[FIX] riemann ASR eigpair mismatch in nonlinear_eigenspace

[nbara]

Summary

• fix issue Riemannian ASR produces incorrect component selection due to mismatched eigenvalues/eigenvectors in nonlinear_eigenspace #99 by returning eigenvalues consistent with optimized eigenvectors in nonlinear_eigenspace
• compute eigenvalues from Rayleigh quotients of the optimized basis (diag(X.T @ L @ X))
• add regression test to ensure returned eigenvalues match returned eigenvectors

Why

The previous implementation returned eigenvalues from a random-initialization matrix (S0) but eigenvectors from the optimizer solution (Xsol.point), producing mismatched eigpairs and unstable component ordering in riemann ASR.

Validation

• reproduced issue behavior before fix (riemann selecting clean channels)
• after fix, reproduced expected behavior (no inverted channel selection)
• tests run:
  • tests/test_cov.py::test_nonlinear_eigenspace_consistent_eigpairs
  • tests/test_asr.py with riemann-focused selection

Closes #99

[Copilot]

Pull request overview

Fixes a Riemannian ASR instability caused by nonlinear_eigenspace returning eigenvalues that don’t correspond to the optimized eigenvectors, leading to mismatched eigpairs and incorrect component ordering/selection.

Changes:

• Update nonlinear_eigenspace to derive returned eigenvalues from the optimized basis (Rayleigh quotients) instead of the random-initialization eigendecomposition output.
• Add a regression test asserting returned eigenvalues are consistent with the returned eigenvectors (when pymanopt is available).

Reviewed changes

Copilot reviewed 2 out of 3 changed files in this pull request and generated 2 comments.

File	Description
meegkit/utils/covariances.py	Computes eigenvalues from the optimized solution basis to avoid returning mismatched eigpairs.
tests/test_cov.py	Adds a regression test checking eigenvalue/eigenvector consistency for nonlinear_eigenspace.

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 83.13%. Comparing base (3721224) to head (4ee8e7e).

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #100      +/-   ##
==========================================
+ Coverage   83.10%   83.13%   +0.02%     
==========================================
  Files          25       25              
  Lines        2818     2823       +5     
==========================================
+ Hits         2342     2347       +5     
  Misses        476      476              

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[sappelhoff]

apart from the uv.lock, this seems to fix it.

[sappelhoff]

why add uv.lock?