TUnfoldDensity Class Reference

An algorithm to unfold distributions from detector to truth level.

TUnfoldDensity is used to decompose a measurement y into several sources x, given the measurement uncertainties, background b 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, TUnfoldDensity has an adjustable regularisation term and also supports an optional constraint on the total number of events. Background sources can be specified, with a normalisation constant and normalisation uncertainty. In addition, variants of the response matrix may be specified, these are taken to determine systematic uncertainties. Complex, multidimensional arrangements of signal and background bins are managed with the help of the class TUnfoldBinning.

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 TUnfoldSys:

• Set up binning schemes for the truth and measured distributions. The binning schemes may be coded in the XML language, for reading use TUnfoldBinningXML.
• 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
• Repeated calls to SubtractBackground() to specify background sources
• Repeated calls to AddSysError() to specify systematic uncertainties
  • 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()
  • or multiple times in a scan to determine the best choice of tau, method ScanTau()
• Unfolding results are retrieved using various GetXXX() methods

A detailed documentation of the various GetXXX() methods to control systematic uncertainties is given with the method TUnfoldSys.

Why to use complex binning schemes

in literature on unfolding, the "standard" test case is a one-dimensional distribution without underflow or overflow bins. The migration matrix is almost diagonal.

This "standard" case is rarely realized for real problems.

Often one has to deal with multi-dimensional distributions. In addition, there are underflow and overflow bins or other background bins, possibly determined with the help of auxiliary measurements.

In TUnfoldDensity, such complex binning schemes are handled with the help of the class TUnfoldBinning. For both the measurement and the truth there is a tree structure. The tree nodes may correspond to single bins (e.g. nuisance parameters) or may hold multi-dimensional distributions.

For example, the "measurement" tree could have two leaves, one for the primary distribution and one for auxiliary measurements. Similarly, the "truth" tree could have two leaves, one for the signal and one for the background. Each of the leaves may then have a multi-dimensional distribution.

The class TUnfoldBinning takes care to map all bins of the "measurement" to a one-dimensional vector y. Similarly, the "truth" bins are mapped to the vector x.

How to choose the regularisation settings

In TUnfoldDensity, two methods are implemented to determine tau**2

1. ScanLcurve() locate the tau where the L-curve plot has a "kink" this function is implemented in the TUnfold class
2. ScanTau() finds the solution such that some variable (e.g. global correlation coefficient) is minimized. This function is implemented in the TUnfoldDensity class

Each of the algorithms has its own advantages and disadvantages. The algorithm (1) does not work if the input data are too similar to the MC prediction. Typical no-go cases of the L-curve scan are:

• the number of measurements is too small (e.g. ny=nx)
• the input data have no statistical fluctuations [identical MC events are used to fill the matrix of migrations and the vector y for a "closure test"]

The algorithm (2) only works if the variable does have a real minimum as a function of tau. If global correlations are minimized, the situation is as follows: The matrix of migration typically introduces negative correlations. The area constraint introduces some positive correlation. Regularisation on the "size" introduces no correlation. Regularisation on 1st or 2nd derivatives adds positive correlations.

For these reasons, "size" regularisation does not work well with the tau-scan: the higher tau, the smaller rho, but there is no minimum. As a result, large values of tau (too strong regularisation) are found. In contrast, the tau-scan is expected to work better with 1st or 2nd derivative regularisation, because at some point the negative correlations from migrations are approximately cancelled by the positive correlations from the regularisation conditions.

whichever algorithm is used, the output has to be checked:

1. The L-curve should have approximate L-shape and the final choice of tau should not be at the very edge of the scanned region
2. The scan result should have a well-defined minimum and the final choice of tau should sit right in the minimum

---

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, with updated doxygen comments and bug-fixes in TUnfoldBinning

History:

• Version 17.5, bug fix in TUnfold also corrects GetEmatrixSysUncorr()
• Version 17.4, in parallel to changes in TUnfoldBinning
• Version 17.3, in parallel to changes in TUnfoldBinning
• Version 17.2, with new options 'N' and 'c' for axis regularisation steering
• Version 17.1, add scan type RhoSquare, small bug fixes with useAxisBinning
• Version 17.0, support for density regularisation, complex binning schemes, tau scan

Definition at line 48 of file TUnfoldDensity.h.

Public Types
enum	EDensityMode { kDensityModeNone =0 , kDensityModeBinWidth =1 , kDensityModeUser =2 , kDensityModeBinWidthAndUser =3 }
	choice of regularisation scale factors to cinstruct the matrix L More...
enum	EScanTauMode {   kEScanTauRhoAvg =0 , kEScanTauRhoMax =1 , kEScanTauRhoAvgSys =2 , kEScanTauRhoMaxSys =3 ,   kEScanTauRhoSquareAvg =4 , kEScanTauRhoSquareAvgSys =5 }
	scan mode for correlation scan More...
Public Types inherited from TUnfoldSys
enum	ESysErrMode { kSysErrModeMatrix =0 , kSysErrModeShift =1 , kSysErrModeRelative =2 }
	type of matrix specified with AddSysError() More...
Public Types inherited from TUnfold
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
	TUnfoldDensity (const TH2 *hist_A, EHistMap histmap, ERegMode regmode=kRegModeCurvature, EConstraint constraint=kEConstraintArea, EDensityMode densityMode=kDensityModeBinWidthAndUser, const TUnfoldBinning *outputBins=nullptr, const TUnfoldBinning *inputBins=nullptr, const char *regularisationDistribution=nullptr, const char *regularisationAxisSteering="*[UOB]")
	Eet up response matrix A, uncorrelated uncertainties of A, regularisation scheme and binning schemes.
	TUnfoldDensity (void)
	Only for use by root streamer or derived classes.
	~TUnfoldDensity (void) override
TH1 *	GetBackground (const char *histogramName, const char *bgrSource=nullptr, const char *histogramTitle=nullptr, const char *distributionName=nullptr, const char *projectionMode=nullptr, Bool_t useAxisBinning=kTRUE, Int_t includeError=3) const
	Retrieve a background source in a new histogram.
TH1 *	GetBias (const char *histogramName, const char *histogramTitle=nullptr, const char *distributionName=nullptr, const char *projectionMode=nullptr, Bool_t useAxisBinning=kTRUE) const
	Retrieve bias vector as a new histogram.
TH1 *	GetDeltaSysBackgroundScale (const char *bgrSource, const char *histogramName, const char *histogramTitle=nullptr, const char *distributionName=nullptr, const char *projectionMode=nullptr, Bool_t useAxisBinning=kTRUE)
	Retrieve systematic 1-sigma shift corresponding to a background scale uncertainty.
TH1 *	GetDeltaSysSource (const char *source, const char *histogramName, const char *histogramTitle=nullptr, const char *distributionName=nullptr, const char *projectionMode=nullptr, Bool_t useAxisBinning=kTRUE)
	Retrieve a correlated systematic 1-sigma shift.
TH1 *	GetDeltaSysTau (const char *histogramName, const char *histogramTitle=nullptr, const char *distributionName=nullptr, const char *projectionMode=nullptr, Bool_t useAxisBinning=kTRUE)
	Retrieve 1-sigma shift corresponding to the previously specified uncertainty on tau.
TH2 *	GetEmatrixInput (const char *histogramName, const char *histogramTitle=nullptr, const char *distributionName=nullptr, const char *projectionMode=nullptr, Bool_t useAxisBinning=kTRUE)
	Get covariance contribution from the input uncertainties (data statistical uncertainties).
TH2 *	GetEmatrixSysBackgroundUncorr (const char *bgrSource, const char *histogramName, const char *histogramTitle=nullptr, const char *distributionName=nullptr, const char *projectionMode=nullptr, Bool_t useAxisBinning=kTRUE)
	Retrieve covariance contribution from uncorrelated background uncertainties.
TH2 *	GetEmatrixSysUncorr (const char *histogramName, const char *histogramTitle=nullptr, const char *distributionName=nullptr, const char *projectionMode=nullptr, Bool_t useAxisBinning=kTRUE)
	Retrieve covariance contribution from uncorrelated (statistical) uncertainties of the response matrix.
TH2 *	GetEmatrixTotal (const char *histogramName, const char *histogramTitle=nullptr, const char *distributionName=nullptr, const char *projectionMode=nullptr, Bool_t useAxisBinning=kTRUE)
	Get covariance matrix including all contributions.
TH1 *	GetFoldedOutput (const char *histogramName, const char *histogramTitle=nullptr, const char *distributionName=nullptr, const char *projectionMode=nullptr, Bool_t useAxisBinning=kTRUE, Bool_t addBgr=kFALSE) const
	Retrieve unfolding result folded back as a new histogram.
TH1 *	GetInput (const char *histogramName, const char *histogramTitle=nullptr, const char *distributionName=nullptr, const char *projectionMode=nullptr, Bool_t useAxisBinning=kTRUE) const
	Retrieve input distribution in a new histogram.
const TUnfoldBinning *	GetInputBinning (const char *distributionName=nullptr) const
	Locate a binning node for the input (measured) quantities.
TH2 *	GetL (const char *histogramName, const char *histogramTitle=nullptr, Bool_t useAxisBinning=kTRUE)
	Access matrix of regularisation conditions in a new histogram.
TUnfoldBinning *	GetLBinning (void) const
	return binning scheme for regularisation conditions (matrix L)
TH1 *	GetLxMinusBias (const char *histogramName, const char *histogramTitle=nullptr)
	Get regularisation conditions multiplied by result vector minus bias L(x-biasScale*biasVector).
TH1 *	GetOutput (const char *histogramName, const char *histogramTitle=nullptr, const char *distributionName=nullptr, const char *projectionMode=nullptr, Bool_t useAxisBinning=kTRUE) const
	retrieve unfolding result as a new histogram
const TUnfoldBinning *	GetOutputBinning (const char *distributionName=nullptr) const
	Locate a binning node for the unfolded (truth level) quantities.
TH2 *	GetProbabilityMatrix (const char *histogramName, const char *histogramTitle=nullptr, Bool_t useAxisBinning=kTRUE) const
	Get matrix of probabilities in a new histogram.
TH2 *	GetRhoIJtotal (const char *histogramName, const char *histogramTitle=nullptr, const char *distributionName=nullptr, const char *projectionMode=nullptr, Bool_t useAxisBinning=kTRUE)
	Retrieve correlation coefficients, including all uncertainties.
TH1 *	GetRhoIstatbgr (const char *histogramName, const char *histogramTitle=nullptr, const char *distributionName=nullptr, const char *projectionMode=nullptr, Bool_t useAxisBinning=kTRUE, TH2 **ematInv=nullptr)
	Retrieve global correlation coefficients including input (statistical) and background uncertainties.
TH1 *	GetRhoItotal (const char *histogramName, const char *histogramTitle=nullptr, const char *distributionName=nullptr, const char *projectionMode=nullptr, Bool_t useAxisBinning=kTRUE, TH2 **ematInv=nullptr)
	Retrieve global correlation coefficients including all uncertainty sources.
virtual Double_t	GetScanVariable (Int_t mode, const char *distribution, const char *projectionMode)
	Calculate the function for ScanTau().
TClass *	IsA () const override
void	RegularizeDistribution (ERegMode regmode, EDensityMode densityMode, const char *distribution, const char *axisSteering)
	Set up regularisation conditions.
virtual Int_t	ScanTau (Int_t nPoint, Double_t tauMin, Double_t tauMax, TSpline **scanResult, Int_t mode=kEScanTauRhoAvg, const char *distribution=nullptr, const char *projectionMode=nullptr, TGraph **lCurvePlot=nullptr, TSpline **logTauXPlot=nullptr, TSpline **logTauYPlot=nullptr)
	Scan a function wrt tau and determine the minimum.
void	Streamer (TBuffer &) override
	Stream an object of class TObject.
void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)
Public Member Functions inherited from TUnfoldSys
	TUnfoldSys (const TH2 *hist_A, EHistMap histmap, ERegMode regmode=kRegModeSize, EConstraint constraint=kEConstraintArea)
	Set up response matrix A, uncorrelated uncertainties of A and regularisation scheme.
	TUnfoldSys (void)
	Only for use by root streamer or derived classes.
	~TUnfoldSys (void) override
void	AddSysError (const TH2 *sysError, const char *name, EHistMap histmap, ESysErrMode mode)
	Specify a correlated systematic uncertainty.
void	GetBackground (TH1 *bgr, const char *bgrSource=nullptr, const Int_t *binMap=nullptr, Int_t includeError=3, Bool_t clearHist=kTRUE) const
	Get background into a histogram.
TSortedList *	GetBgrSources (void) const
	Get a new list of all background sources.
Double_t	GetChi2Sys (void)
	Calculate total chi**2 including all systematic errors.
Bool_t	GetDeltaSysBackgroundScale (TH1 *delta, const char *source, const Int_t *binMap=nullptr)
	Correlated one-sigma shifts from background normalisation uncertainty.
Bool_t	GetDeltaSysSource (TH1 *hist_delta, const char *source, const Int_t *binMap=nullptr)
	Correlated one-sigma shifts correspinding to a given systematic uncertainty.
Bool_t	GetDeltaSysTau (TH1 *delta, const Int_t *binMap=nullptr)
	Correlated one-sigma shifts from shifting tau.
void	GetEmatrixInput (TH2 *ematrix, const Int_t *binMap=nullptr, Bool_t clearEmat=kTRUE)
	Covariance matrix contribution from input measurement uncertainties.
void	GetEmatrixSysBackgroundScale (TH2 *ematrix, const char *source, const Int_t *binMap=nullptr, Bool_t clearEmat=kTRUE)
	Covariance contribution from background normalisation uncertainty.
void	GetEmatrixSysBackgroundUncorr (TH2 *ematrix, const char *source, const Int_t *binMap=nullptr, Bool_t clearEmat=kTRUE)
	Covariance contribution from background uncorrelated uncertainty.
void	GetEmatrixSysSource (TH2 *ematrix, const char *source, const Int_t *binMap=nullptr, Bool_t clearEmat=kTRUE)
	Covariance contribution from a systematic variation of the response matrix.
void	GetEmatrixSysTau (TH2 *ematrix, const Int_t *binMap=nullptr, Bool_t clearEmat=kTRUE)
	Covariance matrix contribution from error on regularisation parameter.
void	GetEmatrixSysUncorr (TH2 *ematrix, const Int_t *binMap=nullptr, Bool_t clearEmat=kTRUE)
	Covariance contribution from uncorrelated uncertainties of the response matrix.
void	GetEmatrixTotal (TH2 *ematrix, const Int_t *binMap=nullptr)
	Get total error matrix, summing up all contributions.
void	GetRhoItotal (TH1 *rhoi, const Int_t *binMap=nullptr, TH2 *invEmat=nullptr)
	Get global correlatiocn coefficients, summing up all contributions.
TSortedList *	GetSysSources (void) const
	Get a new list of all systematic uuncertainty sources.
TClass *	IsA () const override
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) override
	Define the input data for subsequent calls to DoUnfold(Double_t).
void	SetTauError (Double_t delta_tau)
	Specify an uncertainty on tau.
void	Streamer (TBuffer &) override
	Stream an object of class TObject.
void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)
void	SubtractBackground (const TH1 *hist_bgr, const char *name, Double_t scale=1.0, Double_t scale_error=0.0)
	Specify a source of background.
Public Member Functions inherited from TUnfold
	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.
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
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 Public Member Functions inherited from TUnfoldSys
static TClass *	Class ()
static const char *	Class_Name ()
static constexpr Version_t	Class_Version ()
static const char *	DeclFileName ()
Static Public Member Functions inherited from TUnfold
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
Double_t	GetDensityFactor (EDensityMode densityMode, Int_t iBin) const
	Density correction factor for a given bin.
TString	GetOutputBinName (Int_t iBinX) const override
	Get bin name of an output bin.
void	RegularizeDistributionRecursive (const TUnfoldBinning *binning, ERegMode regmode, EDensityMode densityMode, const char *distribution, const char *axisSteering)
	Recursively add regularisation conditions for this node and its children.
void	RegularizeOneDistribution (const TUnfoldBinning *binning, ERegMode regmode, EDensityMode densityMode, const char *axisSteering)
	Regularize the distribution of the given node.
Protected Member Functions inherited from TUnfoldSys
void	ClearResults (void) override
	Clear all data members which depend on the unfolding results.
void	DoBackgroundSubtraction (void)
	Perform background subtraction.
void	GetEmatrixFromVyy (const TMatrixDSparse *vyy, TH2 *ematrix, const Int_t *binMap, Bool_t clearEmat)
	Propagate an error matrix on the input vector to the unfolding result.
TMatrixDSparse *	GetSummedErrorMatrixXX (void)
	Determine total error matrix on the vector x.
TMatrixDSparse *	GetSummedErrorMatrixYY (void)
	Determine total error matrix on the vector Ax.
virtual TMatrixDSparse *	PrepareCorrEmat (const TMatrixDSparse *m1, const TMatrixDSparse *m2, const TMatrixDSparse *dsys)
	Propagate correlated systematic shift to an output vector.
virtual void	PrepareSysError (void)
	Matrix calculations required to propagate systematic errors.
virtual TMatrixDSparse *	PrepareUncorrEmat (const TMatrixDSparse *m1, const TMatrixDSparse *m2)
	Propagate uncorrelated systematic errors to a covariance matrix.
void	ScaleColumnsByVector (TMatrixDSparse *m, const TMatrixTBase< Double_t > *v) const
	Scale columns of a matrix by the corresponding rows of a vector.
void	VectorMapToHist (TH1 *hist_delta, const TMatrixDSparse *delta, const Int_t *binMap)
	Map delta to hist_delta, possibly summing up bins.
Protected Member Functions inherited from TUnfold
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.
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
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 ()

Protected Attributes
const TUnfoldBinning *	fConstInputBins
	binning scheme for the input (detector level)
const TUnfoldBinning *	fConstOutputBins
	binning scheme for the output (truth level)
TUnfoldBinning *	fOwnedInputBins
	pointer to input binning scheme if owned by this class
TUnfoldBinning *	fOwnedOutputBins
	pointer to output binning scheme if owned by this class
TUnfoldBinning *	fRegularisationConditions
	binning scheme for the regularisation conditions
Protected Attributes inherited from TUnfoldSys
TMatrixD *	fAoutside
	Input: underflow/overflow bins.
TMap *	fBgrErrScaleIn
	Input: background sources correlated error.
TMap *	fBgrErrUncorrInSq
	Input: uncorr error squared from bgr sources.
TMap *	fBgrIn
	Input: size of background sources.
TMatrixD *	fDAinColRelSq
	Input: normalized column err.sq. (inp.matr.)
TMatrixDSparse *	fDAinRelSq
	Input: normalized errors from input matrix.
TMap *	fDeltaCorrAx
	Result: syst.shift from fSysIn on fAx.
TMap *	fDeltaCorrX
	Result: syst.shift from fSysIn on fX.
TMatrixDSparse *	fDeltaSysTau
	Result: systematic shift from tau.
Double_t	fDtau
	Input: error on tau.
TMatrixDSparse *	fEmatUncorrAx
	Result: syst.error from fDA2 on fAx.
TMatrixDSparse *	fEmatUncorrX
	Result: syst.error from fDA2 on fX.
TMap *	fSysIn
	Input: correlated errors.
TMatrixDSparse *	fVyyData
	Input: error on fY prior to bgr subtraction.
TMatrixD *	fYData
	Input: fY prior to bgr subtraction.
Protected Attributes inherited from TUnfold
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

Additional Inherited Members
Protected Types inherited from TObject
enum	{ kOnlyPrepStep = (1ULL << ( 3 )) }
Static Protected Member Functions inherited from TUnfold
static void	DeleteMatrix (TMatrixD **m)
	delete matrix and invalidate pointer
static void	DeleteMatrix (TMatrixDSparse **m)
	delete sparse matrix and invalidate pointer

#include <TUnfoldDensity.h>

Inheritance diagram for TUnfoldDensity:

Member Enumeration Documentation

EDensityMode

enum TUnfoldDensity::EDensityMode

choice of regularisation scale factors to cinstruct the matrix L

Enumerator
kDensityModeNone	no scale factors, matrix L is similar to unity matrix
kDensityModeBinWidth	scale factors from multidimensional bin width
kDensityModeUser	scale factors from user function in TUnfoldBinning
kDensityModeBinWidthAndUser	scale factors from multidimensional bin width and user function

Definition at line 63 of file TUnfoldDensity.h.

EScanTauMode

enum TUnfoldDensity::EScanTauMode

scan mode for correlation scan

Enumerator
kEScanTauRhoAvg	average global correlation coefficient (from TUnfold::GetRhoI())
kEScanTauRhoMax	maximum global correlation coefficient (from TUnfold::GetRhoI())
kEScanTauRhoAvgSys	average global correlation coefficient (from TUnfoldSys::GetRhoItotal())
kEScanTauRhoMaxSys	maximum global correlation coefficient (from TUnfoldSys::GetRhoItotal())
kEScanTauRhoSquareAvg	average global correlation coefficient squared (from TUnfold::GetRhoI())
kEScanTauRhoSquareAvgSys	average global correlation coefficient squared (from TUnfoldSys::GetRhoItotal())

Definition at line 105 of file TUnfoldDensity.h.

Constructor & Destructor Documentation

TUnfoldDensity() [1/2]

TUnfoldDensity::TUnfoldDensity

(

void

)

Only for use by root streamer or derived classes.

Definition at line 177 of file TUnfoldDensity.cxx.

TUnfoldDensity() [2/2]

TUnfoldDensity::TUnfoldDensity	(	const TH2 *	hist_A,
		EHistMap	histmap,
		ERegMode	regmode = kRegModeCurvature,
		EConstraint	constraint = kEConstraintArea,
		EDensityMode	densityMode = kDensityModeBinWidthAndUser,
		const TUnfoldBinning *	outputBins = nullptr,
		const TUnfoldBinning *	inputBins = nullptr,
		const char *	regularisationDistribution = nullptr,
		const char *	regularisationAxisSteering = "*[UOB]"
	)

Eet up response matrix A, uncorrelated uncertainties of A, regularisation scheme and binning schemes.

Parameters

[in]	hist_A	matrix that describes the migrations
[in]	histmap	mapping of the histogram axes to the unfolding output
[in]	regmode	(default=kRegModeSize) global regularisation mode
[in]	constraint	(default=kEConstraintArea) type of constraint
[in]	densityMode	(default=kDensityModeBinWidthAndUser) regularisation scale factors to construct the matrix L
[in]	outputBins	(default=0) binning scheme for truth (unfolding output)
[in]	inputBins	(default=0) binning scheme for measurement (unfolding input)
[in]	regularisationDistribution	(default=0) selection of regularized distribution
[in]	regularisationAxisSteering	(default=0) detailed regularisation steering for selected distribution

The parameters hist_A, histmap, constraint are explained with the TUnfoldSys constructor.

The parameters outputBins,inputBins set the binning schemes. If these arguments are zero, simple binning schemes are constructed which correspond to the axes of the histogram hist_A.

The parameters regmode, densityMode, regularisationDistribution, regularisationAxisSteering together control how the initial matrix L of regularisation conditions is constructed. as explained in RegularizeDistribution().

Definition at line 217 of file TUnfoldDensity.cxx.

~TUnfoldDensity()

TUnfoldDensity::~TUnfoldDensity ( void  )

override

Definition at line 166 of file TUnfoldDensity.cxx.

Member Function Documentation

Class()

static TClass * TUnfoldDensity::Class ( )

static

Returns

TClass describing this class

Class_Name()

static const char * TUnfoldDensity::Class_Name ( )

static

Returns

Name of this class

Class_Version()

static constexpr Version_t TUnfoldDensity::Class_Version ( )

inlinestaticconstexpr

Returns

Version of this class

Definition at line 199 of file TUnfoldDensity.h.

DeclFileName()

static const char * TUnfoldDensity::DeclFileName ( )

inlinestatic

Returns

Name of the file containing the class declaration

Definition at line 199 of file TUnfoldDensity.h.

GetBackground()

TH1 * TUnfoldDensity::GetBackground	(	const char *	histogramName,
		const char *	bgrSource = nullptr,
		const char *	histogramTitle = nullptr,
		const char *	distributionName = nullptr,
		const char *	axisSteering = nullptr,
		Bool_t	useAxisBinning = kTRUE,
		Int_t	includeError = 3
	)		const

Retrieve a background source in a new histogram.

Parameters

[in]	histogramName	name of the histogram
[in]	bgrSource	the background source to retrieve
[in]	histogramTitle	(default=0) title of the histogram
[in]	distributionName	(default=0) identifier of the distribution to be extracted
[in]	axisSteering	(default=0) detailed steering within the extracted distribution
[in]	useAxisBinning	(default=true) if set to true, try to extract a histogram with proper binning and axis labels
[in]	includeError	(default=3) type of background errors to be included (+1 uncorrelated bgr errors, +2 correlated bgr errors)

returns a new histogram. See method GetOutput() for a detailed description of the arguments

Definition at line 758 of file TUnfoldDensity.cxx.

GetBias()

TH1 * TUnfoldDensity::GetBias	(	const char *	histogramName,
		const char *	histogramTitle = nullptr,
		const char *	distributionName = nullptr,
		const char *	axisSteering = nullptr,
		Bool_t	useAxisBinning = kTRUE
	)		const

Retrieve bias vector as a new histogram.

Parameters

[in]	histogramName	name of the histogram
[in]	histogramTitle	(default=0) title of the histogram
[in]	distributionName	(default=0) identifier of the distribution to be extracted
[in]	axisSteering	(default=0) detailed steering within the extracted distribution
[in]	useAxisBinning	(default=true) if set to true, try to extract a histogram with proper binning and axis labels

returns a new histogram. See method GetOutput() for a detailed description of the arguments

Definition at line 690 of file TUnfoldDensity.cxx.

GetDeltaSysBackgroundScale()

TH1 * TUnfoldDensity::GetDeltaSysBackgroundScale	(	const char *	bgrSource,
		const char *	histogramName,
		const char *	histogramTitle = nullptr,
		const char *	distributionName = nullptr,
		const char *	axisSteering = nullptr,
		Bool_t	useAxisBinning = kTRUE
	)

Retrieve systematic 1-sigma shift corresponding to a background scale uncertainty.

Parameters

[in]	bgrSource	identifier of the background
[in]	histogramName	name of the histogram
[in]	histogramTitle	(default=0) title of the histogram
[in]	distributionName	(default=0) identifier of the distribution to be extracted
[in]	axisSteering	(default=0) detailed steering within the extracted distribution
[in]	useAxisBinning	(default=true) if set to true, try to extract a histogram with proper binning and axis labels

returns a new histogram. See method GetOutput() for a detailed description of the arguments

Definition at line 954 of file TUnfoldDensity.cxx.

GetDeltaSysSource()

TH1 * TUnfoldDensity::GetDeltaSysSource	(	const char *	source,
		const char *	histogramName,
		const char *	histogramTitle = nullptr,
		const char *	distributionName = nullptr,
		const char *	axisSteering = nullptr,
		Bool_t	useAxisBinning = kTRUE
	)

Retrieve a correlated systematic 1-sigma shift.

Parameters

[in]	source	identifier of the systematic uncertainty source
[in]	histogramName	name of the histogram
[in]	histogramTitle	(default=0) title of the histogram
[in]	distributionName	(default=0) identifier of the distribution to be extracted
[in]	axisSteering	(default=0) detailed steering within the extracted distribution
[in]	useAxisBinning	(default=true) if set to true, try to extract a histogram with proper binning and axis labels

returns a new histogram. See method GetOutput() for a detailed description of the arguments

Definition at line 920 of file TUnfoldDensity.cxx.

GetDeltaSysTau()

TH1 * TUnfoldDensity::GetDeltaSysTau	(	const char *	histogramName,
		const char *	histogramTitle = nullptr,
		const char *	distributionName = nullptr,
		const char *	axisSteering = nullptr,
		Bool_t	useAxisBinning = kTRUE
	)

Retrieve 1-sigma shift corresponding to the previously specified uncertainty on tau.

Parameters

[in]	histogramName	name of the histogram
[in]	histogramTitle	(default=0) title of the histogram
[in]	distributionName	(default=0) identifier of the distribution to be extracted
[in]	axisSteering	(default=0) detailed steering within the extracted distribution
[in]	useAxisBinning	(default=true) if set to true, try to extract a histogram with proper binning and axis labels

returns a new histogram. See method GetOutput() for a detailed description of the arguments

Definition at line 987 of file TUnfoldDensity.cxx.

GetDensityFactor()

Double_t TUnfoldDensity::GetDensityFactor ( EDensityMode  densityMode, Int_t  iBin  ) const

protected

Density correction factor for a given bin.

Parameters

[in]	densityMode	type of factor to calculate
[in]	iBin	bin number

return a multiplicative factor, for scaling the regularisation conditions from this bin.

For densityMode=kDensityModeNone the factor is set to unity. For densityMode=kDensityModeBinWidth the factor is set to 1/binArea where the binArea is the product of the bin widths in all dimensions. If the width of a bin is zero or can not be determined, the factor is set to zero. For densityMode=kDensityModeUser the factor is determined from the method TUnfoldBinning::GetBinFactor(). For densityMode=kDensityModeBinWidthAndUser, the results of kDensityModeBinWidth and kDensityModeUser are multiplied.

Definition at line 332 of file TUnfoldDensity.cxx.

GetEmatrixInput()

TH2 * TUnfoldDensity::GetEmatrixInput	(	const char *	histogramName,
		const char *	histogramTitle = nullptr,
		const char *	distributionName = nullptr,
		const char *	axisSteering = nullptr,
		Bool_t	useAxisBinning = kTRUE
	)

Get covariance contribution from the input uncertainties (data statistical uncertainties).

Parameters

[in]	histogramName	name of the histogram
[in]	histogramTitle	(default=0) title of the histogram
[in]	distributionName	(default=0) identifier of the distribution to be extracted
[in]	axisSteering	(default=0) detailed steering within the extracted distribution
[in]	useAxisBinning	(default=true) if set to true, try to extract a histogram with proper binning and axis labels

returns a new histogram. See method GetOutput() for a detailed description of the arguments

Definition at line 1133 of file TUnfoldDensity.cxx.

GetEmatrixSysBackgroundUncorr()

TH2 * TUnfoldDensity::GetEmatrixSysBackgroundUncorr	(	const char *	bgrSource,
		const char *	histogramName,
		const char *	histogramTitle = nullptr,
		const char *	distributionName = nullptr,
		const char *	axisSteering = nullptr,
		Bool_t	useAxisBinning = kTRUE
	)

Retrieve covariance contribution from uncorrelated background uncertainties.

Parameters

[in]	bgrSource	identifier of the background
[in]	histogramName	name of the histogram
[in]	histogramTitle	(default=0) title of the histogram
[in]	distributionName	(default=0) identifier of the distribution to be extracted
[in]	axisSteering	(default=0) detailed steering within the extracted distribution
[in]	useAxisBinning	(default=true) if set to true, try to extract a histogram with proper binning and axis labels

returns a new histogram. See method GetOutput() for a detailed description of the arguments

Definition at line 1102 of file TUnfoldDensity.cxx.

GetEmatrixSysUncorr()

TH2 * TUnfoldDensity::GetEmatrixSysUncorr	(	const char *	histogramName,
		const char *	histogramTitle = nullptr,
		const char *	distributionName = nullptr,
		const char *	axisSteering = nullptr,
		Bool_t	useAxisBinning = kTRUE
	)

Retrieve covariance contribution from uncorrelated (statistical) uncertainties of the response matrix.

Parameters

[in]	histogramName	name of the histogram
[in]	histogramTitle	(default=0) title of the histogram
[in]	distributionName	(default=0) identifier of the distribution to be extracted
[in]	axisSteering	(default=0) detailed steering within the extracted distribution
[in]	useAxisBinning	(default=true) if set to true, try to extract a histogram with proper binning and axis labels

returns a new histogram. See method GetOutput() for a detailed description of the arguments

Definition at line 1071 of file TUnfoldDensity.cxx.

GetEmatrixTotal()

TH2 * TUnfoldDensity::GetEmatrixTotal	(	const char *	histogramName,
		const char *	histogramTitle = nullptr,
		const char *	distributionName = nullptr,
		const char *	axisSteering = nullptr,
		Bool_t	useAxisBinning = kTRUE
	)

Get covariance matrix including all contributions.

Parameters

[in]	histogramName	name of the histogram
[in]	histogramTitle	(default=0) title of the histogram
[in]	distributionName	(default=0) identifier of the distribution to be extracted
[in]	axisSteering	(default=0) detailed steering within the extracted distribution
[in]	useAxisBinning	(default=true) if set to true, try to extract a histogram with proper binning and axis labels

returns a new histogram. See method GetOutput() for a detailed description of the arguments

Definition at line 1185 of file TUnfoldDensity.cxx.

GetFoldedOutput()

TH1 * TUnfoldDensity::GetFoldedOutput	(	const char *	histogramName,
		const char *	histogramTitle = nullptr,
		const char *	distributionName = nullptr,
		const char *	axisSteering = nullptr,
		Bool_t	useAxisBinning = kTRUE,
		Bool_t	addBgr = kFALSE
	)		const

Retrieve unfolding result folded back as a new histogram.

Parameters

[in]	histogramName	name of the histogram
[in]	histogramTitle	(default=0) title of the histogram
[in]	distributionName	(default=0) identifier of the distribution to be extracted
[in]	axisSteering	(default=0) detailed steering within the extracted distribution
[in]	useAxisBinning	(default=true) if set to true, try to extract a histogram with proper binning and axis labels
[in]	addBgr	(default=false) if true, include the background contribution (useful for direct comparison to data)

returns a new histogram. See method GetOutput() for a detailed description of the arguments

Definition at line 722 of file TUnfoldDensity.cxx.

GetInput()

TH1 * TUnfoldDensity::GetInput	(	const char *	histogramName,
		const char *	histogramTitle = nullptr,
		const char *	distributionName = nullptr,
		const char *	axisSteering = nullptr,
		Bool_t	useAxisBinning = kTRUE
	)		const

Retrieve input distribution in a new histogram.

Parameters

[in]	histogramName	name of the histogram
[in]	histogramTitle	(default=0) title of the histogram
[in]	distributionName	(default=0) identifier of the distribution to be extracted
[in]	axisSteering	(default=0) detailed steering within the extracted distribution
[in]	useAxisBinning	(default=true) if set to true, try to extract a histogram with proper binning and axis labels

returns a new histogram. See method GetOutput() for a detailed description of the arguments

Definition at line 788 of file TUnfoldDensity.cxx.

GetInputBinning()

const TUnfoldBinning * TUnfoldDensity::GetInputBinning

(

const char *

distributionName = nullptr

)

const

Locate a binning node for the input (measured) quantities.

Parameters

[in]

distributionName

(default=0) distribution to look for. if zero, return the root node

returns: pointer to a TUnfoldBinning object or zero if not found

Definition at line 1289 of file TUnfoldDensity.cxx.

GetL()

TH2 * TUnfoldDensity::GetL	(	const char *	histogramName,
		const char *	histogramTitle = nullptr,
		Bool_t	useAxisBinning = kTRUE
	)

Access matrix of regularisation conditions in a new histogram.

Parameters

[in]	histogramName	name of the histogram
[in]	histogramTitle	(default=0) title of the histogram
[in]	useAxisBinning	(default=true) if set to true, try to extract a histogram with proper binning and axis labels

returns a new histogram. if histogramTitle is null, choose a title automatically.

Definition at line 1212 of file TUnfoldDensity.cxx.

GetLBinning()

TUnfoldBinning * TUnfoldDensity::GetLBinning ( void  ) const

inline

return binning scheme for regularisation conditions (matrix L)

Definition at line 197 of file TUnfoldDensity.h.

GetLxMinusBias()

TH1 * TUnfoldDensity::GetLxMinusBias	(	const char *	histogramName,
		const char *	histogramTitle = nullptr
	)

Get regularisation conditions multiplied by result vector minus bias L(x-biasScale*biasVector).

Parameters

[in]	histogramName	name of the histogram
[in]	histogramTitle	(default=0) title of the histogram

returns a new histogram. This is a measure of the level of regularization required per regularisation condition. If there are (negative or positive) spikes, these regularisation conditions dominate over the other regularisation conditions and may introduce the largest biases.

Definition at line 1250 of file TUnfoldDensity.cxx.

GetOutput()

TH1 * TUnfoldDensity::GetOutput	(	const char *	histogramName,
		const char *	histogramTitle = nullptr,
		const char *	distributionName = nullptr,
		const char *	axisSteering = nullptr,
		Bool_t	useAxisBinning = kTRUE
	)		const

retrieve unfolding result as a new histogram

Parameters

[in]	histogramName	name of the histogram
[in]	histogramTitle	(default=0) title of the histogram
[in]	distributionName	(default=0) identifier of the distribution to be extracted
[in]	axisSteering	(default=0) detailed steering within the extracted distribution
[in]	useAxisBinning	(default=true) if set to true, try to extract a histogram with proper binning and axis labels

return value: pointer to a new histogram. If useAxisBinning is set and if the selected distribution fits into a root histogram (1,2,3 dimensions) then return a histogram with the proper binning on each axis. Otherwise, return a 1D histogram with equidistant binning. If the histogram title is zero, a title is assigned automatically.

The axisSteering is defines as follows: "axis[mode];axis[mode];..." where:

• axis = name of an axis or *
• mode = any combination of the letters CUO0123456789
• C collapse axis into one bin (add up results). If any of the numbers 0-9 are given in addition, only these bins are added up. Here bins are counted from zero, whereas in root, bins are counted from 1. Obviously, this only works for up to 10 bins.
• U discard underflow bin
• O discard overflow bin

examples: imagine the binning has two axis, named x and y.

• "*[UO]" exclude underflow and overflow bins for all axis. So here a TH2 is returned but all undeflow and overflow bins are empty
• "x[UOC123]" integrate over the variable x but only using the bins 1,2,3 and not the underflow and overflow in x. Here a TH1 is returned, the axis is labelled "y" and the underflow and overflow (in y) are filled. However only the x-bins 1,2,3 are used to determine the content.
• "x[C];y[UO]" integrate over the variable x, including underflow and overflow but exclude underflow and overflow in y. Here a TH1 is returned, the axis is labelled "y". The underflow and overflow in y are empty.

Definition at line 658 of file TUnfoldDensity.cxx.

GetOutputBinName()

TString TUnfoldDensity::GetOutputBinName ( Int_t  iBinX ) const

overrideprotectedvirtual

Get bin name of an output bin.

Parameters

[in]

iBinX

bin number

Return value: name of the bin. The name is constructed from the entries in the binning scheme and includes information about the bin borders etc.

Reimplemented from TUnfold.

Definition at line 307 of file TUnfoldDensity.cxx.

GetOutputBinning()

const TUnfoldBinning * TUnfoldDensity::GetOutputBinning

(

const char *

distributionName = nullptr

)

const

Locate a binning node for the unfolded (truth level) quantities.

Parameters

[in]

distributionName

(default=0) distribution to look for. if zero, return the root node

returns: pointer to a TUnfoldBinning object or zero if not found

Definition at line 1305 of file TUnfoldDensity.cxx.

GetProbabilityMatrix()

TH2 * TUnfoldDensity::GetProbabilityMatrix	(	const char *	histogramName,
		const char *	histogramTitle = nullptr,
		Bool_t	useAxisBinning = kTRUE
	)		const

Get matrix of probabilities in a new histogram.

Parameters

[in]	histogramName	name of the histogram
[in]	histogramTitle	(default=0) title of the histogram
[in]	useAxisBinning	(default=true) if set to true, try to extract a histogram with proper binning and axis labels

returns a new histogram. if histogramTitle is null, choose a title automatically.

Definition at line 1160 of file TUnfoldDensity.cxx.

GetRhoIJtotal()

TH2 * TUnfoldDensity::GetRhoIJtotal	(	const char *	histogramName,
		const char *	histogramTitle = nullptr,
		const char *	distributionName = nullptr,
		const char *	axisSteering = nullptr,
		Bool_t	useAxisBinning = kTRUE
	)

Retrieve correlation coefficients, including all uncertainties.

Parameters

[in]	histogramName	name of the histogram
[in]	histogramTitle	(default=0) title of the histogram
[in]	distributionName	(default=0) identifier of the distribution to be extracted
[in]	axisSteering	(default=0) detailed steering within the extracted distribution
[in]	useAxisBinning	(default=true) if set to true, try to extract a histogram with proper binning and axis labels

returns a new histogram. See method GetOutput() for a detailed description of the arguments

Definition at line 1019 of file TUnfoldDensity.cxx.

GetRhoIstatbgr()

TH1 * TUnfoldDensity::GetRhoIstatbgr	(	const char *	histogramName,
		const char *	histogramTitle = nullptr,
		const char *	distributionName = nullptr,
		const char *	axisSteering = nullptr,
		Bool_t	useAxisBinning = kTRUE,
		TH2 **	ematInv = nullptr
	)

Retrieve global correlation coefficients including input (statistical) and background uncertainties.

Parameters

[in]	histogramName	name of the histogram
[in]	histogramTitle	(default=0) title of the histogram
[in]	distributionName	(default=0) identifier of the distribution to be extracted
[in]	axisSteering	(default=0) detailed steering within the extracted distribution
[in]	useAxisBinning	(default=true) if set to true, try to extract a histogram with proper binning and axis labels
[out]	ematInv	(default=0) to return the inverse covariance matrix

returns a new histogram. See method GetOutput() for a detailed description of the arguments. The inverse of the covariance matrix is stored in a new histogram returned by ematInv if that pointer is non-zero.

Definition at line 872 of file TUnfoldDensity.cxx.

GetRhoItotal()

TH1 * TUnfoldDensity::GetRhoItotal	(	const char *	histogramName,
		const char *	histogramTitle = nullptr,
		const char *	distributionName = nullptr,
		const char *	axisSteering = nullptr,
		Bool_t	useAxisBinning = kTRUE,
		TH2 **	ematInv = nullptr
	)

Retrieve global correlation coefficients including all uncertainty sources.

Parameters

[in]	histogramName	name of the histogram
[in]	histogramTitle	(default=0) title of the histogram
[in]	distributionName	(default=0) identifier of the distribution to be extracted
[in]	axisSteering	(default=0) detailed steering within the extracted distribution
[in]	useAxisBinning	(default=true) if set to true, try to extract a histogram with proper binning and axis labels
[out]	ematInv	(default=0) to return the inverse covariance matrix

returns a new histogram. See method GetOutput() for a detailed description of the arguments. The inverse of the covariance matrix is stored in a new histogram returned by ematInv if that pointer is non-zero.

Definition at line 821 of file TUnfoldDensity.cxx.

GetScanVariable()

Double_t TUnfoldDensity::GetScanVariable ( Int_t  mode, const char *  distribution, const char *  axisSteering  )

virtual

Calculate the function for ScanTau().

Parameters

[in]	mode	the variable to be calculated
[in]	distribution	distribution for which the variable is to be calculated
[in]	axisSteering	detailed steering for selecting bins on the axes of the distribution (see method GetRhoItotal())

return value: the scan result for the given choice of tau (for which the unfolding was performed prior to calling this method)

In ScanTau() the unfolding is repeated for various choices of tau. For each tau, after unfolding, GetScanVariable() is called to determine the scan result for this choice of tau.

the following modes are implemented

• kEScanTauRhoAvg : average (stat+bgr) global correlation
• kEScanTauRhoSquaredAvg : average (stat+bgr) global correlation squared
• kEScanTauRhoMax : maximum (stat+bgr) global correlation
• kEScanTauRhoAvgSys : average (stat+bgr+sys) global correlation
• kEScanTauRhoAvgSquaredSys : average (stat+bgr+sys) global correlation squared
• kEScanTauRhoMaxSys : maximum (stat+bgr+sys) global correlation

Definition at line 1675 of file TUnfoldDensity.cxx.

IsA()

TClass * TUnfoldDensity::IsA ( ) const

inlineoverridevirtual

Returns

TClass describing current object

Reimplemented from TUnfold.

Definition at line 199 of file TUnfoldDensity.h.

RegularizeDistribution()

void TUnfoldDensity::RegularizeDistribution	(	ERegMode	regmode,
		EDensityMode	densityMode,
		const char *	distribution,
		const char *	axisSteering
	)

Set up regularisation conditions.

Parameters

[in]	regmode	basic regularisation mode (see class TUnfold)
[in]	densityMode	how to apply bin-wise factors
[in]	distribution	name of the TUnfoldBinning node for which the regularisation conditions shall be set (zero matches all nodes)
[in]	axisSteering	regularisation fine-tuning

axisSteering is a string with several tokens, separated by a semicolon: "axisName[options];axisName[options];...".

• axisName: the name of an axis. The special name * matches all. So the argument distribution selects one (or all) distributions. Within the selected distribution(s), steering options may be specified for each axis (or for all axes) to define the regularisation conditions.
• options one or several character as follows:
  • u : exclude underflow bin from derivatives along this axis
  • o : exclude overflow bin from derivatives along this axis
  • U : exclude underflow bin
  • O : exclude overflow bin
  • b : use bin width for derivative calculation
  • B : same as 'b', in addition normalize to average bin width
  • N : completely exclude derivatives along this axis
  • p : axis is periodic (e.g. azimuthal angle), so include derivatives built from combinations involving bins at both ends of the axis "wrap around"

example: axisSteering="*[UOB]" uses bin widths to calculate derivatives but underflow/overflow bins are not regularized

Definition at line 383 of file TUnfoldDensity.cxx.

RegularizeDistributionRecursive()

void TUnfoldDensity::RegularizeDistributionRecursive ( const TUnfoldBinning *  binning, ERegMode  regmode, EDensityMode  densityMode, const char *  distribution, const char *  axisSteering  )

protected

Recursively add regularisation conditions for this node and its children.

Parameters

[in]	binning	current node
[in]	regmode	regularisation mode
[in]	densityMode	type of regularisation scaling
[in]	distribution	target distribution(s) name
[in]	axisSteering	steering within the target distribution(s)

Definition at line 401 of file TUnfoldDensity.cxx.

RegularizeOneDistribution()

void TUnfoldDensity::RegularizeOneDistribution ( const TUnfoldBinning *  binning, ERegMode  regmode, EDensityMode  densityMode, const char *  axisSteering  )

protected

Regularize the distribution of the given node.

Parameters

[in]	binning	current node
[in]	regmode	regularisation mode
[in]	densityMode	type of regularisation scaling
[in]	axisSteering	detailed steering for the axes of the distribution

Definition at line 422 of file TUnfoldDensity.cxx.

ScanTau()

Int_t TUnfoldDensity::ScanTau ( Int_t  nPoint, Double_t  tauMin, Double_t  tauMax, TSpline **  scanResult, Int_t  mode = kEScanTauRhoAvg, const char *  distribution = nullptr, const char *  axisSteering = nullptr, TGraph **  lCurvePlot = nullptr, TSpline **  logTauXPlot = nullptr, TSpline **  logTauYPlot = nullptr  )

virtual

Scan a function wrt tau and determine the minimum.

Parameters

[in]	nPoint	number of points to be scanned
[in]	tauMin	smallest tau value to study
[in]	tauMax	largest tau value to study
[out]	scanResult	the scanned function wrt log(tau)
[in]	mode	1st parameter for the scan function
[in]	distribution	2nd parameter for the scan function
[in]	axisSteering	3rd parameter for the scan function
[out]	lCurvePlot	for monitoring, shows the L-curve
[out]	logTauXPlot	for monitoring, L-curve(X) as a function of log(tau)
[out]	logTauYPlot	for monitoring, L-curve(Y) as a function of log(tau)

Return value: the coordinate number on the curve scanResult which corresponds to the minimum

The function is scanned by repeating the following steps nPoint times

1. Choose a value of tau
2. Perform the unfolding for this choice of tau, DoUnfold(tau)
3. Determine the scan variable GetScanVariable()

The method GetScanVariable() defines scans of correlation coefficients, where mode is chosen from the enum EScanTauMode. In addition one may set distribution and/or projectionMode to refine the calculation of correlations (e.g. restrict the calculation to the signal distribution and/or exclude underflow and overflow bins). See the documentation of GetScanVariable() for details. Alternative scan variables may be defined by overriding the GetScanVariable() method.

Automatic choice of scan range: if (tauMin,tauMax) do not correspond to a valid tau range (e.g. tauMin=tauMax=0.0) then the tau range is determined automatically. Use with care!

Definition at line 1351 of file TUnfoldDensity.cxx.

Streamer()

void TUnfoldDensity::Streamer ( TBuffer &  R__b )

overridevirtual

Stream an object of class TObject.

Reimplemented from TUnfold.

StreamerNVirtual()

void TUnfoldDensity::StreamerNVirtual ( TBuffer &  ClassDef_StreamerNVirtual_b )

inline

Definition at line 199 of file TUnfoldDensity.h.

Member Data Documentation

fConstInputBins

const TUnfoldBinning* TUnfoldDensity::fConstInputBins

protected

binning scheme for the input (detector level)

Definition at line 53 of file TUnfoldDensity.h.

fConstOutputBins

const TUnfoldBinning* TUnfoldDensity::fConstOutputBins

protected

binning scheme for the output (truth level)

Definition at line 51 of file TUnfoldDensity.h.

fOwnedInputBins

TUnfoldBinning* TUnfoldDensity::fOwnedInputBins

protected

pointer to input binning scheme if owned by this class

Definition at line 57 of file TUnfoldDensity.h.

fOwnedOutputBins

TUnfoldBinning* TUnfoldDensity::fOwnedOutputBins

protected

pointer to output binning scheme if owned by this class

Definition at line 55 of file TUnfoldDensity.h.

fRegularisationConditions

TUnfoldBinning* TUnfoldDensity::fRegularisationConditions

protected

binning scheme for the regularisation conditions

Definition at line 59 of file TUnfoldDensity.h.