perf: windowed numba fast path for the RectangularAdaptDensity kernel-CDF transform #457

Overview

The kernel-CDF forward transform of RectangularAdaptDensity 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 no cross-eval caching applies). Phase 3 of the CPU speed campaign, per the PyAutoMind kernel-CDF prompt.

Plan

• Numba kernel _kernel_cdf_dim_windowed in inversion/mesh/interpolator/rectangular.py: per-dimension weighted kernel CDF over sorted points + weight prefix sums with a ±9-bandwidth saturation window (dropped tails < 1e-19 of the weight sum → values match the exact sum to ~1e-13).
• The numpy branch of F_raw uses it; the blocked numpy implementation stays as the JAX branch and the differentiable reference. The module's "no sorts" differentiability guarantee is preserved — the sort is internal evaluation order on the gradient-free numpy path only.
• Beyond ~3.4× the transform is irreducibly O(M×N) for exact values; the measured interpolated-CDF option (K=8192 → Δlnℒ ≤ +4e-3 / ≤ 2e-3 differential, 18–55×) and the default-mesh question are tracked separately (Inference programme: no fast default CPU mesh — Rectangular is the default and slow on CPU (new-user hazard) autolens_profiling#153, programme Phase 14).

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.
• End-to-end Rectangular eval (stacked with 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 pins pass at rtol 1e-6.
• test_autoarray/: 1036 passed (+2 dense-reference equivalence tests); same 3 pre-existing environmental pynufft failures.