[Jammy2211]

Closes #647. Phase 3 of #638. Community proposal: PyAutoLabs/.github#39 (@HRSAstro), reference snippet section 5.

Summary

Matrix-free log-evidence for the interferometer path: ln det H exact from the phase-2 sparse factor; ln det(F + H) = ln det P (exact, from the Powell preconditioner's sparse LU) + ln det(P⁻¹(F + H)) by stochastic Lanczos quadrature (Ubaru, Chen & Saad 2017) in the P inner product (probes ~ N(0, P⁻¹) via P = BᵀB, full reorthogonalisation, Gauss quadrature on the tridiagonal eigenpairs, fixed seed so the estimate is deterministic and smooth in λ). log_evidence_matrix_free_from assembles the five terms with fit_util.log_evidence_from's conventions; an optional log_det_curvature_reg= lets a caller substitute an exact value.

Accuracy finding (documented in the module docstring): on a data-dominated case (500 visibilities, long baselines; eigenvalues of P⁻¹(F+H) in ~[0.6, 1.6]) SLQ at 10 probes / 40 steps is within 0.10–0.14% of the dense ln det (ln Z bias −0.11 to −0.16 nats on ln Z ≈ −1500); across 30 seeds the mean error is 0.21%, worst 0.56%, 93% within 0.5%. On the prior-dominated tiny fixture (40 short-baseline visibilities; eigenvalues ~[0.01, 63]) the Powell preconditioner is a poor match and SLQ is 14–40% off. The tests therefore use the data-dominated case (new uv_scale argument on the test dataset helper); the regime dependence is a phase-5 profiling question (contributor reports ~0.2% on real ALMA data).

API Changes

Additive only: log_det_preconditioner_from, log_det_curvature_reg_via_slq_from, log_evidence_matrix_free_from in inversion_interferometer_matrix_free_util. Callers pass R scaled by √coefficient (H = coefficient·R₀ᵀR₀ from MaternSparse); the SLQ function verifies RᵀR = H on a random vector and raises otherwise.
See full details below.

Test Plan

test_matrix_free_util.py (+9 cases, 20 total in the file): ln det P vs slogdet 2.8e-14; SLQ within 0.5% at 10 probes, deterministic for a fixed seed; 2-probe error larger than 10-probe; evidence with the dense ln det substituted equals fit_util.log_evidence_from on the inversion's fast_chi_squared, regularization_term, both log-dets and noise_normalization (difference 0.0); evidence with SLQ within tolerance; R/H mismatch raises; JAX-blocked subprocess import. Worktree run: pytest test_autoarray/inversion -q → 1061 passed, 4 xfailed.

Heart YELLOW acknowledged by the human on 2026-10-21 (manifest drift 1 mismatch; release validation stale: source moved since rehearsal (PyAutoArray)).

Full API Changes (for automation & release notes)

Added

• inversion_interferometer_matrix_free_util.log_det_preconditioner_from(factor)
• inversion_interferometer_matrix_free_util.log_det_curvature_reg_via_slq_from(operator, regularization_matrix_sparse, regularization_factor_sparse, coefficient, n_probes=10, n_steps=40, seed=20221) → (estimate, per-probe values)
• inversion_interferometer_matrix_free_util.log_evidence_matrix_free_from(...) with optional log_det_curvature_reg=

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