ROOT   Reference Guide

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/.

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 ,
}

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. More...

TUnfold (void)
Only for use by root streamer or derived classes. More...

~TUnfold (void) override

virtual Double_t DoUnfold (Double_t tau)
Perform the unfolding for a given regularisation parameter tau. More...

Double_t DoUnfold (Double_t tau, const TH1 *hist_y, Double_t scaleBias=0.0)
Perform the unfolding for a given input and regularisation. More...

void GetBias (TH1 *bias, const Int_t *binMap=nullptr) const
Get bias vector including bias scale. More...

Double_t GetChi2A (void) const
get χ2A contribution determined in recent unfolding More...

Double_t GetChi2L (void) const
Get $$chi^{2}_{L}$$ contribution determined in recent unfolding. More...

void GetEmatrix (TH2 *ematrix, const Int_t *binMap=nullptr) const
Get output covariance matrix, possibly cumulated over several bins. More...

Double_t GetEpsMatrix (void) const
get numerical accuracy for Eigenvalue analysis when inverting matrices with rank problems More...

void GetFoldedOutput (TH1 *folded, const Int_t *binMap=nullptr) const
Get unfolding result on detector level. More...

void GetInput (TH1 *inputData, const Int_t *binMap=nullptr) const
Input vector of measurements. More...

void GetInputInverseEmatrix (TH2 *ematrix)
Get inverse of the measurement's covariance matrix. More...

void GetL (TH2 *l) const
Get matrix of regularisation conditions. More...

virtual Double_t GetLcurveX (void) const
Get value on x-axis of L-curve determined in recent unfolding. More...

virtual Double_t GetLcurveY (void) const
Get value on y-axis of L-curve determined in recent unfolding. More...

void GetLsquared (TH2 *lsquared) const
Get matrix of regularisation conditions squared. More...

Int_t GetNdf (void) const
get number of degrees of freedom determined in recent unfolding More...

void GetNormalisationVector (TH1 *s, const Int_t *binMap=nullptr) const
Histogram of truth bins, determined from summing over the response matrix. More...

Int_t GetNpar (void) const
Get number of truth parameters determined in recent unfolding. More...

Int_t GetNr (void) const
Get number of regularisation conditions. More...

void GetOutput (TH1 *output, const Int_t *binMap=nullptr) const
Get output distribution, possibly cumulated over several bins. More...

void GetProbabilityMatrix (TH2 *A, EHistMap histmap) const
Get matrix of probabilities. More...

Double_t GetRhoAvg (void) const
get average global correlation determined in recent unfolding More...

Double_t GetRhoI (TH1 *rhoi, const Int_t *binMap=nullptr, TH2 *invEmat=nullptr) const
Get global correlation coefficients, possibly cumulated over several bins. More...

void GetRhoIJ (TH2 *rhoij, const Int_t *binMap=nullptr) const
Get correlation coefficients, possibly cumulated over several bins. More...

Double_t GetRhoMax (void) const
get maximum global correlation determined in recent unfolding More...

Double_t GetTau (void) const
Return regularisation parameter. More...

TClassIsA () const override

Int_t RegularizeBins (int start, int step, int nbin, ERegMode regmode)
Add regularisation conditions for a group of bins. More...

Int_t RegularizeBins2D (int start_bin, int step1, int nbin1, int step2, int nbin2, ERegMode regmode)
Add regularisation conditions for 2d unfolding. More...

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. More...

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. More...

Int_t RegularizeSize (int bin, Double_t scale=1.0)
Add a regularisation condition on the magnitude of a truth bin. More...

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. More...

void SetBias (const TH1 *bias)
Set bias vector. More...

void SetConstraint (EConstraint constraint)
Set type of area constraint. More...

void SetEpsMatrix (Double_t eps)
set numerical accuracy for Eigenvalue analysis when inverting matrices with rank problems More...

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). More...

void Streamer (TBuffer &) override
Stream an object of class TObject. More...

void StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

Public Member Functions inherited from TObject
TObject ()
TObject constructor. More...

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

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

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

Append graphics object to current pad. More...

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

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. More...

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

virtual void Clear (Option_t *="")

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

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

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

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

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

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

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

virtual TObjectDrawClone (Option_t *option="") const
Draw a clone of this object in the current selected pad with: gROOT->SetSelectedPad(c1). More...

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

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

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. More...

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

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

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

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

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

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

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

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

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

virtual Option_tGetOption () const

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

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

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

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

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. More...

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

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

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

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

void InvertBit (UInt_t f)

virtual TClassIsA () const

Bool_t IsDestructed () const
IsDestructed. More...

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

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

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. More...

void MayNotUse (const char *method) const
Use this method to signal that a method (defined in a base class) may not be called in a derived class (in principle against good design since a child class should not provide less functionality than its parent, however, sometimes it is necessary). More...

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

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

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

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

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)

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

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

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

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

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

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

void ResetBit (UInt_t f)

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

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

void SetBit (UInt_t f)

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

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

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

virtual void Streamer (TBuffer &)
Stream an object of class TObject. More...

void StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

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

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. More...

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

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

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

Static Public Member Functions

static TClassClass ()

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. More...

Static Public Member Functions inherited from TObject
static TClassClass ()

static const char * Class_Name ()

static constexpr Version_t Class_Version ()

static const char * DeclFileName ()

static Longptr_t GetDtorOnly ()
Return destructor only flag. More...

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

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

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

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. More...

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. More...

Bool_t AddRegularisationCondition (Int_t nEle, const Int_t *indices, const Double_t *rowData)
Add a row of regularisation conditions to the matrix L. More...

void ClearHistogram (TH1 *h, Double_t x=0.) const
Initialize bin contents and bin errors for a given histogram. More...

virtual void ClearResults (void)
Reset all results. More...

TMatrixDSparseCreateSparseMatrix (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. More...

virtual Double_t DoUnfold (void)
Core unfolding algorithm. More...

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. More...

const TMatrixDSparseGetAx (void) const
vector of folded-back result More...

Int_t GetBinFromRow (int ix) const
converts matrix row to truth histogram bin number More...

const TMatrixDSparseGetDXDAM (int i) const
matrix contributions of the derivative dx/dA More...

const TMatrixDSparseGetDXDAZ (int i) const
vector contributions of the derivative dx/dA More...

const TMatrixDSparseGetDXDtauSquared (void) const
vector of derivative dx/dtauSquared, using internal bin counting More...

const TMatrixDSparseGetDXDY (void) const
matrix of derivatives dx/dy More...

const TMatrixDSparseGetE (void) const
matrix E, using internal bin counting More...

const TMatrixDSparseGetEinv (void) const
matrix E-1, using internal bin counting More...

Int_t GetNx (void) const
returns internal number of output (truth) matrix rows More...

Int_t GetNy (void) const
returns the number of measurement bins More...

virtual TString GetOutputBinName (Int_t iBinX) const
Get bin name of an output bin. More...

Double_t GetRhoIFromMatrix (TH1 *rhoi, const TMatrixDSparse *eOrig, const Int_t *binMap, TH2 *invEmat) const
Get global correlation coefficients with arbitrary min map. More...

Int_t GetRowFromBin (int ix) const
converts truth histogram bin number to matrix row More...

const TMatrixDSparseGetVxx (void) const
covariance matrix of the result More...

const TMatrixDSparseGetVxxInv (void) const
inverse of covariance matrix of the result More...

const TMatrixDSparseGetVyyInv (void) const
inverse of covariance matrix of the data y More...

const TMatrixDGetX (void) const
vector of the unfolding result More...

TMatrixDSparseInvertMSparseSymmPos (const TMatrixDSparse *A, Int_t *rank) const
Get the inverse or pseudo-inverse of a positive, sparse matrix. More...

TMatrixDSparseMultiplyMSparseM (const TMatrixDSparse *a, const TMatrixD *b) const
Multiply sparse matrix and a non-sparse matrix. More...

TMatrixDSparseMultiplyMSparseMSparse (const TMatrixDSparse *a, const TMatrixDSparse *b) const
Multiply two sparse matrices. More...

TMatrixDSparseMultiplyMSparseMSparseTranspVector (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. More...

TMatrixDSparseMultiplyMSparseTranspMSparse (const TMatrixDSparse *a, const TMatrixDSparse *b) const
Multiply a transposed Sparse matrix with another sparse matrix,. More...

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). More...

void MakeZombie ()

Static Protected Member Functions

static void DeleteMatrix (TMatrixD **m)
delete matrix and invalidate pointer More...

static void DeleteMatrix (TMatrixDSparse **m)
delete sparse matrix and invalidate pointer More...

Protected Attributes

TMatrixDSparsefA
response matrix A More...

Double_t fBiasScale
scale factor for the bias More...

EConstraint fConstraint
type of constraint to use for the unfolding More...

TArrayI fHistToX
mapping of histogram bins to matrix indices More...

TMatrixDSparsefL
regularisation conditions L More...

ERegMode fRegMode
type of regularisation More...

TArrayD fSumOverY
truth vector calculated from the non-normalized response matrix More...

Double_t fTauSquared
regularisation parameter tau squared More...

TMatrixDSparsefVyy
covariance matrix Vyy corresponding to y More...

TMatrixDfX0
bias vector x0 More...

TArrayI fXToHist
mapping of matrix indices to histogram bins More...

TMatrixDfY
input (measured) data y More...

Private Member Functions

void InitTUnfold (void)
Initialize data members, for use in constructors. More...

Private Attributes

TMatrixDSparsefAx
result x folded back A*x More...

Double_t fChi2A
chi**2 contribution from (y-Ax)Vyy-1(y-Ax) More...

TMatrixDSparsefDXDAM [2]
matrix contribution to the of derivative dx_k/dA_ij More...

TMatrixDSparsefDXDAZ [2]
vector contribution to the of derivative dx_k/dA_ij More...

TMatrixDSparsefDXDtauSquared
derivative of the result wrt tau squared More...

TMatrixDSparsefDXDY
derivative of the result wrt dx/dy More...

TMatrixDSparsefE
matrix E More...

TMatrixDSparsefEinv
matrix E^(-1) More...

Double_t fEpsMatrix
machine accuracy used to determine matrix rank after eigenvalue analysis More...

Int_t fIgnoredBins
number of input bins which are dropped because they have error=0 More...

Double_t fLXsquared
chi**2 contribution from (x-s*x0)TLTL(x-s*x0) More...

Int_t fNdf
number of degrees of freedom More...

Double_t fRhoAvg
average global correlation coefficient More...

Double_t fRhoMax
maximum global correlation coefficient More...

TMatrixDSparsefVxx
covariance matrix Vxx More...

TMatrixDSparsefVxxInv
inverse of covariance matrix Vxx-1 More...

TMatrixDSparsefVyyInv
inverse of the input covariance matrix Vyy-1 More...

TMatrixDfX
unfolding result x More...

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

#include <TUnfold.h>

Inheritance diagram for TUnfold:
[legend]

◆ 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.

◆ 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

 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)
#define f(i)
Definition: RSha256.hxx:104

which suffered from a bug in old root versions.

Definition at line 931 of file TUnfold.cxx.

 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.

 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 χ2A 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.

◆ 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)TLTL(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.

Libraries for TUnfold:
[legend]

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