AliPoissonCalculator Class Reference

#include <AliPoissonCalculator.h>

Inheritance diagram for AliPoissonCalculator:

Public Member Functions
	AliPoissonCalculator ()
	AliPoissonCalculator (const char *)
	AliPoissonCalculator (const AliPoissonCalculator &o)
virtual	~AliPoissonCalculator ()
AliPoissonCalculator &	operator= (const AliPoissonCalculator &o)
void	SetLumping (UShort_t nx, UShort_t ny)
void	SetXLumping (UShort_t nx)
void	SetYLumping (UShort_t ny)
void	Init (Int_t xLumping=-1, Int_t yLumping=-1)
void	Define (const TAxis &xaxis, const TAxis &yaxis)
void	MakeOutput ()
void	Output (TList *d)
void	Reset (const TH2D *base)
void	Fill (UShort_t strip, UShort_t sec, Bool_t hit, Double_t weight=1)
TH2D *	Result (Bool_t correct=true)
void	FillDiagnostics ()
Bool_t	IsFolder () const
void	Print (const Option_t *option="") const
void	Browse (TBrowser *b)
TH2D *	GetEmptyVsTotal () const
TH1D *	GetMean () const
TH1D *	GetOccupancy () const
TH2D *	GetCorrection () const
Int_t	GetReducedXBin (Int_t ix) const
Int_t	GetReducedXBin (Double_t x) const
Int_t	GetReducedYBin (Int_t iy) const
Int_t	GetReducedYBin (Double_t y) const

Protected Member Functions
Int_t	CheckLumping (char which, Int_t nBins, Int_t lumping) const
void	CleanUp ()
Double_t	CalculateMean (Double_t empty, Double_t total) const
Double_t	CalculateCorrection (Double_t empty, Double_t total) const

Protected Attributes
UShort_t	fXLumping
UShort_t	fYLumping
TH2D *	fTotal
TH2D *	fEmpty
TH2D *	fBasic
TH2D *	fEmptyVsTotal
TH1D *	fMean
TH1D *	fOcc
TH2D *	fCorr

Detailed Description

A class to calculate the multiplicity in \((\eta,\varphi)\) bins using Poisson statistics.

The input is assumed to be binned in \((\eta,\varphi)\) as described by the 2D histogram passwd to the Reset member function.

The data is grouped in to regions as defined by the parameters fXLumping and fYLumping. The total number of cells and number of empty cells is then calculate in each region. The mean multiplicity over the region is then determined as

\[ \langle m\rangle = -\log\left(\frac{e}{t}\right) \]

where \( e\) is the number of empty cells and \(t\) is the total number of cells in the region. A correction for counting statistics, is then applied

\begin{eqnarray*} c &=& \frac{1}{1 - \exp{-\langle m\rangle}}\\ &=& \frac{1}{1 - \frac{e}{t}} \end{eqnarray*}

and the final number in each cell is then \(h_i c \langle m\rangle\) where \(h_i\) is the number of hits in the cell \(i\)

Definition at line 36 of file AliPoissonCalculator.h.

Constructor & Destructor Documentation

AliPoissonCalculator::AliPoissonCalculator

(

)

Constructor

Definition at line 54 of file AliPoissonCalculator.cxx.

AliPoissonCalculator::AliPoissonCalculator

(

const char *

)

Constructor

Definition at line 72 of file AliPoissonCalculator.cxx.

AliPoissonCalculator::AliPoissonCalculator

(

const AliPoissonCalculator &

o

)

Copy constructor

Parameters

o	Object to copy from

Definition at line 89 of file AliPoissonCalculator.cxx.

AliPoissonCalculator::~AliPoissonCalculator ( )

virtual

Destructor

Definition at line 106 of file AliPoissonCalculator.cxx.

Member Function Documentation

void AliPoissonCalculator::Browse

(

TBrowser *

b

)

Browse this object

Parameters

b	Object to browse

Definition at line 451 of file AliPoissonCalculator.cxx.

Double_t AliPoissonCalculator::CalculateCorrection ( Double_t  empty, Double_t  total  ) const

protected

The mean \(\lambda\) calculated above is not the full story. In addition it needs to be corrected using the expression

\[ \frac{1}{1-e^{\lambda}} = \frac{1}{1-\frac{N_{empty}}{N_{total}}} \]

Note the boundary conditions

• \(N_{total}=0 \rightarrow\lambda=0\)
• \(|N_{total}-N_{empty}|<\epsilon\rightarrow N_{empty} = N_{total}-\epsilon\)

Parameters

empty	Number of empty bins
total	Total number of bins

Returns

The correction to the mean.

Definition at line 335 of file AliPoissonCalculator.cxx.

Referenced by FillDiagnostics(), and Result().

Double_t AliPoissonCalculator::CalculateMean ( Double_t  empty, Double_t  total  ) const

protected

Calculate the mean

This is based on the fact that for a Poisson

\[ P(n;\lambda) = \frac{-\lambda^n e^{-\lambda}}{n!} \]

we have the probability for 0 observation

\[ P(0;\lambda) = e^{-\lambda} = \frac{N_{empty}}{N_{total}} \]

and so we get that the mean is the defined region is

\[ \lambda = -\log\left(\frac{N_{empty}}{N_{total}}\right) \]

Note the boundary conditions

• \(N_{total}=0 \rightarrow\lambda=0\)
• \(N_{empty}<\epsilon\rightarrow N_{empty} = \epsilon\)

Parameters

empty	Number of empty bins
total	Total number of bins

Returns

The mean in the defined region

Definition at line 327 of file AliPoissonCalculator.cxx.

Referenced by FillDiagnostics(), and Result().

Int_t AliPoissonCalculator::CheckLumping ( char  which, Int_t  nBins, Int_t  lumping  ) const

protected

check that the lumping parameter makes sense

Parameters

which	Which axis
nBins	Number of bins
lumping	Lumping

Returns

The new value of the lumping

Definition at line 247 of file AliPoissonCalculator.cxx.

Referenced by Reset().

void AliPoissonCalculator::CleanUp ( )

protected

Clean up allocated space

Definition at line 113 of file AliPoissonCalculator.cxx.

Referenced by operator=(), and SetLumping().

void AliPoissonCalculator::Define	(	const TAxis &	xaxis,
		const TAxis &	yaxis
	)

Initialize this object.

Also book the cache histograms

Parameters

xaxis	The X-axis
yaxis	The Y-axis

Definition at line 154 of file AliPoissonCalculator.cxx.

void AliPoissonCalculator::Fill	(	UShort_t	strip,
		UShort_t	sec,
		Bool_t	hit,
		Double_t	weight = 1
	)

Fill in an observation

Parameters

strip	X axis bin number
sec	Y axis bin number
hit	True if hit
weight	Weight if this

Definition at line 309 of file AliPoissonCalculator.cxx.

Referenced by AliFMDDensityCalculator::Calculate(), and TestPoisson().

void AliPoissonCalculator::FillDiagnostics

(

)

After calculating the results, fill the diagnostics histograms

Definition at line 414 of file AliPoissonCalculator.cxx.

Referenced by AliFMDDensityCalculator::Calculate().

TH2D* AliPoissonCalculator::GetCorrection ( ) const

inline

Get the correction histogram

Returns

correction histogram

Definition at line 182 of file AliPoissonCalculator.h.

Referenced by TestPoisson().

TH2D* AliPoissonCalculator::GetEmptyVsTotal ( ) const

inline

Get the empty versus total histogram

Returns

Empty versus total

Definition at line 164 of file AliPoissonCalculator.h.

TH1D* AliPoissonCalculator::GetMean ( ) const

inline

Get the histogram of the means

Returns

Means

Definition at line 170 of file AliPoissonCalculator.h.

Referenced by TestPoisson().

TH1D* AliPoissonCalculator::GetOccupancy ( ) const

inline

Get the occupancy histogram

Returns

Occupancy histogram

Definition at line 176 of file AliPoissonCalculator.h.

Referenced by TestPoisson().

Int_t AliPoissonCalculator::GetReducedXBin

(

Int_t

ix

)

const

Get the X bin in the reduced historgam

Parameters

ix	X bin in full histogram

Returns

X bin in reduced histogram

Definition at line 344 of file AliPoissonCalculator.cxx.

Referenced by Result().

Int_t AliPoissonCalculator::GetReducedXBin

(

Double_t

x

)

const

Get the X bin in the reduced historgam

Parameters

x

X value

Returns

X bin in reduced histogram

Definition at line 352 of file AliPoissonCalculator.cxx.

Int_t AliPoissonCalculator::GetReducedYBin

(

Int_t

iy

)

const

Get the Y bin in the reduced historgam

Parameters

iy	Y bin in full histogram

Returns

Y bin in reduced histogram

Definition at line 359 of file AliPoissonCalculator.cxx.

Referenced by Result().

Int_t AliPoissonCalculator::GetReducedYBin

(

Double_t

y

)

const

Get the Y bin in the reduced historgam

Parameters

y

Y value

Returns

Y bin in reduced histogram

Definition at line 367 of file AliPoissonCalculator.cxx.

void AliPoissonCalculator::Init	(	Int_t	xLumping = -1,
		Int_t	yLumping = -1
	)

Intialize this object

Parameters

xLumping	If larger than 0, set the eta lumping to this
yLumping	If larger than 0, set the phi lumping to this

Definition at line 139 of file AliPoissonCalculator.cxx.

Referenced by AliPoissonCalculator(), operator=(), SetLumping(), and TestPoisson().

Bool_t AliPoissonCalculator::IsFolder ( ) const

inline

Returns

Always true

Definition at line 145 of file AliPoissonCalculator.h.

void AliPoissonCalculator::MakeOutput

(

)

Make output stuff for the passed list

Definition at line 182 of file AliPoissonCalculator.cxx.

Referenced by Init(), and Output().

AliPoissonCalculator & AliPoissonCalculator::operator=

(

const AliPoissonCalculator &

o

)

Assignment operator

Parameters

o	Object to assign from

Returns

Reference to this object

Definition at line 125 of file AliPoissonCalculator.cxx.

void AliPoissonCalculator::Output

(

TList *

d

)

Output stuff to the passed list

Parameters

d	List to add output histograms to

Definition at line 223 of file AliPoissonCalculator.cxx.

void AliPoissonCalculator::Print

(

const Option_t *

option = ""

)

const

Print information

Parameters

option

Not used

Definition at line 432 of file AliPoissonCalculator.cxx.

void AliPoissonCalculator::Reset

(

const TH2D *

base

)

Reset the cache histogram

Parameters

base	Base histogram

Definition at line 261 of file AliPoissonCalculator.cxx.

Referenced by AliPoissonCalculator(), AliFMDDensityCalculator::Calculate(), Define(), operator=(), and TestPoisson().

TH2D * AliPoissonCalculator::Result

(

Bool_t

correct = true

)

Calculate result and store in output

Parameters

correct

Whether to apply correction or not

Returns

The result histogram (fBase overwritten)

Definition at line 377 of file AliPoissonCalculator.cxx.

Referenced by AliFMDDensityCalculator::Calculate(), and TestPoisson().

void AliPoissonCalculator::SetLumping	(	UShort_t	nx,
		UShort_t	ny
	)

Set the number of eta bins to group into a region

Parameters

nx	Number of \(\eta\) bins per region
ny	Number of \(\phi\) bins per region

Definition at line 235 of file AliPoissonCalculator.cxx.

Referenced by AliFMDDensityCalculator::CreateOutputObjects(), SetXLumping(), and SetYLumping().

void AliPoissonCalculator::SetXLumping ( UShort_t  nx )

inline

Set the number of X bins to group into a region

Parameters

nx	Number of eta bins per region

Definition at line 79 of file AliPoissonCalculator.h.

void AliPoissonCalculator::SetYLumping ( UShort_t  ny )

inline

Set the number of Y bins to group into a region

Parameters

ny	Number of eta bins per region

Definition at line 85 of file AliPoissonCalculator.h.

Member Data Documentation

TH2D* AliPoissonCalculator::fBasic

protected

Definition at line 282 of file AliPoissonCalculator.h.

Referenced by AliPoissonCalculator(), Browse(), CleanUp(), Define(), Fill(), GetReducedXBin(), GetReducedYBin(), operator=(), Reset(), and Result().

TH2D* AliPoissonCalculator::fCorr

protected

Definition at line 286 of file AliPoissonCalculator.h.

Referenced by Browse(), CleanUp(), FillDiagnostics(), GetCorrection(), MakeOutput(), and Output().

TH2D* AliPoissonCalculator::fEmpty

protected

Definition at line 281 of file AliPoissonCalculator.h.

Referenced by Browse(), CleanUp(), Fill(), FillDiagnostics(), GetReducedXBin(), GetReducedYBin(), Reset(), and Result().

TH2D* AliPoissonCalculator::fEmptyVsTotal

protected

Definition at line 283 of file AliPoissonCalculator.h.

Referenced by Browse(), CleanUp(), FillDiagnostics(), GetEmptyVsTotal(), Init(), MakeOutput(), Output(), and SetLumping().

TH1D* AliPoissonCalculator::fMean

protected

Definition at line 284 of file AliPoissonCalculator.h.

Referenced by Browse(), CleanUp(), FillDiagnostics(), GetMean(), MakeOutput(), and Output().

TH1D* AliPoissonCalculator::fOcc

protected

Definition at line 285 of file AliPoissonCalculator.h.

Referenced by Browse(), CleanUp(), FillDiagnostics(), GetOccupancy(), MakeOutput(), and Output().

TH2D* AliPoissonCalculator::fTotal

protected

Definition at line 280 of file AliPoissonCalculator.h.

Referenced by Browse(), CleanUp(), Fill(), FillDiagnostics(), Reset(), Result(), and SetLumping().

UShort_t AliPoissonCalculator::fXLumping

protected

Definition at line 278 of file AliPoissonCalculator.h.

Referenced by Init(), MakeOutput(), operator=(), Print(), Reset(), and SetLumping().

UShort_t AliPoissonCalculator::fYLumping

protected

Definition at line 279 of file AliPoissonCalculator.h.

Referenced by Init(), MakeOutput(), operator=(), Print(), Reset(), SetLumping(), SetXLumping(), and SetYLumping().

---

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

• PWGLF/FORWARD/analysis2/AliPoissonCalculator.h
• PWGLF/FORWARD/analysis2/AliPoissonCalculator.cxx