[Jammy2211]

Summary

On the NumPy backend with use_positive_only_solver=False, every likelihood call factorized the same SPD matrix F + H twice: np.linalg.solve (LU) for reconstruction, then np.linalg.cholesky for log_det_curvature_reg_matrix_term. A new cached_property _curvature_reg_matrix_cho_factor computes one scipy.linalg.cho_factor, which serves both. reconstruction solves with cho_solve. The log det is 2 * sum(log(diag(L))) from the same factor, used when every linear object is regularized. The factor is built on a copy, so curvature_reg_matrix is never overwritten.

The factor is None, and the code takes exactly the old routes, in these cases: the JAX backend, the positive-only solver, log_det_method="slogdet", a LinAlgError (scipy's class is numpy's), or a non-finite factor diagonal. Failure behaviour is therefore unchanged:

• An indefinite but nonsingular F + H is still solved by the LU, and the dense Cholesky log det still raises it (or returns 0.0 in test mode).
• A singular F + H still makes the solve raise (or return its test-mode dummy).

Campaign: PyAutoLabs/PyAutoPulse#62 (task interferometer_large_mask_aris).

Closes #633

API Changes

None; the changes are internal only. The new _curvature_reg_matrix_cho_factor is private. The positive-negative NumPy reconstruction now comes from a Cholesky solve rather than an LU. It agrees with the LU to round-off on well-conditioned systems. On ill-conditioned ones it agrees to within the system's conditioning, and is more accurate there (see Witness).

Witness (laptop, single-threaded, Aris SPT2319-55 125×125 interferometer, Delaunay + AdaptSplit, numba route, use_positive_only_solver=False)

vertices	run	load avg	full call median, before → after	change	solve + log det, before → after (breakdown medians)	logL before / after	log det	reconstruction max-abs-rel
1,405	run 1 (nrep 6)	2.2	0.418 → 0.386 s	−7.7%	144.5 → 50.9 ms	identical (14090054.632080655545)	identical	5.2e-14
1,405	repeat (nrep 12)	1.3	0.710 → 0.551 s	−22.4%	215.5 → 99.1 ms	identical (14095945.676112052053)	identical	(same as run 1)
1,405	cProfile (3 calls)	2.2	1.441 → 1.091 s	−24.3%	solve+chol 0.425 s → cho 0.157 s	—	—	—
2,947	run 1 (nrep 6)	2.1	1.635 → 0.801 s	−51.0%	1267.6 → 372.7 ms	14080490.696629 / 14080490.696473 (1.1e-11 rel)	identical	1.6e-3

Pass condition: ≥15% at 1,405 and ≥35% at 2,947.

• At 2,947 vertices: clear pass.
• At 1,405 vertices: run 1's full-call median (−7.7%) fell short. The repeat (−22.4%) and the profiler (−24.3%) pass. The breakdown removes about 94 ms per call in both runs. The full-call median is dominated by numba curvature_matrix noise on a shared machine (227 → 254 ms and 339 → 445 ms between legs with no code change).
• The "before" breakdown's fom_rest (78 / 122 / 544 ms) is a second dense Cholesky: log_det_curvature_reg_matrix_term is a plain property, so figure_of_merit re-ran it after the breakdown's own tick.

Reconstruction clause ("unchanged to 1e-10 relative") is not met at 2,947 vertices, and cannot be met there. At the witness vector, cond(F + H) = 7.67e14, so eps·cond ≈ 0.17. Measured against a longdouble-residual, iteratively refined reference:

solve	forward error (max-rel)	relative residual
old LU	1.49e-3	1.8e-11
new Cholesky	5.1e-4	2.9e-12

So the 1.6e-3 change sits inside the conditioning bound, and the new solve is closer to the true solution. The independent reviewer reproduced these numbers. The log det is bit-identical and logL agrees to 1.1e-11 relative. At 1,405 vertices the clause holds (5.2e-14). The reviewer suggests rewording the Witness to "within conditioning (eps·cond); log det bit-identical; logL within 1e-10 relative". Flagged for the human merge decision.

Test Plan

• New test_autoarray/inversion/inversion/test_positive_negative_shared_cholesky.py (10 tests):
  • imaging and interferometer inversions match the LU solve (rtol 1e-10) and the dense Cholesky log det (1e-9), with one cho_factor call and no mutation of F + H;
  • random SPD system;
  • indefinite matrix: LU kept, log det raises / test-mode 0.0;
  • singular matrix: solve raises / test-mode dummy;
  • non-finite matrix: no factor;
  • slogdet unchanged, no factor;
  • positive-only: no factor;
  • partially regularized: solve uses the factor, log det takes the dense reduced route.
  • No JAX. The file passes under a fake jax that raises ImportError.
• PyAutoArray pytest test_autoarray -x -q: 2065 passed, 4 xfailed
• PyAutoGalaxy pytest test_autogalaxy -x -q (worktree source): 1357 passed
• PyAutoLens pytest test_autolens -x -q (worktree source): 832 passed, 1 xfailed
• Smoke (pyauto-heart smoke, all workspaces, worktree source): 165/165 passed, 0 failed (autofit 8 scripts + 2 notebooks, autogalaxy 14+2, autolens 41+2, autolens_test 37, euclid 9, howtolens 50); autocti/autocti_test not run (smoke env build failed locally: arcticpy needs libgsl-dev, same as PyAutoArray#632)

Full API Changes (for automation & release notes)

Added

• AbstractInversion._curvature_reg_matrix_cho_factor (private cached_property): scipy.linalg.cho_factor tuple of curvature_reg_matrix, or None.

Changed Behaviour

• AbstractInversion.reconstruction (NumPy, positive-negative, log_det_method="cholesky"): cho_solve with the shared factor in place of np.linalg.solve; falls back to the unchanged LU when the factor is None.
• AbstractInversion.log_det_curvature_reg_matrix_term (same gate, all linear objects regularized): read off the shared factor; it does not evaluate the reconstruction.
• Memory: one extra (n, n) array per inversion (~70 MB at n ≈ 3,000), documented in the docstring.

Validation checklist (--auto run — plan was not pre-approved)

• Effective level: safe (header: safe, cap: feature → safe)
• Plan: on the issue (perf: reuse one Cholesky factor of F+H for the solve and the log det #633), written at start, unmodified since
• Gate: tests PyAutoArray 2065 passed/4 xfailed, PyAutoGalaxy 1357 passed, PyAutoLens 832 passed/1 xfailed · smoke 165/165 passed, 0 failed (autofit 8 scripts + 2 notebooks, autogalaxy 14+2, autolens 41+2, autolens_test 37, euclid 9, howtolens 50); autocti/autocti_test not run (smoke env build failed locally: arcticpy needs libgsl-dev, same as PyAutoArray#632) · review CLEAN (independent Opus reader; 6 claims dispositioned basis-cited, incl. the 2,947 reconstruction-accuracy claim; one non-finding edge noted: a numerically singular PSD matrix with tiny-but-positive Cholesky pivots, where the LU hits an exact zero pivot, now returns a large solution instead of raising) · Heart RED, under the development-only override below
• Witness: speed PASS (2,947: −51%; 1,405: −22.4% repeat / −24.3% profile, run 1 −7.7% under load); log det bit-identical; logL ≤1.1e-11 rel; reconstruction 1e-10 clause FAILS as written at 2,947 (cond 7.7e14), new solve measured more accurate
• Human: plan sound in hindsight?
• Human: diff matches plan (no scope creep)?
• Human: accept the reworded reconstruction witness (within conditioning)?
• Human: merge, amend, or reject — then log the outcome

Heart RED development override

Heart was RED at launch and at ship (Heart: RED — Release RED; monitoring RED · 10/100 · 415 unresolved; reasons as listed on #633 / PyAutoArray#626). pyauto-heart readiness --json at ship time reported stale ("release validation stale: source moved since rehearsal (PyAutoFit)"). The live human authorized the development-only override in session 3e3dea38: AskUserQuestion "L1 now under override (Recommended)", 2026-10-15 late. It permits commit, push and PR-open. Merge is a separate human /prm. This PR stops at PR-open; no auto-merge.

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