Random points (glass.points)

The glass.points module provides functionality for simulating point processes on the sphere and sampling random positions.

Sampling

glass.points.positions_from_delta(ngal, delta, bias=None, vis=None, *, bias_model='linear', remove_monopole=False, rng=None)

Generate positions tracing a density contrast.

The map of expected number counts is constructed from the number density, density contrast, an optional bias model, and an optional visibility map.

If remove_monopole is set, the monopole of the computed density contrast is removed. Over the full sky, the mean number density of the map will then match the given number density exactly. This, however, means that an effectively different bias model is being used, unless the monopole is already zero in the first place.

Parameters:

ngalfloat

Number density, expected number of points per arcmin2.

deltaarray_like

Map of the input density contrast. This is fed into the bias model to produce the density contrast for sampling.

biasfloat, optional

Bias parameter, is passed as an argument to the bias model.

visarray_like, optional

Visibility map for the observed points. This is multiplied with the full sky number count map, and must hence be of compatible shape.

bias_modelstr or callable, optional

The bias model to apply. If a string, refers to a function in the points module, e.g. 'linear' for glass.points.linear_bias or 'loglinear' for glass.points.loglinear_bias.

remove_monopolebool, optional

If true, the monopole of the density contrast after biasing is fixed to zero.

rngGenerator, optional

Random number generator. If not given, a default RNG will be used.

Returns:

lon, latarray_like

Columns of longitudes and latitudes for the sampled points.

glass.points.uniform_positions(ngal, *, rng=None)

Generate positions uniformly over the sphere.

Parameters:

ngalfloat

Number density, expected number of positions per arcmin2.

rngGenerator, optional

Random number generator. If not given, a default RNG will be used.

Returns:

lon, latarray_like

Columns of longitudes and latitudes for the sampled points.

Bias

glass.points.effective_bias(z, bz, w)

Effective bias parameter from a redshift-dependent bias function.

This function takes a redshift-dependent bias function \(b(z)\) and computes an effective bias parameter \(\bar{b}\) for a given window function \(w(z)\).

Parameters:

z, bzarray_like

Redshifts and values of the bias function \(b(z)\).

wRadialWindow

The radial window function \(w(z)\).

Returns:

beffarray_like

Effective bias parameter for the window.

Notes

The effective bias parameter \(\bar{b}\) is computed using the window function \(w(z)\) as the weighted average

\[\bar{b} = \frac{\int b(z) \, w(z) \, dz}{\int w(z) \, dz} \;.\]

Bias models

glass.points.linear_bias(delta, b)

linear bias model \(\delta_g = b \, \delta\)

glass.points.loglinear_bias(delta, b)

log-linear bias model \(\ln(1 + \delta_g) = b \ln(1 + \delta)\)