def lorentzian(x, ll, yshift=0.):
    """ Peak normalized Lorentzian function
    :arguments
        x: float / np1darray
        ll: float       Lorentzian FWHM
        yshift: float   shift of y value (used for root finding)
    :returns
        y: float / np1darray
    """

    return ll**2 / (4 * x**2 + ll**2) - yshift