cbl::modelling::twopt Namespace Reference

The namespace of the two-point correlation function modelling More...

Classes
struct	STR_data_model
	the structure STR_data_model More...
struct	STR_data_HOD
	the STR_data_HOD structure More...
class	Modelling_TwoPointCorrelation
	The class Modelling_TwoPointCorrelation. More...
class	Modelling_TwoPointCorrelation1D
	The class Modelling_TwoPointCorrelation1D. More...
class	Modelling_TwoPointCorrelation1D_angular
	The class Modelling_TwoPointCorrelation1D_angular. More...
class	Modelling_TwoPointCorrelation1D_filtered
	The class Modelling_TwoPointCorrelation1D_filtered. More...
class	Modelling_TwoPointCorrelation1D_monopole
	The class Modelling_TwoPointCorrelation1D_monopole. More...
class	Modelling_TwoPointCorrelation2D
	The class Modelling_TwoPointCorrelation2D. More...
class	Modelling_TwoPointCorrelation2D_cartesian
	The class Modelling_TwoPointCorrelation2D_cartesian. More...
class	Modelling_TwoPointCorrelation2D_polar
	The class Modelling_TwoPointCorrelation2D_polar. More...
class	Modelling_TwoPointCorrelation_deprojected
	The class Modelling_TwoPointCorrelation_deprojected. More...
class	Modelling_TwoPointCorrelation_multipoles
	The class Modelling_TwoPointCorrelation_multipoles. More...
class	Modelling_TwoPointCorrelation_projected
	The class Modelling_TwoPointCorrelation_projected. More...
class	Modelling_TwoPointCorrelation_wedges
	The class Modelling_TwoPointCorrelation_wedges. More...

Functions
std::vector< double >	true_k_mu_AP (const double kk, const double mu, const double alpha_perp, const double alpha_par)
	true k and \(\mu\) power spectrum coordinates as a function of observed ones More...
double	Pk_l (const double kk, const int l, const std::string model, const std::vector< double > parameter, const std::vector< std::shared_ptr< glob::FuncGrid >> pk_interp, const double prec=1.e-5, const double alpha_perp=1., const double alpha_par=1.)
	the multipole of order l of the power spectrum More...
std::vector< double >	Pk_l (const std::vector< double > kk, const int l, const std::string model, const std::vector< double > parameter, const std::vector< std::shared_ptr< glob::FuncGrid >> pk_interp, const double prec=1.e-5, const double alpha_perp=1., const double alpha_par=1.)
	the multipole of order l of the power spectrum More...
cbl::glob::FuncGrid	Xil_interp (const std::vector< double > kk, const int l, const std::string model, const std::vector< double > parameter, const std::vector< std::shared_ptr< glob::FuncGrid >> pk_interp, const double prec=1.e-5, const double alpha_perp=1., const double alpha_par=1.)
	the interpolating function of multipole expansion of the two-point correlation function at a given order l More...
std::vector< std::vector< double > >	Xi_l (const std::vector< double > rr, const int nmultipoles, const std::string model, const std::vector< double > parameter, const std::vector< std::shared_ptr< glob::FuncGrid >> pk_interp, const double prec=1.e-5, const double alpha_perp=1., const double alpha_par=1.)
	the multipole of order l of the two-point correlation function More...
std::vector< double >	Xi_l (const std::vector< double > rr, const std::vector< int > dataset_order, const std::vector< bool > use_pole, const std::string model, const std::vector< double > parameter, const std::vector< std::shared_ptr< glob::FuncGrid >> pk_interp, const double prec=1.e-5, const double alpha_perp=1., const double alpha_par=1.)
	the multipole of order l of the two-point correlation function More...
std::vector< std::vector< double > >	Xi_rppi (const std::vector< double > rp, const std::vector< double > pi, const std::string model, const std::vector< double > parameter, const std::vector< std::shared_ptr< glob::FuncGrid >> pk_interp, const double prec=1.e-5, const double alpha_perp=1., const double alpha_par=1.)
	the cartesian two-point correlation function More...
double	Xi_polar (const double rad_fid, const double mu_fid, const double alpha_perpendicular, const double alpha_parallel, const std::vector< std::shared_ptr< cbl::glob::FuncGrid >> xi_multipoles)
	the polar two-point correlation function More...
std::vector< double >	wp_from_Xi_rppi (const std::vector< double > rp, const double pimax, const std::string model, const std::vector< double > parameter, const std::vector< std::shared_ptr< glob::FuncGrid >> pk_interp, const double prec=1.e-5, const double alpha_perp=1., const double alpha_par=1.)
	the projected two-point correlation function More...
std::vector< std::vector< double > >	damped_Pk_terms (const std::vector< double > kk, const double linear_growth_rate, const double SigmaS, const std::shared_ptr< cbl::glob::FuncGrid > PkDM)
	the power spectrum terms obtained integrating the redshift space 2D power spectrum More...
std::vector< double >	damped_Xi (const std::vector< double > ss, const double bias, const double linear_growth_rate, const double SigmaS, const std::vector< double > kk, const std::shared_ptr< cbl::glob::FuncGrid > PkDM)
	the damped two-point correlation monopole; from Sereno et al. 2015 More...
double	Pkmu (const double kk, const double mu, const std::string model, const std::vector< double > parameter, const std::vector< std::shared_ptr< glob::FuncGrid >> pk_interp, const double alpha_perp=1., const double alpha_par=1.)
	the power spectrum as a function of k and \(\mu\) More...
double	Pkmu_DeWiggled (const double kk, const double mu, const double sigmaNL_perp, const double sigmaNL_par, const double linear_growth_rate, const double bias, const double SigmaS, const std::shared_ptr< cbl::glob::FuncGrid > Pk, const std::shared_ptr< cbl::glob::FuncGrid > Pk_NW)
	the redshift-space galaxy power spectrum, as a function of \(k\) and \(\mu\), predicted by the de-wiggled model More...
double	Pkmu_ModeCoupling (const double kk, const double mu, const double linear_growth_rate, const double bias, const double sigmav, const double AMC, const std::shared_ptr< cbl::glob::FuncGrid > PkLin, const std::shared_ptr< cbl::glob::FuncGrid > PkMC)
	the redshift-space galaxy power spectrum, as a function of \(k\) and \(\mu\), predicted by the mode-coupling model More...
double	Pkmu_dispersion (const double kk, const double mu, const std::string DFoG, const double linear_growth_rate, const double bias, const double sigmav, const std::shared_ptr< cbl::glob::FuncGrid > Pklin)
	the redshift-space galaxy power spectrum, as a function of \(k\) and \(\mu\), predicted by the dispersion model More...
double	Pkmu_Scoccimarro (const double kk, const double mu, const std::string DFoG, const double linear_growth_rate, const double bias, const double sigmav, const std::shared_ptr< cbl::glob::FuncGrid > Pk_DeltaDelta, const std::shared_ptr< cbl::glob::FuncGrid > Pk_DeltaTheta, const std::shared_ptr< cbl::glob::FuncGrid > Pk_ThetaTheta)
	the redshift-space galaxy power spectrum, as a function of \(k\) and \(\mu\), predicted by the Scoccimarro model More...
double	Pkmu_Scoccimarro_fitPezzotta (const double kk, const double mu, const std::string DFoG, const double linear_growth_rate, const double bias, const double sigmav, const double kd, const double kt, const std::shared_ptr< cbl::glob::FuncGrid > Pklin, const std::shared_ptr< cbl::glob::FuncGrid > Pknonlin)
	the redshift-space galaxy power spectrum, as a function of \(k\) and \(\mu\), predicted by the Scoccimarro model More...
double	Pkmu_Scoccimarro_fitBel (const double kk, const double mu, const std::string DFoG, const double linear_growth_rate, const double bias, const double sigmav, const double kd, const double bb, const double a1, const double a2, const double a3, const std::shared_ptr< cbl::glob::FuncGrid > Pklin, const std::shared_ptr< cbl::glob::FuncGrid > Pknonlin)
	the redshift-space galaxy power spectrum, as a function of \(k\) and \(\mu\), predicted by the Scoccimarro model More...
double	Pkmu_TNS (const double kk, const double mu, const std::string DFoG, const double linear_growth_rate, const double bias, const double sigmav, const std::shared_ptr< cbl::glob::FuncGrid > Pk_DeltaDelta, const std::shared_ptr< cbl::glob::FuncGrid > Pk_DeltaTheta, const std::shared_ptr< cbl::glob::FuncGrid > Pk_ThetaTheta, const std::shared_ptr< cbl::glob::FuncGrid > Pk_A11, const std::shared_ptr< cbl::glob::FuncGrid > Pk_A12, const std::shared_ptr< cbl::glob::FuncGrid > Pk_A22, const std::shared_ptr< cbl::glob::FuncGrid > Pk_A23, const std::shared_ptr< cbl::glob::FuncGrid > Pk_A33, const std::shared_ptr< cbl::glob::FuncGrid > Pk_B12, const std::shared_ptr< cbl::glob::FuncGrid > Pk_B13, const std::shared_ptr< cbl::glob::FuncGrid > Pk_B14, const std::shared_ptr< cbl::glob::FuncGrid > Pk_B22, const std::shared_ptr< cbl::glob::FuncGrid > Pk_B23, const std::shared_ptr< cbl::glob::FuncGrid > Pk_B24, const std::shared_ptr< cbl::glob::FuncGrid > Pk_B33, const std::shared_ptr< cbl::glob::FuncGrid > Pk_B34, const std::shared_ptr< cbl::glob::FuncGrid > Pk_B44)
	the redshift-space galaxy power spectrum, as a function of \(k\) and \(\mu\), predicted by the TNS (Taruya, Nishimichi and Saito) model More...
double	Pkmu_eTNS (const double kk, const double mu, const std::string DFoG, const double linear_growth_rate, const double bias, const double bias2, const double sigmav, const double Ncorr, const std::shared_ptr< cbl::glob::FuncGrid > Pk_DeltaDelta, const std::shared_ptr< cbl::glob::FuncGrid > Pk_DeltaTheta, const std::shared_ptr< cbl::glob::FuncGrid > Pk_ThetaTheta, const std::shared_ptr< cbl::glob::FuncGrid > Pk_A11, const std::shared_ptr< cbl::glob::FuncGrid > Pk_A12, const std::shared_ptr< cbl::glob::FuncGrid > Pk_A22, const std::shared_ptr< cbl::glob::FuncGrid > Pk_A23, const std::shared_ptr< cbl::glob::FuncGrid > Pk_A33, const std::shared_ptr< cbl::glob::FuncGrid > Pk_B12, const std::shared_ptr< cbl::glob::FuncGrid > Pk_B13, const std::shared_ptr< cbl::glob::FuncGrid > Pk_B14, const std::shared_ptr< cbl::glob::FuncGrid > Pk_B22, const std::shared_ptr< cbl::glob::FuncGrid > Pk_B23, const std::shared_ptr< cbl::glob::FuncGrid > Pk_B24, const std::shared_ptr< cbl::glob::FuncGrid > Pk_B33, const std::shared_ptr< cbl::glob::FuncGrid > Pk_B34, const std::shared_ptr< cbl::glob::FuncGrid > Pk_B44, const std::shared_ptr< cbl::glob::FuncGrid > Pk_b2d, const std::shared_ptr< cbl::glob::FuncGrid > Pk_b2v, const std::shared_ptr< cbl::glob::FuncGrid > Pk_b22, const std::shared_ptr< cbl::glob::FuncGrid > Pk_bs2d, const std::shared_ptr< cbl::glob::FuncGrid > Pk_bs2v, const std::shared_ptr< cbl::glob::FuncGrid > Pk_b2s2, const std::shared_ptr< cbl::glob::FuncGrid > Pk_bs22, const std::shared_ptr< cbl::glob::FuncGrid > sigma32Pklin)
	the redshift-space galaxy power spectrum, as a function of \(k\) and \(\mu\), predicted by the extended TNS (Taruya, Nishimichi and Saito) model More...
std::vector< double >	xi0_BAO_sigmaNL (const std::vector< double > rad, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	model for the BAO signal in the monopole of the two-point correlation function More...
std::vector< double >	xi0_linear (const std::vector< double > rad, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	model for the monopole of the two-point correlation function More...
std::vector< double >	xi0_linear_LinearPoint (const std::vector< double > rad, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	model for the monopole of the two-point correlation function More...
std::vector< double >	xi0_polynomial_LinearPoint (const std::vector< double > rad, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	model for the monopole of the two-point correlation function More...
std::vector< double >	xi0_linear_sigma8_bias (const std::vector< double > rad, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	model for the monopole of the two-point correlation function in redshift space More...
std::vector< double >	xi0_linear_cosmology (const std::vector< double > rad, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	model for the monopole of the two-point correlation function More...
std::vector< double >	xi0_damped_bias_sigmaz (const std::vector< double > rad, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	the damped two-point correlation monopole; from Sereno et al. 2015 More...
std::vector< double >	xi0_damped_scaling_relation_sigmaz (const std::vector< double > rad, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	the damped two-point correlation monopole; from Sereno et al. 2015 More...
std::vector< double >	xi0_damped_scaling_relation_sigmaz_cosmology (const std::vector< double > rad, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	the damped two-point correlation monopole; from Sereno et al. 2015 More...
std::vector< double >	xi0_linear_sigma8_clusters (const std::vector< double > rad, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	model for the monopole of the two-point correlation function, the bias is computed by the input cluster masses, with only \(sigma_8\) as a free parameter More...
std::vector< double >	xi0_linear_one_cosmo_par_clusters (const std::vector< double > rad, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	model for the monopole of the two-point correlation function, the bias is computed by the input cluster masses, with only \(sigma_8\) as a free parameter More...
std::vector< double >	xi0_linear_two_cosmo_pars_clusters (const std::vector< double > rad, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	model for the monopole of the two-point correlation function, the bias is computed by the input cluster masses, with only \(sigma_8\) as a free parameter More...
std::vector< double >	xi0_linear_cosmology_clusters (const std::vector< double > rad, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	model for the monopole of the two-point correlation function, the bias is computed by the input cluster masses More...
std::vector< double >	xi0_linear_bias_cosmology (const std::vector< double > rad, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	model for the monopole of the two-point correlation function More...
std::vector< double >	xi0_linear_cosmology_clusters_selection_function (const std::vector< double > rad, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	model for the monopole of the redshift-space two-point correlation function of galaxy clusters, considering the selection function More...
std::vector< std::vector< double > >	xi2D_dispersion (const std::vector< double > rp, const std::vector< double > pi, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	model for the 2D two-point correlation function, in Cartesian coordinates More...
std::vector< double >	xiMultipoles (const std::vector< double > rad, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	return multipoles of the two-point correlation function More...
std::vector< double >	xiMultipoles_BAO (const std::vector< double > rad, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	return multipoles of the two-point correlation function, intended for anisotropic BAO measurements (Ross et al. 2017). In only works with monopole and quadrupole. More...
std::vector< double >	xiMultipoles_sigma8_bias (const std::vector< double > rad, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	return multipoles of the two-point correlation function More...
std::vector< std::vector< double > >	xi_Wedges (const std::vector< double > rr, const int nWedges, const std::vector< std::vector< double >> mu_integral_limits, const std::string model, const std::vector< double > parameter, const std::vector< std::shared_ptr< glob::FuncGrid >> pk_interp, const double prec=1.e-5, const double alpha_perp=1, const double alpha_par=1.)
	the model wedges of the two-point correlation function More...
std::vector< double >	xi_Wedges (const std::vector< double > rr, const std::vector< int > dataset_order, const std::vector< std::vector< double >> mu_integral_limits, const std::string model, const std::vector< double > parameter, const std::vector< std::shared_ptr< glob::FuncGrid >> pk_interp, const double prec=1.e-5, const double alpha_perp=1., const double alpha_par=1.)
	the wedge of the two-point correlation function More...
std::vector< double >	xiWedges (const std::vector< double > rad, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	the model wedges of the two-point correlation function More...
std::vector< double >	xiWedges_BAO (const std::vector< double > rad, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	return the wedges of the two-point correlation function, intended for anisotropic BAO measurements More...
Functions of the Halo Occupation Distribution (HOD) models
double	Ncen (const double Mass, const double lgMmin, const double sigmalgM)
	the average number of central galaxies hosted in a dark matter halo of a given mass More...
double	Nsat (const double Mass, const double lgMmin, const double sigmalgM, const double lgM0, const double lgM1, const double alpha)
	the average number of satellite galaxies hosted in a dark matter halo of a given mass More...
double	Navg (const double Mass, const double lgMmin, const double sigmalgM, const double lgM0, const double lgM1, const double alpha)
	the average number of galaxies hosted in a dark matter halo of a given mass More...
double	ng (const double lgMmin, const double sigmalgM, const double lgM0, const double lgM1, const double alpha, const std::shared_ptr< void > inputs)
	the galaxy number density More...
double	bias (const double Mmin, const double sigmalgM, const double M0, const double M1, const double alpha, const std::shared_ptr< void > inputs)
	the mean galaxy bias More...
double	NcNs (const double Mass, const double lgMmin, const double sigmalgM, const double lgM0, const double lgM1, const double alpha)
	the mean number of central-satellite galaxy pairs More...
double	NsNs1 (const double Mass, const double lgMmin, const double sigmalgM, const double lgM0, const double lgM1, const double alpha)
	the mean number of satellite-satellite galaxy pairs More...
double	Pk_cs (const double kk, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	model for the central-satellite part of the 1-halo term of the power spectrum More...
double	Pk_ss (const double kk, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	model for the satellite-satellite part of the 1-halo term of the power spectrum More...
double	Pk_1halo (const double kk, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	model for the 1-halo term of the power spectrum More...
double	Pk_2halo (const double kk, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	model for the 2-halo term of the power spectrum More...
double	Pk_HOD (const double kk, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	HOD model of the power spectrum. More...
std::vector< double >	xi_1halo (const std::vector< double > rad, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	model for the 1-halo term of the monopole of the two-point correlation function More...
std::vector< double >	xi_2halo (const std::vector< double > rad, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	model for the 2-halo term of the monopole of the two-point correlation function More...
std::vector< double >	xi_HOD (const std::vector< double > rad, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	HOD model of the monopole of the two-point correlation function. More...
double	xi_zspace (FunctionVectorVectorPtrVectorRef func, const double rp, const double pi, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	function used to compute the redshift-space monopole of the two-point correlation function More...
double	xi_1halo_zspace (const double rp, const double pi, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	model for the 1-halo term of the redshift-space monopole of the two-point correlation function More...
double	xi_2halo_zspace (const double rp, const double pi, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	model for the 2-halo term of the redshift-space monopole of the two-point correlation function More...
double	xi_HOD_zspace (const double rp, const double pi, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	HOD model of the redshift-space monopole of the two-point correlation function. More...
std::vector< double >	wp_from_xi_approx (FunctionVectorVectorPtrVectorRef func, const std::vector< double > rp, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	function used to compute the projected two-point correlation function More...
std::vector< double >	wp_1halo_approx (const std::vector< double > rp, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	model for the 1-halo term of the projected two-point correlation function More...
std::vector< double >	wp_2halo_approx (const std::vector< double > rp, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	model for the 2-halo term of the projected two-point correlation function More...
std::vector< double >	wp_HOD_approx (const std::vector< double > rp, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	HOD model of the projected two-point correlation function. More...
std::vector< double >	wp_from_xi (FunctionDoubleDoubleDoublePtrVectorRef func, const std::vector< double > rp, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	function used to compute the projected two-point correlation function More...
std::vector< double >	wp_1halo (const std::vector< double > rp, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	model for the 1-halo term of the projected two-point correlation function More...
std::vector< double >	wp_2halo (const std::vector< double > rp, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	model for the 2-halo term of the projected two-point correlation function More...
std::vector< double >	wp_HOD (const std::vector< double > rp, const std::shared_ptr< void > inputs, std::vector< double > &parameter)
	HOD model of the projected two-point correlation function. More...

Detailed Description

The namespace of the two-point correlation function modelling

The modelling::twopt namespace contains all the functions and classes to model the two-point correlation function

Function Documentation

bias()

double cbl::modelling::twopt::bias	(	const double	Mmin,
		const double	sigmalgM,
		const double	M0,
		const double	M1,
		const double	alpha,
		const std::shared_ptr< void >	inputs
	)

the mean galaxy bias

this function computes the mean galaxy bias (e.g. Berlind & Weinberg 2002, van den Bosch et al. 2012):

\[\bar{b}(z) = \frac{1}{\bar{n}_{gal}(z)}\int_{M_{min}}^{M_{max}} <N_{gal}|M>\, b_{halo}(M, z)\, n_{halo}(M, z) \,{\rm d}M\]

where \(\bar{n}_{gal}\) is the mean number density of galaxies, \(<N_{gal}|M>\) is the mean number of galaxies hosted in haloes of mass M, \(b_{halo}\) is the linear halo bias and the halo mass function, \(n_h(M_h, z)=dn/dM_h\), is computed by cosmology::Cosmology::mass_function

Parameters

Mmin	\(M_{min}\): the mass scale at which 50% of haloes host a satellite galaxy
sigmalgM	\(\sigma_{\log M_h}\): transition width reflecting the scatter in the luminosity-halo mass relation
M0	\(M_0\): the cutoff mass
M1	\(M_1\): the amplitude of the power law
alpha	\(\alpha\): the slope of the power law
inputs	pointer to the structure that contains the fixed input data used to construct the model

Returns

the mean galaxy bias

Examples

lognormal.cpp.

Definition at line 1026 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

damped_Pk_terms()

std::vector< std::vector< double > > cbl::modelling::twopt::damped_Pk_terms	(	const std::vector< double >	kk,
		const double	linear_growth_rate,
		const double	SigmaS,
		const std::shared_ptr< cbl::glob::FuncGrid >	PkDM
	)

the power spectrum terms obtained integrating the redshift space 2D power spectrum

the function returns the analytic solutions of the integral of the redshift space 2D power spectrum along \(\mu\):

\(P(k,\mu) = P_\mathrm{DM}(k) (b+f\mu^2)^2 \exp(-k^2\mu^2\sigma^2)\).

Solutions are :

\[ P'(k) = P_\mathrm{DM}(k) \frac{\sqrt{\pi}}{2 k \sigma} \mathrm{erf}(k\sigma) ; \\ P''(k) = \frac{f}{(k\sigma)^3} P_\mathrm{DM}(k) \left[\frac{\sqrt{\pi}}{2}\mathrm{erf}(k\sigma) -k\sigma\exp(-k^2\sigma^2)\right] ; \\ P'''(k) = \frac{f^2}{(k\sigma)^5}P_\mathrm{DM}(k) \left\{ \frac{3\sqrt{\pi}}{8}\mathrm{erf}(k\sigma) \right. \\ \left. - \frac{k\sigma}{4}\left[2(k\sigma)^2+3\right]\exp(-k^2\sigma^2)\right\} . \\ \]

Parameters

kk	the binned wave vector modules
linear_growth_rate	the linear growth rate
SigmaS	streaming scale
PkDM	dark matter power spectrum interpolator

Returns

the damped two-point correlation monopole.

Definition at line 560 of file ModelFunction_TwoPointCorrelation.cpp.

damped_Xi()

std::vector< double > cbl::modelling::twopt::damped_Xi	(	const std::vector< double >	ss,
		const double	bias,
		const double	linear_growth_rate,
		const double	SigmaS,
		const std::vector< double >	kk,
		const std::shared_ptr< cbl::glob::FuncGrid >	PkDM
	)

the damped two-point correlation monopole; from Sereno et al. 2015

The function computes the damped two-point correlation monopole:

\(\xi(s) = b^2 \xi'(s) + b \xi''(s) + \xi'''(s) \, ;\)

where b is the linear bias and the terms \(\xi'(s)\), \(\xi''(s)\), \(\xi'''(s)\) are the Fourier anti-transform of the power spectrum terms obtained integrating the redshift space 2D power spectrum along \(\mu\) (see cbl::modelling::twopt.:damped_Pk_terms).

Parameters

ss	vector of scales
bias	the linear bias
linear_growth_rate	the linear growth rate
SigmaS	streaming scale
kk	the binned wave vector modules
PkDM	dark matter power spectrum interpolator

Returns

the damped two-point correlation monopole.

Definition at line 583 of file ModelFunction_TwoPointCorrelation.cpp.

Navg()

double cbl::modelling::twopt::Navg	(	const double	Mass,
		const double	lgMmin,
		const double	sigmalgM,
		const double	lgM0,
		const double	lgM1,
		const double	alpha
	)

the average number of galaxies hosted in a dark matter halo of a given mass

the function computes the average number of galaxies hosted in a dark matter halo of mass \(M_h\) as follows:

\[N_{gal}(M_h)\equiv<N_{gal}|M_h> = <N_{cen}|M_h> + <N_{sat}|M_h>\]

where \(<N_{cen}|M_h>\) and \(<N_{sat}|M_h>\) are computed by cbl::modelling::twopt::Ncen and cbl::modelling::twopt::Nsat, respectively

Parameters

Mass	the mass of the hosting dark matter halo
lgMmin	\(logM_{min}\): the the logarithm of the mass scale at which 50% of haloes host a satellite galaxy
sigmalgM	\(\sigma_{\log M_h}\): transition width reflecting the scatter in the luminosity-halo mass relation
lgM0	\(logM_0\): the logarithm of the cutoff mass
lgM1	\(logM_1\): the logarithm of the amplitude of the power law
alpha	\(\alpha\): the the slope of the power law

Returns

\(N_{gal}(M_h)\)

Definition at line 1000 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

Ncen()

double cbl::modelling::twopt::Ncen	(	const double	Mass,
		const double	lgMmin,
		const double	sigmalgM
	)

the average number of central galaxies hosted in a dark matter halo of a given mass

this function computes the average number of central galaxies hosted in a dark matter halo of mass \(M_h\) as follows (Harikane et al. 2017; see also e.g. Zheng et al. 2005 for a similar formalism):

\[N_{cen}(M_h)\equiv<N_{cen}|M_h>=\frac{1}{2}\left[1+{\rm erf}\left(\frac{\log M_h-\log M_{min}}{\sqrt{2}\sigma_{\log M_h}}\right)\right]\]

Parameters

Mass	the mass of the hosting dark matter halo
lgMmin	\(logM_{min}\): the logarithm of the mass scale at which 50% of haloes host a central galaxy
sigmalgM	\(\sigma_{\log M_h}\): transition width reflecting the scatter in the luminosity-halo mass relation

Returns

\(N_{cen}(M_h)\)

Definition at line 980 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

NcNs()

double cbl::modelling::twopt::NcNs	(	const double	Mass,
		const double	lgMmin,
		const double	sigmalgM,
		const double	lgM0,
		const double	lgM1,
		const double	alpha
	)

the mean number of central-satellite galaxy pairs

this function computes the mean number of central-satellite galaxy pairs, \(<N_{cen}N_{sat}>(M_h)\), as follows:

\[<N_{cen}N_{sat}>(M_h)=N_{cen}(M_h)N_{sat}(M_h)\]

where the average number of central and satellite galaxies, \(N_{cen}\) and \(N_{sat}\) are computed by cbl::modelling::twopt::Ncen and cbl::modelling::twopt::Nsat, respectively

Parameters

Mass	the mass of the hosting dark matter halo
lgMmin	\(logM_{min}\): the logarithm of the mass scale at which 50% of haloes host a satellite galaxy
sigmalgM	\(\sigma_{\log M_h}\): transition width reflecting the scatter in the luminosity-halo mass relation
lgM0	\(logM_0\): the logarithm of the cutoff mass
lgM1	\(logM_1\): the logarithm of the amplitude of the power law
alpha	\(\alpha\): the slope of the power law

Returns

\(<N_{cen}N_{sat}>(M_h)\)

Warning

The current implementation is valid only for Poisson distribution of the satellite galaxy's distribution (see e.g. Harikane et al 2016)

Definition at line 1053 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

ng()

double cbl::modelling::twopt::ng	(	const double	lgMmin,
		const double	sigmalgM,
		const double	lgM0,
		const double	lgM1,
		const double	alpha,
		const std::shared_ptr< void >	inputs
	)

the galaxy number density

this function computes the galaxy number density as follows:

\[n_{gal}(z) = \int_{logM_{min}}^{logM_{max}}n_{h, interp}(M_h, z)N_{gal} (M_h)M_hln(10)\,{\rm d}log(M_h)\]

where \(n_{h, interp}(M_h, z)\) is an interpolation of the halo mass function cosmology::Cosmology::mass_function, and the average number of galaxies hosted in a dark matter halo of a given mass, \(N_{gal}(M_h)\), is computed by cbl::modelling::twopt::Navg

The equation above was obtained from the original expression for \(n_{gal}(z)\) using a change of variable from \(dM_h\) to \(dlogM_h\). The original expression for \(n_{gal}(z)\) is the following:

\[n_{gal}(z) = \int_0^{M_{max}}n_h(M_h, z)N_{gal}(M_h)\,{\rm d}M_h\]

Parameters

lgMmin	\(logM_{min}\): the logarithm of the mass scale at which 50% of haloes host a satellite galaxy
sigmalgM	\(\sigma_{\log M_h}\): transition width reflecting the scatter in the luminosity-halo mass relation
lgM0	\(logM_0\): the logarithm of the cutoff mass
lgM1	\(logM_1\): the logarithm of the amplitude of the power law
alpha	\(\alpha\): the slope of the power law
inputs	pointer to the structure that contains the fixed input data used to construct the model

Returns

the galaxy number density

Warning

in the current implementation, the integral is actually computed in the range \(10^{10} -10^{16}\) solar masses, using GSL_integrate_qag

Definition at line 1009 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

Nsat()

double cbl::modelling::twopt::Nsat	(	const double	Mass,
		const double	lgMmin,
		const double	sigmalgM,
		const double	lgM0,
		const double	lgM1,
		const double	alpha
	)

the average number of satellite galaxies hosted in a dark matter halo of a given mass

this function computes the average number of satellite galaxies hosted in a dark matter halo of mass \(M_h\) as follows (Harikane et al. 2017; see also e.g. Zheng et al. 2005 for a similar formalism):

\[N_{sat}(M_h)\equiv<N_{sat}|M_h> = N_{cen}(M_h)\left(\frac{M_h-M_0}{M_1}\right)^\alpha\]

where \(N_{cen}\) is computed by cbl::modelling::twopt::Ncen

Parameters

Mass	the mass of the hosting dark matter halo
lgMmin	\(logM_{min}\): the logarithm of the mass scale at which 50% of haloes host a satellite galaxy
sigmalgM	\(\sigma_{\log M_h}\): transition width reflecting the scatter in the luminosity-halo mass relation
lgM0	\(logM_0\): the the logarithm of the cutoff mass
lgM1	\(logM_1\): the the logarithm of the amplitude of the power law
alpha	\(\alpha\): the slope of the power law

Returns

\(N_{sat}(M_h)\)

Definition at line 990 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

NsNs1()

double cbl::modelling::twopt::NsNs1	(	const double	Mass,
		const double	lgMmin,
		const double	sigmalgM,
		const double	lgM0,
		const double	lgM1,
		const double	alpha
	)

the mean number of satellite-satellite galaxy pairs

this function computes the mean number of satellite-satellite galaxy pairs, \(<N_{sat}(N_{sat}-1)>(M_h)\), as follows:

\[<N_{sat}(N_{sat}-1)>(M_h)=N_{sat}^2(M_h)\]

where the average number of satellite galaxies, \(N_{sat}\) are computed by cbl::modelling::twopt::Nsat

Parameters

Mass	the mass of the hosting dark matter halo
lgMmin	\(logM_{min}\): the logarithm of the mass scale at which 50% of haloes host a satellite galaxy
sigmalgM	\(\sigma_{\log M_h}\): transition width reflecting the scatter in the luminosity-halo mass relation
lgM0	\(logM_0\): the logarithm of the cutoff mass
lgM1	\(logM_1\): the logarithm of the amplitude of the power law
alpha	\(\alpha\): the slope of the power law

Returns

\(<N_{sat}(N_{sat}-1)>(M_h)\)

Warning

The current implementation is valid only for Poisson distribution of the satellite galaxy's distribution (see e.g. Harikane et al 2016)

Definition at line 1062 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

Pk_1halo()

double cbl::modelling::twopt::Pk_1halo	(	const double	kk,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

model for the 1-halo term of the power spectrum

this function computes the 1-halo term of power spectrum as follows:

\[P_{1halo}(k, z) = P_{cs}(k, z)+P_{ss}(k, z)\]

where the central-satellite term, \(P_{cs}(k, z)\), and the satellite-satellite term, \(P_{ss}(k, z)\) are computed by cbl::modelling::twopt::Pk_cs and cbl::modelling::twopt::Pk_ss, respectively

Parameters

kk	the wave vector module at which the model is computed
inputs	pointer to the structure that contains the fixed input data used to construct the model
parameter	vector containing the model parameters

Returns

the 1-halo term of the power spectrum

Definition at line 1125 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

Pk_2halo()

double cbl::modelling::twopt::Pk_2halo	(	const double	kk,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

model for the 2-halo term of the power spectrum

this function computes the 2-halo term of the power spectrum as follows:

\[P_{2halo}(k, z) = P_{m, interp}(k, z) \left[\frac{1}{n_{gal}(z)} \int_{log(M_{min})}^{log(M_{max})} N_{gal}(M_h)\,n_{h, interp}(M_h, z) \,b_{h, interp}(M_h, z)\,\tilde{u}_h(k, M_h, z)\,M_hln(10){\rm d}log(M_h)\right]^2\]

where \(P_{m, interp}(k, z)\) is an interpolation of the matter power spectrum cbl::cosmology::Cosmology::Pk, the galaxy number density \(n_{gal}(z)\) is computed by cbl::modelling::twopt::ng, the average number of galaxies hosted in a dark matter halo of a given mass, \(N_{gal}(M_h)\), is computed by cbl::modelling::twopt::Navg, \(n_{h, interp}(M_h, z)\) is an interpolation of the halo mass function cosmology::Cosmology::mass_function, \(b_{h, interp}(M_h, z)\) is an interpolation of the halo bias cosmology::Cosmology::bias_halo, and the Fourier transform of the density profile, \(\tilde{u}_h(k, M_h, z)\), is computed by cbl::cosmology::Cosmology::density_profile_FourierSpace

The equation above was obtained from the original expression for \(P_{2halo}(k, z)\) using a change of variable from \(dM_h\) to \(dlogM_h\). The original expression for \(P_{2halo}(k, z)\) (e.g. Harikane et al. 2016) is the following:

\[P_{2halo}(k, z) = P_m(k, z) \left[\frac{1}{n_{gal}(z)} \int_{M_{min}}^{M_{max}} N_{gal}(M_h)\,n_h(M_h, z)\,b_h(M, z)\,\tilde{u}_h(k, M_h, z)\,{\rm d} M_h\right]^2\]

Parameters

kk	the wave vector module at which the model is computed
inputs	pointer to the structure that contains the fixed input data used to construct the model
parameter	vector containing the model parameters

Returns

the 2-halo term of the power spectrum

Definition at line 1134 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

Pk_cs()

double cbl::modelling::twopt::Pk_cs	(	const double	kk,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

model for the central-satellite part of the 1-halo term of the power spectrum

this function computes the central-satellite part of the 1-halo term of power spectrum as follows:

\[P_{cs}(k, z) = \frac{2}{n_{gal}^2(z)} \int_{log(M_{min})}^{log(M_{max})} n_{h, interp}(M_h, z)\,<N_{cen}N_{sat}>(M_h)\, \tilde{u}_h(k, M_h, z)\,M_h\,ln(10)\,{\rm d}log(M_h)\]

where the galaxy number density \(n_{gal}(z)\) is computed by cbl::modelling::twopt::ng, \(n_{h, interp}(M_h, z)\) is an interpolation of the halo mass function cosmology::Cosmology::mass_function, \(<N_{cen}N_{sat}>(M_h)\) is computed by cbl::modelling::twopt::NcNs, and the Fourier transform of the halo density profile \(\tilde{u}_h(k, M_h, z)\) is computed by cbl::cosmology::Cosmology::density_profile_FourierSpace

The equation above was obtained from the original expression for \(P_{cs}(k, z)\) using a change of variable from \(dM_h\) to \(dlogM_h\). The original expression for \(P_{cs}(k, z)\) (e.g. Harikane et al. 2016) is the following:

\[P_{cs}(k, z) = \frac{2}{n_{gal}^2(z)} \int_{M_{min}}^{M_{max}} <N_{cen}N_{sat}>(M_h)\,n_h(M_h, z)\,\tilde{u}_h(k, M_h, z)\,{\rm d} M_h\]

Parameters

kk	the wave vector module at which the model is computed
inputs	pointer to the structure that contains the fixed input data used to construct the model
parameter	vector containing the model parameters

Returns

the central-satellite part of the 1-halo term of the power spectrum

Definition at line 1071 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

Pk_HOD()

double cbl::modelling::twopt::Pk_HOD	(	const double	kk,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

HOD model of the power spectrum.

this function computes the power spectrum as follows:

\[P(k, z) = P_{1halo}(k, z)+P_{2halo}(k, z)\]

where the 1-halo and 2-halo terms of the power spectrum, \(P_{1halo}(k, z)\) and \(P_{2halo}(k, z)\) are computed by cbl::modelling::twopt::Pk_1halo and cbl::modelling::twopt::Pk_2halo, respectively

Parameters

kk	the wave vector module at which the model is computed
inputs	pointer to the structure that contains the fixed input data used to construct the model
parameter	vector containing the model parameters

Returns

the HOD model of the power spectrum

Definition at line 1160 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

Pk_l() [1/2]

double cbl::modelling::twopt::Pk_l	(	const double	kk,
		const int	l,
		const std::string	model,
		const std::vector< double >	parameter,
		const std::vector< std::shared_ptr< glob::FuncGrid >>	pk_interp,
		const double	prec = 1.e-5,
		const double	alpha_perp = 1.,
		const double	alpha_par = 1.
	)

the multipole of order l of the power spectrum

The function computes the legendre polynomial expansion of the \(P(k, \mu)\):

\[ P_l(k) = \frac{2l+1}{2} \int_{-1}^{1} \mathrm{d}\mu P(k, \mu) L_l(\mu) \]

where \(l\) is the order of the expansion and \(L_l(\mu)\) is the Legendere polynomial of order \(l\); \(P(k, \mu)\) is computed by cbl::modelling::twopt::Pkmu

Parameters

kk	the wave vector module
l	the order of the expansion
model	the \(P(k,\mu)\) model
parameter	vector containing parameter values
pk_interp	vector containing power spectrum interpolating functions
prec	the integral precision
alpha_perp	the shift transverse to the l.o.s.
alpha_par	the shift parallel to the l.o.s.

Returns

the multipole expansion of \(P(k, \mu)\) at given \(k\)

Definition at line 403 of file ModelFunction_TwoPointCorrelation.cpp.

Pk_l() [2/2]

std::vector< double > cbl::modelling::twopt::Pk_l	(	const std::vector< double >	kk,
		const int	l,
		const std::string	model,
		const std::vector< double >	parameter,
		const std::vector< std::shared_ptr< glob::FuncGrid >>	pk_interp,
		const double	prec = 1.e-5,
		const double	alpha_perp = 1.,
		const double	alpha_par = 1.
	)

the multipole of order l of the power spectrum

The function computes the legendre polynomial expansion of the \(P(k, \mu)\):

\[ P_l(k) = \frac{2l+1}{2} \int_{-1}^{1} \mathrm{d}\mu P(k, \mu) L_l(\mu) \]

where \(l\) is the order of the expansion and \(L_l(\mu)\) is the Legendere polynomial of order \(l\); \(P(k, \mu)\) is computed by cbl::modelling::twopt::Pkmu

Parameters

kk	the wave vector module vector
l	the order of the expansion
model	the \(P(k,\mu)\) model
parameter	vector containing parameter values
pk_interp	vector containing power spectrum interpolating functions
prec	the integral precision
alpha_perp	the shift transverse to the l.o.s.
alpha_par	the shift parallel to the l.o.s.

Returns

the multipole expansion of \(P(k, \mu)\) at given \(k\)

Definition at line 416 of file ModelFunction_TwoPointCorrelation.cpp.

Pk_ss()

double cbl::modelling::twopt::Pk_ss	(	const double	kk,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

model for the satellite-satellite part of the 1-halo term of the power spectrum

this function computes the satellite-satellite part of the 1-halo term of power spectrum as follows

\[P_{ss}(k, z) = \frac{1}{n_{gal}^2(z)} \int_{log(M_{min})}^{log(M_{max})} n_{h, interp}(M_h, z)\,<N_{sat}(N_{sat}-1)>(M_h) \,{\tilde{u}_h}^2(k, M_h, z)\,M_hln(10){\rm d}log(M_h)\]

where the galaxy number density \(n_{gal}(z)\) is computed by cbl::modelling::twopt::ng, \(n_{h, interp}(M_h, z)\) is an interpolation of the halo mass function cosmology::Cosmology::mass_function, \(<N_{sat}(N_{sat}-1)>(M_h)\) is computed by cbl::modelling::twopt::NsNs1, and the Fourier transform of the halo density profile \(\tilde{u}_h(k, M_h, z)\) is computed by cbl::cosmology::Cosmology::density_profile_FourierSpace

The equation above was obtained from the original expression for \(P_{ss}(k, z)\) using a change of variable from \(dM_h\) to \(dlogM_h\). The original expression for \(P_{ss}(k, z)\) (e.g. Harikane et al. 2016) is the following:

\[P_{ss}(k, z) = \frac{1}{n_{gal}^2(z)} \int_{M_{min}}^{M_{max}} <N_{sat}(N_{sat}-1)>(M_h)\,n_h(M_h, z)\,\tilde{u}_h^2(k, M_h, z)\,{\rm d} M_h\]

Parameters

kk	the wave vector module at which the model is computed
inputs	pointer to the structure that contains the fixed input data used to construct the model
parameter	vector containing the model parameters

Returns

the satellite-satellite part of the 1-halo term of the power spectrum

Definition at line 1098 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

Pkmu()

double cbl::modelling::twopt::Pkmu	(	const double	kk,
		const double	mu,
		const std::string	model,
		const std::vector< double >	parameter,
		const std::vector< std::shared_ptr< glob::FuncGrid >>	pk_interp,
		const double	alpha_perp = 1.,
		const double	alpha_par = 1.
	)

the power spectrum as a function of k and \(\mu\)

this function computes the redshift-space power spectrum:

\[ \frac{P(k', \mu')}{\alpha_\perp^2\alpha_\parallel} \]

where

\[ k' = \frac{k}{\alpha_\perp} \sqrt{1+\mu^2 \left[ \left( \frac{\alpha_\parallel}{\alpha_\perp}\right)^{-2}-1 \right]} \, , \]

\[ \mu' = \mu\frac{\alpha_\perp}{\alpha_\parallel} \frac{1}{\sqrt{1+\mu^2\left[\left( \frac{\alpha_\parallel}{\alpha_\perp} \right)^{-2}-1\right]}} \, , \]

with one of the following models:

• the dispersion + de-wiggled model, implemented in cbl::modelling::twopt::Pkmu_DeWiggled
• the dispersion + mode-coupling model, implemented in cbl::modelling::twopt::Pkmu_ModeCoupling
• the dispersion model with either Gaussian or Lorentzian damping, implemented in cbl::modelling::twopt::Pkmu_dispersion
• the Scoccimarro model with either Gaussian or Lorentzian damping, implemented in cbl::modelling::twopt::Pkmu_Scoccimarro, cbl::modelling::twopt::Pkmu_Scoccimarro_fitPezzotta and cbl::modelling::twopt::Pkmu_Scoccimarro_fitBel
• the TNS model with either Gaussian or Lorentzian damping, implemented in cbl::modelling::twopt::Pkmu_TNS
• the extended model with either Gaussian or Lorentzian damping, implemented in cbl::modelling::twopt::Pkmu_eTNS

The Alcock-Paczynski term has been introduced following Ballinger et al. 1998, (https://arxiv.org/pdf/astro-ph/9605017.pdf), Beutler et al. 2016, sec 5.2 (https://arxiv.org/pdf/1607.03150.pdf)

The above models may differ for both the redshit-space distortions and the non-linear power spectrum implementation, and may have different numbers of free parameters.

Parameters

kk	the true wave vector module, \(k'\)
mu	the true line-of-sight cosine. \(\mu'\)
model	the anisotropic power spectrum model; the possible options are: dispersion_Gauss, dispersion_Lorentz, dispersion_dewiggled, dispersion_modecoupling, Scoccimarro_Gauss, Scoccimarro_Lorentz Scoccimarro_Pezzotta_Gauss, Scoccimarro_Pezzotta_Lorentz, Scoccimarro_Bel_Gauss, Scoccimarro_Bel_Lorentz, TNS_Gauss, TNS_Lorentz, eTNS_Gauss, eTNS_Lorentz
parameter	vector containing parameter values
pk_interp	vector containing power spectrum interpolating functions
alpha_perp	the shift transverse to the l.o.s.
alpha_par	the shift parallel to the l.o.s.

Returns

\( \frac{P(k', \mu')}{\alpha_\perp^2\alpha_\parallel} \)

Definition at line 302 of file ModelFunction_TwoPointCorrelation.cpp.

Pkmu_DeWiggled()

double cbl::modelling::twopt::Pkmu_DeWiggled	(	const double	kk,
		const double	mu,
		const double	sigmaNL_perp,
		const double	sigmaNL_par,
		const double	linear_growth_rate,
		const double	bias,
		const double	SigmaS,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_NW
	)

the redshift-space galaxy power spectrum, as a function of \(k\) and \(\mu\), predicted by the de-wiggled model

this function computes the redshift-space BAO-damped power spectrum model \(P(k, \mu)\) (see e.g. Beutler et al. 2016 https://arxiv.org/pdf/1607.03149.pdf); Vargas-Magana et al. 2018 https://arxiv.org/pdf/1610.03506.pdf):

\[ P(k, \mu) = \left(1+\beta\mu^2 \right)^2 \left( \frac{1}{1+\left(kf\Sigma_S\mu\right)^2} \right)^2 P_{NL}(k) \]

where

\[ P_{NL}(k) = b^2 \left\{ \left[ P_{lin}(k) - P_{nw}(k) \right] e^{-k^2\Sigma_{NL}^2}+P_{nw}(k) \right\} , \]

\(\mu = k_{\parallel} / k\), \(P_{lin}\), \(P_{nw}\) are the linear and the de-wiggled power spectra, respectively (Eisenstein et al. 1998), and \(\beta = f/b\) with \(f\) the linear growth rate and \(b\) the bias, and \(\Sigma_S\) is the streaming scale that parameterises the Fingers of God effect at small scales. The BAO damping is parametrised via \(\Sigma^2_{NL} = 0.5 (1-\mu'^2)\Sigma^2_{\perp}+\mu'^2\Sigma^2_{\parallel} \), where \(\Sigma_{\perp}\) and \(\Sigma_{\parallel}\) are the damping term in the transverse and parallel directions to the line of sight, respectively.

Parameters

kk	the wave vector module
mu	the line of sight cosine
sigmaNL_perp	the damping in the direction transverse to the l.o.s.
sigmaNL_par	the damping in the direction parallel to the l.o.s.
linear_growth_rate	the linear growth rate
bias	the linear bias
SigmaS	streaming scale
Pk	linear power spectrum interpolator
Pk_NW	de-wiggled power spectrum interpolator

Returns

\(P(k, \mu)\)

Definition at line 57 of file ModelFunction_TwoPointCorrelation.cpp.

Pkmu_dispersion()

double cbl::modelling::twopt::Pkmu_dispersion	(	const double	kk,
		const double	mu,
		const std::string	DFoG,
		const double	linear_growth_rate,
		const double	bias,
		const double	sigmav,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pklin
	)

the redshift-space galaxy power spectrum, as a function of \(k\) and \(\mu\), predicted by the dispersion model

this function computes the redshift-space power spectrum \(P(k, \mu)\) for the so-called dispersion model (see e.g. Pezzotta et al. 2017 https://arxiv.org/abs/1612.05645):

\[ P(k, \mu) = D_{FoG}(k, \mu, f, \sigma_v)\left(1+\frac{f}{b}\mu^2\right)^2b^2P^{lin}(k) \]

where \(f\) is the linear growth rate, \(b\) is the linear galaxy bias, \(\mu\) is the cosine of the angle between the line-of-sight and the comoving separation, \(P^{lin}(k')\) is the real-space matter power spectrum, which is computed by cbl::cosmology::Cosmology::Pk_matter, and \(D_{FoG}\) is a damping factor used to model the random peculiar motions at small scales, which can be either Gaussian:

\[ D_{FoG}(k, \mu, f, \sigma_v) = e^{-k^2\mu^2f^2\sigma_v^2} \]

or Lorentzian:

\[ D_{FoG}(k, \mu, f, \sigma_v) = \frac{1}{1+k^2\mu^2f^2\sigma_v^2} \]

Author

J.E. Garcia-Farieta

joega.nosp@m.rcia.nosp@m.fa@un.nosp@m.al.e.nosp@m.du.co

Parameters

kk	the wave vector module
mu	the line of sight cosine
DFoG	the damping factor (Gaussian or Lorentzian)
linear_growth_rate	the linear growth rate
bias	the linear bias
sigmav	the streaming scale
Pklin	linear power spectrum interpolator

Returns

\(P(k, \mu)\)

Definition at line 94 of file ModelFunction_TwoPointCorrelation.cpp.

Pkmu_eTNS()

double cbl::modelling::twopt::Pkmu_eTNS	(	const double	kk,
		const double	mu,
		const std::string	DFoG,
		const double	linear_growth_rate,
		const double	bias,
		const double	bias2,
		const double	sigmav,
		const double	Ncorr,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_DeltaDelta,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_DeltaTheta,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_ThetaTheta,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_A11,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_A12,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_A22,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_A23,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_A33,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_B12,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_B13,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_B14,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_B22,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_B23,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_B24,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_B33,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_B34,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_B44,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_b2d,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_b2v,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_b22,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_bs2d,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_bs2v,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_b2s2,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_bs22,
		const std::shared_ptr< cbl::glob::FuncGrid >	sigma32Pklin
	)

the redshift-space galaxy power spectrum, as a function of \(k\) and \(\mu\), predicted by the extended TNS (Taruya, Nishimichi and Saito) model

this function computes the so-called extended TNS redshift-space power spectrum \(P(k, \mu)\) (see e.g. Beutler et al. 2014 https://arxiv.org/abs/1312.4611; Gil-Marìn et al. 2014 https://arxiv.org/abs/1407.1836; de la Torre et al. https://arxiv.org/abs/1612.05647) which is computed in 1-loop aproximation using (standard) Perturbation Theory (Taruya et al. 2010 https://arxiv.org/abs/1006.0699; Taruya et al. 2013 https://arxiv.org/abs/1301.3624; McDonald and Roy 2019 https://arxiv.org/abs/0902.0991):

\[ P(k, \mu) = D_{FoG}(k, \mu, f, \sigma_v)\left[P_{\mathrm{g}, \delta \delta}(k) +2 f \mu^{2} P_{\mathrm{g}, \delta \theta}(k)+f^{2} \mu^{4} P_{\theta \theta}(k) + b_{1}^{3} A(k, \mu, f/b_{1})+b_{1}^{4} B(k, \mu, f/b_{1})\right] \]

where

\[ P_{\mathrm{g}, \delta \delta}(k) = b_{1}^{2} P_{\delta \delta}(k)+2 b_{2} b_{1} P_{b 2, \delta}(k)+2 b_{s^2} b_{1} P_{b s 2, \delta}(k) \\ +2 b_{3 \mathrm{nl}} b_{1} \sigma_{3}^{2}(k) P_{\mathrm{m}}^{\mathrm{lin}}(k)+b_{2}^{2} P_{b 22}(k) \\ +2 b_{2} b_{s^2} P_{b 2 s 2}(k)+b_{s^2}^{2} P_{b s 22}(k)+N \]

\[ P_{\mathrm{g}, \delta \theta}(k) = b_{1} P_{\delta \theta}(k)+b_{2} P_{b 2, \theta}(k)+b_{s^2} P_{b s 2, \theta}(k) \\ +b_{3 \mathrm{nl}} \sigma_{3}^{2}(k) P_{\mathrm{m}}^{\mathrm{lin}}(k) \]

and

\[ A(k, \mu ; f) = j_{1} \int d^{3} r\, e^{i \boldsymbol{k} \cdot \boldsymbol{r}}\left\langle A_{1} A_{2} A_{3}\right\rangle_{c} = k \mu f \int \frac{d^{3} p}{(2 \pi)^{3}} \frac{p_{z}}{p^{2}}\left\{B_{\sigma}(\boldsymbol{p}, \boldsymbol{k}-\boldsymbol{p},-\boldsymbol{k}) - B_{\sigma}(\boldsymbol{p}, \boldsymbol{k},-\boldsymbol{k}-\boldsymbol{p})\right\} \, , \]

\[ B(k, \mu ; f) = j_{1}^{2} \int d^{3} r\, e^{i \boldsymbol{k} \cdot \boldsymbol{r}}\left\langle A_{1} A_{2}\right\rangle_{c}\left\langle A_{1} A_{3}\right\rangle_{c} = (k \mu f)^{2} \int \frac{d^{3} p}{(2 \pi)^{3}} F_{\sigma}(\boldsymbol{p}) F_{\sigma}(\boldsymbol{k}-\boldsymbol{p}) \, , \]

\[ b_{s^2} = -\frac{4}{7}(b_1-1)\, , \]

\[ b_{3 \mathrm{nl}} = \frac{32}{315}(b_1-1) \]

where \(f\) is the linear growth rate, \(b\) is the linear galaxy bias, \(\mu\) is the cosine of the angle between the line-of-sight and the comoving separation, \(P_{\delta\delta}(k)\), \(P_{\delta\theta}(k)\) and \(P_{\theta\theta}(k)\) are the real-space matter power spectrum and the real-space density-velocity divergence cross-spectrum and the real-space velocity divergence auto-spectrum, computed at 1-loop using (Standard) Perturbation Theory as implemented in the CPT Library [http://www2.yukawa.kyoto-u.ac.jp/~atsushi.taruya/cpt_pack.html] by cbl::cosmology::Cosmology::Pk_TNS_dd_dt_tt, all the terms in the power spectrum correction correction terms are computed by cbl::cosmology::Cosmology::Pk_TNS_AB_terms_1loop and cbl::cosmology::Cosmology::Pk_eTNS_terms_1loop, \(D_{FoG}\) is a damping factor used to model the random peculiar motions at small scales, which can be either Gaussian:

\[ D_{FoG}(k, \mu, f, \sigma_v) = e^{-k^2\mu^2f^2\sigma_v^2} \]

or Lorentzian:

\[ D_{FoG}(k, \mu, f, \sigma_v) = \frac{1}{1+k^2\mu^2f^2\sigma_v^2} \]

Author

J.E. Garcia-Farieta

joega.nosp@m.rcia.nosp@m.fa@un.nosp@m.al.e.nosp@m.du.co

Parameters

kk	the wave vector module
mu	the line of sight cosine
DFoG	the damping factor (Gaussian or Lorentzian)
linear_growth_rate	the linear growth rate
bias	the linear bias
bias2	the second order local bias
sigmav	the streaming scale
Ncorr	constant stochasticity term
Pk_DeltaDelta	power spectrum interpolator
Pk_DeltaTheta	power spectrum interpolator
Pk_ThetaTheta	power spectrum interpolator
Pk_A11	power spectrum interpolator
Pk_A12	power spectrum interpolator
Pk_A22	power spectrum interpolator
Pk_A23	power spectrum interpolator
Pk_A33	power spectrum interpolator
Pk_B12	power spectrum interpolator
Pk_B13	power spectrum interpolator
Pk_B14	power spectrum interpolator
Pk_B22	power spectrum interpolator
Pk_B23	power spectrum interpolator
Pk_B24	power spectrum interpolator
Pk_B33	power spectrum interpolator
Pk_B34	power spectrum interpolator
Pk_B44	power spectrum interpolator
Pk_b2d	power spectrum interpolator
Pk_b2v	power spectrum interpolator
Pk_b22	power spectrum interpolator
Pk_bs2d	power spectrum interpolator
Pk_bs2v	power spectrum interpolator
Pk_b2s2	power spectrum interpolator
Pk_bs22	power spectrum interpolator
sigma32Pklin	power spectrum interpolator

Returns

\(P(k, \mu)\)

Definition at line 236 of file ModelFunction_TwoPointCorrelation.cpp.

Pkmu_ModeCoupling()

double cbl::modelling::twopt::Pkmu_ModeCoupling	(	const double	kk,
		const double	mu,
		const double	linear_growth_rate,
		const double	bias,
		const double	sigmav,
		const double	AMC,
		const std::shared_ptr< cbl::glob::FuncGrid >	PkLin,
		const std::shared_ptr< cbl::glob::FuncGrid >	PkMC
	)

the redshift-space galaxy power spectrum, as a function of \(k\) and \(\mu\), predicted by the mode-coupling model

this function computes the redshift-space mode-coupling power spectrum model \(P(k, \mu)\) (see e.g. Sanchez et al. 2013 https://arxiv.org/pdf/1312.4854.pdf; Beutler et al. 2016 https://arxiv.org/pdf/1607.03149.pdf):

\[ P(k, \mu) = \left(1+\beta\mu^2 \right)^2 \left( \frac{1}{1+\left(kf\sigma_v\mu\right)^2} \right)^2 P_{NL}(k) \]

where

\[ P_{NL}(k) = b^2 \left\{ P_{L}(k)e^{-(k\mu\sigma_v)^2} +A_{MC}P_{MC}(k) \right\} , \]

\(\mu = k_{\parallel} / k\), \(P_{lin}\), \(P_{MC}\) are the linear and the linear and 1loop correction power spectra, and \(\beta = f/b\) with \(f\) the linear growth rate and \(b\) the bias, \(\sigma_v\) is the streaming scale that parameterises the Fingers of God effect at small scales and A_{MC} is the mode coupling bias.

Parameters

kk	the wave vector module
mu	the line of sight cosine
linear_growth_rate	the linear growth rate
bias	the linear bias
sigmav	the streaming scale
AMC	the mode coupling bias
PkLin	linear power spectrum interpolator
PkMC	the 1loop power spectrum correction

Returns

\(P(k, \mu)\)

Definition at line 76 of file ModelFunction_TwoPointCorrelation.cpp.

Pkmu_Scoccimarro()

double cbl::modelling::twopt::Pkmu_Scoccimarro	(	const double	kk,
		const double	mu,
		const std::string	DFoG,
		const double	linear_growth_rate,
		const double	bias,
		const double	sigmav,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_DeltaDelta,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_DeltaTheta,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_ThetaTheta
	)

the redshift-space galaxy power spectrum, as a function of \(k\) and \(\mu\), predicted by the Scoccimarro model

this function computes the redshift-space power spectrum \(P(k, \mu)\) for the Scoccimarro model, in 1-loop approximation using (standard) Perturbation Theory (see e.g. Scoccimarro 2004 https://arxiv.org/abs/astro-ph/0407214):

\[ P(k, \mu) = D_{FoG}(k, \mu, f \sigma_v) \left(b^2P_{\delta\delta}(k) + 2fb\mu^2P_{\delta\theta}(k) + f^2\mu^4P_{\theta\theta}(k)\right) \]

where \(f\) is the linear growth rate, \(b\) is the linear galaxy bias, \(\mu\) is the cosine of the angle between the line-of-sight and the comoving separation, \(P_{\delta\delta}(k)\), \(P_{\delta\theta}(k)\) and \(P_{\theta\theta}(k)\) are the real-space matter power spectrum and the real-space density-velocity divergence cross-spectrum and the real-space velocity divergence auto-spectrum, computed at 1-loop using (Standard) Perturbation Theory as implemented in the CPT Library [http://www2.yukawa.kyoto-u.ac.jp/~atsushi.taruya/cpt_pack.html] by cbl::cosmology::Cosmology::Pk_TNS_dd_dt_tt, \(D_{FoG}\) is a damping factor used to model the random peculiar motions at small scales, which can be either Gaussian:

\[ D_{FoG}(k, \mu, f, \sigma_v) = e^{-k^2\mu^2f^2\sigma_v^2} \]

or Lorentzian:

\[ D_{FoG}(k, \mu, f, \sigma_v) = \frac{1}{1+k^2\mu^2f^2\sigma_v^2} \]

Author

J.E. Garcia-Farieta

joega.nosp@m.rcia.nosp@m.fa@un.nosp@m.al.e.nosp@m.du.co

Parameters

kk	the wave vector module
mu	the line of sight cosine
DFoG	the damping factor (Gaussian or Lorentzian)
linear_growth_rate	the linear growth rate
bias	the linear bias
sigmav	the streaming scale
Pk_DeltaDelta	power spectrum interpolator
Pk_DeltaTheta	power spectrum interpolator
Pk_ThetaTheta	power spectrum interpolator

Returns

\(P(k, \mu)\)

Definition at line 113 of file ModelFunction_TwoPointCorrelation.cpp.

Pkmu_Scoccimarro_fitBel()

double cbl::modelling::twopt::Pkmu_Scoccimarro_fitBel	(	const double	kk,
		const double	mu,
		const std::string	DFoG,
		const double	linear_growth_rate,
		const double	bias,
		const double	sigmav,
		const double	kd,
		const double	bb,
		const double	a1,
		const double	a2,
		const double	a3,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pklin,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pknonlin
	)

the redshift-space galaxy power spectrum, as a function of \(k\) and \(\mu\), predicted by the Scoccimarro model

this function computes the redshift-space power spectrum \(P(k, \mu)\) for the Scoccimarro model, using fitting functions for \(P_{\delta\theta}(k)\) and \(P_{\theta\theta}(k)\) folowing Bel et al. 2019 https://arxiv.org/abs/1809.09338 :

\[ P(k, \mu) = D_{FoG}(k, \mu, f \sigma_v) \left(b^2P_{\delta\delta}(k) + 2fb\mu^2P_{\delta\theta}(k) + f^2\mu^4P_{\theta\theta}(k)\right) \]

where \(f\) is the linear growth rate, \(b\) is the linear galaxy bias, \(\mu\) is the cosine of the angle between the line-of-sight and the comoving separation, \(D_{FoG}\) is a damping factor used to model the random peculiar motions at small scales, which can be either Gaussian:

\[ D_{FoG}(k, \mu, f, \sigma_v) = e^{-k^2\mu^2f^2\sigma_v^2} \]

or Lorentzian:

\[ D_{FoG}(k, \mu, f, \sigma_v) = \frac{1}{1+k^2\mu^2f^2\sigma_v^2} \]

and \(P_{\delta\delta}(k)\), \(P_{\delta\theta}(k)\) and \(P_{\theta\theta}(k)\) are the real-space matter power spectrum, the real-space density-velocity divergence cross-spectrum and the real-space velocity divergence auto-spectrum. \(P_{\delta\theta}(k)\) and \(P_{\theta\theta}(k)\) are approximated as follows:

\[ P_{\delta\theta}(k) = \left(P_{\delta\delta}(k)P^{lin}(k)\right)^{1/2}e^{-k/k_\delta-a_0k^6} \, , \]

\[ P_{\theta\theta}(k) = P^{lin}(k)e^{-k(a_1+a_2k+a_3k^2)} \]

where both the linear power spectrum \(P^{lin}(k)\), and the non-linear power spectrum \(P_{\delta\delta}(k)\) are computed by cbl::cosmology::Cosmology::Pk_matter, and \(k_\delta\), \(a_0\), \(a_1\), \(a_2\), \(a_3\) are free parameters.

Author

J.E. Garcia-Farieta

joega.nosp@m.rcia.nosp@m.fa@un.nosp@m.al.e.nosp@m.du.co

Parameters

kk	the wave vector module
mu	the line of sight cosine
DFoG	the damping factor (Gaussian or Lorentzian)
linear_growth_rate	the linear growth rate
bias	the linear bias
sigmav	the streaming scale
kd	fitting parameter
bb	fitting parameter
a1	fitting parameter
a2	fitting parameter
a3	fitting parameter
Pklin	linear power spectrum interpolator
Pknonlin	nolinear power spectrum interpolator

Returns

\(P(k, \mu)\)

Definition at line 163 of file ModelFunction_TwoPointCorrelation.cpp.

Pkmu_Scoccimarro_fitPezzotta()

double cbl::modelling::twopt::Pkmu_Scoccimarro_fitPezzotta	(	const double	kk,
		const double	mu,
		const std::string	DFoG,
		const double	linear_growth_rate,
		const double	bias,
		const double	sigmav,
		const double	kd,
		const double	kt,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pklin,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pknonlin
	)

the redshift-space galaxy power spectrum, as a function of \(k\) and \(\mu\), predicted by the Scoccimarro model

this function computes the redshift-space power spectrum \(P(k, \mu)\) for the Scoccimarro model, using fitting functions for \(P_{\delta\theta}(k)\) and \(P_{\theta\theta}(k)\) following Pezzotta et al. 2017 https://arxiv.org/abs/1612.05645, Mohammad et al. 2018 https://arxiv.org/abs/1807.05999, Bel et al. 2019 https://arxiv.org/abs/1809.09338 :

\[ P(k, \mu) = D_{FoG}(k, \mu, f \sigma_v) \left(b^2P_{\delta\delta}(k) + 2fb\mu^2P_{\delta\theta}(k) + f^2\mu^4P_{\theta\theta}(k)\right) \]

where \(f\) is the linear growth rate, \(b\) is the linear galaxy bias, \(\mu\) is the cosine of the angle between the line-of-sight and the comoving separation, \(D_{FoG}\) is a damping factor used to model the random peculiar motions at small scales, which can be either Gaussian:

\[ D_{FoG}(k, \mu, f, \sigma_v) = e^{-k^2\mu^2f^2\sigma_v^2} \]

or Lorentzian:

\[ D_{FoG}(k, \mu, f, \sigma_v) = \frac{1}{1+k^2\mu^2f^2\sigma_v^2} \]

and \(P_{\delta\delta}(k)\), \(P_{\delta\theta}(k)\) and \(P_{\theta\theta}(k)\) are the real-space matter power spectrum, the real-space density-velocity divergence cross-spectrum and the real-space velocity divergence auto-spectrum. \(P_{\delta\theta}(k)\) and \(P_{\theta\theta}(k)\) are approximated as follows:

\[ P_{\delta\theta}(k) = \left(P_{\delta\delta}(k)P^{lin}(k)e^{-k/k_\delta} \right)^{1/2} \,, \]

\[ P_{\theta\theta}(k) = P^{lin}(k)e^{-k/k_\theta} \]

where both the linear power spectrum \(P^{lin}(k)\), and the non-linear power spectrum \(P_{\delta\delta}(k)\) are computed by cbl::cosmology::Cosmology::Pk_matter, and \(k_\delta\), \(k_\theta\) are free parameters.

Author

J.E. Garcia-Farieta

joega.nosp@m.rcia.nosp@m.fa@un.nosp@m.al.e.nosp@m.du.co

Parameters

kk	the wave vector module
mu	the line of sight cosine
DFoG	the damping factor (Gaussian or Lorentzian)
linear_growth_rate	the linear growth rate
bias	the linear bias
sigmav	the streaming scale
kd	fitting parameter
kt	fitting parameter
Pklin	linear power spectrum interpolator
Pknonlin	nolinear power spectrum interpolator

Returns

\(P(k, \mu)\)

Definition at line 139 of file ModelFunction_TwoPointCorrelation.cpp.

Pkmu_TNS()

double cbl::modelling::twopt::Pkmu_TNS	(	const double	kk,
		const double	mu,
		const std::string	DFoG,
		const double	linear_growth_rate,
		const double	bias,
		const double	sigmav,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_DeltaDelta,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_DeltaTheta,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_ThetaTheta,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_A11,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_A12,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_A22,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_A23,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_A33,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_B12,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_B13,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_B14,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_B22,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_B23,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_B24,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_B33,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_B34,
		const std::shared_ptr< cbl::glob::FuncGrid >	Pk_B44
	)

the redshift-space galaxy power spectrum, as a function of \(k\) and \(\mu\), predicted by the TNS (Taruya, Nishimichi and Saito) model

this function computes the redshift-space power spectrum \(P(k, \mu)\) for the (Taruya, Nishimichi and Saito) TNS model, in 1-loop approximation using (standard) Perturbation Theory (see e.g. Taruya et. al, 2010 https://arxiv.org/abs/1006.0699 and Taruya et al., 2013 https://arxiv.org/abs/1301.3624):

\[ P(k, \mu) = D_{FoG}(k, \mu, f, \sigma_v)\left(b^2P_{\delta\delta}(k) + 2fb\mu^2P_{\delta\theta}(k) + f^2\mu^4P_{\theta\theta}(k) + b^3A(k, \mu, f) + b^4B(k, \mu, f)\right) \]

\[ A(k, \mu ; f) = j_{1} \int d^{3} r e^{i \boldsymbol{k} \cdot \boldsymbol{r}}\left\langle A_{1} A_{2} A_{3}\right\rangle_{c}=k \mu f \int \frac{d^{3} p}{(2 \pi)^{3}} \frac{p_{z}}{p^{2}}\left\{B_{\sigma}(\boldsymbol{p}, \boldsymbol{k}-\boldsymbol{p},-\boldsymbol{k})-B_{\sigma}(\boldsymbol{p}, \boldsymbol{k},-\boldsymbol{k}-\boldsymbol{p})\right\}\, , \]

\[ B(k, \mu ; f)=j_{1}^{2} \int d^{3} r e^{i \boldsymbol{k} \cdot \boldsymbol{r}}\left\langle A_{1} A_{2}\right\rangle_{c}\left\langle A_{1} A_{3}\right\rangle_{c}=(k \mu f)^{2} \int \frac{d^{3} p}{(2 \pi)^{3}} F_{\sigma}(\boldsymbol{p}) F_{\sigma}(\boldsymbol{k}-\boldsymbol{p}) \]

where \(f\) is the linear growth rate, \(b\) is the linear galaxy bias, \(\mu\) is the cosine of the angle between the line-of-sight and the comoving separation, \(P_{\delta\delta}(k)\), \(P_{\delta\theta}(k)\) and \(P_{\theta\theta}(k)\) are the real-space matter power spectrum and the real-space density-velocity divergence cross-spectrum and the real-space velocity divergence auto-spectrum, computed at 1-loop using (Standard) Perturbation Theory as implemented in the CPT Library [http://www2.yukawa.kyoto-u.ac.jp/~atsushi.taruya/cpt_pack.html] by cbl::cosmology::Cosmology::Pk_TNS_dd_dt_tt, all the terms in the power spectrum correction correction terms are computed by cbl::cosmology::Cosmology::Pk_TNS_AB_terms_1loop, \(D_{FoG}\) is a damping factor used to model the random peculiar motions at small scales, which can be either Gaussian:

\[ D_{FoG}(k, \mu, f, \sigma_v) = e^{-k^2\mu^2f^2\sigma_v^2} \]

or Lorentzian:

\[ D_{FoG}(k, \mu, f, \sigma_v) = \frac{1}{1+k^2\mu^2f^2\sigma_v^2} \]

Author

J.E. Garcia-Farieta

joega.nosp@m.rcia.nosp@m.fa@un.nosp@m.al.e.nosp@m.du.co

Parameters

kk	the wave vector module
mu	the line of sight cosine
DFoG	the damping factor (Gaussian or Lorentzian)
linear_growth_rate	the linear growth rate
bias	the linear bias
sigmav	the streaming scale
Pk_DeltaDelta	power spectrum interpolator
Pk_DeltaTheta	power spectrum interpolator
Pk_ThetaTheta	power spectrum interpolator
Pk_A11	power spectrum interpolator
Pk_A12	power spectrum interpolator
Pk_A22	power spectrum interpolator
Pk_A23	power spectrum interpolator
Pk_A33	power spectrum interpolator
Pk_B12	power spectrum interpolator
Pk_B13	power spectrum interpolator
Pk_B14	power spectrum interpolator
Pk_B22	power spectrum interpolator
Pk_B23	power spectrum interpolator
Pk_B24	power spectrum interpolator
Pk_B33	power spectrum interpolator
Pk_B34	power spectrum interpolator
Pk_B44	power spectrum interpolator

Returns

\(P(k, \mu)\)

Definition at line 185 of file ModelFunction_TwoPointCorrelation.cpp.

true_k_mu_AP()

std::vector< double > cbl::modelling::twopt::true_k_mu_AP	(	const double	kk,
		const double	mu,
		const double	alpha_perp,
		const double	alpha_par
	)

true k and \(\mu\) power spectrum coordinates as a function of observed ones

this function computes k' and \(\mu'\) power spectrum coordinates in the true cosmology from k and \(\mu\) coordinates estimated in a fiducial cosmology, using the Alcock-Paczynski parameters (see e.g. Beutler et al. 2016, sec 5.2 ( https://arxiv.org/pdf/1607.03150.pdf):

\[ k' = \frac{k}{\alpha_\perp} \sqrt{1+\mu^2 \left[ \left( \frac{\alpha_\parallel}{\alpha_\perp}\right)^{-2}-1 \right]} \, , \]

\[ \mu' = \mu\frac{\alpha_\perp}{\alpha_\parallel} \frac{1}{\sqrt{1+\mu^2\left[\left( \frac{\alpha_\parallel}{\alpha_\perp} \right)^{-2}-1\right]}} \, , \]

Parameters

kk	the wave vector module
mu	the line of sight cosine
alpha_perp	the shift transverse to the l.o.s.
alpha_par	the shift parallel to the l.o.s.

Returns

a vector containing k' and \(\mu'\) coordinates

Definition at line 46 of file ModelFunction_TwoPointCorrelation.cpp.

wp_1halo()

std::vector< double > cbl::modelling::twopt::wp_1halo	(	const std::vector< double >	rp,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

model for the 1-halo term of the projected two-point correlation function

this function computes the 1-halo term of the projected correlation function by integrating the redshift-space 2D correlation function (e.g. van den Bosch et al. 2012):

\[w_{p, 1halo}(r_p, z) = 2\int_{0}^{\pi_{max}}\xi_{1halo}(r_p, \pi, z)\,{\rm d}\pi\]

where the 1-halo term of the redshift-space galaxy correlation function, \(\xi_{1halo}(r_p, \pi, z)\), is computed by cbl::modelling::twopt::xi_1halo_zspace

Parameters

rp	\(r_p\): the scale perpendicular to the line of sight at which the model is computed
inputs	pointer to the structure that contains the fixed input data used to construct the model
parameter	vector containing the model parameters

Returns

the 1-halo term of the projected two-point correlation function

Warning

This function accounts for residual redshift-space distortions (RRSD) caused by the finite integration range used with real data (see e.g. sec. 2.3 of van den Bosch et al. 2012). Its accuracy depends on the accuracy of the redshift-space distortion model used to describe \(\xi_g(r_p, \pi, z)\).

Definition at line 131 of file ModelFunction_TwoPointCorrelation_projected.cpp.

wp_1halo_approx()

std::vector< double > cbl::modelling::twopt::wp_1halo_approx	(	const std::vector< double >	rp,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

model for the 1-halo term of the projected two-point correlation function

this function estimates the 1-halo term of the projected correlation function by integrating the 1-halo term of the real-space spherically averaged two-point correlation function, as follows:

\[w_{p, 1halo}(r_p, z) = 2\int_{r_p}^{r_{out}}\xi_{1halo}(r, z)\frac{r\,{\rm d}r} {\sqrt{r^2-r_p^2}} \]

where \(r_{out}=\sqrt{r_p^2+r_{max}^2}\) and \(\xi_{1halo}(r, z)\) is computed by cbl::modelling::twopt::xi_1halo

in the limit \(r_{max}\rightarrow\infty\), this function is completely independent of peculiar velocities

Parameters

rp	\(r_p\): the scale perpendicular to the line of sight at which the model is computed
inputs	pointer to the structure that contains the fixed input data used to construct the model
parameter	vector containing the model parameters

Returns

the 1-halo term of the projected two-point correlation function

Warning

This function does not account for residual redshift-space distortions (RRSD) caused by the finite integration range used (i.e. \(r_{max}<\infty\)). If it is used to model the projected correlation function measured from real data, it introduces a bias casued by neglecting the RRSD (see e.g. sec. 2.3 of van den Bosch et al. 2012). It is thus useful only for testing these errors, or for general theoretical investigations not dealing with real data.

Definition at line 76 of file ModelFunction_TwoPointCorrelation_projected.cpp.

wp_2halo()

std::vector< double > cbl::modelling::twopt::wp_2halo	(	const std::vector< double >	rp,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

model for the 2-halo term of the projected two-point correlation function

this function computes the 2-halo term of the projected correlation function by integrating the redshift-space 2D correlation function (e.g. van den Bosch et al. 2012):

\[w_{p, 2halo}(r_p, z) = 2\int_{0}^{\pi_{max}}\xi_{2halo}(r_p, \pi, z)\,{\rm d}\pi\]

where the 2-halo term of the redshift-space galaxy correlation function, \(\xi_{2halo}(r_p, \pi, z)\), is computed by cbl::modelling::twopt::xi_2halo_zspace

Parameters

rp	\(r_p\): the scale perpendicular to the line of sight at which the model is computed
inputs	pointer to the structure that contains the fixed input data used to construct the model
parameter	vector containing the model parameters

Returns

the 2-halo term of the projected two-point correlation function

Warning

This function accounts for residual redshift-space distortions (RRSD) caused by the finite integration range used with real data (see e.g. sec. 2.3 of van den Bosch et al. 2012). Its accuracy depends on the accuracy of the redshift-space distortion model used to describe \(\xi_g(r_p, \pi, z)\).

Definition at line 140 of file ModelFunction_TwoPointCorrelation_projected.cpp.

wp_2halo_approx()

std::vector< double > cbl::modelling::twopt::wp_2halo_approx	(	const std::vector< double >	rp,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

model for the 2-halo term of the projected two-point correlation function

this function estimates the 2-halo term of the projected correlation function by integrating the 2-halo term of the real-space spherically averaged two-point correlation function, as follows:

\[w_{p, 2halo}(r_p, z) = 2\int_{r_p}^{r_{out}}\xi_{2halo}(r, z)\frac{r\,{\rm d}r} {\sqrt{r^2-r_p^2}} \]

where \(r_{out}=\sqrt{r_p^2+r_{max}^2}\) and \(\xi_{2halo}(r, z)\) is computed by cbl::modelling::twopt::xi_2halo

in the limit \(r_{max}\rightarrow\infty\), this function is completely independent of peculiar velocities

Parameters

rp	\(r_p\): the scale perpendicular to the line of sight at which the model is computed
inputs	pointer to the structure that contains the fixed input data used to construct the model
parameter	vector containing the model parameters

Returns

the 2-halo term of the projected two-point correlation function

Warning

This function does not account for residual redshift-space distortions (RRSD) caused by the finite integration range used (i.e. \(r_{max}<\infty\)). If it is used to model the projected correlation function measured from real data, it introduces a bias casued by neglecting the RRSD (see e.g. sec. 2.3 of van den Bosch et al. 2012). It is thus useful only for testing these errors, or for general theoretical investigations not dealing with real data.

Definition at line 85 of file ModelFunction_TwoPointCorrelation_projected.cpp.

wp_from_xi()

std::vector< double > cbl::modelling::twopt::wp_from_xi	(	FunctionDoubleDoubleDoublePtrVectorRef	func,
		const std::vector< double >	rp,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

function used to compute the projected two-point correlation function

this function is used to compute the projected correlation function by integrating the redshift-space 2D correlation function (e.g. van den Bosch et al. 2012):

\[w_{p}(r_p, z) = 2\int_{0}^{\pi_{max}}\xi(r_p, \pi, z)\,{\rm d}\pi\]

where the redshift-space galaxy correlation function, \(\xi(r_p, \pi, z)\), is either the 1-halo, the 2-halo, or the full-shape redshift-space correlation function, computed by either cbl::modelling::twopt::xi_1halo_zspace, cbl::modelling::twopt::xi_2halo_zspace, or cbl::modelling::twopt::xi_HOD_space, respectively

Parameters

func	the redshift-space two-point correlation function that will be integrated (it can be either the 1-halo, the 2-halo, or the full-shape correlation function)
rp	\(r_p\): the scale perpendicular to the line of sight at which the model is computed
inputs	pointer to the structure that contains the fixed input data used to construct the model
parameter	vector containing the model parameters

Returns

the projected two-point correlation function

Warning

This function accounts for residual redshift-space distortions (RRSD) caused by the finite integration range used with real data (see e.g. sec. 2.3 of van den Bosch et al. 2012). Its accuracy depends on the accuracy of the redshift-space distortion model used to describe \(\xi_g(r_p, \pi, z)\).

Definition at line 103 of file ModelFunction_TwoPointCorrelation_projected.cpp.

wp_from_xi_approx()

std::vector< double > cbl::modelling::twopt::wp_from_xi_approx	(	FunctionVectorVectorPtrVectorRef	func,
		const std::vector< double >	rp,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

function used to compute the projected two-point correlation function

this function is used to compute the projected correlation function by integrating the real-space spherically averaged two-point correlation function, as follows:

\[w_{p}(r_p, z) = 2\int_{r_p}^{r_{out}}\xi(r, z)\frac{r\,{\rm d}r} {\sqrt{r^2-r_p^2}} \]

where \(r_{out}=\sqrt{r_p^2+r_{max}^2}\) and \(\xi(r, z)\) is either the 1-halo, the 2-halo, or the full-shape real-space correlation function, computed by either cbl::modelling::twopt::xi_1halo, cbl::modelling::twopt::xi_2halo, or cbl::modelling::twopt::xi_HOD, respectively

in the limit \(r_{max}\rightarrow\infty\), this function is completely independent of peculiar velocities

Parameters

func	the two-point real-space correlation function that will be integrated (it can be either the 1-halo, the 2-halo, or the full-shape correlation function)
rp	\(r_p\): the scale perpendicular to the line of sight at which the model is computed
inputs	pointer to the structure that contains the fixed input data used to construct the model
parameter	vector containing the model parameters

Returns

the projected two-point correlation function

Warning

This function does not account for residual redshift-space distortions (RRSD) caused by the finite integration range used (i.e. \(r_{max}<\infty\)). If it is used to model the projected correlation function measured from real data, it introduces a bias casued by neglecting the RRSD (see e.g. sec. 2.3 of van den Bosch et al. 2012). It is thus useful only for testing these errors, or for general theoretical investigations not dealing with real data.

Definition at line 47 of file ModelFunction_TwoPointCorrelation_projected.cpp.

wp_from_Xi_rppi()

std::vector< double > cbl::modelling::twopt::wp_from_Xi_rppi	(	const std::vector< double >	rp,
		const double	pimax,
		const std::string	model,
		const std::vector< double >	parameter,
		const std::vector< std::shared_ptr< glob::FuncGrid >>	pk_interp,
		const double	prec = 1.e-5,
		const double	alpha_perp = 1.,
		const double	alpha_par = 1.
	)

the projected two-point correlation function

The function computes the projected two-point correlation function from the 2D two-point correlation function in Cartesian coordinates:

\[ w_p(r_p) = \int_0^{\pi_{max}} \mathrm{d}\pi \xi(r_p, \pi) \]

where \(xi(r_p, \pi)\) is the Cartesian two-point correlation function

Parameters

rp	vector of scales transverse to the line of sight
pimax	the maximum scale of integration
model	the \(P(k,\mu)\) model
parameter	vector containing parameter values
pk_interp	vector containing power spectrum interpolating functions
prec	the integral precision
alpha_perp	the shift transverse to the l.o.s.
alpha_par	the shift parallel to the l.o.s.

Returns

the cartesian two-point correlation function.

Definition at line 541 of file ModelFunction_TwoPointCorrelation.cpp.

wp_HOD()

std::vector< double > cbl::modelling::twopt::wp_HOD	(	const std::vector< double >	rp,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

HOD model of the projected two-point correlation function.

this function computes:

\[w_p(r_p, z) = w_{p,1halo}(r_p, z)+w_{p,2halo}(r_p, z)\]

where \(w_{p,1halo}(r_p)\) and \(w_{p,2halo}(r_p)\) are computed by cbl::modelling::twopt::wp_1halo and cbl::modelling::twopt::wp_2halo, respectively

Parameters

rp	\(r_p\): the scale perpendicular to the line of sight at which the model is computed
inputs	pointer to the structure that contains the fixed input data used to construct the model
parameter	vector containing the model parameters

Returns

the HOD projected two-point correlation function

Warning

This function accounts for residual redshift-space distortions (RRSD) caused by the finite integration range used with real data (see e.g. sec. 2.3 of van den Bosch et al. 2012). Its accuracy depends on the accuracy of the redshift-space distortion model used to describe \(\xi_g(r_p, \pi, z)\).

Definition at line 149 of file ModelFunction_TwoPointCorrelation_projected.cpp.

wp_HOD_approx()

std::vector< double > cbl::modelling::twopt::wp_HOD_approx	(	const std::vector< double >	rp,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

HOD model of the projected two-point correlation function.

the function computes:

\[w_p(r_p, z) = w_{p,1halo}(r_p, z)+w_{p,2halo}(r_p, z)\]

where \(w_{p,1halo}(r_p)\) and \(w_{p,2halo}(r_p)\) are computed by cbl::modelling::twopt::wp_1halo_approx and cbl::modelling::twopt::wp_2halo_approx, respectively

in the limit \(r_{max}\rightarrow\infty\), this function is completely independent of peculiar velocities

Parameters

rp	\(r_p\): the scale perpendicular to the line of sight at which the model is computed
inputs	pointer to the structure that contains the fixed input data used to construct the model
parameter	vector containing the model parameters

Returns

the HOD projected two-point correlation function

Warning

This function does not account for residual redshift-space distortions (RRSD) caused by the finite integration range used (i.e. \(r_{max}<\infty\)). If it is used to model the projected correlation function measured from real data, it introduces a bias casued by neglecting the RRSD (see e.g. sec. 2.3 of van den Bosch et al. 2012). It is thus useful only for testing these errors, or for general theoretical investigations not dealing with real data.

Definition at line 94 of file ModelFunction_TwoPointCorrelation_projected.cpp.

xi0_BAO_sigmaNL()

std::vector< double > cbl::modelling::twopt::xi0_BAO_sigmaNL	(	const std::vector< double >	rad,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

model for the BAO signal in the monopole of the two-point correlation function

the function computes:

\[\xi_0(s) = B^2 \cdot \xi_{\rm DM}(\alpha\cdot s, \Sigma_{NL}) + A_0 + A_1/s + A_2/s^2\]

the model has 6 parameters:

• \(\Sigma_{NL}\)
• \(\alpha\)
• \(B\)
• \(A_0\)
• \(A_1\)
• \(A_2\)

the dark matter two-point correlation function is fixed and provided in input

Parameters

rad	the scale at which the model is computed
inputs	pointer to the structure that contains the dark matter power spectrum
parameter	6D vector containing the input parameters

Returns

the monopole of the two-point correlation function

Definition at line 48 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

xi0_damped_bias_sigmaz()

std::vector< double > cbl::modelling::twopt::xi0_damped_bias_sigmaz	(	const std::vector< double >	rad,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

the damped two-point correlation monopole; from Sereno et al. 2015

The function computes the damped two-point correlation monopole:

\(\xi(s) = b^2 \xi'(s) + b \xi''(s) + \xi'''(s) \, ;\)

where b is the linear bias and the terms \(\xi'(s)\), \(\xi''(s)\), \(\xi'''(s)\) are the Fourier anti-transform of the power spectrum terms obtained integrating the redshift space 2D power spectrum along \(\mu\) (see cbl::modelling::twopt.:damped_Pk_terms, see cbl::modelling::twopt.:damped_Xi).

the model has 2 parameters:

• bias the linear bias
• \(\sigma_z$\) the redshift error

Parameters

rad	the scale at which the model is computed
inputs	pointer to the structure that contains the cosmological paramters used to compute the dark matter two-point correlation function
parameter	1D vector containing the linear bias

Returns

the damped two-point correlation monopole.

Definition at line 685 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

xi0_damped_scaling_relation_sigmaz()

std::vector< double > cbl::modelling::twopt::xi0_damped_scaling_relation_sigmaz	(	const std::vector< double >	rad,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

the damped two-point correlation monopole; from Sereno et al. 2015

The function computes the damped two-point correlation monopole:

\(\xi(s) = b^2 \xi'(s) + b \xi''(s) + \xi'''(s) \, ;\)

where b is the linear bias and the terms \(\xi'(s)\), \(\xi''(s)\), \(\xi'''(s)\) are the Fourier anti-transform of the power spectrum terms obtained integrating the redshift space 2D power spectrum along \(\mu\) (see cbl::modelling::twopt.:damped_Pk_terms, see cbl::modelling::twopt.:damped_Xi).

the model has 4 parameters:

• M0 the intercept of the scaling relation
• slope the slope of the scaling relation
• scatter the scattr of the scaling relation
• \(\sigma_z$\) the redshift error

the linear bias is computed and used in the modelling. It is provided as an output parameter

Parameters

rad	the scale at which the model is computed
inputs	pointer to the structure that contains the cosmological paramters used to compute the dark matter two-point correlation function
parameter	1D vector containing the linear bias

Returns

the damped two-point correlation monopole.

Definition at line 413 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

xi0_damped_scaling_relation_sigmaz_cosmology()

std::vector< double > cbl::modelling::twopt::xi0_damped_scaling_relation_sigmaz_cosmology	(	const std::vector< double >	rad,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

the damped two-point correlation monopole; from Sereno et al. 2015

The function computes the damped two-point correlation monopole:

\(\xi(s) = b^2 \xi'(s) + b \xi''(s) + \xi'''(s) \, ;\)

where b is the linear bias and the terms \(\xi'(s)\), \(\xi''(s)\), \(\xi'''(s)\) are the Fourier anti-transform of the power spectrum terms obtained integrating the redshift space 2D power spectrum along \(\mu\) (see cbl::modelling::twopt.:damped_Pk_terms, see cbl::modelling::twopt.:damped_Xi).

Parameters

rad	the scale at which the model is computed
inputs	pointer to the structure that contains the cosmological paramters used to compute the dark matter two-point correlation function
parameter	1D vector containing the linear bias

Returns

the damped two-point correlation monopole.

Definition at line 461 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

xi0_linear()

std::vector< double > cbl::modelling::twopt::xi0_linear	(	const std::vector< double >	rad,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

model for the monopole of the two-point correlation function

the function computes:

\[\xi_0(s) = \left[ (b\sigma_8)^2 + \frac{2}{3} f\sigma_8 \cdot b\sigma_8 + \frac{1}{5}(f\sigma_8)^2 \right] \cdot \xi_{\rm DM}(\alpha\cdot s)/\sigma_8^2 + A_0 + A_1/s + A_2/s^2\]

the model has 6 parameters:

• \(\alpha\)
• \(f(z)\sigma_8(z)\)
• \(b(z)\sigma_8(z)\)
• \(A_0\)
• \(A_1\)
• \(A_2\)

the dark matter two-point correlation function is fixed and provided in input

Parameters

rad	the scale at which the model is computed
inputs	pointer to the structure that contains the dark matter two-point correlation function and \(\sigma_8(z)\), computed at a given (fixed) cosmology
parameter	6D vector containing the input parameters

Returns

the monopole of the two-point correlation function

Definition at line 97 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

xi0_linear_bias_cosmology()

std::vector< double > cbl::modelling::twopt::xi0_linear_bias_cosmology	(	const std::vector< double >	rad,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

model for the monopole of the two-point correlation function

the function computes:

\[\xi_0(s) = \left[ b^2 + \frac{2}{3}f \cdot b + \frac{1}{5}f^2 \right] \cdot \xi_{\rm DM} \left( \frac{D_V(z)}{D_V^{fid}(z)}\cdot s \right) \]

the model has 1+n parameters:

• \(b\)
• cosmological paramters

the dark matter two-point correlation function is computed using the input cosmological parameters

Parameters

rad	the scale at which the model is computed
inputs	pointer to the structure that contains the cosmological paramters used to compute the dark matter two-point correlation function
parameter	1D vector containing the linear bias

Returns

the monopole of the two-point correlation function

alpha

Definition at line 375 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

xi0_linear_cosmology()

std::vector< double > cbl::modelling::twopt::xi0_linear_cosmology	(	const std::vector< double >	rad,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

model for the monopole of the two-point correlation function

the function computes:

\[\xi_0(s) = \left[ (b\sigma_8)^2 + \frac{2}{3} f\sigma_8 \cdot b\sigma_8 + \frac{1}{5}(f\sigma_8)^2 \right] \cdot \xi_{\rm DM}(\alpha\cdot s)/\sigma_8^2 + A_0 + A_1/s + A_2/s^2\]

the model has 6 parameters:

• \(\alpha\)
• \(f(z)\sigma_8(z)\)
• \(b(z)\sigma_8(z)\)
• \(A_0\)
• \(A_1\)
• \(A_2\)

the dark matter two-point correlation function is computed using the input cosmological parameters

Parameters

rad	the scale at which the model is computed
inputs	pointer to the structure that contains the cosmological paramters used to compute the dark matter two-point correlation function
parameter	1D vector containing the linear bias

Returns

the monopole of the two-point correlation function

Definition at line 330 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

xi0_linear_cosmology_clusters()

std::vector< double > cbl::modelling::twopt::xi0_linear_cosmology_clusters	(	const std::vector< double >	rad,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

model for the monopole of the two-point correlation function, the bias is computed by the input cluster masses

the function computes:

\[\xi_0(s) = \left[ (b\sigma_8)^2 + \frac{2}{3} f\sigma_8 \cdot b\sigma_8 + \frac{1}{5}(f\sigma_8)^2 \right] \cdot \xi_{\rm DM}(s)/\sigma_8^2\]

the model has N cosmological parameters

the dark matter two-point correlation function and the linear effective bias are computed using the input cosmological parameters

Parameters

rad	the scale at which the model is computed
inputs	pointer to the structure that contains the cosmological paramters used to compute the dark matter two-point correlation function
parameter	1D vector containing the linear bias

Returns

the monopole of the two-point correlation function

alpha

Definition at line 840 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

xi0_linear_cosmology_clusters_selection_function()

std::vector< double > cbl::modelling::twopt::xi0_linear_cosmology_clusters_selection_function	(	const std::vector< double >	rad,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

model for the monopole of the redshift-space two-point correlation function of galaxy clusters, considering the selection function

the function computes:

\[ \xi_0(s) = \xi_{DM}\left(\frac{D_V(z)}{D_V^{fit}(z)}\cdot s\right) b^2\left[1 + \frac{2\beta}{3} + \frac{\beta^2}{5}\right] \]

where \( \beta=\beta(z)=\frac{f(z)}{b(z)} \). The Kaiser factor \( \left[1 + \frac{2\beta}{3} + \frac{\beta^2}{5}\right] \) is computed by cbl::xi_ratio, while the linear growth rate \( f(z) \) is computed by cbl::cosmology::Cosmology::linear_growth_rate

the model has 1+n parameters:

• the bias \(b\)
• n cosmological paramters provided in input

the dark matter two-point correlation function is computed using the input cosmological parameters

Parameters

rad	the scale at which the model is computed
inputs	pointer to the structure that contains the cosmological paramters used to compute the dark matter two-point correlation function
parameter	1D vector containing the linear bias

Returns

the monopole of the two-point correlation function in redshift-space

Definition at line 893 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

xi0_linear_LinearPoint()

std::vector< double > cbl::modelling::twopt::xi0_linear_LinearPoint	(	const std::vector< double >	rad,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

model for the monopole of the two-point correlation function

the function computes:

\(\xi_0(s) = \left[ (b\sigma_8)^2 + \frac{2}{3} f\sigma_8 \cdot b\sigma_8 + \frac{1}{5}(f\sigma_8)^2 \right] \cdot \xi_{\rm DM}(\alpha\cdot s)/\sigma_8^2 + A_0 + A_1/s + A_2/s^2\)

the model has 6 parameters:

• \(\alpha\)
• \(f(z)\sigma_8(z)\)
• \(b(z)\sigma_8(z)\)
• \(A_0\)
• \(A_1\)
• \(A_2\)

the dark matter two-point correlation function is fixed and provided in input

Parameters

rad	the scale at which the model is computed
inputs	pointer to the structure that contains the dark matter two-point correlation function and \(\sigma_8(z)\), computed at a given (fixed) cosmology
parameter	6D vector containing the input parameters

Returns

the monopole of the two-point correlation function

Definition at line 218 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

xi0_linear_one_cosmo_par_clusters()

std::vector< double > cbl::modelling::twopt::xi0_linear_one_cosmo_par_clusters	(	const std::vector< double >	rad,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

model for the monopole of the two-point correlation function, the bias is computed by the input cluster masses, with only \(sigma_8\) as a free parameter

the function computes:

\[\xi_0(s) = \left[ (b\sigma_8)^2 + \frac{2}{3} f\sigma_8 \cdot b\sigma_8 + \frac{1}{5}(f\sigma_8)^2 \right] \cdot \xi_{\rm DM}(s)/\sigma_8^2\]

the model has 1 cosmological parameter

the dark matter two-point correlation function and the linear effective bias are computed using the input cosmological parameters

Parameters

rad	the scale at which the model is computed
inputs	pointer to the structure that contains the cosmological paramters used to compute the dark matter two-point correlation function
parameter	1D vector containing the cosmological parameter

Returns

the monopole of the two-point correlation function

Definition at line 770 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

xi0_linear_sigma8_bias()

std::vector< double > cbl::modelling::twopt::xi0_linear_sigma8_bias	(	const std::vector< double >	rad,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

model for the monopole of the two-point correlation function in redshift space

the function computes:

\[\xi_0(s) = \left[ (b\sigma_8)^2 + \frac{2}{3} f(z)\sigma_8(z) \cdot b(z)\sigma_8(z) + \frac{1}{5}(f(z)^2\sigma_8(z)^2) \right] \cdot \xi_{\rm DM}(s)\frac{\sigma_8^2}{\sigma_8^2(z)} \]

the model has 2 parameters:

• \(\sigma_8(z)\)
• \(b(z)\)

the dark matter two-point correlation function is computed using the input cosmological parameters

Parameters

rad	the scale at which the model is computed
inputs	pointer to the structure that contains the cosmological paramters used to compute the dark matter two-point correlation function
parameter	1D vector containing the linear bias

Returns

the monopole of the two-point correlation function

Definition at line 293 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

xi0_linear_sigma8_clusters()

std::vector< double > cbl::modelling::twopt::xi0_linear_sigma8_clusters	(	const std::vector< double >	rad,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

model for the monopole of the two-point correlation function, the bias is computed by the input cluster masses, with only \(sigma_8\) as a free parameter

the function computes:

\[\xi_0(s) = \left[ (b\sigma_8)^2 + \frac{2}{3} f\sigma_8 \cdot b\sigma_8 + \frac{1}{5}(f\sigma_8)^2 \right] \cdot \xi_{\rm DM}(s)/\sigma_8^2\]

the model has 1 parameter: \(\sigma_8\)

the dark matter two-point correlation function and the linear effective bias are computed using the input cosmological parameters

Parameters

rad	the scale at which the model is computed
inputs	pointer to the structure that contains the cosmological paramters used to compute the dark matter two-point correlation function
parameter	1D vector containing the linear bias

Returns

the monopole of the two-point correlation function

Definition at line 705 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

xi0_linear_two_cosmo_pars_clusters()

std::vector< double > cbl::modelling::twopt::xi0_linear_two_cosmo_pars_clusters	(	const std::vector< double >	rad,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

model for the monopole of the two-point correlation function, the bias is computed by the input cluster masses, with only \(sigma_8\) as a free parameter

the function computes:

\[\xi_0(s) = \left[ (b\sigma_8)^2 + \frac{2}{3} f\sigma_8 \cdot b\sigma_8 + \frac{1}{5}(f\sigma_8)^2 \right] \cdot \xi_{\rm DM}(s)/\sigma_8^2\]

the model has 2 cosmological parameters

the dark matter two-point correlation function and the linear effective bias are computed using the input cosmological parameters

Parameters

rad	the scale at which the model is computed
inputs	pointer to the structure that contains the cosmological paramters used to compute the dark matter two-point correlation function
parameter	2D vector containing the cosmological parameters

Returns

the monopole of the two-point correlation function

the AP parameter

Definition at line 804 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

xi0_polynomial_LinearPoint()

std::vector< double > cbl::modelling::twopt::xi0_polynomial_LinearPoint	(	const std::vector< double >	rad,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

model for the monopole of the two-point correlation function

the function computes the monopole as a polynomial of used-defined order

Parameters

rad	the scale at which the model is computed
inputs	pointer to the structure that contains the dark matter two-point correlation function and \(\sigma_8(z)\), computed at a given (fixed) cosmology
parameter	6D vector containing the input parameters

Returns

the monopole of the two-point correlation function

Definition at line 133 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

xi2D_dispersion()

std::vector< std::vector< double > > cbl::modelling::twopt::xi2D_dispersion	(	const std::vector< double >	rp,
		const std::vector< double >	pi,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

model for the 2D two-point correlation function, in Cartesian coordinates

the function computes \(\xi(r_p,\pi)\) with the dispersion model (see e.g. Marulli et al. 2012 http://arxiv.org/abs/1203.1002), which is computed with either cbl::xi2D_lin_model or cbl::xi2D_model

Parameters

rp	the scale perpendicular to the line of sight at which the model is computed
pi	the scale parallel to the line of sight at which the model is computed
inputs	pointer to the structure that contains all the data required to implement the dispersion model
parameter	5D vector containing the input parameters

Returns

the 2D two-point correlation function in redshift space

Definition at line 48 of file ModelFunction_TwoPointCorrelation2D_cartesian.cpp.

xi_1halo()

vector< double > cbl::modelling::twopt::xi_1halo	(	const std::vector< double >	rad,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

model for the 1-halo term of the monopole of the two-point correlation function

this function computes the 1-halo term of the two-point correlation function by Fourier transforming the 1-halo term of the power spectrum:

\[\xi_{1halo}(r, z) = \frac{1}{2\pi^2}\int_{0}^{k_{max}}{\rm d}k\, k^2P_{1halo}(k, z)\frac{\sin (kr)}{kr}\]

where the 1-halo term of the power spectrum \(P_{1halo}(k, z)\), is computed by cbl::modelling::twopt::Pk_1halo

so the integral that is actually computed is the following:

\[\xi_{1halo}(r, z) = \frac{1}{2\pi^2}\int_{0}^{k_{max}}{\rm d}k\, \left[P_{cs}(k, z)+P_{ss}(k, z)\right]\frac{k\sin (kr)}{r} = \]

\[= \frac{ln(10)}{2\pi^2n_{gal}^2(z)}\int_{0}^{k_{max}}{\rm d}k\, \int_{log(M_{min})}^{log(M_{max})}{\rm d} log(M_h)M_h\, \tilde{u}_h(k, M_h, z)\,n_{h, interp}(M_h, z)\,\left[ 2<N_{cen}N_{sat}>(M_h)\,+ <N_{sat}(N_{sat}-1)>(M_h)\, \tilde{u}_h(k, M_h, z)\right]\frac{k\sin (kr)}{r} \]

where the galaxy number density, \(n_{gal}(z)\) is computed by cbl::modelling::twopt::ng, the Fourier transform of the halo density profile \(\tilde{u}_h(k, M_h, z)\) is computed by cbl::cosmology::Cosmology::density_profile_FourierSpace, \(n_{h, interp}(M_h, z)\) is an interpolation of the halo mass function cosmology::Cosmology::mass_function, \(<N_{cen}N_{sat}>(M_h)\) is computed by cbl::modelling::twopt::NcNs and \(<N_{sat}(N_{sat}-1)>(M_h)\) is computed by cbl::modelling::twopt::NsNs1

Parameters

rad	the scale at which the model is computed
inputs	pointer to the structure that contains the fixed input data used to construct the model
parameter	vector containing the model parameters

Returns

the 1-halo term of the monopole of the two-point correlation function

Definition at line 1169 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

xi_1halo_zspace()

double cbl::modelling::twopt::xi_1halo_zspace	(	const double	rp,
		const double	pi,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

model for the 1-halo term of the redshift-space monopole of the two-point correlation function

this function computes the 1-halo term of redshift-space spherically averaged correlation function with a modified version of the Kaiser model (sec. 2.3 of van den Bosch et al. 2012); it is used to derive the model of the 1-halo term of the projected correlation function accounting for residual redshift-space distortions caused by finite integration range

\[\xi_{1halo}(r_p, \pi, z) = \sum_{l=0}^2\xi_{2l}(r, z)\mathcal{P}_{2l}(\mu)\]

where

\[\xi_0(r, z) = \left(1 + \frac{2}{3}\beta + \frac{1}{5}\beta^2\right)\xi_{1halo}(r, z)\,,\]

\[\xi_2(r, z) = \left(\frac{4}{3}\beta + \frac{4}{7}\beta^2\right)\left[\xi_{1halo}(r, z)-3J_3(r, z)\right]\,,\]

\[\xi_4(r, z) = \frac{8}{35}\beta^2\left[\xi_{1halo}(r, z)+\frac{15}{2}J_3(r, z)-\frac{35}{2}J_5(r, z)\right]\,,\]

\[J_n(r, z) = \frac{1}{r^n}\int_0^r\xi_{1halo}(y, z)y^{n-1}{\rm d}y\]

the real-space galaxy correlation function \(\xi_{g, 1halo}(r, z)\) is computed by cbl::modelling::twopt::xi_1halo

Parameters

rp	the scale perpendicular to the line of sight at which the model is computed
pi	the scale parallel to the line of sight at which the model is computed
inputs	pointer to the structure that contains the fixed input data used to construct the model
parameter	vector containing the model parameters

Returns

the 1-halo term of the redshift-space monopole of the two-point correlation function

Definition at line 1274 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

xi_2halo()

vector< double > cbl::modelling::twopt::xi_2halo	(	const std::vector< double >	rad,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

model for the 2-halo term of the monopole of the two-point correlation function

this function computes the 2-halo term of the two-point correlation function by Fourier transforming the 2-halo term of the power spectrum:

\[\xi_{2halo}(r, z) = \frac{1}{2\pi^2}\int_{0}^{k_{max}}{\rm d}k\,k^2P_{2halo}(k, z)\frac{\sin (kr)}{kr}\]

where the 2-halo term of the power spectrum \(P_{2halo}(k, z)\), is computed by cbl::modelling::twopt::Pk_2halo

so the integral that is actually computed is the following:

\[\xi_{2halo}(r, z) = \frac{ln(10)}{2\pi^2n_{gal}^2(z)}\int_{0}^{k_{max}}{\rm d}k\, P_{m, interp}(k, z)\,\int_{log(M_{min})}^{log(M_{max})}{\rm d} log(M_h)M_h\, N_{gal}(M_h)\,n_{h, interp}(M_h, z)\,\,b_{h, interp}(M_h, z)\,\tilde{u}_h(k, M_h, z)\frac{k\sin (kr)}{r} \]

where the galaxy number density, \(n_{gal}(z)\) is computed by cbl::modelling::twopt::ng, \(P_{m, interp}(k, z)\) is an interpolation of the matter power spectrum cbl::cosmology::Cosmology::Pk, the average number of galaxies hosted in a dark matter halo of a given mass, \(N_{gal}(M_h)\), is computed by cbl::modelling::twopt::Navg, \(n_{h, interp}(M_h, z)\) is an interpolation of the halo mass function cosmology::Cosmology::mass_function, \(b_{h, interp}(M_h, z)\) is an interpolation of the halo bias cosmology::Cosmology::bias_halo and the Fourier transform of the halo density profile \(\tilde{u}_h(k, M_h, z)\) is computed by cbl::cosmology::Cosmology::density_profile_FourierSpace

Parameters

rad	the scale at which the model is computed
inputs	pointer to the structure that contains the fixed input data used to construct the model
parameter	vector containing the model parameters

Returns

the 2-halo term of the monopole of the two-point correlation function

Definition at line 1190 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

xi_2halo_zspace()

double cbl::modelling::twopt::xi_2halo_zspace	(	const double	rp,
		const double	pi,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

model for the 2-halo term of the redshift-space monopole of the two-point correlation function

this function computes the 2-halo term of redshift-space spherically averaged correlation function with a modified version of the Kaiser model (sec. 2.3 of van den Bosch et al. 2012); it is used to derive the model of the 2-halo term of the projected correlation function accounting for residual redshift-space distortions caused by finite integration range

\[\xi_{2halo}(r_p, \pi, z) = \sum_{l=0}^2\xi_{2l}(r, z)\mathcal{P}_{2l}(\mu)\]

where

\[\xi_0(r, z) = \left(1 + \frac{2}{3}\beta + \frac{1}{5}\beta^2\right)\xi_{2halo}(r, z)\,,\]

\[\xi_2(r, z) = \left(\frac{4}{3}\beta + \frac{4}{7}\beta^2\right)\left[\xi_{2halo}(r, z)-3J_3(r, z)\right]\,,\]

\[\xi_4(r, z) = \frac{8}{35}\beta^2\left[\xi_{2halo}(r, z)+\frac{15}{2}J_3(r, z)-\frac{35}{2}J_5(r, z)\right]\,,\]

\[J_n(r, z) = \frac{1}{r^n}\int_0^r\xi_{2halo}(y, z)y^{n-1}{\rm d}y\]

the real-space galaxy correlation function \(\xi_{g, 2halo}(r, z)\) is computed by cbl::modelling::twopt::xi_2halo

Parameters

rp	the scale perpendicular to the line of sight at which the model is computed
pi	the scale parallel to the line of sight at which the model is computed
inputs	pointer to the structure that contains the fixed input data used to construct the model
parameter	vector containing the model parameters

Returns

the 2-halo term of redshift-space monopole of the two-point correlation function

Definition at line 1283 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

xi_HOD()

std::vector< double > cbl::modelling::twopt::xi_HOD	(	const std::vector< double >	rad,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

HOD model of the monopole of the two-point correlation function.

the function computes:

\[\xi(r, z) = \xi_{1halo}(r, z)+\xi_{2halo}(r, z)\]

where \(\xi_{1halo}(r, z)\) and \(\xi_{2halo}(r, z)\) are computed by cbl::modelling::twopt::xi_1halo and cbl::modelling::twopt::xi_2halo, respectively

Parameters

rad	the scale at which the model is computed
inputs	pointer to the structure that contains the fixed input data used to construct the model
parameter	vector containing the model parameters

Returns

the HOD monopole of the two-point correlation function

Definition at line 1212 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

xi_HOD_zspace()

double cbl::modelling::twopt::xi_HOD_zspace	(	const double	rp,
		const double	pi,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

HOD model of the redshift-space monopole of the two-point correlation function.

this function computes the redshift-space spherically averaged correlation function with a modified version of the Kaiser model (sec. 2.3 of van den Bosch et al. 2012); it is used to derive the model of the projected correlation function accounting for residual redshift-space distortions caused by finite integration range

\[\xi(r_p, \pi, z) = \xi_{1halo}(r_p, \pi, z)+\xi_{2halo}(r_p, \pi, z)\]

where \(\xi_{1halo}(r_p, \pi, z)\) and \(\xi_{2halo}(r_p, \pi, z)\) are computed by cbl::modelling::twopt::xi_1halo_zspace and cbl::modelling::twopt::xi_2halo_zspace, respectively

Parameters

rp	the scale perpendicular to the line of sight at which the model is computed
pi	the scale parallel to the line of sight at which the model is computed
inputs	pointer to the structure that contains the fixed input data used to construct the model
parameter	vector containing the model parameters

Returns

the HOD redshift-space monopole of the two-point correlation function

Definition at line 1292 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

Xi_l() [1/2]

std::vector< std::vector< double > > cbl::modelling::twopt::Xi_l	(	const std::vector< double >	rr,
		const int	nmultipoles,
		const std::string	model,
		const std::vector< double >	parameter,
		const std::vector< std::shared_ptr< glob::FuncGrid >>	pk_interp,
		const double	prec = 1.e-5,
		const double	alpha_perp = 1.,
		const double	alpha_par = 1.
	)

the multipole of order l of the two-point correlation function

The function computes the multipoles of the two-point correlation function:

\[ \xi_l(s) = i^l \int \frac{\mathrm{d} k}{2\pi^2} k^2 P_l(k) j_l(ks) \]

where \(j_l(ks)\) are the Bessel functions, and \(P_l(k)\) is computed by cbl::modelling::twopt::Pk_l

Parameters

rr	vector of scales to compute multipoles
nmultipoles	the number of (even) multipoles to compute
model	the \(P(k,\mu)\) model
parameter	vector containing parameter values
pk_interp	vector containing power spectrum interpolating functions
prec	the integral precision
alpha_perp	the shift transverse to the l.o.s.
alpha_par	the shift parallel to the l.o.s.

Returns

the multipole of order l of the two-point correlation function

Definition at line 453 of file ModelFunction_TwoPointCorrelation.cpp.

Xi_l() [2/2]

std::vector< double > cbl::modelling::twopt::Xi_l	(	const std::vector< double >	rr,
		const std::vector< int >	dataset_order,
		const std::vector< bool >	use_pole,
		const std::string	model,
		const std::vector< double >	parameter,
		const std::vector< std::shared_ptr< glob::FuncGrid >>	pk_interp,
		const double	prec = 1.e-5,
		const double	alpha_perp = 1.,
		const double	alpha_par = 1.
	)

the multipole of order l of the two-point correlation function

The function computes the multipoles of the two-point correlation function:

\[ \xi_l(s) = i^l \int \frac{\mathrm{d} k}{2\pi^2} k^2 P_l(k) j_l(ks) \]

where \(j_l(ks)\) are the Bessel functions, and \(P_l(k)\) is computed by cbl::modelling::twopt::Pk_l

Parameters

rr	vector of scales to compute multipoles
dataset_order	vector that specify the multipole to be computed for each scale
use_pole	vector of booleans specifying if a given multipole should be computed
model	the \(P(k,\mu)\) model
parameter	vector containing parameter values
pk_interp	vector containing power spectrum interpolating functions
prec	the integral precision
alpha_perp	the shift transverse to the l.o.s.
alpha_par	the shift parallel to the l.o.s.

Returns

the multipole of order l of the two-point correlation function

Definition at line 471 of file ModelFunction_TwoPointCorrelation.cpp.

Xi_polar()

double cbl::modelling::twopt::Xi_polar	(	const double	rad_fid,
		const double	mu_fid,
		const double	alpha_perpendicular,
		const double	alpha_parallel,
		const std::vector< std::shared_ptr< cbl::glob::FuncGrid >>	xi_multipoles
	)

the polar two-point correlation function

The function computes the polar two-point correlation function from its multipoles as expressed in Kazin et al. 2013 (https://arxiv.org/pdf/1303.4391.pdf, appendix A)

\[ \xi(s_{\mathrm{true}}, \mu_{\mathrm{true}}) = \sum\xi_l(s_{\mathrm{true}}(s_{\mathrm{fid}}, \mu_{\mathrm{fid}}, \alpha_{\perp}, \alpha_{\parallel})) L_l(\mu_{\mathrm{true}}(\mu_{\mathrm{fid}}, \alpha_{\perp}, \alpha_{\parallel})) \]

where \(\xi_l(s)\) are the two-point correlation function monopoles up to l=4, and \( \mathcal{L}_l(\mu)\) are the Legendre polynomial.

The relations between fiducial and true quantities are:

\[ s_{\mathrm{true}} = s_{\mathrm{fid}} \sqrt{\alpha_{\|}^{2} \mu_{\mathrm{fid}}^{2}+\alpha_{\perp}^2\left(1-\mu_{\mathrm{fid}}^2\right)} \]

\[ \mu_{\mathrm{true}} = \mu_{\mathrm{fid}} \frac{\alpha_{\|}}{\sqrt{\alpha_{\|}^{2} \mu_{\mathrm{fid}}^{2}+\alpha_{\perp}^2\left(1-\mu_{\mathrm{fid}}^2\right)}} \]

Parameters

rad_fid	fiducial separation
mu_fid	fiducial \(\mu\)
alpha_perpendicular	Alcock-Paczynski perpendicular parameter
alpha_parallel	Alcock-Paczynski perpendicular parameter
xi_multipoles	vector containing two-point correlation function multipoles interpolating functions

Returns

the polar two-point correlation function.

Definition at line 492 of file ModelFunction_TwoPointCorrelation.cpp.

Xi_rppi()

std::vector< std::vector< double > > cbl::modelling::twopt::Xi_rppi	(	const std::vector< double >	rp,
		const std::vector< double >	pi,
		const std::string	model,
		const std::vector< double >	parameter,
		const std::vector< std::shared_ptr< glob::FuncGrid >>	pk_interp,
		const double	prec = 1.e-5,
		const double	alpha_perp = 1.,
		const double	alpha_par = 1.
	)

the cartesian two-point correlation function

The function computes the cartesian two-point correlation function:

\[ \xi_(r_p, \pi) = \xi_0(s) + \xi_2(s) \mathcal{L}_2(\mu)+ \xi_4(s) \mathcal{L}_4(\mu) \]

where \(xi_0(s), \xi_2(s), \xi_4(s)\) are the two-point correlation function monopoles and \( \mathcal{L}_l(\mu)\) are the Legendre polynomial.

Parameters

rp	vector of scales transverse to the line of sight
pi	vector of scales parallel to the line of sight
model	the \(P(k,\mu)\) model
parameter	vector containing parameter values
pk_interp	vector containing power spectrum interpolating functions
prec	the integral precision
alpha_perp	the shift transverse to the l.o.s.
alpha_par	the shift parallel to the l.o.s.

Returns

the cartesian two-point correlation function.

Definition at line 512 of file ModelFunction_TwoPointCorrelation.cpp.

xi_Wedges() [1/2]

std::vector< std::vector< double > > cbl::modelling::twopt::xi_Wedges	(	const std::vector< double >	rr,
		const int	nWedges,
		const std::vector< std::vector< double >>	mu_integral_limits,
		const std::string	model,
		const std::vector< double >	parameter,
		const std::vector< std::shared_ptr< glob::FuncGrid >>	pk_interp,
		const double	prec = 1.e-5,
		const double	alpha_perp = 1,
		const double	alpha_par = 1.
	)

the model wedges of the two-point correlation function

this function computes the wedges of the two-point correlation function either with the de-wiggled model or with the mode-coupling model (Kazin et al. 2012):

\[ \xi(\Delta \mu, s) = \xi_0(s)+\frac{1}{2} \left( \frac{ \mu_{max}^3- \mu_{min}^3}{\mu_{max}-\mu_{min}} -1 \right)\xi_2(s)+ \frac{1}{8} \left( \frac{ 7 \left(\mu_{max}^5-\mu_{min}^5\right)-10 \left(\mu_{max}^3- \mu_{min}^3 \right)}{\mu_{max}-\mu_{min}}+3 \right) \xi_4(s). \]

where \(\xi_0(s), \xi_2(s), \xi_4(s)\) are the two-point correlation function multipoles computed by cbl::modelling::twopt::Xi_l

Parameters

rr	vector of scales to compute wedges
nWedges	the number of wedges
mu_integral_limits	the \(\mu\) integral limits used to measure the wedges
model	the \(P(k,\mu)\) model; the possible options are: dispersion_dewiggled, dispersion_modecoupling
parameter	vector containing parameter values
pk_interp	vector containing power spectrum interpolating functions
prec	the integral precision
alpha_perp	the shift transverse to the l.o.s.
alpha_par	the shift parallel to the l.o.s.

Returns

the wedges of the two-point correlation function.

Definition at line 70 of file ModelFunction_TwoPointCorrelation_wedges.cpp.

xi_Wedges() [2/2]

std::vector< double > cbl::modelling::twopt::xi_Wedges	(	const std::vector< double >	rr,
		const std::vector< int >	dataset_order,
		const std::vector< std::vector< double >>	mu_integral_limits,
		const std::string	model,
		const std::vector< double >	parameter,
		const std::vector< std::shared_ptr< glob::FuncGrid >>	pk_interp,
		const double	prec = 1.e-5,
		const double	alpha_perp = 1.,
		const double	alpha_par = 1.
	)

the wedge of the two-point correlation function

The function computes the wedges of the two-point correlation function (Kazin et al. 2012):

\[ \xi(\Delta \mu, s) = \xi_0(s)+\frac{1}{2} \left( \frac{ \mu_{max}^3- \mu_{min}^3}{\mu_{max}-\mu_{min}} -1 \right)\xi_2(s)+ \frac{1}{8} \left( \frac{ 7 \left(\mu_{max}^5-\mu_{min}^5\right)-10 \left(\mu_{max}^3- \mu_{min}^3 \right)}{\mu_{max}-\mu_{min}}+3 \right) \xi_4(s). \]

where \(\xi_0(s), \xi_2(s), \xi_4(s)\) are the two-point correlation function multipoles

Parameters

rr	vector of scales to compute wedges
dataset_order	vector that specify the wedges to be computed for each scale
mu_integral_limits	the \(\mu\) integral limits used to measure the wedges
model	the \(P(k,\mu)\) model; the possible options are: dispersion_dewiggled, dispersion_modecoupling
parameter	vector containing parameter values
pk_interp	vector containing power spectrum interpolating functions
prec	the integral precision
alpha_perp	the shift transverse to the l.o.s.
alpha_par	the shift parallel to the l.o.s.

Returns

the wedges of the two-point correlation function.

Definition at line 47 of file ModelFunction_TwoPointCorrelation_wedges.cpp.

xi_zspace()

double cbl::modelling::twopt::xi_zspace	(	FunctionVectorVectorPtrVectorRef	func,
		const double	rp,
		const double	pi,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

function used to compute the redshift-space monopole of the two-point correlation function

this function is used to compute the redshift-space spherically averaged correlation function with a modified version of the Kaiser model (sec. 2.3 of van den Bosch et al. 2012); it is used to derive the model projected correlation function accounting for residual redshift-space distortions caused by finite integration range

\[\xi(r_p, \pi, z) = \sum_{l=0}^2\xi_{2l}(r, z)\mathcal{P}_{2l}(\mu)\]

where

\[\xi_0(r, z) = \left(1 + \frac{2}{3}\beta + \frac{1}{5}\beta^2\right)\xi(r, z)\,,\]

\[\xi_2(r, z) = \left(\frac{2}{3}\beta + \frac{4}{7}\beta^2\right)\left[\xi(r, z)-3J_3(r, z)\right]\,,\]

\[\xi_4(r, z) = \frac{8}{35}\beta^2\left[\xi(r, z)+\frac{15}{2}J_3(r, z)-\frac{35}{2}J_5(r, z)\right]\,,\]

\[J_n(r, z) = \frac{1}{r^n}\int_0^r\xi(y, z)y^{n-1}{\rm d}y\]

the real-space galaxy correlation function \(\xi(r, z)\) is either the 1-halo, the 2-halo, or the full-shape real-space correlation function, computed by either cbl::modelling::twopt::xi_1halo, cbl::modelling::twopt::xi_2halo, or cbl::modelling::twopt::xi_HOD, respectively

Parameters

func	the two-point correlation function that will be integrated (it can be either the 1-halo, the 2-halo, or the full-shape correlation function)
rp	the scale perpendicular to the line of sight at which the model is computed
pi	the scale parallel to the line of sight at which the model is computed
inputs	pointer to the structure that contains the fixed input data used to construct the model
parameter	vector containing the model parameters

Returns

the redshift-space monopole of the two-point correlation function

Definition at line 1232 of file ModelFunction_TwoPointCorrelation1D_monopole.cpp.

Xil_interp()

cbl::glob::FuncGrid cbl::modelling::twopt::Xil_interp	(	const std::vector< double >	kk,
		const int	l,
		const std::string	model,
		const std::vector< double >	parameter,
		const std::vector< std::shared_ptr< glob::FuncGrid >>	pk_interp,
		const double	prec = 1.e-5,
		const double	alpha_perp = 1.,
		const double	alpha_par = 1.
	)

the interpolating function of multipole expansion of the two-point correlation function at a given order l

The function computes the multipoles of the two-point correlation function:

\[ \xi_l(s) = i^l \int \frac{\mathrm{d} k}{2\pi^2} k^2 P_l(k) j_l(ks) \]

where \(j_l(ks)\) are the Bessel functions, and \(P_l(k)\) is computed by cbl::modelling::twopt::Pk_l

Parameters

kk	the wave vector module vector
l	the order of the expansion
model	the \(P(k,\mu)\) model
parameter	vector containing parameter values
pk_interp	vector containing power spectrum interpolating functions
prec	the integral precision
alpha_perp	the shift transverse to the l.o.s.
alpha_par	the shift parallel to the l.o.s.

Returns

the interpolation function of the multipole expansion of two-point correlation function at a given order l

Definition at line 437 of file ModelFunction_TwoPointCorrelation.cpp.

xiMultipoles()

std::vector< double > cbl::modelling::twopt::xiMultipoles	(	const std::vector< double >	rad,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

return multipoles of the two-point correlation function

The functions computes the multipoles of the two-point correlation function

\[ \xi_l(s) = i^l \int \frac{\mathrm{d} k}{2\pi^2} k^2 P_l(k) j_l(ks); \]

where \(j_l(ks)\) are the Bessel functions.

The function takes as inputs four fundamental parameters

• \(\alpha_{\perp}\)
• \(\alpha_{\parallel}\)
• \(f(z)\sigma_8(z)\)
• \(b(z)\sigma_8(z)\)
• \( \Sigma_S \)

Parameters

rad	the scale at which the model is computed
inputs	pointer to the structure that contains the data required to construct the model
parameter	4D vector containing the input parameters

Returns

the multipoles of the two-point correlation function

Definition at line 48 of file ModelFunction_TwoPointCorrelation_multipoles.cpp.

xiMultipoles_BAO()

std::vector< double > cbl::modelling::twopt::xiMultipoles_BAO	(	const std::vector< double >	rad,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

return multipoles of the two-point correlation function, intended for anisotropic BAO measurements (Ross et al. 2017). In only works with monopole and quadrupole.

The functions computes the multipoles of the two-point correlation function:

\[ \xi_0(s) = B_0\xi_0(s, \alpha_{\perp}, \alpha_{\parallel})+A_0^0+\frac{A_0^1}{s}+\frac{A_0^2}{s^2} \]

\[ \xi_2(s) = \frac{5}{2}\left[B_2\xi_{\mu2}(s, \alpha_{\perp}, \alpha_{\parallel})-B_0\xi_0(s, \alpha_{\perp}, \alpha_{\parallel})\right] +A_2^0+\frac{A_2^1}{s}+\frac{A_2^2}{s^2} \]

where \(\xi_0(s, \alpha_{\perp}, \alpha_{\parallel})\) is the monopole computed at the fiducial cosmology, \(\xi_{\mu2}(s, \alpha_{\perp}, \alpha_{\parallel}) = 3\int_0^1\mathrm{d}\mu\mu^2\xi(s, \mu, \alpha_{\perp}, \alpha_{\parallel})\).

The function takes as inputs ten parameters

• \(\alpha_{\perp}\)
• \(\alpha_{\parallel}\)
• \(B_0\)
• \(B_2\)
• \(A^0_0\)
• \(A^0_1\)
• \(A^0_2\)
• \(A^2_0\)
• \(A^2_1\)
• \(A^2_2\)

Parameters

rad	the scale at which the model is computed
inputs	pointer to the structure that contains the data required to construct the model
parameter	10D vector containing the input parameters

Returns

the multipoles of the two-point correlation function

Definition at line 192 of file ModelFunction_TwoPointCorrelation_multipoles.cpp.

xiMultipoles_sigma8_bias()

std::vector< double > cbl::modelling::twopt::xiMultipoles_sigma8_bias	(	const std::vector< double >	rad,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

return multipoles of the two-point correlation function

The functions computes the multipoles of the two-point correlation function

\[ \xi_l(s) = i^l \int \frac{\mathrm{d} k}{2\pi^2} k^2 P_l(k) j_l(ks); \]

where \(j_l(ks)\) are the Bessel functions.

The function takes as inputs 2 parameters

• \(\sigma_8(z)\)
• \(b(z)\)

Parameters

rad	the scale at which the model is computed
inputs	pointer to the structure that contains the data required to construct the model
parameter	vector containing the input parameters

Returns

the multipoles of the two-point correlation function

Definition at line 157 of file ModelFunction_TwoPointCorrelation_multipoles.cpp.

xiWedges()

std::vector< double > cbl::modelling::twopt::xiWedges	(	const std::vector< double >	rad,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

the model wedges of the two-point correlation function

this functions computes the wedges of the two-point either with the de-wiggled model or with the mode-coupling model; specifically, the wedges are computed by cbl::modelling::twopt::xi_Wedges

the wedges of the two-point correlation functions are defined as follows:

\[ \xi_w(s) = \frac{1}{\mu_{max}-\mu_{min}} \int_{\mu_{min}}^{\mu_{max}} \mathrm{\mu} \xi(s', \mu'); \]

where \( \xi(s', \mu')\) is the polar two-point correlation function computed at shifted positions \(s' = s\sqrt{\mu^2\alpha^2_{\parallel}+(1-\mu^2)\alpha^2_{\perp}}\), \(\mu' = \mu\alpha_{\parallel}/\sqrt{\mu^2\alpha^2_{\parallel}+(1-\mu^2)\alpha^2_{\perp}}\)

Parameters

rad	the scale at which the model is computed
inputs	pointer to the structure that contains the de-wiggled power spectrum, the number of wedges and \(\sigma_8(z)\), computed at a given (fixed) cosmology
parameter	vector containing the input parameters

Returns

the wedges of the two-point correlation function

Definition at line 94 of file ModelFunction_TwoPointCorrelation_wedges.cpp.

xiWedges_BAO()

std::vector< double > cbl::modelling::twopt::xiWedges_BAO	(	const std::vector< double >	rad,
		const std::shared_ptr< void >	inputs,
		std::vector< double > &	parameter
	)

return the wedges of the two-point correlation function, intended for anisotropic BAO measurements

the wedges of the two-point correlation function are computed as follows (Ross et al. 2017):

\[ \xi_{\perp}(s) = B_{\perp}\xi_{\perp}(s, \alpha_{\perp}, \alpha_{\parallel})+A_{\perp}^0+\frac{A_{\perp}^1}{s}+\frac{A_{\perp}^2}{s^2}; \\ \xi_{\parallel}(s) = B_{\parallel}\xi_{\parallel}(s, \alpha_{\parallel}, \alpha_{\parallel})+A_{\parallel}^0+\frac{A_{\parallel}^1}{s}+\frac{A_{\parallel}^2}{s^2}; \\ \]

where \(\xi_{\perp}\), \(\xi_{\parallel}\) are the two wedges of the two-point correlation function.

The function takes as inputs ten parameters

• \(\alpha_{\perp}\)
• \(\alpha_{\parallel}\)
• \(B_0\)
• \(B_2\)
• \(A^0_0\)
• \(A^0_1\)
• \(A^0_2\)
• \(A^2_0\)
• \(A^2_1\)
• \(A^2_2\)

Parameters

rad	the scale at which the model is computed
inputs	pointer to the structure that contains the de-wiggled power spectrum, the number of wedges and \(\sigma_8(z)\), computed at a given (fixed) cosmology
parameter	10D vector containing the input parameters

Returns

the wedges of the two-point correlation function

Definition at line 203 of file ModelFunction_TwoPointCorrelation_wedges.cpp.