tjpcov.clusters_helpers#

Module Contents#

Classes#

MassRichnessRelation

Helper class to hold different mass richness relations

FFTHelper

Cluster covariance needs to use fast fourier transforms in combination
class tjpcov.clusters_helpers.MassRichnessRelation[source]#

Bases: object

Helper class to hold different mass richness relations

static MurataCostanzi(ln_true_mass, h0)[source]#

Uses constants from Murata et al - ArxIv 1707.01907 and Costanzi et al ArxIv 1810.09456v1 to derive the log-normal mass-richness relation

Parameters:

  • ln_true_mass (float) – True mass

  • h0 (float) – Hubble’s constant

Returns:

The parameterized average and spread of the log-normal mass-richness relation

Return type:

tuple of float

class tjpcov.clusters_helpers.FFTHelper(cosmo, z_min, z_max)[source]#

Bases: object

Cluster covariance needs to use fast fourier transforms in combination with numerical approximations to evaluate rapidly oscillating integrals that appear in the calculation of the covariance. These are stored in this helper class.

Constructor for the FFTHelper class

Parameters:

  • cosmo (pyccl.Cosmology) – Input cosmology

  • z_min (float) – Lower bound on redshift integral

  • z_max (float) – Upper bound on redshift integral

bias_fft = 1.4165[source]#
k_min = 0.0001[source]#
k_max = 3[source]#
N = 1024[source]#
_set_fft_params(z_min, z_max)[source]#

The numerical implementation of the FFT needs some values set by some simple calculations. Those are performed here.

See Eqn 7.16 N. Ferreira disseration.

Parameters:

  • z_min (float) – Lower bound on redshift integral

  • z_max (float) – Upper bound on redshift integral

two_fast_algorithm(z1, z2)[source]#

2-FAST algorithm implementation used to evaluate the double bessel integral. See https://arxiv.org/pdf/1709.02401v3.pdf for more details

See Eqn 7.4 of N. Ferreira

Parameters:

  • z1 (float) – Lower redshift bound

  • z2 (float) – Upper redshift bound

Returns:

Numerical approximation of double bessel function

Return type:

float

_I_ell_algorithm(i, ratio)[source]#

Calculating the function M_0_0 the formula below only valid for R <=1, l = 0, formula B2 ASZ and 31 from 2-fast paper https://arxiv.org/pdf/1709.02401v3.pdf

Parameters:

  • i (int) – iteration

  • ratio (float) – Ratio between comoving coordinates

Returns:

Fourier transform of spherical bessel function

Return type:

float