TUnfold Class Reference

An algorithm to unfold distributions from detector to truth level.

TUnfold is used to decompose a measurement y into several sources x, given the measurement uncertainties and a matrix of migrations A. The method can be applied to a large number of problems, where the measured distribution y is a linear superposition of several Monte Carlo shapes. Beyond such a simple template fit, TUnfold has an adjustable regularisation term and also supports an optional constraint on the total number of events.

For most applications, it is better to use the derived class TUnfoldDensity instead of TUnfold. TUnfoldDensity adds various features to TUnfold, such as: background subtraction, propagation of systematic uncertainties, complex multidimensional arrangements of the bins. For innocent users, the most notable improvement of TUnfoldDensity over TUnfold are the getter functions. For TUnfold, histograms have to be booked by the user and the getter functions fill the histogram bins. TUnfoldDensity simply returns a new, already filled histogram.

If you use this software, please consider the following citation

S.Schmitt, JINST 7 (2012) T10003 [arXiv:1205.6201]

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

Brief recipe to use TUnfold:

• a matrix (truth,reconstructed) is given as a two-dimensional histogram as argument to the constructor of TUnfold
• a vector of measurements is given as one-dimensional histogram using the SetInput() method
• The unfolding is performed
• either once with a fixed parameter tau, method DoUnfold(tau)
• or multiple times in a scan to determine the best choice of tau, method ScanLCurve()
• Unfolding results are retrieved using various GetXXX() methods

Basic formulae:

\[ \chi^{2}_{A}=(Ax-y)^{T}V_{yy}^{-1}(Ax-y) \\ \chi^{2}_{L}=(x-f*x_{0})^{T}L^{T}L(x-f*x_{0}) \\ \chi^{2}_{unf}=\chi^{2}_{A}+\tau^{2}\chi^{2}_{L}+\lambda\Sigma_{i}(Ax-y)_{i} \]

• \( x \):result,
• \( A \):probabilities,
• \( y \):data,
• \( V_{yy} \):data covariance,
• \( f \):bias scale,
• \( x_{0} \):bias,
• \( L \):regularisation conditions,
• \( \tau \):regularisation strength,
• \( \lambda \):Lagrangian multiplier.

Without area constraint, \( \lambda \) is set to zero, and \( \chi^{2}_{unf} \) is minimized to determine \( x \). With area constraint, both \( x \) and \( \lambda \) are determined.

---

This file is part of TUnfold.

TUnfold is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

TUnfold is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with TUnfold. If not, see http://www.gnu.org/licenses/.

Version 17.6, updated doxygen-style comments, add one argument for scanLCurve

History:

• Version 17.5, fix memory leak with fVyyInv, bugs in GetInputInverseEmatrix(), GetInput(), bug in MultiplyMSparseMSparseTranspVector
• Version 17.4, in parallel to changes in TUnfoldBinning
• Version 17.3, in parallel to changes in TUnfoldBinning
• Version 17.2, bug fix with GetProbabilityMatrix
• Version 17.1, bug fixes in GetFoldedOutput, GetOutput
• Version 17.0, option to specify an error matrix with SetInput(), new ScanRho() method
• Version 16.2, in parallel to bug-fix in TUnfoldSys
• Version 16.1, fix bug with error matrix in case kEConstraintArea is used
• Version 16.0, fix calculation of global correlations, improved error messages
• Version 15, simplified L-curve scan, new tau definition, new error calc., area preservation
• Version 14, with changes in TUnfoldSys.cxx
• Version 13, new methods for derived classes and small bug fix
• Version 12, report singular matrices
• Version 11, reduce the amount of printout
• Version 10, more correct definition of the L curve, update references
• Version 9, faster matrix inversion and skip edge points for L-curve scan
• Version 8, replace all TMatrixSparse matrix operations by private code
• Version 7, fix problem with TMatrixDSparse,TMatrixD multiplication
• Version 6, replace class XY by std::pair
• Version 5, replace run-time dynamic arrays by new and delete[]
• Version 4, fix new bug from V3 with initial regularisation condition
• Version 3, fix bug with initial regularisation condition
• Version 2, with improved ScanLcurve() algorithm
• Version 1, added ScanLcurve() method
• Version 0, stable version of basic unfolding algorithm

Definition at line 103 of file TUnfold.h.

Public Types
enum	EConstraint { kEConstraintNone =0 , kEConstraintArea =1 }
	type of extra constraint More...
enum	EHistMap { kHistMapOutputHoriz = 0 , kHistMapOutputVert = 1 }
	arrangement of axes for the response matrix (TH2 histogram) More...
enum	ERegMode {   kRegModeNone = 0 , kRegModeSize = 1 , kRegModeDerivative = 2 , kRegModeCurvature = 3 ,   kRegModeMixed = 4 }
	choice of regularisation scheme More...
Public Types inherited from TObject
enum	{   kIsOnHeap = 0x01000000 , kNotDeleted = 0x02000000 , kZombie = 0x04000000 , kInconsistent = 0x08000000 ,   kBitMask = 0x00ffffff }
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 )) }

Public Member Functions
	TUnfold (const TH2 *hist_A, EHistMap histmap, ERegMode regmode=kRegModeSize, EConstraint constraint=kEConstraintArea)
	Set up response matrix and regularisation scheme.
	TUnfold (void)
	Only for use by root streamer or derived classes.
	~TUnfold (void) override
virtual Double_t	DoUnfold (Double_t tau)
	Perform the unfolding for a given regularisation parameter tau.
Double_t	DoUnfold (Double_t tau, const TH1 *hist_y, Double_t scaleBias=0.0)
	Perform the unfolding for a given input and regularisation.
void	GetBias (TH1 *bias, const Int_t *binMap=nullptr) const
	Get bias vector including bias scale.
Double_t	GetChi2A (void) const
	get χ2A contribution determined in recent unfolding
Double_t	GetChi2L (void) const
	Get \( chi^{2}_{L} \) contribution determined in recent unfolding.
void	GetEmatrix (TH2 *ematrix, const Int_t *binMap=nullptr) const
	Get output covariance matrix, possibly cumulated over several bins.
Double_t	GetEpsMatrix (void) const
	get numerical accuracy for Eigenvalue analysis when inverting matrices with rank problems
void	GetFoldedOutput (TH1 *folded, const Int_t *binMap=nullptr) const
	Get unfolding result on detector level.
void	GetInput (TH1 *inputData, const Int_t *binMap=nullptr) const
	Input vector of measurements.
void	GetInputInverseEmatrix (TH2 *ematrix)
	Get inverse of the measurement's covariance matrix.
void	GetL (TH2 *l) const
	Get matrix of regularisation conditions.
virtual Double_t	GetLcurveX (void) const
	Get value on x-axis of L-curve determined in recent unfolding.
virtual Double_t	GetLcurveY (void) const
	Get value on y-axis of L-curve determined in recent unfolding.
void	GetLsquared (TH2 *lsquared) const
	Get matrix of regularisation conditions squared.
Int_t	GetNdf (void) const
	get number of degrees of freedom determined in recent unfolding
void	GetNormalisationVector (TH1 *s, const Int_t *binMap=nullptr) const
	Histogram of truth bins, determined from summing over the response matrix.
Int_t	GetNpar (void) const
	Get number of truth parameters determined in recent unfolding.
Int_t	GetNr (void) const
	Get number of regularisation conditions.
void	GetOutput (TH1 *output, const Int_t *binMap=nullptr) const
	Get output distribution, possibly cumulated over several bins.
void	GetProbabilityMatrix (TH2 *A, EHistMap histmap) const
	Get matrix of probabilities.
Double_t	GetRhoAvg (void) const
	get average global correlation determined in recent unfolding
Double_t	GetRhoI (TH1 *rhoi, const Int_t *binMap=nullptr, TH2 *invEmat=nullptr) const
	Get global correlation coefficients, possibly cumulated over several bins.
void	GetRhoIJ (TH2 *rhoij, const Int_t *binMap=nullptr) const
	Get correlation coefficients, possibly cumulated over several bins.
Double_t	GetRhoMax (void) const
	get maximum global correlation determined in recent unfolding
Double_t	GetTau (void) const
	Return regularisation parameter.
TClass *	IsA () const override
Int_t	RegularizeBins (int start, int step, int nbin, ERegMode regmode)
	Add regularisation conditions for a group of bins.
Int_t	RegularizeBins2D (int start_bin, int step1, int nbin1, int step2, int nbin2, ERegMode regmode)
	Add regularisation conditions for 2d unfolding.
Int_t	RegularizeCurvature (int left_bin, int center_bin, int right_bin, Double_t scale_left=1.0, Double_t scale_right=1.0)
	Add a regularisation condition on the curvature of three truth bin.
Int_t	RegularizeDerivative (int left_bin, int right_bin, Double_t scale=1.0)
	Add a regularisation condition on the difference of two truth bin.
Int_t	RegularizeSize (int bin, Double_t scale=1.0)
	Add a regularisation condition on the magnitude of a truth bin.
virtual Int_t	ScanLcurve (Int_t nPoint, Double_t tauMin, Double_t tauMax, TGraph **lCurve, TSpline **logTauX=nullptr, TSpline **logTauY=nullptr, TSpline **logTauCurvature=nullptr)
	Scan the L curve, determine tau and unfold at the final value of tau.
void	SetBias (const TH1 *bias)
	Set bias vector.
void	SetConstraint (EConstraint constraint)
	Set type of area constraint.
void	SetEpsMatrix (Double_t eps)
	set numerical accuracy for Eigenvalue analysis when inverting matrices with rank problems
virtual Int_t	SetInput (const TH1 *hist_y, Double_t scaleBias=0.0, Double_t oneOverZeroError=0.0, const TH2 *hist_vyy=nullptr, const TH2 *hist_vyy_inv=nullptr)
	Define input data for subsequent calls to DoUnfold(tau).
void	Streamer (TBuffer &) override
	Stream an object of class TObject.
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.
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	Clear (Option_t *="")
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 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 TObject *	DrawClone (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 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 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_t *	GetOption () 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)
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 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 TClass *	Class ()
static const char *	Class_Name ()
static constexpr Version_t	Class_Version ()
static const char *	DeclFileName ()
static const char *	GetTUnfoldVersion (void)
	Return a string describing the TUnfold version.
Static Public Member Functions inherited from TObject
static TClass *	Class ()
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 Member Functions
void	AddMSparse (TMatrixDSparse *dest, Double_t f, const TMatrixDSparse *src) const
	Add a sparse matrix, scaled by a factor, to another scaled matrix.
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.)
	Add a row of regularisation conditions to the matrix L.
Bool_t	AddRegularisationCondition (Int_t nEle, const Int_t *indices, const Double_t *rowData)
	Add a row of regularisation conditions to the matrix L.
void	ClearHistogram (TH1 *h, Double_t x=0.) const
	Initialize bin contents and bin errors for a given histogram.
virtual void	ClearResults (void)
	Reset all results.
TMatrixDSparse *	CreateSparseMatrix (Int_t nrow, Int_t ncol, Int_t nele, Int_t *row, Int_t *col, Double_t *data) const
	Create a sparse matrix, given the nonzero elements.
virtual Double_t	DoUnfold (void)
	Core unfolding algorithm.
void	ErrorMatrixToHist (TH2 *ematrix, const TMatrixDSparse *emat, const Int_t *binMap, Bool_t doClear) const
	Add up an error matrix, also respecting the bin mapping.
const TMatrixDSparse *	GetAx (void) const
	vector of folded-back result
Int_t	GetBinFromRow (int ix) const
	converts matrix row to truth histogram bin number
const TMatrixDSparse *	GetDXDAM (int i) const
	matrix contributions of the derivative dx/dA
const TMatrixDSparse *	GetDXDAZ (int i) const
	vector contributions of the derivative dx/dA
const TMatrixDSparse *	GetDXDtauSquared (void) const
	vector of derivative dx/dtauSquared, using internal bin counting
const TMatrixDSparse *	GetDXDY (void) const
	matrix of derivatives dx/dy
const TMatrixDSparse *	GetE (void) const
	matrix E, using internal bin counting
const TMatrixDSparse *	GetEinv (void) const
	matrix E-1, using internal bin counting
Int_t	GetNx (void) const
	returns internal number of output (truth) matrix rows
Int_t	GetNy (void) const
	returns the number of measurement bins
virtual TString	GetOutputBinName (Int_t iBinX) const
	Get bin name of an output bin.
Double_t	GetRhoIFromMatrix (TH1 *rhoi, const TMatrixDSparse *eOrig, const Int_t *binMap, TH2 *invEmat) const
	Get global correlation coefficients with arbitrary min map.
Int_t	GetRowFromBin (int ix) const
	converts truth histogram bin number to matrix row
const TMatrixDSparse *	GetVxx (void) const
	covariance matrix of the result
const TMatrixDSparse *	GetVxxInv (void) const
	inverse of covariance matrix of the result
const TMatrixDSparse *	GetVyyInv (void) const
	inverse of covariance matrix of the data y
const TMatrixD *	GetX (void) const
	vector of the unfolding result
TMatrixDSparse *	InvertMSparseSymmPos (const TMatrixDSparse *A, Int_t *rank) const
	Get the inverse or pseudo-inverse of a positive, sparse matrix.
TMatrixDSparse *	MultiplyMSparseM (const TMatrixDSparse *a, const TMatrixD *b) const
	Multiply sparse matrix and a non-sparse matrix.
TMatrixDSparse *	MultiplyMSparseMSparse (const TMatrixDSparse *a, const TMatrixDSparse *b) const
	Multiply two sparse matrices.
TMatrixDSparse *	MultiplyMSparseMSparseTranspVector (const TMatrixDSparse *m1, const TMatrixDSparse *m2, const TMatrixTBase< Double_t > *v) const
	Calculate a sparse matrix product \( M1*V*M2^{T} \) where the diagonal matrix V is given by a vector.
TMatrixDSparse *	MultiplyMSparseTranspMSparse (const TMatrixDSparse *a, const TMatrixDSparse *b) const
	Multiply a transposed Sparse matrix with another sparse matrix,.
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	DeleteMatrix (TMatrixD **m)
	delete matrix and invalidate pointer
static void	DeleteMatrix (TMatrixDSparse **m)
	delete sparse matrix and invalidate pointer

Protected Attributes
TMatrixDSparse *	fA
	response matrix A
Double_t	fBiasScale
	scale factor for the bias
EConstraint	fConstraint
	type of constraint to use for the unfolding
TArrayI	fHistToX
	mapping of histogram bins to matrix indices
TMatrixDSparse *	fL
	regularisation conditions L
ERegMode	fRegMode
	type of regularisation
TArrayD	fSumOverY
	truth vector calculated from the non-normalized response matrix
Double_t	fTauSquared
	regularisation parameter tau squared
TMatrixDSparse *	fVyy
	covariance matrix Vyy corresponding to y
TMatrixD *	fX0
	bias vector x0
TArrayI	fXToHist
	mapping of matrix indices to histogram bins
TMatrixD *	fY
	input (measured) data y

Private Member Functions
void	InitTUnfold (void)
	Initialize data members, for use in constructors.

Private Attributes
TMatrixDSparse *	fAx
	result x folded back A*x
Double_t	fChi2A
	chi**2 contribution from (y-Ax)Vyy-1(y-Ax)
TMatrixDSparse *	fDXDAM [2]
	matrix contribution to the of derivative dx_k/dA_ij
TMatrixDSparse *	fDXDAZ [2]
	vector contribution to the of derivative dx_k/dA_ij
TMatrixDSparse *	fDXDtauSquared
	derivative of the result wrt tau squared
TMatrixDSparse *	fDXDY
	derivative of the result wrt dx/dy
TMatrixDSparse *	fE
	matrix E
TMatrixDSparse *	fEinv
	matrix E^(-1)
Double_t	fEpsMatrix
	machine accuracy used to determine matrix rank after eigenvalue analysis
Int_t	fIgnoredBins
	number of input bins which are dropped because they have error=0
Double_t	fLXsquared
	chi**2 contribution from (x-s*x0)TLTL(x-s*x0)
Int_t	fNdf
	number of degrees of freedom
Double_t	fRhoAvg
	average global correlation coefficient
Double_t	fRhoMax
	maximum global correlation coefficient
TMatrixDSparse *	fVxx
	covariance matrix Vxx
TMatrixDSparse *	fVxxInv
	inverse of covariance matrix Vxx-1
TMatrixDSparse *	fVyyInv
	inverse of the input covariance matrix Vyy-1
TMatrixD *	fX
	unfolding result x

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

#include <TUnfold.h>

Inheritance diagram for TUnfold:

Member Enumeration Documentation

EConstraint

enum TUnfold::EConstraint

type of extra constraint

Enumerator
kEConstraintNone	use no extra constraint
kEConstraintArea	enforce preservation of the area

Definition at line 109 of file TUnfold.h.

EHistMap

enum TUnfold::EHistMap

arrangement of axes for the response matrix (TH2 histogram)

Enumerator
kHistMapOutputHoriz	truth level on x-axis of the response matrix
kHistMapOutputVert	truth level on y-axis of the response matrix

Definition at line 139 of file TUnfold.h.

ERegMode

enum TUnfold::ERegMode

choice of regularisation scheme

Enumerator
kRegModeNone	no regularisation, or defined later by RegularizeXXX() methods
kRegModeSize	regularise the amplitude of the output distribution
kRegModeDerivative	regularize the 1st derivative of the output distribution
kRegModeCurvature	regularize the 2nd derivative of the output distribution
kRegModeMixed	mixed regularisation pattern

Definition at line 119 of file TUnfold.h.

Constructor & Destructor Documentation

TUnfold() [1/2]

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

Set up response matrix and regularisation scheme.

Parameters

[in]	hist_A	matrix of MC events that describes the migrations
[in]	histmap	mapping of the histogram axes
[in]	regmode	(default=kRegModeSize) global regularisation mode
[in]	constraint	(default=kEConstraintArea) type of constraint

Treatment of overflow bins in the matrix hist_A

• Events reconstructed in underflow or overflow bins are counted as inefficiency. They have to be filled properly.
• Events where the truth level is in underflow or overflow bins are treated as a part of the generator level distribution. The full truth level distribution (including underflow and overflow) is unfolded.

If unsure, do the following:

• store evens where the truth is in underflow or overflow (sometimes called "fakes") in a separate TH1. Ensure that the truth-level underflow and overflow bins of hist_A are all zero.
• the fakes are background to the measurement. Use the classes TUnfoldSys and TUnfoldDensity instead of the plain TUnfold for subtracting background.

Definition at line 1716 of file TUnfold.cxx.

TUnfold() [2/2]

TUnfold::TUnfold

(

void

)

Only for use by root streamer or derived classes.

Definition at line 249 of file TUnfold.cxx.

~TUnfold()

TUnfold::~TUnfold ( void  )

override

Definition at line 133 of file TUnfold.cxx.

Member Function Documentation

AddMSparse()

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

protected

Add a sparse matrix, scaled by a factor, to another scaled matrix.

Parameters

[in,out]	dest	destination matrix
[in]	f	scaling factor
[in]	src	matrix to be added to dest

a replacement for

(*dest) += f * (*src)

which suffered from a bug in old root versions.

Definition at line 931 of file TUnfold.cxx.

AddRegularisationCondition() [1/2]

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

Add a row of regularisation conditions to the matrix L.

Parameters

[in]	i0	truth histogram bin number
[in]	f0	entry in the matrix L, column i0
[in]	i1	truth histogram bin number
[in]	f1	entry in the matrix L, column i1
[in]	i2	truth histogram bin number
[in]	f2	entry in the matrix L, column i2

the arguments are used to form one row (k) of the matrix L, where \( L_{k,i0}=f0 \) and \( L_{k,i1}=f1 \) and \( L_{k,i2}=f2 \) negative indexes i0,i1,i2 are ignored.

Definition at line 1936 of file TUnfold.cxx.

AddRegularisationCondition() [2/2]

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

protected

Add a row of regularisation conditions to the matrix L.

Parameters

[in]	nEle	number of valid entries in indices and rowData
[in]	indices	column numbers of L to fill
[in]	rowData	data to fill into the new row of L

returns true if a row was added, false otherwise

A new row k is added to the matrix L, its dimension is expanded. The new elements \( L_{ki} \) are filled from the array rowData[] where the indices i which are taken from the array indices[].

Definition at line 1974 of file TUnfold.cxx.

Class()

static TClass * TUnfold::Class ( )

static

Returns

TClass describing this class

Class_Name()

static const char * TUnfold::Class_Name ( )

static

Returns

Name of this class

Class_Version()

static constexpr Version_t TUnfold::Class_Version ( )

inlinestaticconstexpr

Returns

Version of this class

Definition at line 341 of file TUnfold.h.

ClearHistogram()

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

protected

Initialize bin contents and bin errors for a given histogram.

Parameters

[out]	h	histogram
[in]	x	new histogram content

all histgram errors are set to zero, all contents are set to x

Definition at line 3644 of file TUnfold.cxx.

ClearResults()

void TUnfold::ClearResults ( void  )

protectedvirtual

Reset all results.

Reimplemented in TUnfoldSys.

Definition at line 219 of file TUnfold.cxx.

CreateSparseMatrix()

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

protected

Create a sparse matrix, given the nonzero elements.

Parameters

[in]	nrow	number of rows
[in]	ncol	number of columns
[in]	nel	number of non-zero elements
[in]	row	row indexes of non-zero elements
[in]	col	column indexes of non-zero elements
[in]	data	non-zero elements data

return pointer to a new sparse matrix

shortcut to new TMatrixDSparse() followed by SetMatrixArray().

Definition at line 592 of file TUnfold.cxx.

DeclFileName()

static const char * TUnfold::DeclFileName ( )

inlinestatic

Returns

Name of the file containing the class declaration

Definition at line 341 of file TUnfold.h.

DeleteMatrix() [1/2]

void TUnfold::DeleteMatrix ( TMatrixD **  m )

staticprotected

delete matrix and invalidate pointer

Delete matrix and invalidate pointer.

Parameters

[in,out]

m

pointer to a matrix-pointer

If the matrix pointer os non-zero, the matrix id deleted. The matrix pointer is set to zero.

Definition at line 196 of file TUnfold.cxx.

DeleteMatrix() [2/2]

void TUnfold::DeleteMatrix ( TMatrixDSparse **  m )

staticprotected

delete sparse matrix and invalidate pointer

Delete sparse matrix and invalidate pointer.

Parameters

[in,out]

m

pointer to a matrix-pointer

if the matrix pointer os non-zero, the matrix id deleted. The matrix pointer is set to zero.

Definition at line 210 of file TUnfold.cxx.

DoUnfold() [1/3]

Double_t TUnfold::DoUnfold ( Double_t  tau )

virtual

Perform the unfolding for a given regularisation parameter tau.

Parameters

[in]

tau

regularisation parameter

This method sets tau and then calls the core unfolding algorithm required data members:

• fA: matrix to relate x and y
• fY: measured data points
• fX0: bias on x
• fBiasScale: scale factor for fX0
• fV: inverse of covariance matrix for y
• fL: regularisation conditions modified data members:
• fTauSquared and those documented in DoUnfold(void)

Definition at line 2518 of file TUnfold.cxx.

DoUnfold() [2/3]

Double_t TUnfold::DoUnfold	(	Double_t	tau_reg,
		const TH1 *	input,
		Double_t	scaleBias = 0.0
	)

Perform the unfolding for a given input and regularisation.

Parameters

[in]	tau_reg	regularisation parameter
[in]	input	input distribution with uncertainties
[in]	scaleBias	(default=0.0) scale factor applied to the bias

This is a shortcut for { SetInput(input,scaleBias); DoUnfold(tau); }

Data members required:

• fA, fX0, fL Data members modified:
• those documented in SetInput() and those documented in DoUnfold(Double_t) Return value:
• maximum global correlation coefficient NOTE!!! return value >=1.0 means error, and the result is junk

Overflow bins of the input distribution are ignored!

Definition at line 2266 of file TUnfold.cxx.

DoUnfold() [3/3]

Double_t TUnfold::DoUnfold ( void  )

protectedvirtual

Core unfolding algorithm.

Main unfolding algorithm. Declared virtual, because other algorithms could be implemented

Purpose: unfold y -> x

• Data members required:
  • fA: matrix to relate x and y
  • fY: measured data points
  • fX0: bias on x
  • fBiasScale: scale factor for fX0
  • fVyy: covariance matrix for y
  • fL: regularisation conditions
  • fTauSquared: regularisation strength
  • fConstraint: whether the constraint is applied
• Data members modified:
  • fVyyInv: inverse of input data covariance matrix
  • fNdf: number of degrees of freedom
  • fEinv: inverse of the matrix needed for unfolding calculations
  • fE: the matrix needed for unfolding calculations
  • fX: unfolded data points
  • fDXDY: derivative of x wrt y (for error propagation)
  • fVxx: error matrix (covariance matrix) on x
  • fAx: estimate of distribution y from unfolded data
  • fChi2A: contribution to chi**2 from y-Ax
  • fChi2L: contribution to chi**2 from L*(x-x0)
  • fDXDtauSquared: derivative of x wrt tau
  • fDXDAM[0,1]: matrix parts of derivative x wrt A
  • fDXDAZ[0,1]: vector parts of derivative x wrt A
  • fRhoMax: maximum global correlation coefficient
  • fRhoAvg: average global correlation coefficient
• Return code:
  • fRhoMax if(fRhoMax>=1.0) then the unfolding has failed!

Definition at line 291 of file TUnfold.cxx.

ErrorMatrixToHist()

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

protected

Add up an error matrix, also respecting the bin mapping.

Parameters

[in,out]	ematrix	error matrix histogram
[in]	emat	error matrix stored with internal mapping (member fXToHist)
[in]	binMap	mapping of histogram bins
[in]	doClear	if true, ematrix is cleared prior to adding elements of emat to it.

the array binMap is explained with the method GetOutput(). The matrix emat must have dimension NxN where N=fXToHist.size() The flag doClear may be used to add covariance matrices from several uncertainty sources.

Definition at line 3344 of file TUnfold.cxx.

GetAx()

const TMatrixDSparse * TUnfold::GetAx ( void  ) const

inlineprotected

vector of folded-back result

Definition at line 244 of file TUnfold.h.

GetBias()

void TUnfold::GetBias	(	TH1 *	out,
		const Int_t *	binMap = nullptr
	)		const

Get bias vector including bias scale.

Parameters

[out]	out	histogram to store the scaled bias vector. The bin contents are overwritten
[in]	binMap	(default=0) array for mapping truth bins to histogram bins

This method returns the bias vector times scaling factor, f*x_{0}

The use of binMap is explained with the documentation of the GetOutput() method

Definition at line 2923 of file TUnfold.cxx.

GetBinFromRow()

Int_t TUnfold::GetBinFromRow ( int  ix ) const

inlineprotected

converts matrix row to truth histogram bin number

Definition at line 232 of file TUnfold.h.

GetChi2A()

Double_t TUnfold::GetChi2A ( void  ) const

inline

get χ²_A contribution determined in recent unfolding

Definition at line 313 of file TUnfold.h.

GetChi2L()

Double_t TUnfold::GetChi2L

(

void

)

const

Get \( chi^{2}_{L} \) contribution determined in recent unfolding.

Definition at line 3195 of file TUnfold.cxx.

GetDXDAM()

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

inlineprotected

matrix contributions of the derivative dx/dA

Definition at line 248 of file TUnfold.h.

GetDXDAZ()

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

inlineprotected

vector contributions of the derivative dx/dA

Definition at line 250 of file TUnfold.h.

GetDXDtauSquared()

const TMatrixDSparse * TUnfold::GetDXDtauSquared ( void  ) const

inlineprotected

vector of derivative dx/dtauSquared, using internal bin counting

Definition at line 261 of file TUnfold.h.

GetDXDY()

const TMatrixDSparse * TUnfold::GetDXDY ( void  ) const

inlineprotected

matrix of derivatives dx/dy

Definition at line 246 of file TUnfold.h.

GetE()

const TMatrixDSparse * TUnfold::GetE ( void  ) const

inlineprotected

matrix E, using internal bin counting

Definition at line 254 of file TUnfold.h.

GetEinv()

const TMatrixDSparse * TUnfold::GetEinv ( void  ) const

inlineprotected

matrix E^-1, using internal bin counting

Definition at line 252 of file TUnfold.h.

GetEmatrix()

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

Get output covariance matrix, possibly cumulated over several bins.

Parameters

[out]	ematrix	histogram to store the covariance. The bin contents are overwritten.
[in]	binMap	(default=0) array for mapping truth bins to histogram bins

The use of binMap is explained with the documentation of the GetOutput() method

Definition at line 3411 of file TUnfold.cxx.

GetEpsMatrix()

Double_t TUnfold::GetEpsMatrix ( void  ) const

inline

get numerical accuracy for Eigenvalue analysis when inverting matrices with rank problems

Definition at line 336 of file TUnfold.h.

GetFoldedOutput()

void TUnfold::GetFoldedOutput	(	TH1 *	out,
		const Int_t *	binMap = nullptr
	)		const

Get unfolding result on detector level.

Parameters

[out]	out	histogram to store the correlation coefficients. The bin contents and errors are overwritten.
[in]	binMap	(default=0) array for mapping truth bins to histogram bins

This method returns the unfolding output folded by the response matrix, i.e. the vector Ax.

The use of binMap is explained with the documentation of the GetOutput() method

Definition at line 2949 of file TUnfold.cxx.

GetInput()

void TUnfold::GetInput	(	TH1 *	out,
		const Int_t *	binMap = nullptr
	)		const

Input vector of measurements.

Parameters

[out]	out	histogram to store the measurements. Bin content and bin errors are overwrite.
[in]	binMap	(default=0) array for mapping truth bins to histogram bins

Bins which had an uncertainty of zero in the call to SetInput() may acquire bin contents or bin errors different from the original settings in SetInput().

The use of binMap is explained with the documentation of the GetOutput() method

Definition at line 3032 of file TUnfold.cxx.

GetInputInverseEmatrix()

void TUnfold::GetInputInverseEmatrix

(

TH2 *

out

)

Get inverse of the measurement's covariance matrix.

Parameters

[out]

out

histogram to store the inverted covariance

Definition at line 3061 of file TUnfold.cxx.

GetL()

void TUnfold::GetL

(

TH2 *

out

)

const

Get matrix of regularisation conditions.

Parameters

[out]

out

histogram to store the regularisation conditions. the bin contents are overwritten

The histogram should have dimension nr (x-axis) times nx (y-axis). nr corresponds to the number of regularisation conditions, it can be obtained using the method GetNr(). nx corresponds to the number of histogram bins in the response matrix along the truth axis.

Definition at line 3154 of file TUnfold.cxx.

GetLcurveX()

Double_t TUnfold::GetLcurveX ( void  ) const

virtual

Get value on x-axis of L-curve determined in recent unfolding.

\( x=log_{10}(GetChi2A()) \)

Definition at line 3217 of file TUnfold.cxx.

GetLcurveY()

Double_t TUnfold::GetLcurveY ( void  ) const

virtual

Get value on y-axis of L-curve determined in recent unfolding.

\( y=log_{10}(GetChi2L()) \)

Definition at line 3227 of file TUnfold.cxx.

GetLsquared()

void TUnfold::GetLsquared

(

TH2 *

out

)

const

Get matrix of regularisation conditions squared.

Parameters

[out]

out

histogram to store the squared matrix of regularisation conditions. the bin contents are overwritten

This returns the square matrix L^{T}L as a histogram

The histogram should have dimension nx times nx, where nx corresponds to the number of histogram bins in the response matrix along the truth axis.

Definition at line 3114 of file TUnfold.cxx.

GetNdf()

Int_t TUnfold::GetNdf ( void  ) const

inline

get number of degrees of freedom determined in recent unfolding

This returns the number of valid measurements minus the number of unfolded truth bins. If the area constraint is active, one further degree of freedom is subtracted

Definition at line 323 of file TUnfold.h.

GetNormalisationVector()

void TUnfold::GetNormalisationVector	(	TH1 *	out,
		const Int_t *	binMap = nullptr
	)		const

Histogram of truth bins, determined from summing over the response matrix.

Parameters

[out]	out	histogram to store the truth bins. The bin contents are overwritten
[in]	binMap	(default=0) array for mapping truth bins to histogram bins

This vector is also used to initialize the bias x_{0}. However, the bias vector may be changed using the SetBias() method.

The use of binMap is explained with the documentation of the GetOutput() method.

Definition at line 2899 of file TUnfold.cxx.

GetNpar()

Int_t TUnfold::GetNpar

(

void

)

const

Get number of truth parameters determined in recent unfolding.

empty bins of the response matrix or bins which can not be unfolded due to rank deficits are not counted

Definition at line 3207 of file TUnfold.cxx.

GetNr()

Int_t TUnfold::GetNr

(

void

)

const

Get number of regularisation conditions.

This returns the number of regularisation conditions, useful for booking a histogram for a subsequent call of GetL().

Definition at line 3139 of file TUnfold.cxx.

GetNx()

Int_t TUnfold::GetNx ( void  ) const

inlineprotected

returns internal number of output (truth) matrix rows

Definition at line 226 of file TUnfold.h.

GetNy()

Int_t TUnfold::GetNy ( void  ) const

inlineprotected

returns the number of measurement bins

Definition at line 234 of file TUnfold.h.

GetOutput()

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

Get output distribution, possibly cumulated over several bins.

Parameters

[out]	output	existing output histogram. content and errors will be updated.
[in]	binMap	(default=0) array for mapping truth bins to histogram bins

If nonzero, the array binMap must have dimension n+2, where n corresponds to the number of bins on the truth axis of the response matrix (the histogram specified with the TUnfold constructor). The indexes of binMap correspond to the truth bins (including underflow and overflow) of the response matrix. The element binMap[i] specifies the histogram number in output where the corresponding truth bin will be stored. It is possible to specify the same output bin number for multiple indexes, in which case these bins are added. Set binMap[i]=-1 to ignore an unfolded truth bin. The uncertainties are calculated from the corresponding parts of the covariance matrix, properly taking care of added truth bins.

If the pointer binMap is zero, the bins are mapped one-to-one. Truth bin zero (underflow) is stored in the output underflow, truth bin 1 is stored in bin number 1, etc.

• output: output histogram
• binMap: for each bin of the original output distribution specify the destination bin. A value of -1 means that the bin is discarded. 0 means underflow bin, 1 first bin, ...
  • binMap[0] : destination of underflow bin
  • binMap[1] : destination of first bin ...

Definition at line 3264 of file TUnfold.cxx.

GetOutputBinName()

TString TUnfold::GetOutputBinName ( Int_t  iBinX ) const

protectedvirtual

Get bin name of an output bin.

Parameters

[in]

iBinX

bin number

Return value: name of the bin

For TUnfold and TUnfoldSys, this function simply returns the bin number as a string. This function really only makes sense in the context of TUnfoldDensity, where binning schemes are implemented using the class TUnfoldBinning, and non-trivial bin names are returned.

Reimplemented in TUnfoldDensity.

Definition at line 1685 of file TUnfold.cxx.

GetProbabilityMatrix()

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

Get matrix of probabilities.

Parameters

[out]	A	two-dimensional histogram to store the probabilities (normalized response matrix). The bin contents are overwritten
[in]	histmap	specify axis along which the truth bins are oriented

Definition at line 2997 of file TUnfold.cxx.

GetRhoAvg()

Double_t TUnfold::GetRhoAvg ( void  ) const

inline

get average global correlation determined in recent unfolding

Definition at line 311 of file TUnfold.h.

GetRhoI()

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

Get global correlation coefficients, possibly cumulated over several bins.

Parameters

[out]	rhoi	histogram to store the global correlation coefficients. The bin contents are overwritten.
[in]	binMap	(default=0) array for mapping truth bins to histogram bins
[out]	invEmat	(default=0) histogram to store the inverted covariance matrix

for a given bin, the global correlation coefficient is defined as \( \rho_{i} = \sqrt{1-\frac{1}{(V_{ii}*V^{-1}_{ii})}} \)

such that the calculation of global correlation coefficients possibly involves the inversion of a covariance matrix.

return value: maximum global correlation coefficient

The use of binMap is explained with the documentation of the GetOutput() method

Definition at line 3467 of file TUnfold.cxx.

GetRhoIFromMatrix()

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

protected

Get global correlation coefficients with arbitrary min map.

• rhoi: global correlation histogram
• emat: error matrix
• binMap: for each bin of the original output distribution specify the destination bin. A value of -1 means that the bin is discarded. 0 means underflow bin, 1 first bin, ...
  • binMap[0] : destination of underflow bin
  • binMap[1] : destination of first bin ... return value: maximum global correlation

Definition at line 3529 of file TUnfold.cxx.

GetRhoIJ()

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

Get correlation coefficients, possibly cumulated over several bins.

Parameters

[out]	rhoij	histogram to store the correlation coefficients. The bin contents are overwritten.
[in]	binMap	(default=0) array for mapping truth bins to histogram bins

The use of binMap is explained with the documentation of the GetOutput() method

Definition at line 3426 of file TUnfold.cxx.

GetRhoMax()

Double_t TUnfold::GetRhoMax ( void  ) const

inline

get maximum global correlation determined in recent unfolding

Definition at line 309 of file TUnfold.h.

GetRowFromBin()

Int_t TUnfold::GetRowFromBin ( int  ix ) const

inlineprotected

converts truth histogram bin number to matrix row

Definition at line 230 of file TUnfold.h.

GetTau()

Double_t TUnfold::GetTau

(

void

)

const

Return regularisation parameter.

Definition at line 3186 of file TUnfold.cxx.

GetTUnfoldVersion()

const char * TUnfold::GetTUnfoldVersion ( void  )

static

Return a string describing the TUnfold version.

The version is reported in the form Vmajor.minor Changes of the minor version number typically correspond to bug-fixes. Changes of the major version may result in adding or removing data attributes, such that the streamer methods are not compatible between different major versions.

Definition at line 3681 of file TUnfold.cxx.

GetVxx()

const TMatrixDSparse * TUnfold::GetVxx ( void  ) const

inlineprotected

covariance matrix of the result

Definition at line 240 of file TUnfold.h.

GetVxxInv()

const TMatrixDSparse * TUnfold::GetVxxInv ( void  ) const

inlineprotected

inverse of covariance matrix of the result

Definition at line 242 of file TUnfold.h.

GetVyyInv()

const TMatrixDSparse * TUnfold::GetVyyInv ( void  ) const

inlineprotected

inverse of covariance matrix of the data y

Definition at line 256 of file TUnfold.h.

GetX()

const TMatrixD * TUnfold::GetX ( void  ) const

inlineprotected

vector of the unfolding result

Definition at line 238 of file TUnfold.h.

InitTUnfold()

void TUnfold::InitTUnfold ( void  )

private

Initialize data members, for use in constructors.

Definition at line 150 of file TUnfold.cxx.

InvertMSparseSymmPos()

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

protected

Get the inverse or pseudo-inverse of a positive, sparse matrix.

Parameters

[in]	A	the sparse matrix to be inverted, has to be positive
[in,out]	rankPtr	if zero, suppress calculation of pseudo-inverse otherwise the rank of the matrix is returned in *rankPtr

return value: 0 or a new sparse matrix

• if(rankPtr==0) return the inverse if it exists, or return 0
• else return a (pseudo-)inverse and store the rank of the matrix in *rankPtr

the matrix inversion is optimized in performance for the case where a large submatrix of A is diagonal

Definition at line 1008 of file TUnfold.cxx.

IsA()

TClass * TUnfold::IsA ( ) const

inlineoverridevirtual

Returns

TClass describing current object

Reimplemented from TObject.

Reimplemented in TUnfoldDensity, and TUnfoldSys.

Definition at line 341 of file TUnfold.h.

MultiplyMSparseM()

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

protected

Multiply sparse matrix and a non-sparse matrix.

Parameters

[in]	a	sparse matrix
[in]	b	matrix

returns a new sparse matrix a*b. A replacement for: new TMatrixDSparse(a,TMatrixDSparse::kMult,b) the root implementation had problems in older versions of root.

Definition at line 774 of file TUnfold.cxx.

MultiplyMSparseMSparse()

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

protected

Multiply two sparse matrices.

Parameters

[in]	a	sparse matrix
[in]	b	sparse matrix

returns a new sparse matrix a*b.

A replacement for: new TMatrixDSparse(a,TMatrixDSparse::kMult,b) the root implementation had problems in older versions of root.

Definition at line 618 of file TUnfold.cxx.

MultiplyMSparseMSparseTranspVector()

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

protected

Calculate a sparse matrix product \( M1*V*M2^{T} \) where the diagonal matrix V is given by a vector.

Parameters

[in]	m1	pointer to sparse matrix with dimension I*K
[in]	m2	pointer to sparse matrix with dimension J*K
[in]	v	pointer to vector (matrix) with dimension K*1

returns a sparse matrix R with elements \( r_{ij}=\Sigma_{k}M1_{ik}V_{k}M2_{jk} \)

Definition at line 833 of file TUnfold.cxx.

MultiplyMSparseTranspMSparse()

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

protected

Multiply a transposed Sparse matrix with another sparse matrix,.

Parameters

[in]	a	sparse matrix (to be transposed)
[in]	b	sparse matrix

returns a new sparse matrix a^{T}*b

this is a replacement for the root constructors new TMatrixDSparse(TMatrixDSparse(TMatrixDSparse::kTransposed,*a), TMatrixDSparse::kMult,*b)

Definition at line 693 of file TUnfold.cxx.

RegularizeBins()

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

Add regularisation conditions for a group of bins.

Parameters

[in]	start	first bin number
[in]	step	step size
[in]	nbin	number of bins
[in]	regmode	regularisation mode (one of: kRegModeSize, kRegModeDerivative, kRegModeCurvature)

add regularisation conditions for a group of equidistant bins. There are nbin bins, starting with bin start and with a distance of step between bins.

Return value: number of regularisation conditions which could not be added.

Conditions which are not added typically correspond to bin numbers where the truth can not be unfolded (either response matrix is empty or the data do not constrain).

Definition at line 2162 of file TUnfold.cxx.

RegularizeBins2D()

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

Add regularisation conditions for 2d unfolding.

Parameters

[in]	start_bin	first bin number
[in]	step1	step size, 1st dimension
[in]	nbin1	number of bins, 1st dimension
[in]	step2	step size, 2nd dimension
[in]	nbin2	number of bins, 2nd dimension
[in]	regmode	regularisation mode (one of: kRegModeSize, kRegModeDerivative, kRegModeCurvature)

add regularisation conditions for a grid of bins. The start bin is start_bin. Along the first (second) dimension, there are nbin1 (nbin2) bins and adjacent bins are spaced by step1 (step2) units.

Return value: number of regularisation conditions which could not be added. Conditions which are not added typically correspond to bin numbers where the truth can not be unfolded (either response matrix is empty or the data do not constrain).

Definition at line 2223 of file TUnfold.cxx.

RegularizeCurvature()

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
	)

Add a regularisation condition on the curvature of three truth bin.

Parameters

[in]	left_bin	bin number
[in]	center_bin	bin number
[in]	right_bin	bin number
[in]	scale_left	(default=1) scale factor
[in]	scale_right	(default=1) scale factor

this adds one row to L, where the element left_bin takes the value -scale_left, the element right_bin takes the value -scale_right and the element center_bin takes the value scale_left+scale_right

return value: 0 if ok, 1 if the condition has not been added. Conditions which are not added typically correspond to bin numbers where the truth can not be unfolded (either response matrix is empty or the data do not constrain).

The RegularizeXXX() methods can be used to set up a custom matrix of regularisation conditions. In this case, start with an empty matrix L (argument regmode=kRegModeNone in the constructor)

Definition at line 2118 of file TUnfold.cxx.

RegularizeDerivative()

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

Add a regularisation condition on the difference of two truth bin.

Parameters

[in]	left_bin	bin number
[in]	right_bin	bin number
[in]	scale	(default=1) scale factor

this adds one row to L, where the element left_bin takes the value -scale and the element right_bin takes the value +scale

return value: 0 if ok, 1 if the condition has not been added. Conditions which are not added typically correspond to bin numbers where the truth can not be unfolded (either response matrix is empty or the data do not constrain).

The RegularizeXXX() methods can be used to set up a custom matrix of regularisation conditions. In this case, start with an empty matrix L (argument regmode=kRegModeNone in the constructor)

Definition at line 2079 of file TUnfold.cxx.

RegularizeSize()

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

Add a regularisation condition on the magnitude of a truth bin.

Parameters

[in]	bin	bin number
[in]	scale	(default=1) scale factor

this adds one row to L, where the element bin takes the value scale

return value: 0 if ok, 1 if the condition has not been added. Conditions which are not added typically correspond to bin numbers where the truth can not be unfolded (either response matrix is empty or the data do not constrain).

The RegularizeXXX() methods can be used to set up a custom matrix of regularisation conditions. In this case, start with an empty matrix L (argument regmode=kRegModeNone in the constructor)

Definition at line 2045 of file TUnfold.cxx.

ScanLcurve()

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

virtual

Scan the L curve, determine tau and unfold at the final value of tau.

Parameters

[in]	nPoint	number of points used for the scan
[in]	tauMin	smallest tau value to study
[in]	tauMax	largest tau value to study. If tauMin=tauMax=0, a scan interval is determined automatically.
[out]	lCurve	if nonzero, a new TGraph is returned, containing the L-curve
[out]	logTauX	if nonzero, a new TSpline is returned, to parameterize the L-curve's x-coordinates as a function of log10(tau)
[out]	logTauY	if nonzero, a new TSpline is returned, to parameterize the L-curve's y-coordinates as a function of log10(tau)
[out]	logTauCurvature	if nonzero, a new TSpline is returned of the L-curve curvature as a function of log10(tau)

return value: the coordinate number in the logTauX,logTauY graphs corresponding to the "final" choice of tau

Recommendation: always check logTauCurvature, it should be a peaked function (similar to a Gaussian), the maximum corresponding to the final choice of tau. Also, check the lCurve it should be approximately L-shaped. If in doubt, adjust tauMin and tauMax until the results are satisfactory.

Definition at line 2549 of file TUnfold.cxx.

SetBias()

void TUnfold::SetBias

(

const TH1 *

bias

)

Set bias vector.

Parameters

[in]

bias

histogram with new bias vector

the initial bias vector is determined from the response matrix but may be changed by using this method

Definition at line 1913 of file TUnfold.cxx.

SetConstraint()

void TUnfold::SetConstraint

(

EConstraint

constraint

)

Set type of area constraint.

results of a previous unfolding are reset

Definition at line 3174 of file TUnfold.cxx.

SetEpsMatrix()

void TUnfold::SetEpsMatrix

(

Double_t

eps

)

set numerical accuracy for Eigenvalue analysis when inverting matrices with rank problems

Definition at line 3667 of file TUnfold.cxx.

SetInput()

Int_t TUnfold::SetInput ( const TH1 *  input, Double_t  scaleBias = 0.0, Double_t  oneOverZeroError = 0.0, const TH2 *  hist_vyy = nullptr, const TH2 *  hist_vyy_inv = nullptr  )

virtual

Define input data for subsequent calls to DoUnfold(tau).

Parameters

[in]	input	input distribution with uncertainties
[in]	scaleBias	(default=0) scale factor applied to the bias
[in]	oneOverZeroError	(default=0) for bins with zero error, this number defines 1/error.
[in]	hist_vyy	(default=0) if non-zero, this defines the data covariance matrix
[in]	hist_vyy_inv	(default=0) if non-zero and hist_vyy is set, defines the inverse of the data covariance matrix. This feature can be useful for repeated unfoldings in cases where the inversion of the input covariance matrix is lengthy

Return value: nError1+10000*nError2

• nError1: number of bins where the uncertainty is zero. these bins either are not used for the unfolding (if oneOverZeroError==0) or 1/uncertainty is set to oneOverZeroError.
• nError2: return values>10000 are fatal errors, because the unfolding can not be done. The number nError2 corresponds to the number of truth bins which are not constrained by data points.

Data members modified:

• fY, fVyy, , fBiasScale Data members cleared
• fVyyInv, fNdf
• + see ClearResults

Reimplemented in TUnfoldSys.

Definition at line 2301 of file TUnfold.cxx.

Streamer()

void TUnfold::Streamer ( TBuffer &  R__b )

overridevirtual

Stream an object of class TObject.

Reimplemented from TObject.

Reimplemented in TUnfoldDensity, and TUnfoldSys.

StreamerNVirtual()

void TUnfold::StreamerNVirtual ( TBuffer &  ClassDef_StreamerNVirtual_b )

inline

Definition at line 341 of file TUnfold.h.

Member Data Documentation

fA

TMatrixDSparse* TUnfold::fA

protected

response matrix A

Definition at line 150 of file TUnfold.h.

fAx

TMatrixDSparse* TUnfold::fAx

private

result x folded back A*x

Definition at line 187 of file TUnfold.h.

fBiasScale

Double_t TUnfold::fBiasScale

protected

scale factor for the bias

Definition at line 158 of file TUnfold.h.

fChi2A

Double_t TUnfold::fChi2A

private

chi**2 contribution from (y-Ax)Vyy^-1(y-Ax)

Definition at line 189 of file TUnfold.h.

fConstraint

EConstraint TUnfold::fConstraint

protected

type of constraint to use for the unfolding

Definition at line 170 of file TUnfold.h.

fDXDAM

TMatrixDSparse* TUnfold::fDXDAM[2]

private

matrix contribution to the of derivative dx_k/dA_ij

Definition at line 199 of file TUnfold.h.

fDXDAZ

TMatrixDSparse* TUnfold::fDXDAZ[2]

private

vector contribution to the of derivative dx_k/dA_ij

Definition at line 201 of file TUnfold.h.

fDXDtauSquared

TMatrixDSparse* TUnfold::fDXDtauSquared

private

derivative of the result wrt tau squared

Definition at line 203 of file TUnfold.h.

fDXDY

TMatrixDSparse* TUnfold::fDXDY

private

derivative of the result wrt dx/dy

Definition at line 205 of file TUnfold.h.

fE

TMatrixDSparse* TUnfold::fE

private

matrix E

Definition at line 209 of file TUnfold.h.

fEinv

TMatrixDSparse* TUnfold::fEinv

private

matrix E^(-1)

Definition at line 207 of file TUnfold.h.

fEpsMatrix

Double_t TUnfold::fEpsMatrix

private

machine accuracy used to determine matrix rank after eigenvalue analysis

Definition at line 177 of file TUnfold.h.

fHistToX

TArrayI TUnfold::fHistToX

protected

mapping of histogram bins to matrix indices

Definition at line 166 of file TUnfold.h.

fIgnoredBins

Int_t TUnfold::fIgnoredBins

private

number of input bins which are dropped because they have error=0

Definition at line 175 of file TUnfold.h.

fL

TMatrixDSparse* TUnfold::fL

protected

regularisation conditions L

Definition at line 152 of file TUnfold.h.

fLXsquared

Double_t TUnfold::fLXsquared

private

chi**2 contribution from (x-s*x0)^TL^TL(x-s*x0)

Definition at line 191 of file TUnfold.h.

fNdf

Int_t TUnfold::fNdf

private

number of degrees of freedom

Definition at line 197 of file TUnfold.h.

fRegMode

ERegMode TUnfold::fRegMode

protected

type of regularisation

Definition at line 172 of file TUnfold.h.

fRhoAvg

Double_t TUnfold::fRhoAvg

private

average global correlation coefficient

Definition at line 195 of file TUnfold.h.

fRhoMax

Double_t TUnfold::fRhoMax

private

maximum global correlation coefficient

Definition at line 193 of file TUnfold.h.

fSumOverY

TArrayD TUnfold::fSumOverY

protected

truth vector calculated from the non-normalized response matrix

Definition at line 168 of file TUnfold.h.

fTauSquared

Double_t TUnfold::fTauSquared

protected

regularisation parameter tau squared

Definition at line 162 of file TUnfold.h.

fVxx

TMatrixDSparse* TUnfold::fVxx

private

covariance matrix Vxx

Definition at line 181 of file TUnfold.h.

fVxxInv

TMatrixDSparse* TUnfold::fVxxInv

private

inverse of covariance matrix Vxx^-1

Definition at line 183 of file TUnfold.h.

fVyy

TMatrixDSparse* TUnfold::fVyy

protected

covariance matrix Vyy corresponding to y

Definition at line 156 of file TUnfold.h.

fVyyInv

TMatrixDSparse* TUnfold::fVyyInv

private

inverse of the input covariance matrix Vyy^-1

Definition at line 185 of file TUnfold.h.

fX

TMatrixD* TUnfold::fX

private

unfolding result x

Definition at line 179 of file TUnfold.h.

fX0

TMatrixD* TUnfold::fX0

protected

bias vector x0

Definition at line 160 of file TUnfold.h.

fXToHist

TArrayI TUnfold::fXToHist

protected

mapping of matrix indices to histogram bins

Definition at line 164 of file TUnfold.h.

fY

TMatrixD* TUnfold::fY

protected

input (measured) data y

Definition at line 154 of file TUnfold.h.