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def mid(x, base=None):
    '''Return mean value of adjacent member of an array.
    Useful for plotting bin counts.
    '''
    if base is None:
        x = np.asarray(x)
        return  (x[1:] + x[:-1])/2.
    elif base == 'log':
        return np.exp(mid(np.log(x)))
    elif base == 'exp':
        return np.log(mid(np.exp(x)))
    else:
        assert base > 0
        return np.log(mid(base**x))/np.log(base)