def sigmascale (nsigma):
    """Say we take a Gaussian bivariate and convert the parameters of the
    distribution to an ellipse (major, minor, PA). By what factor should we
    scale those axes to make the area of the ellipse correspond to the n-sigma
    confidence interval?

    Negative or zero values result in NaN.

    """
    from scipy.special import erfc
    return np.sqrt (-2 * np.log (erfc (nsigma / np.sqrt (2))))