Rewrite get_pe_res: numerical FWHM calculation

[benedikt-nagler]

Fix #130.

The previous implementation of the get_pe_res function was incorrect. Since there is no closed formula for the FWHM of a gaussian mixture, it is now calculated numerically.

For each given subset of the gaussian mixture model, the maximum of the resulting PDF is calculated by dividing the interval [0.8, 1.2] into small steps. The step size depends on the largest variance of the individual gaussians, which ensures a high enough accuracy for the estimated maximum.

After that, all values where the half maximum is reached are calculated with the find_zeros function from Roots.jl. The FWHM then corresponds to the difference between the largest and the smallest position.

[codecov]

Codecov Report

Attention: Patch coverage is 0% with 14 lines in your changes missing coverage. Please review.

Project coverage is 28.24%. Comparing base (4a43dfa) to head (cb331e9).
Report is 16 commits behind head on main.

Files with missing lines	Patch %	Lines
src/sipmfit.jl	0.00%	14 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #137      +/-   ##
==========================================
- Coverage   28.39%   28.24%   -0.16%     
==========================================
  Files          37       37              
  Lines        3564     3583      +19     
==========================================
  Hits         1012     1012              
- Misses       2552     2571      +19     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[fhagemann]

Unit tests?

[fhagemann]

Manchmal sieht man den Wald vor lauter Bäumen nicht 🥠🌳🔥

[theHenks]

I am happy with the PR. Let's finish this soon and merge!
Thanks a lot @benedikt-nagler 😍

[benedikt-nagler]

I am happy with the PR. Let's finish this soon and merge! Thanks a lot @benedikt-nagler 😍

Glad I could help!

[fhagemann]

If this works without throwing an error, I would also be happy to merge.

[theHenks]

If this works without throwing an error, I would also be happy to merge.

I take this as a yes.