cl_to_corr¶
Compute correlation functions xi+, xi-, w, and gamma_t from C_ell
File |
shear/cl_to_corr/cl_to_corr.py |
Attribution |
CosmoSIS Team |
URL |
The correlation functions are related to the spectra via Bessel functions:
\(\xi_{+}(\theta) = \int_0^\infty C^{ss}_\ell J_{0}(\ell \theta) \ell d\ell / 2\pi\)
\(\xi_{-}(\theta) = \int_0^\infty C^{ss}_\ell J_{4}(\ell \theta) \ell d\ell / 2\pi\)
\(w{-}(\theta) = \int_0^\infty C^{gg}_\ell J_{4}(\ell \theta) \ell d\ell / 2\pi\)
\(\gamma_t(\theta) = \int_0^\infty C^{gs}_\ell J_{(0,4)}(\ell \theta) \ell d\ell / 2\pi\)
where s=shear and g=galaxy position. In this module that integral is done via a Hankel Transform.
Assumptions¶
Input C_ell sufficiently well-sampled over chosen range
Ell and theta values consistently chosen
Setup Parameters¶
Name |
Type |
Default |
Description |
|---|---|---|---|
corr_type |
str |
Either w, gamma, or xi depending which transforms you want |
|
input_section_name |
str |
Name of the angular power spectrum input section. See shear/spectra module. (Default: ‘shear_cl’, ‘galaxy_cl’, or ‘galaxy_shear_cl’ depending on corr_type) |
|
output_section_name |
str |
Name of the angular correlation function output section (Default: ‘shear_xi’, ‘galaxy_xi’, or’galaxy_shear_xi’ depending on corr_type) |
|
n_transform |
int |
8192 |
Number of points in the transform. |
ell_min_extrapolate |
real |
0.0001 |
Minimum value of ell to extrapolate the input ell to in the transform. |
ell_max_extrapolate |
real |
5000000.0 |
Maximum value of ell to extrapolate the input ell to in the transform. |
theta_min |
real |
0.1 |
Minimum value of output theta values to go to, in arcmin |
theta_max |
real |
1000 |
Maximum value of output theta values to go to, in arcmin |
Input values¶
Section |
Name |
Type |
Default |
Description |
|---|---|---|---|---|
input_section_name |
ell |
real 1d |
Sample ell values for input C_ell |
|
nbin_a |
int |
The number of redshift bins in the first quantity |
||
nbin_b |
int |
The number of redshift bins in thesecond quantity |
||
nbin |
int |
Number of redshift bins used if nbin_a or b not found. |
||
bin_{i}_{j} |
real 1d |
C_ell (no l(l+1) factor) for bin i and j. Only need j<=i for modes 0 and 1. |
Output values¶
Section |
Name |
Type |
Description |
|---|---|---|---|
output_section_name |
theta |
real 1d |
Sample theta values for output xi(theta) |
xiplus_i_j |
real 1d |
xi_plus(theta) bin i and j, only if mode=xi Only stores j<=i. |
|
ximinus_i_j |
real 1d |
xi_minus(theta) bin i and j, only if mode=xi. Only stores j<=i. |
|
bin_i_j |
real 1d |
w(theta) or gamma_t(theta) for bin i and j, only if mode=w or gamma respectively. Only stores j<=i. |
|
nbin_a |
int |
Number of i tomographic bins |
|
nbin_b |
int |
Number of j tomographic bins |