Replace Brandts sorting with LAPACK DTRSEN, stabilize Gram-Schmidt#64
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Replace Brandts sorting with LAPACK DTRSEN, stabilize Gram-Schmidt#64Marius1311 wants to merge 1 commit intomainfrom
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- Replace 624-line Python Brandts sorting (_sort_real_schur.py) with a single LAPACK DTRSEN call in sorted_brandts_schur(). Same Bai-Demmel algorithm, compiled Fortran instead of Python loops. Fixes subspace angle failures for n >= 100. - Replace single-pass Modified Gram-Schmidt in _gram_schmidt_mod() with Householder QR (np.linalg.qr, LAPACK DGEQRF). Single-pass MGS lost orthogonality for ill-conditioned inputs (kappa up to 1e16). QR is backward stable regardless of conditioning. Same O(nm^2) complexity, faster in practice (compiled LAPACK vs Python loops). - Replace fragile constant-vector detection (element-wise constancy check with tight tolerance) with cosine similarity against sqrt(eta). The old check failed when Schur vectors were only approximately constant due to numerical noise from different eigenvalue orderings. - Recompute R in _do_schur() after re-orthogonalization to maintain the Schur relation in the new basis. - Update tests accordingly.
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Replace 624-line Python Brandts sorting (_sort_real_schur.py) with a single LAPACK DTRSEN call in sorted_brandts_schur(). Same Bai-Demmel algorithm, compiled Fortran instead of Python loops. Fixes subspace angle failures for n >= 100.
Replace single-pass Modified Gram-Schmidt in _gram_schmidt_mod() with Householder QR (np.linalg.qr, LAPACK DGEQRF). Single-pass MGS lost orthogonality for ill-conditioned inputs (kappa up to 1e16). QR is backward stable regardless of conditioning. Same O(nm^2) complexity, faster in practice (compiled LAPACK vs Python loops).
Replace fragile constant-vector detection (element-wise constancy check with tight tolerance) with cosine similarity against sqrt(eta). The old check failed when Schur vectors were only approximately constant due to numerical noise from different eigenvalue orderings.
Recompute R in _do_schur() after re-orthogonalization to maintain the Schur relation in the new basis.
Update tests accordingly.