def __min_birth_max_death(persistence, band=0.0):
    """This function returns (min_birth, max_death) from the persistence.

    :param persistence: The persistence to plot.
    :type persistence: list of tuples(dimension, tuple(birth, death)).
    :param band: band
    :type band: float.
    :returns: (float, float) -- (min_birth, max_death).
    """
    # Look for minimum birth date and maximum death date for plot optimisation
    max_death = 0
    min_birth = persistence[0][1][0]
    for interval in reversed(persistence):
        if float(interval[1][1]) != float("inf"):
            if float(interval[1][1]) > max_death:
                max_death = float(interval[1][1])
        if float(interval[1][0]) > max_death:
            max_death = float(interval[1][0])
        if float(interval[1][0]) < min_birth:
            min_birth = float(interval[1][0])
    if band > 0.0:
        max_death += band
    return (min_birth, max_death)