apfel::Integrator Class Reference

The Integrator class performs unidimensional numerical integrations using the Guassian quadrature. More...

#include <integrator.h>

Public Types
Enumerator for the currently available integration
methods.
enum	IntegrationMethod : int { GAUSS_LEGENDRE , GAUSS_KRONROD }

Constructors
List of constructors.
std::function< double(double const &)> const	_func
	The integrand function.
IntegrationMethod const	_method
	The integration method.
	Integrator (std::function< double(double const &)> const &func, IntegrationMethod const &method=GAUSS_KRONROD)
	The Integrator constructor.
double	integrate (double const &xmin, double const &xmax, double const &eps) const
	Function that integrates the integrand with a given relative accuracy using the method defined in the constructor.
double	integrate (double const &xmin, double const &xmax, std::vector< double > const &FixPts, double const &eps) const
	Function that integrates the integrand with a given relative accuracy using a set of fixed point on the integration range.
double	integrate (std::vector< double > const &FixPts, double const &eps) const
	Function that integrates the integrand with a given relative accuracy using a set of fixed point on the integration range. In this case, the vector also contains the lower and upper bounds.
double	integrate (double const &xmin, double const &xmax, int const &n=1) const
	Function that integrates the integrand with a given relative accuracy using the method defined in the constructor.
double	integrate (double const &xmin, double const &xmax, std::vector< double > const &FixPts, int const &n=1) const
	Function that integrates the integrand with a given relative accuracy using a set of fixed point on the integration range.
double	integrate (std::vector< double > const &FixPts, int const &n=1) const
	Function that integrates the integrand with a given relative accuracy using a set of fixed point on the integration range. In this case, the vector also contains the lower and upper bounds.
double	integrand (double const &x) const
	Function for the integrand.
IntegrationMethod	Method () const
	Function that returns the integration method.
std::pair< double, double >	integrateGL (double const &xmin, double const &xmax) const
	Function that integrates the integrand using the Gauss-Legendre method.
std::pair< double, double >	integrateGK (double const &xmin, double const &xmax) const
	Function that integrates the integrand using the Gauss-Kronrod method.
double	integrateGL (double const &xmin, double const &xmax, int const &n) const
	Function that integrates the integrand using the Gauss-Legendre method (no accuracy estimate).
double	integrateGK (double const &xmin, double const &xmax, int const &n) const
	Function that integrates the integrand using the Gauss-Kronrod method (no accuracy estimate).

Detailed Description

The Integrator class performs unidimensional numerical integrations using the Guassian quadrature.

Examples

integrator_test.cc, ogata_test.cc, principal_value_test.cc, and qgriddist_test.cc.

Member Enumeration Documentation

IntegrationMethod

enum apfel::Integrator::IntegrationMethod : int

Enumerator
GAUSS_LEGENDRE
GAUSS_KRONROD

Constructor & Destructor Documentation

Integrator()

apfel::Integrator::Integrator	(	std::function< double(double const &)> const &	func,
		IntegrationMethod const &	method = GAUSS_KRONROD )

The Integrator constructor.

Parameters

func	The function of one variable to be integrated
method	The integration method to be used (default: GAUSS_KRONROD)

Member Function Documentation

integrand()

double apfel::Integrator::integrand ( double const & x ) const

inline

Function for the integrand.

Parameters

x	the integration variable

Returns

the integrand evaluated at x

integrate() [1/6]

double apfel::Integrator::integrate	(	double const &	xmin,
		double const &	xmax,
		double const &	eps ) const

Function that integrates the integrand with a given relative accuracy using the method defined in the constructor.

Parameters

xmin	the lower bound integration bound
xmax	the upper bound integration bound
eps	the required relative accuracy

Returns

the value of the integral

Examples

qgriddist_test.cc.

integrate() [2/6]

double apfel::Integrator::integrate	(	double const &	xmin,
		double const &	xmax,
		int const &	n = 1 ) const

Function that integrates the integrand with a given relative accuracy using the method defined in the constructor.

Parameters

xmin	the lower bound integration bound
xmax	the upper bound integration bound
n	index associated to the number of points used for the integration: 0 for 8/7 points for Gauss-Legendre/Kronrod, 1 for 16/15 points for Gauss-Legendre/Kronrod (default: 1)

Returns

the value of the integral

integrate() [3/6]

double apfel::Integrator::integrate	(	double const &	xmin,
		double const &	xmax,
		std::vector< double > const &	FixPts,
		double const &	eps ) const

Function that integrates the integrand with a given relative accuracy using a set of fixed point on the integration range.

Parameters

xmin	the lower bound integration bound
xmax	the upper bound integration bound
FixPts	the vector of fixed points of the integration
eps	the required relative accuracy

Returns

the value of the integral

integrate() [4/6]

double apfel::Integrator::integrate	(	double const &	xmin,
		double const &	xmax,
		std::vector< double > const &	FixPts,
		int const &	n = 1 ) const

Function that integrates the integrand with a given relative accuracy using a set of fixed point on the integration range.

Parameters

xmin	the lower bound integration bound
xmax	the upper bound integration bound
FixPts	the vector of fixed points of the integration
n	index associated to the number of points used for the integration: 0 for 8/7 points for Gauss-Legendre/Kronrod, 1 for 16/15 points for Gauss-Legendre/Kronrod (default: 1)

Returns

the value of the integral

integrate() [5/6]

double apfel::Integrator::integrate	(	std::vector< double > const &	FixPts,
		double const &	eps ) const

Function that integrates the integrand with a given relative accuracy using a set of fixed point on the integration range. In this case, the vector also contains the lower and upper bounds.

Parameters

FixPts	the vector of fixed points of the integration
eps	the required relative accuracy integration: 0 for 8/7 points for Gauss-Legendre/Kronrod, 1 for 16/15 points for Gauss-Legendre/Kronrod (default: 1)

Returns

the value of the integral

Note

In order to make this function as fast as possible, no manipulation of the vector "FixPts" is made. To be used with care.

integrate() [6/6]

double apfel::Integrator::integrate	(	std::vector< double > const &	FixPts,
		int const &	n = 1 ) const

Function that integrates the integrand with a given relative accuracy using a set of fixed point on the integration range. In this case, the vector also contains the lower and upper bounds.

Parameters

FixPts	the vector of fixed points of the integration
n	index associated to the number of points used for the integration: 0 for 8/7 points for Gauss-Legendre/Kronrod, 1 for 16/15 points for Gauss-Legendre/Kronrod (default: 1)

Returns

the value of the integral

Note

In order to make this function as fast as possible, no manipulation of the vector "FixPts" is made. To be used with care.

integrateGK() [1/2]

std::pair< double, double > apfel::Integrator::integrateGK ( double const & xmin, double const & xmax ) const

private

Function that integrates the integrand using the Gauss-Kronrod method.

Parameters

xmin	the lower bound integration bound
xmax	the upper bound integration bound

Returns

a pair containing the value of the integral computed with the 15-point method and the relative difference w.r.t. the 7-point one.

integrateGK() [2/2]

double apfel::Integrator::integrateGK ( double const & xmin, double const & xmax, int const & n ) const

private

Function that integrates the integrand using the Gauss-Kronrod method (no accuracy estimate).

Parameters

xmin	the lower bound integration bound
xmax	the upper bound integration bound
n	index associated to the number of points used for the integration: 0 for 7 points for Gauss-Legendr, 1 for 15 points

Returns

the value of the integral

integrateGL() [1/2]

std::pair< double, double > apfel::Integrator::integrateGL ( double const & xmin, double const & xmax ) const

private

Function that integrates the integrand using the Gauss-Legendre method.

Parameters

xmin	the lower bound integration bound
xmax	the upper bound integration bound

Returns

a pair containing the value of the integral computed with the 16-point method and the relative difference w.r.t. the 8-point one.

integrateGL() [2/2]

double apfel::Integrator::integrateGL ( double const & xmin, double const & xmax, int const & n ) const

private

Function that integrates the integrand using the Gauss-Legendre method (no accuracy estimate).

Parameters

xmin	the lower bound integration bound
xmax	the upper bound integration bound
n	index associated to the number of points used for the integration: 0 for 8 points for Gauss-Legendr, 1 for 16 points

Returns

the value of the integral

Method()

IntegrationMethod apfel::Integrator::Method ( ) const

inline

Function that returns the integration method.

Member Data Documentation

_func

std::function<double(double const&)> const apfel::Integrator::_func

private

The integrand function.

_method

IntegrationMethod const apfel::Integrator::_method

private

The integration method.

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

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