add low level 2d profile plot function and 2d profile function

[EchoRLiu]

This PR is to address #1651.

To do so, I added two new visualization functions:

1. profile_lowlevel_2d() - Visualizes the relationship between two parameters during profiling

• Shows one profiled parameter on the x-axis and tracks a second parameter on the y-axis
• Uses color mapping (via scatter plot) to indicate objective ratio or function values along the profile path

2. visualize_2d_profile() - High-level n by n profile grid:

• Diagonal plots: Shows traditional 1D profiles for each parameter
• Off-diagonal plots: Shows 2D parameter relationships during profiling using profile_lowlevel_2d()

This would provide a complete overview of how parameters interact during profile likelihood computation

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Codecov Report

❌ Patch coverage is 88.35616% with 17 lines in your changes missing coverage. Please review.
✅ Project coverage is 83.90%. Comparing base (9ccf617) to head (3e4f818).

Files with missing lines	Patch %	Lines
pypesto/visualize/profiles.py	88.27%	17 Missing ⚠️
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Additional details and impacted files

@@             Coverage Diff             @@
##           develop    #1652      +/-   ##
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+ Coverage    83.86%   83.90%   +0.03%     
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  Files          164      164              
  Lines        14346    14491     +145     
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+ Hits         12031    12158     +127     
- Misses        2315     2333      +18     

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[Doresic]

Remaining TODO list from @EchoRLiu

TODO List for still needed improvements:

• there is some weird jumps when doing profile

This will be taken care of in the another PR dealing with profiling enhancements.

• some range can not be profiled

This is weird, I saw it a couple of times. We'll need to check what happens, why does profiling stop prematurely sometimes. It might be the weird conditions in adaptive searches that doesn't have a else, so profiling can fail silently. Needs to be investigated.

• color scheme can be improved

Good as initial visualization, can be changed via user.

• original profile function can also be improved with threshold

For another PR as it deals with general profiling.

[dweindl]

Thanks, looks mostly good to me.

Two minor things looking at https://pypesto--1652.org.readthedocs.build/en/1652/example/getting_started.html:

• I find the top-left y-label confusing. how about showing all y-labels, or at least always for the first, the diagonal, and the first off-diagonal subplot?
• the markers in the off-diagonal plots look all black. I guess this is just due to the overlap here. it might be preferable to plot them from low to high log-posterior ratio or setting the z-order accordingly.

[PaulJonasJost]

One thing that is bugging me a bit is that if we have a lot of points in a small intervall, the black borders of the point overshadow the coloring.

[Doresic]

Ok some updates

• some separation of the plots
• y and x labels on each of the plots, bolded so it's easy to read
• fixed the black border (removed) and plotting the better points on top on the worse ones, so we see the better areas nicer
  Some examples:
  The same example from getting started:

And another example (Boehm). It has huge parameter names so they kinda overlap a bit, but I wouldn't reduce the plot font sizes, as usually parameters aren't so large.