T01 IDL vs Python differences about geopack HOT 4 OPEN

The python T01 use different coefficients "c_sy" (in func "full_rc") and "a" (in func "t01") as the original FORTRAN77 T01. I think it's the main cause of the difference results between python and IDL T01. However, I don't know why they have different coefficients, since both of them have the comments ”LATEST MODIFICATIONS/BUGS REMOVED: JUNE 24, 2006“.

Another weird point is that the IDL and the FORTRAN77 version still have slightly differnent results, but much smaller difference than that between python and FORTRAN77. The IDL geopack should be compiled from FORTRAN77 codes, so there shouldn't be differences in theory.

The situation is so complicated in T01 that I finally gave up dealing with the bugs of it.

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Interesting! I wonder if Haje Korth has made a few changes in the Fortran T01 code in the process of developing the IDL version?

I'm going to try using ChatGPT-4 to translate the TA15 and TA16 Fortran models to Python. If that goes well, maybe I'll redo T01 the same way and see what happens.

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I did another test, if I keep python coefficients "c_sy" (in func "full_rc"), "a" (in func "t01"), "a1,a2,rrc1,dd1,rrc2,dd2,p1,r1,dr1,dla1,p2,r2,dr2,dla2,p3,r3,dr3" (in func "ap") the same with FORTRAN77, then they got close results (less than 1% difference). That means the python T01 code may not have serious bugs, the main difference of the results only comes from coefficients differences.

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@madokatext : After making the changes you suggested, I also see much improved results when comparing to IDL! The maximum error is now down to about 0.25 nT in the inner magnetosphere. I'll submit a PR, and hopefully we can get all the model corrections released to pypi soon.

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