ellipticity parameterization

[jmeyers314]

We should think about (and implement!) different ways to parameterize ellipses, and think about which will be most robust.

Current parameterization of {radius, axis-ratio, position angle} is degenerate at axis-ratio = 1, for instance. Alternatives could include second moments {Ixx, Ixy, Iyy}, or radius/ellipticity {r, e1, e2} for instance.

[davidwhogg]

I like e sin 2 theta and e cos 2 theta.

But I also like just using a compact representation of the ellipticity tensor.

[drphilmarshall]

I agree: e1 = e cos 2 theta and e2 = e sin 2 theta

We should check the GREAT3 manual for recommended definitions of e. In the past I used e = (1-b/a)/(1+b/a) so that in the WL regime e_obs = (e_int + g) /(1+g*e_int), where g = gamma/(1-kappa), but then I was operating in the cluster regime. (Still, we'll do better at the high shear end with this definition, if the data were generated realistically.)

On Fri, Dec 6, 2013 at 5:16 PM, David W. Hogg notifications@github.comwrote:

I like e sin 2 theta and e cos 2 theta.

But I also like just using a compact representation of the ellipticity tensor.

— Reply to this email directly or view it on GitHubhttps://github.com/dstndstn/tractor/issues/3#issuecomment-30034404 .

[jmeyers314]

Appendix A1 of Zuntz++13 discusses this somewhat. They found that tricks were necessary to use {e1, e2} effectively, due to the boundary at abs(e) <= 1.

Second moments also have boundaries (Ixx > 0, Iyy > 0), although we might be able to just ignore this and map Ixx -> abs(Ixx) when evaluating a profile, for example. One potential advantage is that it's easy to combine second moments of non-coelliptical, non-concentric profiles.

[dstndstn]

The Great3 manual doesn't really say much about effective parameterizations.

I'm going to take a look at different options this weekend / next week.

[dstndstn]

I just pushed a new EllipseE class that can be used as a drop-in replacement for the default GalaxyShape class, using e1,e2,log(r), with a sigmoid-like nonlinearity on e to avoid any edges in the parameter space.

[jmeyers314]

Can we use epsilon1 and epsilon2, as opposed to e1 and e2 for this Ellipse parameterization? e1 and e2 in galsim/GREAT3, for instance, are consistent with |e| = (a^2-b^2)/(a^2+b^2), which I think is different than whats being done here, and it would be nice to avoid confusion.

[dstndstn]

sorry, wontfix