code: def meanFracdet(map_fracdet, lon_population, lat_population, radius_population):
      
      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
docs: 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