gh-104: Add EuclidLikelihood_DarkEmu_RealSpace for real-space GC/GGL (+ optional WL)

[ryusei172525]

🚀 Pull Request Checklist

✅ Summary

Add a likelihood class for real-space two-point statistics (w_p(R), ΔΣ(R), and optional WL ξ±) with theory predictions from the Dark Emulator. The existing photo likelihoods (EuclidLikelihood_WL, GCph, GGL, 3x2pt) are built on angular power spectra C_ℓ and do not accept real-space data or use the Dark Emulator. This PR adds EuclidLikelihood_DarkEmu_RealSpace so that analyses that fit real-space GC/GGL with the Dark Emulator (e.g. HSC-style) can use cloelike with a single loglike(parameters) interface.

🔄 Changes

• Feature: New EuclidLikelihood_DarkEmu_RealSpace in EuclidLikelihood_DarkEmu_RealSpace.py — accepts optional data_gc (w_p), data_ggl (ΔΣ), data_wl (ξ±); uses DarkEmuHODPerturbations for GC/GGL theory; scale cuts via settings; Gaussian log-likelihood over combined data vector.
• Feature: Export EuclidLikelihood_DarkEmu_RealSpace from cloelike/__init__.py.
• Bug fix 1
• Other improvements

🛠 How to Test

1. From a Python environment with cloelib, cloelike, and dark_emulator_public available:

   from cloelike import EuclidLikelihood_DarkEmu_RealSpace
   from cloelib.cosmology.camb_cosmology import CAMBBackground
   # Build minimal data dicts (e.g. data_gc with keys: wp, R_bins, z_sample, covariance, pimax)
   # and settings (e.g. R_min_gc, R_max_gc, hod_params_fixed).
   # likelihood = EuclidLikelihood_DarkEmu_RealSpace(data_gc=data_gc, settings=settings, Background=CAMBBackground)
   # logl = likelihood.loglike(parameters_dict)
   # assert np.isfinite(logl)

2. Optional: run the playground notebooks that use this likelihood (playground/tutorials/dark_emulator/fitting_gc_wp.ipynb, fitting_ggl_delta_sigma.ipynb, or fitting_3x2pt.ipynb) against a checkout that includes this cloelike branch.

📝 Documentation

• This PR updates documentation

• This PR does not require documentation changes

• Issue created for documentation update: Don't forget to link the task!

• Module and class docstrings in EuclidLikelihood_DarkEmu_RealSpace.py describe the API. Usage is documented in the playground repo (tutorials/dark_emulator/).

🏗 Related Issues

• Resolves Add real-space likelihood for GC/GGL (and optional WL) using Dark Emulator #104

(Replace with the cloelike issue number for "Add real-space likelihood for GC/GGL (and optional WL) using Dark Emulator".)

📸 Screenshots (if applicable)

• N/A (library change only).

📌 Additional Notes

• Observables (w_p, ΔΣ) are obtained from the Dark Emulator via cloelib’s DarkEmuHODPerturbations, not from cloelib’s native C_ℓ/Limber pipeline. See playground/tutorials/dark_emulator/dark_emulator_observables_usage.ipynb for the intended retrieval pattern.
• A corresponding playground PR adds tutorials and scripts that use this likelihood.

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✅ PR Checklist for Developers

• I have titled this PR before merging as "gh-#:", where "#" represents the task it closes
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✅ PR Checklist for Reviewers

• The next PR targets the correct branch
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• Check that the code can still be installed if new packages are imported
• If necessary, the notebooks in the playground will be updated in a corresponding follow-up PR
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