feat: Phase 3 — mirror Nautilus profiling scripts

[Jammy2211]

Summary

Phase 3 of the autolens_profiling z_feature roadmap — stands up autolens_profiling/searches/ with sampler profiling for the Nautilus sampler only, mirrored from autolens_workspace_developer/searches_minimal/. Other samplers (Dynesty, Emcee, BlackJAX, NumPyro, PocoMC, NSS, LBFGS) are explicitly out of scope; the folder layout is designed so they slot in under their own follow-up prompts.

_developer stays the source of truth — the originals do not move.

Closes #5.

What changed

• 4 files mirrored from clean origin/main of _developer/searches_minimal/:
  • _setup.py (shared dataset/model/analysis builder) → searches/_setup.py
  • _metrics.py (MLTracker for evals/time to ML) → searches/_metrics.py
  • nautilus_simple.py (NumPy backend) → searches/nautilus/simple.py
  • nautilus_jax.py (JAX-JIT'd likelihood) → searches/nautilus/jax.py
• Path rewrites in _setup.py:
  • _DATASET_SUBPATH: Path(\"jax_profiling\") / \"dataset\" / \"imaging\" / \"hst\" → Path(\"dataset\") / \"imaging\" / \"hst\" (matches Phase 1's top-level layout).
  • Replaced the should_simulate subprocess block (which invoked _developer/jax_profiling/dataset_setup/imaging.py) with a clean FileNotFoundError pointing readers back at _developer for regeneration — same pattern Phase 1 used.
  • Dropped now-unused subprocess + sys imports.
  • Docstring + cross-references updated to the new layout (from searches._setup, likelihood/imaging/mge.py).
• Import rewrites in nautilus/{simple,jax}.py:
  • from searches_minimal._{metrics,setup} → from searches._{metrics,setup}.
  • Added sys.path injection at the top of each script (_REPO_ROOT = Path(__file__).resolve().parents[2]) so they work invariant to invocation style (python searches/nautilus/<name>.py or python -m searches.nautilus.<name>).
• Output convention upgrade: the originals wrote a freeform <script>_summary.txt to output/. The mirror writes versioned JSON + bar-chart PNG to results/searches/nautilus/<script>_summary_v<al.__version__>.{json,png} matching the Phase 1 convention so Phase 4's dashboard can pick them up.
  • JSON has sections: sampler, backend, instrument, model, sampler_config, results, performance, convergence, version.
  • PNG: horizontal bar chart of headline timings (wall_time, time_per_eval, time_to_ml; plus jit_compile on jax.py).
• 2 READMEs:
  • searches/README.md (replaces Phase 0 placeholder): section overview, shared helper roles, supported-samplers table (Nautilus ✓, 7 others marked planned), versioned-artifact convention, run instructions.
  • searches/nautilus/README.md: narrative grounded in _developer/searches_minimal/sweep_findings.md — expected converged logZ ≈ -169k for this MGE setup, caveats (upstream JAX-gradient pathology PyAutoLens#514), headline-run-times table placeholder for Phase 4.

F1 lesson applied

Copies came from the worktree's clean origin/main of _developer, NOT the canonical (which is currently dirty with ~36 modified files). This is the same lesson that prompted F1's re-mirror PR #3 for Phase 1.

Test plan

• py_compile PASSES for all 4 mirrored files (_setup.py, _metrics.py, nautilus/simple.py, nautilus/jax.py).
• grep -r searches_minimal on the mirrored searches/ returns no residual references — only the section README references the upstream folder by name in context.
• sys.path injection lets both scripts resolve from searches._{setup,metrics} regardless of cwd / invocation style.
• .gitignore already covers results/searches/ from Phase 1 — smoke artifacts won't leak.
• Full runtime smoke skipped: python searches/nautilus/simple.py at default n_live=200 takes 30+ min on CPU. Phase 5 (issue #7) will add the AUTOLENS_PROFILING_SMOKE=1 env-var short-circuit that makes future smokes cheap; until then the static checks above + the matching pattern with Phase 1's already-shipped scripts give sufficient confidence to ship. The Nautilus scripts can be smoked manually after this lands by running them with whatever n_live the user wants.

Refs

• Phase 1 (likelihood mirror, shipped): feat: Phase 1 — mirror JIT likelihood profiling scripts #2, F1 re-mirror fix: re-mirror likelihood scripts and datasets from clean origin/main of _developer #3.
• Phase 2 (simulators mirror, queued): feat: Phase 2 — mirror simulator profiling scripts #4.
• Phase 4 (dashboard, queued): feat: Phase 4 — instrument-framed README dashboard #6.
• Phase 5 (CI, queued): feat: Phase 5 — GitHub Actions for lint + profile re-run #7.

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