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main.c to test_mathieu.cpp in the tests dir. I ran clang-format on all .h files.
functions to replace duplicated code.
and that's what I have.
fix the failed builds in CI.
and lapack which are requred for Mathieu fcns. Also fix the same build problem when using pixi. Also rerun clang-format on all files.
as well as the entirety of scipy.
eigendecomposition on the full NxN recursion matrix, the new dstevd is for tridiagonal, symmetric matrices, so it runs significantly faster.
matrices (this didn't cause a bug because the problem was mostly in variable naming), updates to the choice of c, removal of the c=0 branch for the modified fcns, and others.
setting c. Minor comments added to make_matrix_tridiagonal.h.
col (m-2)/2 in the oe coeff fcn.
size scale with q somehow for better accuracy at high q. Also run clang-format on everything.
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I figured I'd pop in here again and show some test results. All tests are on GitHub under https://github.com/brorson/ScipyMathieuTesting You can use them to check my impl if desired. Meanwhile here is the eigenvalue spectrum of the existing SciPy Mathieu implementation and my new one:
Here are the Wronskian errors RMS(W(Mx1, Mx2) - 2/pi) for Mc and Ms computed by the existing SciPy impl: And the new impl: |
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Fixes #47 |
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I am back. I withdrew my last pull request for my updated Mathieu function impl since I decided to polish the implementation further. Now I am back after making improvements to the impl and fixing some bugs. I received some help from Ho-Chul Shin, whose paper on computing the Mathieu functions appeared in the SIAM Journal in Dec 2025.
Besides improving my implementation I wrote a paper on the details of my implementation. I realize it's difficult to accept a big blob of code implementing a difficult special function without understanding what's in the code. I attempt to explain my implementation in this paper:
https://github.com/brorson/ScipyMathieuPaper
I maintain both Latex and .pdf copies on that GitHub page.
As part of my impl I subjected my functions to some tests to validate their correctness. Results of testing are presented in that paper.
Please reach out to me with any questions -- I am eager to help get this into the SciPy/xsf trunk.
Stuart Brorson
Northeatern University
Boston, Mass, USA