The template class QGrids is a mother class for the interpolation in Q. This class also implements methods for the subgrid interpolation relevant for example in a VFNS evolution. More...

#include <qgrid.h>

Inheritance diagram for apfel::QGrid< T >:

Public Member Functions
T	Evaluate (double const &Q) const
	Function that interpolates on the grid in Q.

T	Derive (double const &Q) const
	Function that derives on the grid in Q.

T	Integrate (double const &Qa, double const &Qb) const
	Function that integrates on the grid in Q.

double	Interpolant (int const &tQ, int const &tau, double const &fq) const
	Interpolation functions on QGrid.

double	DerInterpolant (int const &tQ, int const &tau, double const &Q) const
	Derivative of the interpolation functions on QGrid.

double	IntInterpolant (int const &tQ, int const &tau, double const &Qa, double const &Qb) const
	Derivative of the interpolation functions on QGrid.

std::tuple< int, int, int >	SumBounds (double const &Q) const
	Computes the control parameter of the interpolant, the lower and upper bounds over which the sum is limited.

void	Print () const
	Print the QGrid object.

Constructors
List of constructors.
	QGrid ()=delete

	QGrid (int const &nQ, double const &QMin, double const &QMax, int const &InterDegree, std::vector< double > const &Thresholds, std::function< double(double const &)> const &TabFunc, std::function< double(double const &)> const &InvTabFunc)
	The QGrid constructor.

	QGrid (int const &nQ, double const &QMin, double const &QMax, int const &InterDegree, std::vector< double > const &Thresholds, double const &Lambda=0.25)
	The QGrid constructor.

	QGrid (std::vector< double > const &Qg, int const &InterDegree)
	The QGrid constructor.

Comparison operators
Collection of operators for comparing QGrid objects
bool	operator== (QGrid const &sg) const

bool	operator!= (QGrid const &sg) const

Protected Attributes
int	_nQ
	Number intervals.

double	_QMin
	Minumim value of Q.

double	_QMax
	Maximum value of Q.

int	_InterDegree
	Interpolation degree.

std::vector< double >	_Thresholds
	Thresholds.

std::function< double(double const &)	_TabFunc )
	Function whose constant step is used for the tabulation.

std::vector< double >	_Qg
	Grid in Q.

std::vector< double >	_fQg
	Grid in _TabFunc(Q)

std::vector< int >	_nQg
	Indices of the nodes on which there is either a bound or a threshold.

std::vector< T >	_GridValues
	Vector of values to be interpolated on the grid.

Friends
template<class U >
std::ostream &	operator<< (std::ostream &os, QGrid< U > const &dt)

Getters
std::function< double(double const &)> const	TabFunc )() const
	return the tabulation function

int	nQ () const
	return the number of Q interval

int	InterDegree () const
	return the interpolation degree

double	QMin () const
	return the minimum node value

double	QMax () const
	return the maximum node value

std::vector< double > const &	GetThresholds () const
	return the heavy quark thresholds

std::vector< double > const &	GetQGrid () const
	return the grid in Q

std::vector< double > const &	GetFQGrid () const
	return the grid in _TabFunc(Q)

std::vector< int > const &	GetThesholdIndices () const
	return the indices of the thresholds on the grid

std::vector< T > const &	GetQGridValues () const
	return the tabulated objects on the grid.

Detailed Description

template<class T>
class apfel::QGrid< T >

The template class QGrids is a mother class for the interpolation in Q. This class also implements methods for the subgrid interpolation relevant for example in a VFNS evolution.

Examples: qgrid_test.cc.

Constructor & Destructor Documentation

◆ QGrid() [1/4]

template<class T >

apfel::QGrid< T >::QGrid ( )

delete

◆ QGrid() [2/4]

template<class T >

apfel::QGrid< T >::QGrid	(	int const &	nQ,
		double const &	QMin,
		double const &	QMax,
		int const &	InterDegree,
		std::vector< double > const &	Thresholds,
		std::function< double(double const &)> const &	TabFunc,
		std::function< double(double const &)> const &	InvTabFunc )

The QGrid constructor.

Parameters

nQ	the number of grid intervals in Q
QMin	the lower edge of the grid in Q
QMax	the upper edge of the grid in Q
InterDegree	the interpolation degree
Thresholds	the fixed point of the grid over which interpolation is forbidden
TabFunc	the function used to tabulate the grid in Q
InvTabFunc	the inverse function of TabFunc (an analytic expression is necessary)

◆ QGrid() [3/4]

template<class T >

apfel::QGrid< T >::QGrid	(	int const &	nQ,
		double const &	QMin,
		double const &	QMax,
		int const &	InterDegree,
		std::vector< double > const &	Thresholds,
		double const &	Lambda = 0.25 )

The QGrid constructor.

Parameters

nQ	the number of grid intervals in Q
QMin	the lower edge of the grid in Q
QMax	the upper edge of the grid in Q
InterDegree	the interpolation degree
Thresholds	the fixed point of the grid over which interpolation is forbidden
Lambda	the parameter of the function log(log(Q/Lambda)) used for the tabulation on the grid in Q

◆ QGrid() [4/4]

template<class T >

apfel::QGrid< T >::QGrid	(	std::vector< double > const &	Qg,
		int const &	InterDegree )

The QGrid constructor.

Parameters

Qg	the user-defined interpolation grid
InterDegree	the interpolation degree

Note: This constructor assumes that the function used to compute the interpolating functions is linear. In addition, the input vector 'Qg' is assumed to be ordered and 'well-behaved'. To be used with care.

Member Function Documentation

◆ DerInterpolant()

template<class T >

double apfel::QGrid< T >::DerInterpolant	(	int const &	tQ,
		int const &	tau,
		double const &	Q ) const

Derivative of the interpolation functions on QGrid.

Parameters

tQ	interpolation control parameter
tau	the grid index
Q	the value of Q of the required interpolation

Returns: the derivarive of the interpolation weights

◆ Derive()

template<class T >

T apfel::QGrid< T >::Derive ( double const & Q ) const

Function that derives on the grid in Q.

Parameters

Q	the value of the required interpolation

Returns: the interpolated derivative

◆ Evaluate()

template<class T >

T apfel::QGrid< T >::Evaluate ( double const & Q ) const

Function that interpolates on the grid in Q.

Parameters

Q	the value of the required interpolation

Returns: the interpolated value

Examples: dglap_test.cc, dglap_test_streamlined.cc, gpd_test.cc, structurefunction_cc_test.cc, structurefunction_massive_test.cc, structurefunction_nc_pol_test.cc, structurefunction_nc_test.cc, and tmd_test.cc.

◆ GetFQGrid()

template<class T >

std::vector< double > const & apfel::QGrid< T >::GetFQGrid ( ) const

inline

return the grid in _TabFunc(Q)

◆ GetQGrid()

template<class T >

std::vector< double > const & apfel::QGrid< T >::GetQGrid ( ) const

inline

return the grid in Q

◆ GetQGridValues()

template<class T >

std::vector< T > const & apfel::QGrid< T >::GetQGridValues ( ) const

inline

return the tabulated objects on the grid.

◆ GetThesholdIndices()

template<class T >

std::vector< int > const & apfel::QGrid< T >::GetThesholdIndices ( ) const

inline

return the indices of the thresholds on the grid

◆ GetThresholds()

template<class T >

std::vector< double > const & apfel::QGrid< T >::GetThresholds ( ) const

inline

return the heavy quark thresholds

◆ Integrate()

template<class T >

T apfel::QGrid< T >::Integrate	(	double const &	Qa,
		double const &	Qb ) const

Function that integrates on the grid in Q.

Parameters

Qa	the lower integration bound
Qb	the upper integration bound

Returns: the interpolated integral

◆ InterDegree()

template<class T >

int apfel::QGrid< T >::InterDegree ( ) const

inline

return the interpolation degree

◆ Interpolant()

template<class T >

double apfel::QGrid< T >::Interpolant	(	int const &	tQ,
		int const &	tau,
		double const &	fq ) const

Interpolation functions on QGrid.

Parameters

tQ	interpolation control parameter
tau	the grid index
fq	the value of _TabFunc(Q) of the required interpolation

Returns: the interpolation weights

◆ IntInterpolant()

template<class T >

double apfel::QGrid< T >::IntInterpolant	(	int const &	tQ,
		int const &	tau,
		double const &	Qa,
		double const &	Qb ) const

Derivative of the interpolation functions on QGrid.

Parameters

tQ	interpolation control parameter
tau	the grid index
Qa	the value of the lower integration bound
Qb	the value of the upper integration bound

Returns: the integral of interpolation weights

◆ nQ()

template<class T >

int apfel::QGrid< T >::nQ ( ) const

inline

return the number of Q interval

◆ operator!=()

template<class T >

bool apfel::QGrid< T >::operator!= ( QGrid< T > const & sg ) const

◆ operator==()

template<class T >

bool apfel::QGrid< T >::operator== ( QGrid< T > const & sg ) const

◆ Print()

template<class T >

void apfel::QGrid< T >::Print ( ) const

inline

Print the QGrid object.

◆ QMax()

template<class T >

double apfel::QGrid< T >::QMax ( ) const

inline

return the maximum node value

◆ QMin()

template<class T >

double apfel::QGrid< T >::QMin ( ) const

inline

return the minimum node value

◆ SumBounds()

template<class T >

std::tuple< int, int, int > apfel::QGrid< T >::SumBounds ( double const & Q ) const

Computes the control parameter of the interpolant, the lower and upper bounds over which the sum is limited.

Parameters

Q	the value of the required interpolation

Returns: the lower and upper bounds of tau

Friends And Related Symbol Documentation

◆ operator<<

template<class T >

template<class U >

std::ostream & operator<<	(	std::ostream &	os,
		QGrid< U > const &	dt )

friend

Member Data Documentation

◆ _fQg

template<class T >

std::vector<double> apfel::QGrid< T >::_fQg

protected

Grid in _TabFunc(Q)

◆ _GridValues

template<class T >

std::vector<T> apfel::QGrid< T >::_GridValues

protected

Vector of values to be interpolated on the grid.

◆ _InterDegree

template<class T >

int apfel::QGrid< T >::_InterDegree

protected

Interpolation degree.

◆ _nQ

template<class T >

int apfel::QGrid< T >::_nQ

protected

Number intervals.

◆ _nQg

template<class T >

std::vector<int> apfel::QGrid< T >::_nQg

protected

Indices of the nodes on which there is either a bound or a threshold.

◆ _Qg

template<class T >

std::vector<double> apfel::QGrid< T >::_Qg

protected

Grid in Q.

◆ _QMax

template<class T >

double apfel::QGrid< T >::_QMax

protected

Maximum value of Q.

◆ _QMin

template<class T >

double apfel::QGrid< T >::_QMin

protected

Minumim value of Q.

◆ _TabFunc

template<class T >

std::function<double(double const&) apfel::QGrid< T >::_TabFunc)

protected

Function whose constant step is used for the tabulation.

◆ _Thresholds

template<class T >

std::vector<double> apfel::QGrid< T >::_Thresholds

protected

Thresholds.

◆ TabFunc

template<class T >

std::function< double(double const &)> const apfel::QGrid< T >::TabFunc) () const

inline

return the tabulation function

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

/Users/vb262523/Codes/apfelxx/inc/apfel/qgrid.h

Public Member Functions

Protected Attributes

Friends

Getters

Detailed Description

Constructor & Destructor Documentation

◆ QGrid() [1/4]

◆ QGrid() [2/4]

◆ QGrid() [3/4]

◆ QGrid() [4/4]

Member Function Documentation

◆ DerInterpolant()

◆ Derive()

◆ Evaluate()

◆ GetFQGrid()

◆ GetQGrid()

◆ GetQGridValues()

◆ GetThesholdIndices()

◆ GetThresholds()

◆ Integrate()

◆ InterDegree()

◆ Interpolant()

◆ IntInterpolant()

◆ nQ()

◆ operator!=()

◆ operator==()

◆ Print()

◆ QMax()

◆ QMin()

◆ SumBounds()

Friends And Related Symbol Documentation

◆ operator<<

Member Data Documentation

◆ _fQg

◆ _GridValues

◆ _InterDegree

◆ _nQ

◆ _nQg

◆ _Qg

◆ _QMax

◆ _QMin

◆ _TabFunc

◆ _Thresholds

◆ TabFunc