Observations

The following functions provide functionality for simulating observational effects of surveys.

Redshift distribution

glass.gaussian_nz(z, mean, sigma, *, norm=None)

Gaussian redshift distribution.

The redshift follows a Gaussian distribution with the given mean and standard deviation.

If mean or sigma are array_like, their axes will be the leading axes of the redshift distribution.

Parameters:

• z (ndarray[tuple[int, ...], dtype[float64]]) – Redshift values of the distribution.

• mean (float | ndarray[tuple[int, ...], dtype[float64]]) – Mean(s) of the redshift distribution.

• sigma (float | ndarray[tuple[int, ...], dtype[float64]]) – Standard deviation(s) of the redshift distribution.

• norm (float | ndarray[tuple[int, ...], dtype[float64]] | None) – If given, the normalisation of the distribution.

Returns:

The redshift distribution at the given z values.

Return type:

ndarray[tuple[int, ...], dtype[float64]]

glass.smail_nz(z, z_mode, alpha, beta, *, norm=None)

Redshift distribution following Smail et al. (1994).

The redshift follows the Smail et al. [Smail94] redshift distribution.

Parameters:

• z (ndarray[tuple[int, ...], dtype[float64]]) – Redshift values of the distribution.

• z_mode (float | ndarray[tuple[int, ...], dtype[float64]]) – Mode of the redshift distribution, must be positive.

• alpha (float | ndarray[tuple[int, ...], dtype[float64]]) – Power law exponent (z/z0)^alpha, must be positive.

• beta (float | ndarray[tuple[int, ...], dtype[float64]]) – Log-power law exponent exp[-(z/z0)^beta], must be positive.

• norm (float | ndarray[tuple[int, ...], dtype[float64]] | None) – If given, the normalisation of the distribution.

Returns:

The redshift distribution at the given z values.

Return type:

ndarray[tuple[int, ...], dtype[float64]]

Notes

The probability distribution function \(p(z)\) for redshift \(z\) is given by Amara & Refregier [Amara07] as

\[p(z) \sim \left(\frac{z}{z_0}\right)^\alpha \exp\left[-\left(\frac{z}{z_0}\right)^\beta\right] \;,\]

where \(z_0\) is matched to the given mode of the distribution.

glass.fixed_zbins(zmin, zmax, *, nbins=None, dz=None)

Tomographic redshift bins of fixed size.

This function creates contiguous tomographic redshift bins of fixed size. It takes either the number or size of the bins.

Parameters:

• zmin (float) – Extent of the redshift binning.

• zmax (float) – Extent of the redshift binning.

• nbins (int | None) – Number of redshift bins. Only one of nbins and dz can be given.

• dz (float | None) – Size of redshift bin. Only one of nbins and dz can be given.

Returns:

A list of redshift bin edges.

Raises:

ValueError – If both nbins and dz are given.

Return type:

list[tuple[float, float]]

glass.equal_dens_zbins(z, nz, nbins)

Equal density tomographic redshift bins.

This function subdivides a source redshift distribution into nbins tomographic redshift bins with equal density.

Parameters:

• z (ndarray[tuple[int, ...], dtype[float64]]) – The source redshift distribution. Must be one-dimensional.

• nz (ndarray[tuple[int, ...], dtype[float64]]) – The source redshift distribution. Must be one-dimensional.

• nbins (int) – Number of redshift bins.

Returns:

A list of redshift bin edges.

Return type:

list[tuple[float, float]]

glass.tomo_nz_gausserr(z, nz, sigma_0, zbins)

Tomographic redshift bins with a Gaussian redshift error.

This function takes a _true_ overall source redshift distribution z, nz and returns tomographic source redshift distributions for the tomographic redshift bins given by zbins. It is assumed that sources are assigned a tomographic redshift bin with a Gaussian error [Amara07]. The standard deviation of the Gaussian depends on redshift and is given by sigma(z) = sigma_0*(1 + z).

Parameters:

• z (ndarray[tuple[int, ...], dtype[float64]]) – The true source redshift distribution. Must be one-dimensional.

• nz (ndarray[tuple[int, ...], dtype[float64]]) – The true source redshift distribution. Must be one-dimensional.

• sigma_0 (float) – Redshift error in the tomographic binning at zero redshift.

• zbins (list[tuple[float, float]]) – List of redshift bin edges.

Returns:

The tomographic redshift bins convolved with a gaussian error. Array has a shape (nbins, len(z))

Return type:

ndarray[tuple[int, ...], dtype[float64]]

See also

equal_dens_zbins

produce equal density redshift bins

fixed_zbins

produce redshift bins of fixed size

Visibility

glass.vmap_galactic_ecliptic(nside, galactic=(30, 90), ecliptic=(20, 80))

Visibility map masking galactic and ecliptic plane.

This function returns a visibility map that blocks out stripes for the galactic and ecliptic planes. The location of the stripes is set with optional parameters.

Parameters:

• nside (int) – The NSIDE parameter of the resulting HEALPix map.

• galactic (tuple[float, float]) – The location of the galactic plane in the respective coordinate system.

• ecliptic (tuple[float, float]) – The location of the ecliptic plane in the respective coordinate system.

Returns:

A HEALPix visibility map.

Raises:

• TypeError – If the galactic argument is not a pair of numbers.

• TypeError – If the ecliptic argument is not a pair of numbers.

Return type:

ndarray[tuple[int, ...], dtype[float64]]