Stabilize extreme-scale PSD projection

[FlorianPfaff]

Bug

nearest_symmetric_psd(...) symmetrized finite inputs safely, but passed the unscaled matrix directly to numpy.linalg.eigh(...).

For a dense rank-one covariance whose entries are float64.max, the mathematical projection is the original finite matrix. NumPy's unscaled eigendecomposition instead returns an infinite leading eigenvalue, and reconstruction produces an all-inf matrix.

Fix

• preserve the existing stable symmetrization;
• scale the symmetric matrix and requested eigenvalue floor into a bounded range before eigendecomposition;
• reconstruct in normalized coordinates and restore the original scale afterward;
• preserve the existing empty-matrix behavior.

Regression coverage

Add a focused regression using a 2 x 2 matrix filled with numpy.finfo(float).max. It verifies that the projected matrix remains finite and agrees with the finite PSD input.

Validation

• reproduced the previous all-inf projection;
• verified the scaled implementation returns the original finite covariance;
• compared old and new projections on randomized ordinary-scale matrices and multiple eigenvalue floors with rtol=1e-12, atol=1e-12;
• branch is based directly on current main (f196ec41d1d8681e279936db9f1a0a3abfa276e7), 2 commits ahead and 0 behind;
• final diff is limited to 11 changed implementation lines and one 19-line regression module.

GitHub Actions is authoritative for the full backend, lint, packaging, documentation, and integration matrix.

[github-actions]

✅MegaLinter analysis: Success

Descriptor	Linter	Files	Fixed	Errors	Warnings	Elapsed time
✅ COPYPASTE	jscpd	yes		no	no	29.1s
✅ JSON	prettier	7	0	0	0	1.07s
✅ JSON	v8r	7		0	0	3.78s
✅ MARKDOWN	markdownlint	68	0	0	0	2.06s
✅ MARKDOWN	markdown-table-formatter	68	0	0	0	0.76s
✅ PYTHON	black	1867	87	0	0	100.24s
✅ PYTHON	isort	1867	141	0	0	2.91s
✅ REPOSITORY	betterleaks	yes		no	no	2.43s
✅ REPOSITORY	checkov	yes		no	no	55.25s
✅ REPOSITORY	gitleaks	yes		no	no	18.1s
✅ REPOSITORY	git_diff	yes		no	no	0.31s
✅ REPOSITORY	secretlint	yes		no	no	86.88s
✅ REPOSITORY	syft	yes		no	no	5.76s
✅ REPOSITORY	trivy-sbom	yes		no	no	6.48s
✅ REPOSITORY	trufflehog	yes		no	no	33.05s
✅ YAML	prettier	11	0	0	0	0.76s
✅ YAML	v8r	11		0	0	12.66s
✅ YAML	yamllint	11		0	0	0.71s

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