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ROOT 6.14/05 Reference Guide |
SVD Approach to Data Unfolding.
Reference: Nucl. Instrum. Meth. A372, 469 (1996) [hep-ph/9509307]
TSVDUnfold implements the singular value decomposition based unfolding method (see reference). Currently, the unfolding of one-dimensional histograms is supported, with the same number of bins for the measured and the unfolded spectrum.
The unfolding procedure is based on singular value decomposition of the response matrix. The regularisation of the unfolding is implemented via a discrete minimum-curvature condition.
Monte Carlo inputs:
xini
: true underlying spectrum (TH1D, n bins) bini
: reconstructed spectrum (TH1D, n bins) Adet
: response matrix (TH2D, nxn bins) Consider the unfolding of a measured spectrum bdat
with covariance matrix Bcov
(if not passed explicitly, a diagonal covariance will be built given the errors of bdat
). The corresponding spectrum in the Monte Carlo is given by bini
, with the true underlying spectrum given by xini
. The detector response is described by Adet
, with Adet
filled with events (not probabilities) with the true observable on the y-axis and the reconstructed observable on the x-axis.
The measured distribution can be unfolded for any combination of resolution, efficiency and acceptance effects, provided an appropriate definition of xini
and Adet
.
The unfolding can be performed by
TSVDUnfold *tsvdunf = new TSVDUnfold( bdat, Bcov, bini, xini, Adet ); TH1D* unfresult = tsvdunf->Unfold( kreg );
where kreg
determines the regularisation of the unfolding. In general, overregularisation (too small kreg
) will bias the unfolded spectrum towards the Monte Carlo input, while underregularisation (too large kreg
) will lead to large fluctuations in the unfolded spectrum. The optimal regularisation can be determined following guidelines in Nucl. Instrum. Meth. A372, 469 (1996) [hep-ph/9509307] using the distribution of the |d_i|<> that can be obtained by
tsvdunf->GetD()
and/or using pseudo-experiments.
Covariance matrices on the measured spectrum (for either the total uncertainties or individual sources of uncertainties) can be propagated to covariance matrices using the
GetUnfoldCovMatrix
method, which uses pseudo experiments for the propagation. In addition, GetAdetCovMatrix
allows for the propagation of the statistical uncertainties on the response matrix using pseudo experiments. The covariance matrix corresponding to Bcov
is also computed as described in Nucl. Instrum. Meth. A372, 469 (1996) [hep-ph/9509307] and can be obtained from tsvdunf->GetXtau()
and its (regularisation independent) inverse from tsvdunf->GetXinv()
. The distribution of singular values can be retrieved using tsvdunf->GetSV()
.
See also the tutorial for a toy example.
Definition at line 46 of file TSVDUnfold.h.
Public Member Functions | |
TSVDUnfold (const TH1D *bdat, const TH1D *bini, const TH1D *xini, const TH2D *Adet) | |
Alternative constructor User provides data and MC test spectra, as well as detector response matrix, diagonal covariance matrix of measured spectrum built from the uncertainties on measured spectrum. More... | |
TSVDUnfold (const TH1D *bdat, TH2D *Bcov, const TH1D *bini, const TH1D *xini, const TH2D *Adet) | |
Default constructor Initialisation of TSVDUnfold User provides data and MC test spectra, as well as detector response matrix and the covariance matrix of the measured distribution. More... | |
TSVDUnfold (const TSVDUnfold &other) | |
Copy constructor. More... | |
virtual | ~TSVDUnfold () |
Destructor. More... | |
Double_t | ComputeChiSquared (const TH1D &truspec, const TH1D &unfspec) |
Helper routine to compute chi-squared between distributions using the computed inverse of the covariance matrix for the unfolded spectrum as given in paper. More... | |
TH2D * | GetAdetCovMatrix (Int_t ntoys, Int_t seed=1) |
Determine covariance matrix of unfolded spectrum from finite statistics in response matrix using pseudo experiments "ntoys" - number of pseudo experiments used for the propagation "seed" - seed for pseudo experiments. More... | |
TH2D * | GetBCov () const |
Returns the covariance matrix. More... | |
TH1D * | GetD () const |
Returns d vector (for choosing appropriate regularisation) More... | |
Int_t | GetKReg () const |
TH1D * | GetSV () const |
Returns singular values vector. More... | |
TH2D * | GetUnfoldCovMatrix (const TH2D *cov, Int_t ntoys, Int_t seed=1) |
Determine for given input error matrix covariance matrix of unfolded spectrum from toy simulation given the passed covariance matrix on measured spectrum "cov" - covariance matrix on the measured spectrum, to be propagated "ntoys" - number of pseudo experiments used for the propagation "seed" - seed for pseudo experiments Note that this covariance matrix will contain effects of forced normalisation if spectrum is normalised to unit area. More... | |
TH2D * | GetXinv () const |
Returns the computed inverse of the covariance matrix. More... | |
TH2D * | GetXtau () const |
Returns the computed regularized covariance matrix corresponding to total uncertainties on measured spectrum as passed in the constructor. More... | |
void | SetNormalize (Bool_t normalize) |
TH1D * | Unfold (Int_t kreg) |
Perform the unfolding with regularisation parameter kreg. More... | |
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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 () |
Checked and record whether for 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 TObject * | Clone (const char *newname="") const |
Make a clone of an object using the Streamer facility. More... | |
virtual Int_t | Compare (const TObject *obj) const |
Compare abstract method. More... | |
virtual void | Copy (TObject &object) const |
Copy this to obj. More... | |
virtual void | Delete (Option_t *option="") |
Delete this object. More... | |
virtual Int_t | DistancetoPrimitive (Int_t px, Int_t py) |
Computes distance from point (px,py) to the object. More... | |
virtual void | Draw (Option_t *option="") |
Default Draw method for all objects. More... | |
virtual void | DrawClass () const |
Draw class inheritance tree of the class to which this object belongs. More... | |
virtual TObject * | DrawClone (Option_t *option="") const |
Draw a clone of this object in the current 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 TObject * | FindObject (const char *name) const |
Must be redefined in derived classes. More... | |
virtual TObject * | FindObject (const TObject *obj) const |
Must be redefined in derived classes. More... | |
virtual Option_t * | GetDrawOption () const |
Get option used by the graphics system to draw this object. More... | |
virtual 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_t * | GetOption () 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... | |
void * | operator new (size_t sz) |
void * | operator new (size_t sz, void *vp) |
void * | operator new[] (size_t sz) |
void * | operator new[] (size_t sz, void *vp) |
TObject & | operator= (const TObject &rhs) |
TObject assignment operator. 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... | |
Private Member Functions | |
void | FillCurvatureMatrix (TMatrixD &tCurv, TMatrixD &tC) const |
void | InitHistos () |
Static Private Member Functions | |
static TVectorD | CompProd (const TVectorD &vec1, const TVectorD &vec2) |
Multiply entries of two vectors. More... | |
static Double_t | GetCurvature (const TVectorD &vec, const TMatrixD &curv) |
Compute curvature of vector. More... | |
static void | H2M (const TH2D *histo, TMatrixD &mat) |
Fill 2D histogram into matrix. More... | |
static void | H2V (const TH1D *histo, TVectorD &vec) |
Fill 1D histogram into vector. More... | |
static void | H2Verr (const TH1D *histo, TVectorD &vec) |
Fill 1D histogram errors into vector. More... | |
static void | M2H (const TMatrixD &mat, TH2D &histo) |
Fill 2D histogram into matrix. More... | |
static TMatrixD | MatDivVec (const TMatrixD &mat, const TVectorD &vec, Int_t zero=0) |
Divide matrix entries by vector. More... | |
static void | RegularisedSymMatInvert (TMatrixDSym &mat, Double_t eps=1e-3) |
naive regularised inversion cuts off small elements More... | |
static void | V2H (const TVectorD &vec, TH1D &histo) |
Fill vector into 1D histogram. More... | |
static TVectorD | VecDiv (const TVectorD &vec1, const TVectorD &vec2, Int_t zero=0) |
Divide entries of two vectors. More... | |
Private Attributes | |
const TH2D * | fAdet |
TH2D * | fBcov |
const TH1D * | fBdat |
Computed inverse of covariance matrix. More... | |
const TH1D * | fBini |
Int_t | fDdim |
Truth and reconstructed dimensions. More... | |
TH1D * | fDHist |
Regularisation parameter. More... | |
Int_t | fKReg |
Normalize unfolded spectrum to 1. More... | |
Bool_t | fMatToyMode |
Internal switch for covariance matrix propagation. More... | |
Int_t | fNdim |
Bool_t | fNormalize |
Derivative for curvature matrix. More... | |
TH1D * | fSVHist |
Distribution of d (for checking regularization) More... | |
TH1D * | fToyhisto |
TH2D * | fToymat |
Toy MC histogram. More... | |
Bool_t | fToyMode |
Toy MC detector response matrix. More... | |
const TH1D * | fXini |
TH2D * | fXinv |
Computed regularized covariance matrix. More... | |
TH2D * | fXtau |
Distribution of singular values. More... | |
Additional Inherited Members | |
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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) } |
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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... | |
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virtual void | DoError (int level, const char *location, const char *fmt, va_list va) const |
Interface to ErrorHandler (protected). More... | |
void | MakeZombie () |
#include <TSVDUnfold.h>
TSVDUnfold::TSVDUnfold | ( | const TH1D * | bdat, |
const TH1D * | bini, | ||
const TH1D * | xini, | ||
const TH2D * | Adet | ||
) |
Alternative constructor User provides data and MC test spectra, as well as detector response matrix, diagonal covariance matrix of measured spectrum built from the uncertainties on measured spectrum.
Definition at line 79 of file TSVDUnfold.cxx.
TSVDUnfold::TSVDUnfold | ( | const TH1D * | bdat, |
TH2D * | Bcov, | ||
const TH1D * | bini, | ||
const TH1D * | xini, | ||
const TH2D * | Adet | ||
) |
Default constructor Initialisation of TSVDUnfold User provides data and MC test spectra, as well as detector response matrix and the covariance matrix of the measured distribution.
Definition at line 132 of file TSVDUnfold.cxx.
TSVDUnfold::TSVDUnfold | ( | const TSVDUnfold & | other | ) |
Copy constructor.
Definition at line 177 of file TSVDUnfold.cxx.
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virtual |
Destructor.
Definition at line 202 of file TSVDUnfold.cxx.
Multiply entries of two vectors.
Definition at line 708 of file TSVDUnfold.cxx.
Helper routine to compute chi-squared between distributions using the computed inverse of the covariance matrix for the unfolded spectrum as given in paper.
Definition at line 886 of file TSVDUnfold.cxx.
Definition at line 725 of file TSVDUnfold.cxx.
Determine covariance matrix of unfolded spectrum from finite statistics in response matrix using pseudo experiments "ntoys" - number of pseudo experiments used for the propagation "seed" - seed for pseudo experiments.
Definition at line 517 of file TSVDUnfold.cxx.
TH2D * TSVDUnfold::GetBCov | ( | ) | const |
Returns the covariance matrix.
Definition at line 618 of file TSVDUnfold.cxx.
Compute curvature of vector.
Definition at line 718 of file TSVDUnfold.cxx.
TH1D * TSVDUnfold::GetD | ( | ) | const |
Returns d vector (for choosing appropriate regularisation)
Definition at line 582 of file TSVDUnfold.cxx.
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inline |
Definition at line 86 of file TSVDUnfold.h.
TH1D * TSVDUnfold::GetSV | ( | ) | const |
Returns singular values vector.
Definition at line 593 of file TSVDUnfold.cxx.
Determine for given input error matrix covariance matrix of unfolded spectrum from toy simulation given the passed covariance matrix on measured spectrum "cov" - covariance matrix on the measured spectrum, to be propagated "ntoys" - number of pseudo experiments used for the propagation "seed" - seed for pseudo experiments Note that this covariance matrix will contain effects of forced normalisation if spectrum is normalised to unit area.
Definition at line 411 of file TSVDUnfold.cxx.
TH2D * TSVDUnfold::GetXinv | ( | ) | const |
Returns the computed inverse of the covariance matrix.
Definition at line 610 of file TSVDUnfold.cxx.
TH2D * TSVDUnfold::GetXtau | ( | ) | const |
Returns the computed regularized covariance matrix corresponding to total uncertainties on measured spectrum as passed in the constructor.
Note that this covariance matrix will not contain the effects of forced normalization if spectrum is normalized to unit area.
Definition at line 602 of file TSVDUnfold.cxx.
Fill 2D histogram into matrix.
Definition at line 650 of file TSVDUnfold.cxx.
Fill 1D histogram into vector.
Definition at line 626 of file TSVDUnfold.cxx.
Fill 1D histogram errors into vector.
Definition at line 634 of file TSVDUnfold.cxx.
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private |
Definition at line 813 of file TSVDUnfold.cxx.
Fill 2D histogram into matrix.
Definition at line 662 of file TSVDUnfold.cxx.
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staticprivate |
Divide matrix entries by vector.
Definition at line 690 of file TSVDUnfold.cxx.
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staticprivate |
naive regularised inversion cuts off small elements
Definition at line 833 of file TSVDUnfold.cxx.
Definition at line 66 of file TSVDUnfold.h.
Perform the unfolding with regularisation parameter kreg.
Definition at line 243 of file TSVDUnfold.cxx.
Fill vector into 1D histogram.
Definition at line 642 of file TSVDUnfold.cxx.
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staticprivate |
Divide entries of two vectors.
Definition at line 674 of file TSVDUnfold.cxx.
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private |
Definition at line 141 of file TSVDUnfold.h.
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private |
Definition at line 138 of file TSVDUnfold.h.
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private |
Computed inverse of covariance matrix.
Definition at line 137 of file TSVDUnfold.h.
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private |
Definition at line 139 of file TSVDUnfold.h.
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private |
Truth and reconstructed dimensions.
Definition at line 128 of file TSVDUnfold.h.
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private |
Regularisation parameter.
Definition at line 131 of file TSVDUnfold.h.
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private |
Normalize unfolded spectrum to 1.
Definition at line 130 of file TSVDUnfold.h.
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private |
Internal switch for covariance matrix propagation.
Definition at line 147 of file TSVDUnfold.h.
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private |
Definition at line 127 of file TSVDUnfold.h.
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private |
Derivative for curvature matrix.
Definition at line 129 of file TSVDUnfold.h.
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private |
Distribution of d (for checking regularization)
Definition at line 132 of file TSVDUnfold.h.
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private |
Definition at line 144 of file TSVDUnfold.h.
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private |
Toy MC histogram.
Definition at line 145 of file TSVDUnfold.h.
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private |
Toy MC detector response matrix.
Definition at line 146 of file TSVDUnfold.h.
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private |
Definition at line 140 of file TSVDUnfold.h.
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private |
Computed regularized covariance matrix.
Definition at line 134 of file TSVDUnfold.h.
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private |
Distribution of singular values.
Definition at line 133 of file TSVDUnfold.h.