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Reference Guide
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TUnfold Class Reference

An algorithm to unfold distributions from detector to truth level.

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

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

If you use this software, please consider the following citation

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

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

Brief recipe to use TUnfold:

Basic formulae:

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

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


This file is part of TUnfold.

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

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

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

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

History:

Definition at line 104 of file TUnfold.h.

Public Types

enum  EConstraint { kEConstraintNone =0, kEConstraintArea =1 }
 type of extra constraint More...
 
enum  EHistMap { kHistMapOutputHoriz = 0, kHistMapOutputVert = 1 }
 arrangement of axes for the response matrix (TH2 histogram) More...
 
enum  ERegMode {
  kRegModeNone = 0, kRegModeSize = 1, kRegModeDerivative = 2, kRegModeCurvature = 3,
  kRegModeMixed = 4
}
 choice of regularisation scheme More...
 
- Public Types inherited from TObject
enum  {
  kIsOnHeap = 0x01000000, kNotDeleted = 0x02000000, kZombie = 0x04000000, kInconsistent = 0x08000000,
  kBitMask = 0x00ffffff
}
 
enum  { kSingleKey = BIT(0), kOverwrite = BIT(1), kWriteDelete = BIT(2) }
 
enum  EDeprecatedStatusBits { kObjInCanvas = BIT(3) }
 
enum  EStatusBits {
  kCanDelete = BIT(0), kMustCleanup = BIT(3), kIsReferenced = BIT(4), kHasUUID = BIT(5),
  kCannotPick = BIT(6), kNoContextMenu = BIT(8), kInvalidObject = BIT(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...
 
virtual ~TUnfold (void)
 
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=0) 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=0) 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=0) const
 Get unfolding result on detector level. More...
 
void GetInput (TH1 *inputData, const Int_t *binMap=0) 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=0) 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=0) 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=0, TH2 *invEmat=0) const
 Get global correlation coefficients, possibly cumulated over several bins. More...
 
void GetRhoIJ (TH2 *rhoij, const Int_t *binMap=0) 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...
 
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=0, TSpline **logTauY=0, TSpline **logTauCurvature=0)
 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=0, const TH2 *hist_vyy_inv=0)
 Define input data for subsequent calls to DoUnfold(tau). More...
 
- 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...
 
virtual void AppendPad (Option_t *option="")
 Append graphics object to current pad. More...
 
virtual void Browse (TBrowser *b)
 Browse object. May be overridden for another default action. More...
 
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 for instance with: gROOT->SetSelectedPad(gPad). 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=0)
 Execute method on this object with the given parameter string, e.g. More...
 
virtual void Execute (TMethod *method, TObjArray *params, Int_t *error=0)
 Execute method on this object with parameters stored in the TObjArray. More...
 
virtual void ExecuteEvent (Int_t event, Int_t px, Int_t py)
 Execute action corresponding to an event at (px,py). More...
 
virtual 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 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...
 
voidoperator new (size_t sz)
 
voidoperator new (size_t sz, void *vp)
 
voidoperator new[] (size_t sz)
 
voidoperator 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, Bool_t set)
 Set or unset the user status bits as specified in f. More...
 
void SetBit (UInt_t f)
 
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 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=0, Int_t option=0, Int_t bufsize=0)
 Write this object to the current directory. More...
 
virtual Int_t Write (const char *name=0, Int_t option=0, Int_t bufsize=0) const
 Write this object to the current directory. More...
 

Static Public Member Functions

static const char * GetTUnfoldVersion (void)
 Return a string describing the TUnfold version. More...
 
- Static Public Member Functions inherited from TObject
static Long_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...
 

#include <TUnfold.h>

Inheritance diagram for TUnfold:
[legend]

Member Enumeration Documentation

◆ EConstraint

type of extra constraint

Enumerator
kEConstraintNone 

use no extra constraint

kEConstraintArea 

enforce preservation of the area

Definition at line 110 of file TUnfold.h.

◆ 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 140 of file TUnfold.h.

◆ 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 120 of file TUnfold.h.

Constructor & Destructor Documentation

◆ TUnfold() [1/2]

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

Set up response matrix and regularisation scheme.

Parameters
[in]hist_Amatrix of MC events that describes the migrations
[in]histmapmapping 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 1715 of file TUnfold.cxx.

◆ TUnfold() [2/2]

TUnfold::TUnfold ( void  )

Only for use by root streamer or derived classes.

Definition at line 248 of file TUnfold.cxx.

◆ ~TUnfold()

TUnfold::~TUnfold ( void  )
virtual

Definition at line 132 of file TUnfold.cxx.

Member Function Documentation

◆ AddMSparse()

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

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

Parameters
[in,out]destdestination matrix
[in]fscaling factor
[in]srcmatrix to be added to dest

a replacement for

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

which suffered from a bug in old root versions.

Definition at line 930 of file TUnfold.cxx.

◆ AddRegularisationCondition() [1/2]

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

Add a row of regularisation conditions to the matrix L.

Parameters
[in]i0truth histogram bin number
[in]f0entry in the matrix L, column i0
[in]i1truth histogram bin number
[in]f1entry in the matrix L, column i1
[in]i2truth histogram bin number
[in]f2entry in the matrix L, column i2

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

Definition at line 1936 of file TUnfold.cxx.

◆ AddRegularisationCondition() [2/2]

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

Add a row of regularisation conditions to the matrix L.

Parameters
[in]nElenumber of valid entries in indices and rowData
[in]indicescolumn numbers of L to fill
[in]rowDatadata 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.

◆ ClearHistogram()

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

Initialize bin contents and bin errors for a given histogram.

Parameters
[out]hhistogram
[in]xnew histogram content

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

Definition at line 3643 of file TUnfold.cxx.

◆ ClearResults()

void TUnfold::ClearResults ( void  )
protectedvirtual

Reset all results.

Reimplemented in TUnfoldSys.

Definition at line 218 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]nrownumber of rows
[in]ncolnumber of columns
[in]nelnumber of non-zero elements
[in]rowrow indexes of non-zero elements
[in]colcolumn indexes of non-zero elements
[in]datanon-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.

◆ DeleteMatrix() [1/2]

void TUnfold::DeleteMatrix ( TMatrixD **  m)
staticprotected

delete matrix and invalidate pointer

Delete matrix and invalidate pointer.

Parameters
[in,out]mpointer 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 195 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]mpointer 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 209 of file TUnfold.cxx.

◆ DoUnfold() [1/3]

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 290 of file TUnfold.cxx.

◆ DoUnfold() [2/3]

Double_t TUnfold::DoUnfold ( Double_t  tau)
virtual

Perform the unfolding for a given regularisation parameter tau.

Parameters
[in]tauregularisation 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 2517 of file TUnfold.cxx.

◆ DoUnfold() [3/3]

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_regregularisation parameter
[in]inputinput 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 2265 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]ematrixerror matrix histogram
[in]ematerror matrix stored with internal mapping (member fXToHist)
[in]binMapmapping of histogram bins
[in]doClearif 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 3343 of file TUnfold.cxx.

◆ GetAx()

const TMatrixDSparse* TUnfold::GetAx ( void  ) const
inlineprotected

vector of folded-back result

Definition at line 245 of file TUnfold.h.

◆ GetBias()

void TUnfold::GetBias ( TH1 out,
const Int_t binMap = 0 
) const

Get bias vector including bias scale.

Parameters
[out]outhistogram 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 2922 of file TUnfold.cxx.

◆ GetBinFromRow()

Int_t TUnfold::GetBinFromRow ( int  ix) const
inlineprotected

converts matrix row to truth histogram bin number

Definition at line 233 of file TUnfold.h.

◆ GetChi2A()

Double_t TUnfold::GetChi2A ( void  ) const
inline

get χ2A contribution determined in recent unfolding

Definition at line 314 of file TUnfold.h.

◆ GetChi2L()

Double_t TUnfold::GetChi2L ( void  ) const

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

Definition at line 3194 of file TUnfold.cxx.

◆ GetDXDAM()

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

matrix contributions of the derivative dx/dA

Definition at line 249 of file TUnfold.h.

◆ GetDXDAZ()

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

vector contributions of the derivative dx/dA

Definition at line 251 of file TUnfold.h.

◆ GetDXDtauSquared()

const TMatrixDSparse* TUnfold::GetDXDtauSquared ( void  ) const
inlineprotected

vector of derivative dx/dtauSquared, using internal bin counting

Definition at line 262 of file TUnfold.h.

◆ GetDXDY()

const TMatrixDSparse* TUnfold::GetDXDY ( void  ) const
inlineprotected

matrix of derivatives dx/dy

Definition at line 247 of file TUnfold.h.

◆ GetE()

const TMatrixDSparse* TUnfold::GetE ( void  ) const
inlineprotected

matrix E, using internal bin counting

Definition at line 255 of file TUnfold.h.

◆ GetEinv()

const TMatrixDSparse* TUnfold::GetEinv ( void  ) const
inlineprotected

matrix E-1, using internal bin counting

Definition at line 253 of file TUnfold.h.

◆ GetEmatrix()

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

Get output covariance matrix, possibly cumulated over several bins.

Parameters
[out]ematrixhistogram 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 3410 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 337 of file TUnfold.h.

◆ GetFoldedOutput()

void TUnfold::GetFoldedOutput ( TH1 out,
const Int_t binMap = 0 
) const

Get unfolding result on detector level.

Parameters
[out]outhistogram 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 2948 of file TUnfold.cxx.

◆ GetInput()

void TUnfold::GetInput ( TH1 out,
const Int_t binMap = 0 
) const

Input vector of measurements.

Parameters
[out]outhistogram 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 3031 of file TUnfold.cxx.

◆ GetInputInverseEmatrix()

void TUnfold::GetInputInverseEmatrix ( TH2 out)

Get inverse of the measurement's covariance matrix.

Parameters
[out]outhistogram to store the inverted covariance

Definition at line 3060 of file TUnfold.cxx.

◆ GetL()

void TUnfold::GetL ( TH2 out) const

Get matrix of regularisation conditions.

Parameters
[out]outhistogram 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 3153 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 3216 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 3226 of file TUnfold.cxx.

◆ GetLsquared()

void TUnfold::GetLsquared ( TH2 out) const

Get matrix of regularisation conditions squared.

Parameters
[out]outhistogram 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 3113 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 324 of file TUnfold.h.

◆ GetNormalisationVector()

void TUnfold::GetNormalisationVector ( TH1 out,
const Int_t binMap = 0 
) const

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

Parameters
[out]outhistogram 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 2898 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 3206 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 3138 of file TUnfold.cxx.

◆ GetNx()

Int_t TUnfold::GetNx ( void  ) const
inlineprotected

returns internal number of output (truth) matrix rows

Definition at line 227 of file TUnfold.h.

◆ GetNy()

Int_t TUnfold::GetNy ( void  ) const
inlineprotected

returns the number of measurement bins

Definition at line 235 of file TUnfold.h.

◆ GetOutput()

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

Get output distribution, possibly cumulated over several bins.

Parameters
[out]outputexisting 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 3263 of file TUnfold.cxx.

◆ GetOutputBinName()

TString TUnfold::GetOutputBinName ( Int_t  iBinX) const
protectedvirtual

Get bin name of an output bin.

Parameters
[in]iBinXbin 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 1684 of file TUnfold.cxx.

◆ GetProbabilityMatrix()

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

Get matrix of probabilities.

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

Definition at line 2996 of file TUnfold.cxx.

◆ GetRhoAvg()

Double_t TUnfold::GetRhoAvg ( void  ) const
inline

get average global correlation determined in recent unfolding

Definition at line 312 of file TUnfold.h.

◆ GetRhoI()

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

Get global correlation coefficients, possibly cumulated over several bins.

Parameters
[out]rhoihistogram 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 3466 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 3528 of file TUnfold.cxx.

◆ GetRhoIJ()

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

Get correlation coefficients, possibly cumulated over several bins.

Parameters
[out]rhoijhistogram 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 3425 of file TUnfold.cxx.

◆ GetRhoMax()

Double_t TUnfold::GetRhoMax ( void  ) const
inline

get maximum global correlation determined in recent unfolding

Definition at line 310 of file TUnfold.h.

◆ GetRowFromBin()

Int_t TUnfold::GetRowFromBin ( int  ix) const
inlineprotected

converts truth histogram bin number to matrix row

Definition at line 231 of file TUnfold.h.

◆ GetTau()

Double_t TUnfold::GetTau ( void  ) const

Return regularisation parameter.

Definition at line 3185 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 3680 of file TUnfold.cxx.

◆ GetVxx()

const TMatrixDSparse* TUnfold::GetVxx ( void  ) const
inlineprotected

covariance matrix of the result

Definition at line 241 of file TUnfold.h.

◆ GetVxxInv()

const TMatrixDSparse* TUnfold::GetVxxInv ( void  ) const
inlineprotected

inverse of covariance matrix of the result

Definition at line 243 of file TUnfold.h.

◆ GetVyyInv()

const TMatrixDSparse* TUnfold::GetVyyInv ( void  ) const
inlineprotected

inverse of covariance matrix of the data y

Definition at line 257 of file TUnfold.h.

◆ GetX()

const TMatrixD* TUnfold::GetX ( void  ) const
inlineprotected

vector of the unfolding result

Definition at line 239 of file TUnfold.h.

◆ InitTUnfold()

void TUnfold::InitTUnfold ( void  )
private

Initialize data members, for use in constructors.

Definition at line 149 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]Athe sparse matrix to be inverted, has to be positive
[in,out]rankPtrif 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.

◆ MultiplyMSparseM()

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

Multiply sparse matrix and a non-sparse matrix.

Parameters
[in]asparse matrix
[in]bmatrix

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 773 of file TUnfold.cxx.

◆ MultiplyMSparseMSparse()

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

Multiply two sparse matrices.

Parameters
[in]asparse matrix
[in]bsparse 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 617 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]m1pointer to sparse matrix with dimension I*K
[in]m2pointer to sparse matrix with dimension J*K
[in]vpointer 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]asparse matrix (to be transposed)
[in]bsparse 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]startfirst bin number
[in]stepstep size
[in]nbinnumber of bins
[in]regmoderegularisation 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 2161 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_binfirst bin number
[in]step1step size, 1st dimension
[in]nbin1number of bins, 1st dimension
[in]step2step size, 2nd dimension
[in]nbin2number of bins, 2nd dimension
[in]regmoderegularisation 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 2222 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_binbin number
[in]center_binbin number
[in]right_binbin 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 2117 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_binbin number
[in]right_binbin 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 2078 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]binbin 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 2044 of file TUnfold.cxx.

◆ ScanLcurve()

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

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

Parameters
[in]nPointnumber of points used for the scan
[in]tauMinsmallest tau value to study
[in]tauMaxlargest tau value to study. If tauMin=tauMax=0, a scan interval is determined automatically.
[out]lCurveif nonzero, a new TGraph is returned, containing the L-curve
[out]logTauXif nonzero, a new TSpline is returned, to parameterize the L-curve's x-coordinates as a function of log10(tau)
[out]logTauYif nonzero, a new TSpline is returned, to parameterize the L-curve's y-coordinates as a function of log10(tau)
[out]logTauCurvatureif 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 2548 of file TUnfold.cxx.

◆ SetBias()

void TUnfold::SetBias ( const TH1 bias)

Set bias vector.

Parameters
[in]biashistogram 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 1912 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 3173 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 3666 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 = 0,
const TH2 hist_vyy_inv = 0 
)
virtual

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

Parameters
[in]inputinput 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 2300 of file TUnfold.cxx.

Member Data Documentation

◆ fA

TMatrixDSparse* TUnfold::fA
protected

response matrix A

Definition at line 151 of file TUnfold.h.

◆ fAx

TMatrixDSparse* TUnfold::fAx
private

result x folded back A*x

Definition at line 188 of file TUnfold.h.

◆ fBiasScale

Double_t TUnfold::fBiasScale
protected

scale factor for the bias

Definition at line 159 of file TUnfold.h.

◆ fChi2A

Double_t TUnfold::fChi2A
private

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

Definition at line 190 of file TUnfold.h.

◆ fConstraint

EConstraint TUnfold::fConstraint
protected

type of constraint to use for the unfolding

Definition at line 171 of file TUnfold.h.

◆ fDXDAM

TMatrixDSparse* TUnfold::fDXDAM[2]
private

matrix contribution to the of derivative dx_k/dA_ij

Definition at line 200 of file TUnfold.h.

◆ fDXDAZ

TMatrixDSparse* TUnfold::fDXDAZ[2]
private

vector contribution to the of derivative dx_k/dA_ij

Definition at line 202 of file TUnfold.h.

◆ fDXDtauSquared

TMatrixDSparse* TUnfold::fDXDtauSquared
private

derivative of the result wrt tau squared

Definition at line 204 of file TUnfold.h.

◆ fDXDY

TMatrixDSparse* TUnfold::fDXDY
private

derivative of the result wrt dx/dy

Definition at line 206 of file TUnfold.h.

◆ fE

TMatrixDSparse* TUnfold::fE
private

matrix E

Definition at line 210 of file TUnfold.h.

◆ fEinv

TMatrixDSparse* TUnfold::fEinv
private

matrix E^(-1)

Definition at line 208 of file TUnfold.h.

◆ fEpsMatrix

Double_t TUnfold::fEpsMatrix
private

machine accuracy used to determine matrix rank after eigenvalue analysis

Definition at line 178 of file TUnfold.h.

◆ fHistToX

TArrayI TUnfold::fHistToX
protected

mapping of histogram bins to matrix indices

Definition at line 167 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 176 of file TUnfold.h.

◆ fL

TMatrixDSparse* TUnfold::fL
protected

regularisation conditions L

Definition at line 153 of file TUnfold.h.

◆ fLXsquared

Double_t TUnfold::fLXsquared
private

chi**2 contribution from (x-s*x0)TLTL(x-s*x0)

Definition at line 192 of file TUnfold.h.

◆ fNdf

Int_t TUnfold::fNdf
private

number of degrees of freedom

Definition at line 198 of file TUnfold.h.

◆ fRegMode

ERegMode TUnfold::fRegMode
protected

type of regularisation

Definition at line 173 of file TUnfold.h.

◆ fRhoAvg

Double_t TUnfold::fRhoAvg
private

average global correlation coefficient

Definition at line 196 of file TUnfold.h.

◆ fRhoMax

Double_t TUnfold::fRhoMax
private

maximum global correlation coefficient

Definition at line 194 of file TUnfold.h.

◆ fSumOverY

TArrayD TUnfold::fSumOverY
protected

truth vector calculated from the non-normalized response matrix

Definition at line 169 of file TUnfold.h.

◆ fTauSquared

Double_t TUnfold::fTauSquared
protected

regularisation parameter tau squared

Definition at line 163 of file TUnfold.h.

◆ fVxx

TMatrixDSparse* TUnfold::fVxx
private

covariance matrix Vxx

Definition at line 182 of file TUnfold.h.

◆ fVxxInv

TMatrixDSparse* TUnfold::fVxxInv
private

inverse of covariance matrix Vxx-1

Definition at line 184 of file TUnfold.h.

◆ fVyy

TMatrixDSparse* TUnfold::fVyy
protected

covariance matrix Vyy corresponding to y

Definition at line 157 of file TUnfold.h.

◆ fVyyInv

TMatrixDSparse* TUnfold::fVyyInv
private

inverse of the input covariance matrix Vyy-1

Definition at line 186 of file TUnfold.h.

◆ fX

TMatrixD* TUnfold::fX
private

unfolding result x

Definition at line 180 of file TUnfold.h.

◆ fX0

TMatrixD* TUnfold::fX0
protected

bias vector x0

Definition at line 161 of file TUnfold.h.

◆ fXToHist

TArrayI TUnfold::fXToHist
protected

mapping of matrix indices to histogram bins

Definition at line 165 of file TUnfold.h.

◆ fY

TMatrixD* TUnfold::fY
protected

input (measured) data y

Definition at line 155 of file TUnfold.h.

Libraries for TUnfold:
[legend]

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