feat: analytically-solved point-source likelihood variants (#657)

[Jammy2211]

Summary

Implements the analytically-solved point-source likelihood variants designed in #657 (phase 2 of 5; Lombardi 2024, arXiv:2406.15280). Point-source models no longer need to sample a source-plane centre (y,x) — or a flux, or a reference time — as non-linear free parameters: paired with the new zero-parameter al.ps.PointSolved profile, the *Solved fit classes solve them in closed form each likelihood call. The source-plane variant uses the paper's linearized likelihood with full Jacobian-tensor noise weighting (exact per-eigendirection stretch weighting; the traditional scalar µ²/σ² remains available as weighting="magnification") plus the analytic marginalization determinant term. The solved image-plane variants (all-to-all and pair-repeat) feed the solved centre into the existing PointSolver forward solve — an extension in the spirit of glafic's source-position optimization, not a paper result. Also: pluggable fit_flux_cls/fit_time_delays_cls hooks (previously hard-wired), pytree registration for the new classes and FitPositionsSource, informative errors replacing bare AttributeError on profile/fit mismatches, and a truth sweep of five docstrings that claimed an unimplemented "barycenter" option.

API Changes

All additions — existing classes, defaults, and behaviour are unchanged. Five new fit classes (FitPositionsSourceSolved, FitPositionsImagePairAllSolved, FitPositionsImagePairRepeatSolved, FitFluxesSolved, FitTimeDelaysSolved), the SolvedCentre mixin, and two new optional keywords (fit_flux_cls, fit_time_delays_cls) on FitPointDataset/AnalysisPoint. Invalid profile×fit pairings now raise informative PointExtractionExceptions instead of bare AttributeErrors.
See full details below.

Test Plan

• pytest test_autolens/point/ (85 passed locally) and full pytest test_autolens/ (473 passed locally)
• Correctness tests included: solved centre/flux/time equal brute-force optima; solved log-likelihood matches free-parameter likelihood profiled over the parameter; tensor-vs-scalar anisotropic ordering matches the image-plane chi-squared; PairAll permutation-count penalty regression; loud-failure matrix over {Point, PointFlux, PointSolved} × fit classes

Full API Changes (for automation & release notes)

Added

• al.FitPositionsSourceSolved — source-plane chi-squared with analytically-solved centre (Lombardi 2024 §5.1); class attribute weighting = "jacobian" (default, exact tensor) or "magnification" (traditional scalar µ²/σ²); includes the analytic marginalization term -0.5*log(det(ΣWᵢ)/(2π)²).
• al.FitPositionsImagePairAllSolved, al.FitPositionsImagePairRepeatSolved — existing image-plane chi-squareds driven by the solved centre (glafic-style extension).
• al.FitFluxesSolved — flux solved in closed form (F* = Σµᵢf̂ᵢ/σᵢ² / Σµᵢ²/σᵢ², magnification-first flux space); works with Point or PointSolved; raises on PointFlux (its flux prior would be silently ignored).
• al.FitTimeDelaysSolved — precision-weighted analytic reference time T* (alternative to the min-subtraction in FitTimeDelays, which is unchanged).
• autolens.point.fit.solved.SolvedCentre mixin + precision_tensor_components_from — the shared β* linear algebra.
• FitPointDataset(..., fit_flux_cls=FitFluxes, fit_time_delays_cls=FitTimeDelays) and the same on AnalysisPoint — previously hard-wired; defaults preserve current behaviour exactly.
• Pytree registration for the five new classes and (new) FitPositionsSource.

Changed Behaviour

• Profile/fit mismatches raise informative PointExtractionExceptions naming the fix (e.g. centre-bearing profile × *Solved fit; profile without centre × centre-requiring fit; PointFlux × FitFluxesSolved), instead of bare AttributeErrors.
• Docstrings only: five files no longer claim an unimplemented "barycenter of ray-traced positions" option; FitPositionsSource's "common centroid" wording corrected (the reference point is the profile centre, or β* in the Solved class).

Migration

• No changes required to existing scripts. To adopt: point_0 = af.Model(al.ps.PointSolved) (0 free parameters) + al.AnalysisPoint(..., fit_positions_cls=al.FitPositionsSourceSolved) (or an ImagePair*Solved class; add fit_flux_cls=al.FitFluxesSolved / fit_time_delays_cls=al.FitTimeDelaysSolved for datasets with fluxes/delays).

Depends on the companion PyAutoArray PR (xp threading through Grid2DIrregular.grid_2d_via_deflection_grid_from) and PyAutoGalaxy PR (ag.ps.PointSolved) on the same branch name — merge those first.

Closes nothing on merge — #657 stays open for phases 3–5 (workspace/profiling examples, guides, JAX gradients).

Generated by the PyAutoLabs agent workflow.

[Jammy2211]

Phase 3 workspace PRs:
PyAutoLabs/autolens_workspace_test#237
PyAutoLabs/autolens_profiling#96
PyAutoLabs/autolens_workspace_developer#121