(self)
return self._new(L), self._new(D)
Returns the LDL Decomposition (matrices ``L`` and ``D``) of matrix
        ``A``, such that ``L * D * L.T == A``. ``A`` must be a square,
        symmetric, positive-definite and non-singular.

        This method eliminates the use of square root and ensures that all
        the diagonal entries of L are 1.

        Examples
        ========

        >>> from sympy.matrices import SparseMatrix
        >>> A = SparseMatrix(((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
        True
Returns the LDL Decomposition (matrices ``L`` and ``D``) of matrix
        ``A``, such that ``L * D * L.T == A``. ``A`` must be a square,
        symmetric, positive-definite and non-singular.
Returns the LDL Decomposition ( matrices L and D ) of matrix A such that L * D * L . T == A . A must be a square symmetric positive - definite and non - singular .
def LDLdecomposition(self):
        """
        Returns the LDL Decomposition (matrices ``L`` and ``D``) of matrix
        ``A``, such that ``L * D * L.T == A``. ``A`` must be a square,
        symmetric, positive-definite and non-singular.

        This method eliminates the use of square root and ensures that all
        the diagonal entries of L are 1.

        Examples
        ========

        >>> from sympy.matrices import SparseMatrix
        >>> A = SparseMatrix(((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
        True

        """
        from sympy.core.numbers import nan, oo
        if not self.is_symmetric():
            raise ValueError('LDL decomposition applies only to '
                'symmetric matrices.')
        L, D = self.as_mutable()._LDL_sparse()
        if L.has(nan) or L.has(oo) or D.has(nan) or D.has(oo):
            raise ValueError('LDL decomposition applies only to '
                'positive-definite matrices')

        return self._new(L), self._new(D)
def LDLdecomposition ( self ) : from sympy . core . numbers import nan , oo if not self . is_symmetric ( ) : raise ValueError ( 'LDL decomposition applies only to ' 'symmetric matrices.' ) L , D = self . as_mutable ( ) . _LDL_sparse ( ) if L . has ( nan ) or L . has ( oo ) or D . has ( nan ) or D . has ( oo ) : raise ValueError ( 'LDL decomposition applies only to ' 'positive-definite matrices' ) return self . _new ( L ) , self . _new ( D )