clmm.utils.beta_lens module

General utility functions that are used in multiple modules

clmm.utils.beta_lens.compute_beta(z_src, z_cl, cosmo)[source]

Geometric lensing efficicency

\[\beta = max(0, D_{a,\ ls}/D_{a,\ s})\]

Eq.2 in https://arxiv.org/pdf/1611.03866.pdf

Parameters:

z_src (float, array_like) -- Source galaxy redshift
z_cl (float) -- Galaxy cluster redshift
cosmo (clmm.Cosmology) -- CLMM Cosmology object

Returns:

Geometric lensing efficicency

Return type:

float, array

clmm.utils.beta_lens.compute_beta_s(z_src, z_cl, z_inf, cosmo)[source]

Geometric lensing efficicency ratio

\[\beta_s = \beta(z_{src})/\beta(z_{inf})\]

Parameters:

z_src (float, array_like) -- Source galaxy redshift
z_cl (float) -- Galaxy cluster redshift
z_inf (float) -- Redshift at infinity
cosmo (clmm.Cosmology) -- CLMM Cosmology object

Returns:

Geometric lensing efficicency ratio

Return type:

numpy array

clmm.utils.beta_lens.compute_beta_s_func(z_src, z_cl, z_inf, cosmo, func, *args, **kwargs)[source]

Geometric lensing efficicency ratio times a value of a function

\[\beta_{s}\times \text{func} = \beta_s(z_{src}, z_{cl}, z_{inf}) \times\text{func}(*args,\ **kwargs)\]

Parameters:

z_src (array_like, float, function) -- Information on the background source galaxy redshift(s). Value required depends on z_src_info (see below).
z_cl (float) -- Galaxy cluster redshift
z_inf (float) -- Redshift at infinity
cosmo (clmm.Cosmology) -- CLMM Cosmology object
func (callable) -- A scalar function
*args (positional arguments) -- args to be passed to func
**kwargs (keyword arguments) -- kwargs to be passed to func

Returns:

Geometric lensing efficicency ratio for each source

Return type:

numpy array

clmm.utils.beta_lens.compute_beta_s_mean_from_distribution(z_cl, z_inf, cosmo, zmax=10.0, delta_z_cut=0.1, zmin=None, z_distrib_func=None)[source]

Mean value of the geometric lensing efficicency

\[\left<\beta_s\right> = \frac{\int_{z = z_{min}}^{z_{max}}\beta_s(z)N(z)} {\int_{z = z_{min}}^{z_{max}}N(z)}\]

Parameters:

z_cl (float) -- Galaxy cluster redshift
z_inf (float) -- Redshift at infinity
cosmo (clmm.Cosmology) -- CLMM Cosmology object
zmax (float, optional) -- Maximum redshift to be set as the source of the galaxy when performing the sum. Default: 10
delta_z_cut (float, optional) -- Redshift interval to be summed with $z_{cl}$ to return $z_{min}$. This feature is not used if $z_{min}$ is provided by the user. Default: 0.1
zmin (float, None, optional) -- Minimum redshift to be set as the source of the galaxy when performing the sum. Default: None
z_distrib_func (one-parameter function, optional) -- Redshift distribution function. Default is Chang et al (2013) distribution function.

Returns:

Mean value of the geometric lensing efficicency

Return type:

float

clmm.utils.beta_lens.compute_beta_s_mean_from_weights(z_src, z_cl, z_inf, cosmo, shape_weights)[source]

Mean square value of the geometric lensing efficicency ratio

\[\left<\beta_s\right> =\frac{\sum_i \beta_s(z_i)w_i} {\sum_i w_i}\]

Parameters:

z_src (float, array_like) -- Invididual source galaxies redshift.
z_cl (float) -- Galaxy cluster redshift.
z_inf (float) -- Redshift at infinity.
cosmo (clmm.Cosmology) -- CLMM Cosmology object
shape_weights (float, array_like) -- Individual source galaxies shape weights.If not None, the function uses Eq.(13) fromhttps://arxiv.org/pdf/1611.03866.pdf with evenly distributedweights summing to one.

Returns:

Mean value of the geometric lensing efficicency ratio.

Return type:

float

clmm.utils.beta_lens.compute_beta_s_square_mean_from_distribution(z_cl, z_inf, cosmo, zmax=10.0, delta_z_cut=0.1, zmin=None, z_distrib_func=None)[source]

Mean square value of the geometric lensing efficicency ratio

\[\left<\beta_s^2\right> =\frac{\int_{z = z_{min}}^{z_{max}}\beta_s^2(z)N(z)} {\int_{z = z_{min}}^{z_{max}}N(z)}\]

Parameters:

z_cl (float) -- Galaxy cluster redshift
z_inf (float) -- Redshift at infinity
cosmo (clmm.Cosmology) -- CLMM Cosmology object
zmax (float) -- Minimum redshift to be set as the source of the galaxywhen performing the sum.
delta_z_cut (float) -- Redshift interval to be summed with $z_cl$ to return$zmin$. This feature is not used if $z_min$ is provided by the user.
zmin (float, None, optional) -- Minimum redshift to be set as the source of the galaxy when performing the sum. Default: None
z_distrib_func (one-parameter function, optional) -- Redshift distribution function. Default is Chang et al (2013) distribution function.

Returns:

Mean square value of the geometric lensing efficicency ratio.

Return type:

float

clmm.utils.beta_lens.compute_beta_s_square_mean_from_weights(z_src, z_cl, z_inf, cosmo, shape_weights)[source]

Mean square value of the geometric lensing efficicency ratio

\[\left<\beta_s^2\right> =\frac{\sum_i \beta_s^2(z_i)w_i} {\sum_i w_i}\]

Parameters:

z_src (float, array_like) -- Invididual source galaxies redshift.
z_cl (float) -- Galaxy cluster redshift.
z_inf (float) -- Redshift at infinity.
cosmo (clmm.Cosmology) -- CLMM Cosmology object
shape_weights (float, array_like) -- Individual source galaxies shape weights.

Returns:

Mean square value of the geometric lensing efficicency ratio.

Return type:

float