perf: windowed numba fast path for the kernel-CDF forward transform

[Jammy2211]

Closes #457.

What

The RectangularAdaptDensity kernel-CDF forward transform dominates the numba CPU likelihood on the default Rectangular route — 1.66 s = 55% of a euclid eval, 27 s = 89% at hst (PyAutoLabs/autolens_profiling#151): an O(M×N) blocked erf broadcast with ~126 MB per-block temporaries, rebuilt every evaluation (the traced grid moves with the mass model, so nothing can be memoized across evals).

One file of source change (inversion/mesh/interpolator/rectangular.py): the numpy branch of F_raw now evaluates each dimension's weighted kernel CDF with a numba kernel (_kernel_cdf_dim_windowed) over sorted points + weight prefix sums, using a ±9-bandwidth saturation window — points below the window contribute exactly their weight via the prefix sum, points above contribute zero, and only the window is summed with erfc. Dropped tail terms are < 1e-19 of the weight sum, so values match the exact blocked sum to ~1e-13 (fp accumulation noise).

Differentiability guarantee preserved: the module's "no sorts anywhere" invariant is a JAX-gradient property; the sort here is internal evaluation order on the gradient-free xp is np branch only, and the blocked numpy implementation remains the JAX branch and the differentiable reference.

Results (4-core cloud container)

• Transform step: euclid 1.50 → 0.50 s (3.0×), hst 28.2 → 8.3 s (3.4×); max deviation 1e-13 on real fiducial inputs.
• End-to-end Rectangular numba eval, stacked with the merged perf: in-place Cholesky buffer + copy-free numba solves for fnnls_cholesky #453 + perf: cross-eval memo for MGE operated mapping matrices (numba CPU inversion) #455: euclid 3.08 → 1.17 s, hst ~30 → 10.1 s; both autolens_profiling pixelization_numba pinned log-likelihoods pass at rtol 1e-6.
• Beyond ~3.4× the exact transform is irreducibly O(M×N); the measured interpolated-CDF option and the default-CPU-mesh question are tracked in Inference programme: no fast default CPU mesh — Rectangular is the default and slow on CPU (new-user hazard) autolens_profiling#153 (programme Phase 14).

Testing

• New: two dense-reference equivalence tests in test_autoarray/inversion/pixelization/interpolator/test_rectangular.py (weighted + unweighted, atol 1e-12, with out-of-box queries exercising the saturated tails).
• All 10 existing interpolator property tests (monotonicity, unit-square mapping, etc.) pass unchanged on the new path; test_autoarray/ 1036 passed, 51 skipped; only the 3 pynufft transformer tests that fail identically on stock main in this environment.

Downstream

No public API change; JAX path untouched; interferometer and all other meshes untouched. Likelihood values shift at the ~1e-13 level (below the solver's own bistability).

🤖 Generated with Claude Code

https://claude.ai/code/session_01Vcc7MUBMnNU6n8qqS9ioVZ

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