cl_to_xi_nicaea¶
Compute WL correlation functions xi+, xi- from C_ell
File |
shear/cl_to_xi_nicaea/nicaea_interface.so |
Attribution |
Martin Kilbinger |
Nicaea Team |
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URL |
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Citations |
The correlation functions are related to the spectra via Bessel functions: \(\xi_{(+/-)}(\theta) = \int_0^\infty C_\ell J_{(0/4)}(\ell \theta) \ell d\ell / 2\pi\)
In this module that integral is done via a Hankel Transform.
This module is a part of the Nicaea code, with the interface written by Niall Maccrann. It avoids the ringing problems of the alternative cl_to_xi code but generates results only on a fixed range in theta .
The output theta values will always be from about 2.0e-07 to 1.0e+04 radians, but only in part of that regime, from about 1 to a few hundred arcmin, will the results be numerically valid. The input ell must include the corresponding range, and will be extrapolated linearlly before that and cubically after it.
Assumptions¶
Input C_ell sufficiently well-sampled over standard pre-defined range
Setup Parameters¶
Name |
Type |
Default |
Description |
|---|---|---|---|
corr_type |
int |
Either 0 (to do shear EE C_ell -> xi+(theta) and xi-(theta)), or 1 (to convert galaxy position C_ell to w(theta)) or 2 (to convert the cross galaxy position-shear C_ell to gamma_t(theta)) |
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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) |
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output_section_name |
str |
Name of the angular correlation function output section (Default: ‘shear_xi’, ‘galaxy_shear_xi’, or ‘galaxy_xi’ depending on corr_type) |
Input values¶
Section |
Name |
Type |
Default |
Description |
|---|---|---|---|---|
input_section_name |
ell |
real 1d |
Sample ell values for input C_ell |
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nbin_a |
int |
The number of redshift bins in the first quantity |
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nbin_b |
int |
The number of redshift bins in the second quantity |
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nbin |
int |
Number of redshift bins used if nbin_a or b not found. |
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bin_i_j |
real 1d |
S 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=0 Only stores j<=i. |
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ximinus_i_j |
real 1d |
xi_minus(theta) bin i and j, only if mode=0. Only stores j<=i. |
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bin_i_j |
real 1d |
w(theta) or gamma_t(theta) for bin i and j, only if mode=1 or 2 respectively. Only stores j<=i. |
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nbin_a |
int |
Number of i tomographic bins |
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nbin_b |
int |
Number of j tomographic bins |