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    template<typename Real, int Dim> | 
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    class SquareMatrix : public RectMatrix<Real, Dim, Dim> { | 
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        public: | 
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            typedef Real ElemType; | 
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            typedef Real* ElemPoinerType; | 
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        /** default constructor */ | 
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        SquareMatrix() { | 
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            for (unsigned int i = 0; i < Dim; i++) | 
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                for (unsigned int j = 0; j < Dim; j++) | 
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                    data_[i][j] = 0.0; | 
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         } | 
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            /** default constructor */ | 
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            SquareMatrix() { | 
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                for (unsigned int i = 0; i < Dim; i++) | 
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                    for (unsigned int j = 0; j < Dim; j++) | 
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                        data_[i][j] = 0.0; | 
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             } | 
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        /** copy constructor */ | 
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        SquareMatrix(const RectMatrix<Real, Dim, Dim>& m)  : RectMatrix<Real, Dim, Dim>(m) { | 
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        } | 
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         | 
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        /** copy assignment operator */ | 
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        SquareMatrix<Real, Dim>& operator =(const RectMatrix<Real, Dim, Dim>& m) { | 
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            RectMatrix<Real, Dim, Dim>::operator=(m); | 
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            return *this; | 
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        } | 
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                                | 
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        /** Retunrs  an identity matrix*/ | 
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       static SquareMatrix<Real, Dim> identity() { | 
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            SquareMatrix<Real, Dim> m; | 
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            /** copy constructor */ | 
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            SquareMatrix(const RectMatrix<Real, Dim, Dim>& m) : RectMatrix<Real, Dim, Dim>(m) { | 
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            } | 
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             | 
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            for (unsigned int i = 0; i < Dim; i++)  | 
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                for (unsigned int j = 0; j < Dim; j++)  | 
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                    if (i == j) | 
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                        m(i, j) = 1.0; | 
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                    else | 
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                        m(i, j) = 0.0; | 
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            /** copy assignment operator */ | 
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            SquareMatrix<Real, Dim>& operator =(const RectMatrix<Real, Dim, Dim>& m) { | 
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                RectMatrix<Real, Dim, Dim>::operator=(m); | 
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                return *this; | 
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            } | 
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                                    | 
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            /** Retunrs  an identity matrix*/ | 
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            return m; | 
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        } | 
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           static SquareMatrix<Real, Dim> identity() { | 
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                SquareMatrix<Real, Dim> m; | 
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                 | 
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                for (unsigned int i = 0; i < Dim; i++)  | 
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                    for (unsigned int j = 0; j < Dim; j++)  | 
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                        if (i == j) | 
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                            m(i, j) = 1.0; | 
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                        else | 
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                            m(i, j) = 0.0; | 
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 | 
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        /**  | 
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         * Retunrs  the inversion of this matrix.  | 
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         * @todo need implementation | 
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         */ | 
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         SquareMatrix<Real, Dim>  inverse() { | 
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             SquareMatrix<Real, Dim> result; | 
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                return m; | 
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            } | 
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 | 
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             return result; | 
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        }         | 
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            /**  | 
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             * Retunrs  the inversion of this matrix.  | 
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             * @todo need implementation | 
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             */ | 
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             SquareMatrix<Real, Dim>  inverse() { | 
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                 SquareMatrix<Real, Dim> result; | 
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        /** | 
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         * Returns the determinant of this matrix. | 
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         * @todo need implementation | 
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         */ | 
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        Real determinant() const { | 
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            Real det; | 
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            return det; | 
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        } | 
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                 return result; | 
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            }         | 
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        /** Returns the trace of this matrix. */ | 
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        Real trace() const { | 
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           Real tmp = 0; | 
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            | 
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            for (unsigned int i = 0; i < Dim ; i++) | 
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                tmp += data_[i][i]; | 
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            /** | 
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             * Returns the determinant of this matrix. | 
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             * @todo need implementation | 
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             */ | 
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            Real determinant() const { | 
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                Real det; | 
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                return det; | 
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            } | 
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            return tmp; | 
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        } | 
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            /** Returns the trace of this matrix. */ | 
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            Real trace() const { | 
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               Real tmp = 0; | 
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                | 
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                for (unsigned int i = 0; i < Dim ; i++) | 
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                    tmp += data_[i][i]; | 
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        /** Tests if this matrix is symmetrix. */             | 
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        bool isSymmetric() const { | 
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            for (unsigned int i = 0; i < Dim - 1; i++) | 
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                for (unsigned int j = i; j < Dim; j++) | 
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                    if (fabs(data_[i][j] - data_[j][i]) > oopse::epsilon)  | 
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                        return false; | 
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            return true; | 
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        } | 
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                return tmp; | 
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            } | 
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 | 
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            /** Tests if this matrix is symmetrix. */             | 
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            bool isSymmetric() const { | 
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                for (unsigned int i = 0; i < Dim - 1; i++) | 
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                    for (unsigned int j = i; j < Dim; j++) | 
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                        if (fabs(data_[i][j] - data_[j][i]) > oopse::epsilon)  | 
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                            return false; | 
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                return true; | 
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            } | 
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        /** Tests if this matrix is orthogonal. */             | 
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        bool isOrthogonal() { | 
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            SquareMatrix<Real, Dim> tmp; | 
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            /** Tests if this matrix is orthogonal. */             | 
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            bool isOrthogonal() { | 
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                SquareMatrix<Real, Dim> tmp; | 
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            tmp = *this * transpose(); | 
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                tmp = *this * transpose(); | 
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            return tmp.isDiagonal(); | 
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        } | 
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                return tmp.isDiagonal(); | 
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            } | 
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        /** Tests if this matrix is diagonal. */ | 
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        bool isDiagonal() const { | 
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            for (unsigned int i = 0; i < Dim ; i++) | 
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                for (unsigned int j = 0; j < Dim; j++) | 
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                    if (i !=j && fabs(data_[i][j]) > oopse::epsilon)  | 
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                        return false; | 
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            return true; | 
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        } | 
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            /** Tests if this matrix is diagonal. */ | 
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            bool isDiagonal() const { | 
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                for (unsigned int i = 0; i < Dim ; i++) | 
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                    for (unsigned int j = 0; j < Dim; j++) | 
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                        if (i !=j && fabs(data_[i][j]) > oopse::epsilon)  | 
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                            return false; | 
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                return true; | 
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            } | 
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        /** Tests if this matrix is the unit matrix. */ | 
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        bool isUnitMatrix() const { | 
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            if (!isDiagonal()) | 
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                return false; | 
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             | 
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            for (unsigned int i = 0; i < Dim ; i++) | 
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                if (fabs(data_[i][i] - 1) > oopse::epsilon) | 
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            /** Tests if this matrix is the unit matrix. */ | 
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            bool isUnitMatrix() const { | 
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                if (!isDiagonal()) | 
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                    return false; | 
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            return true; | 
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        }          | 
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                for (unsigned int i = 0; i < Dim ; i++) | 
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                    if (fabs(data_[i][i] - 1) > oopse::epsilon) | 
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                        return false; | 
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                     | 
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                return true; | 
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            }          | 
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        /** @todo need implementation */ | 
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        void diagonalize() { | 
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            //jacobi(m, eigenValues, ortMat); | 
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        } | 
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            /** @todo need implementation */ | 
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            void diagonalize() { | 
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                //jacobi(m, eigenValues, ortMat); | 
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            } | 
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        /** | 
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         * Jacobi iteration routines for computing eigenvalues/eigenvectors of  | 
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         * real symmetric matrix | 
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         * | 
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         * @return true if success, otherwise return false | 
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         * @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is | 
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         *     overwritten | 
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         * @param w will contain the eigenvalues of the matrix On return of this function | 
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         * @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are  | 
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         *    normalized and mutually orthogonal.  | 
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         */ | 
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        | 
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        static int jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& d,  | 
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                              SquareMatrix<Real, Dim>& v); | 
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            /** | 
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             * Jacobi iteration routines for computing eigenvalues/eigenvectors of  | 
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> | 
             * real symmetric matrix | 
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> | 
             * | 
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             * @return true if success, otherwise return false | 
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             * @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is | 
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             *     overwritten | 
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             * @param w will contain the eigenvalues of the matrix On return of this function | 
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> | 
             * @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are  | 
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             *    normalized and mutually orthogonal.  | 
| 168 | 
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             */ | 
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            | 
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            static int jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& d,  | 
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                                  SquareMatrix<Real, Dim>& v); | 
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    };//end SquareMatrix | 
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