Overview
NFWTruncatedSph.potential_2d_from currently uses a 30-component MGE approximation whose potential is not self-consistent with the profile's analytic deflection field: the full mass-profile sweep reports a median grad(psi)=alpha error of about (7.1\times10^{-2}), roughly 100 times worse than the other NFW variants.
Baltz, Marshall & Oguri (2009), arXiv:0705.0682, Appendix A equation 18 gives an exact analytic lensing potential for precisely the (n=1) smoothly truncated NFW density convention implemented by this class. Replace the approximate production path with that analytic expression.
Plan
- Port the analytic (n=1) potential from Baltz, Marshall & Oguri equation 18.
- Derive its PyAutoGalaxy normalization from the existing analytic deflection rather than copying the paper's physical-unit prefactor.
- Preserve NumPy/JAX compatibility and implement stable behaviour at (x=0), (x=1), and ( au=1).
- Add derivative-based regression tests and independently cross-check the implementation.
- Correct the profile docstring's arXiv identifier from
0705.0735 to 0705.0682.
Detailed implementation plan
Affected Repositories
- PyAutoGalaxy (primary and only source repository)
Suggested branch
feature/nfw-truncated-analytic-potential
Implementation Steps
- In
autogalaxy/profiles/mass/dark/nfw_truncated.py, replace the MGE call in NFWTruncatedSph.potential_2d_from with the (n=1) analytic expression from equation 18.
- Reuse the existing auxiliary functions consistently: inherited (F(x)) support and the current logarithmic helper corresponding to the paper's (L(x)).
- Map the paper's normalization onto PyAutoGalaxy units by differentiating the candidate expression and requiring agreement with
deflections_yx_2d_from; the expected scale is proportional to (2\kappa_s r_s^2).
- Handle branch values and removable singularities without Python conditionals on possible JAX tracers. Thread
xp through every nested operation.
- In
test_autogalaxy/profiles/mass/dark/test_nfw_truncated.py, add parameterized finite-difference tests over multiple ( au=r_t/r_s) values:
- (
abla\psi=\alpha);
- (
abla^2\psi=2\kappa);
- the large-( au) NFW limit, comparing potential differences because the additive constant is arbitrary.
- Cross-check representative potential differences against the independent lenstronomy TNFW implementation.
- Run the focused tests, the PyAutoGalaxy mass-profile suite, NumPy/JAX parity coverage, and
PYAUTO_MASS_MODE=full python scripts/mass/dark.py.
Key Files
autogalaxy/profiles/mass/dark/nfw_truncated.py — analytic potential and corrected literature reference.test_autogalaxy/profiles/mass/dark/test_nfw_truncated.py — derivative and limiting-behaviour regressions.autolens_workspace_test/scripts/mass/dark.py — existing full self-consistency validation; validation-only unless a genuine test defect is found.
Scope boundary
The MGE implementation may be retained only as an independent comparison. Do not tune the Gaussian range as the production fix. Do not expand this PR to the separate (n=2) truncated profile.
Original Prompt
This starts from PyAutoMind draft/bug/autogalaxy/nfw_truncated_potential_accuracy.md, updated by the approved decision to prefer the exact analytic Baltz–Marshall–Oguri potential over MGE refinement.
Overview
NFWTruncatedSph.potential_2d_fromcurrently uses a 30-component MGE approximation whose potential is not self-consistent with the profile's analytic deflection field: the full mass-profile sweep reports a mediangrad(psi)=alphaerror of about (7.1\times10^{-2}), roughly 100 times worse than the other NFW variants.Baltz, Marshall & Oguri (2009), arXiv:0705.0682, Appendix A equation 18 gives an exact analytic lensing potential for precisely the (n=1) smoothly truncated NFW density convention implemented by this class. Replace the approximate production path with that analytic expression.
Plan
0705.0735to0705.0682.Detailed implementation plan
Affected Repositories
Suggested branch
feature/nfw-truncated-analytic-potentialImplementation Steps
autogalaxy/profiles/mass/dark/nfw_truncated.py, replace the MGE call inNFWTruncatedSph.potential_2d_fromwith the (n=1) analytic expression from equation 18.deflections_yx_2d_from; the expected scale is proportional to (2\kappa_s r_s^2).xpthrough every nested operation.test_autogalaxy/profiles/mass/dark/test_nfw_truncated.py, add parameterized finite-difference tests over multiple ( au=r_t/r_s) values:abla\psi=\alpha);
abla^2\psi=2\kappa);
PYAUTO_MASS_MODE=full python scripts/mass/dark.py.Key Files
autogalaxy/profiles/mass/dark/nfw_truncated.py— analytic potential and corrected literature reference.test_autogalaxy/profiles/mass/dark/test_nfw_truncated.py— derivative and limiting-behaviour regressions.autolens_workspace_test/scripts/mass/dark.py— existing full self-consistency validation; validation-only unless a genuine test defect is found.Scope boundary
The MGE implementation may be retained only as an independent comparison. Do not tune the Gaussian range as the production fix. Do not expand this PR to the separate (n=2) truncated profile.
Original Prompt
This starts from PyAutoMind
draft/bug/autogalaxy/nfw_truncated_potential_accuracy.md, updated by the approved decision to prefer the exact analytic Baltz–Marshall–Oguri potential over MGE refinement.