x_analytical_values.py 文件源码

def analytical_value_h_renyi(distr, alpha, par):
    """ Analytical value of the Renyi entropy for the given distribution.

    Parameters
    ----------    
    distr : str
            Name of the distribution.
    alpha : float, alpha \ne 1
            Parameter of the Renyi entropy.
    par : dictionary
          Parameters of the distribution. If distr = 'uniform': par["a"], 
          par["b"], par["l"] <- lxU[a,b]. If distr = 'normal' : par["cov"]
          is the covariance matrix.

    Returns
    -------
    h : float
        Analytical value of the Renyi entropy.

    References
    ----------
    Kai-Sheng Song. Renyi information, loglikelihood and an intrinsic 
    distribution measure. Journal of Statistical Planning and Inference
    93: 51-69, 2001.

    """

    if distr == 'uniform':
        # par = {"a": a, "b": b, "l": l}
        # We also apply the transformation rule of the Renyi entropy in
        # case of linear transformations:
        h = log(prod(par["b"] - par["a"])) + log(absolute(det(par["l"]))) 
    elif distr == 'normal': 
        # par = {"cov": c}
        dim = par["cov"].shape[0]  # =c.shape[1]
        h = log((2*pi)**(dim / 2) * sqrt(absolute(det(par["cov"])))) -\
            dim * log(alpha) / 2 / (1 - alpha)        
    else:
        raise Exception('Distribution=?')

    return h