Add 2nd central moments to base+compound GSObjects

[jmeyers314]

I think it would be nice to have unweighted second central moment properties for our analytic GSObjects:

obj = galsim.Gaussian(half_light_radius=1)
print(obj.Ixx)  # 0.7205
print(obj.Ixy)  # 0.0

I think it's straightforward to define these for at least the analytic profiles in base.py. It should also be straightforward to propagate these through transformations and sums/convolutions, though it's probably good to avoid InterpolatedImage moments, or using moments as input.

[rmandelb]

How relevant are the analytic ones, considering that they ignore pixel convolution?

[jmeyers314]

How relevant are the analytic ones, considering that they ignore pixel convolution?

I think we can leave the pixel convolution up to the user:

gal = galsim.Gaussian(half_light_radius=1)
print(gal.Ixx)  # 0.7205
pix = galsim.Pixel(1)
print(pix.Ixx)  # 0.0833  (i.e., 1./12)
obj = galsim.Convolve(gal, pix)
print(obj.Ixx)  # 0.80383 = 0.7205+0.0833

[rmandelb]

Are you not concerned about the fact that we generally discourage users from explicitly doing the pixel convolution, hiding it under the rug in drawImage with the default image rendering methods, and here to get it right they do have to explicitly do it?

I'm trying to decide what I think about this. I don't love it but I suppose with adequate documentation plus maybe a demonstration in the demos, it's OK.

[rmjarvis]

I don't have a problem with this. Many of these objects have attributes like fwhm or half_light_radius when those are analytically known, and they don't include a pixel convolution. So it seems consistent for these not to as well.

If you do this, you should remember to update the calculateMomentRadius function to look for these values when they exist and skip the calculation. Right now, it only does so for Gaussian.