Perform the (forward biased) Hankel and associated transforms using the FFTLog algorithm. More...

#include <fftlog.hpp>

Inheritance diagram for trv::maths::HankelTransform:

Collaboration diagram for trv::maths::HankelTransform:

Public Member Functions
	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
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

Perform the (forward biased) Hankel and associated transforms using the FFTLog algorithm.

Definition at line 68 of file fftlog.hpp.

Constructor & Destructor Documentation

◆ HankelTransform()

trv::maths::HankelTransform::HankelTransform	(	double	mu,
		double	q,
		bool	threaded = true )

Construct the Hankel transform.

Parameters

mu	Order of the Hankel transform.
q	Power-law bias index.
threaded	If `true` (default), use multi-threads FFT.

Definition at line 39 of file fftlog.cpp.

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◆ ~HankelTransform()

trv::maths::HankelTransform::~HankelTransform ( )

Destruct the Hankel transform.

Definition at line 65 of file fftlog.cpp.

Member Function Documentation

◆ initialise() [1/2]

void trv::maths::HankelTransform::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.

This sets up the pre- and post-transform samples as well as the transform kernel and the pivot value.

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.

Exceptions

trv::sys::InvalidParameterError	When the size of `sample_pts` is less than 2.
trv::sys::InvalidParameterError	When `sample_pts` is not logarithmically spaced.
trv::sys::InvalidParameterError	When the size of `sample_pts` is not even with extrapolation enabled.
trv::sys::InvalidParameterError	When `extrap_exp` results in a shrunken sample size.
trv::sys::InvalidParameterError	When `kr_c` is non-positive while `lowring` is false.

Definition at line 102 of file fftlog.cpp.

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◆ initialise() [2/2]

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

Initialise the Hankel transform.

This sets up the pre- and post-transform samples as well as the transform kernel and the pivot value.

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 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 246 of file fftlog.cpp.

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◆ biased_transform()

void trv::maths::HankelTransform::biased_transform	(	std::complex< double > *	a,
		std::complex< double > *	b )

Perform the (forward biased) Hankel transform.

The transform is defined here as

\[ b(k) = \int_0^\infty k \mathrm{d}r \, (k r)^q J_\mu(k r) a(r) \,. \]

Parameters

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

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

Definition at line 346 of file fftlog.cpp.

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◆ compute_kernel_coeff()

std::vector< std::complex< double > > trv::maths::HankelTransform::compute_kernel_coeff ( )

Compute the FFTLog transform kernel coefficients \( u \).

Returns: Kernel coefficients.

Definition at line 287 of file fftlog.cpp.

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◆ calc_lowring_pivot()

double trv::maths::HankelTransform::calc_lowring_pivot	(	double	delta,
		double	kr_c = 1. )

Calculate a low-ringing FFTLog transform pivot value \( k r = k_c r_c \).

Parameters

delta	Logarithmic-interval sample spacing.
kr_c	Initial pivot value (default is 1.). If zero, it is calculated directly; otherwise, it is adjusted from the initial value.

Returns: Low-ringing pivot value.

Note: This is not bound to the logarithmic-interval sample spacing initialised.

Definition at line 255 of file fftlog.cpp.

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Member Data Documentation

◆ order

double trv::maths::HankelTransform::order

order of the Hankel transform

Definition at line 70 of file fftlog.hpp.

◆ bias

double trv::maths::HankelTransform::bias

power-law bias index

Definition at line 71 of file fftlog.hpp.

◆ nsamp

int trv::maths::HankelTransform::nsamp = 0

number of samples provided

Definition at line 72 of file fftlog.hpp.

◆ nsamp_trans

int trv::maths::HankelTransform::nsamp_trans = 0

number of samples transformed

Definition at line 73 of file fftlog.hpp.

◆ logres

double trv::maths::HankelTransform::logres = 0.

logarithmic interval sample spacing

Definition at line 74 of file fftlog.hpp.

◆ pivot

double trv::maths::HankelTransform::pivot = 1.

pivot value

Definition at line 75 of file fftlog.hpp.

◆ pre_sampts

std::vector<double> trv::maths::HankelTransform::pre_sampts

logarithmically linearly-spaced sample points pre-transform

Definition at line 78 of file fftlog.hpp.

◆ post_sampts

std::vector<double> trv::maths::HankelTransform::post_sampts

logarithmically linearly-spaced sample points post-transform

Definition at line 81 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

◆ HankelTransform()

◆ ~HankelTransform()

Member Function Documentation

◆ initialise() [1/2]

◆ initialise() [2/2]

◆ biased_transform()

◆ compute_kernel_coeff()

◆ calc_lowring_pivot()

Member Data Documentation

◆ order

◆ bias

◆ nsamp

◆ nsamp_trans

◆ logres

◆ pivot

◆ pre_sampts

◆ post_sampts