apfel::OgataQuadrature Class Reference

The OgataQuadrature class implements the Hankel-transform of the input function using the Ogata quadrature method described here: http://www.kurims.kyoto-u.ac.jp/~okamoto/paper/Publ_RIMS_DE/41-4-40.pdf. More...

#include <ogataquadrature.h>

Public Member Functions
	OgataQuadrature (int const &nu=0, double const &CutOff=1e-5, double const &h=0.001, int const &nZeroMax=1000)
	The Integrator constructor.
void	InitialiseWeights (int const &nZeroMax)
	Function that initialises the coordinates and the weights for the Ogata quadrature.
template<typename T >
T	transform (std::function< T(double const &)> const &func, double const &qT, bool const &Dynh=true, int const &nmax=1000, int const &period=10) const
	Function that transform the input function.
double	GetBesselOrder () const
	Function that returns the Bessel order.
double	GetCutOff () const
	Function that returns the Ogata cut-off parameter.
double	GetStepParameter () const
	Function that returns the Ogata step parameter.
std::vector< double >	GetCoordinates () const
	Function that returns the unscaled coordinates used in the Ogata quadrature.
std::vector< double >	GetWeights () const
	Function that returns the weights used in the Ogata quadrature.
void	SetStepParameter (double const &h)
	Function that sets the Ogata step parameter.
void	JnuZerosGenerator (int const &nu) const
	Function that writes on screan the first 1000 zeros of the Bessel function J0. This function essentially generates the std::vector<double> j0Zeros above. This function requires BOOST and thus it is not available by defaults.

Private Attributes
int const	_nu
	The Bessel order.
double const	_CutOff
	The target accuracy parameter.
double	_h
	The step parameter.
int const	_nZeroMax
	The maximum number of zero's initialised.
std::vector< double >	_xf
	Unscaled coordinates.
std::vector< double >	_weights
	Weights of the quadrature.

Detailed Description

The OgataQuadrature class implements the Hankel-transform of the input function using the Ogata quadrature method described here: http://www.kurims.kyoto-u.ac.jp/~okamoto/paper/Publ_RIMS_DE/41-4-40.pdf.

Examples

ogata_test.cc, and tmd_test.cc.

Constructor & Destructor Documentation

OgataQuadrature()

apfel::OgataQuadrature::OgataQuadrature	(	int const &	nu = 0,
		double const &	CutOff = 1e-5,
		double const &	h = 0.001,
		int const &	nZeroMax = 1000 )

The Integrator constructor.

Parameters

nu	the order of the Bessel function (default: 0)
CutOff	the accuracy computed as a cutoff on the size of the last computed term relative to the total (default: 10-5)
h	internal variable of the algorithm (default: 0.001)
nZeroMax	maximum number of terms in the Ogata quadrature (default: 1000)

Note

Note that the default value of the parameter 'h' (0.001) is based of studies of Drell-Yan transverse-momentum distributions. However, this values could possibly be badly non-optimal in other contexts. A good value of 'h' should take into account the decay rate of the integrand. In particular, the faster the decay the smaller the value of 'h' has to be.

Member Function Documentation

GetBesselOrder()

double apfel::OgataQuadrature::GetBesselOrder ( ) const

inline

Function that returns the Bessel order.

Returns

the Bessel order

GetCoordinates()

std::vector< double > apfel::OgataQuadrature::GetCoordinates ( ) const

inline

Function that returns the unscaled coordinates used in the Ogata quadrature.

Returns

the unscales coordinates

GetCutOff()

double apfel::OgataQuadrature::GetCutOff ( ) const

inline

Function that returns the Ogata cut-off parameter.

Returns

the cut-off parameter

GetStepParameter()

double apfel::OgataQuadrature::GetStepParameter ( ) const

inline

Function that returns the Ogata step parameter.

Returns

the step parameter

GetWeights()

std::vector< double > apfel::OgataQuadrature::GetWeights ( ) const

inline

Function that returns the weights used in the Ogata quadrature.

Returns

the weights

InitialiseWeights()

void apfel::OgataQuadrature::InitialiseWeights

(

int const &

nZeroMax

)

Function that initialises the coordinates and the weights for the Ogata quadrature.

Parameters

nZeroMax

maximum number of terms in the Ogata quadrature

JnuZerosGenerator()

void apfel::OgataQuadrature::JnuZerosGenerator

(

int const &

nu

)

const

Function that writes on screan the first 1000 zeros of the Bessel function J0. This function essentially generates the std::vector<double> j0Zeros above. This function requires BOOST and thus it is not available by defaults.

Parameters

nu	the order of the Bessel function

SetStepParameter()

void apfel::OgataQuadrature::SetStepParameter ( double const & h )

inline

Function that sets the Ogata step parameter.

Parameters

h	step parameter

transform()

template<typename T >

T apfel::OgataQuadrature::transform	(	std::function< T(double const &)> const &	func,
		double const &	qT,
		bool const &	Dynh = true,
		int const &	nmax = 1000,
		int const &	period = 10 ) const

Function that transform the input function.

Parameters

func	function to be transformed
qT	value of qT in which to compute the transform
Dynh	switch to compute the step parameter _h dynamically (default: true)
nmax	maximum number of terms in the Ogata quadrature (default: 1000)
period	interval across which the integral is checked to determine where the sum is truncated (default: 10)

Returns

the value of the transform

Examples

tmd_test.cc.

Member Data Documentation

_CutOff

double const apfel::OgataQuadrature::_CutOff

private

The target accuracy parameter.

_h

double apfel::OgataQuadrature::_h

private

The step parameter.

_nu

int const apfel::OgataQuadrature::_nu

private

The Bessel order.

_nZeroMax

int const apfel::OgataQuadrature::_nZeroMax

private

The maximum number of zero's initialised.

_weights

std::vector<double> apfel::OgataQuadrature::_weights

private

Weights of the quadrature.

_xf

std::vector<double> apfel::OgataQuadrature::_xf

private

Unscaled coordinates.

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

• /Users/vb262523/Codes/apfelxx/inc/apfel/ogataquadrature.h