Fixup covar2d shrinker and get_cwf_coeffs for noise_var=0

[garrettwrong]

Cleaned up a little so we no longer crash with div0 or singular matrices. However, estimated result for clean case get_cwf_coeffs doesn't seem right (to me).

Maybe its too degenerate a case and my expectations are wrong? If that is the case we can document, log, then no-op or something.. Essentially I'm hoping to be able to setup some code and turn noise on/off without effectively writing a totally new experiment... We might need that for say integrating with class averaging or other developmental codes using clean images to start with...

Closes #420

[codecov]

Codecov Report

Merging #421 (cbb27f6) into develop (004ba5e) will increase coverage by 0.79%.
The diff coverage is 95.45%.

@@             Coverage Diff             @@
##           develop     #421      +/-   ##
===========================================
+ Coverage    86.93%   87.73%   +0.79%     
===========================================
  Files           91       95       +4     
  Lines         6171     6630     +459     
===========================================
+ Hits          5365     5817     +452     
- Misses         806      813       +7     

Impacted Files	Coverage Δ
src/aspire/covariance/covar2d.py	93.94% <95.45%> (+1.39%)	⬆️
src/aspire/commands/_config.py	0.00% <0.00%> (ø)
src/aspire/ctf/ctf_estimator.py	98.87% <0.00%> (ø)
src/aspire/commands/estimate_ctf.py	0.00% <0.00%> (ø)
src/aspire/ctf/__init__.py	100.00% <0.00%> (ø)
src/aspire/utils/misc.py	100.00% <0.00%> (+2.77%)	⬆️
src/aspire/image/image.py	92.88% <0.00%> (+4.05%)	⬆️
src/aspire/utils/coor_trans.py	96.11% <0.00%> (+7.76%)	⬆️

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[garrettwrong]

I think the batched issue was because may be because were on the edge of tolerance in singles. Probably the larger magnitudes (dividing by small noise_var) helped before. It's possible there is more to it though...

The tutorial result, while still passable, appears to have more error now. I was expecting it to be tail noise, but its noticeable.

For noise_var=0 I think its still not right (even with get_cwf_coeffs returning the coeffs identically now). I get closer with negation, and I see a curious negative sign in the tutorial plots. Maybe its superfluous, but do you recall why that would be there?

[janden]

I think the batched issue was because may be because were on the edge of tolerance in singles. Probably the larger magnitudes (dividing by small noise_var) helped before. It's possible there is more to it though...

Ah ok. I assumed it had something to do with the new default noise_var. It was using noise_var = 1 before, which shouldn't have resulted in large magnitudes.

The tutorial result, while still passable, appears to have more error now. I was expecting it to be tail noise, but its noticeable.

That's strange. Are you talking about with non-zero noise_var? It could be that I messed up the formulas for the shrinkage (although the relevant tests pass, so that shouldn't happen). What happens if you try without shrinkage?

For noise_var=0 I think its still not right (even with get_cwf_coeffs returning the coeffs identically now). I get closer with negation, and I see a curious negative sign in the tutorial plots. Maybe its superfluous, but do you recall why that would be there?

There's bound to be some residual error due to projection onto the basis (I see some rings outside of the central disk), but otherwise it should be similar, especially if get_cwf_coeffs is set to pass through for noise_var = 0, since then it's just a matter of evaluate_t followed by evaluate.

[garrettwrong]

shrinker=None with the stock noise_var in the cov2d tutorial is closer (probably okay). Closer than frobenius_norm.

Can't compare the shrinker=None with noise_var=0 because that case was previously not working.

I think in the tutorial I am seeing other things, maybe its okay. Can talk about it tomorrow. I'll try to have them ready to run and maybe can close this out then.