feat: PowerLawIntermediate profile + herculens power-law parity via COOLEST

[Jammy2211]

Overview

Follow-up to #612 (COOLEST interop, merged). Adds ag.mp.PowerLawIntermediate — an elliptical power-law whose einstein_radius parameter is the COOLEST intermediate-axis θ_E — making the COOLEST mapping for it an identity (no √q factors), i.e. a direct parameter-level link to herculens/lenstronomy's power-law. A herculens cross-code parity script then proves the link empirically: the same COOLEST template produces numerically matching convergence and deflections in both codes.

Plan

• PyAutoGalaxy: behavior-preserving einstein_radius_major_from(xp) hook in the power-law implementation, then PowerLawIntermediate(PowerLaw) overriding it with the certified conversion θ_ag = θ_int/√q · ((1+q)/2)^(1/(γ−1)). Exported as ag.mp.PowerLawIntermediate with a priors-config block.
• COOLEST layer: PowerLawIntermediate → PEMD identity mapping; intermediate=True import option (threaded through al.interop.coolest.from_coolest) to rebuild PEMDs as PowerLawIntermediate.
• Tests: PowerLawIntermediate ≡ PowerLaw equivalence under the θ rescale (parametrized over q, γ); COOLEST identity + analytic certification; round trip.
• autolens_workspace_test: scripts/coolest_herculens_parity.py — export a PowerLawIntermediate model to a COOLEST template, load it into herculens, assert matching convergence/deflections on a shared grid (herculens installed in the env only, never a library dependency).

Detailed implementation plan

Affected Repositories

• PyAutoGalaxy (primary implementation)
• PyAutoLens (from_coolest intermediate kwarg)
• autolens_workspace_test (parity script)

Branch

feature/coolest-powerlaw-herculens, worktree ~/Code/PyAutoLabs-wt/coolest-powerlaw-herculens/

Implementation Steps

1. autogalaxy/profiles/mass/total/power_law_core.py: add PowerLawCore.einstein_radius_major_from(self, xp) returning self.einstein_radius; use it in einstein_radius_rescaled and in PowerLaw.deflections_yx_2d_from's Einstein-radius line. Numerically unchanged for all existing profiles (full suite is the regression net).
2. power_law.py: PowerLawIntermediate(PowerLaw) — same constructor; overrides the hook with the xp-threaded conversion (JAX-safe via self.axis_ratio(xp)); docstring documents the convention and factor.
3. Namespace exports (profiles/mass/total/__init__.py, profiles/mass/__init__.py) + PowerLawIntermediate: block in config/priors/mass/total/power_law.yaml.
4. autogalaxy/interop/coolest/mass.py: register PowerLawIntermediate → PEMD (identity θ_E); mass_profile_from(..., intermediate=True) builds PowerLawIntermediate; thread intermediate through autolens/interop/coolest.py::from_coolest.
5. Tests in test_autogalaxy/profiles/mass/total/ + test_autogalaxy/interop/ + test_autolens/interop/ (numpy-only).
6. Workspace leg: pip install herculens (dry-run first; --no-deps fallback if it moves the pinned jax 0.10.2), scripts/coolest_herculens_parity.py comparing convergence + deflections from the same COOLEST template; settles empirically whether herculens EPL θ_E is lenstronomy-convention (identity) or carries the SPEMD √((1+q²)/(2q)) factor.

Key Files

• PyAutoGalaxy/autogalaxy/profiles/mass/total/{power_law,power_law_core}.py
• PyAutoGalaxy/autogalaxy/interop/coolest/mass.py, PyAutoGalaxy/autogalaxy/config/priors/mass/total/power_law.yaml
• PyAutoLens/autolens/interop/coolest.py
• autolens_workspace_test/scripts/coolest_herculens_parity.py (new)

Original Prompt

Click to expand starting prompt

See PyAutoMind/active/coolest_powerlaw_herculens_parity.md.

[Jammy2211]

All three PRs open — parity PROVEN

• PyAutoGalaxy: feat: PowerLawIntermediate — intermediate-axis (COOLEST) Einstein radius power-law PyAutoGalaxy#503 — ag.mp.PowerLawIntermediate (988 tests passed)
• PyAutoLens: feat: from_coolest(intermediate=True) — rebuild PEMDs as PowerLawIntermediate #617 — from_coolest(intermediate=True) (387 tests passed)
• autolens_workspace_test: feat: herculens power-law parity script via COOLEST autolens_workspace_test#175 — herculens parity script

Key empirical result: herculens 0.3.0's EPL theta_E is exactly the COOLEST intermediate-axis convention (probe ratio 1.0 to machine precision — the SPEMD sqrt((1+q²)/(2q)) factor does not apply to EPL). The direct link therefore holds with identity parameters: the same COOLEST template produces matching convergence AND deflection angles in herculens and PyAutoLens (rtol 1e-8 / 1e-6), including the spherical limit.

Shipped through Heart RED (5 pre-existing unrelated reasons) on user ack. Merge order: PyAutoGalaxy#503 → PyAutoLens#617 → awst#175.

[Jammy2211]

Shipped — 2026-07-17

PRs (all MERGED, in order)

• feat: PowerLawIntermediate — intermediate-axis (COOLEST) Einstein radius power-law PyAutoGalaxy#503
• feat: from_coolest(intermediate=True) — rebuild PEMDs as PowerLawIntermediate #617
• feat: herculens power-law parity script via COOLEST autolens_workspace_test#175

Summary

ag.mp.PowerLawIntermediate is live: a power-law whose einstein_radius is the COOLEST intermediate-axis θ_E, with an identity PEMD mapping and from_coolest(intermediate=True). The parity script proves the direct link to herculens's EPL — same COOLEST template, matching convergence and deflections in both codes, identity parameters throughout (herculens EPL θ_E confirmed to be the COOLEST convention exactly).

This completes the COOLEST arc from the original Slack thread (#612 + #616).