def METHOD_NAME(a, permute_l=False, overwrite_a=False, check_finite=True):
    """
    Compute pivoted LU decomposition of a matrix.
    The decomposition is::
        A = P L U
    where P is a permutation matrix, L lower triangular with unit
    diagonal elements, and U upper triangular.
    Parameters
    ----------
    a : (M, N) array_like
        Array to decompose
    permute_l : bool, optional
        Perform the multiplication P*L  (Default: do not permute)
    overwrite_a : bool, optional
        Whether to overwrite data in a (may improve performance)
    check_finite : bool, optional
        Whether to check that the input matrix contains only finite numbers.
        Disabling may give a performance gain, but may result in problems
        (crashes, non-termination) if the inputs do contain infinities or NaNs.
    Returns
    -------
    **(If permute_l == False)**
    p : (M, M) ndarray
        Permutation matrix
    l : (M, K) ndarray
        Lower triangular or trapezoidal matrix with unit diagonal.
        K = min(M, N)
    u : (K, N) ndarray
        Upper triangular or trapezoidal matrix
    **(If permute_l == True)**
    pl : (M, K) ndarray
        Permuted L matrix.
        K = min(M, N)
    u : (K, N) ndarray
        Upper triangular or trapezoidal matrix
    Notes
    -----
    This is a LU factorization routine written for Scipy.
    Examples
    --------
    >>> from scipy.linalg import lu
    >>> A = np.array([[2, 5, 8, 7], [5, 2, 2, 8], [7, 5, 6, 6], [5, 4, 4, 8]])
    >>> p, l, u = lu(A)
    >>> np.allclose(A - p @ l @ u, np.zeros((4, 4)))
    True
    """
    if check_finite:
        a1 = asarray_chkfinite(a)
    else:
        a1 = asarray(a)
    if len(a1.shape) != 2:
        raise ValueError('expected matrix')
    overwrite_a = overwrite_a or (_datacopied(a1, a))
    flu, = get_flinalg_funcs(('lu',), (a1,))
    p, l, u, info = flu(a1, permute_l=permute_l, overwrite_a=overwrite_a)
    if info < 0:
        raise ValueError('illegal value in %d-th argument of '
                         'internal lu.getrf' % -info)
    if permute_l:
        return l, u
    return p, l, u