x_analytical_values.py 文件源码

def analytical_value_d_hellinger(distr1, distr2, par1, par2):
    """ Analytical value of Hellinger distance for the given distributions.

    Parameters
    ----------
    distr1, distr2 : str-s
                    Names of the distributions.
    par1, par2 : dictionary-s
                 Parameters of the distributions. If distr1 = distr2 =
                 'normal': par1["mean"], par1["cov"] and par2["mean"],
                 par2["cov"] are the means and the covariance matrices.

    Returns
    -------
    d : float
        Analytical value of the Hellinger distance.

    """

    if distr1 == 'normal' and distr2 == 'normal':
        # covariance matrices, expectations:
        c1, m1 = par1['cov'], par1['mean']
        c2, m2 = par2['cov'], par2['mean']

        # "https://en.wikipedia.org/wiki/Hellinger_distance": Examples:
        diffm = m1 - m2
        avgc = (c1 + c2) / 2
        inv_avgc = inv(avgc)
        d = 1 - det(c1)**(1/4) * det(c2)**(1/4) / sqrt(det(avgc)) * \
            exp(-dot(diffm, dot(inv_avgc, diffm))/8)  # D^2

        d = sqrt(d)
    else:
        raise Exception('Distribution=?')

    return d