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

It uses the plug-in manager to load advanced numerical integration algorithms from 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 102 of file Integrator.h.

Public Types
typedef IntegrationOneDim::Type	Type

Public Member Functions
	IntegratorOneDim (IntegrationOneDim::Type type=IntegrationOneDim::kDEFAULT, double absTol=-1, double relTol=-1, unsigned int size=0, unsigned int rule=0)
	Constructor of one dimensional Integrator, default type is adaptive. More...

	IntegratorOneDim (const IGenFunction &f, IntegrationOneDim::Type type=IntegrationOneDim::kDEFAULT, double absTol=-1, double relTol=-1, unsigned int size=0, int rule=0)
	Constructor of one dimensional Integrator passing a function interface. More...

template<class Function >
	IntegratorOneDim (Function &f, IntegrationOneDim::Type type=IntegrationOneDim::kDEFAULT, double absTol=-1, double relTol=-1, unsigned int size=0, int rule=0)
	Template Constructor of one dimensional Integrator passing a generic function object. More...

virtual	~IntegratorOneDim ()
	destructor (will delete contained pointers) More...

template<class Function >
void	SetFunction (Function &f)
	method to set the a generic integration function More...

void	SetFunction (const IGenFunction &f, bool copy=false)
	set one dimensional function for 1D integration More...

void	SetFunction (const IMultiGenFunction &f, unsigned int icoord, const double *x)
	Set integration function from a multi-dim function type. More...

template<class Function >
double	Integral (Function &f, double a, double b)
	evaluate the Integral of a function f over the defined interval (a,b) 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	IntegralUp (const IGenFunction &f, double a)
	evaluate the Integral of a function f over the semi-infinite interval (a,+inf) 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...

template<class Function >
double	Integral (Function &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 (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...

template<class Function >
double	IntegralCauchy (Function &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	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	Integral (double a, double b)
	evaluate the Integral over the defined interval (a,b) using the function previously set with Integrator::SetFunction method More...

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

double	operator() (double x)
	define operator() for IntegralLow More...

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

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

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

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

int	NEval () const
	return number of function evaluations in calculating the integral (if integrator do not implement this function returns -1) More...

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

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

VirtualIntegratorOneDim *	GetIntegrator ()
	return a pointer to integrator object More...

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

ROOT::Math::IntegratorOneDimOptions	Options () const
	retrieve the options More...

std::string	Name () const
	return name of integrator More...

Static Public Member Functions
static IntegrationOneDim::Type	GetType (const char *name)
	static function to get the enumeration from a string More...

static std::string	GetName (IntegrationOneDim::Type)
	static function to get a string from the enumeration More...

Protected Member Functions
VirtualIntegratorOneDim *	CreateIntegrator (IntegrationOneDim::Type type, double absTol, double relTol, unsigned int size, int rule)

Private Member Functions
	IntegratorOneDim (const IntegratorOneDim &)

IntegratorOneDim &	operator= (const IntegratorOneDim &)

Private Attributes
VirtualIntegratorOneDim *	fIntegrator

IGenFunction *	fFunc

#include <Math/Integrator.h>

Member Typedef Documentation

typedef IntegrationOneDim::Type ROOT::Math::IntegratorOneDim::Type

Definition at line 106 of file Integrator.h.

Constructor & Destructor Documentation

ROOT::Math::IntegratorOneDim::IntegratorOneDim	(	IntegrationOneDim::Type	type = `IntegrationOneDim::kDEFAULT`,
		double	absTol = `-1`,
		double	relTol = `-1`,
		unsigned int	size = `0`,
		unsigned int	rule = `0`
	)

inlineexplicit

Constructor of one dimensional Integrator, default type is adaptive.

Parameters

type	integration type (adaptive, non-adaptive, etc..)
absTol	desired absolute Error
relTol	desired relative Error
size	maximum number of sub-intervals
rule	Gauss-Kronrod integration rule (only for GSL kADAPTIVE type)

Possible type values are : kGAUSS (simple Gauss method), kADAPTIVE (from GSL), kADAPTIVESINGULAR (from GSL), kNONADAPTIVE (from GSL) Possible rule values are kGAUS15 (rule = 1), kGAUS21( rule = 2), kGAUS31(rule =3), kGAUS41 (rule=4), kGAUS51 (rule =5), kGAUS61(rule =6) lower rules are indicated for singular functions while higher for smooth functions to get better accuracies

NOTE: When the default values are passed, the values used are taken from the default defined in ROOT::Math::IntegratorOneDimOptions

Definition at line 127 of file Integrator.h.

ROOT::Math::IntegratorOneDim::IntegratorOneDim	(	const IGenFunction &	f,
		IntegrationOneDim::Type	type = `IntegrationOneDim::kDEFAULT`,
		double	absTol = `-1`,
		double	relTol = `-1`,
		unsigned int	size = `0`,
		int	rule = `0`
	)

inlineexplicit

Constructor of one dimensional Integrator passing a function interface.

Parameters

f	integration function (1D interface). It is copied inside
type	integration type (adaptive, non-adaptive, etc..)
absTol	desired absolute tolerance. The algorithm will stop when either the absolute OR the relative tolerance are satisfied.
relTol	desired relative tolerance
size	maximum number of sub-intervals
rule	Gauss-Kronrod integration rule (only for GSL ADAPTIVE type)

NOTE: When no values are passed, the values used are taken from the default defined in ROOT::Math::IntegratorOneDimOptions

Definition at line 146 of file Integrator.h.

template<class Function >

ROOT::Math::IntegratorOneDim::IntegratorOneDim	(	Function &	f,
		IntegrationOneDim::Type	type = `IntegrationOneDim::kDEFAULT`,
		double	absTol = `-1`,
		double	relTol = `-1`,
		unsigned int	size = `0`,
		int	rule = `0`
	)

inlineexplicit

Template Constructor of one dimensional Integrator passing a generic function object.

Parameters

f	integration function (any C++ callable object implementing operator()(double x)
type	integration type (adaptive, non-adaptive, etc..)
absTol	desired absolute tolerance. The algorithm will stop when either the absolute OR the relative tolerance are satisfied.
relTol	desired relative tolerance
size	maximum number of sub-intervals
rule	Gauss-Kronrod integration rule (only for GSL ADAPTIVE type)

NOTE: When no values are passed, the values used are taken from the default defined in ROOT::Math::IntegratorOneDimOptions

Definition at line 169 of file Integrator.h.

virtual ROOT::Math::IntegratorOneDim::~IntegratorOneDim ( )

inlinevirtual

destructor (will delete contained pointers)

Definition at line 177 of file Integrator.h.

ROOT::Math::IntegratorOneDim::IntegratorOneDim ( const IntegratorOneDim & )

inlineprivate

Definition at line 185 of file Integrator.h.

Member Function Documentation

VirtualIntegratorOneDim * ROOT::Math::IntegratorOneDim::CreateIntegrator	(	IntegrationOneDim::Type	type,
		double	absTol,
		double	relTol,
		unsigned int	size,
		int	rule
	)

protected

Definition at line 115 of file Integrator.cxx.

Referenced by IntegratorOneDim().

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

inline

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

Definition at line 420 of file Integrator.h.

Referenced by TF1::IntegralOneDim(), and testIntegration().

VirtualIntegratorOneDim* ROOT::Math::IntegratorOneDim::GetIntegrator ( )

inline

return a pointer to integrator object

Definition at line 450 of file Integrator.h.

std::string ROOT::Math::IntegratorOneDim::GetName ( IntegrationOneDim::Type type )

static

static function to get a string from the enumeration

Definition at line 67 of file Integrator.cxx.

Referenced by CreateIntegrator(), ROOT::Math::IntegratorOneDimOptions::DefaultIntegrator(), TF1::IntegralOneDim(), and ROOT::Math::IntegratorOneDimOptions::Integrator().

IntegrationOneDim::Type ROOT::Math::IntegratorOneDim::GetType ( const char * name )

static

static function to get the enumeration from a string

Definition at line 54 of file Integrator.cxx.

Referenced by GetName(), ROOT::Math::IntegratorOneDimOptions::SetDefaultIntegrator(), and ROOT::Math::IntegratorOneDimOptions::SetIntegrator().

template<class Function >

double ROOT::Math::IntegratorOneDim::Integral	(	Function &	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 be a C++ callable object implementing operator()(double x)
a	lower value of the integration interval
b	upper value of the integration interval

Definition at line 506 of file Integrator.h.

Referenced by TUnuranContDist::Cdf(), TKDE::ComputeKernelIntegral(), TKDE::ComputeKernelL2Norm(), TKDE::ComputeKernelMu(), TKDE::ComputeKernelSigma2(), TF1Convolution::EvalNumConv(), TF1::IntegralOneDim(), Integration(), testAnalyticalIntegrals(), testIntegPerf(), testIntegration(), and testIntegration1D().

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

inline

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 245 of file Integrator.h.

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

inline

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

Parameters

f	integration function. The function type must be a C++ callable object implementing operator()(double x) evaluate the Integral of a function f over the infinite interval (-inf,+inf)
f	integration function. The function type must implement the mathlib::IGenFunction interface

Definition at line 262 of file Integrator.h.

template<class Function >

double ROOT::Math::IntegratorOneDim::Integral	(	Function &	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 be a C++ callable object implementing operator()(double x)
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 536 of file Integrator.h.

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

inline

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 320 of file Integrator.h.

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

inline

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

Parameters

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

Definition at line 359 of file Integrator.h.

double ROOT::Math::IntegratorOneDim::Integral ( )

inline

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

Definition at line 368 of file Integrator.h.

Referenced by Integral().

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

inline

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

Definition at line 400 of file Integrator.h.

template<class Function >

double ROOT::Math::IntegratorOneDim::IntegralCauchy	(	Function &	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 be a C++ callable object implementing operator()(double x)
a	lower value of the integration interval
b	upper value of the integration interval
c	position of singularity

Definition at line 543 of file Integrator.h.

Referenced by IntegralCauchy().

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

inline

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 value of the integration interval
b	upper value of the integration interval
c	position of singularity

Definition at line 344 of file Integrator.h.

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

inline

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

Definition at line 408 of file Integrator.h.

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

inline

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

Parameters

f	integration function. The function type must be a C++ callable object implementing operator()(double x)
b	upper value of the integration interval evaluate the Integral of a function f over the over the semi-infinite interval (-inf,b)
f	integration function. The function type must implement the mathlib::IGenFunction interface
b	upper value of the integration interval

Definition at line 300 of file Integrator.h.

Referenced by TF1Convolution::EvalNumConv(), TF1::IntegralOneDim(), and operator()().

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

inline

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

Parameters

b	upper value of the integration interval

Definition at line 384 of file Integrator.h.

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

inline

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

Parameters

f	integration function. The function type must be a C++ callable object implementing operator()(double x)
a	lower value of the integration interval evaluate the Integral of a function f over the semi-infinite interval (a,+inf)
f	integration function. The function type must implement the mathlib::IGenFunction interface
a	lower value of the integration interval

Definition at line 282 of file Integrator.h.

Referenced by TF1Convolution::EvalNumConv(), and TF1::IntegralOneDim().

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

inline

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

Parameters

a	lower value of the integration interval

Definition at line 376 of file Integrator.h.

std::string ROOT::Math::IntegratorOneDim::Name ( ) const

inline

return name of integrator

Definition at line 463 of file Integrator.h.

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

inline

return number of function evaluations in calculating the integral (if integrator do not implement this function returns -1)

Definition at line 431 of file Integrator.h.

double ROOT::Math::IntegratorOneDim::operator() ( double x )

inline

define operator() for IntegralLow

Definition at line 390 of file Integrator.h.

IntegratorOneDim& ROOT::Math::IntegratorOneDim::operator= ( const IntegratorOneDim & )

inlineprivate

Definition at line 186 of file Integrator.h.

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

inline

retrieve the options

Definition at line 460 of file Integrator.h.

Referenced by Name().

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

inline

return the Result of the last Integral calculation

Definition at line 415 of file Integrator.h.

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

inline

set the desired absolute Error

Definition at line 445 of file Integrator.h.

template<class Function >

void ROOT::Math::IntegratorOneDim::SetFunction ( Function & f )

inline

method to set the a generic integration function

Parameters

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

Definition at line 499 of file Integrator.h.

Referenced by TKDE::ComputeKernelIntegral(), TKDE::ComputeKernelL2Norm(), TKDE::ComputeKernelMu(), TKDE::ComputeKernelSigma2(), Integral(), IntegralCauchy(), IntegralLow(), IntegralUp(), IntegratorOneDim(), SetFunction(), testAnalyticalIntegrals(), testIntegPerf(), testIntegration(), and testIntegration1D().

void ROOT::Math::IntegratorOneDim::SetFunction	(	const IGenFunction &	f,
		bool	copy = `false`
	)

inline

set one dimensional function for 1D integration

Definition at line 206 of file Integrator.h.

void ROOT::Math::IntegratorOneDim::SetFunction	(	const IMultiGenFunction &	f,
		unsigned int	icoord,
		const double *	x
	)

Set integration function from a multi-dim function type.

Can be used in case of having 1D function implementing the generic interface

Parameters

f	integration function
icoord	index of coordinate on which the integration is performed
x	array of the passed variables values. In case of dim=1 a 0 can be passed

Definition at line 101 of file Integrator.cxx.

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

inline

set the options

Definition at line 455 of file Integrator.h.

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

inline

set the desired relative Error

Definition at line 439 of file Integrator.h.

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

inline

return the Error Status of the last Integral calculation

Definition at line 425 of file Integrator.h.

Referenced by TF1::IntegralOneDim().

Member Data Documentation

IGenFunction* ROOT::Math::IntegratorOneDim::fFunc

private

Definition at line 479 of file Integrator.h.

Referenced by SetFunction(), and ~IntegratorOneDim().

VirtualIntegratorOneDim* ROOT::Math::IntegratorOneDim::fIntegrator

private

Definition at line 478 of file Integrator.h.

Referenced by Error(), GetIntegrator(), Integral(), IntegralCauchy(), IntegralLow(), IntegralUp(), IntegratorOneDim(), Name(), NEval(), Options(), Result(), SetAbsTolerance(), SetFunction(), SetOptions(), SetRelTolerance(), Status(), and ~IntegratorOneDim().

Collaboration diagram for ROOT::Math::IntegratorOneDim:

[legend]

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

math/mathcore/inc/Math/Integrator.h
math/mathcore/src/Integrator.cxx

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation