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Implements the Gauss-Kronrod integration algorithm.

An adaptive Gaussian quadrature method for numerical integration in which error is estimated based on evaluation at special points known as the "Kronrod points". By suitably picking these points, abscissas from previous iterations can be reused as part of the new set of points, whereas usual Gaussian quadrature would require recomputation of all abscissas at each iteration.

This class automatically handles (-inf,+inf) integrals by dividing the integration in three regions (-inf,-1), (-1,1), (1,inf) and calculating the 1st and 3rd term using a $$x \rightarrow 1/x$$ coordinate transformation.

This class embeds the adaptive Gauss-Kronrod integrator from the GNU Scientific Library version 1.5 and applies a chosen rule ( 10-, 21-, 31-, 41, 51- or 61-point). The integration domain is subdivided and recursively integrated until the required precision is reached.

For integrands with integrable singularities the Wynn epsilon rule can be selected to speed up the convergence of these integrals.

Definition at line 24 of file RooAdaptiveGaussKronrodIntegrator1D.h.

## Public Member Functions

RooAdaptiveGaussKronrodIntegrator1D (const RooAbsFunc &function, const RooNumIntConfig &config)
Constructor taking a function binding and a configuration object.

RooAdaptiveGaussKronrodIntegrator1D (const RooAbsFunc &function, double xmin, double xmax, const RooNumIntConfig &config)
Constructor taking a function binding, an integration range and a configuration object.

Destructor.

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

double integral (const double *yvec=nullptr) override
Calculate and return integral at at given parameter values.

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 RooAbsFuncintegrand () 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 Types

enum  DomainType { Closed , OpenLo , OpenHi , Open }

## Protected Member Functions

bool initialize ()
Initialize integrator allocate buffers and setup GSL workspace.

doublexvec (double &xx)

## Static Protected Member Functions

static void registerIntegrator (RooNumIntFactory &fact)
Register this class with RooNumIntConfig as a possible choice of numeric integrator for one-dimensional integrals over finite and infinite domains.

## Protected Attributes

DomainType _domainType

double _epsAbs
Current coordinate.

double _epsRel

Int_t _maxSeg

Int_t _methodKey

bool _useIntegrandLimits

void * _workspace = nullptr

std::vector< double_x

double _xmax
Lower integration bound.

double _xmin

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

double RooAdaptiveGaussKronrodIntegrator1D_GSL_GlueFunction (double x, void *data)
Glue function interacing to GSL code.

class RooNumIntFactory

#include </home/sftnight/build/workspace/root-makedoc-master/rootspi/rdoc/src/master/roofit/roofitmore/src/RooAdaptiveGaussKronrodIntegrator1D.h>

[legend]

## ◆ DomainType

 protected
Enumerator
Closed
OpenLo
OpenHi
Open

Definition at line 48 of file RooAdaptiveGaussKronrodIntegrator1D.h.

## Constructor & Destructor Documentation

Constructor taking a function binding and a configuration object.

Definition at line 186 of file RooAdaptiveGaussKronrodIntegrator1D.cxx.

 RooAdaptiveGaussKronrodIntegrator1D::RooAdaptiveGaussKronrodIntegrator1D ( const RooAbsFunc & function, double xmin, double xmax, const RooNumIntConfig & config )

Constructor taking a function binding, an integration range and a configuration object.

Definition at line 203 of file RooAdaptiveGaussKronrodIntegrator1D.cxx.

override

Destructor.

Definition at line 238 of file RooAdaptiveGaussKronrodIntegrator1D.cxx.

## ◆ checkLimits()

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 270 of file RooAdaptiveGaussKronrodIntegrator1D.cxx.

## ◆ initialize()

protected

Initialize integrator allocate buffers and setup GSL workspace.

Definition at line 224 of file RooAdaptiveGaussKronrodIntegrator1D.cxx.

## ◆ integral()

 double RooAdaptiveGaussKronrodIntegrator1D::integral ( const double * yvec = nullptr )
overridevirtual

Calculate and return integral at at given parameter values.

Implements RooAbsIntegrator.

Definition at line 312 of file RooAdaptiveGaussKronrodIntegrator1D.cxx.

## ◆ registerIntegrator()

 void RooAdaptiveGaussKronrodIntegrator1D::registerIntegrator ( RooNumIntFactory & fact )
staticprotected

Register this class with RooNumIntConfig as a possible choice of numeric integrator for one-dimensional integrals over finite and infinite domains.

Definition at line 156 of file RooAdaptiveGaussKronrodIntegrator1D.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 RooAdaptiveGaussKronrodIntegrator1D::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 252 of file RooAdaptiveGaussKronrodIntegrator1D.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 RooAdaptiveGaussKronrodIntegrator1D::setUseIntegrandLimits ( bool flag )
inlineoverridevirtual

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

Reimplemented from RooAbsIntegrator.

Definition at line 37 of file RooAdaptiveGaussKronrodIntegrator1D.h.

## ◆ xvec()

 double * RooAdaptiveGaussKronrodIntegrator1D::xvec ( double & xx )
inlineprotected

Definition at line 57 of file RooAdaptiveGaussKronrodIntegrator1D.h.

## Friends And Related Symbol Documentation

 double RooAdaptiveGaussKronrodIntegrator1D_GSL_GlueFunction ( double x, void * data )
friend

Glue function interacing to GSL code.

Definition at line 301 of file RooAdaptiveGaussKronrodIntegrator1D.cxx.

## ◆ RooNumIntFactory

 friend class RooNumIntFactory
friend

Definition at line 45 of file RooAdaptiveGaussKronrodIntegrator1D.h.

## ◆ _domainType

mutableprotected

Definition at line 49 of file RooAdaptiveGaussKronrodIntegrator1D.h.

## ◆ _epsAbs

protected

Current coordinate.

Definition at line 65 of file RooAdaptiveGaussKronrodIntegrator1D.h.

## ◆ _epsRel

protected

Definition at line 66 of file RooAdaptiveGaussKronrodIntegrator1D.h.

## ◆ _maxSeg

protected

Definition at line 68 of file RooAdaptiveGaussKronrodIntegrator1D.h.

## ◆ _methodKey

protected

Definition at line 67 of file RooAdaptiveGaussKronrodIntegrator1D.h.

## ◆ _useIntegrandLimits

protected

Definition at line 55 of file RooAdaptiveGaussKronrodIntegrator1D.h.

## ◆ _workspace

protected

Definition at line 69 of file RooAdaptiveGaussKronrodIntegrator1D.h.

## ◆ _x

protected

Definition at line 63 of file RooAdaptiveGaussKronrodIntegrator1D.h.