Kernel Density Estimation class.

The three main references are:

"Scott DW, Multivariate Density Estimation. Theory, Practice and Visualization. New York: Wiley",
"Jann Ben - ETH Zurich, Switzerland -, Univariate kernel density estimation document for KDENS: Stata module for univariate kernel density estimation."
"Hardle W, Muller M, Sperlich S, Werwatz A, Nonparametric and Semiparametric Models. Springer."
"Cranmer KS, Kernel Estimation in High-Energy Physics. Computer Physics Communications 136:198-207,2001" - e-Print Archive: hep ex/0011057.

The algorithm is briefly described in (4). A binned version is also implemented to address the performance issue due to its data size dependance.

Definition at line 34 of file TKDE.h.

Classes
class	TKernel

Public Types
enum	EBinning { kUnbinned , kRelaxedBinning , kForcedBinning }
	Data binning option. More...

enum	EIteration { kAdaptive , kFixed }
	Iteration types. They can be set using SetIteration() More...

enum	EKernelType { kGaussian , kEpanechnikov , kBiweight , kCosineArch , kUserDefined , kTotalKernels }
	Types of Kernel functions They can be set using the function SetKernelType() More...

enum	EMirror { kNoMirror , kMirrorLeft , kMirrorRight , kMirrorBoth , kMirrorAsymLeft , kMirrorRightAsymLeft , kMirrorAsymRight , kMirrorLeftAsymRight , kMirrorAsymBoth }
	Data "mirroring" option to address the probability "spill out" boundary effect They can be set using SetMirror() More...

Public Types inherited from TObject
enum	{ kIsOnHeap = 0x01000000 , kNotDeleted = 0x02000000 , kZombie = 0x04000000 , kInconsistent = 0x08000000 , kBitMask = 0x00ffffff }

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

enum	EDeprecatedStatusBits { kObjInCanvas = BIT(3) }

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

Public Member Functions
	TKDE ()
	default constructor used only by I/O

template<class KernelFunction >
	TKDE (const Char_t , const KernelFunction &kernfunc, UInt_t events, const Double_t data, const Double_t dataWeight, Double_t xMin=0.0, Double_t xMax=0.0, const Option_t option="KernelType:UserDefined;Iteration:Adaptive;Mirror:noMirror;Binning:RelaxedBinning", Double_t rho=1.0)
	Constructor for weighted data and a user defined kernel function.

template<class KernelFunction >
	TKDE (const Char_t , const KernelFunction &kernfunc, UInt_t events, const Double_t data, Double_t xMin=0.0, Double_t xMax=0.0, const Option_t *option="KernelType:UserDefined;Iteration:Adaptive;Mirror:noMirror;Binning:RelaxedBinning", Double_t rho=1.0)
	Constructor for unwweighted data and a user defined kernel function.

	TKDE (UInt_t events, const Double_t data, const Double_t dataWeight, Double_t xMin=0.0, Double_t xMax=0.0, const Option_t *option="KernelType:Gaussian;Iteration:Adaptive;Mirror:noMirror;Binning:RelaxedBinning", Double_t rho=1.0)
	Constructor for weighted data.

	TKDE (UInt_t events, const Double_t data, Double_t xMin=0.0, Double_t xMax=0.0, const Option_t option="KernelType:Gaussian;Iteration:Adaptive;Mirror:noMirror;Binning:RelaxedBinning", Double_t rho=1.0)
	Constructor for unweighted data Varius option for TKDE can be passed in the option string as below.

virtual	~TKDE ()

virtual void	Draw (const Option_t *option="")
	Draws either the KDE functions or its errors.

void	Fill (Double_t data)

void	Fill (Double_t data, Double_t weight)

const Double_t *	GetAdaptiveWeights () const

TF1 *	GetApproximateBias (UInt_t npx=100, Double_t xMin=1.0, Double_t xMax=0.0)

Double_t	GetBias (Double_t x) const

TF1 *	GetDrawnFunction ()

TGraphErrors *	GetDrawnGraph ()

TF1 *	GetDrawnLowerFunction ()

TF1 *	GetDrawnUpperFunction ()

Double_t	GetError (Double_t x) const

Double_t	GetFixedWeight () const

TF1 *	GetFunction (UInt_t npx=100, Double_t xMin=1.0, Double_t xMax=0.0)

TGraphErrors *	GetGraphWithErrors (UInt_t npx=100, Double_t xMin=1.0, Double_t xMax=0.0)
	return a TGraphErrors with the KDE values and errors The return object is managed by the user

TF1 *	GetLowerFunction (Double_t confidenceLevel=0.95, UInt_t npx=100, Double_t xMin=1.0, Double_t xMax=0.0)

Double_t	GetMean () const

Double_t	GetRAMISE () const

Double_t	GetSigma () const

TF1 *	GetUpperFunction (Double_t confidenceLevel=0.95, UInt_t npx=100, Double_t xMin=1.0, Double_t xMax=0.0)

Double_t	GetValue (Double_t x) const

Double_t	operator() (const Double_t x, const Double_t p=0) const

Double_t	operator() (Double_t x) const

void	SetBinning (EBinning)

void	SetIteration (EIteration iter)

void	SetKernelType (EKernelType kern)

void	SetMirror (EMirror mir)

void	SetNBins (UInt_t nbins)

void	SetRange (Double_t xMin, Double_t xMax)

void	SetTuneFactor (Double_t rho)

void	SetUseBinsNEvents (UInt_t nEvents)

Public Member Functions inherited from TNamed
	TNamed ()

	TNamed (const char name, const char title)

	TNamed (const TNamed &named)
	TNamed copy ctor.

	TNamed (const TString &name, const TString &title)

virtual	~TNamed ()
	TNamed destructor.

virtual void	Clear (Option_t *option="")
	Set name and title to empty strings ("").

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

virtual Int_t	Compare (const TObject *obj) const
	Compare two TNamed objects.

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

virtual void	FillBuffer (char *&buffer)
	Encode TNamed into output buffer.

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

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

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

virtual Bool_t	IsSortable () const

virtual void	ls (Option_t *option="") const
	List TNamed name and title.

TNamed &	operator= (const TNamed &rhs)
	TNamed assignment operator.

virtual void	Print (Option_t *option="") const
	Print TNamed name and title.

virtual void	SetName (const char *name)
	Set the name of the TNamed.

virtual void	SetNameTitle (const char name, const char title)
	Set all the TNamed parameters (name and title).

virtual void	SetTitle (const char *title="")
	Set the title of the TNamed.

virtual Int_t	Sizeof () const
	Return size of the TNamed part of the TObject.

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.

virtual void	AppendPad (Option_t *option="")
	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	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 TObject *	DrawClone (Option_t *option="") const
	Draw a clone of this object in the current selected pad for instance with: `gROOT->SetSelectedPad(gPad)`.

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=0)
	Execute method on this object with the given parameter string, e.g.

virtual void	Execute (TMethod method, TObjArray params, Int_t *error=0)
	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 TObject *	FindObject (const char *name) const
	Must be redefined in derived classes.

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

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

virtual const char *	GetIconName () const
	Returns mime type 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_t *	GetOption () const

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.

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)

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

R__ALWAYS_INLINE Bool_t	IsZombie () const

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.

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)
	Operator delete [].

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)

TObject &	operator= (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 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.

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=0, Int_t option=0, Int_t bufsize=0)
	Write this object to the current directory.

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

Private Types
typedef ROOT::Math::IBaseFunctionOneDim *	KernelFunction_Ptr

Private Member Functions
	TKDE (TKDE &kde)

Double_t	ApproximateBias (const Double_t x, const Double_t ) const

void	AssureOptions ()

Double_t	BiweightKernel (Double_t x) const

void	CheckKernelValidity ()

void	CheckOptions (Bool_t isUserDefinedKernel=kFALSE)

void	ComputeDataStats ()
	Internal funciton to compute statistics (mean,stddev) using always all the provided data (i.e. no binning)

Double_t	ComputeKernelIntegral () const

Double_t	ComputeKernelL2Norm () const

Double_t	ComputeKernelMu () const

Double_t	ComputeKernelSigma2 () const

Double_t	ComputeMidspread ()

Double_t	CosineArchKernel (Double_t x) const

void	DrawConfidenceInterval (TString &drawOpt, double cl=0.95)
	// Draws the KDE and its confidence interval

void	DrawErrors (TString &drawOpt)
	Draws a TGraphErrors wih KDE values and errors.

Double_t	EpanechnikovKernel (Double_t x) const

Double_t	GaussianKernel (Double_t x) const

TF1 *	GetKDEApproximateBias (UInt_t npx=100, Double_t xMin=1.0, Double_t xMax=0.0)

TF1 *	GetKDEFunction (UInt_t npx=100, Double_t xMin=1.0, Double_t xMax=0.0)

void	GetOptions (std::string optionType, std::string option)

TF1 *	GetPDFLowerConfidenceInterval (Double_t confidenceLevel=0.95, UInt_t npx=100, Double_t xMin=1.0, Double_t xMax=0.0)

TF1 *	GetPDFUpperConfidenceInterval (Double_t confidenceLevel=0.95, UInt_t npx=100, Double_t xMin=1.0, Double_t xMax=0.0)

UInt_t	Index (Double_t x) const
	compute the bin index given a data point x

void	InitFromNewData ()

void	Instantiate (KernelFunction_Ptr kernfunc, UInt_t events, const Double_t data, const Double_t weight, Double_t xMin, Double_t xMax, const Option_t *option, Double_t rho)

Double_t	LowerConfidenceInterval (const Double_t x, const Double_t p) const

TKDE	operator= (TKDE &kde)

void	ReInit ()

void	SetBinCentreData (Double_t xmin, Double_t xmax)

void	SetBinCountData ()

void	SetCanonicalBandwidths ()

void	SetData (const Double_t data, const Double_t weights)

void	SetDrawOptions (const Option_t *option, TString &plotOpt, TString &drawOpt)

void	SetHistogram ()

void	SetKernel ()

void	SetKernelFunction (KernelFunction_Ptr kernfunc=0)

void	SetKernelSigmas2 ()

void	SetMean ()

void	SetMirror ()

void	SetMirroredEvents ()
	Intgernal function to mirror the data.

void	SetOptions (const Option_t *option, Double_t rho)

void	SetSigma (Double_t R)

void	SetUseBins ()

void	SetUserCanonicalBandwidth ()

void	SetUserKernelSigma2 ()

Double_t	UpperConfidenceInterval (const Double_t x, const Double_t p) const

Private Attributes
Double_t	fAdaptiveBandwidthFactor

TF1 *	fApproximateBias
	Output Kernel Density Estimation lower confidence interval PDF function.

Bool_t	fAsymLeft

Bool_t	fAsymRight

std::vector< Double_t >	fBinCount

EBinning	fBinning

std::vector< Double_t >	fCanonicalBandwidths

std::vector< Double_t >	fData

std::vector< Double_t >	fEvents

std::vector< Double_t >	fEventWeights

TGraphErrors *	fGraph
	Output Kernel Density Estimation approximate bias.

EIteration	fIteration

std::unique_ptr< TKernel >	fKernel
	! internal kernel class. Transient because it is recreated after reading from a file

KernelFunction_Ptr	fKernelFunction
	! pointer to kernel function

std::vector< Double_t >	fKernelSigmas2

EKernelType	fKernelType
	Graph with the errors.

TF1 *	fLowerPDF
	Output Kernel Density Estimation upper confidence interval PDF function.

Double_t	fMean

EMirror	fMirror

Bool_t	fMirrorLeft

Bool_t	fMirrorRight

UInt_t	fNBins

UInt_t	fNEvents

Bool_t	fNewData

TF1 *	fPDF

Double_t	fRho

std::vector< Bool_t >	fSettedOptions

Double_t	fSigma

Double_t	fSigmaRob

Double_t	fSumOfCounts

TF1 *	fUpperPDF
	Output Kernel Density Estimation PDF function.

Bool_t	fUseBins

UInt_t	fUseBinsNEvents

Bool_t	fUseMinMaxFromData

Bool_t	fUseMirroring

Double_t	fWeightSize

Double_t	fXMax

Double_t	fXMin

Friends
struct	KernelIntegrand

class	TKernel

Additional Inherited Members
Static Public Member Functions inherited from TObject
static Long_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 inherited from TObject
enum	{ kOnlyPrepStep = BIT(3) }

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 ()

Protected Attributes inherited from TNamed
TString	fName

TString	fTitle

#include <TKDE.h>

Inheritance diagram for TKDE:

[legend]

Member Typedef Documentation

◆ KernelFunction_Ptr

typedef ROOT::Math::IBaseFunctionOneDim* TKDE::KernelFunction_Ptr

private

Definition at line 178 of file TKDE.h.

Member Enumeration Documentation

◆ EBinning

enum TKDE::EBinning

Data binning option.

They can be set using SetBinning()

Enumerator
kUnbinned
kRelaxedBinning
kForcedBinning

Definition at line 71 of file TKDE.h.

◆ EIteration

enum TKDE::EIteration

Iteration types. They can be set using SetIteration()

Enumerator
kAdaptive
kFixed

Definition at line 50 of file TKDE.h.

◆ EKernelType

enum TKDE::EKernelType

Types of Kernel functions They can be set using the function SetKernelType()

Enumerator
kGaussian
kEpanechnikov
kBiweight
kCosineArch
kUserDefined
kTotalKernels

Definition at line 40 of file TKDE.h.

◆ EMirror

enum TKDE::EMirror

Data "mirroring" option to address the probability "spill out" boundary effect They can be set using SetMirror()

Enumerator
kNoMirror
kMirrorLeft
kMirrorRight
kMirrorBoth
kMirrorAsymLeft
kMirrorRightAsymLeft
kMirrorAsymRight
kMirrorLeftAsymRight
kMirrorAsymBoth

Definition at line 57 of file TKDE.h.

Constructor & Destructor Documentation

◆ TKDE() [1/6]

TKDE::TKDE ( )

default constructor used only by I/O

default constructor used by I/O

Definition at line 63 of file TKDE.cxx.

◆ TKDE() [2/6]

TKDE::TKDE	(	UInt_t	events,
		const Double_t *	data,
		Double_t	xMin = `0.0`,
		Double_t	xMax = `0.0`,
		const Option_t *	option = `"KernelType:Gaussian;Iteration:Adaptive;Mirror:noMirror;Binning:RelaxedBinning"`,
		Double_t	rho = `1.0`
	)

inline

Constructor for unweighted data Varius option for TKDE can be passed in the option string as below.

Note that min and max will define the plotting range but will not restrict the data in the unbinned case Instead when use binning, only the data in the range will be considered. Note also, that when some data exists outside the range, one should not use the mirror option with unbinned. Adaptive will be soon very slow especially for Nevents > 10000. For this reason, by default for Nevents >=10000, the data are automatically binned in nbins=Min(10000,Nevents/10) In case of ForceBinning option the default number of bins is 1000

Definition at line 89 of file TKDE.h.

◆ TKDE() [3/6]

TKDE::TKDE	(	UInt_t	events,
		const Double_t *	data,
		const Double_t *	dataWeight,
		Double_t	xMin = `0.0`,
		Double_t	xMax = `0.0`,
		const Option_t *	option = `"KernelType:Gaussian;Iteration:Adaptive;Mirror:noMirror;Binning:RelaxedBinning"`,
		Double_t	rho = `1.0`
	)

inline

Constructor for weighted data.

Definition at line 95 of file TKDE.h.

◆ TKDE() [4/6]

template<class KernelFunction >

TKDE::TKDE	(	const Char_t *	,
		const KernelFunction &	kernfunc,
		UInt_t	events,
		const Double_t *	data,
		Double_t	xMin = `0.0`,
		Double_t	xMax = `0.0`,
		const Option_t *	option = `"KernelType:UserDefined;Iteration:Adaptive;Mirror:noMirror;Binning:RelaxedBinning"`,
		Double_t	rho = `1.0`
	)

inline

Constructor for unwweighted data and a user defined kernel function.

Definition at line 102 of file TKDE.h.

◆ TKDE() [5/6]

template<class KernelFunction >

TKDE::TKDE	(	const Char_t *	,
		const KernelFunction &	kernfunc,
		UInt_t	events,
		const Double_t *	data,
		const Double_t *	dataWeight,
		Double_t	xMin = `0.0`,
		Double_t	xMax = `0.0`,
		const Option_t *	option = `"KernelType:UserDefined;Iteration:Adaptive;Mirror:noMirror;Binning:RelaxedBinning"`,
		Double_t	rho = `1.0`
	)

inline

Constructor for weighted data and a user defined kernel function.

Definition at line 107 of file TKDE.h.

◆ ~TKDE()

TKDE::~TKDE ( )

virtual

Definition at line 79 of file TKDE.cxx.

◆ TKDE() [6/6]

TKDE::TKDE ( TKDE & kde )

private

Member Function Documentation

◆ ApproximateBias()

Double_t TKDE::ApproximateBias	(	const Double_t *	x,
		const Double_t *
	)		const

inlineprivate

Definition at line 250 of file TKDE.h.

◆ AssureOptions()

void TKDE::AssureOptions ( )

private

Definition at line 272 of file TKDE.cxx.

◆ BiweightKernel()

Double_t TKDE::BiweightKernel ( Double_t x ) const

inlineprivate

Definition at line 240 of file TKDE.h.

◆ CheckKernelValidity()

void TKDE::CheckKernelValidity ( )

private

Definition at line 1102 of file TKDE.cxx.

◆ CheckOptions()

void TKDE::CheckOptions ( Bool_t isUserDefinedKernel = kFALSE )

private

Definition at line 288 of file TKDE.cxx.

◆ ComputeDataStats()

void TKDE::ComputeDataStats ( )

private

Internal funciton to compute statistics (mean,stddev) using always all the provided data (i.e. no binning)

Definition at line 1164 of file TKDE.cxx.

◆ ComputeKernelIntegral()

Double_t TKDE::ComputeKernelIntegral ( ) const

private

Definition at line 1153 of file TKDE.cxx.

◆ ComputeKernelL2Norm()

Double_t TKDE::ComputeKernelL2Norm ( ) const

private

Definition at line 1126 of file TKDE.cxx.

◆ ComputeKernelMu()

Double_t TKDE::ComputeKernelMu ( ) const

private

Definition at line 1144 of file TKDE.cxx.

◆ ComputeKernelSigma2()

Double_t TKDE::ComputeKernelSigma2 ( ) const

private

Definition at line 1135 of file TKDE.cxx.

◆ ComputeMidspread()

Double_t TKDE::ComputeMidspread ( )

private

Definition at line 1193 of file TKDE.cxx.

◆ CosineArchKernel()

Double_t TKDE::CosineArchKernel ( Double_t x ) const

inlineprivate

Definition at line 244 of file TKDE.h.

◆ Draw()

void TKDE::Draw ( const Option_t * option = "" )

virtual

Draws either the KDE functions or its errors.

Definition at line 897 of file TKDE.cxx.

◆ DrawConfidenceInterval()

void TKDE::DrawConfidenceInterval	(	TString &	drawOpt,
		double	cl = `0.95`
	)

private

// Draws the KDE and its confidence interval

Definition at line 967 of file TKDE.cxx.

◆ DrawErrors()

void TKDE::DrawErrors ( TString & drawOpt )

private

Draws a TGraphErrors wih KDE values and errors.

Definition at line 933 of file TKDE.cxx.

◆ EpanechnikovKernel()

Double_t TKDE::EpanechnikovKernel ( Double_t x ) const

inlineprivate

Definition at line 237 of file TKDE.h.

◆ Fill() [1/2]

void TKDE::Fill ( Double_t data )

Definition at line 715 of file TKDE.cxx.

◆ Fill() [2/2]

void TKDE::Fill	(	Double_t	data,
		Double_t	weight
	)

Definition at line 726 of file TKDE.cxx.

◆ GaussianKernel()

Double_t TKDE::GaussianKernel ( Double_t x ) const

inlineprivate

Definition at line 232 of file TKDE.h.

◆ GetAdaptiveWeights()

const Double_t * TKDE::GetAdaptiveWeights ( ) const

Definition at line 992 of file TKDE.cxx.

◆ GetApproximateBias()

TF1 * TKDE::GetApproximateBias	(	UInt_t	npx = `100`,
		Double_t	xMin = `1.0`,
		Double_t	xMax = `0.0`
	)

Definition at line 710 of file TKDE.cxx.

◆ GetBias()

Double_t TKDE::GetBias ( Double_t x ) const

Definition at line 1084 of file TKDE.cxx.

◆ GetDrawnFunction()

TF1 * TKDE::GetDrawnFunction ( )

inline

Definition at line 147 of file TKDE.h.

◆ GetDrawnGraph()

TGraphErrors * TKDE::GetDrawnGraph ( )

inline

Definition at line 150 of file TKDE.h.

◆ GetDrawnLowerFunction()

TF1 * TKDE::GetDrawnLowerFunction ( )

inline

Definition at line 149 of file TKDE.h.

◆ GetDrawnUpperFunction()

TF1 * TKDE::GetDrawnUpperFunction ( )

inline

Definition at line 148 of file TKDE.h.

◆ GetError()

Double_t TKDE::GetError ( Double_t x ) const

Definition at line 1093 of file TKDE.cxx.

◆ GetFixedWeight()

Double_t TKDE::GetFixedWeight ( ) const

Definition at line 981 of file TKDE.cxx.

◆ GetFunction()

TF1 * TKDE::GetFunction	(	UInt_t	npx = `100`,
		Double_t	xMin = `1.0`,
		Double_t	xMax = `0.0`
	)

Definition at line 691 of file TKDE.cxx.

◆ GetGraphWithErrors()

TGraphErrors * TKDE::GetGraphWithErrors	(	UInt_t	npx = `100`,
		Double_t	xMin = `1.0`,
		Double_t	xMax = `0.0`
	)

return a TGraphErrors with the KDE values and errors The return object is managed by the user

Definition at line 942 of file TKDE.cxx.

◆ GetKDEApproximateBias()

TF1 * TKDE::GetKDEApproximateBias	(	UInt_t	npx = `100`,
		Double_t	xMin = `1.0`,
		Double_t	xMax = `0.0`
	)

private

Definition at line 1273 of file TKDE.cxx.

◆ GetKDEFunction()

TF1 * TKDE::GetKDEFunction	(	UInt_t	npx = `100`,
		Double_t	xMin = `1.0`,
		Double_t	xMax = `0.0`
	)

private

Definition at line 1233 of file TKDE.cxx.

◆ GetLowerFunction()

TF1 * TKDE::GetLowerFunction	(	Double_t	confidenceLevel = `0.95`,
		UInt_t	npx = `100`,
		Double_t	xMin = `1.0`,
		Double_t	xMax = `0.0`
	)

Definition at line 705 of file TKDE.cxx.

◆ GetMean()

Double_t TKDE::GetMean ( ) const

Definition at line 753 of file TKDE.cxx.

◆ GetOptions()

void TKDE::GetOptions	(	std::string	optionType,
		std::string	option
	)

private

Definition at line 200 of file TKDE.cxx.

◆ GetPDFLowerConfidenceInterval()

TF1 * TKDE::GetPDFLowerConfidenceInterval	(	Double_t	confidenceLevel = `0.95`,
		UInt_t	npx = `100`,
		Double_t	xMin = `1.0`,
		Double_t	xMax = `0.0`
	)

private

Definition at line 1260 of file TKDE.cxx.

◆ GetPDFUpperConfidenceInterval()

TF1 * TKDE::GetPDFUpperConfidenceInterval	(	Double_t	confidenceLevel = `0.95`,
		UInt_t	npx = `100`,
		Double_t	xMin = `1.0`,
		Double_t	xMax = `0.0`
	)

private

Definition at line 1247 of file TKDE.cxx.

◆ GetRAMISE()

Double_t TKDE::GetRAMISE ( ) const

Definition at line 765 of file TKDE.cxx.

◆ GetSigma()

Double_t TKDE::GetSigma ( ) const

Definition at line 759 of file TKDE.cxx.

◆ GetUpperFunction()

TF1 * TKDE::GetUpperFunction	(	Double_t	confidenceLevel = `0.95`,
		UInt_t	npx = `100`,
		Double_t	xMin = `1.0`,
		Double_t	xMax = `0.0`
	)

Definition at line 700 of file TKDE.cxx.

◆ GetValue()

Double_t TKDE::GetValue ( Double_t x ) const

inline

Definition at line 129 of file TKDE.h.

◆ Index()

UInt_t TKDE::Index ( Double_t x ) const

private

compute the bin index given a data point x

Definition at line 1052 of file TKDE.cxx.

◆ InitFromNewData()

void TKDE::InitFromNewData ( )

private

Definition at line 502 of file TKDE.cxx.

◆ Instantiate()

void TKDE::Instantiate	(	KernelFunction_Ptr	kernfunc,
		UInt_t	events,
		const Double_t *	data,
		const Double_t *	weight,
		Double_t	xMin,
		Double_t	xMax,
		const Option_t *	option,
		Double_t	rho
	)

private

Definition at line 93 of file TKDE.cxx.

◆ LowerConfidenceInterval()

Double_t TKDE::LowerConfidenceInterval	(	const Double_t *	x,
		const Double_t *	p
	)		const

private

Definition at line 1074 of file TKDE.cxx.

◆ operator()() [1/2]

Double_t TKDE::operator()	(	const Double_t *	x,
		const Double_t *	p = `0`
	)		const

Definition at line 738 of file TKDE.cxx.

◆ operator()() [2/2]

Double_t TKDE::operator() ( Double_t x ) const

Definition at line 743 of file TKDE.cxx.

◆ operator=()

TKDE TKDE::operator= ( TKDE & kde )

private

◆ ReInit()

void TKDE::ReInit ( )

private

Definition at line 480 of file TKDE.cxx.

◆ SetBinCentreData()

void TKDE::SetBinCentreData	(	Double_t	xmin,
		Double_t	xmax
	)

private

Definition at line 821 of file TKDE.cxx.

◆ SetBinCountData()

void TKDE::SetBinCountData ( )

private

Definition at line 830 of file TKDE.cxx.

◆ SetBinning()

void TKDE::SetBinning ( EBinning bin )

Definition at line 341 of file TKDE.cxx.

◆ SetCanonicalBandwidths()

void TKDE::SetCanonicalBandwidths ( )

private

Definition at line 674 of file TKDE.cxx.

◆ SetData()

void TKDE::SetData	(	const Double_t *	data,
		const Double_t *	weights
	)

private

Definition at line 444 of file TKDE.cxx.

◆ SetDrawOptions()

void TKDE::SetDrawOptions	(	const Option_t *	option,
		TString &	plotOpt,
		TString &	drawOpt
	)

private

Definition at line 154 of file TKDE.cxx.

◆ SetHistogram()

void TKDE::SetHistogram ( )

private

◆ SetIteration()

void TKDE::SetIteration ( EIteration iter )

Definition at line 323 of file TKDE.cxx.

◆ SetKernel()

void TKDE::SetKernel ( )

private

Definition at line 598 of file TKDE.cxx.

◆ SetKernelFunction()

void TKDE::SetKernelFunction ( KernelFunction_Ptr kernfunc = 0 )

private

Definition at line 627 of file TKDE.cxx.

◆ SetKernelSigmas2()

void TKDE::SetKernelSigmas2 ( )

private

Definition at line 683 of file TKDE.cxx.

◆ SetKernelType()

void TKDE::SetKernelType ( EKernelType kern )

Definition at line 311 of file TKDE.cxx.

◆ SetMean()

void TKDE::SetMean ( )

private

Definition at line 587 of file TKDE.cxx.

◆ SetMirror() [1/2]

void TKDE::SetMirror ( )

private

Definition at line 435 of file TKDE.cxx.

◆ SetMirror() [2/2]

void TKDE::SetMirror ( EMirror mir )

Definition at line 330 of file TKDE.cxx.

◆ SetMirroredEvents()

void TKDE::SetMirroredEvents ( )

private

Intgernal function to mirror the data.

Definition at line 528 of file TKDE.cxx.

◆ SetNBins()

void TKDE::SetNBins ( UInt_t nbins )

Definition at line 348 of file TKDE.cxx.

◆ SetOptions()

void TKDE::SetOptions	(	const Option_t *	option,
		Double_t	rho
	)

private

Definition at line 128 of file TKDE.cxx.

◆ SetRange()

void TKDE::SetRange	(	Double_t	xMin,
		Double_t	xMax
	)

Definition at line 382 of file TKDE.cxx.

◆ SetSigma()

void TKDE::SetSigma ( Double_t R )

private

Definition at line 592 of file TKDE.cxx.

◆ SetTuneFactor()

void TKDE::SetTuneFactor ( Double_t rho )

Definition at line 372 of file TKDE.cxx.

◆ SetUseBins()

void TKDE::SetUseBins ( )

private

Definition at line 396 of file TKDE.cxx.

◆ SetUseBinsNEvents()

void TKDE::SetUseBinsNEvents ( UInt_t nEvents )

Definition at line 366 of file TKDE.cxx.

◆ SetUserCanonicalBandwidth()

void TKDE::SetUserCanonicalBandwidth ( )

private

Definition at line 1204 of file TKDE.cxx.

◆ SetUserKernelSigma2()

void TKDE::SetUserKernelSigma2 ( )

private

Definition at line 1209 of file TKDE.cxx.

◆ UpperConfidenceInterval()

Double_t TKDE::UpperConfidenceInterval	(	const Double_t *	x,
		const Double_t *	p
	)		const

private

Definition at line 1065 of file TKDE.cxx.

Friends And Related Symbol Documentation

◆ KernelIntegrand

friend struct KernelIntegrand

friend

Definition at line 227 of file TKDE.h.

◆ TKernel

friend class TKernel

friend

Definition at line 170 of file TKDE.h.

Member Data Documentation

◆ fAdaptiveBandwidthFactor

Double_t TKDE::fAdaptiveBandwidthFactor

private

Definition at line 215 of file TKDE.h.

◆ fApproximateBias

TF1* TKDE::fApproximateBias

private

Output Kernel Density Estimation lower confidence interval PDF function.

Definition at line 190 of file TKDE.h.

◆ fAsymLeft

Bool_t TKDE::fAsymLeft

private

Definition at line 199 of file TKDE.h.

◆ fAsymRight

Bool_t TKDE::fAsymRight

private

Definition at line 199 of file TKDE.h.

◆ fBinCount

std::vector<Double_t> TKDE::fBinCount

private

Definition at line 222 of file TKDE.h.

◆ fBinning

EBinning TKDE::fBinning

private

Definition at line 196 of file TKDE.h.

◆ fCanonicalBandwidths

std::vector<Double_t> TKDE::fCanonicalBandwidths

private

Definition at line 219 of file TKDE.h.

◆ fData

std::vector<Double_t> TKDE::fData

private

Definition at line 183 of file TKDE.h.

◆ fEvents

std::vector<Double_t> TKDE::fEvents

private

Definition at line 184 of file TKDE.h.

◆ fEventWeights

std::vector<Double_t> TKDE::fEventWeights

private

Definition at line 185 of file TKDE.h.

◆ fGraph

TGraphErrors* TKDE::fGraph

private

Output Kernel Density Estimation approximate bias.

Definition at line 191 of file TKDE.h.

◆ fIteration

EIteration TKDE::fIteration

private

Definition at line 194 of file TKDE.h.

◆ fKernel

std::unique_ptr<TKernel> TKDE::fKernel

private

! internal kernel class. Transient because it is recreated after reading from a file

Definition at line 181 of file TKDE.h.

◆ fKernelFunction

KernelFunction_Ptr TKDE::fKernelFunction

private

! pointer to kernel function

Definition at line 179 of file TKDE.h.

◆ fKernelSigmas2

std::vector<Double_t> TKDE::fKernelSigmas2

private

Definition at line 220 of file TKDE.h.

◆ fKernelType

EKernelType TKDE::fKernelType

private

Graph with the errors.

Definition at line 193 of file TKDE.h.

◆ fLowerPDF

TF1* TKDE::fLowerPDF

private

Output Kernel Density Estimation upper confidence interval PDF function.

Definition at line 189 of file TKDE.h.

◆ fMean

Double_t TKDE::fMean

private

Definition at line 209 of file TKDE.h.

◆ fMirror

EMirror TKDE::fMirror

private

Definition at line 195 of file TKDE.h.

◆ fMirrorLeft

Bool_t TKDE::fMirrorLeft

private

Definition at line 199 of file TKDE.h.

◆ fMirrorRight

Bool_t TKDE::fMirrorRight

private

Definition at line 199 of file TKDE.h.

◆ fNBins

UInt_t TKDE::fNBins

private

Definition at line 204 of file TKDE.h.

◆ fNEvents

UInt_t TKDE::fNEvents

private

Definition at line 205 of file TKDE.h.

◆ fNewData

Bool_t TKDE::fNewData

private

Definition at line 201 of file TKDE.h.

◆ fPDF

TF1* TKDE::fPDF

private

Definition at line 187 of file TKDE.h.

◆ fRho

Double_t TKDE::fRho

private

Definition at line 214 of file TKDE.h.

◆ fSettedOptions

std::vector<Bool_t> TKDE::fSettedOptions

private

Definition at line 224 of file TKDE.h.

◆ fSigma

Double_t TKDE::fSigma

private

Definition at line 210 of file TKDE.h.

◆ fSigmaRob

Double_t TKDE::fSigmaRob

private

Definition at line 211 of file TKDE.h.

◆ fSumOfCounts

Double_t TKDE::fSumOfCounts

private

Definition at line 206 of file TKDE.h.

◆ fUpperPDF

TF1* TKDE::fUpperPDF

private

Output Kernel Density Estimation PDF function.

Definition at line 188 of file TKDE.h.

◆ fUseBins

Bool_t TKDE::fUseBins

private

Definition at line 200 of file TKDE.h.

◆ fUseBinsNEvents

UInt_t TKDE::fUseBinsNEvents

private

Definition at line 207 of file TKDE.h.

◆ fUseMinMaxFromData

Bool_t TKDE::fUseMinMaxFromData

private

Definition at line 202 of file TKDE.h.

◆ fUseMirroring

Bool_t TKDE::fUseMirroring

private

Definition at line 199 of file TKDE.h.

◆ fWeightSize

Double_t TKDE::fWeightSize

private

Definition at line 217 of file TKDE.h.

◆ fXMax

Double_t TKDE::fXMax

private

Definition at line 213 of file TKDE.h.

◆ fXMin

Double_t TKDE::fXMin

private

Definition at line 212 of file TKDE.h.

Libraries for TKDE:

[legend]

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

hist/hist/inc/TKDE.h
hist/hist/src/TKDE.cxx

Classes

Public Types

Public Member Functions

Private Types

Private Member Functions

Private Attributes

Friends

Additional Inherited Members

Member Typedef Documentation

◆ KernelFunction_Ptr

Member Enumeration Documentation

◆ EBinning

◆ EIteration

◆ EKernelType

◆ EMirror

Constructor & Destructor Documentation

◆ TKDE() [1/6]

◆ TKDE() [2/6]

◆ TKDE() [3/6]

◆ TKDE() [4/6]

◆ TKDE() [5/6]

◆ ~TKDE()

◆ TKDE() [6/6]

Member Function Documentation

◆ ApproximateBias()

◆ AssureOptions()

◆ BiweightKernel()

◆ CheckKernelValidity()

◆ CheckOptions()

◆ ComputeDataStats()

◆ ComputeKernelIntegral()

◆ ComputeKernelL2Norm()

◆ ComputeKernelMu()

◆ ComputeKernelSigma2()

◆ ComputeMidspread()

◆ CosineArchKernel()

◆ Draw()

◆ DrawConfidenceInterval()

◆ DrawErrors()

◆ EpanechnikovKernel()

◆ Fill() [1/2]

◆ Fill() [2/2]

◆ GaussianKernel()

◆ GetAdaptiveWeights()

◆ GetApproximateBias()

◆ GetBias()

◆ GetDrawnFunction()

◆ GetDrawnGraph()

◆ GetDrawnLowerFunction()

◆ GetDrawnUpperFunction()

◆ GetError()

◆ GetFixedWeight()

◆ GetFunction()

◆ GetGraphWithErrors()

◆ GetKDEApproximateBias()

◆ GetKDEFunction()

◆ GetLowerFunction()

◆ GetMean()

◆ GetOptions()

◆ GetPDFLowerConfidenceInterval()

◆ GetPDFUpperConfidenceInterval()

◆ GetRAMISE()

◆ GetSigma()

◆ GetUpperFunction()

◆ GetValue()

◆ Index()

◆ InitFromNewData()

◆ Instantiate()

◆ LowerConfidenceInterval()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator=()

◆ ReInit()

◆ SetBinCentreData()

◆ SetBinCountData()

◆ SetBinning()

◆ SetCanonicalBandwidths()

◆ SetData()

◆ SetDrawOptions()

◆ SetHistogram()