How to use the pyriemann.utils.base.logm function in pyriemann

def test_logm():
    """Test matrix logarithm"""
    C = 2*np.eye(3)
    Ctrue = np.log(2)*np.eye(3)
    assert_array_almost_equal(logm(C), Ctrue)

def distance_logeuclid(A, B):
    """Log Euclidean distance between two covariance matrices A and B.

    .. math::
            d = \Vert \log(\mathbf{A}) - \log(\mathbf{B}) \Vert_F

    :param A: First covariance matrix
    :param B: Second covariance matrix
    :returns: Log-Eclidean distance between A and B

    """
    return distance_euclid(logm(A), logm(B))

else:
        C = init
    k = 0
    nu = 1.0
    tau = numpy.finfo(numpy.float64).max
    crit = numpy.finfo(numpy.float64).max
    # stop when J<10^-9 or max iteration = 50
    while (crit > tol) and (k < maxiter) and (nu > tol):
        k = k + 1
        C12 = sqrtm(C)
        Cm12 = invsqrtm(C)
        J = numpy.zeros((Ne, Ne))

        for index in range(Nt):
            tmp = numpy.dot(numpy.dot(Cm12, covmats[index, :, :]), Cm12)
            J += sample_weight[index] * logm(tmp)

        crit = numpy.linalg.norm(J, ord='fro')
        h = nu * crit
        C = numpy.dot(numpy.dot(C12, expm(nu * J)), C12)
        if h < tau:
            nu = 0.95 * nu
            tau = h
        else:
            nu = 0.5 * nu

    return C

"""Return the mean covariance matrix according to the log-euclidean metric.

    .. math::
            \mathbf{C} = \exp{(\\frac{1}{N} \sum_i \log{\mathbf{C}_i})}

    :param covmats: Covariance matrices set, Ntrials X Nchannels X Nchannels
    :param sample_weight: the weight of each sample

    :returns: the mean covariance matrix

    """
    sample_weight = _get_sample_weight(sample_weight, covmats)
    Nt, Ne, Ne = covmats.shape
    T = numpy.zeros((Ne, Ne))
    for index in range(Nt):
        T += sample_weight[index] * logm(covmats[index, :, :])
    C = expm(T)

    return C

:param Cref: np.ndarray
        The reference covariance matrix
    :returns: np.ndarray
        the Tangent space , a matrix of Ntrials X (Nchannels*(Nchannels+1)/2)

    """
    Nt, Ne, Ne = covmats.shape
    Cm12 = invsqrtm(Cref)
    idx = numpy.triu_indices_from(Cref)
    Nf = int(Ne * (Ne + 1) / 2)
    T = numpy.empty((Nt, Nf))
    coeffs = (numpy.sqrt(2) * numpy.triu(numpy.ones((Ne, Ne)), 1) +
              numpy.eye(Ne))[idx]
    for index in range(Nt):
        tmp = numpy.dot(numpy.dot(Cm12, covmats[index, :, :]), Cm12)
        tmp = logm(tmp)
        T[index, :] = numpy.multiply(coeffs, tmp[idx])
    return T

Matrices', PLoS ONE, 2015

    """
    sample_weight = _get_sample_weight(sample_weight, covmats)
    Nt, Ne, Ne = covmats.shape
    crit = numpy.inf
    k = 0

    # init with AJD
    B, _ = ajd_pham(covmats)
    while (crit > tol) and (k < maxiter):
        k += 1
        J = numpy.zeros((Ne, Ne))

        for index, Ci in enumerate(covmats):
            tmp = logm(numpy.dot(numpy.dot(B.T, Ci), B))
            J += sample_weight[index] * tmp

        update = numpy.diag(numpy.diag(expm(J)))
        B = numpy.dot(B, invsqrtm(update))

        crit = distance_riemann(numpy.eye(Ne), update)

    A = numpy.linalg.inv(B)

    J = numpy.zeros((Ne, Ne))
    for index, Ci in enumerate(covmats):
        tmp = logm(numpy.dot(numpy.dot(B.T, Ci), B))
        J += sample_weight[index] * tmp

    C = numpy.dot(numpy.dot(A.T, expm(J)), A)
    return C