crow.recipes.binned_exact module

Module for defining the classes used in the BinnedClusterRecipe cluster recipe.

class crow.recipes.binned_exact.ExactBinnedClusterRecipe(cluster_theory, redshift_distribution, mass_distribution, completeness: Completeness = None, purity: Purity = None, mass_interval: tuple[float, float] = (11.0, 17.0), true_z_interval: tuple[float, float] = (0.0, 5.0))

Bases: BinnedClusterRecipe

Concrete implementation of BinnedClusterRecipe using direct numerical integration.

This recipe evaluates cluster observables by explicitly integrating over mass, redshift, and mass proxy using a numerical integrator. It assumes:

• Murata et al. (2019) mass–richness relation

• Perfectly measured spectroscopic redshifts

• No precomputed grids or interpolation (fully numerical evaluation)

The integration is performed using a configurable integrator (NumCosmoIntegrator), which maps the theoretical prediction into an integrable function over the relevant parameter space.

Compared to other implementations, this class: - Does not rely on interpolation tables - Computes predictions on-the-fly via numerical quadrature - Handles purity/completeness through explicit modification of the integrand

Notes

This implementation is computationally more expensive but provides a reference "exact" evaluation of the model under the stated assumptions.

evaluate_theory_prediction_counts(z_edges, log_proxy_edges, sky_area: float, average_on: None | ClusterProperty = None) → float

Compute predicted cluster number counts within a bin.

This method performs a multidimensional numerical integral over:

• halo mass

• redshift

• mass proxy

Parameters:

• z_edges (array-like of shape (2,)) -- Redshift bin limits.

• log_proxy_edges (array-like of shape (2,)) -- Mass proxy bin limits in log10 space.

• sky_area (float) -- Survey area in square degrees.

• average_on (ClusterProperty, optional) -- Observable over which to average (e.g., mass, redshift).

Returns:

Expected number of clusters in the bin.

Return type:

float

Notes

• Uses NumCosmoIntegrator for numerical quadrature.

• Handles purity and completeness internally by modifying the integrand.

• Assumes perfect redshift measurements.

evaluate_theory_prediction_lensing_profile(z_edges, log_proxy_edges, radius_centers, sky_area: float, average_on: None | ClusterProperty = None) → float

Compute the predicted stacked lensing (shear) profile.

This method integrates the theoretical lensing signal over:

• halo mass

• redshift

• mass proxy

and evaluates it at multiple radial bins.

Parameters:

• z_edges (array-like of shape (2,)) -- Redshift bin limits.

• log_proxy_edges (array-like of shape (2,)) -- Mass proxy bin limits in log10 space.

• radius_centers (array-like) -- Radii at which the shear profile is evaluated.

• sky_area (float) -- Survey area in square degrees.

• average_on (ClusterProperty, optional) -- Observable defining the weighting of the prediction. Must include shear-related properties.

Returns:

Predicted shear profile evaluated at each radius.

Return type:

ndarray

Notes

• Each radius is integrated independently.

• The integrand includes the halo shear profile computed from the

  underlying cluster theory model.

• Purity and completeness modify the integrand similarly to the

  number counts case.

setup()

Perform any necessary pre-computation before evaluation.

This method is intended to be implemented by subclasses. It should initialize any internal quantities required for evaluating theoretical predictions (e.g., reseting/ precomputing grids, normalization factors, or integrators).

Notes

This method must be called before any evaluation method.