LU decomposition for NLTE population solver

[AlexHls]

📝 Description

Type: 🚀 feature
Attempt to implement a LU decomposition solver for the NLTE population equation.

Currently as extra module, but if it works it should replace the root find method (probably).

[codecov]

Codecov Report

Attention: 35 lines in your changes are missing coverage. Please review.

Comparison is base (a7534c1) 67.17% compared to head (c3bd2b6) 68.67%.
Report is 2 commits behind head on master.

Files	Patch %	Lines
tardis/plasma/tests/test_nlte_solver.py	62.26%	20 Missing ⚠️
...dis/plasma/properties/nlte_rate_equation_solver.py	94.57%	12 Missing ⚠️
tardis/plasma/standard_plasmas.py	66.66%	3 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2465      +/-   ##
==========================================
+ Coverage   67.17%   68.67%   +1.50%     
==========================================
  Files         156      157       +1     
  Lines       13763    13978     +215     
==========================================
+ Hits         9245     9600     +355     
+ Misses       4518     4378     -140     

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

[sonachitchyan]

Needs rebasing

[AlexHls]

Any comments on the new structure? I've merged both solvers into one file, sharing function calls wherever possible. There is still a bit more to be done (docs, tests etc.), but I thought it's probably best to get some feedback at this point before I start polishing this a bit more...
(This should be, if I didn't miss anything, a non-breaking feature)

[tardis-bot]

*beep* *bop*

Hi, human.

The docs workflow has succeeded ✔️

Click here to see your results.

[AlexHls]

This should now be ready for final review @chvogl @sonachitchyan

[andrewfullard]

Frankly, I don't understand exactly how the solver works. However, the code is well-written so I will approve it on the basis with the caveat that I don't see any examples showing the functionality of the solver working as expected (e.g. compared to some reference).

My other major comment is that given the computational intensity of this solver, the code would really benefit from being made Numba-compatible in the future.

[wkerzendorf]

we merged it in a new PR