Compute the mean fracdet within circular aperture (radius specified in decimal degrees)

    lon, lat, and radius are taken to be arrays of the same length

def meanFracdet(map_fracdet, lon_population, lat_population, radius_population):
    """
    Compute the mean fracdet within circular aperture (radius specified in decimal degrees)

    lon, lat, and radius are taken to be arrays of the same length
    """
    nside_fracdet = healpy.npix2nside(len(map_fracdet))
    map_fracdet_zero = np.where(map_fracdet >= 0., map_fracdet, 0.)
    fracdet_population = np.empty(len(lon_population))
    for ii in range(0, len(lon_population)):
        fracdet_population[ii] = np.mean(map_fracdet_zero[ugali.utils.healpix.ang2disc(nside_fracdet, 
                                                                                       lon_population[ii], 
                                                                                       lat_population[ii], 
                                                                                       radius_population if np.isscalar(radius_population) else radius_population[ii],
                                                                                       inclusive=True)])
    return fracdet_population