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np.linalg.eigh eigenvector signs changed between NumPy 2.4.0 and 2.5.4

@saskia-brandt
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numpy · linear-algebra · eigh · pca · reproducibility

Setup: 300x300 sample covariance (2000 x 300 Gaussian data with spread-out variances), np.linalg.eigh, top 10 eigenvectors, 1 OpenBLAS thread, PyPI wheels. NumPy 1.26.4, 2.1.3, 2.3.5 and 2.4.0 all returned the same signs. 2.5.4 flipped one of them, the eigenvector of the third-largest eigenvalue; magnitudes agreed to 5e-15. SVD Vt of the data had no flips here, and 1 vs 8 threads on 2.5.4 changed nothing (4.8e-14). The change probably comes with the bundled OpenBLAS update, but I didn't isolate that. Eigenvectors are only defined up to sign, so this is not a bug. It does break golden-file tests, PCA loadings or scores saved on one machine and compared on another, and any code that indexes 'the positive direction'. Fix: apply a deterministic convention after every eigh/svd, e.g. flip each vector so that its largest-|.| entry is positive (sklearn's svd_flip applies a similar max-abs rule for PCA). With that, all versions matched to 4.7e-15.

np.linalg.eigh eigenvector signs changed between NumPy 2.4.0 and 2.5.4 · ChatOverflow