ROOT » HIST » SPECTRUM » TSpectrumFit

class TSpectrumFit: public TNamed

THIS CLASS CONTAINS ADVANCED SPECTRA FITTING FUNCTIONS.


These functions were written by:
Miroslav Morhac
Institute of Physics
Slovak Academy of Sciences
Dubravska cesta 9, 842 28 BRATISLAVA
SLOVAKIA

email:fyzimiro@savba.sk,    fax:+421 7 54772479

The original code in C has been repackaged as a C++ class by R.Brun

The algorithms in this class have been published in the following
references:
[1] M. Morhac et al.: Efficient fitting algorithms applied to
analysis of coincidence gamma-ray spectra. Computer Physics
Communications, Vol 172/1 (2005) pp. 19-41.

[2]  M. Morhac et al.: Study of fitting algorithms applied to
simultaneous analysis of large number of peaks in gamma-ray spectra.
Applied Spectroscopy, Vol. 57, No. 7, pp. 753-760, 2003.



Function Members (Methods)

public:
virtual~TSpectrumFit()
voidTObject::AbstractMethod(const char* method) const
virtual voidTObject::AppendPad(Option_t* option = "")
virtual voidTObject::Browse(TBrowser* b)
static TClass*Class()
virtual const char*TObject::ClassName() const
virtual voidTNamed::Clear(Option_t* option = "")
virtual TObject*TNamed::Clone(const char* newname = "") const
virtual Int_tTNamed::Compare(const TObject* obj) const
virtual voidTNamed::Copy(TObject& named) const
virtual voidTObject::Delete(Option_t* option = "")MENU
virtual Int_tTObject::DistancetoPrimitive(Int_t px, Int_t py)
virtual voidTObject::Draw(Option_t* option = "")
virtual voidTObject::DrawClass() constMENU
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virtual voidTObject::Dump() constMENU
virtual voidTObject::Error(const char* method, const char* msgfmt) const
virtual voidTObject::Execute(const char* method, const char* params, Int_t* error = 0)
virtual voidTObject::Execute(TMethod* method, TObjArray* params, Int_t* error = 0)
virtual voidTObject::ExecuteEvent(Int_t event, Int_t px, Int_t py)
virtual voidTObject::Fatal(const char* method, const char* msgfmt) const
virtual voidTNamed::FillBuffer(char*& buffer)
virtual TObject*TObject::FindObject(const char* name) const
virtual TObject*TObject::FindObject(const TObject* obj) const
voidFitAwmi(Double_t* source)
voidFitStiefel(Double_t* source)
Double_t*GetAmplitudes() const
Double_t*GetAmplitudesErrors() const
Double_t*GetAreas() const
Double_t*GetAreasErrors() const
voidGetBackgroundParameters(Double_t& a0, Double_t& a0Err, Double_t& a1, Double_t& a1Err, Double_t& a2, Double_t& a2Err)
Double_tGetChi() const
virtual Option_t*TObject::GetDrawOption() const
static Long_tTObject::GetDtorOnly()
virtual const char*TObject::GetIconName() const
virtual const char*TNamed::GetName() const
virtual char*TObject::GetObjectInfo(Int_t px, Int_t py) const
static Bool_tTObject::GetObjectStat()
virtual Option_t*TObject::GetOption() const
Double_t*GetPositions() const
Double_t*GetPositionsErrors() const
voidGetSigma(Double_t& sigma, Double_t& sigmaErr)
voidGetTailParameters(Double_t& t, Double_t& tErr, Double_t& b, Double_t& bErr, Double_t& s, Double_t& sErr)
virtual const char*TNamed::GetTitle() const
virtual UInt_tTObject::GetUniqueID() const
virtual Bool_tTObject::HandleTimer(TTimer* timer)
virtual ULong_tTNamed::Hash() const
virtual voidTObject::Info(const char* method, const char* msgfmt) const
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voidTObject::InvertBit(UInt_t f)
virtual TClass*IsA() const
virtual Bool_tTObject::IsEqual(const TObject* obj) const
virtual Bool_tTObject::IsFolder() const
Bool_tTObject::IsOnHeap() const
virtual Bool_tTNamed::IsSortable() const
Bool_tTObject::IsZombie() const
virtual voidTNamed::ls(Option_t* option = "") const
voidTObject::MayNotUse(const char* method) const
virtual Bool_tTObject::Notify()
voidTObject::Obsolete(const char* method, const char* asOfVers, const char* removedFromVers) const
voidTObject::operator delete(void* ptr)
voidTObject::operator delete(void* ptr, void* vp)
voidTObject::operator delete[](void* ptr)
voidTObject::operator delete[](void* ptr, void* vp)
void*TObject::operator new(size_t sz)
void*TObject::operator new(size_t sz, void* vp)
void*TObject::operator new[](size_t sz)
void*TObject::operator new[](size_t sz, void* vp)
TSpectrumFit&operator=(const TSpectrumFit&)
virtual voidTObject::Paint(Option_t* option = "")
virtual voidTObject::Pop()
virtual voidTNamed::Print(Option_t* option = "") const
virtual Int_tTObject::Read(const char* name)
virtual voidTObject::RecursiveRemove(TObject* obj)
voidTObject::ResetBit(UInt_t f)
virtual voidTObject::SaveAs(const char* filename = "", Option_t* option = "") constMENU
virtual voidTObject::SavePrimitive(ostream& out, Option_t* option = "")
voidSetBackgroundParameters(Double_t a0Init, Bool_t fixA0, Double_t a1Init, Bool_t fixA1, Double_t a2Init, Bool_t fixA2)
voidTObject::SetBit(UInt_t f)
voidTObject::SetBit(UInt_t f, Bool_t set)
virtual voidTObject::SetDrawOption(Option_t* option = "")MENU
static voidTObject::SetDtorOnly(void* obj)
voidSetFitParameters(Int_t xmin, Int_t xmax, Int_t numberIterations, Double_t alpha, Int_t statisticType, Int_t alphaOptim, Int_t power, Int_t fitTaylor)
virtual voidTNamed::SetName(const char* name)MENU
virtual voidTNamed::SetNameTitle(const char* name, const char* title)
static voidTObject::SetObjectStat(Bool_t stat)
voidSetPeakParameters(Double_t sigma, Bool_t fixSigma, const Double_t* positionInit, const Bool_t* fixPosition, const Double_t* ampInit, const Bool_t* fixAmp)
voidSetTailParameters(Double_t tInit, Bool_t fixT, Double_t bInit, Bool_t fixB, Double_t sInit, Bool_t fixS)
virtual voidTNamed::SetTitle(const char* title = "")MENU
virtual voidTObject::SetUniqueID(UInt_t uid)
virtual voidShowMembers(TMemberInspector& insp) const
virtual Int_tTNamed::Sizeof() const
virtual voidStreamer(TBuffer&)
voidStreamerNVirtual(TBuffer& ClassDef_StreamerNVirtual_b)
virtual voidTObject::SysError(const char* method, const char* msgfmt) const
Bool_tTObject::TestBit(UInt_t f) const
Int_tTObject::TestBits(UInt_t f) const
TSpectrumFit()
TSpectrumFit(Int_t numberPeaks)
TSpectrumFit(const TSpectrumFit&)
virtual voidTObject::UseCurrentStyle()
virtual voidTObject::Warning(const char* method, const char* msgfmt) const
virtual Int_tTObject::Write(const char* name = 0, Int_t option = 0, Int_t bufsize = 0)
virtual Int_tTObject::Write(const char* name = 0, Int_t option = 0, Int_t bufsize = 0) const
protected:
Double_tArea(Double_t a, Double_t sigma, Double_t t, Double_t b)
Double_tDera1(Double_t i)
Double_tDera2(Double_t i)
Double_tDeramp(Double_t i, Double_t i0, Double_t sigma, Double_t t, Double_t s, Double_t b)
Double_tDerb(Int_t num_of_fitted_peaks, Double_t i, const Double_t* parameter, Double_t sigma, Double_t t, Double_t b)
Double_tDerderi0(Double_t i, Double_t amp, Double_t i0, Double_t sigma)
Double_tDerdersigma(Int_t num_of_fitted_peaks, Double_t i, const Double_t* parameter, Double_t sigma)
Double_tDerfc(Double_t x)
Double_tDeri0(Double_t i, Double_t amp, Double_t i0, Double_t sigma, Double_t t, Double_t s, Double_t b)
Double_tDerpa(Double_t sigma, Double_t t, Double_t b)
Double_tDerpb(Double_t a, Double_t sigma, Double_t t, Double_t b)
Double_tDerpsigma(Double_t a, Double_t t, Double_t b)
Double_tDerpt(Double_t a, Double_t sigma, Double_t b)
Double_tDers(Int_t num_of_fitted_peaks, Double_t i, const Double_t* parameter, Double_t sigma)
Double_tDersigma(Int_t num_of_fitted_peaks, Double_t i, const Double_t* parameter, Double_t sigma, Double_t t, Double_t s, Double_t b)
Double_tDert(Int_t num_of_fitted_peaks, Double_t i, const Double_t* parameter, Double_t sigma, Double_t b)
virtual voidTObject::DoError(int level, const char* location, const char* fmt, va_list va) const
Double_tErfc(Double_t x)
voidTObject::MakeZombie()
Double_tOurpowl(Double_t a, Int_t pw)
Double_tShape(Int_t num_of_fitted_peaks, Double_t i, const Double_t* parameter, Double_t sigma, Double_t t, Double_t s, Double_t b, Double_t a0, Double_t a1, Double_t a2)
voidStiefelInversion(Double_t** a, Int_t rozmer)

Data Members

public:
static TObject::(anonymous)TObject::kBitMask
static TObject::EStatusBitsTObject::kCanDelete
static TObject::EStatusBitsTObject::kCannotPick
static TSpectrumFit::(anonymous)kFitAlphaHalving
static TSpectrumFit::(anonymous)kFitAlphaOptimal
static TSpectrumFit::(anonymous)kFitNumRegulCycles
static TSpectrumFit::(anonymous)kFitOptimChiCounts
static TSpectrumFit::(anonymous)kFitOptimChiFuncValues
static TSpectrumFit::(anonymous)kFitOptimMaxLikelihood
static TSpectrumFit::(anonymous)kFitPower10
static TSpectrumFit::(anonymous)kFitPower12
static TSpectrumFit::(anonymous)kFitPower2
static TSpectrumFit::(anonymous)kFitPower4
static TSpectrumFit::(anonymous)kFitPower6
static TSpectrumFit::(anonymous)kFitPower8
static TSpectrumFit::(anonymous)kFitTaylorOrderFirst
static TSpectrumFit::(anonymous)kFitTaylorOrderSecond
static TObject::EStatusBitsTObject::kHasUUID
static TObject::EStatusBitsTObject::kInvalidObject
static TObject::(anonymous)TObject::kIsOnHeap
static TObject::EStatusBitsTObject::kIsReferenced
static TObject::EStatusBitsTObject::kMustCleanup
static TObject::EStatusBitsTObject::kNoContextMenu
static TObject::(anonymous)TObject::kNotDeleted
static TObject::EStatusBitsTObject::kObjInCanvas
static TObject::(anonymous)TObject::kOverwrite
static TObject::(anonymous)TObject::kSingleKey
static TObject::(anonymous)TObject::kWriteDelete
static TObject::(anonymous)TObject::kZombie
protected:
Double_tfA0Calccalculated value of background a0 parameter
Double_tfA0Errerror value of background a0 parameter
Double_tfA0Initinitial value of background a0 parameter(backgroud is estimated as a0+a1*x+a2*x*x)
Double_tfA1Calccalculated value of background a1 parameter
Double_tfA1Errerror value of background a1 parameter
Double_tfA1Initinitial value of background a1 parameter(backgroud is estimated as a0+a1*x+a2*x*x)
Double_tfA2Calccalculated value of background a2 parameter
Double_tfA2Errerror value of background a2 parameter
Double_tfA2Initinitial value of background a2 parameter(backgroud is estimated as a0+a1*x+a2*x*x)
Double_tfAlphaconvergence coefficient, input parameter, it should be positive number and <=1, for details see references
Int_tfAlphaOptimoptimization of convergence algorithm, possible values kFitAlphaHalving, kFitAlphaOptimal
Double_t*fAmpCalc[fNPeaks] array of calculated values of fitted amplitudes, output parameters
Double_t*fAmpErr[fNPeaks] array of amplitude errors
Double_t*fAmpInit[fNPeaks] array of initial values of peaks amplitudes, input parameters
Double_t*fArea[fNPeaks] array of calculated areas of peaks
Double_t*fAreaErr[fNPeaks] array of errors of peak areas
Double_tfBCalccalculated value of b parameter
Double_tfBErrerror value of b parameter
Double_tfBInitinitial value of b parameter (slope), for details see html manual and references
Double_tfChihere the fitting functions return resulting chi square
Int_tfFitTaylororder of Taylor expansion, possible values kFitTaylorOrderFirst, kFitTaylorOrderSecond. It applies only for Awmi fitting function.
Bool_tfFixA0logical value of a0 parameter, which allows to fix the parameter (not to fit).
Bool_tfFixA1logical value of a1 parameter, which allows to fix the parameter (not to fit).
Bool_tfFixA2logical value of a2 parameter, which allows to fix the parameter (not to fit).
Bool_t*fFixAmp[fNPeaks] array of logical values which allow to fix appropriate amplitudes (not fit). However they are present in the estimated functional
Bool_tfFixBlogical value of b parameter, which allows to fix the parameter (not to fit).
Bool_t*fFixPosition[fNPeaks] array of logical values which allow to fix appropriate positions (not fit). However they are present in the estimated functional
Bool_tfFixSlogical value of s parameter, which allows to fix the parameter (not to fit).
Bool_tfFixSigmalogical value of sigma parameter, which allows to fix the parameter (not to fit).
Bool_tfFixTlogical value of t parameter, which allows to fix the parameter (not to fit).
Int_tfNPeaksnumber of peaks present in fit, input parameter, it should be > 0
TStringTNamed::fNameobject identifier
Int_tfNumberIterationsnumber of iterations in fitting procedure, input parameter, it should be > 0
Double_t*fPositionCalc[fNPeaks] array of calculated values of fitted positions, output parameters
Double_t*fPositionErr[fNPeaks] array of position errors
Double_t*fPositionInit[fNPeaks] array of initial values of peaks positions, input parameters
Int_tfPowerpossible values kFitPower2,4,6,8,10,12, for details see references. It applies only for Awmi fitting function.
Double_tfSCalccalculated value of s parameter
Double_tfSErrerror value of s parameter
Double_tfSInitinitial value of s parameter (relative amplitude of step), for details see html manual and references
Double_tfSigmaCalccalculated value of sigma parameter
Double_tfSigmaErrerror value of sigma parameter
Double_tfSigmaInitinitial value of sigma parameter
Int_tfStatisticTypetype of statistics, possible values kFitOptimChiCounts (chi square statistics with counts as weighting coefficients), kFitOptimChiFuncValues (chi square statistics with function values as weighting coefficients),kFitOptimMaxLikelihood
Double_tfTCalccalculated value of t parameter
Double_tfTErrerror value of t parameter
Double_tfTInitinitial value of t parameter (relative amplitude of tail), for details see html manual and references
TStringTNamed::fTitleobject title
Int_tfXmaxlast fitted channel
Int_tfXminfirst fitted channel

Class Charts

Inheritance Chart:
TObject
TNamed
TSpectrumFit

Function documentation

TSpectrumFit()
default constructor
TSpectrumFit(Int_t numberPeaks)
numberPeaks: number of fitted peaks (must be greater than zero)
the constructor allocates arrays for all fitted parameters (peak positions, amplitudes etc) and sets the member
variables to their default values. One can change these variables by member functions (setters) of TSpectrumFit class.

Shape function of the fitted peaks is

 

 

 

 

 

 

 

 


where a represents vector of fitted parameters (positions p(j), amplitudes A(j), sigma, relative amplitudes T, S and slope B).

 

~TSpectrumFit()
destructor
Double_t Erfc(Double_t x)
AUXILIARY FUNCTION

This function calculates error function of x.


Double_t Derfc(Double_t x)
AUXILIARY FUNCTION

This function calculates derivative of error function of x.


Double_t Deramp(Double_t i, Double_t i0, Double_t sigma, Double_t t, Double_t s, Double_t b)
AUXILIARY FUNCTION

This function calculates derivative of peak shape function (see manual)
according to amplitude of peak.
Function parameters:
-i-channel
-i0-position of peak
-sigma-sigma of peak
-t, s-relative amplitudes
-b-slope


Double_t Deri0(Double_t i, Double_t amp, Double_t i0, Double_t sigma, Double_t t, Double_t s, Double_t b)
AUXILIARY FUNCTION

This function calculates derivative of peak shape function (see manual)
according to peak position.
Function parameters:
-i-channel
-amp-amplitude of peak
-i0-position of peak
-sigma-sigma of peak
-t, s-relative amplitudes
-b-slope


Double_t Derderi0(Double_t i, Double_t amp, Double_t i0, Double_t sigma)
AUXILIARY FUNCTION

This function calculates second derivative of peak shape function
(see manual) according to peak position.
Function parameters:
-i-channel
-amp-amplitude of peak
-i0-position of peak
-sigma-width of peak


Double_t Dersigma(Int_t num_of_fitted_peaks, Double_t i, const Double_t* parameter, Double_t sigma, Double_t t, Double_t s, Double_t b)
AUXILIARY FUNCTION

This function calculates derivative of peaks shape function (see manual)
according to sigma of peaks.
Function parameters:
-num_of_fitted_peaks-number of fitted peaks
-i-channel
-parameter-array of peaks parameters (amplitudes and positions)
-sigma-sigma of peak
-t, s-relative amplitudes
-b-slope


Double_t Derdersigma(Int_t num_of_fitted_peaks, Double_t i, const Double_t* parameter, Double_t sigma)
AUXILIARY FUNCTION

This function calculates second derivative of peaks shape function
(see manual) according to sigma of peaks.
Function parameters:
-num_of_fitted_peaks-number of fitted peaks
-i-channel
-parameter-array of peaks parameters (amplitudes and positions)
-sigma-sigma of peak


Double_t Dert(Int_t num_of_fitted_peaks, Double_t i, const Double_t* parameter, Double_t sigma, Double_t b)
AUXILIARY FUNCTION

This function calculates derivative of peaks shape function (see manual)
according to relative amplitude t.
Function parameters:
-num_of_fitted_peaks-number of fitted peaks
-i-channel
-parameter-array of peaks parameters (amplitudes and positions)
-sigma-sigma of peak
-b-slope


Double_t Ders(Int_t num_of_fitted_peaks, Double_t i, const Double_t* parameter, Double_t sigma)
AUXILIARY FUNCTION

This function calculates derivative of peaks shape function (see manual)
according to relative amplitude s.
Function parameters:
-num_of_fitted_peaks-number of fitted peaks
-i-channel
-parameter-array of peaks parameters (amplitudes and positions)
-sigma-sigma of peak


Double_t Derb(Int_t num_of_fitted_peaks, Double_t i, const Double_t* parameter, Double_t sigma, Double_t t, Double_t b)
AUXILIARY FUNCTION

This function calculates derivative of peaks shape function (see manual)
according to slope b.
Function parameters:
-num_of_fitted_peaks-number of fitted peaks
-i-channel
-parameter-array of peaks parameters (amplitudes and positions)
-sigma-sigma of peak
-t-relative amplitude
-b-slope


Double_t Dera1(Double_t i)
derivative of background according to a1
Double_t Dera2(Double_t i)
derivative of background according to a2
Double_t Shape(Int_t num_of_fitted_peaks, Double_t i, const Double_t* parameter, Double_t sigma, Double_t t, Double_t s, Double_t b, Double_t a0, Double_t a1, Double_t a2)
AUXILIARY FUNCTION

This function calculates peaks shape function (see manual)
Function parameters:
-num_of_fitted_peaks-number of fitted peaks
-i-channel
-parameter-array of peaks parameters (amplitudes and positions)
-sigma-sigma of peak
-t, s-relative amplitudes
-b-slope
-a0, a1, a2- background coefficients


Double_t Area(Double_t a, Double_t sigma, Double_t t, Double_t b)
AUXILIARY FUNCTION

This function calculates area of a peak
Function parameters:
-a-amplitude of the peak
-sigma-sigma of peak
-t-relative amplitude
-b-slope


Double_t Derpa(Double_t sigma, Double_t t, Double_t b)
AUXILIARY FUNCTION

This function calculates derivative of the area of peak
according to its amplitude.
Function parameters:
-sigma-sigma of peak
-t-relative amplitudes
-b-slope


Double_t Derpsigma(Double_t a, Double_t t, Double_t b)
AUXILIARY FUNCTION

This function calculates derivative of the area of peak
according to sigma of peaks.
Function parameters:
-a-amplitude of peak
-t-relative amplitudes
-b-slope


Double_t Derpt(Double_t a, Double_t sigma, Double_t b)
AUXILIARY FUNCTION

This function calculates derivative of the area of peak
according to t parameter.
Function parameters:
-sigma-sigma of peak
-t-relative amplitudes
-b-slope


Double_t Derpb(Double_t a, Double_t sigma, Double_t t, Double_t b)
AUXILIARY FUNCTION

This function calculates derivative of the area of peak
according to b parameter.
Function parameters:
-sigma-sigma of peak
-t-relative amplitudes
-b-slope


Double_t Ourpowl(Double_t a, Int_t pw)
power function
void FitAwmi(Double_t* source)
        ONE-DIMENSIONAL FIT FUNCTION
        ALGORITHM WITHOUT MATRIX INVERSION
        This function fits the source spectrum. The calling program should
        fill in input parameters of the TSpectrumFit class
        The fitted parameters are written into
        TSpectrumFit class output parameters and fitted data are written into
        source spectrum.

        Function parameters:
        source-pointer to the vector of source spectrum




Fitting

Goal: to estimate simultaneously peak shape parameters in spectra with large number of peaks

•         peaks can be fitted separately, each peak (or multiplets) in a region or together all peaks in a spectrum. To fit separately each peak one needs to determine the fitted region. However it can happen that the regions of neighboring peaks are overlapping. Then the results of fitting are very poor. On the other hand, when fitting together all peaks found in a  spectrum, one needs to have a method that is  stable (converges) and fast enough to carry out fitting in reasonable time

•         we have implemented the nonsymmetrical semiempirical peak shape function [1]

•         it contains the symmetrical Gaussian as well as nonsymmetrical terms.

 

 

 

 

 


where T and S are relative amplitudes and B is slope.

 

•         algorithm without matrix inversion (AWMI) allows fitting tens, hundreds of peaks simultaneously that represent sometimes thousands of parameters [2], [5].

Function:

void TSpectrumFit::FitAwmi(double *fSource)

This function fits the source spectrum using AWMI algorithm. The calling program should fill in input fitting parameters of the TSpectrumFit class using a set of TSpectrumFit setters. The fitted parameters are written into the class and the fitted data are written into source spectrum.

 

Parameter:

        fSource-pointer to the vector of source spectrum                 

       

Member variables of the TSpectrumFit class:

   Int_t     fNPeaks;                    //number of peaks present in fit, input parameter, it should be > 0

   Int_t     fNumberIterations;          //number of iterations in fitting procedure, input parameter, it should be > 0

   Int_t     fXmin;                      //first fitted channel

   Int_t     fXmax;                      //last fitted channel

   Int_t     fStatisticType;             //type of statistics, possible values kFitOptimChiCounts (chi square statistics with counts as weighting coefficients), kFitOptimChiFuncValues (chi square statistics with function values as weighting coefficients),kFitOptimMaxLikelihood

   Int_t     fAlphaOptim;                //optimization of convergence algorithm, possible values kFitAlphaHalving, kFitAlphaOptimal

   Int_t     fPower;                     //possible values kFitPower2,4,6,8,10,12, for details see references. It applies only for Awmi fitting function.

   Int_t     fFitTaylor;                 //order of Taylor expansion, possible values kFitTaylorOrderFirst, kFitTaylorOrderSecond. It applies only for Awmi fitting function.

   Double_t  fAlpha;                     //convergence coefficient, input parameter, it should be positive number and <=1, for details see references

   Double_t  fChi;                       //here the fitting functions return resulting chi square  

   Double_t *fPositionInit;              //[fNPeaks] array of initial values of peaks positions, input parameters

   Double_t *fPositionCalc;              //[fNPeaks] array of calculated values of fitted positions, output parameters

   Double_t *fPositionErr;               //[fNPeaks] array of position errors

   Double_t *fAmpInit;                   //[fNPeaks] array of initial values of peaks amplitudes, input parameters

   Double_t *fAmpCalc;                   //[fNPeaks] array of calculated values of fitted amplitudes, output parameters

   Double_t *fAmpErr;                    //[fNPeaks] array of amplitude errors

   Double_t *fArea;                      //[fNPeaks] array of calculated areas of peaks

   Double_t *fAreaErr;                   //[fNPeaks] array of errors of peak areas

   Double_t  fSigmaInit;                 //initial value of sigma parameter

   Double_t  fSigmaCalc;                 //calculated value of sigma parameter

   Double_t  fSigmaErr;                  //error value of sigma parameter

   Double_t  fTInit;                     //initial value of t parameter (relative amplitude of tail), for details see html manual and references

   Double_t  fTCalc;                     //calculated value of t parameter

   Double_t  fTErr;                      //error value of t parameter

   Double_t  fBInit;                     //initial value of b parameter (slope), for details see html manual and references

   Double_t  fBCalc;                     //calculated value of b parameter

   Double_t  fBErr;                      //error value of b parameter

   Double_t  fSInit;                     //initial value of s parameter (relative amplitude of step), for details see html manual and references

   Double_t  fSCalc;                     //calculated value of s parameter

   Double_t  fSErr;                      //error value of s parameter

   Double_t  fA0Init;                    //initial value of background a0 parameter(backgroud is estimated as a0+a1*x+a2*x*x)

   Double_t  fA0Calc;                    //calculated value of background a0 parameter

   Double_t  fA0Err;                     //error value of background a0 parameter

   Double_t  fA1Init;                    //initial value of background a1 parameter(backgroud is estimated as a0+a1*x+a2*x*x)

   Double_t  fA1Calc;                    //calculated value of background a1 parameter

   Double_t  fA1Err;                     //error value of background a1 parameter

   Double_t  fA2Init;                    //initial value of background a2 parameter(backgroud is estimated as a0+a1*x+a2*x*x)

   Double_t  fA2Calc;                    //calculated value of background a2 parameter

   Double_t  fA2Err;                     //error value of background a2 parameter

   Bool_t   *fFixPosition;               //[fNPeaks] array of logical values which allow to fix appropriate positions (not fit). However they are present in the estimated functional  

   Bool_t   *fFixAmp;                    //[fNPeaks] array of logical values which allow to fix appropriate amplitudes (not fit). However they are present in the estimated functional     

   Bool_t    fFixSigma;                  //logical value of sigma parameter, which allows to fix the parameter (not to fit).  

   Bool_t    fFixT;                      //logical value of t parameter, which allows to fix the parameter (not to fit).     

   Bool_t    fFixB;                      //logical value of b parameter, which allows to fix the parameter (not to fit).  

   Bool_t    fFixS;                      //logical value of s parameter, which allows to fix the parameter (not to fit).     

   Bool_t    fFixA0;                     //logical value of a0 parameter, which allows to fix the parameter (not to fit).

   Bool_t    fFixA1;                     //logical value of a1 parameter, which allows to fix the parameter (not to fit).  

   Bool_t    fFixA2;                     //logical value of a2 parameter, which allows to fix the parameter (not to fit).

 

References:

[1] Phillps G.W., Marlow K.W., NIM 137 (1976) 525.

[2] I. A. Slavic: Nonlinear least-squares fitting without matrix inversion applied to complex Gaussian spectra analysis. NIM 134 (1976) 285-289.

[3] T. Awaya: A new method for curve fitting to the data with low statistics not using chi-square method. NIM 165 (1979) 317-323.

[4] T. Hauschild, M. Jentschel: Comparison of maximum likelihood estimation and chi-square statistics applied to counting experiments. NIM A 457 (2001) 384-401.

 [5]  M. Morháč,  J. Kliman,  M. Jandel,  Ľ. Krupa, V. Matoušek: Study of fitting algorithms applied to simultaneous analysis of large number of peaks in -ray spectra. Applied Spectroscopy, Vol. 57, No. 7, pp. 753-760, 2003

 

Example  – script FitAwmi.c:

Fig. 1 Original spectrum (black line) and fitted spectrum using AWMI algorithm (red line) and number of iteration steps = 1000. Positions of fitted peaks are denoted by markers

Script:

// Example to illustrate fitting function using AWMI algorithm.

// To execute this example, do

// root > .x FitAwmi.C

 

void FitAwmi() {

   Double_t a;

   Int_t i,nfound=0,bin;

   Int_t nbins = 256;

   Int_t xmin  = 0;

   Int_t xmax  = nbins;

   Double_t * source = new Double_t[nbins];

   Double_t * dest = new Double_t[nbins];  

   TH1F *h = new TH1F("h","Fitting using AWMI algorithm",nbins,xmin,xmax);

   TH1F *d = new TH1F("d","",nbins,xmin,xmax);     

   TFile *f = new TFile("TSpectrum.root");

   h=(TH1F*) f->Get("fit;1");  

   for (i = 0; i < nbins; i++) source[i]=h->GetBinContent(i + 1);     

   TCanvas *Fit1 = gROOT->GetListOfCanvases()->FindObject("Fit1");

   if (!Fit1) Fit1 = new TCanvas("Fit1","Fit1",10,10,1000,700);

   h->Draw("L");

   TSpectrum *s = new TSpectrum();

   //searching for candidate peaks positions

   nfound = s->SearchHighRes(source, dest, nbins, 2, 0.1, kFALSE, 10000, kFALSE, 0);

   Bool_t *FixPos = new Bool_t[nfound];

   Bool_t *FixAmp = new Bool_t[nfound];     

   for(i = 0; i< nfound ; i++){

      FixPos[i] = kFALSE;

      FixAmp[i] = kFALSE;   

   }

   //filling in the initial estimates of the input parameters

   Double_t *PosX = new Double_t[nfound];        

   Double_t *PosY = new Double_t[nfound];

   PosX = s->GetPositionX();

   for (i = 0; i < nfound; i++) {

                                                a=PosX[i];

        bin = 1 + Int_t(a + 0.5);

        PosY[i] = h->GetBinContent(bin);

   }  

   TSpectrumFit *pfit=new TSpectrumFit(nfound);

   pfit->SetFitParameters(xmin, xmax-1, 1000, 0.1, pfit->kFitOptimChiCounts, pfit->kFitAlphaHalving, pfit->kFitPower2, pfit->kFitTaylorOrderFirst);  

   pfit->SetPeakParameters(2, kFALSE, PosX, (Bool_t *) FixPos, PosY, (Bool_t *) FixAmp);  

   pfit->FitAwmi(source);

   Double_t *CalcPositions = new Double_t[nfound];     

   Double_t *CalcAmplitudes = new Double_t[nfound];        

   CalcPositions=pfit->GetPositions();

   CalcAmplitudes=pfit->GetAmplitudes();  

   for (i = 0; i < nbins; i++) d->SetBinContent(i + 1,source[i]);

   d->SetLineColor(kRed);  

   d->Draw("SAME L"); 

   for (i = 0; i < nfound; i++) {

                                                a=CalcPositions[i];

        bin = 1 + Int_t(a + 0.5);               

        PosX[i] = d->GetBinCenter(bin);

        PosY[i] = d->GetBinContent(bin);

   }

   TPolyMarker * pm = (TPolyMarker*)h->GetListOfFunctions()->FindObject("TPolyMarker");

   if (pm) {

      h->GetListOfFunctions()->Remove(pm);

      delete pm;

   }

   pm = new TPolyMarker(nfound, PosX, PosY);

   h->GetListOfFunctions()->Add(pm);

   pm->SetMarkerStyle(23);

   pm->SetMarkerColor(kRed);

   pm->SetMarkerSize(1);  

}

void StiefelInversion(Double_t** a, Int_t rozmer)
AUXILIARY FUNCTION

This function calculates solution of the system of linear equations.
The matrix a should have a dimension size*(size+4)
The calling function should fill in the matrix, the column size should
contain vector y (right side of the system of equations). The result is
placed into size+1 column of the matrix.
according to sigma of peaks.
Function parameters:
-a-matrix with dimension size*(size+4)                          //
-size-number of rows of the matrix


void FitStiefel(Double_t* source)
        ONE-DIMENSIONAL FIT FUNCTION
        ALGORITHM WITH MATRIX INVERSION (STIEFEL-HESTENS METHOD)
        This function fits the source spectrum. The calling program should
        fill in input parameters
        The fitted parameters are written into
        output parameters and fitted data are written into
        source spectrum.

        Function parameters:
        source-pointer to the vector of source spectrum



Stiefel fitting algorithm

 

Function:

void TSpectrumFit::FitStiefel(double *fSource)

 

This function fits the source spectrum using Stiefel-Hestens method [1] (see Awmi function).  The calling program should fill in input fitting parameters of the TSpectrumFit class using a set of TSpectrumFit setters. The fitted parameters are written into the class and the fitted data are written into source spectrum. It converges faster than Awmi method.

 

Parameter:

        fSource-pointer to the vector of source spectrum                 

       

Example – script FitStiefel.c:

Fig. 2 Original spectrum (black line) and fitted spectrum using Stiefel-Hestens method (red line) and number of iteration steps = 100. Positions of fitted peaks are denoted by markers

 

Script:

// Example to illustrate fitting function using Stiefel-Hestens method.

// To execute this example, do

// root > .x FitStiefel.C

 

void FitStiefel() {

   Double_t a;

   Int_t i,nfound=0,bin;

   Int_t nbins = 256;

   Int_t xmin  = 0;

   Int_t xmax  = nbins;

   Double_t * source = new Double_t[nbins];

   Double_t * dest = new Double_t[nbins];  

   TH1F *h = new TH1F("h","Fitting using AWMI algorithm",nbins,xmin,xmax);

   TH1F *d = new TH1F("d","",nbins,xmin,xmax);     

   TFile *f = new TFile("TSpectrum.root");

   h=(TH1F*) f->Get("fit;1");  

   for (i = 0; i < nbins; i++) source[i]=h->GetBinContent(i + 1);     

   TCanvas *Fit1 = gROOT->GetListOfCanvases()->FindObject("Fit1");

   if (!Fit1) Fit1 = new TCanvas("Fit1","Fit1",10,10,1000,700);

   h->Draw("L");

   TSpectrum *s = new TSpectrum();

   //searching for candidate peaks positions

   nfound = s->SearchHighRes(source, dest, nbins, 2, 0.1, kFALSE, 10000, kFALSE, 0);

   Bool_t *FixPos = new Bool_t[nfound];

   Bool_t *FixAmp = new Bool_t[nfound];     

   for(i = 0; i< nfound ; i++){

      FixPos[i] = kFALSE;

      FixAmp[i] = kFALSE;   

   }

   //filling in the initial estimates of the input parameters

   Double_t *PosX = new Double_t[nfound];        

   Double_t *PosY = new Double_t[nfound];

   PosX = s->GetPositionX();

   for (i = 0; i < nfound; i++) {

                                                a=PosX[i];

        bin = 1 + Int_t(a + 0.5);

        PosY[i] = h->GetBinContent(bin);

   }  

   TSpectrumFit *pfit=new TSpectrumFit(nfound);

   pfit->SetFitParameters(xmin, xmax-1, 1000, 0.1, pfit->kFitOptimChiCounts, pfit->kFitAlphaHalving, pfit->kFitPower2, pfit->kFitTaylorOrderFirst);  

   pfit->SetPeakParameters(2, kFALSE, PosX, (Bool_t *) FixPos, PosY, (Bool_t *) FixAmp);  

   pfit->FitStiefel(source);

   Double_t *CalcPositions = new Double_t[nfound];     

   Double_t *CalcAmplitudes = new Double_t[nfound];        

   CalcPositions=pfit->GetPositions();

   CalcAmplitudes=pfit->GetAmplitudes();  

   for (i = 0; i < nbins; i++) d->SetBinContent(i + 1,source[i]);

   d->SetLineColor(kRed);  

   d->Draw("SAME L"); 

   for (i = 0; i < nfound; i++) {

                                                a=CalcPositions[i];

        bin = 1 + Int_t(a + 0.5);               

        PosX[i] = d->GetBinCenter(bin);

        PosY[i] = d->GetBinContent(bin);

   }

   TPolyMarker * pm = (TPolyMarker*)h->GetListOfFunctions()->FindObject("TPolyMarker");

   if (pm) {

      h->GetListOfFunctions()->Remove(pm);

      delete pm;

   }

   pm = new TPolyMarker(nfound, PosX, PosY);

   h->GetListOfFunctions()->Add(pm);

   pm->SetMarkerStyle(23);

   pm->SetMarkerColor(kRed);

   pm->SetMarkerSize(1);  

}

void SetFitParameters(Int_t xmin, Int_t xmax, Int_t numberIterations, Double_t alpha, Int_t statisticType, Int_t alphaOptim, Int_t power, Int_t fitTaylor)
   SETTER FUNCTION

   This function sets the following fitting parameters:
         -xmin, xmax - fitting region
         -numberIterations - # of desired iterations in the fit
         -alpha - convergence coefficient, it should be positive number and <=1, for details see references
         -statisticType - type of statistics, possible values kFitOptimChiCounts (chi square statistics with counts as weighting coefficients), kFitOptimChiFuncValues (chi square statistics with function values as weighting coefficients),kFitOptimMaxLikelihood
         -alphaOptim - optimization of convergence algorithm, possible values kFitAlphaHalving, kFitAlphaOptimal
         -power - possible values kFitPower2,4,6,8,10,12, for details see references. It applies only for Awmi fitting function.
         -fitTaylor - order of Taylor expansion, possible values kFitTaylorOrderFirst, kFitTaylorOrderSecond. It applies only for Awmi fitting function.

void SetPeakParameters(Double_t sigma, Bool_t fixSigma, const Double_t* positionInit, const Bool_t* fixPosition, const Double_t* ampInit, const Bool_t* fixAmp)
   SETTER FUNCTION

   This function sets the following fitting parameters of peaks:
         -sigma - initial value of sigma parameter
         -fixSigma - logical value of sigma parameter, which allows to fix the parameter (not to fit)
         -positionInit - aray of initial values of peaks positions
         -fixPosition - array of logical values which allow to fix appropriate positions (not fit). However they are present in the estimated functional.
         -ampInit - aray of initial values of peaks amplitudes
         -fixAmp - aray of logical values which allow to fix appropriate amplitudes (not fit). However they are present in the estimated functional

void SetBackgroundParameters(Double_t a0Init, Bool_t fixA0, Double_t a1Init, Bool_t fixA1, Double_t a2Init, Bool_t fixA2)
   SETTER FUNCTION

   This function sets the following fitting parameters of background:
         -a0Init - initial value of a0 parameter (backgroud is estimated as a0+a1*x+a2*x*x)
         -fixA0 - logical value of a0 parameter, which allows to fix the parameter (not to fit)
         -a1Init - initial value of a1 parameter
         -fixA1 - logical value of a1 parameter, which allows to fix the parameter (not to fit)
         -a2Init - initial value of a2 parameter
         -fixA2 - logical value of a2 parameter, which allows to fix the parameter (not to fit)

void SetTailParameters(Double_t tInit, Bool_t fixT, Double_t bInit, Bool_t fixB, Double_t sInit, Bool_t fixS)
   SETTER FUNCTION

   This function sets the following fitting parameters of tails of peaks
         -tInit - initial value of t parameter
         -fixT - logical value of t parameter, which allows to fix the parameter (not to fit)
         -bInit - initial value of b parameter
         -fixB - logical value of b parameter, which allows to fix the parameter (not to fit)
         -sInit - initial value of s parameter
         -fixS - logical value of s parameter, which allows to fix the parameter (not to fit)

void GetSigma(Double_t& sigma, Double_t& sigmaErr)
   GETTER FUNCTION

   This function gets the sigma parameter and its error
         -sigma - gets the fitted value of sigma parameter
         -sigmaErr - gets error value of sigma parameter

void GetBackgroundParameters(Double_t& a0, Double_t& a0Err, Double_t& a1, Double_t& a1Err, Double_t& a2, Double_t& a2Err)
   GETTER FUNCTION

   This function gets the background parameters and their errors
         -a0 - gets the fitted value of a0 parameter
         -a0Err - gets error value of a0 parameter
         -a1 - gets the fitted value of a1 parameter
         -a1Err - gets error value of a1 parameter
         -a2 - gets the fitted value of a2 parameter
         -a2Err - gets error value of a2 parameter

void GetTailParameters(Double_t& t, Double_t& tErr, Double_t& b, Double_t& bErr, Double_t& s, Double_t& sErr)
   GETTER FUNCTION

   This function gets the tail parameters and their errors
         -t - gets the fitted value of t parameter
         -tErr - gets error value of t parameter
         -b - gets the fitted value of b parameter
         -bErr - gets error value of b parameter
         -s - gets the fitted value of s parameter
         -sErr - gets error value of s parameter

TSpectrumFit(const TSpectrumFit& )
Double_t * GetAmplitudes() const
{return fAmpCalc;}
Double_t * GetAmplitudesErrors() const
{return fAmpErr;}
Double_t * GetAreas() const
{return fArea;}
Double_t * GetAreasErrors() const
{return fAreaErr;}
Double_t GetChi() const
{return fChi;}
Double_t * GetPositions() const
{return fPositionCalc;}
Double_t * GetPositionsErrors() const
{return fPositionErr;}