feat: opt-in gradient-safe log-det via Settings (default unchanged)

[Jammy2211]

Closes #391.

Adds an opt-in, non-default gradient-safe log-determinant method to inversions, selected via Settings. The default evidence path is unchanged and byte-identical.

Why

The two Bayesian-evidence log-det terms compute 2*sum(log(diag(cholesky(M)))). On the JAX backend the Cholesky returns NaN (numpy raises) when M is not numerically positive-definite — which stalls gradient-based searches on ill-conditioned regularization matrices (autolens_workspace_developer#104: the pixelized likelihood's NaN wall localised to exactly this term).

Why opt-in and not a default change

An independent adversarial review of the reg-logdet investigation established that the current evidence is scientifically correct — d log det(H) / d log λ = 1798 to machine precision, so the coefficient-dependence that drives inference is right, and the 1e-8 conditioning term is only a constant offset. A relative lift would be a regression; a pseudo-determinant would break archived-evidence comparability. So the default is deliberately preserved and this adds an alternative only, for gradient work and for comparison.

Change

Settings.log_det_method, following the existing Optional[…] = None → conf general.yaml pattern (mirrors use_positive_only_solver):

• "cholesky" (default) — the historical computation, byte-for-byte unchanged including the test-mode LinAlgError guard. Both terms now route through a shared _log_det_symmetric_from helper; the default branch is the identical expression.
• "slogdet" — logabsdet of xp.linalg.slogdet(M): identical where M is positive-definite, finite and differentiable where the Cholesky would NaN. General (serves the adaptive schemes, unlike an analytic precomputed-eigenvalue route). Opt-in via al.SettingsInversion(log_det_method="slogdet").

Applies to both evidence log-det terms (log_det_curvature_reg_matrix_term and log_det_regularization_matrix_term) — a gradient search needs both finite.

API Changes

Additive only. New optional Settings(log_det_method=...) field, default None → config "cholesky" → current behaviour. No removed/renamed/changed symbols; no downstream migration.

Detail

• Added: Settings.log_det_method (optional kwarg + property); AbstractInversion._log_det_symmetric_from (private helper); inversion.log_det_method: cholesky in packaged general.yaml.
• Removed / Renamed / Changed Signature: none.
• Changed Behaviour: none at default — the two log-det properties produce the identical value; only an explicit log_det_method="slogdet" opt-in differs.
• Migration: n/a. No workspace config mirroring required — packaged-only keys layer through production config (verified against the existing packaged-only nnls_target_kappa).

Testing

• Full test_autoarray/ suite: 926 passed. Every existing log_evidence test (fit_imaging / fit_interferometer / fit_dataset) unchanged — this is the byte-identical-default gate.
• New unit tests: default log_det_method == "cholesky" and reproduces numpy log det; slogdet == cholesky on a positive-definite matrix (~1e-8); slogdet finite (== np.linalg.slogdet) on a non-PD matrix where Cholesky fails.
• Note: on ill-conditioned PD matrices slogdet matches the true log det more closely than Cholesky (~2.5e-7 on a 25-pixel Constant reg matrix, slogdet being the accurate one) — a further reason it is non-default and for comparison rather than a silent swap.

Follow-ups (not in this PR)

• JAX gradient-finiteness assertion → autogalaxy_workspace_test (mirrors autofit_workspace_test/scripts/jax_assertions/fitness_nan_gradient_contract.py).
• Two independent bugs this investigation surfaced, filed as separate PyAutoMind prompts: ConstantZeroth is dead code (shape + missing-arg), and Adapt's double-square 4th-power coefficient.

Gate

• Tests — 926 passed in the task worktree.
• Smoke — n/a at library level; downstream JAX assertion follows to autogalaxy_workspace_test.
• Heart — RED, acknowledged contemporaneously by the human on 5 pre-existing unrelated reasons; RED reason verbatim: PyAutoLens: 1 uncommitted source change(s) (a stray paper_jax/paper.md edit in the main checkout, untouched by this branch).