x_analytical_values.py 文件源码

def analytical_value_i_renyi(distr, alpha, par):
    """ Analytical value of the Renyi mutual information.

    Parameters
    ----------    
    distr : str
            Name of the distribution.
    alpha : float
            Parameter of the Renyi mutual information.
    par : dictionary
          Parameters of the distribution. If distr = 'normal': par["cov"]
          is the covariance matrix.

    Returns
    -------
    i : float
        Analytical value of the Renyi mutual information.

    """

    if distr == 'normal':
        c = par["cov"]        

        t1 = -alpha / 2 * log(det(c))
        t2 = -(1 - alpha) / 2 * log(prod(diag(c)))
        t3 = log(det(alpha * inv(c) + (1 - alpha) * diag(1 / diag(c)))) / 2
        i = 1 / (alpha - 1) * (t1 + t2 - t3)            
    else:
        raise Exception('Distribution=?')

    return i