defines
    the structure of the outer factors of the factorization.

    .. versionadded:: 1.1.0

    References
    ----------
    .. [1] J.R. Bunch, L. Kaufman, Some stable methods for calculating
       inertia and solving symmetric linear systems, Math. Comput. Vol.31,
       1977. :doi:`10.2307/2005787`

    Examples
    --------
    Given an upper triangular array ``a`` that represents the full symmetric
    array with its entries, obtain ``l``, 'd' and the permutation vector `perm`:

    >>> import numpy as np
    >>> from scipy.linalg import ldl
    >>> a = np.array([[2, -1, 3], [0, 2, 0], [0, 0, 1]])
    >>> lu, d, perm = ldl(a, lower=0) # Use the upper part
    >>> lu
    array([[ 0. ,  0. ,  1. ],
           [ 0. ,  1. , -0.5],
           [ 1. ,  1. ,  1.5]])
    >>> d
    array([[-5. ,  0. ,  0. ],
           [ 0. ,  1.5,  0. ],
           [ 0. ,  0. ,  2. ]])
    >>> perm
    array([2, 1, 0])
    >>> lu[perm, :]
    array([[ 1. ,  1. ,  1.5],
           [ 0. ,  1. , -0.5],
           [ 0. ,  0. ,  1. ]])
    >>> lu.dot(d).dot(lu.T)
    array([[ 2., -1.,  3.],
           [-1.,  2.,  0.],
           [ 3.,  0.,  1.]])

    )