r"""
    checks whether T is reversible in terms of given stationary distribution.
    If no distribution is given, it will be calculated out of T.

    performs follwing check:
    :math:`\pi_i P_{ij} = \pi_j P_{ji}
    Parameters
    ----------
    T : scipy.sparse matrix
        Transition matrix
    mu : numpy.ndarray vector
        stationary distribution
    tol : float
        tolerance to check with

    Returns
    -------
    Truth value : bool
        True, if T is a stochastic matrix
        False, otherwise

def is_reversible(T, mu=None, tol=1e-15):
    r"""
    checks whether T is reversible in terms of given stationary distribution.
    If no distribution is given, it will be calculated out of T.

    performs follwing check:
    :math:`\pi_i P_{ij} = \pi_j P_{ji}
    Parameters
    ----------
    T : scipy.sparse matrix
        Transition matrix
    mu : numpy.ndarray vector
        stationary distribution
    tol : float
        tolerance to check with

    Returns
    -------
    Truth value : bool
        True, if T is a stochastic matrix
        False, otherwise
    """
    if not is_transition_matrix(T, tol):
        raise ValueError("given matrix is not a valid transition matrix.")

    T = T.tocsr()

    if mu is None:
        from .decomposition import stationary_distribution
        mu = stationary_distribution(T)

    Mu = diags(mu, 0)
    prod = Mu * T

    return allclose_sparse(prod, prod.transpose(), rtol=tol)