Adaptive numerical integration algorithm.

It uses Romberg's method with trapezoids or midpoints. The integrand is approximated by \( 1, 2, 4, 8, \ldots, 2^n \) trapezoids, and Richardson series acceleration is applied to the series. For refinement step \( n \), that is

\[ R(n,m) = \frac{1}{4^m - 1} \left( 4^m R(n, m-1) - R(n-1, m-1) \right) \]

The integrator will evaluate the first six refinements (i.e. 64 points) in one go, apply a five-point series acceleration, and successively add more steps until the desired precision is reached.

Definition at line 36 of file RooRombergIntegrator.h.

Public Types
enum	SummationRule { Trapezoid , Midpoint }

Public Member Functions
	RooRombergIntegrator (const RooAbsFunc &function, const RooNumIntConfig &config, int nDim=1, bool doSegmentation=false)
	Construct integrator on given function binding, using specified configuration object.

	RooRombergIntegrator (const RooAbsFunc &function, double xmin, double xmax, const RooNumIntConfig &config, int nDim=1)
	Construct integrator on given function binding, using specified configuration object and integration range.

	RooRombergIntegrator (const RooAbsFunc &function, double xmin, double xmax, SummationRule rule=Trapezoid, int maxSteps=0, double eps=0)
	Construct integrator on given function binding for given range, using specified summation rule, maximum number of steps and conversion tolerance.

	RooRombergIntegrator (const RooAbsFunc &function, SummationRule rule=Trapezoid, int maxSteps=0, double eps=0)
	Construct integrator on given function binding, using specified summation rule, maximum number of steps and conversion tolerance.

bool	checkLimits () const override
	Check that our integration range is finite and otherwise return false.

double	integral (const double *yvec=nullptr) override

virtual bool	setLimits (double , double )

bool	setLimits (double xmin, double xmax) override
	Change our integration limits.

virtual bool	setLimits (double xmin, double xmax)
	Interface to set limits on integration.

bool	setUseIntegrandLimits (bool flag) override
	Interface function that allows to defer limit definition to integrand definition.

Public Member Functions inherited from RooAbsIntegrator
	RooAbsIntegrator ()

	RooAbsIntegrator (const RooAbsFunc &function, bool printEvalCounter=false)
	Copy constructor.

virtual	~RooAbsIntegrator ()=default

double	calculate (const double *yvec=nullptr)
	Calculate integral value with given array of parameter values.

const RooAbsFunc *	integrand () const
	Return integrand function binding.

double	integrand (const double x[]) const
	Return value of integrand at given observable values.

bool	isValid () const
	Is integrator in valid state.

bool	printEvalCounter () const

void	setPrintEvalCounter (bool value)

Protected Member Functions
bool	initialize ()
	Initialize the integrator.

double	integral (int iDim, int nSeg, std::span< double > wksp)
	Calculate numeric integral at given set of function binding parameters.

Static Protected Member Functions
static void	registerIntegrator (RooNumIntFactory &fact)
	Register integrator plugins, their parameters and capabilities with RooNumIntFactory.

Protected Attributes
bool	_doExtrap = true
	Apply conversion step?

double	_epsAbs
	Absolute convergence tolerance.

double	_epsRel
	Relative convergence tolerance.

int	_fixSteps = 0
	Fixed number of steps.

int	_maxSteps
	Maximum number of steps.

int	_minStepsZero = 999
	Minimum number of steps to declare convergence to zero.

int	_nDim = 1

int	_nSeg = 1
	Number of segments.

SummationRule	_rule

bool	_useIntegrandLimits
	If true limits of function binding are used.

std::vector< double >	_wksp
	! Integrator workspace

std::vector< double >	_x

std::vector< double >	_xmax
	! Upper integration bounds

std::vector< double >	_xmin
	! Lower integration bounds

Protected Attributes inherited from RooAbsIntegrator
const RooAbsFunc *	_function = nullptr
	Pointer to function binding of integrand.

bool	_printEvalCounter = false
	If true print number of function evaluation required for integration.

bool	_valid = false
	Is integrator in valid state?

Friends
class	RooNumIntFactory

#include </home/sftnight/build/workspace/root-makedoc-master/rootspi/rdoc/src/master/roofit/roofitcore/src/RooRombergIntegrator.h>

Inheritance diagram for RooRombergIntegrator:

[legend]

Member Enumeration Documentation

◆ SummationRule

enum RooRombergIntegrator::SummationRule

Enumerator
Trapezoid
Midpoint

Definition at line 39 of file RooRombergIntegrator.h.

Constructor & Destructor Documentation

◆ RooRombergIntegrator() [1/4]

RooRombergIntegrator::RooRombergIntegrator	(	const RooAbsFunc &	function,
		SummationRule	rule = `Trapezoid`,
		int	maxSteps = `0`,
		double	eps = `0`
	)

Construct integrator on given function binding, using specified summation rule, maximum number of steps and conversion tolerance.

The integration limits are taken from the function binding.

Definition at line 308 of file RooRombergIntegrator.cxx.

◆ RooRombergIntegrator() [2/4]

RooRombergIntegrator::RooRombergIntegrator	(	const RooAbsFunc &	function,
		double	xmin,
		double	xmax,
		SummationRule	rule = `Trapezoid`,
		int	maxSteps = `0`,
		double	eps = `0`
	)

Construct integrator on given function binding for given range, using specified summation rule, maximum number of steps and conversion tolerance.

The integration limits are taken from the function binding.

Definition at line 320 of file RooRombergIntegrator.cxx.

◆ RooRombergIntegrator() [3/4]

RooRombergIntegrator::RooRombergIntegrator	(	const RooAbsFunc &	function,
		const RooNumIntConfig &	config,
		int	nDim = `1`,
		bool	doSegmentation = `false`
	)

Construct integrator on given function binding, using specified configuration object.

The integration limits are taken from the function binding

Definition at line 339 of file RooRombergIntegrator.cxx.

◆ RooRombergIntegrator() [4/4]

RooRombergIntegrator::RooRombergIntegrator	(	const RooAbsFunc &	function,
		double	xmin,
		double	xmax,
		const RooNumIntConfig &	config,
		int	nDim = `1`
	)

Construct integrator on given function binding, using specified configuration object and integration range.

Definition at line 373 of file RooRombergIntegrator.cxx.

Member Function Documentation

◆ checkLimits()

bool RooRombergIntegrator::checkLimits ( ) const

overridevirtual

Check that our integration range is finite and otherwise return false.

Update the limits from the integrand if requested.

Reimplemented from RooAbsIntegrator.

Definition at line 450 of file RooRombergIntegrator.cxx.

◆ initialize()

bool RooRombergIntegrator::initialize ( )

protected

Initialize the integrator.

Definition at line 397 of file RooRombergIntegrator.cxx.

◆ integral() [1/2]

double RooRombergIntegrator::integral ( const double * yvec = nullptr )

overridevirtual

Implements RooAbsIntegrator.

Definition at line 477 of file RooRombergIntegrator.cxx.

◆ integral() [2/2]

double RooRombergIntegrator::integral	(	int	iDim,
		int	nSeg,
		std::span< double >	wksp
	)

protected

Calculate numeric integral at given set of function binding parameters.

Definition at line 492 of file RooRombergIntegrator.cxx.

◆ registerIntegrator()

void RooRombergIntegrator::registerIntegrator ( RooNumIntFactory & fact )

staticprotected

Register integrator plugins, their parameters and capabilities with RooNumIntFactory.

Definition at line 239 of file RooRombergIntegrator.cxx.

◆ setLimits() [1/3]

virtual bool RooAbsIntegrator::setLimits	(	double *	,
		double *
	)

inlinevirtual

Reimplemented from RooAbsIntegrator.

Definition at line 54 of file RooAbsIntegrator.h.

◆ setLimits() [2/3]

bool RooRombergIntegrator::setLimits	(	double *	xmin,
		double *	xmax
	)

overridevirtual

Change our integration limits.

Return true if the new limits are ok, or otherwise false. Always returns false and does nothing if this object was constructed to always use our integrand's limits.

Reimplemented from RooAbsIntegrator.

Definition at line 430 of file RooRombergIntegrator.cxx.

◆ setLimits() [3/3]

bool RooAbsIntegrator::setLimits	(	double	xmin,
		double	xmax
	)

virtual

Interface to set limits on integration.

Reimplemented from RooAbsIntegrator.

Definition at line 55 of file RooAbsIntegrator.cxx.

◆ setUseIntegrandLimits()

bool RooRombergIntegrator::setUseIntegrandLimits ( bool flag )

inlineoverridevirtual

Interface function that allows to defer limit definition to integrand definition.

Reimplemented from RooAbsIntegrator.

Definition at line 55 of file RooRombergIntegrator.h.

Friends And Related Symbol Documentation

◆ RooNumIntFactory

friend class RooNumIntFactory

friend

Definition at line 62 of file RooRombergIntegrator.h.

Member Data Documentation

◆ _doExtrap

bool RooRombergIntegrator::_doExtrap = true

protected

Apply conversion step?

Definition at line 78 of file RooRombergIntegrator.h.

◆ _epsAbs

double RooRombergIntegrator::_epsAbs

protected

Absolute convergence tolerance.

Definition at line 76 of file RooRombergIntegrator.h.

◆ _epsRel

double RooRombergIntegrator::_epsRel

protected

Relative convergence tolerance.

Definition at line 77 of file RooRombergIntegrator.h.

◆ _fixSteps

int RooRombergIntegrator::_fixSteps = 0

protected

Fixed number of steps.

Definition at line 75 of file RooRombergIntegrator.h.

◆ _maxSteps

int RooRombergIntegrator::_maxSteps

protected

Maximum number of steps.

Definition at line 73 of file RooRombergIntegrator.h.

◆ _minStepsZero

int RooRombergIntegrator::_minStepsZero = 999

protected

Minimum number of steps to declare convergence to zero.

Definition at line 74 of file RooRombergIntegrator.h.

◆ _nDim

int RooRombergIntegrator::_nDim = 1

protected

Definition at line 71 of file RooRombergIntegrator.h.

◆ _nSeg

int RooRombergIntegrator::_nSeg = 1

protected

Number of segments.

Definition at line 79 of file RooRombergIntegrator.h.

◆ _rule

SummationRule RooRombergIntegrator::_rule

protected

Definition at line 72 of file RooRombergIntegrator.h.

◆ _useIntegrandLimits

bool RooRombergIntegrator::_useIntegrandLimits

protected

If true limits of function binding are used.

Definition at line 68 of file RooRombergIntegrator.h.

◆ _wksp

std::vector<double> RooRombergIntegrator::_wksp

protected

! Integrator workspace

Definition at line 84 of file RooRombergIntegrator.h.

◆ _x

std::vector<double> RooRombergIntegrator::_x

protected

Definition at line 85 of file RooRombergIntegrator.h.

◆ _xmax

std::vector<double> RooRombergIntegrator::_xmax

protected

! Upper integration bounds

Definition at line 81 of file RooRombergIntegrator.h.

◆ _xmin

std::vector<double> RooRombergIntegrator::_xmin

protected

! Lower integration bounds

Definition at line 80 of file RooRombergIntegrator.h.

roofit/roofitcore/src/RooRombergIntegrator.h

roofit/roofitcore/src/RooRombergIntegrator.cxx

Public Types

Public Member Functions

Protected Member Functions

Static Protected Member Functions

Protected Attributes

Friends

Member Enumeration Documentation

◆ SummationRule

Constructor & Destructor Documentation

◆ RooRombergIntegrator() [1/4]

◆ RooRombergIntegrator() [2/4]

◆ RooRombergIntegrator() [3/4]

◆ RooRombergIntegrator() [4/4]

Member Function Documentation

◆ checkLimits()

◆ initialize()

◆ integral() [1/2]

◆ integral() [2/2]

◆ registerIntegrator()

◆ setLimits() [1/3]

◆ setLimits() [2/3]

◆ setLimits() [3/3]

◆ setUseIntegrandLimits()

Friends And Related Symbol Documentation

◆ RooNumIntFactory

Member Data Documentation

◆ _doExtrap

◆ _epsAbs

◆ _epsRel

◆ _fixSteps

◆ _maxSteps

◆ _minStepsZero

◆ _nDim

◆ _nSeg

◆ _rule

◆ _useIntegrandLimits

◆ _wksp

◆ _x

◆ _xmax

◆ _xmin