TUnfold is used to decompose a measurement y into several sources x given the measurement uncertainties and a matrix of migrations A.

For most applications, it is better to use TUnfoldDensity instead of using TUnfoldSys or TUnfold**

If you use this software, please consider the following citation S.Schmitt, JINST 7 (2012) T10003 [arXiv:1205.6201]

More documentation and updates are available on http://www.desy.de/~sschmitt

A short summary of the algorithm is given in the following: the "best" x matching the measurement y within errors is determined by minimizing the function L1+L2+L3

where L1 = (y-Ax)# Vyy^-1 (y-Ax) L2 = tau^2 (L(x-x0))# L(x-x0) L3 = lambda sum_i(y_i -(Ax)_i)

[the notation # means that the matrix is transposed ]

The term L1 is familiar from a least-square minimisation The term L2 defines the regularisation (smootheness condition on x), where the parameter tau^2 gives the strength of teh regularisation The term L3 is an optional area constraint with Lagrangian parameter lambda, ensuring that that the normalisation of x is consistent with the normalisation of y

The method can be applied to a very large number of problems, where the measured distribution y is a linear superposition of several Monte Carlo shapes

Input from measurement:

y: vector of measured quantities (dimension ny) Vyy: covariance matrix for y (dimension ny x ny) in many cases V is diagonal and calculated from the errors of y

From simulation:

A: migration matrix (dimension ny x nx)

Result

x: unknown underlying distribution (dimension nx) The error matrix of x, V_xx, is also determined

Regularisation

tau: parameter, defining the regularisation strength L: matrix of regularisation conditions (dimension nl x nx) depends on the structure of the input data x0: bias distribution, from simulation

Preservation of the area

lambda: lagrangian multiplier y_i: one component of the vector y (Ax)_i: one component of the vector Ax

Determination of the unfolding result x:

(a) not constrained: minimisation is performed as a function of x for fixed lambda=0
(b) constrained: stationary point is found as a function of x and lambda

The constraint can be useful to reduce biases on the result x in cases where the vector y follows non-Gaussian probability densities (example: Poisson statistics at counting experiments in particle physics)

Some random examples:

measure a cross-section as a function of, say, E_T(detector) and unfold it to obtain the underlying distribution E_T(generator)
measure a lifetime distribution and unfold the contributions from different flavours
measure the transverse mass and decay angle and unfold for the true mass distribution plus background

Documentation

Some technical documentation is available here: http://www.desy.de/~sschmitt

Note:

For most applications it is better to use the derived class TUnfoldSys or even better TUnfoldDensity

TUnfoldSys extends the functionality of TUnfold such that systematic errors are propagated to teh result and that the unfolding can be done with proper background subtraction

TUnfoldDensity extends further the functionality of TUnfoldSys complex binning schemes are supported The binning of input histograms is handeld consistently: (1) the regularisation may be done by density, i.e respecting the bin widths (2) methods are provided which preserve the proper binning of the result histograms

Implementation

The result of the unfolding is calculated as follows:

Lsquared = L::L regularisation conditions squared

epsilon_j = sum_i A_ij vector of efficiencies

E^-1 = ((A# Vyy^-1 A)+tau^2 Lsquared)

x = E (A# Vyy^-1 y + tau^2 Lsquared x0 +lambda/2 * epsilon) is the result

The derivatives dx_k/dy_i dx_k/dA_ij dx_k/d(tau^2) are calculated for further usage.

The covariance matrix V_xx is calculated as: Vxx_ij = sum_kl dx_i/dy_k Vyy_kl dx_j/dy_l

Warning:

The algorithm is based on "standard" matrix inversion, with the known limitations in numerical accuracy and computing cost for matrices with large dimensions.

Thus the algorithm should not used for large dimensions of x and y nx should not be much larger than 200 ny should not be much larger than 1000

Proper choice of tau

One of the difficult questions is about the choice of tau. The method implemented in TUnfold is the L-curve method: a two-dimensional curve is plotted x-axis: log10(chisquare) y-axis: log10(regularisation condition) In many cases this curve has an L-shape. The best choice of tau is in the kink of the L

Within TUnfold a simple version of the L-curve analysis is available. It tests a given number of points in a predefined tau-range and searches for the maximum of the curvature in the L-curve (kink position). if no tau range is given, the range of the scan is determined automatically

A nice overview of the L-curve method is given in: The L-curve and Its Use in the Numerical Treatment of Inverse Problems (2000) by P. C. Hansen, in Computational Inverse Problems in Electrocardiology, ed. P. Johnston, Advances in Computational Bioengineering http://www.imm.dtu.dk/~pch/TR/Lcurve.ps

Alternative Regularisation conditions

Regularisation is needed for most unfolding problems, in order to avoid large oscillations and large correlations on the output bins. It means that some extra conditions are applied on the output bins

Within TUnfold these conditions are posed on the difference (x-x0), where x: unfolding output x0: the bias distribution, by default calculated from the input matrix A. There is a method SetBias() to change the bias distribution. The 3rd argument to DoUnfold() is a scale factor applied to the bias bias_default[j] = sum_i A[i][j] x0[j] = scaleBias*bias[j] The scale factor can be used to (a) completely suppress the bias by setting it to zero (b) compensate differences in the normalisation between data and Monte Carlo

If the regularisation is strong, i.e. large parameter tau, then the distribution x or its derivatives will look like the bias distribution. If the parameter tau is small, the distribution x is independent of the bias.

Three basic types of regularisation are implemented in TUnfold

condition	regularisation
kRegModeNone	none
kRegModeSize	minimize the size of (x-x0)
kRegModeDerivative	minimize the 1st derivative of (x-x0)
kRegModeCurvature	minimize the 2nd derivative of (x-x0)

kRegModeSize is the regularisation scheme which often is found in literature. The second derivative is often named curvature. Sometimes the bias is not discussed, equivalent to a bias scale factor of zero.

The regularisation schemes kRegModeDerivative and kRegModeCurvature have the nice feature that they create correlations between x-bins, whereas the non-regularized unfolding tends to create negative correlations between bins. For these regularisation schemes the parameter tau could be tuned such that the correlations are smallest, as an alternative to the L-curve method.

If kRegModeSize is chosen or if x is a smooth function through all bins, the regularisation condition can be set on all bins together by giving the appropriate argument in the constructor (see examples above).

If x is composed of independent groups of bins (for example, signal and background binning in two variables), it may be necessary to set regularisation conditions for the individual groups of bins. In this case, give kRegModeNone in the constructor and specify the bin grouping with calls to RegularizeBins() specify a 1-dimensional group of bins RegularizeBins2D() specify a 2-dimensional group of bins

Note, the class TUnfoldDensity provides an automatic setup of complex regularisation schemes

For ultimate flexibility, the regularisation condition can be set on each bin individually -> give kRegModeNone in the constructor and use RegularizeSize() regularize one bin RegularizeDerivative() regularize the slope given by two bins RegularizeCurvature() regularize the curvature given by three bins AddRegularisationCondition() define an arbitrary regulatisation condition

Definition at line 99 of file TUnfold.h.

Public Types
enum	EConstraint { kEConstraintNone =0, kEConstraintArea =1 }

enum	ERegMode { kRegModeNone = 0, kRegModeSize = 1, kRegModeDerivative = 2, kRegModeCurvature = 3, kRegModeMixed = 4 }

enum	EHistMap { kHistMapOutputHoriz = 0, kHistMapOutputVert = 1 }

Public Types inherited from TObject
enum	EStatusBits { kCanDelete = BIT(0), kMustCleanup = BIT(3), kObjInCanvas = BIT(3), kIsReferenced = BIT(4), kHasUUID = BIT(5), kCannotPick = BIT(6), kNoContextMenu = BIT(8), kInvalidObject = BIT(13) }

enum	{ kIsOnHeap = 0x01000000, kNotDeleted = 0x02000000, kZombie = 0x04000000, kBitMask = 0x00ffffff }

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

Public Member Functions
	TUnfold (const TH2 *hist_A, EHistMap histmap, ERegMode regmode=kRegModeSize, EConstraint constraint=kEConstraintArea)

virtual	~TUnfold (void)

void	SetBias (const TH1 *bias)

void	SetConstraint (EConstraint constraint)

Int_t	RegularizeSize (int bin, Double_t scale=1.0)

Int_t	RegularizeDerivative (int left_bin, int right_bin, Double_t scale=1.0)

Int_t	RegularizeCurvature (int left_bin, int center_bin, int right_bin, Double_t scale_left=1.0, Double_t scale_right=1.0)

Int_t	RegularizeBins (int start, int step, int nbin, ERegMode regmode)

Int_t	RegularizeBins2D (int start_bin, int step1, int nbin1, int step2, int nbin2, ERegMode regmode)

Double_t	DoUnfold (Double_t tau, const TH1 *hist_y, Double_t scaleBias=0.0)

virtual Int_t	SetInput (const TH1 hist_y, Double_t scaleBias=0.0, Double_t oneOverZeroError=0.0, const TH2 hist_vyy=0, const TH2 *hist_vyy_inv=0)

virtual Double_t	DoUnfold (Double_t tau)

virtual Int_t	ScanLcurve (Int_t nPoint, Double_t tauMin, Double_t tauMax, TGraph lCurve, TSpline logTauX=0, TSpline **logTauY=0)

void	GetProbabilityMatrix (TH2 *A, EHistMap histmap) const

void	GetNormalisationVector (TH1 s, const Int_t binMap=0) const

void	GetOutput (TH1 output, const Int_t binMap=0) const

void	GetBias (TH1 bias, const Int_t binMap=0) const

void	GetFoldedOutput (TH1 folded, const Int_t binMap=0) const

void	GetInput (TH1 inputData, const Int_t binMap=0) const

void	GetRhoIJ (TH2 rhoij, const Int_t binMap=0) const

void	GetEmatrix (TH2 ematrix, const Int_t binMap=0) const

Double_t	GetRhoI (TH1 rhoi, const Int_t binMap=0, TH2 *invEmat=0) const

void	GetLsquared (TH2 *lsquared) const

Int_t	GetNr (void) const

void	GetL (TH2 *l) const

void	GetInputInverseEmatrix (TH2 *ematrix)

Double_t	GetTau (void) const

Double_t	GetRhoMax (void) const

Double_t	GetRhoAvg (void) const

Double_t	GetChi2A (void) const

Double_t	GetChi2L (void) const

virtual Double_t	GetLcurveX (void) const

virtual Double_t	GetLcurveY (void) const

Int_t	GetNdf (void) const

Int_t	GetNpar (void) const

Double_t	GetEpsMatrix (void) const

void	SetEpsMatrix (Double_t eps)

Public Member Functions inherited from TObject
	TObject ()

	TObject (const TObject &object)
	TObject copy ctor. More...

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

virtual	~TObject ()
	TObject destructor. More...

virtual void	AppendPad (Option_t *option="")
	Append graphics object to current pad. More...

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

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

virtual void	Clear (Option_t *="")

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

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

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

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

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

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

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

virtual TObject *	DrawClone (Option_t *option="") const
	Draw a clone of this object in the current pad. More...

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

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. More...

virtual void	Execute (TMethod method, TObjArray params, Int_t *error=0)
	Execute method on this object with parameters stored in the TObjArray. More...

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

virtual TObject *	FindObject (const char *name) const
	Must be redefined in derived classes. More...

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

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

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

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

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

virtual Option_t *	GetOption () const

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

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

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

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

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

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

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

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

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

virtual Bool_t	IsSortable () const

Bool_t	IsOnHeap () const

Bool_t	IsZombie () const

virtual Bool_t	Notify ()
	This method must be overridden to handle object notification. More...

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

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

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

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

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

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

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

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

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

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

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

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

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

void *	operator new (size_t sz)

void *	operator new[] (size_t sz)

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

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

void	operator delete (void *ptr)
	Operator delete. More...

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

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

void	SetBit (UInt_t f)

void	ResetBit (UInt_t f)

Bool_t	TestBit (UInt_t f) const

Int_t	TestBits (UInt_t f) const

void	InvertBit (UInt_t f)

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

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

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

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

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

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

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). More...

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

Static Public Member Functions
static const char *	GetTUnfoldVersion (void)

Static Public Member Functions inherited from TObject
static Long_t	GetDtorOnly ()
	Return destructor only flag. More...

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

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

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

Protected Member Functions
	TUnfold (void)

virtual Double_t	DoUnfold (void)

virtual void	ClearResults (void)

void	ClearHistogram (TH1 *h, Double_t x=0.) const

virtual TString	GetOutputBinName (Int_t iBinX) const

TMatrixDSparse *	MultiplyMSparseM (const TMatrixDSparse a, const TMatrixD b) const

TMatrixDSparse *	MultiplyMSparseMSparse (const TMatrixDSparse a, const TMatrixDSparse b) const

TMatrixDSparse *	MultiplyMSparseTranspMSparse (const TMatrixDSparse a, const TMatrixDSparse b) const

TMatrixDSparse *	MultiplyMSparseMSparseTranspVector (const TMatrixDSparse m1, const TMatrixDSparse m2, const TMatrixTBase< Double_t > *v) const

TMatrixDSparse *	InvertMSparseSymmPos (const TMatrixDSparse A, Int_t rank) const

void	AddMSparse (TMatrixDSparse dest, Double_t f, const TMatrixDSparse src) const

TMatrixDSparse *	CreateSparseMatrix (Int_t nrow, Int_t ncol, Int_t nele, Int_t row, Int_t col, Double_t *data) const

Int_t	GetNx (void) const

Int_t	GetNy (void) const

void	ErrorMatrixToHist (TH2 ematrix, const TMatrixDSparse emat, const Int_t *binMap, Bool_t doClear) const

Double_t	GetRhoIFromMatrix (TH1 rhoi, const TMatrixDSparse eOrig, const Int_t binMap, TH2 invEmat) const

const TMatrixDSparse *	GetDXDY (void) const

const TMatrixDSparse *	GetDXDAM (int i) const

const TMatrixDSparse *	GetDXDAZ (int i) const

const TMatrixDSparse *	GetDXDtauSquared (void) const

const TMatrixDSparse *	GetAx (void) const

const TMatrixDSparse *	GetEinv (void) const

const TMatrixDSparse *	GetE (void) const

const TMatrixDSparse *	GetVxx (void) const

const TMatrixDSparse *	GetVxxInv (void) const

const TMatrixDSparse *	GetVyyInv (void) const

const TMatrixD *	GetX (void) const

Int_t	GetRowFromBin (int ix) const

Int_t	GetBinFromRow (int ix) const

Bool_t	AddRegularisationCondition (Int_t i0, Double_t f0, Int_t i1=-1, Double_t f1=0., Int_t i2=-1, Double_t f2=0.)

Bool_t	AddRegularisationCondition (Int_t nEle, const Int_t indices, const Double_t rowData)

Protected Member Functions inherited from TObject
void	MakeZombie ()

virtual void	DoError (int level, const char location, const char fmt, va_list va) const
	Interface to ErrorHandler (protected). More...

Static Protected Member Functions
static void	DeleteMatrix (TMatrixD **m)

static void	DeleteMatrix (TMatrixDSparse **m)

Protected Attributes
TMatrixDSparse *	fA

TMatrixDSparse *	fL

TMatrixDSparse *	fVyy

TMatrixD *	fY

TMatrixD *	fX0

Double_t	fTauSquared

Double_t	fBiasScale

TArrayI	fXToHist

TArrayI	fHistToX

TArrayD	fSumOverY

EConstraint	fConstraint

ERegMode	fRegMode

Private Member Functions
void	InitTUnfold (void)

Private Attributes
Int_t	fIgnoredBins

Double_t	fEpsMatrix

TMatrixD *	fX

TMatrixDSparse *	fVyyInv

TMatrixDSparse *	fVxx

TMatrixDSparse *	fVxxInv

TMatrixDSparse *	fAx

Double_t	fChi2A

Double_t	fLXsquared

Double_t	fRhoMax

Double_t	fRhoAvg

Int_t	fNdf

TMatrixDSparse *	fDXDAM [2]

TMatrixDSparse *	fDXDAZ [2]

TMatrixDSparse *	fDXDtauSquared

TMatrixDSparse *	fDXDY

TMatrixDSparse *	fEinv

TMatrixDSparse *	fE

#include <TUnfold.h>

Inheritance diagram for TUnfold:

Collaboration diagram for TUnfold:

Member Enumeration Documentation

enum TUnfold::EConstraint

Enumerator
kEConstraintNone
kEConstraintArea

Definition at line 103 of file TUnfold.h.

enum TUnfold::EHistMap

Enumerator
kHistMapOutputHoriz
kHistMapOutputVert

Definition at line 188 of file TUnfold.h.

enum TUnfold::ERegMode

Enumerator
kRegModeNone
kRegModeSize
kRegModeDerivative
kRegModeCurvature
kRegModeMixed

Definition at line 107 of file TUnfold.h.

Constructor & Destructor Documentation

TUnfold::TUnfold ( void )

protected

Definition at line 372 of file TUnfold.cxx.

TUnfold::TUnfold	(	const TH2 *	hist_A,
		EHistMap	histmap,
		ERegMode	regmode = `kRegModeSize`,
		EConstraint	constraint = `kEConstraintArea`
	)

Definition at line 1745 of file TUnfold.cxx.

TUnfold::~TUnfold ( void )

virtual

Definition at line 1948 of file TUnfold.cxx.

Member Function Documentation

void TUnfold::AddMSparse	(	TMatrixDSparse *	dest,
		Double_t	f,
		const TMatrixDSparse *	src
	)		const

protected

Definition at line 1001 of file TUnfold.cxx.

Referenced by DoUnfold(), TUnfoldSys::GetSummedErrorMatrixXX(), TUnfoldSys::GetSummedErrorMatrixYY(), and TUnfoldSys::PrepareSysError().

Bool_t TUnfold::AddRegularisationCondition	(	Int_t	i0,
		Double_t	f0,
		Int_t	i1 = `-1`,
		Double_t	f1 = `0.`,
		Int_t	i2 = `-1`,
		Double_t	f2 = `0.`
	)

protected

Definition at line 1973 of file TUnfold.cxx.

Referenced by RegularizeCurvature(), RegularizeDerivative(), and RegularizeSize().

Bool_t TUnfold::AddRegularisationCondition	(	Int_t	nEle,
		const Int_t *	indices,
		const Double_t *	rowData
	)

protected

Definition at line 2007 of file TUnfold.cxx.

void TUnfold::ClearHistogram	(	TH1 *	h,
		Double_t	x = `0.`
	)		const

protected

Definition at line 3394 of file TUnfold.cxx.

Referenced by GetBias(), GetFoldedOutput(), GetInput(), GetNormalisationVector(), GetOutput(), GetRhoI(), and TUnfoldSys::GetRhoItotal().

void TUnfold::ClearResults ( void )

protectedvirtual

Reimplemented in TUnfoldSys.

Definition at line 345 of file TUnfold.cxx.

Referenced by TUnfoldSys::ClearResults(), DoUnfold(), SetConstraint(), SetInput(), and ~TUnfold().

TMatrixDSparse * TUnfold::CreateSparseMatrix	(	Int_t	nrow,
		Int_t	ncol,
		Int_t	nele,
		Int_t *	row,
		Int_t *	col,
		Double_t *	data
	)		const

protected

Definition at line 698 of file TUnfold.cxx.

Referenced by DoUnfold(), TUnfoldSys::PrepareSysError(), SetInput(), and TUnfold().

void TUnfold::DeleteMatrix ( TMatrixD ** m )

staticprotected

Definition at line 333 of file TUnfold.cxx.

Referenced by TUnfoldSys::ClearResults(), ClearResults(), TUnfoldSys::DoBackgroundSubtraction(), DoUnfold(), TUnfoldSys::GetChi2Sys(), GetFoldedOutput(), GetLsquared(), GetRhoIFromMatrix(), TUnfoldSys::GetRhoItotal(), TUnfoldSys::GetSummedErrorMatrixXX(), TUnfoldSys::GetSummedErrorMatrixYY(), TUnfoldSys::PrepareSysError(), SetBias(), SetInput(), TUnfoldSys::SetTauError(), ~TUnfold(), and TUnfoldSys::~TUnfoldSys().

void TUnfold::DeleteMatrix ( TMatrixDSparse ** m )

staticprotected

Definition at line 339 of file TUnfold.cxx.

Double_t TUnfold::DoUnfold ( void )

protectedvirtual

Definition at line 378 of file TUnfold.cxx.

Referenced by DoUnfold(), and ScanLcurve().

Double_t TUnfold::DoUnfold	(	Double_t	tau,
		const TH1 *	hist_y,
		Double_t	scaleBias = `0.0`
	)

Definition at line 2186 of file TUnfold.cxx.

Double_t TUnfold::DoUnfold ( Double_t tau )

virtual

Definition at line 2407 of file TUnfold.cxx.

void TUnfold::ErrorMatrixToHist	(	TH2 *	ematrix,
		const TMatrixDSparse *	emat,
		const Int_t *	binMap,
		Bool_t	doClear
	)		const

protected

Definition at line 3109 of file TUnfold.cxx.

Referenced by GetEmatrix().

const TMatrixDSparse* TUnfold::GetAx ( void ) const

inlineprotected

Definition at line 174 of file TUnfold.h.

Referenced by TUnfoldSys::GetChi2Sys().

void TUnfold::GetBias	(	TH1 *	bias,
		const Int_t *	binMap = `0`
	)		const

Definition at line 2794 of file TUnfold.cxx.

Referenced by TUnfoldDensity::GetBias().

Int_t TUnfold::GetBinFromRow ( int ix ) const

inlineprotected

Definition at line 182 of file TUnfold.h.

Double_t TUnfold::GetChi2A ( void ) const

inline

Definition at line 239 of file TUnfold.h.

Double_t TUnfold::GetChi2L ( void ) const

Definition at line 3009 of file TUnfold.cxx.

const TMatrixDSparse* TUnfold::GetDXDAM ( int i ) const

inlineprotected

Definition at line 171 of file TUnfold.h.

Referenced by TUnfoldSys::PrepareSysError().

const TMatrixDSparse* TUnfold::GetDXDAZ ( int i ) const

inlineprotected

Definition at line 172 of file TUnfold.h.

const TMatrixDSparse* TUnfold::GetDXDtauSquared ( void ) const

inlineprotected

Definition at line 173 of file TUnfold.h.

Referenced by TUnfoldSys::PrepareSysError().

const TMatrixDSparse* TUnfold::GetDXDY ( void ) const

inlineprotected

Definition at line 170 of file TUnfold.h.

const TMatrixDSparse* TUnfold::GetE ( void ) const

inlineprotected

Definition at line 176 of file TUnfold.h.

const TMatrixDSparse* TUnfold::GetEinv ( void ) const

inlineprotected

Definition at line 175 of file TUnfold.h.

void TUnfold::GetEmatrix	(	TH2 *	ematrix,
		const Int_t *	binMap = `0`
	)		const

Definition at line 3175 of file TUnfold.cxx.

Referenced by TUnfoldSys::GetEmatrixTotal(), and GetRhoIJ().

Double_t TUnfold::GetEpsMatrix ( void ) const

inline

Definition at line 246 of file TUnfold.h.

void TUnfold::GetFoldedOutput	(	TH1 *	folded,
		const Int_t *	binMap = `0`
	)		const

Definition at line 2815 of file TUnfold.cxx.

Referenced by TUnfoldDensity::GetFoldedOutput().

void TUnfold::GetInput	(	TH1 *	inputData,
		const Int_t *	binMap = `0`
	)		const

Definition at line 2884 of file TUnfold.cxx.

Referenced by TUnfoldDensity::GetInput().

void TUnfold::GetInputInverseEmatrix ( TH2 * ematrix )

Definition at line 2917 of file TUnfold.cxx.

Referenced by DoUnfold().

void TUnfold::GetL ( TH2 * l ) const

Definition at line 2977 of file TUnfold.cxx.

Referenced by TUnfoldDensity::GetL().

Double_t TUnfold::GetLcurveX ( void ) const

virtual

Definition at line 3021 of file TUnfold.cxx.

Referenced by ScanLcurve().

Double_t TUnfold::GetLcurveY ( void ) const

virtual

Definition at line 3027 of file TUnfold.cxx.

Referenced by ScanLcurve().

void TUnfold::GetLsquared ( TH2 * lsquared ) const

Definition at line 2958 of file TUnfold.cxx.

Int_t TUnfold::GetNdf ( void ) const

inline

Definition at line 243 of file TUnfold.h.

Referenced by ScanLcurve().

void TUnfold::GetNormalisationVector	(	TH1 *	s,
		const Int_t *	binMap = `0`
	)		const

Definition at line 2774 of file TUnfold.cxx.

Int_t TUnfold::GetNpar ( void ) const

Definition at line 3015 of file TUnfold.cxx.

Referenced by GetInputInverseEmatrix().

Int_t TUnfold::GetNr ( void ) const

inline

Definition at line 231 of file TUnfold.h.

Referenced by GetL().

Int_t TUnfold::GetNx ( void ) const

inlineprotected

Definition at line 162 of file TUnfold.h.

Referenced by DoUnfold(), GetBias(), GetLsquared(), GetNormalisationVector(), GetNpar(), GetRhoI(), GetRhoIFromMatrix(), SetBias(), and TUnfold().

Int_t TUnfold::GetNy ( void ) const

inlineprotected

Definition at line 165 of file TUnfold.h.

Referenced by TUnfoldSys::DoBackgroundSubtraction(), DoUnfold(), GetFoldedOutput(), GetInput(), GetInputInverseEmatrix(), TUnfoldSys::PrepareSysError(), and SetInput().

void TUnfold::GetOutput	(	TH1 *	output,
		const Int_t *	binMap = `0`
	)		const

Definition at line 3033 of file TUnfold.cxx.

Referenced by TUnfoldDensity::GetOutput().

TString TUnfold::GetOutputBinName ( Int_t iBinX ) const

protectedvirtual

Reimplemented in TUnfoldDensity.

Definition at line 1737 of file TUnfold.cxx.

Referenced by TUnfoldDensity::GetOutputBinName(), and SetInput().

void TUnfold::GetProbabilityMatrix	(	TH2 *	A,
		EHistMap	histmap
	)		const

Definition at line 2863 of file TUnfold.cxx.

Referenced by TUnfoldDensity::GetProbabilityMatrix().

Double_t TUnfold::GetRhoAvg ( void ) const

inline

Definition at line 238 of file TUnfold.h.

Double_t TUnfold::GetRhoI	(	TH1 *	rhoi,
		const Int_t *	binMap = `0`,
		TH2 *	invEmat = `0`
	)		const

Definition at line 3216 of file TUnfold.cxx.

Referenced by TUnfoldDensity::GetRhoIstatbgr().

Double_t TUnfold::GetRhoIFromMatrix	(	TH1 *	rhoi,
		const TMatrixDSparse *	eOrig,
		const Int_t *	binMap,
		TH2 *	invEmat
	)		const

protected

Definition at line 3275 of file TUnfold.cxx.

Referenced by GetRhoI(), and TUnfoldSys::GetRhoItotal().

void TUnfold::GetRhoIJ	(	TH2 *	rhoij,
		const Int_t *	binMap = `0`
	)		const

Definition at line 3188 of file TUnfold.cxx.

Double_t TUnfold::GetRhoMax ( void ) const

inline

Definition at line 237 of file TUnfold.h.

Int_t TUnfold::GetRowFromBin ( int ix ) const

inlineprotected

Definition at line 181 of file TUnfold.h.

Double_t TUnfold::GetTau ( void ) const

Definition at line 3003 of file TUnfold.cxx.

static const char* TUnfold::GetTUnfoldVersion ( void )

static

const TMatrixDSparse* TUnfold::GetVxx ( void ) const

inlineprotected

Definition at line 177 of file TUnfold.h.

Referenced by TUnfoldSys::GetSummedErrorMatrixXX().

const TMatrixDSparse* TUnfold::GetVxxInv ( void ) const

inlineprotected

Definition at line 178 of file TUnfold.h.

const TMatrixDSparse* TUnfold::GetVyyInv ( void ) const

inlineprotected

Definition at line 179 of file TUnfold.h.

Referenced by TUnfoldSys::DoBackgroundSubtraction().

const TMatrixD* TUnfold::GetX ( void ) const

inlineprotected

Definition at line 180 of file TUnfold.h.

void TUnfold::InitTUnfold ( void )

private

Definition at line 295 of file TUnfold.cxx.

Referenced by TUnfold().

TMatrixDSparse * TUnfold::InvertMSparseSymmPos	(	const TMatrixDSparse *	A,
		Int_t *	rank
	)		const

protected

Definition at line 1064 of file TUnfold.cxx.

Referenced by DoUnfold(), TUnfoldSys::GetChi2Sys(), GetInputInverseEmatrix(), and GetRhoIFromMatrix().

TMatrixDSparse * TUnfold::MultiplyMSparseM	(	const TMatrixDSparse *	a,
		const TMatrixD *	b
	)		const

protected

Definition at line 858 of file TUnfold.cxx.

Referenced by DoUnfold(), and TUnfoldSys::GetChi2Sys().

TMatrixDSparse * TUnfold::MultiplyMSparseMSparse	(	const TMatrixDSparse *	a,
		const TMatrixDSparse *	b
	)		const

protected

Definition at line 711 of file TUnfold.cxx.

Referenced by DoUnfold(), GetFoldedOutput(), TUnfoldSys::GetSummedErrorMatrixYY(), and TUnfoldSys::PrepareSysError().

TMatrixDSparse * TUnfold::MultiplyMSparseMSparseTranspVector	(	const TMatrixDSparse *	m1,
		const TMatrixDSparse *	m2,
		const TMatrixTBase< Double_t > *	v
	)		const

protected

Definition at line 911 of file TUnfold.cxx.

Referenced by DoUnfold(), TUnfoldSys::GetSummedErrorMatrixXX(), and TUnfoldSys::GetSummedErrorMatrixYY().

TMatrixDSparse * TUnfold::MultiplyMSparseTranspMSparse	(	const TMatrixDSparse *	a,
		const TMatrixDSparse *	b
	)		const

protected

Definition at line 780 of file TUnfold.cxx.

Referenced by DoUnfold(), GetLsquared(), and SetInput().

Int_t TUnfold::RegularizeBins	(	int	start,
		int	step,
		int	nbin,
		ERegMode	regmode
	)

Definition at line 2123 of file TUnfold.cxx.

Referenced by RegularizeBins2D(), and TUnfold().

Int_t TUnfold::RegularizeBins2D	(	int	start_bin,
		int	step1,
		int	nbin1,
		int	step2,
		int	nbin2,
		ERegMode	regmode
	)

Definition at line 2163 of file TUnfold.cxx.

Int_t TUnfold::RegularizeCurvature	(	int	left_bin,
		int	center_bin,
		int	right_bin,
		Double_t	scale_left = `1.0`,
		Double_t	scale_right = `1.0`
	)

Definition at line 2099 of file TUnfold.cxx.

Referenced by RegularizeBins().

Int_t TUnfold::RegularizeDerivative	(	int	left_bin,
		int	right_bin,
		Double_t	scale = `1.0`
	)

Definition at line 2083 of file TUnfold.cxx.

Referenced by RegularizeBins().

Int_t TUnfold::RegularizeSize	(	int	bin,
		Double_t	scale = `1.0`
	)

Definition at line 2069 of file TUnfold.cxx.

Referenced by RegularizeBins().

Int_t TUnfold::ScanLcurve	(	Int_t	nPoint,
		Double_t	tauMin,
		Double_t	tauMax,
		TGraph **	lCurve,
		TSpline **	logTauX = `0`,
		TSpline **	logTauY = `0`
	)

virtual

Definition at line 2424 of file TUnfold.cxx.

void TUnfold::SetBias ( const TH1 * bias )

Definition at line 1961 of file TUnfold.cxx.

void TUnfold::SetConstraint ( EConstraint constraint )

Definition at line 2995 of file TUnfold.cxx.

Referenced by TUnfold().

void TUnfold::SetEpsMatrix ( Double_t eps )

Definition at line 3418 of file TUnfold.cxx.

Int_t TUnfold::SetInput	(	const TH1 *	hist_y,
		Double_t	scaleBias = `0.0`,
		Double_t	oneOverZeroError = `0.0`,
		const TH2 *	hist_vyy = `0`,
		const TH2 *	hist_vyy_inv = `0`
	)