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RooAdaptiveGaussKronrodIntegrator1D 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.

TClassIsA () const 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.

void Streamer (TBuffer &) override
Stream an object of class TObject.

void StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

Public Member Functions inherited from RooAbsIntegrator
RooAbsIntegrator ()

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

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)

void StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

Public Member Functions inherited from TObject
TObject ()
TObject constructor.

TObject (const TObject &object)
TObject copy ctor.

virtual ~TObject ()
TObject destructor.

void AbstractMethod (const char *method) const
Use this method to implement an "abstract" method that you don't want to leave purely abstract.

Append graphics object to current pad.

virtual void Browse (TBrowser *b)
Browse object. May be overridden for another default action.

ULong_t CheckedHash ()
Check and record whether this class has a consistent Hash/RecursiveRemove setup (*) and then return the regular Hash value for this object.

virtual const char * ClassName () const
Returns name of class to which the object belongs.

virtual void Clear (Option_t *="")

virtual TObjectClone (const char *newname="") const
Make a clone of an object using the Streamer facility.

virtual Int_t Compare (const TObject *obj) const
Compare abstract method.

virtual void Copy (TObject &object) const
Copy this to obj.

virtual void Delete (Option_t *option="")
Delete this object.

virtual Int_t DistancetoPrimitive (Int_t px, Int_t py)
Computes distance from point (px,py) to the object.

virtual void Draw (Option_t *option="")
Default Draw method for all objects.

virtual void DrawClass () const
Draw class inheritance tree of the class to which this object belongs.

virtual TObjectDrawClone (Option_t *option="") const
Draw a clone of this object in the current selected pad with: gROOT->SetSelectedPad(c1).

virtual void Dump () const
Dump contents of object on stdout.

virtual void Error (const char *method, const char *msgfmt,...) const
Issue error message.

virtual void Execute (const char *method, const char *params, Int_t *error=nullptr)
Execute method on this object with the given parameter string, e.g.

virtual void Execute (TMethod *method, TObjArray *params, Int_t *error=nullptr)
Execute method on this object with parameters stored in the TObjArray.

virtual void ExecuteEvent (Int_t event, Int_t px, Int_t py)
Execute action corresponding to an event at (px,py).

virtual void Fatal (const char *method, const char *msgfmt,...) const
Issue fatal error message.

virtual TObjectFindObject (const char *name) const
Must be redefined in derived classes.

virtual TObjectFindObject (const TObject *obj) const
Must be redefined in derived classes.

virtual Option_tGetDrawOption () const
Get option used by the graphics system to draw this object.

virtual const char * GetIconName () const
Returns mime type name of object.

virtual const char * GetName () const
Returns name of object.

virtual char * GetObjectInfo (Int_t px, Int_t py) const
Returns string containing info about the object at position (px,py).

virtual Option_tGetOption () const

virtual const char * GetTitle () const
Returns title of object.

virtual UInt_t GetUniqueID () const
Return the unique object id.

virtual Bool_t HandleTimer (TTimer *timer)
Execute action in response of a timer timing out.

virtual ULong_t Hash () const
Return hash value for this object.

Bool_t HasInconsistentHash () const
Return true is the type of this object is known to have an inconsistent setup for Hash and RecursiveRemove (i.e.

virtual void Info (const char *method, const char *msgfmt,...) const
Issue info message.

virtual Bool_t InheritsFrom (const char *classname) const
Returns kTRUE if object inherits from class "classname".

virtual Bool_t InheritsFrom (const TClass *cl) const
Returns kTRUE if object inherits from TClass cl.

virtual void Inspect () const
Dump contents of this object in a graphics canvas.

void InvertBit (UInt_t f)

Bool_t IsDestructed () const
IsDestructed.

virtual Bool_t IsEqual (const TObject *obj) const
Default equal comparison (objects are equal if they have the same address in memory).

virtual Bool_t IsFolder () const
Returns kTRUE in case object contains browsable objects (like containers or lists of other objects).

R__ALWAYS_INLINE Bool_t IsOnHeap () const

virtual Bool_t IsSortable () const

R__ALWAYS_INLINE Bool_t IsZombie () const

virtual void ls (Option_t *option="") const
The ls function lists the contents of a class on stdout.

void MayNotUse (const char *method) const
Use this method to signal that a method (defined in a base class) may not be called in a derived class (in principle against good design since a child class should not provide less functionality than its parent, however, sometimes it is necessary).

virtual Bool_t Notify ()
This method must be overridden to handle object notification (the base implementation is no-op).

void Obsolete (const char *method, const char *asOfVers, const char *removedFromVers) const
Use this method to declare a method obsolete.

void operator delete (void *ptr)
Operator delete.

void operator delete (void *ptr, void *vp)
Only called by placement new when throwing an exception.

void operator delete[] (void *ptr)
Operator delete [].

void operator delete[] (void *ptr, void *vp)
Only called by placement new[] when throwing an exception.

void * operator new (size_t sz)

void * operator new (size_t sz, void *vp)

void * operator new[] (size_t sz)

void * operator new[] (size_t sz, void *vp)

TObjectoperator= (const TObject &rhs)
TObject assignment operator.

virtual void Paint (Option_t *option="")
This method must be overridden if a class wants to paint itself.

virtual void Pop ()
Pop on object drawn in a pad to the top of the display list.

virtual void Print (Option_t *option="") const
This method must be overridden when a class wants to print itself.

virtual Int_t Read (const char *name)
Read contents of object with specified name from the current directory.

virtual void RecursiveRemove (TObject *obj)
Recursively remove this object from a list.

void ResetBit (UInt_t f)

virtual void SaveAs (const char *filename="", Option_t *option="") const
Save this object in the file specified by filename.

virtual void SavePrimitive (std::ostream &out, Option_t *option="")
Save a primitive as a C++ statement(s) on output stream "out".

void SetBit (UInt_t f)

void SetBit (UInt_t f, Bool_t set)
Set or unset the user status bits as specified in f.

virtual void SetDrawOption (Option_t *option="")
Set drawing option for object.

virtual void SetUniqueID (UInt_t uid)
Set the unique object id.

void StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

virtual void SysError (const char *method, const char *msgfmt,...) const
Issue system error message.

R__ALWAYS_INLINE Bool_t TestBit (UInt_t f) const

Int_t TestBits (UInt_t f) const

virtual void UseCurrentStyle ()
Set current style settings in this object This function is called when either TCanvas::UseCurrentStyle or TROOT::ForceStyle have been invoked.

virtual void Warning (const char *method, const char *msgfmt,...) const
Issue warning message.

virtual Int_t Write (const char *name=nullptr, Int_t option=0, Int_t bufsize=0)
Write this object to the current directory.

virtual Int_t Write (const char *name=nullptr, Int_t option=0, Int_t bufsize=0) const
Write this object to the current directory.

## Static Public Member Functions

static TClassClass ()

static const char * Class_Name ()

static constexpr Version_t Class_Version ()
Upper integration bound.

static const char * DeclFileName ()

Static Public Member Functions inherited from RooAbsIntegrator
static TClassClass ()

static const char * Class_Name ()

static constexpr Version_t Class_Version ()

static const char * DeclFileName ()

Static Public Member Functions inherited from TObject
static TClassClass ()

static const char * Class_Name ()

static constexpr Version_t Class_Version ()

static const char * DeclFileName ()

static Longptr_t GetDtorOnly ()
Return destructor only flag.

static Bool_t GetObjectStat ()
Get status of object stat flag.

static void SetDtorOnly (void *obj)
Set destructor only flag.

static void SetObjectStat (Bool_t stat)
Turn on/off tracking of objects in the TObjectTable.

## Protected Types

enum  DomainType { Closed , OpenLo , OpenHi , Open }

Protected Types inherited from TObject
enum  { kOnlyPrepStep = (1ULL << ( 3 )) }

## Protected Member Functions

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

doublexvec (double &xx)

Protected Member Functions inherited from TObject
virtual void DoError (int level, const char *location, const char *fmt, va_list va) const
Interface to ErrorHandler (protected).

void MakeZombie ()

## 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

Public Types inherited from TObject
enum  {
kIsOnHeap = 0x01000000 , kNotDeleted = 0x02000000 , kZombie = 0x04000000 , kInconsistent = 0x08000000 ,
}

enum  { kSingleKey = (1ULL << ( 0 )) , kOverwrite = (1ULL << ( 1 )) , kWriteDelete = (1ULL << ( 2 )) }

enum  EDeprecatedStatusBits { kObjInCanvas = (1ULL << ( 3 )) }

enum  EStatusBits {
kCanDelete = (1ULL << ( 0 )) , kMustCleanup = (1ULL << ( 3 )) , kIsReferenced = (1ULL << ( 4 )) , kHasUUID = (1ULL << ( 5 )) ,
kCannotPick = (1ULL << ( 6 )) , kNoContextMenu = (1ULL << ( 8 )) , kInvalidObject = (1ULL << ( 13 ))
}

#include <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 189 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 209 of file RooAdaptiveGaussKronrodIntegrator1D.cxx.

override

Destructor.

Definition at line 245 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 277 of file RooAdaptiveGaussKronrodIntegrator1D.cxx.

## ◆ Class()

 static TClass * RooAdaptiveGaussKronrodIntegrator1D::Class ( )
static
Returns
TClass describing this class

## ◆ Class_Name()

 static const char * RooAdaptiveGaussKronrodIntegrator1D::Class_Name ( )
static
Returns
Name of this class

## ◆ Class_Version()

 static constexpr Version_t RooAdaptiveGaussKronrodIntegrator1D::Class_Version ( )
inlinestaticconstexpr

Upper integration bound.

Returns
Version of this class

Definition at line 72 of file RooAdaptiveGaussKronrodIntegrator1D.h.

## ◆ DeclFileName()

 static const char * RooAdaptiveGaussKronrodIntegrator1D::DeclFileName ( )
inlinestatic
Returns
Name of the file containing the class declaration

Definition at line 72 of file RooAdaptiveGaussKronrodIntegrator1D.h.

## ◆ initialize()

protected

Initialize integrator allocate buffers and setup GSL workspace.

Definition at line 231 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 319 of file RooAdaptiveGaussKronrodIntegrator1D.cxx.

## ◆ IsA()

 TClass * RooAdaptiveGaussKronrodIntegrator1D::IsA ( ) const
inlineoverridevirtual
Returns
TClass describing current object

Reimplemented from RooAbsIntegrator.

Definition at line 72 of file RooAdaptiveGaussKronrodIntegrator1D.h.

## ◆ 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 159 of file RooAdaptiveGaussKronrodIntegrator1D.cxx.

## ◆ setLimits() [1/3]

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

Reimplemented from RooAbsIntegrator.

Definition at line 53 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 259 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 54 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 38 of file RooAdaptiveGaussKronrodIntegrator1D.h.

## ◆ Streamer()

 void RooAdaptiveGaussKronrodIntegrator1D::Streamer ( TBuffer & R__b )
overridevirtual

Stream an object of class TObject.

Reimplemented from RooAbsIntegrator.

## ◆ StreamerNVirtual()

 void RooAdaptiveGaussKronrodIntegrator1D::StreamerNVirtual ( TBuffer & ClassDef_StreamerNVirtual_b )
inline

Definition at line 72 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 308 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 63 of file RooAdaptiveGaussKronrodIntegrator1D.h.

## ◆ _epsRel

protected

Definition at line 64 of file RooAdaptiveGaussKronrodIntegrator1D.h.

## ◆ _maxSeg

protected

Definition at line 66 of file RooAdaptiveGaussKronrodIntegrator1D.h.

## ◆ _methodKey

protected

Definition at line 65 of file RooAdaptiveGaussKronrodIntegrator1D.h.

## ◆ _useIntegrandLimits

protected

Definition at line 55 of file RooAdaptiveGaussKronrodIntegrator1D.h.

## ◆ _workspace

protected

Definition at line 67 of file RooAdaptiveGaussKronrodIntegrator1D.h.

## ◆ _x

protected

Definition at line 61 of file RooAdaptiveGaussKronrodIntegrator1D.h.

## ◆ _xmax

mutableprotected

Lower integration bound.

Definition at line 70 of file RooAdaptiveGaussKronrodIntegrator1D.h.