perf: warm-start the positive-only NNLS solve from the previous evaluation's passive set (#498)

[Jammy2211]

Summary

Phase 3a of the numba CPU sparse-operator likelihood speed restoration (epic numba-cpu-likelihood, closes #498). The positive-only reconstruction solve (fnnls_cholesky, Bro & De Jong active set) is iteration-bound: its warm start — the sign of the unconstrained dense solve — gets ~70–95 of ~1310 passive-set entries wrong on the Delaunay-1250 fiducial, and every wrong entry costs an active-set iteration. This PR (1) instruments the solver, (2) makes the warm start reuse one Cholesky factorisation instead of a dense solve plus a from-scratch refactorisation, and (3) adds a process-local cross-evaluation memo that seeds the next solve from the previous evaluation's final passive set (Settings.nnls_warm_start_memo, default on, kill-switch AUTOARRAY_NNLS_WARM_START=0).

Measured on the euclid + hst Delaunay-1250 + MGE-60 fiducial (autolens_profiling PR to follow; AUTOARRAY_NUMBA_OPERATED_MEMO=0, 30-step random-walk and i.i.d. instance sequences, memo off vs on):

instrument	sequence	median iterations off→on	solve s off→on	eval s off→on
euclid	random walk	69.5 → 7.0 (9.9×)	0.544 → 0.051	1.510 → 0.564
euclid	i.i.d.	86 → 94	0.347 → 0.309	0.906 → 0.838
hst	random walk	32 → 8 (4.0×)	0.245 → 0.067	1.733 → 1.594
hst	i.i.d.	42 → 69.5	0.268 → 0.260	1.687 → 1.867

Log-likelihood parity memo on vs off: max relative Δ 3e-14; max |Δreconstruction| 1.6e-8; 0 memo-seed failures in 240 evaluations. Solve seconds are ≤ off in every cell (the memo also skips the dense unconstrained solve), so uncorrelated jumps cost iterations but not time. Step-0 re-profile after #453/#497: the solve is now 40% (euclid) / 17% (hst) of an evaluation, not the ~72% the issue was filed on.

Robustness across lens models (32-cell matrix, results/notes/nnls_warm_start_memo_matrix.md: PowerLaw, NFW subhalo, no / Sersic lens light, rectangular mesh, adaptive regularization, no edge-zeroing, complex source, 600 / 2000-pixel meshes; euclid + hst): parity ≤ 4e-14 in every cell, zero seeded-solve failures, median solve time never worse than memo-off by >2%; every random-walk cell gains (3.2×–118× — rectangular meshes most, their dense-sign start is 44–70% wrong); only i.i.d. sequences lose iterations (worst 0.52×), never time.

Wiggle room — a relative fallback guard (Settings.nnls_warm_start_error_tolerance, default 1.5): each memo entry remembers the error fraction of the last dense-sign-started solve for its key; a seed that comes out worse than tolerance × that reference is dropped and the next solve restarts dense, refreshing the reference. Relative because the absolute seed error fraction does not separate helpful from harmful seeds (0.048–0.138 overlap) while the seed/dense ratio does (helpful ≤ 0.89, worst 1.42). Fired 3 times in 240 re-run evaluations, all in the one cell at ratio 1.42. Non-finite / non-positive tolerance disables it.

A correctness fix rides along: a warm passive set containing entries with a non-positive unconstrained solution used to be clipped only, and an all-True P skipped the outer loop entirely and returned that clipped vector. Unreachable from the dense-sign start, reachable from a memo seed — repaired before the outer loop (explicit drop-and-refactor; fix_constraint_cholesky has no prior feasible iterate there and its alpha is 0/0).

API Changes

Additive. fnnls_cholesky gains an optional stats dict and accepts a bool mask or index array as P_initial; reconstruction_positive_only_from gains fingerprint=; Settings gains nnls_warm_start_memo and nnls_warm_start_error_tolerance (config general.inversion.nnls_warm_start_memo, packaged default true; a shadowing workspace general.yaml without the key also resolves to true); new module autoarray.inversion.inversion.nnls_memo. Behaviour change: on the NumPy/numba path the positive-only solve now warm-starts from the previous evaluation's passive set by default — the solution is the unique NNLS optimum and is unchanged to round-off. JAX path untouched.
See full details below.

Test Plan

• pytest test_autoarray — 1279 passed (new: test_cholesky_inplace.py +7, test_jax_nnls.py +4, test_nnls_memo.py new, test_settings_dict.py +1)
• euclid + hst Delaunay-1250 pinned log-likelihoods unchanged (delaunay_numba.py pins PASSED; memo on/off parity 3e-14)
• CI green on all legs

Full API Changes (for automation & release notes)

Added

• autoarray.util.fnnls.fnnls_cholesky(ZTZ, ZTx, P_initial=, stats: Optional[dict] = None) — stats is filled with outer_iterations, inner_iterations, passive_set, n_passive, warm_start_errors; P_initial may be a bool mask or an int index array
• autoarray.inversion.inversion.inversion_util.reconstruction_positive_only_from(..., fingerprint=None) — identifies the passive set's index space for the memo; None disables the memo for that call
• autoarray.Settings(nnls_warm_start_memo: Optional[bool] = None) + property — NumPy/numba path only
• autoarray/config/general.yaml → inversion.nnls_warm_start_memo: true
• autoarray.Settings(nnls_warm_start_error_tolerance: Optional[float] = None) + property — config inversion.nnls_warm_start_error_tolerance: 1.5; non-finite / ≤ 0 disables the guard
• autoarray.inversion.inversion.nnls_memo — MemoEntry(passive_set, dense_error_fraction), memo_enabled(), memo_key(n, fingerprint), passive_set_get(key, n) -> Optional[MemoEntry], passive_set_put(key, passive_set, dense_error_fraction), memo_drop(key); FIFO, 8 entries; env AUTOARRAY_NNLS_WARM_START=0 disables
• reconstruction_positive_only_from writes stats["seed_source"] ("memo"/"dense") and stats["warm_start_fallback"] after the solve
• AbstractInversion._nnls_warm_start_fingerprint(ids_to_keep=None) (private)

Changed Behaviour

• fnnls_cholesky: warm start factorises the initial passive set once and extends it in place (was: dense scipy.linalg.solve + full cholesky on the first outer iteration); a warm passive set with non-positive entries is repaired before the outer loop (was: clipped, and returned unsolved when P was all-True); near-singular warm-start systems now raise LinAlgError from cholesky instead of LinAlgWarning + garbage from solve
• reconstruction_positive_only_from (NumPy path): warm-starts from the memo when settings.nnls_warm_start_memo and a fingerprint are given; a memo-seeded solve that raises retries once from the dense-sign start before the InversionException path

Migration

• None required. To restore the previous start: aa.Settings(nnls_warm_start_memo=False) or AUTOARRAY_NNLS_WARM_START=0.

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[Jammy2211]

Workspace leg: PyAutoLabs/autolens_profiling#184 (merges after this PR — library-first gate).