class for adaptive quadrature integration in multi-dimensions using rectangular regions.

Algorithm from A.C. Genz, A.A. Malik, An adaptive algorithm for numerical integration over an N-dimensional rectangular region, J. Comput. Appl. Math. 6 (1980) 295-302.

Converted/adapted by R.Brun to C++ from Fortran CERNLIB routine RADMUL (D120) The new code features many changes compared to the Fortran version.

Control parameters are:

minpts: Minimum number of function evaluations requested. Must not exceed maxpts.
        if minpts < 1 minpts is set to 2^n +2*n*(n+1) +1 where n is the function dimension

maxpts: Maximum number of function evaluations to be allowed. maxpts >= 2^n +2*n*(n+1) +1 if maxpts<minpts, maxpts is set to 10*minpts epstol, epsrel : Specified relative and absolute accuracy.

The integral will stop if the relative error is less than relative tolerance OR the absolute error is less than the absolute tolerance

The class computes in addition to the integral of the function is the desired interval:

an estimation of the relative accuracy of the result.
number of function evaluations performed.
status code  :
   0 Normal exit.  . At least minpts and at most maxpts calls to the function were performed.
   1 maxpts is too small for the specified accuracy eps.
     The result and relerr contain the values obtainable for the
     specified value of maxpts.
   3 n<2 or n>15

Method:

An integration rule of degree seven is used together with a certain strategy of subdivision. For a more detailed description of the method see References.

Notes:

1.Multi-dimensional integration is time-consuming. For each rectangular subregion, the routine requires function evaluations. Careful programming of the integrand might result in substantial saving of time. 2.Numerical integration usually works best for smooth functions. Some analysis or suitable transformations of the integral prior to numerical work may contribute to numerical efficiency.

References:

1.A.C. Genz and A.A. Malik, Remarks on algorithm 006: An adaptive algorithm for numerical integration over an N-dimensional rectangular region, J. Comput. Appl. Math. 6 (1980) 295-302. 2.A. van Doren and L. de Ridder, An adaptive algorithm for numerical integration over an n-dimensional cube, J.Comput. Appl. Math. 2 (1976) 207-217.

Definition at line 89 of file AdaptiveIntegratorMultiDim.h.

Public Member Functions
	AdaptiveIntegratorMultiDim (double absTol=0.0, double relTol=1E-9, unsigned int maxpts=100000, unsigned int size=0)
	construct given optionally tolerance (absolute and relative), maximum number of function evaluation (maxpts) and size of the working array. More...

	AdaptiveIntegratorMultiDim (const IMultiGenFunction &f, double absTol=0.0, double relTol=1E-9, unsigned int maxcall=100000, unsigned int size=0)
	Construct with a reference to the integrand function and given optionally tolerance (absolute and relative), maximum number of function evaluation (maxpts) and size of the working array. More...

virtual	~AdaptiveIntegratorMultiDim ()
	destructor (no operations) More...

double	Integral (const double xmin, const double xmax)
	evaluate the integral with the previously given function between xmin[] and xmax[] More...

double	Integral (const IMultiGenFunction &f, const double xmin, const double xmax)
	evaluate the integral passing a new function More...

void	SetFunction (const IMultiGenFunction &f)
	set the integration function (must implement multi-dim function interface: IBaseFunctionMultiDim) More...

double	Result () const
	return result of integration More...

double	Error () const
	return integration error More...

double	RelError () const
	return relative error More...

int	Status () const
	return status of integration More...

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

void	SetRelTolerance (double relTol)
	set relative tolerance More...

void	SetAbsTolerance (double absTol)
	set absolute tolerance More...

void	SetSize (unsigned int size)
	set workspace size More...

void	SetMinPts (unsigned int n)
	set min points More...

void	SetMaxPts (unsigned int n)
	set max points More...

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

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

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

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

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

Protected Member Functions
double	DoIntegral (const double xmin, const double xmax, bool absVal=false)

Private Attributes
unsigned int	fDim

unsigned int	fMinPts

unsigned int	fMaxPts

unsigned int	fSize

double	fAbsTol

double	fRelTol

double	fResult

double	fError

double	fRelError

int	fNEval

int	fStatus

const IMultiGenFunction *	fFun

#include <Math/AdaptiveIntegratorMultiDim.h>

Inheritance diagram for ROOT::Math::AdaptiveIntegratorMultiDim:

[legend]

Constructor & Destructor Documentation

ROOT::Math::AdaptiveIntegratorMultiDim::AdaptiveIntegratorMultiDim	(	double	absTol = `0.0`,
		double	relTol = `1E-9`,
		unsigned int	maxpts = `100000`,
		unsigned int	size = `0`
	)

explicit

construct given optionally tolerance (absolute and relative), maximum number of function evaluation (maxpts) and size of the working array.

The integration will stop when the absolute error is less than the absolute tolerance OR when the relative error is less than the relative tolerance. The absolute tolerance by defult is not used (it is equal to zero). The size of working array represents the number of sub-division used for calculating the integral. Higher the dimension, larger sizes are required for getting the same accuracy. The size must be larger than >= (2N + 3) * (1 + MAXPTS/(2**N + 2N(N + 1) + 1))/2). For smaller value passed, the minimum allowed will be used

Definition at line 17 of file AdaptiveIntegratorMultiDim.cxx.

ROOT::Math::AdaptiveIntegratorMultiDim::AdaptiveIntegratorMultiDim	(	const IMultiGenFunction &	f,
		double	absTol = `0.0`,
		double	relTol = `1E-9`,
		unsigned int	maxcall = `100000`,
		unsigned int	size = `0`
	)

explicit

Construct with a reference to the integrand function and given optionally tolerance (absolute and relative), maximum number of function evaluation (maxpts) and size of the working array.

Definition at line 37 of file AdaptiveIntegratorMultiDim.cxx.

virtual ROOT::Math::AdaptiveIntegratorMultiDim::~AdaptiveIntegratorMultiDim ( )

inlinevirtual

destructor (no operations)

Definition at line 117 of file AdaptiveIntegratorMultiDim.h.

Member Function Documentation

double ROOT::Math::AdaptiveIntegratorMultiDim::DoIntegral	(	const double *	xmin,
		const double *	xmax,
		bool	absVal = `false`
	)

protected

Definition at line 76 of file AdaptiveIntegratorMultiDim.cxx.

Referenced by Integral().

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

inlinevirtual

return integration error

Implements ROOT::Math::VirtualIntegrator.

Definition at line 138 of file AdaptiveIntegratorMultiDim.h.

Referenced by DoIntegral(), and integral_num().

double ROOT::Math::AdaptiveIntegratorMultiDim::Integral	(	const double *	xmin,
		const double *	xmax
	)

inlinevirtual

evaluate the integral with the previously given function between xmin[] and xmax[]

Implements ROOT::Math::VirtualIntegratorMultiDim.

Definition at line 123 of file AdaptiveIntegratorMultiDim.h.

Referenced by RooAdaptiveIntegratorND::integral(), Integral(), integral_num(), and TF1::IntegralMultiple().

double ROOT::Math::AdaptiveIntegratorMultiDim::Integral	(	const IMultiGenFunction &	f,
		const double *	xmin,
		const double *	xmax
	)

evaluate the integral passing a new function

Definition at line 385 of file AdaptiveIntegratorMultiDim.cxx.

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

inlinevirtual

return number of function evaluations in calculating the integral

Reimplemented from ROOT::Math::VirtualIntegrator.

Definition at line 147 of file AdaptiveIntegratorMultiDim.h.

Referenced by integral_num(), and TF1::IntegralMultiple().

ROOT::Math::IntegratorMultiDimOptions ROOT::Math::AdaptiveIntegratorMultiDim::Options ( ) const

virtual

get the option used for the integration

Implements ROOT::Math::VirtualIntegratorMultiDim.

Definition at line 393 of file AdaptiveIntegratorMultiDim.cxx.

double ROOT::Math::AdaptiveIntegratorMultiDim::RelError ( ) const

inline

return relative error

Definition at line 141 of file AdaptiveIntegratorMultiDim.h.

Referenced by RooAdaptiveIntegratorND::integral(), and TF1::IntegralMultiple().

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

inlinevirtual

return result of integration

Implements ROOT::Math::VirtualIntegrator.

Definition at line 135 of file AdaptiveIntegratorMultiDim.h.

Referenced by integral_num().

void ROOT::Math::AdaptiveIntegratorMultiDim::SetAbsTolerance ( double absTol )

virtual

set absolute tolerance

Implements ROOT::Math::VirtualIntegrator.

Definition at line 73 of file AdaptiveIntegratorMultiDim.cxx.

Referenced by SetOptions().

void ROOT::Math::AdaptiveIntegratorMultiDim::SetFunction ( const IMultiGenFunction & f )

virtual

set the integration function (must implement multi-dim function interface: IBaseFunctionMultiDim)

Implements ROOT::Math::VirtualIntegratorMultiDim.

Definition at line 63 of file AdaptiveIntegratorMultiDim.cxx.

Referenced by integral_num(), and RooAdaptiveIntegratorND::RooAdaptiveIntegratorND().

void ROOT::Math::AdaptiveIntegratorMultiDim::SetMaxPts ( unsigned int n )

inline

set max points

Definition at line 162 of file AdaptiveIntegratorMultiDim.h.

Referenced by SetOptions().

void ROOT::Math::AdaptiveIntegratorMultiDim::SetMinPts ( unsigned int n )

inline

set min points

Definition at line 159 of file AdaptiveIntegratorMultiDim.h.

void ROOT::Math::AdaptiveIntegratorMultiDim::SetOptions ( const ROOT::Math::IntegratorMultiDimOptions & opt )

virtual

set the options

Reimplemented from ROOT::Math::VirtualIntegratorMultiDim.

Definition at line 404 of file AdaptiveIntegratorMultiDim.cxx.

void ROOT::Math::AdaptiveIntegratorMultiDim::SetRelTolerance ( double relTol )

virtual

set relative tolerance

Implements ROOT::Math::VirtualIntegrator.

Definition at line 70 of file AdaptiveIntegratorMultiDim.cxx.

Referenced by SetOptions().

void ROOT::Math::AdaptiveIntegratorMultiDim::SetSize ( unsigned int size )

inline

set workspace size

Definition at line 156 of file AdaptiveIntegratorMultiDim.h.

Referenced by SetOptions().

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

inlinevirtual

return status of integration

Implements ROOT::Math::VirtualIntegrator.

Definition at line 144 of file AdaptiveIntegratorMultiDim.h.

Referenced by RooAdaptiveIntegratorND::integral(), and TF1::IntegralMultiple().

Member Data Documentation

double ROOT::Math::AdaptiveIntegratorMultiDim::fAbsTol

private

Definition at line 181 of file AdaptiveIntegratorMultiDim.h.

Referenced by AdaptiveIntegratorMultiDim(), DoIntegral(), Options(), and SetAbsTolerance().

unsigned int ROOT::Math::AdaptiveIntegratorMultiDim::fDim

private

Definition at line 177 of file AdaptiveIntegratorMultiDim.h.

Referenced by DoIntegral(), and SetFunction().

double ROOT::Math::AdaptiveIntegratorMultiDim::fError

private

Definition at line 185 of file AdaptiveIntegratorMultiDim.h.

Referenced by DoIntegral(), and Error().

const IMultiGenFunction* ROOT::Math::AdaptiveIntegratorMultiDim::fFun

private

Definition at line 190 of file AdaptiveIntegratorMultiDim.h.

Referenced by DoIntegral(), Integral(), and SetFunction().

unsigned int ROOT::Math::AdaptiveIntegratorMultiDim::fMaxPts

private

Definition at line 179 of file AdaptiveIntegratorMultiDim.h.

Referenced by AdaptiveIntegratorMultiDim(), DoIntegral(), Options(), and SetMaxPts().

unsigned int ROOT::Math::AdaptiveIntegratorMultiDim::fMinPts

private

Definition at line 178 of file AdaptiveIntegratorMultiDim.h.

Referenced by DoIntegral(), and SetMinPts().

int ROOT::Math::AdaptiveIntegratorMultiDim::fNEval

private

Definition at line 187 of file AdaptiveIntegratorMultiDim.h.

Referenced by DoIntegral(), and NEval().

double ROOT::Math::AdaptiveIntegratorMultiDim::fRelError

private

Definition at line 186 of file AdaptiveIntegratorMultiDim.h.

Referenced by DoIntegral(), and RelError().

double ROOT::Math::AdaptiveIntegratorMultiDim::fRelTol

private

Definition at line 182 of file AdaptiveIntegratorMultiDim.h.

Referenced by AdaptiveIntegratorMultiDim(), DoIntegral(), Options(), and SetRelTolerance().

double ROOT::Math::AdaptiveIntegratorMultiDim::fResult

private

Definition at line 184 of file AdaptiveIntegratorMultiDim.h.

Referenced by DoIntegral(), and Result().

unsigned int ROOT::Math::AdaptiveIntegratorMultiDim::fSize

private

Definition at line 180 of file AdaptiveIntegratorMultiDim.h.

Referenced by AdaptiveIntegratorMultiDim(), DoIntegral(), Options(), and SetSize().

int ROOT::Math::AdaptiveIntegratorMultiDim::fStatus

private

Definition at line 188 of file AdaptiveIntegratorMultiDim.h.

Referenced by DoIntegral(), and Status().

Collaboration diagram for ROOT::Math::AdaptiveIntegratorMultiDim:

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

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

Public Member Functions

Protected Member Functions

Private Attributes

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation