User class for performing function integration.

It will use the Gauss Method for function integration in a given interval. This class is implemented from TF1::Integral().

Definition at line 39 of file GaussIntegrator.h.

Public Member Functions
	GaussIntegrator (double absTol=-1, double relTol=-1)
	Default Constructor. More...

virtual	~GaussIntegrator ()
	Destructor. More...

void	AbsValue (bool flag)
	Static function: set the fgAbsValue flag. More...

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

double	Integral (double a, double b)
	Returns Integral of function between a and b. More...

double	Integral ()
	Returns Integral of function on an infinite interval. More...

double	Integral (const std::vector< double > &pts)
	This method is not implemented. More...

double	IntegralCauchy (double a, double b, double c)
	This method is not implemented. More...

double	IntegralLow (double b)
	Returns Integral of function on a lower semi-infinite interval. More...

double	IntegralUp (double a)
	Returns Integral of function on an upper semi-infinite interval. More...

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

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

virtual void	SetAbsTolerance (double eps)
	This method is not implemented. More...

void	SetFunction (const IGenFunction &)
	Set integration function (flag control if function must be copied inside). More...

virtual void	SetOptions (const ROOT::Math::IntegratorOneDimOptions &opt)
	set the options (should be re-implemented by derived classes -if more options than tolerance exist More...

virtual void	SetRelTolerance (double eps)
	Set the desired relative Error. More...

int	Status () const
	return the status of the last integration - 0 in case of success 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 ()

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

Protected Attributes
double	fEpsAbs

double	fEpsRel

const IGenFunction *	fFunction

double	fLastError

double	fLastResult

bool	fUsedOnce

Static Protected Attributes
static bool	fgAbsValue = false

Private Member Functions
virtual double	DoIntegral (double a, double b, const IGenFunction *func)
	Integration surrogate method. More...

#include <Math/GaussIntegrator.h>

Inheritance diagram for ROOT::Math::GaussIntegrator:

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Constructor & Destructor Documentation

◆ ~GaussIntegrator()

ROOT::Math::GaussIntegrator::~GaussIntegrator ( )

virtual

Destructor.

Definition at line 44 of file GaussIntegrator.cxx.

◆ GaussIntegrator()

ROOT::Math::GaussIntegrator::GaussIntegrator	(	double	absTol = `-1`,
		double	relTol = `-1`
	)

Default Constructor.

If the tolerance are not given, use default values specified in ROOT::Math::IntegratorOneDimOptions

Definition at line 25 of file GaussIntegrator.cxx.

Member Function Documentation

◆ AbsValue()

void ROOT::Math::GaussIntegrator::AbsValue ( bool flag )

Static function: set the fgAbsValue flag.

By default TF1::Integral uses the original function value to compute the integral However, TF1::Moment, CentralMoment require to compute the integral using the absolute value of the function.

Definition at line 49 of file GaussIntegrator.cxx.

◆ DoIntegral()

double ROOT::Math::GaussIntegrator::DoIntegral	(	double	a,
		double	b,
		const IGenFunction *	func
	)

privatevirtual

Integration surrogate method.

Return integral of passed function in interval [a,b] Derived class (like GaussLegendreIntegrator) can re-implement this method to modify to use an improved algorithm

Reimplemented in ROOT::Math::GaussLegendreIntegrator.

Definition at line 71 of file GaussIntegrator.cxx.

◆ Error()

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

virtual

Return the estimate of the absolute Error of the last Integral calculation.

Implements ROOT::Math::VirtualIntegrator.

Definition at line 176 of file GaussIntegrator.cxx.

◆ Integral() [1/3]

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

virtual

Returns Integral of function between a and b.

Based on original CERNLIB routine DGAUSS by Sigfried Kolbig converted to C++ by Rene Brun

This function computes, to an attempted specified accuracy, the value of the integral.

Method: For any interval [a,b] we define g8(a,b) and g16(a,b) to be the 8-point and 16-point Gaussian quadrature approximations to

\[ I = \int^{b}_{a} f(x)dx \]

and define

\[ r(a,b) = \frac{\left|g_{16}(a,b)-g_{8}(a,b)\right|}{1+\left|g_{16}(a,b)\right|} \]

Then,

\[ G = \sum_{i=1}^{k}g_{16}(x_{i-1},x_{i}) \]

where, starting with \(x_{0} = A\) and finishing with \(x_{k} = B\), the subdivision points \(x_{i}(i=1,2,...)\) are given by

\[ x_{i} = x_{i-1} + \lambda(B-x_{i-1}) \]

\(\lambda\) is equal to the first member of the sequence 1,1/2,1/4,... for which \(r(x_{i-1}, x_{i}) < EPS\). If, at any stage in the process of subdivision, the ratio

\[ q = \left|\frac{x_{i}-x_{i-1}}{B-A}\right| \]

is so small that 1+0.005q is indistinguishable from 1 to machine accuracy, an error exit occurs with the function value set equal to zero.

Accuracy: The user provides absolute and relative error bounds (epsrel and epsabs) and the algorithm will stop when the estimated error is less than the epsabs OR is less than |I| * epsrel. Unless there is severe cancellation of positive and negative values of f(x) over the interval [A,B], the relative error may be considered as specifying a bound on the relative error of I in the case |I|>1, and a bound on the absolute error in the case |I|<1. More precisely, if k is the number of sub-intervals contributing to the approximation (see Method), and if

\[ I_{abs} = \int^{B}_{A} \left|f(x)\right|dx \]

then the relation

\[ \frac{\left|G-I\right|}{I_{abs}+k} < EPS \]

will nearly always be true, provided the routine terminates without printing an error message. For functions f having no singularities in the closed interval [A,B] the accuracy will usually be much higher than this.

Error handling: The requested accuracy cannot be obtained (see Method). The function value is set equal to zero.

Note 1: Values of the function f(x) at the interval end-points A and B are not required. The subprogram may therefore be used when these values are undefined

Implements ROOT::Math::VirtualIntegratorOneDim.

Definition at line 52 of file GaussIntegrator.cxx.

◆ Integral() [2/3]

double ROOT::Math::GaussIntegrator::Integral ( )

virtual

Returns Integral of function on an infinite interval.

This function computes, to an attempted specified accuracy, the value of the integral:

\[ I = \int^{\infty}_{-\infty} f(x)dx \]

Usage: In any arithmetic expression, this function has the approximate value of the integral I.

The integral is mapped onto [0,1] using a transformation then integral computation is surrogated to DoIntegral.

Implements ROOT::Math::VirtualIntegratorOneDim.

Definition at line 56 of file GaussIntegrator.cxx.

◆ Integral() [3/3]

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

virtual

This method is not implemented.

Implements ROOT::Math::VirtualIntegratorOneDim.

Definition at line 190 of file GaussIntegrator.cxx.

◆ IntegralCauchy()

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

virtual

This method is not implemented.

Implements ROOT::Math::VirtualIntegratorOneDim.

Definition at line 197 of file GaussIntegrator.cxx.

◆ IntegralLow()

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

virtual

Returns Integral of function on a lower semi-infinite interval.

This function computes, to an attempted specified accuracy, the value of the integral:

\[ I = \int^{B}_{-\infty} f(x)dx \]

Usage: In any arithmetic expression, this function has the approximate value of the integral I.

B: upper end-point of integration interval.

The integral is mapped onto [0,1] using a transformation then integral computation is surrogated to DoIntegral.

Implements ROOT::Math::VirtualIntegratorOneDim.

Definition at line 66 of file GaussIntegrator.cxx.

◆ IntegralUp()

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

virtual

Returns Integral of function on an upper semi-infinite interval.

This function computes, to an attempted specified accuracy, the value of the integral:

\[ I = \int^{\infty}_{A} f(x)dx \]

Usage: In any arithmetic expression, this function has the approximate value of the integral I.

A: lower end-point of integration interval.

The integral is mapped onto [0,1] using a transformation then integral computation is surrogated to DoIntegral.

Implements ROOT::Math::VirtualIntegratorOneDim.

Definition at line 61 of file GaussIntegrator.cxx.

◆ Options()

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

virtual

get the option used for the integration

Implements ROOT::Math::VirtualIntegratorOneDim.

Reimplemented in ROOT::Math::GaussLegendreIntegrator.

Definition at line 210 of file GaussIntegrator.cxx.

◆ Result()

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

virtual

Returns the result of the last Integral calculation.

Implements ROOT::Math::VirtualIntegrator.

Definition at line 166 of file GaussIntegrator.cxx.

◆ SetAbsTolerance()

virtual void ROOT::Math::GaussIntegrator::SetAbsTolerance ( double eps )

inlinevirtual

This method is not implemented.

Implements ROOT::Math::VirtualIntegrator.

Reimplemented in ROOT::Math::GaussLegendreIntegrator.

Definition at line 67 of file GaussIntegrator.h.

◆ SetFunction()

void ROOT::Math::GaussIntegrator::SetFunction ( const IGenFunction & function )

virtual

Set integration function (flag control if function must be copied inside).

@param f Function to be used in the calculations.

Implements ROOT::Math::VirtualIntegratorOneDim.

Definition at line 182 of file GaussIntegrator.cxx.

◆ SetOptions()

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

virtual

set the options (should be re-implemented by derived classes -if more options than tolerance exist

Reimplemented from ROOT::Math::VirtualIntegratorOneDim.

Reimplemented in ROOT::Math::GaussLegendreIntegrator.

Definition at line 204 of file GaussIntegrator.cxx.

◆ SetRelTolerance()

virtual void ROOT::Math::GaussIntegrator::SetRelTolerance ( double eps )

inlinevirtual

Set the desired relative Error.

Implements ROOT::Math::VirtualIntegrator.

Reimplemented in ROOT::Math::GaussLegendreIntegrator.

Definition at line 64 of file GaussIntegrator.h.

◆ Status()

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

virtual

return the status of the last integration - 0 in case of success

Implements ROOT::Math::VirtualIntegrator.

Definition at line 179 of file GaussIntegrator.cxx.

Member Data Documentation

◆ fEpsAbs

double ROOT::Math::GaussIntegrator::fEpsAbs

protected

Definition at line 222 of file GaussIntegrator.h.

◆ fEpsRel

double ROOT::Math::GaussIntegrator::fEpsRel

protected

Definition at line 221 of file GaussIntegrator.h.

◆ fFunction

const IGenFunction* ROOT::Math::GaussIntegrator::fFunction

protected

Definition at line 226 of file GaussIntegrator.h.

◆ fgAbsValue

bool ROOT::Math::GaussIntegrator::fgAbsValue = false

staticprotected

Definition at line 220 of file GaussIntegrator.h.

◆ fLastError

double ROOT::Math::GaussIntegrator::fLastError

protected

Definition at line 225 of file GaussIntegrator.h.

◆ fLastResult

double ROOT::Math::GaussIntegrator::fLastResult

protected

Definition at line 224 of file GaussIntegrator.h.

◆ fUsedOnce

bool ROOT::Math::GaussIntegrator::fUsedOnce

protected

Definition at line 223 of file GaussIntegrator.h.

Libraries for ROOT::Math::GaussIntegrator:

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Public Member Functions

Protected Attributes

Static Protected Attributes

Private Member Functions

Constructor & Destructor Documentation

◆ ~GaussIntegrator()

◆ GaussIntegrator()

Member Function Documentation

◆ AbsValue()

◆ DoIntegral()

◆ Error()

◆ Integral() [1/3]

◆ Integral() [2/3]

◆ Integral() [3/3]

◆ IntegralCauchy()

◆ IntegralLow()

◆ IntegralUp()

◆ Options()

◆ Result()

◆ SetAbsTolerance()

◆ SetFunction()

◆ SetOptions()

◆ SetRelTolerance()

◆ Status()

Member Data Documentation

◆ fEpsAbs

◆ fEpsRel

◆ fFunction

◆ fgAbsValue

◆ fLastError

◆ fLastResult

◆ fUsedOnce