feat: MGE/CSE fallback for zero-returning mass profiles

[Jammy2211]

Overview

16 mass profiles return np.zeros for convergence_2d_from or potential_2d_from — placeholders where no analytic formula was implemented. Replace these with proper implementations: direct analytic formulas for trivial cases (PointMass, MassSheet), and MGE decomposition fallback for the rest. Phase 3 of the mass profiles refactoring epic (#445), depends on Phase 2 (CSE JAX port, #446, shipped).

Plan

• Implement analytic potential_2d_from for PointMass (ψ = R_E² ln(r)) and MassSheet (ψ = ½κ r²) — trivial closed forms
• Implement MGE-based potential_2d_from fallback for profiles that have a convergence_func but no analytic potential: Sersic, Gaussian, Chameleon, PowerLawBroken, dPIEMass, dPIEPotential
• Implement CSE-based convergence_2d_from for cNFW/cNFWSph (which have deflections via CSE but return zeros for convergence)
• Implement CSE or MGE-based potential_2d_from for NFWTruncatedSph, cNFW/cNFWSph
• Leave ExternalShear and PowerLawMultipole convergence as zeros — physically correct
• Verify via Phase 1 self-consistency test suite (autolens_workspace_test scripts/mass/)

Detailed implementation plan

Affected Repositories

• PyAutoGalaxy (primary)

Work Classification

Library

Branch Survey

Repository	Current Branch	Dirty?
PyAutoGalaxy	main	modified CLAUDE.md only

Suggested branch: feature/mge-cse-fallback
Worktree root: ~/Code/PyAutoLabs-wt/mge-cse-fallback/

Implementation Steps

1. PointMass — point/point.py: replace zeros with potential = einstein_radius**2 * xp.log(r) where r = xp.sqrt(y**2 + x**2)

2. MassSheet — sheets/mass_sheet.py: replace zeros with potential = 0.5 * kappa * (y**2 + x**2)

3. cNFW/cNFWSph — dark/cnfw.py: implement convergence_2d_from via CSE decomposition (already has CSE infrastructure from MassProfileCSE mixin). Implement potential_2d_from via MGE decomposition of the convergence.

4. NFWTruncatedSph — dark/nfw_truncated.py: implement potential_2d_from via MGE fallback

5. Sersic/SersicSph — stellar/sersic.py (AbstractSersic): implement potential_2d_from via MGE decomposition of Sersic convergence

6. Gaussian — stellar/gaussian.py: implement potential_2d_from via MGE (Gaussian is itself a single MGE component — may have a direct formula)

7. Chameleon/ChameleonSph — stellar/chameleon.py: implement potential_2d_from via MGE

8. PowerLawBroken/Sph — total/power_law_broken.py: implement potential_2d_from via MGE

9. dPIEMass/Sph — total/dual_pseudo_isothermal_mass.py: implement potential_2d_from via MGE or check literature for analytic form

10. dPIEPotential/Sph — total/dual_pseudo_isothermal_potential.py: implement potential_2d_from via MGE (ironic that the "Potential" variant has no potential method)

11. Run pytest test_autogalaxy/profiles/mass/ — verify no regressions

12. Run Phase 1 self-consistency tests — verify previously-SKIP profiles now PASS

Key Files

• autogalaxy/profiles/mass/abstract/abstract.py — may need base-class MGE potential helper
• autogalaxy/profiles/mass/abstract/mge.py — MGEDecomposer (already mature, JAX-ready)
• Individual profile files listed above

Original Prompt

Click to expand starting prompt

Implement MGE/CSE fallback for mass profiles that currently return zeros for convergence or potential. 16 mass profiles return zeros — replace with MGE decomposition (preferred, JAX-ready) or CSE decomposition. PointMass and MassSheet get trivial analytic implementations. ExternalShear and PowerLawMultipole stay as zeros (physically correct).

[Jammy2211]

Shipped — 2026-05-26

PR

• feat: MGE/CSE fallback for zero-returning mass profile potentials #449

Summary

Replaced zero-returning potential_2d_from and convergence_2d_from across 10 mass profiles with proper implementations. Added MGEDecomposer.potential_2d_via_mge_from() using the E1 exponential integral formula (Shajib 2019, cross-validated against Jax-Lensing-Profiles). PointMass and MassSheet got trivial analytic potentials. cNFW got MGE-based convergence. All other profiles got MGE-based potential. 406 unit tests pass.

Session Notes

• The MGE potential formula was validated against known-good analytic profiles (Isothermal, PowerLaw): self-consistency laplacian(ψ)=2κ holds to 0.3% median. The ~5% error vs analytic is inherent to the MGE decomposition quality (convergence itself has similar error), not the potential formula.
• E1 approximation uses Abramowitz & Stegun polynomial/rational form — JAX-compatible (branchless via xp.where).
• Reference: Jax-Lensing-Profiles (Herculens) uses the same formula for their circular Gaussian potential. Elliptical case uses quadrature in their code; our decorator system handles ellipticity via coordinate transformation so the circular formula suffices.
• Phase 3 of mass profiles refactoring epic (refactor: mass profiles — MGE/CSE fallback, JAX port, testing & docs #445). Next: Phase 4 — spring clean (autogalaxy/mass_profiles_spring_clean.md).