Class for performing numerical integration of a function in one dimension.

It uses the numerical integration algorithms of GSL, which reimplements the algorithms used in the QUADPACK, a numerical integration package written in Fortran.

Various types of adaptive and non-adaptive integration are supported. These include integration over infinite and semi-infinite ranges and singular integrals.

The integration type is selected using the Integration::type enumeration in the class constructor. The default type is adaptive integration with singularity (ADAPTIVESINGULAR or QAGS in the QUADPACK convention) applying a Gauss-Kronrod 21-point integration rule. In the case of ADAPTIVE type, the integration rule can also be specified via the Integration::GKRule. The default rule is 31 points.

In the case of integration over infinite and semi-infinite ranges, the type used is always ADAPTIVESINGULAR applying a transformation from the original interval into (0,1).

The ADAPTIVESINGULAR type is the most sophicticated type. When performances are important, it is then recommened to use the NONADAPTIVE type in case of smooth functions or ADAPTIVE with a lower Gauss-Kronrod rule.

For detailed description on GSL integration algorithms see the GSL Manual.

Definition at line 90 of file GSLIntegrator.h.

Public Member Functions
	GSLIntegrator (double absTol=1.E-9, double relTol=1E-6, size_t size=1000)
	Default constructor of GSL Integrator for Adaptive Singular integration. More...

	GSLIntegrator (const Integration::Type type, double absTol=1.E-9, double relTol=1E-6, size_t size=1000)
	constructor of GSL Integrator. More...

	GSLIntegrator (const Integration::Type type, const Integration::GKRule rule, double absTol=1.E-9, double relTol=1E-6, size_t size=1000)
	generic constructor for GSL Integrator More...

	GSLIntegrator (const char *type, int rule, double absTol, double relTol, size_t size)
	constructor of GSL Integrator. More...

virtual	~GSLIntegrator ()

double	Error () const
	return the estimate of the absolute Error of the last Integral calculation More...

IntegrationOneDim::Type	GetType () const
	get type name More...

const char *	GetTypeName () const
	return the name More...

double	Integral (const IGenFunction &f, double a, double b)
	evaluate the Integral of a function f over the defined interval (a,b) More...

double	Integral (const IGenFunction &f)
	evaluate the Integral of a function f over the infinite interval (-inf,+inf) More...

double	Integral (const IGenFunction &f, const std::vector< double > &pts)
	evaluate the Integral of a function f with known singular points over the defined Integral (a,b) More...

double	Integral (double a, double b)
	evaluate the Integral over the defined interval (a,b) using the function previously set with GSLIntegrator::SetFunction method More...

double	Integral ()
	evaluate the Integral over the infinite interval (-inf,+inf) using the function previously set with GSLIntegrator::SetFunction method. More...

double	Integral (const std::vector< double > &pts)
	evaluate the Integral over the defined interval (a,b) using the function previously set with GSLIntegrator::SetFunction method. More...

double	Integral (GSLFuncPointer f, void *p, double a, double b)
	signature for function pointers used by GSL More...

double	Integral (GSLFuncPointer f, void *p)
	evaluate the Integral of a function f over the infinite interval (-inf,+inf) passing a free function pointer More...

double	Integral (GSLFuncPointer f, void *p, const std::vector< double > &pts)
	evaluate the Integral of a function f with knows singular points over the over a defined interval passing a free function pointer More...

double	IntegralCauchy (double a, double b, double c)
	evaluate the Cauchy principal value of the integral of a previously defined function f over the defined interval (a,b) with a singularity at c More...

double	IntegralCauchy (const IGenFunction &f, double a, double b, double c)
	evaluate the Cauchy principal value of the integral of a function f over the defined interval (a,b) with a singularity at c More...

double	IntegralLow (const IGenFunction &f, double b)
	evaluate the Integral of a function f over the over the semi-infinite interval (-inf,b) More...

double	IntegralLow (double b)
	evaluate the Integral of a function f over the over the semi-infinite interval (-inf,b) using the function previously set with GSLIntegrator::SetFunction method. More...

double	IntegralLow (GSLFuncPointer f, void *p, double b)
	evaluate the Integral of a function f over the over the semi-infinite interval (-inf,b) passing a free function pointer More...

double	IntegralUp (const IGenFunction &f, double a)
	evaluate the Integral of a function f over the semi-infinite interval (a,+inf) More...

double	IntegralUp (double a)
	evaluate the Integral of a function f over the semi-infinite interval (a,+inf) using the function previously set with GSLIntegrator::SetFunction method. More...

double	IntegralUp (GSLFuncPointer f, void *p, double a)
	evaluate the Integral of a function f over the semi-infinite interval (a,+inf) passing a free function pointer More...

int	NEval () const
	return number of function evaluations in calculating the integral More...

virtual ROOT::Math::IntegratorOneDimOptions	Options () const
	get the option used for the integration More...

double	Result () const
	return the Result of the last Integral calculation More...

void	SetAbsTolerance (double absTolerance)
	set the desired absolute Error More...

void	SetFunction (const IGenFunction &f)
	method to set the a generic integration function More...

void	SetFunction (GSLFuncPointer f, void *p=0)
	Set function from a GSL pointer function type. More...

void	SetIntegrationRule (Integration::GKRule)
	set the integration rule (Gauss-Kronrod rule). More...

virtual void	SetOptions (const ROOT::Math::IntegratorOneDimOptions &opt)
	set the options More...

void	SetRelTolerance (double relTolerance)
	set the desired relative Error More...

int	Status () const
	return the Error Status of the last Integral calculation More...

Public Member Functions inherited from ROOT::Math::VirtualIntegratorOneDim
virtual	~VirtualIntegratorOneDim ()
	destructor: no operation More...

virtual ROOT::Math::IntegrationOneDim::Type	Type () const

Public Member Functions inherited from ROOT::Math::VirtualIntegrator
virtual	~VirtualIntegrator ()

Protected Member Functions
bool	CheckFunction ()

Private Member Functions
	GSLIntegrator (const GSLIntegrator &)

GSLIntegrator &	operator= (const GSLIntegrator &)

Private Attributes
double	fAbsTol

double	fError

GSLFunctionWrapper *	fFunction

size_t	fMaxIntervals

int	fNEval

double	fRelTol

double	fResult

Integration::GKRule	fRule

size_t	fSize

int	fStatus

Integration::Type	fType

GSLIntegrationWorkspace *	fWorkspace

#include <Math/GSLIntegrator.h>

Inheritance diagram for ROOT::Math::GSLIntegrator:

[legend]

Constructor & Destructor Documentation

◆ GSLIntegrator() [1/5]

ROOT::Math::GSLIntegrator::GSLIntegrator	(	double	absTol = `1.E-9`,
		double	relTol = `1E-6`,
		size_t	size = `1000`
	)

Default constructor of GSL Integrator for Adaptive Singular integration.

Parameters

absTol	desired absolute Error
relTol	desired relative Error
size	maximum number of sub-intervals

Definition at line 77 of file GSLIntegrator.cxx.

◆ GSLIntegrator() [2/5]

ROOT::Math::GSLIntegrator::GSLIntegrator	(	const Integration::Type	type,
		double	absTol = `1.E-9`,
		double	relTol = `1E-6`,
		size_t	size = `1000`
	)

constructor of GSL Integrator.

In the case of Adaptive integration the Gauss-Krond rule of 31 points is used

Parameters

type	type of integration. The possible types are defined in the Integration::Type enumeration
absTol	desired absolute Error
relTol	desired relative Error
size	maximum number of sub-intervals

Definition at line 95 of file GSLIntegrator.cxx.

◆ GSLIntegrator() [3/5]

ROOT::Math::GSLIntegrator::GSLIntegrator	(	const Integration::Type	type,
		const Integration::GKRule	rule,
		double	absTol = `1.E-9`,
		double	relTol = `1E-6`,
		size_t	size = `1000`
	)

generic constructor for GSL Integrator

Parameters

type	type of integration. The possible types are defined in the Integration::Type enumeration
rule	Gauss-Kronrod rule. It is used only for ADAPTIVE::Integration types. The possible rules are defined in the Integration::GKRule enumeration
absTol	desired absolute Error
relTol	desired relative Error
size	maximum number of sub-intervals

Definition at line 56 of file GSLIntegrator.cxx.

◆ GSLIntegrator() [4/5]

ROOT::Math::GSLIntegrator::GSLIntegrator	(	const char *	type,
		int	rule,
		double	absTol,
		double	relTol,
		size_t	size
	)

constructor of GSL Integrator.

In the case of Adaptive integration the Gauss-Krond rule of 31 points is used This is used by the plug-in manager (need a char * instead of enumerations)

Parameters

type	type of integration. The possible types are defined in the Integration::Type enumeration
rule	Gauss-Kronrod rule (from 1 to 6)
absTol	desired absolute Error
relTol	desired relative Error
size	maximum number of sub-intervals

Definition at line 114 of file GSLIntegrator.cxx.

◆ ~GSLIntegrator()

ROOT::Math::GSLIntegrator::~GSLIntegrator ( )

virtual

Definition at line 151 of file GSLIntegrator.cxx.

◆ GSLIntegrator() [5/5]

ROOT::Math::GSLIntegrator::GSLIntegrator ( const GSLIntegrator & )

private

Definition at line 158 of file GSLIntegrator.cxx.

Member Function Documentation

◆ CheckFunction()

bool ROOT::Math::GSLIntegrator::CheckFunction ( )

protected

Definition at line 408 of file GSLIntegrator.cxx.

◆ Error()

double ROOT::Math::GSLIntegrator::Error ( ) const

virtual

return the estimate of the absolute Error of the last Integral calculation

Implements ROOT::Math::VirtualIntegrator.

Definition at line 390 of file GSLIntegrator.cxx.

◆ GetType()

IntegrationOneDim::Type ROOT::Math::GSLIntegrator::GetType ( ) const

inline

get type name

Definition at line 362 of file GSLIntegrator.h.

◆ GetTypeName()

const char * ROOT::Math::GSLIntegrator::GetTypeName ( ) const

return the name

Definition at line 459 of file GSLIntegrator.cxx.

◆ Integral() [1/9]

double ROOT::Math::GSLIntegrator::Integral	(	const IGenFunction &	f,
		double	a,
		double	b
	)

evaluate the Integral of a function f over the defined interval (a,b)

Parameters

f	integration function. The function type must implement the mathlib::IGenFunction interface
a	lower value of the integration interval
b	upper value of the integration interval

Definition at line 323 of file GSLIntegrator.cxx.

◆ Integral() [2/9]

double ROOT::Math::GSLIntegrator::Integral ( const IGenFunction & f )

evaluate the Integral of a function f over the infinite interval (-inf,+inf)

Parameters

f	integration function. The function type must implement the mathlib::IGenFunction interface

Definition at line 329 of file GSLIntegrator.cxx.

◆ Integral() [3/9]

double ROOT::Math::GSLIntegrator::Integral	(	const IGenFunction &	f,
		const std::vector< double > &	pts
	)

evaluate the Integral of a function f with known singular points over the defined Integral (a,b)

Parameters

f	integration function. The function type must implement the mathlib::IGenFunction interface
pts	vector containing both the function singular points and the lower/upper edges of the interval. The vector must have as first element the lower edge of the integration Integral ( a) and last element the upper value.

Definition at line 347 of file GSLIntegrator.cxx.

◆ Integral() [4/9]

double ROOT::Math::GSLIntegrator::Integral	(	double	a,
		double	b
	)

virtual

evaluate the Integral over the defined interval (a,b) using the function previously set with GSLIntegrator::SetFunction method

Parameters

a	lower value of the integration interval
b	upper value of the integration interval

Implements ROOT::Math::VirtualIntegratorOneDim.

Definition at line 190 of file GSLIntegrator.cxx.

◆ Integral() [5/9]

double ROOT::Math::GSLIntegrator::Integral ( )

virtual

evaluate the Integral over the infinite interval (-inf,+inf) using the function previously set with GSLIntegrator::SetFunction method.

Implements ROOT::Math::VirtualIntegratorOneDim.

Definition at line 274 of file GSLIntegrator.cxx.

◆ Integral() [6/9]

double ROOT::Math::GSLIntegrator::Integral ( const std::vector< double > & pts )

virtual

evaluate the Integral over the defined interval (a,b) using the function previously set with GSLIntegrator::SetFunction method.

The function has known singular points.

Parameters

pts	vector containing both the function singular points and the lower/upper edges of the interval. The vector must have as first element the lower edge of the integration Integral ( a) and last element the upper value.

Implements ROOT::Math::VirtualIntegratorOneDim.

Definition at line 252 of file GSLIntegrator.cxx.

◆ Integral() [7/9]

double ROOT::Math::GSLIntegrator::Integral	(	GSLFuncPointer	f,
		void *	p,
		double	a,
		double	b
	)

signature for function pointers used by GSL

evaluate the Integral of of a function f over the defined interval (a,b) passing a free function pointer The integration function must be a free function and have a signature consistent with GSL functions:

double my_function ( double x, void * p ) { ...... }

This method is the most efficient since no internal adapter to GSL function is created.

Parameters

f	pointer to the integration function
p	pointer to the Parameters of the function
a	lower value of the integration interval
b	upper value of the integration interval

Definition at line 356 of file GSLIntegrator.cxx.

◆ Integral() [8/9]

double ROOT::Math::GSLIntegrator::Integral	(	GSLFuncPointer	f,
		void *	p
	)

evaluate the Integral of a function f over the infinite interval (-inf,+inf) passing a free function pointer

Definition at line 362 of file GSLIntegrator.cxx.

◆ Integral() [9/9]

double ROOT::Math::GSLIntegrator::Integral	(	GSLFuncPointer	f,
		void *	p,
		const std::vector< double > &	pts
	)

evaluate the Integral of a function f with knows singular points over the over a defined interval passing a free function pointer

Definition at line 380 of file GSLIntegrator.cxx.

◆ IntegralCauchy() [1/2]

double ROOT::Math::GSLIntegrator::IntegralCauchy	(	double	a,
		double	b,
		double	c
	)

virtual

evaluate the Cauchy principal value of the integral of a previously defined function f over the defined interval (a,b) with a singularity at c

Parameters

a	lower interval value
b	lower interval value
c	singular value of f

Implements ROOT::Math::VirtualIntegratorOneDim.

Definition at line 230 of file GSLIntegrator.cxx.

◆ IntegralCauchy() [2/2]

double ROOT::Math::GSLIntegrator::IntegralCauchy	(	const IGenFunction &	f,
		double	a,
		double	b,
		double	c
	)

evaluate the Cauchy principal value of the integral of a function f over the defined interval (a,b) with a singularity at c

Parameters

f	integration function. The function type must implement the mathlib::IGenFunction interface
a	lower interval value
b	lower interval value
c	singular value of f

Definition at line 241 of file GSLIntegrator.cxx.

◆ IntegralLow() [1/3]

double ROOT::Math::GSLIntegrator::IntegralLow	(	const IGenFunction &	f,
		double	b
	)

evaluate the Integral of a function f over the over the semi-infinite interval (-inf,b)

Parameters

f	integration function. The function type must implement the mathlib::IGenFunction interface
b	upper value of the integration interval

Definition at line 341 of file GSLIntegrator.cxx.

◆ IntegralLow() [2/3]

double ROOT::Math::GSLIntegrator::IntegralLow ( double b )

virtual

evaluate the Integral of a function f over the over the semi-infinite interval (-inf,b) using the function previously set with GSLIntegrator::SetFunction method.

Parameters

b	upper value of the integration interval

Implements ROOT::Math::VirtualIntegratorOneDim.

Definition at line 306 of file GSLIntegrator.cxx.

◆ IntegralLow() [3/3]

double ROOT::Math::GSLIntegrator::IntegralLow	(	GSLFuncPointer	f,
		void *	p,
		double	b
	)

evaluate the Integral of a function f over the over the semi-infinite interval (-inf,b) passing a free function pointer

Definition at line 374 of file GSLIntegrator.cxx.

◆ IntegralUp() [1/3]

double ROOT::Math::GSLIntegrator::IntegralUp	(	const IGenFunction &	f,
		double	a
	)

evaluate the Integral of a function f over the semi-infinite interval (a,+inf)

Parameters

f	integration function. The function type must implement the mathlib::IGenFunction interface
a	lower value of the integration interval

Definition at line 335 of file GSLIntegrator.cxx.

◆ IntegralUp() [2/3]

double ROOT::Math::GSLIntegrator::IntegralUp ( double a )

virtual

evaluate the Integral of a function f over the semi-infinite interval (a,+inf) using the function previously set with GSLIntegrator::SetFunction method.

Parameters

a	lower value of the integration interval

Implements ROOT::Math::VirtualIntegratorOneDim.

Definition at line 290 of file GSLIntegrator.cxx.

◆ IntegralUp() [3/3]

double ROOT::Math::GSLIntegrator::IntegralUp	(	GSLFuncPointer	f,
		void *	p,
		double	a
	)

evaluate the Integral of a function f over the semi-infinite interval (a,+inf) passing a free function pointer

Definition at line 368 of file GSLIntegrator.cxx.

◆ NEval()

int ROOT::Math::GSLIntegrator::NEval ( ) const

inlinevirtual

return number of function evaluations in calculating the integral

Reimplemented from ROOT::Math::VirtualIntegrator.

Definition at line 333 of file GSLIntegrator.h.

◆ operator=()

GSLIntegrator & ROOT::Math::GSLIntegrator::operator= ( const GSLIntegrator & rhs )

private

Definition at line 164 of file GSLIntegrator.cxx.

◆ Options()

ROOT::Math::IntegratorOneDimOptions ROOT::Math::GSLIntegrator::Options ( ) const

virtual

get the option used for the integration

Implements ROOT::Math::VirtualIntegratorOneDim.

Definition at line 442 of file GSLIntegrator.cxx.

◆ Result()

double ROOT::Math::GSLIntegrator::Result ( ) const

virtual

return the Result of the last Integral calculation

Implements ROOT::Math::VirtualIntegrator.

Definition at line 388 of file GSLIntegrator.cxx.

◆ SetAbsTolerance()

void ROOT::Math::GSLIntegrator::SetAbsTolerance ( double absTolerance )

virtual

set the desired absolute Error

Implements ROOT::Math::VirtualIntegrator.

Definition at line 399 of file GSLIntegrator.cxx.

◆ SetFunction() [1/2]

void ROOT::Math::GSLIntegrator::SetFunction ( const IGenFunction & f )

virtual

method to set the a generic integration function

Parameters

f	integration function. The function type must implement the assigment operator, double operator() ( double x )

Implements ROOT::Math::VirtualIntegratorOneDim.

Definition at line 182 of file GSLIntegrator.cxx.

◆ SetFunction() [2/2]

void ROOT::Math::GSLIntegrator::SetFunction	(	GSLFuncPointer	f,
		void *	p = `0`
	)

Set function from a GSL pointer function type.

Definition at line 175 of file GSLIntegrator.cxx.

◆ SetIntegrationRule()

void ROOT::Math::GSLIntegrator::SetIntegrationRule ( Integration::GKRule rule )

set the integration rule (Gauss-Kronrod rule).

The possible rules are defined in the Integration::GKRule enumeration. The integration rule can be modified only for ADAPTIVE type integrations

Definition at line 406 of file GSLIntegrator.cxx.

◆ SetOptions()

void ROOT::Math::GSLIntegrator::SetOptions ( const ROOT::Math::IntegratorOneDimOptions & opt )

virtual

set the options

Reimplemented from ROOT::Math::VirtualIntegratorOneDim.

Definition at line 416 of file GSLIntegrator.cxx.

◆ SetRelTolerance()

void ROOT::Math::GSLIntegrator::SetRelTolerance ( double relTolerance )

virtual

set the desired relative Error

Implements ROOT::Math::VirtualIntegrator.

Definition at line 403 of file GSLIntegrator.cxx.

◆ Status()

int ROOT::Math::GSLIntegrator::Status ( ) const

virtual

return the Error Status of the last Integral calculation

Implements ROOT::Math::VirtualIntegrator.

Definition at line 392 of file GSLIntegrator.cxx.

Member Data Documentation

◆ fAbsTol

double ROOT::Math::GSLIntegrator::fAbsTol

private

Definition at line 380 of file GSLIntegrator.h.

◆ fError

double ROOT::Math::GSLIntegrator::fError

private

Definition at line 388 of file GSLIntegrator.h.

◆ fFunction

GSLFunctionWrapper* ROOT::Math::GSLIntegrator::fFunction

private

Definition at line 394 of file GSLIntegrator.h.

◆ fMaxIntervals

size_t ROOT::Math::GSLIntegrator::fMaxIntervals

private

Definition at line 383 of file GSLIntegrator.h.

◆ fNEval

int ROOT::Math::GSLIntegrator::fNEval

private

Definition at line 390 of file GSLIntegrator.h.

◆ fRelTol

double ROOT::Math::GSLIntegrator::fRelTol

private

Definition at line 381 of file GSLIntegrator.h.

◆ fResult

double ROOT::Math::GSLIntegrator::fResult

private

Definition at line 387 of file GSLIntegrator.h.

◆ fRule

Integration::GKRule ROOT::Math::GSLIntegrator::fRule

private

Definition at line 379 of file GSLIntegrator.h.

◆ fSize

size_t ROOT::Math::GSLIntegrator::fSize

private

Definition at line 382 of file GSLIntegrator.h.

◆ fStatus

int ROOT::Math::GSLIntegrator::fStatus

private

Definition at line 389 of file GSLIntegrator.h.

◆ fType

Integration::Type ROOT::Math::GSLIntegrator::fType

private

Definition at line 378 of file GSLIntegrator.h.

◆ fWorkspace

GSLIntegrationWorkspace* ROOT::Math::GSLIntegrator::fWorkspace

private

Definition at line 395 of file GSLIntegrator.h.

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

math/mathmore/inc/Math/GSLIntegrator.h
math/mathmore/src/GSLIntegrator.cxx

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Constructor & Destructor Documentation

◆ GSLIntegrator() [1/5]

◆ GSLIntegrator() [2/5]

◆ GSLIntegrator() [3/5]

◆ GSLIntegrator() [4/5]

◆ ~GSLIntegrator()

◆ GSLIntegrator() [5/5]

Member Function Documentation

◆ CheckFunction()

◆ Error()

◆ GetType()

◆ GetTypeName()

◆ Integral() [1/9]

◆ Integral() [2/9]

◆ Integral() [3/9]

◆ Integral() [4/9]

◆ Integral() [5/9]

◆ Integral() [6/9]

◆ Integral() [7/9]

◆ Integral() [8/9]

◆ Integral() [9/9]

◆ IntegralCauchy() [1/2]

◆ IntegralCauchy() [2/2]

◆ IntegralLow() [1/3]

◆ IntegralLow() [2/3]

◆ IntegralLow() [3/3]

◆ IntegralUp() [1/3]

◆ IntegralUp() [2/3]

◆ IntegralUp() [3/3]

◆ NEval()

◆ operator=()

◆ Options()

◆ Result()

◆ SetAbsTolerance()

◆ SetFunction() [1/2]

◆ SetFunction() [2/2]

◆ SetIntegrationRule()

◆ SetOptions()

◆ SetRelTolerance()

◆ Status()

Member Data Documentation

◆ fAbsTol

◆ fError

◆ fFunction

◆ fMaxIntervals

◆ fNEval

◆ fRelTol

◆ fResult

◆ fRule

◆ fSize

◆ fStatus

◆ fType

◆ fWorkspace