Add write function to FitResult

[Astro-Kirsty]

This PR is to include a write function in the FitResult and partly resolves #5154

The following is implemented
#5255 (comment)

Not sure why 'total_stat' is not saving as a value but instead like this

[codecov]

Codecov Report

Attention: Patch coverage is 35.00000% with 13 lines in your changes are missing coverage. Please review.

Project coverage is 75.25%. Comparing base (67efb7e) to head (9089db5).
Report is 1 commits behind head on main.

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Files	Patch %	Lines
gammapy/modeling/fit.py	35.00%	13 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #5258      +/-   ##
==========================================
- Coverage   75.27%   75.25%   -0.03%     
==========================================
  Files         234      234              
  Lines       35148    35168      +20     
==========================================
+ Hits        26458    26465       +7     
- Misses       8690     8703      +13     

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[QRemy]

Thanks @Astro-Kirsty, could you add a test for that ?
How do you produce the bad outpout for total_stat ?
I tried with the analysis_2 toturial and the output seems fine.

[bkhelifi]

I have some minor comments. This PR is globally ready to be merged! Thanks you a lot

[bkhelifi]

Just as a comment, some information stored as data are in fact metadata, e.g.

            "optimize_result": {
                "backend": self.optimize_result.backend,
                "method": self.optimize_result.method,

I propose to fix that later on a separated PR about metadata handling.

[Astro-Kirsty]

Thanks @Astro-Kirsty, could you add a test for that ? How do you produce the bad outpout for total_stat ? I tried with the analysis_2 toturial and the output seems fine.

Using this code snippet

The print is fine, but then the output in the yaml file is not

[QRemy]

Thanks @Astro-Kirsty, the yaml file written by the test seems ok.

[registerrier]

Thnaks @Astro-Kirsty . My review is a bit late.
Some general comments:

• What about a read method? The point of the write method is to be able to retrieve the result later.
• I think we would need a more generic scheme to be able to handle different steps. I would suggest to implement a to_dict() method on the FitStepResult.
• There is code duplication between this write and to_yaml methods and those implemented on Models.write and Datasets.write. Maybe we should improve gammapy.utils.scripts.write_yaml to support all these cases.

[registerrier]

Maybe start with optimize_results then covariance_result and finally models.

[registerrier]

What happens if covariance has not been run?

[registerrier]

Just as a comment, some information stored as data are in fact metadata, e.g.

            "optimize_result": {
                "backend": self.optimize_result.backend,
                "method": self.optimize_result.method,

I propose to fix that later on a separated PR about metadata handling.

FitResult is not meant to be a data product. I don't think we should try to have a scheme of data vs metadata here.

[QRemy]

• What about a read method? The point of the write method is to be able to retrieve the result later.

@registerrier Do we really need a read method for objects that are only used for diagnostics and not configuration ?