clenspy.selection.selection_function.SelectionFunction

class clenspy.selection.selection_function.SelectionFunction(lambda_edges, z_edges, mor, emg_params, sigma_z, bracket_width=8.0, n_quad=64)

Bases: object

\(\mathcal S_{ij}(M, z^{\rm tr})\), and its two factors.

NOTE: units are dimensionless; ln_mass is \(\ln M\) with M in \(h^{-1}M_\odot\). See the module NOTE.

Parameters:

• lambda_edges (array-like, shape (n_lambda + 1,)) – Observed-richness bin edges, ascending and contiguous.

• z_edges (array-like, shape (n_z + 1,)) – Observed-redshift bin edges, ascending and contiguous.

• mor (LogNormalMor or HodMor) – The mass–observable relation. Stored verbatim; supplies pdf, mean and std.

• emg_params (EmgParams) – The observed-richness kernel parameters.

• sigma_z (float or array-like) – Photo-z scatter (not the 3-sigma window – see clenspy.kernels.photoz). A scalar, or one value per redshift bin.

• bracket_width (float, optional) – \(L\) in \(\mu_{\rm eff} \pm L\sigma_{\rm eff}\) (default: 8).

• n_quad (int, optional) – Gauss–Legendre order (default: 64).

__init__(lambda_edges, z_edges, mor, emg_params, sigma_z, bracket_width=8.0, n_quad=64)

Parameters:

• bracket_width (float)

• n_quad (int)

Methods

S_i(ln_mass, z)	\(S_i(M, z)\) for every richness bin.
S_ij(ln_mass, z)	\(\mathcal S_{ij} = S_i\,\mathcal S_j\).
S_j(z)	\(\mathcal S_j(z^{\rm tr})\) for every redshift bin.
__init__(lambda_edges, z_edges, mor, ...[, ...])
bracket(ln_mass, z)	(a, b): the \(\lambda^{\rm tr}\) quadrature bracket.
first_moment_i(ln_mass, z)	\int d\lambda^{\rm tr}\,P(\lambda^{\rm tr}\mid M,z)\,M_i, for every richness bin.
first_moment_ij(ln_mass, z)	first_moment_i * S_j, the \(\lambda^{\rm ob}\) first moment's share of \(\mathcal S_{ij}\).
residual(ln_mass, z)	How much \(\lambda^{\rm tr}\) probability the bracket misses.

Attributes

n_lambda_bins
n_z_bins

property n_lambda_bins

property n_z_bins

bracket(ln_mass, z)

(a, b): the \(\lambda^{\rm tr}\) quadrature bracket.

\[a = \max(0,\;\mu_{\rm eff} - L\sigma_{\rm eff}), \qquad b = \mu_{\rm eff} + L\sigma_{\rm eff}\]

NOTE: clipped at zero, never at the lowest bin edge. Clipping at \(\lambda_i^{\min}\) would be wrong: the projection tail scatters low-richness haloes up into the bin, so the integrand is non-zero well below the bin’s own edge. That upscatter is the entire physical effect this package exists to model.

S_i(ln_mass, z)

\(S_i(M, z)\) for every richness bin.

Returns shape (*broadcast(ln_mass, z).shape, n_lambda_bins).

first_moment_i(ln_mass, z)

\int d\lambda^{\rm tr}\,P(\lambda^{\rm tr}\mid M,z)\,M_i, for every richness bin.

The same \(\lambda^{\rm tr}\) quadrature S_i uses, contracted against ~clenspy.selection.richness_kernel.richness_bin_first_moment instead of richness_bin_probability. Dividing element-wise by S_i gives the observed-richness mean of haloes of mass \(M\) at redshift \(z\) that land in bin \(i\).

Returns shape (*broadcast(ln_mass, z).shape, n_lambda_bins).

S_j(z)

\(\mathcal S_j(z^{\rm tr})\) for every redshift bin.

Returns shape (*np.shape(z), n_z_bins).

S_ij(ln_mass, z)

\(\mathcal S_{ij} = S_i\,\mathcal S_j\).

Returns shape (..., n_lambda_bins, n_z_bins).

first_moment_ij(ln_mass, z)

first_moment_i * S_j, the \(\lambda^{\rm ob}\) first moment’s share of \(\mathcal S_{ij}\).

Factorises exactly like S_ij: the redshift factor \(\mathcal S_j\) carries no \(\lambda^{\rm ob}\) dependence, so it multiplies through unchanged. This is the numerator clenspy.observables.ClusterCounts.mean_richness needs – dividing its \((\ln M, z)\) integral by counts gives \(\langle\lambda^{\rm ob}\rangle_{ij}\).

Returns shape (..., n_lambda_bins, n_z_bins).

residual(ln_mass, z)

How much \(\lambda^{\rm tr}\) probability the bracket misses.

\(1 - \int_a^b P(\lambda^{\rm tr}\mid M,z)\, d\lambda^{\rm tr}\), computed on the same nodes the quadrature uses.

NOTE: this is the module’s named approximation, made measurable. A value of \(10^{-6}\) says the bracket is fine; \(10^{-2}\) says \(S_i\) is low by about a percent and bracket_width needs raising. There is no way to know without evaluating it, which is why it is a method and not a comment.