L_);

            // check if it's really SPD
            if (info == 0 && is_symmetric && min(abs(diag(L_))) > eps*100)
                isspd = true;
            else
                isspd = false;

            L_ = lowerm(L_);
    #else
            const_temp_matrix<EXP> A(A_);

            isspd = true;

            const long n = A.nc();
            L_.set_size(n,n);

            const type eps = max(abs(diag(A)))*std::sqrt(std::numeric_limits<type>::epsilon())/100;

            // Main loop.
            for (long j = 0; j < n; j++)
            {
                type d(0.0);
                for (long k = 0; k < j; k++)
                {
                    type s(0.0);
                    for (long i = 0; i < k; i++)
                    {
                        s += L_(k,i)*L_(j,i);
                    }

                    // if L_(k,k) != 0
                    if (std::abs(L_(k,k)) > eps)
                    {
                        s = (A(j,k) - s)/L_(k,k);
                    }
                    else
                    {
                        s = (A(j,k) - s);
                        isspd = false;
                    }

                    L_(j,k) = s;

                    d = d + s*s;

                    // this is approximately doing: isspd = isspd && ( A(k,j) == A(j,k))
                    isspd = isspd && (std::abs(A(k,j) - A(j,k)) < eps );
                }
                d = A(j,j) - d;
                isspd = isspd && (d > eps);
                L_(j,j) = sqrt(d > 0.0 ? d : 0.0);
                for (long k = j+1; k < n; k++)
                {
                    L_(j,k) = 0.0;
                }
            }
    #endif
        }

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

        template <typename matrix_exp_type>
        template <typename EXP>
        const typename EXP::matrix_type cholesky_decomposition<matrix_exp_type>::
        solve(
            const matrix_exp<EXP>& B
        ) const
        {
            COMPILE_TIME_ASSERT((is_same_type<type, typename EXP::type>::value));

            // make sure requires clause is not broken
            DLIB_ASSERT(L_.nr() == B.nr(),
                "\tconst matrix cholesky_decomposition::solve(B)"
                << "\n\tInvalid arguments were given to this function."
                << "\n\tL_.nr():  " << L_.nr()
                << "\n\tB.nr():   " << B.nr()
                << "\n\tthis:     " << this
                );

            matrix<type, NR, EXP::NC, mem_manager_type, layout_type>  X(B);

            using namespace blas_bindings;
            // Solve L*y = b;
            triangular_solver(CblasLeft, CblasLower, CblasNoTrans, CblasNonUnit, L_, X);
            // Solve L'*X = Y;
            triangular_solver(CblasLeft, CblasLower, CblasTrans, CblasNonUnit, L_, X);
            return X;
        }

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

    }

    #endif // DLIB_MATRIX_CHOLESKY_DECOMPOSITION_H