def normalize_zero_center(x):
    """
    normalize vector / matrix to mean 0 and std 1: (x - mean(x)) / std(x).
    if the standard deviation of `x` is 0, an ZeroDivisionError will be raised.
    :param x: a numpy array.
    :return: x normalized to mean 0 and std 1
    """
    x = x - x.mean()
    x = x / x.std()
    return x