Impact of finite differences on metacalibration

[EiffL]

The zeroth order thing we want to check is whether the fact that ngmix relies on finite differences to measure the gradients can have a measurable impact on the response matrix, on a galaxy per galaxy basis, and more importantly for a sample of galaxies.

Things to do for this:

• [x] #39
• [x] On a galaxy per galaxy basis, make a plot of R_finitediff vs R_autodiff, estimate bias if bias there is
• [x] For the entire sample, estimate the impact of errors, do they average out?
• [x] Answer the question: Should we worry about using finite differences in practice?
• [ ] Write paper section on it

[EiffL]

I'm gonna start by ctr+c/ctr+v a preliminary plot made by @andrevitorelli showing the relative error between responses as measured by finite diff vs auto diff on a galaxy per galaxy basis: (showing the results for various SNR from 10 to 1000)

This would seem to indicate that the relative gradient error would can be of order 1%, but that's on a galaxy per galaxy basis.

[andrevitorelli]

For the entire sample, estimate the impact of errors, do they average out?

R: No.

[andrevitorelli]

For the penultimate question, I will do the tf vs ngmix test on different levels of shear, and see the residual m between AD & FD respective to different step sizes.

[andrevitorelli]

On the question

Answer the question: Should we worry about using finite differences in practice?

It seems that no, when we're at m ~5e-2. Lower than that it might get different. ~Plots~ Numbers coming soon...