Monte Carlo inverse code fixes

[hayakawa16]

A bug was found in mc_inverse_Win.m. Correct bug and add more comments to clarify what code is doing.

[hayakawa16]

All works well on Windows with latest updates to this branch.
On Linux, I try to run this line 51:
system('./mc infile=infile_pMC_db_gen.txt');
and get:
Failed to load /usr/lib/dotnet/host/fxr/8.0.8/libhostfxr.so, error: /usr/local/MATLAB/R2023b/sys/os/glnxa64/libstdc++.so.6: version `GLIBCXX_3.4.29' not found (required by /usr/lib/dotnet/host/fxr/8.0.8/libhostfxr.so)
The library libhostfxr.so was found, but loading it from /usr/lib/dotnet/host/fxr/8.0.8/libhostfxr.so failed

• Installing .NET prerequisites might help resolve this problem.
  https://go.microsoft.com/fwlink/?linkid=2063370
  ./mc infile=infile_pMC_db_gen.txt: Interrupt

I went to https://go.microsoft.com/fwlink/?linkid=2063370 and made sure all dependencies were indeed installed.

I can run this line outside of MATLAB, just not inside MATLAB.

[hayakawa16]

I found the answer! I don't know why this link didn't come up this weekend:
https://www.mathworks.com/matlabcentral/answers/1907290-how-to-manually-select-the-libstdc-library-to-use-to-resolve-a-version-glibcxx_-not-found
I added:
export LD_PRELOAD=/lib/x86_64-linux-gnu/libstdc++.so.6
to my .bashrc

[hayakawa16]

I cleaned up and debugged the mc_inverse_Win.m and mc_inverse.m code. When I first coded this software, I did a comparison between the results that lsqcurvefit provided and fminsearch (back in 2021). Since then the SpectralDictionary.xlsx has been expanded, my MATLAB version is now 2023b (used to be 2021b?) which means lsqcurvefit methods may have been modified. I show the plots of the prior study and the plots of the current study. Errors are comparable. Linux version produces exactly the same results.
notes_monte_carlo_inverse.pdf