#include "harmonic.h"

Include dependency graph for harmonic.c:

Functions
int	harmonic_cl_at_l (struct harmonic phr, double l, double cl_tot, double cl_md, double cl_md_ic)

int	harmonic_init (struct precision ppr, struct background pba, struct perturbations ppt, struct primordial ppm, struct fourier pfo, struct transfer ptr, struct harmonic *phr)

int	harmonic_free (struct harmonic *phr)

int	harmonic_indices (struct background pba, struct perturbations ppt, struct transfer ptr, struct primordial ppm, struct harmonic *phr)

int	harmonic_cls (struct background pba, struct perturbations ppt, struct transfer ptr, struct primordial ppm, struct harmonic *phr)

int	harmonic_compute_cl (struct background pba, struct perturbations ppt, struct transfer ptr, struct primordial ppm, struct harmonic phr, int index_md, int index_ic1, int index_ic2, int index_l, int cl_integrand_num_columns, double cl_integrand, double primordial_pk, double transfer_ic1, double *transfer_ic2)

int	harmonic_pk_at_z (struct background pba, struct harmonic phr, enum linear_or_logarithmic mode, double z, double output_tot, double output_ic, double output_cb_tot, double output_cb_ic)

int	harmonic_pk_at_k_and_z (struct background pba, struct primordial ppm, struct harmonic phr, double k, double z, double pk_tot, double pk_ic, double pk_cb_tot, double *pk_cb_ic)

int	harmonic_pk_nl_at_z (struct background pba, struct harmonic phr, enum linear_or_logarithmic mode, double z, double output_tot, double output_cb_tot)

int	harmonic_pk_nl_at_k_and_z (struct background pba, struct primordial ppm, struct harmonic phr, double k, double z, double pk_tot, double *pk_cb_tot)

int	harmonic_fast_pk_at_kvec_and_zvec (struct background pba, struct harmonic phr, double kvec, int kvec_size, double zvec, int zvec_size, double pk_tot_out, double pk_cb_tot_out, int nonlinear)

int	harmonic_sigma (struct background pba, struct primordial ppm, struct harmonic phr, double R, double z, double sigma)

int	harmonic_sigma_cb (struct background pba, struct primordial ppm, struct harmonic phr, double R, double z, double sigma_cb)

int	harmonic_tk_at_z (struct background pba, struct harmonic phr, double z, double *output)

int	harmonic_tk_at_k_and_z (struct background pba, struct harmonic phr, double k, double z, double *output)

Detailed Description

Documented harmonic module

Julien Lesgourgues, 1.11.2019

This module computes the harmonic power spectra $C_l^{X}$ 's given the transfer functions and the primordial spectra.

The following functions can be called from other modules:

harmonic_init() at the beginning (but after transfer_init())
harmonic_cl_at_l() at any time for computing individual 's at any l
harmonic_free() at the end

Function Documentation

◆ harmonic_cl_at_l()

int harmonic_cl_at_l	(	struct harmonic *	phr,
		double	l,
		double *	cl_tot,
		double **	cl_md,
		double **	cl_md_ic
	)

Anisotropy power spectra 's for all types, modes and initial conditions.

This routine evaluates all the 's at a given value of l by interpolating in the pre-computed table. When relevant, it also sums over all initial conditions for each mode, and over all modes.

This function can be called from whatever module at whatever time, provided that harmonic_init() has been called before, and harmonic_free() has not been called yet.

Parameters

phr	Input: pointer to harmonic structure (containing pre-computed table)
l	Input: multipole number
cl_tot	Output: total 's for all types (TT, TE, EE, etc..)
cl_md	Output: 's for all types (TT, TE, EE, etc..) decomposed mode by mode (scalar, tensor, ...) when relevant
cl_md_ic	Output: 's for all types (TT, TE, EE, etc..) decomposed by pairs of initial conditions (adiabatic, isocurvatures) for each mode (usually, only for the scalar mode) when relevant

Returns: the error status

Summary:

define local variables
(a) treat case in which there is only one mode and one initial condition. Then, only cl_tot needs to be filled.
(b) treat case in which there is only one mode with several initial condition. Fill cl_md_ic[index_md=0] and sum it to get cl_tot.
(c) loop over modes
--> (c.1.) treat case in which the mode under consideration has only one initial condition. Fill cl_md[index_md].
--> (c.2.) treat case in which the mode under consideration has several initial conditions. Fill cl_md_ic[index_md] and sum it to get cl_md[index_md]
--> (c.3.) add contribution of cl_md[index_md] to cl_tot

◆ harmonic_init()

int harmonic_init	(	struct precision *	ppr,
		struct background *	pba,
		struct perturbations *	ppt,
		struct primordial *	ppm,
		struct fourier *	pfo,
		struct transfer *	ptr,
		struct harmonic *	phr
	)

This routine initializes the harmonic structure (in particular, computes table of anisotropy and Fourier spectra $C_l^{X}, P(k), ...$ )

Parameters

ppr	Input: pointer to precision structure
pba	Input: pointer to background structure (will provide H, Omega_m at redshift of interest)
ppt	Input: pointer to perturbation structure
ptr	Input: pointer to transfer structure
ppm	Input: pointer to primordial structure
pfo	Input: pointer to fourier structure
phr	Output: pointer to initialized harmonic structure

Returns: the error status

Summary:

check that we really want to compute at least one spectrum
initialize indices and allocate some of the arrays in the harmonic structure
deal with 's, if any
a pointer to the fourier structure is stored in the spectra structure. This odd, unusual and unelegant feature has been introduced in v2.8 in order to keep in use some deprecated functions harmonic_pk_...() that are now pointing at new function fourier_pk_...(). In the future, if the deprecated functions are removed, it will be possible to remove also this pointer.

◆ harmonic_free()

int harmonic_free ( struct harmonic * phr )

This routine frees all the memory space allocated by harmonic_init().

To be called at the end of each run, only when no further calls to harmonic_cls_at_l(), harmonic_pk_at_z(), harmonic_pk_at_k_and_z() are needed.

Parameters

phr	Input: pointer to harmonic structure (which fields must be freed)

Returns: the error status

◆ harmonic_indices()

int harmonic_indices	(	struct background *	pba,
		struct perturbations *	ppt,
		struct transfer *	ptr,
		struct primordial *	ppm,
		struct harmonic *	phr
	)

This routine defines indices and allocates tables in the harmonic structure

Parameters

pba	Input: pointer to background structure
ppt	Input: pointer to perturbation structure
ptr	Input: pointer to transfer structure
ppm	Input: pointer to primordial structure
phr	Input/output: pointer to harmonic structure

Returns: the error status

◆ harmonic_cls()

int harmonic_cls	(	struct background *	pba,
		struct perturbations *	ppt,
		struct transfer *	ptr,
		struct primordial *	ppm,
		struct harmonic *	phr
	)

This routine computes a table of values for all harmonic spectra 's, given the transfer functions and primordial spectra.

Parameters

pba	Input: pointer to background structure
ppt	Input: pointer to perturbation structure
ptr	Input: pointer to transfer structure
ppm	Input: pointer to primordial structure
phr	Input/Output: pointer to harmonic structure

Returns: the error status

Summary:

define local variables
allocate pointers to arrays where results will be stored
store values of l
loop over modes (scalar, tensors, etc). For each mode:
--> (a) store number of l values for this mode
--> (b) allocate arrays where results will be stored
--> (c) loop over initial conditions
—> loop over l values defined in the transfer module. For each l, compute the 's for all types (TT, TE, ...) by convolving primordial spectra with transfer functions. This elementary task is assigned to harmonic_compute_cl()
--> (d) now that for a given mode, all possible 's have been computed, compute second derivative of the array in which they are stored, in view of spline interpolation.

◆ harmonic_compute_cl()

int harmonic_compute_cl	(	struct background *	pba,
		struct perturbations *	ppt,
		struct transfer *	ptr,
		struct primordial *	ppm,
		struct harmonic *	phr,
		int	index_md,
		int	index_ic1,
		int	index_ic2,
		int	index_l,
		int	cl_integrand_num_columns,
		double *	cl_integrand,
		double *	primordial_pk,
		double *	transfer_ic1,
		double *	transfer_ic2
	)

This routine computes the 's for a given mode, pair of initial conditions and multipole, but for all types (TT, TE...), by convolving the transfer functions with the primordial spectra.

Parameters

pba	Input: pointer to background structure
ppt	Input: pointer to perturbation structure
ptr	Input: pointer to transfer structure
ppm	Input: pointer to primordial structure
phr	Input/Output: pointer to harmonic structure (result stored here)
index_md	Input: index of mode under consideration
index_ic1	Input: index of first initial condition in the correlator
index_ic2	Input: index of second initial condition in the correlator
index_l	Input: index of multipole under consideration
cl_integrand_num_columns	Input: number of columns in cl_integrand
cl_integrand	Input: an allocated workspace
primordial_pk	Input: table of primordial spectrum values
transfer_ic1	Input: table of transfer function values for first initial condition
transfer_ic2	Input: table of transfer function values for second initial condition

Returns: the error status

◆ harmonic_pk_at_z()

int harmonic_pk_at_z	(	struct background *	pba,
		struct harmonic *	phr,
		enum linear_or_logarithmic	mode,
		double	z,
		double *	output_tot,
		double *	output_ic,
		double *	output_cb_tot,
		double *	output_cb_ic
	)

Matter power spectrum for arbitrary redshift and for all initial conditions.

This function is deprecated since v2.8. Try using fourier_pk_at_z() instead.

Parameters

pba	Input: pointer to background structure (used for converting z into tau)
phr	Input: pointer to harmonic structure (containing pre-computed table)
mode	Input: linear or logarithmic
z	Input: redshift
output_tot	Output: total matter power spectrum P(k) in (linear mode), or its logarithms (logarithmic mode)
output_ic	Output: for each pair of initial conditions, matter power spectra P(k) in (linear mode), or their logarithms and cross-correlation angles (logarithmic mode)
output_cb_tot	Output: CDM+baryon power spectrum P_cb(k) in (linear mode), or its logarithms (logarithmic mode)
output_cb_ic	Output: for each pair of initial conditions, CDM+baryon power spectra P_cb(k) in (linear mode), or their logarithms and cross-correlation angles (logarithmic mode)

Returns: the error status

◆ harmonic_pk_at_k_and_z()

int harmonic_pk_at_k_and_z	(	struct background *	pba,
		struct primordial *	ppm,
		struct harmonic *	phr,
		double	k,
		double	z,
		double *	pk_tot,
		double *	pk_ic,
		double *	pk_cb_tot,
		double *	pk_cb_ic
	)

Matter power spectrum for arbitrary wavenumber, redshift and initial condition.

This function is deprecated since v2.8. Try using fourier_pk_linear_at_k_and_z() instead.

Parameters

pba	Input: pointer to background structure (used for converting z into tau)
ppm	Input: pointer to primordial structure (used only in the case 0 < k < kmin)
phr	Input: pointer to harmonic structure (containing pre-computed table)
k	Input: wavenumber in 1/Mpc
z	Input: redshift
pk_tot	Output: total matter power spectrum P(k) in
pk_ic	Output: for each pair of initial conditions, matter power spectra P(k) in
pk_cb_tot	Output: b+CDM power spectrum P(k) in
pk_cb_ic	Output: for each pair of initial conditions, b+CDM power spectra P(k) in

Returns: the error status

◆ harmonic_pk_nl_at_z()

int harmonic_pk_nl_at_z	(	struct background *	pba,
		struct harmonic *	phr,
		enum linear_or_logarithmic	mode,
		double	z,
		double *	output_tot,
		double *	output_cb_tot
	)

Non-linear total matter power spectrum for arbitrary redshift.

This function is deprecated since v2.8. Try using fourier_pk_at_z() instead.

Parameters

pba	Input: pointer to background structure (used for converting z into tau)
phr	Input: pointer to harmonic structure (containing pre-computed table)
mode	Input: linear or logarithmic
z	Input: redshift
output_tot	Output: total matter power spectrum P(k) in (linear mode), or its logarithms (logarithmic mode)
output_cb_tot	Output: b+CDM power spectrum P(k) in (linear mode), or its logarithms (logarithmic mode)

Returns: the error status

◆ harmonic_pk_nl_at_k_and_z()

int harmonic_pk_nl_at_k_and_z	(	struct background *	pba,
		struct primordial *	ppm,
		struct harmonic *	phr,
		double	k,
		double	z,
		double *	pk_tot,
		double *	pk_cb_tot
	)

Non-linear total matter power spectrum for arbitrary wavenumber and redshift.

This function is deprecated since v2.8. Try using fourier_pk_at_k_and_z() instead.

Parameters

pba	Input: pointer to background structure (used for converting z into tau)
ppm	Input: pointer to primordial structure (used only in the case 0 < k < kmin)
phr	Input: pointer to harmonic structure (containing pre-computed table)
k	Input: wavenumber in 1/Mpc
z	Input: redshift
pk_tot	Output: total matter power spectrum P(k) in
pk_cb_tot	Output: b+CDM power spectrum P(k) in

Returns: the error status

◆ harmonic_fast_pk_at_kvec_and_zvec()

int harmonic_fast_pk_at_kvec_and_zvec	(	struct background *	pba,
		struct harmonic *	phr,
		double *	kvec,
		int	kvec_size,
		double *	zvec,
		int	zvec_size,
		double *	pk_tot_out,
		double *	pk_cb_tot_out,
		int	nonlinear
	)

Return the P(k,z) for a grid of (k_i,z_j) passed in input, for all available pk types (_m, _cb), either linear or nonlinear depending on input.

This function is deprecated since v2.8. Try using fourier_pks_at_kvec_and_zvec() instead.

Parameters

pba	Input: pointer to background structure
phr	Input: pointer to harmonic structure
kvec	Input: array of wavenumbers in ascending order (in 1/Mpc)
kvec_size	Input: size of array of wavenumbers
zvec	Input: array of redshifts in arbitrary order
zvec_size	Input: size of array of redshifts
pk_tot_out	Output: P(k_i,z_j) for total matter (if available) in Mpc**3
pk_cb_tot_out	Output: P_cb(k_i,z_j) for cdm+baryons (if available) in Mpc**3
nonlinear	Input: TRUE or FALSE (to output nonlinear or linear P(k,z))

Returns: the error status

◆ harmonic_sigma()

int harmonic_sigma	(	struct background *	pba,
		struct primordial *	ppm,
		struct harmonic *	phr,
		double	R,
		double	z,
		double *	sigma
	)

This routine computes sigma(R) given P(k) for total matter power spectrum (does not check that k_max is large enough)

This function is deprecated since v2.8. Try using fourier_sigmas_at_z() instead.

Parameters

pba	Input: pointer to background structure
ppm	Input: pointer to primordial structure
phr	Input: pointer to harmonic structure
R	Input: radius in Mpc
z	Input: redshift
sigma	Output: variance in a sphere of radius R (dimensionless)

Returns: the error status

◆ harmonic_sigma_cb()

int harmonic_sigma_cb	(	struct background *	pba,
		struct primordial *	ppm,
		struct harmonic *	phr,
		double	R,
		double	z,
		double *	sigma_cb
	)

This routine computes sigma(R) given P(k) for baryon+cdm power spectrum (does not check that k_max is large enough)

This function is deprecated since v2.8. Try using fourier_sigmas_at_z() instead.

Parameters

pba	Input: pointer to background structure
ppm	Input: pointer to primordial structure
phr	Input: pointer to harmonic structure
R	Input: radius in Mpc
z	Input: redshift
sigma_cb	Output: variance in a sphere of radius R (dimensionless)

Returns: the error status

◆ harmonic_tk_at_z()

int harmonic_tk_at_z	(	struct background *	pba,
		struct harmonic *	phr,
		double	z,
		double *	output
	)

Obsolete function, superseeded by perturbations_sources_at_tau() (at the time of the switch, this function was anyway never used anywhere)

Parameters

pba	Input: pointer to background structure (used for converting z into tau)
phr	Input: pointer to harmonic structure (containing pre-computed table)
z	Input: redshift
output	Output: matter transfer functions

Returns: the error status

◆ harmonic_tk_at_k_and_z()

int harmonic_tk_at_k_and_z	(	struct background *	pba,
		struct harmonic *	phr,
		double	k,
		double	z,
		double *	output
	)

Obsolete function, superseeded by perturbations_sources_at_tau() (at the time of the switch, this function was anyway never used anywhere)

Parameters

pba	Input: pointer to background structure (used for converting z into tau)
phr	Input: pointer to harmonic structure (containing pre-computed table)
k	Input: wavenumber in 1/Mpc
z	Input: redshift
output	Output: matter transfer functions

Returns: the error status

Functions

Detailed Description

Function Documentation

◆ harmonic_cl_at_l()

◆ harmonic_init()

◆ harmonic_free()

◆ harmonic_indices()

◆ harmonic_cls()

◆ harmonic_compute_cl()

◆ harmonic_pk_at_z()

◆ harmonic_pk_at_k_and_z()

◆ harmonic_pk_nl_at_z()

◆ harmonic_pk_nl_at_k_and_z()

◆ harmonic_fast_pk_at_kvec_and_zvec()

◆ harmonic_sigma()

◆ harmonic_sigma_cb()

◆ harmonic_tk_at_z()

◆ harmonic_tk_at_k_and_z()