Convert a pure action to the corresponding mixed action.

    Parameters
    ----------
    num_actions : scalar(int)
        The number of the pure actions (= the length of a mixed action).

    action : scalar(int)
        The pure action to convert to the corresponding mixed action.

    Returns
    -------
    ndarray(float, ndim=1)
        The mixed action representation of the given pure action.

def pure2mixed(num_actions, action):
    """
    Convert a pure action to the corresponding mixed action.

    Parameters
    ----------
    num_actions : scalar(int)
        The number of the pure actions (= the length of a mixed action).

    action : scalar(int)
        The pure action to convert to the corresponding mixed action.

    Returns
    -------
    ndarray(float, ndim=1)
        The mixed action representation of the given pure action.

    """
    mixed_action = np.zeros(num_actions)
    mixed_action[action] = 1
    return mixed_action