#include <fftlog.hpp>

Inheritance diagram for trv::maths::SphericalBesselTransform:

Collaboration diagram for trv::maths::SphericalBesselTransform:

Public Member Functions
	SphericalBesselTransform (int ell, int n, bool threaded=true)
	Construct the spherical Bessel transform.

void	initialise (std::vector< double > sample_pts, double kr_c, bool lowring=true, trva::ExtrapOption extrap=trva::ExtrapOption::NONE, double extrap_exp=2.)
	Initialise the spherical Bessel transform.

void	initialise (std::vector< double > sample_pts, double kr_c, bool lowring=true, int extrap=0, double extrap_exp=2.)
	Initialise the spherical Bessel transform.

void	biased_transform (std::vector< std::complex< double > > &a, std::vector< std::complex< double > > &b)
	Perform the (forward biased) spherical Bessel transform.

void	transform_cosmological_multipole (int dir, std::vector< std::complex< double > > &pre_samples, std::vector< std::complex< double > > &post_samples)
	Transform csomological multipole samples.

Public Member Functions inherited from trv::maths::HankelTransform
	HankelTransform (double mu, double q, bool threaded=true)
	Construct the Hankel transform.

	~HankelTransform ()
	Destruct the Hankel transform.

void	initialise (std::vector< double > sample_pts, double kr_c, bool lowring=true, trva::ExtrapOption extrap=trva::ExtrapOption::NONE, double extrap_exp=2.)
	Initialise the Hankel transform.

void	initialise (std::vector< double > sample_pts, double kr_c, bool lowring=true, int extrap=0, double extrap_exp=2.)
	Initialise the Hankel transform.

void	biased_transform (std::complex< double > a, std::complex< double > b)
	Perform the (forward biased) Hankel transform.

std::vector< std::complex< double > >	compute_kernel_coeff ()
	Compute the FFTLog transform kernel coefficients \( u \).

double	calc_lowring_pivot (double delta, double kr_c=1.)
	Calculate a low-ringing FFTLog transform pivot value \( k r = k_c r_c \).

Public Attributes
int	degree
	degree of the spherical Bessel transform

Public Attributes inherited from trv::maths::HankelTransform
double	order
	order of the Hankel transform

double	bias
	power-law bias index

int	nsamp = 0
	number of samples provided

int	nsamp_trans = 0
	number of samples transformed

double	logres = 0.
	logarithmic interval sample spacing

double	pivot = 1.
	pivot value

std::vector< double >	pre_sampts
	logarithmically linearly-spaced sample points pre-transform

std::vector< double >	post_sampts
	logarithmically linearly-spaced sample points post-transform

Detailed Description

Definition at line 259 of file fftlog.hpp.

Constructor & Destructor Documentation

◆ SphericalBesselTransform()

trv::maths::SphericalBesselTransform::SphericalBesselTransform	(	int	ell,
		int	n,
		bool	threaded = true )

Construct the spherical Bessel transform.

Parameters

ell	Degree of the spherical Bessel transform.
n	Power-law bias index.
threaded	If `true` (default), use multi-threads FFT.

Definition at line 503 of file fftlog.cpp.

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Member Function Documentation

◆ initialise() [1/2]

void trv::maths::SphericalBesselTransform::initialise	(	std::vector< double >	sample_pts,
		double	kr_c,
		bool	lowring = true,
		trva::ExtrapOption	extrap = trva::ExtrapOption::NONE,
		double	extrap_exp = 2. )

Initialise the spherical Bessel transform.

This sets up the underlying Hankel transform with order \( \mu = \ell + 1/2 \). The low-ringing pivot value is enforced from an initial value of 1.

Parameters

sample_pts	Logarithmically linearly-spaced sample points. Must be even in length if extrapolation is enabled.
kr_c	Pivot value.
lowring	If true (default), set the pivot value by the low-ringing condition.
extrap	Extrapolation option. If not trv::array::ExtrapOption::NONE (default), the sample size for the transform is the smallest power of 2 that is greater than or equal to `extrap_exp` times the original number of sample points; the pre-transform samples are assumed to be real and must be even in length.
extrap_exp	Sample size expansion factor (default is 2) for extrapolation. The smallest power of 2 greater than or equal to this times the original number of sample points is used as the sample size for the transform.

Definition at line 509 of file fftlog.cpp.

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◆ initialise() [2/2]

void trv::maths::SphericalBesselTransform::initialise	(	std::vector< double >	sample_pts,
		double	kr_c,
		bool	lowring = true,
		int	extrap = 0,
		double	extrap_exp = 2. )

Initialise the spherical Bessel transform.

This sets up the underlying Hankel transform with order \( \mu = \ell + 1/2 \). The low-ringing pivot value is enforced from an initial value of 1.

Parameters

sample_pts	Logarithmically linearly-spaced sample points. Must even in length if extrapolation is enabled.
kr_c	Pivot value.
lowring	If true (default), set the pivot value by the low-ringing condition.
extrap	Extrapolation option. If not 0 (default), the sample size for the transform is the smallest power of 2 that is greater than or equal to `extrap_exp` times the original number of sample points; the pre-transform samples are assumed to be real and must be even in length.
extrap_exp	Sample size expansion factor (default is 2) for extrapolation. The smallest power of 2 greater than or equal to this times the original number of sample points is used as the sample size for the transform.

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 516 of file fftlog.cpp.

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◆ biased_transform()

void trv::maths::SphericalBesselTransform::biased_transform	(	std::vector< std::complex< double > > &	a,
		std::vector< std::complex< double > > &	b )

Perform the (forward biased) spherical Bessel transform.

The transform is defined here as

\[ b(k) = 4\pi \int_0^\infty r^2 \mathrm{d}r \, (k r)^q j_\ell(k r) a(r) \,. \]

Note: This is equivalent to the (forward biased) Hankel transform for \( A(r) = r^{3/2} a(r) \) and \( B(k) = (2\pi / k)^{3/2} b(k) \) with \( \mu = \ell + 1/2 \) and the same \( q \).

Parameters

[in]	a	Pre-transform sample values. Must even in length if extrapolation is enabled.
[out]	b	Post-transform sample values.

Attention: If extrapolation is enabled by extrap, the pre-transform samples are assumed to be real.

Definition at line 523 of file fftlog.cpp.

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◆ transform_cosmological_multipole()

void trv::maths::SphericalBesselTransform::transform_cosmological_multipole	(	int	dir,
		std::vector< std::complex< double > > &	pre_samples,
		std::vector< std::complex< double > > &	post_samples )

Transform csomological multipole samples.

Parameters

[in]	dir	Transform direction: +1 (forward) for configuration to Fourier space, -1 (backward) for Fourier to configuration space.
[in]	pre_samples	Pre-transform multipole samples. Must be even in length if extrapolation is enabled.
[out]	post_samples	Post-transform multipoles samples.

Attention: If extrapolation is enabled (extrap not trv::array::ExtrapOption::NONE, the pre-transform samples are assumed to be real.

Definition at line 553 of file fftlog.cpp.

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Member Data Documentation

◆ degree

int trv::maths::SphericalBesselTransform::degree

degree of the spherical Bessel transform

Definition at line 261 of file fftlog.hpp.

The documentation for this class was generated from the following files:

/home/docs/checkouts/readthedocs.org/user_builds/triumvirate/checkouts/latest/src/triumvirate/include/fftlog.hpp
/home/docs/checkouts/readthedocs.org/user_builds/triumvirate/checkouts/latest/src/triumvirate/src/fftlog.cpp

Public Member Functions

Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ SphericalBesselTransform()

Member Function Documentation

◆ initialise() [1/2]

◆ initialise() [2/2]

◆ biased_transform()

◆ transform_cosmological_multipole()

Member Data Documentation

◆ degree