Add a StereoDispCombiner

[Hckjs]

This is basically the StereoCombiner already implemented here
in magic-cta-pipe.

It combines the mono DISP reconstruction by

1. calculating combinations of 2 telescopes for every array event
2. calculating the minimum distance for the 4 possible SIGN pairs for each combination
3. calculating the weighted average for the minimum distance SIGN pair (fov lon/lat) per combination
4. calculating the weighted average of all combinations for an array event with the summed weights from 3).

[maxnoe]

How does this algorithm differ from the implementation in EventDisplay by @GernotMaier ?

[kosack]

also maybe a good citation: https://ui.adsabs.harvard.edu/abs/1999APh....12..135H/abstract, as this is essentially an implementation of "algorithm 3" of that paper.

[kosack]

I think I've made this comment before: can we pick a better name here, since calling it "konrad" is not very helpful? This weighting is intensity x aspect-ratio, so we could call it "intensity-aspect-ratio" or "aspect-weighted-intensity" or "shape-intensity" or similar? maybe there is a shorter word... I think I prefer "aspect-weighted-intensity" , even though it's long, it is easy to understand.

[kosack]

We have a predicted disp.sign_score that is not used in this method, which seems odd. Is that the reason why the pair-wise average including both disps is made rather than a simple weighted average over predictions? Is there citation for the MARS method, by the way? i'd be interested to see if simpler methods were tested.

[kosack]

you don't actually have to convert or strip the units here, as astropy Quantities work automatically for numpy functions

>>> np.sin(90*u.deg) == np.sin(np.pi/2.0*u.rad)
True

>> np.sin(90*u.m)
UnitTypeError: Can only apply 'sin' function to quantities with angle units

That means you can avoid manually adding back the units later as well.

[LukasBeiske]

We have a predicted disp.sign_score that is not used in this method, which seems odd. Is that the reason why the pair-wise average including both disps is made rather than a simple weighted average over predictions? Is there citation for the MARS method, by the way? i'd be interested to see if simpler methods were tested.

This sign_score is mostly meant for performance plots (sign_score = np.abs(2 * sign_proba - 1.0) where sign_proba is the output of the sign classifier).
The weighted average over telescope-wise (alt, az) predictions is what the StereoMeanCombiner does for the disp reconstruction, but this method here seemed to perform better in a master thesis in Dortmund some years ago. We can add some performance plots here once the remaining issues are figured out.

[maxnoe]

The weighted average over telescope-wise (alt, az) predictions is what the StereoMeanCombiner does for the disp reconstruction, but this method was proven to perform better in a master thesis in Dortmund some years ago.

It's also easy to argue why: especially at low energies, disp sign is not really reconstructible (random guess, sign_score ~ 0.5). But with multiple telescopes, it's quite easy to see which option is actually correct and make the weighted average over the correct locations.

There are still a couple of different options for stereo disp, but most of them do not actually use the sign prediction, that is only used for mono as far as I know.

The MAGIC MARS method is explained in a short paragraph here:

Foreach of them, the disp identifies two possible reconstructed
source positions (head-tail ambiguity). At this stage for
each stereoscopic event, melibea evaluates all four possible
combinations of position pairs, and chooses the closest pair,
but only if its distance is smaller than a certain value. If none
of the pairs satisfies this condition, the event is rejected. The
stereo-reconstructed position is determined as the weighted
average of the chosen pair of positions.

https://cbpf.br/icrc2013/papers/icrc2013-0773.pdf