Update coincident event search using large shower events

[SeiyaNozaki]

Since the time offset depends on the observation dates, we needed to tune the offset scan region if we use the current method. This PR adds an option (all_combination) to select the best time offset among all possible combinations using large shower events. For the moment, 50 (MAGIC) x 50 (LST) events are selected by default to compute all possible time offsets and count coincident events with an assumed offset.

[SeiyaNozaki]

The updated procedure is

• Pre offset search

1. Large-intensity events (100 LST x 100 MAGIC) are extracted
2. Compute all possible time offsets
3. Find the best offset giving the largest numbers of coincident events
4. Define +/- full window width (600 ns) around the best offset as the offset scan region

• Time offset scan using this offset and full datasets
  Since offset scan region can be different between M1 and M2, profile data frame is like below:
  

Since the final coincident event search is performed using full datasets, the same coincident events are extracted w/ or w/o this method. The only weak point is that it does not work if the number of coincident events is too low (<10 events), but I think it is negligible.

[aleberti]

Thanks Seiya for the implementation! I left some comments for your attention. One thing: did you try to see as x-check if you get similar/same results if you use the "all combination" approach and the old one with a time offset equal to the one found in the new method? Looking at the code it should, but since it should be a quick check, if you can do it, it would be great!

[SeiyaNozaki]

Thank you Alessio for the comments!

One thing: did you try to see as x-check if you get similar/same results if you use the "all combination" approach and the old one with a time offset equal to the one found in the new method?

Yes! Here you can also see the difference in the results between the current method and the updated one ('all combination' approach) using 2962 LST subrun data taken in March 2023.

[SeiyaNozaki]

Following the comment by @YoshikiOhtani in the meeting, I changed the scan range to +/-3 x half_window_width (1.5 x full window width) around the offset the pre-search found. Using this offset scan range, I got completely the same results (time offset, n_coincidence_events) as the current method for all of LST subruns.

[YoshikiOhtani]

Thank you very much @SeiyaNozaki for this implementation! Even though I did not check the code in detail, I can already approve this pull request, based on the presentation in the meeting. So if we resolve all the comments by @aleberti (and no more comments from @jsitarek), I think we can merge this.