(self)
return self._LDLdecomposition()
Returns the LDL Decomposition (L, D) of matrix A,
        such that L * D * L.T == A
        This method eliminates the use of square root.
        Further this ensures that all the diagonal entries of L are 1.
        A must be a square, symmetric, positive-definite
        and non-singular matrix.

        Examples
        ========

        >>> from sympy.matrices import Matrix, eye
        >>> A = Matrix(((25, 15, -5), (15, 18, 0), (-5, 0, 11)))
        >>> L, D = A.LDLdecomposition()
        >>> L
        Matrix([
        [   1,   0, 0],
        [ 3/5,   1, 0],
        [-1/5, 1/3, 1]])
        >>> D
        Matrix([
        [25, 0, 0],
        [ 0, 9, 0],
        [ 0, 0, 9]])
        >>> L * D * L.T * A.inv() == eye(A.rows)
        True

        See Also
        ========

        cholesky
        LUdecomposition
        QRdecomposition
Returns the LDL Decomposition (L, D) of matrix A,
        such that L * D * L.T == A
        This method eliminates the use of square root.
        Further this ensures that all the diagonal entries of L are 1.
        A must be a square, symmetric, positive-definite
        and non-singular matrix.
Returns the LDL Decomposition ( L D ) of matrix A such that L * D * L . T == A This method eliminates the use of square root . Further this ensures that all the diagonal entries of L are 1 . A must be a square symmetric positive - definite and non - singular matrix .
def LDLdecomposition(self):
        """Returns the LDL Decomposition (L, D) of matrix A,
        such that L * D * L.T == A
        This method eliminates the use of square root.
        Further this ensures that all the diagonal entries of L are 1.
        A must be a square, symmetric, positive-definite
        and non-singular matrix.

        Examples
        ========

        >>> from sympy.matrices import Matrix, eye
        >>> A = Matrix(((25, 15, -5), (15, 18, 0), (-5, 0, 11)))
        >>> L, D = A.LDLdecomposition()
        >>> L
        Matrix([
        [   1,   0, 0],
        [ 3/5,   1, 0],
        [-1/5, 1/3, 1]])
        >>> D
        Matrix([
        [25, 0, 0],
        [ 0, 9, 0],
        [ 0, 0, 9]])
        >>> L * D * L.T * A.inv() == eye(A.rows)
        True

        See Also
        ========

        cholesky
        LUdecomposition
        QRdecomposition
        """
        if not self.is_square:
            raise NonSquareMatrixError("Matrix must be square.")
        if not self.is_symmetric():
            raise ValueError("Matrix must be symmetric.")
        return self._LDLdecomposition()
def LDLdecomposition ( self ) : if not self . is_square : raise NonSquareMatrixError ( "Matrix must be square." ) if not self . is_symmetric ( ) : raise ValueError ( "Matrix must be symmetric." ) return self . _LDLdecomposition ( )