cl_to_xi_fullsky

Transform angular power spectra C_ell to real-space correlation functions

File	shear/cl_to_xi_fullsky/cl_to_xi_interface.py
Attribution	CosmoSIS Team
URL

This module transforms angular power spectra C_ell to real-space correlation functions xi(theta) using Legendre polynomial integration. It supports various correlation function types:

• xi+/xi- (spin-2 shear correlations)

• w(theta) (scalar galaxy correlations)

• gamma_t (galaxy-shear cross correlation)

• E/B mode combinations

The module supports both exact calculations at theta points and bin-averaged calculations over theta ranges. It includes high-ell filtering to reduce ringing artifacts.

Assumptions

• ell values have sufficient range

Setup Parameters

Name	Type	Default	Description
xi_type	str		Type of correlation function (‘22’, ‘22+’, ‘22-’, ‘EB’, ‘00’, ‘02’, ‘02+’)
ell_max	int		Maximum ell value to include in transform
bin_avg	bool	False	Whether to use bin-averaged Legendre coefficients
theta_file	str		FITS file containing theta values for measurement
theta_section	str	depends on xi_type	Section name in theta_file to read from
high_l_filter	real	0.75	High-ell filter parameter to reduce ringing (0=off, 1=maximum)
two_thirds_midpoint	bool	True	Use 2/3-weighted midpoint for theta from bin edges
input_section_name	str	depends on xi_type	Section containing input C_ell values
output_section_name	str	depends on xi_type	Section name for output correlation functions
save_name	str		Custom name for saving outputs
theta_min	real	1.0	Minimum theta value in arcmin (if not using theta_file)
theta_max	real	300.0	Maximum theta value in arcmin (if not using theta_file)
n_theta	int	20	Number of theta points (if not using theta_file or bin_avg)
n_theta_bins	int	20	Number of theta bins (if using bin_avg and not theta_file)
theta	real 1d		Specific theta values in arcmin (alternative to min/max/n)
theta_edges	real 1d		Theta bin edges in arcmin (for bin averaging)

Input values

Section	Name	Type	Default	Description
shear_cl	ell	int 1d		Angular multipole values
	nbin	int		Number of redshift bins
	bin_{i}_{j}	real 1d		Shear power spectrum for bins i,j
	sample_a	str		Name identifier for first tomographic sample
	sample_b	str		Name identifier for second tomographic sample
	is_auto	bool		Whether this is an autocorrelation (True) or cross-correlation (False)
shear_cl_bb	ell	int 1d		Angular multipole values for B-modes (if xi_type=’EB’)
	bin_{i}_{j}	real 1d		B-mode shear power spectrum for bins i,j (if xi_type=’EB’)
galaxy_cl	ell	int 1d		Angular multipole values (if xi_type=’00’)
	bin_{i}_{j}	real 1d		Galaxy power spectrum for bins i,j (if xi_type=’00’)
galaxy_shear_cl	ell	int 1d		Angular multipole values (if xi_type=’02’)
	bin_{i}_{j}	real 1d		Galaxy-shear cross power spectrum for bins i,j (if xi_type=’02’)

Output values

Output values

Section	Name	Type	Description
shear_xi_plus	theta	real 1d	Angular separation values in arcmin
	nbin	int	Number of redshift bins
	bin_{i}_{j}	real 1d	xi+ correlation function for bins i,j
	nbin_a	int	Number of redshift bins in first quantity
	nbin_b	int	Number of redshift bins in second quantity
	sample_a	str	Name identifier for first tomographic sample
	sample_b	str	Name identifier for second tomographic sample
	is_auto	bool	Whether this is an autocorrelation (True) or cross-correlation (False)
	cl_section	str	Name of input section that C_ell values were read from
	sep_name	str	Name of the separation variable (‘theta’)
	save_name	str	Custom save name if specified
	bin_avg	bool	Whether bin averaging was used
	theta_edges	real 1d	Theta bin edges in radians (if bin_avg=True)
shear_xi_minus	theta	real 1d	Angular separation values in arcmin
	nbin	int	Number of redshift bins
	bin_{i}_{j}	real 1d	xi- correlation function for bins i,j
	nbin_a	int	Number of redshift bins in first quantity
	nbin_b	int	Number of redshift bins in second quantity
	sample_a	str	Name identifier for first tomographic sample
	sample_b	str	Name identifier for second tomographic sample
	is_auto	bool	Whether this is an autocorrelation (True) or cross-correlation (False)
	cl_section	str	Name of input section that C_ell values were read from
	sep_name	str	Name of the separation variable (‘theta’)
	save_name	str	Custom save name if specified
	bin_avg	bool	Whether bin averaging was used
	theta_edges	real 1d	Theta bin edges in radians (if bin_avg=True)
galaxy_xi	theta	real 1d	Angular separation values in arcmin (if xi_type=’00’)
	bin_{i}_{j}	real 1d	w(theta) correlation function for bins i,j (if xi_type=’00’)
galaxy_shear_xi	theta	real 1d	Angular separation values in arcmin (if xi_type=’02’)
	bin_{i}_{j}	real 1d	gamma_t correlation function for bins i,j (if xi_type=’02’)