Advanced 1-dimensional spectra fitting functions.

Author: Miroslav Morhac

Class for fitting 1D spectra using AWMI (algorithm without matrix inversion) and conjugate gradient algorithms for symmetrical matrices (Stiefel-Hestens method). AWMI method allows to fit simultaneously 100s up to 1000s peaks. Stiefel method is very stable, it converges faster, but is more time consuming

The algorithms in this class have been published in the following references:

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.
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.

Definition at line 18 of file TSpectrumFit.h.

Public Types
enum	{ kFitOptimChiCounts =0 , kFitOptimChiFuncValues =1 , kFitOptimMaxLikelihood =2 , kFitAlphaHalving =0 , kFitAlphaOptimal =1 , kFitPower2 =2 , kFitPower4 =4 , kFitPower6 =6 , kFitPower8 =8 , kFitPower10 =10 , kFitPower12 =12 , kFitTaylorOrderFirst =0 , kFitTaylorOrderSecond =1 , kFitNumRegulCycles =100 }

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
	TSpectrumFit (Int_t numberPeaks)
	numberPeaks: number of fitted peaks (must be greater than zero)

	TSpectrumFit (void)
	Default constructor.

virtual	~TSpectrumFit ()
	Destructor.

void	FitAwmi (Double_t *source)
	This function fits the source spectrum.

void	FitStiefel (Double_t *source)
	This function fits the source spectrum.

Double_t *	GetAmplitudes () const

Double_t *	GetAmplitudesErrors () const

Double_t *	GetAreas () const

Double_t *	GetAreasErrors () const

void	GetBackgroundParameters (Double_t &a0, Double_t &a0Err, Double_t &a1, Double_t &a1Err, Double_t &a2, Double_t &a2Err)
	This function gets the background parameters and their errors.

Double_t	GetChi () const

Double_t *	GetPositions () const

Double_t *	GetPositionsErrors () const

void	GetSigma (Double_t &sigma, Double_t &sigmaErr)
	This function gets the sigma parameter and its error.

void	GetTailParameters (Double_t &t, Double_t &tErr, Double_t &b, Double_t &bErr, Double_t &s, Double_t &sErr)
	This function gets the tail parameters and their errors.

void	SetBackgroundParameters (Double_t a0Init, Bool_t fixA0, Double_t a1Init, Bool_t fixA1, Double_t a2Init, Bool_t fixA2)
	This function sets the following fitting parameters of background:

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)
	This function sets the following fitting parameters:

void	SetPeakParameters (Double_t sigma, Bool_t fixSigma, const Double_t positionInit, const Bool_t fixPosition, const Double_t ampInit, const Bool_t fixAmp)
	This function sets the following fitting parameters of peaks:

void	SetTailParameters (Double_t tInit, Bool_t fixT, Double_t bInit, Bool_t fixB, Double_t sInit, Bool_t fixS)
	This function sets the following fitting parameters of tails of peaks.

Public Member Functions inherited from TNamed
	TNamed ()

	TNamed (const char name, const char title)

	TNamed (const TNamed &named)
	TNamed copy ctor.

	TNamed (const TString &name, const TString &title)

virtual	~TNamed ()
	TNamed destructor.

virtual void	Clear (Option_t *option="")
	Set name and title to empty strings ("").

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

virtual Int_t	Compare (const TObject *obj) const
	Compare two TNamed objects.

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

virtual void	FillBuffer (char *&buffer)
	Encode TNamed into output buffer.

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

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

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

virtual Bool_t	IsSortable () const

virtual void	ls (Option_t *option="") const
	List TNamed name and title.

TNamed &	operator= (const TNamed &rhs)
	TNamed assignment operator.

virtual void	Print (Option_t *option="") const
	Print TNamed name and title.

virtual void	SetName (const char *name)
	Set the name of the TNamed.

virtual void	SetNameTitle (const char name, const char title)
	Set all the TNamed parameters (name and title).

virtual void	SetTitle (const char *title="")
	Set the title of the TNamed.

virtual Int_t	Sizeof () const
	Return size of the TNamed part of the TObject.

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

	TObject (const TObject &object)
	TObject copy ctor.

virtual	~TObject ()
	TObject destructor.

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

virtual void	AppendPad (Option_t *option="")
	Append graphics object to current pad.

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

ULong_t	CheckedHash ()
	Check and record whether this class has a consistent Hash/RecursiveRemove setup (*) and then return the regular Hash value for this object.

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

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

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

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

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

virtual TObject *	DrawClone (Option_t *option="") const
	Draw a clone of this object in the current selected pad for instance with: `gROOT->SetSelectedPad(gPad)`.

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

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

virtual void	Execute (const char method, const char params, Int_t *error=0)
	Execute method on this object with the given parameter string, e.g.

virtual void	Execute (TMethod method, TObjArray params, Int_t *error=0)
	Execute method on this object with parameters stored in the TObjArray.

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

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

virtual TObject *	FindObject (const char *name) const
	Must be redefined in derived classes.

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

virtual Option_t *	GetDrawOption () const
	Get option used by the graphics system to draw this object.

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

virtual char *	GetObjectInfo (Int_t px, Int_t py) const
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virtual Option_t *	GetOption () const

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

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

Bool_t	HasInconsistentHash () const
	Return true is the type of this object is known to have an inconsistent setup for Hash and RecursiveRemove (i.e.

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

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

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

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

void	InvertBit (UInt_t f)

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

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

R__ALWAYS_INLINE Bool_t	IsOnHeap () const

R__ALWAYS_INLINE Bool_t	IsZombie () const

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

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

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

void	operator delete (void *ptr)
	Operator delete.

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

void *	operator new (size_t sz)

void *	operator new (size_t sz, void *vp)

void *	operator new[] (size_t sz)

void *	operator new[] (size_t sz, void *vp)

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

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

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

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

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

void	ResetBit (UInt_t f)

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

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

void	SetBit (UInt_t f)

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

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

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

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

R__ALWAYS_INLINE Bool_t	TestBit (UInt_t f) const

Int_t	TestBits (UInt_t f) const

virtual void	UseCurrentStyle ()
	Set current style settings in this object This function is called when either TCanvas::UseCurrentStyle or TROOT::ForceStyle have been invoked.

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

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

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

Protected Member Functions
Double_t	Area (Double_t a, Double_t sigma, Double_t t, Double_t b)
	This function calculates area of a peak Function parameters:

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	Deramp (Double_t i, Double_t i0, Double_t sigma, Double_t t, Double_t s, Double_t b)
	This function calculates derivative of peak shape function (see manual) according to amplitude 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)
	This function calculates derivative of peaks shape function (see manual) according to slope b.

Double_t	Derderi0 (Double_t i, Double_t amp, Double_t i0, Double_t sigma)
	This function calculates second derivative of peak shape function (see manual) according to peak position.

Double_t	Derdersigma (Int_t num_of_fitted_peaks, Double_t i, const Double_t *parameter, Double_t sigma)
	This function calculates second derivative of peaks shape function (see manual) according to sigma of peaks.

Double_t	Derfc (Double_t x)
	This function calculates derivative of error function of x.

Double_t	Deri0 (Double_t i, Double_t amp, Double_t i0, Double_t sigma, Double_t t, Double_t s, Double_t b)
	This function calculates derivative of peak shape function (see manual) according to peak position.

Double_t	Derpa (Double_t sigma, Double_t t, Double_t b)
	This function calculates derivative of the area of peak according to its amplitude.

Double_t	Derpb (Double_t a, Double_t sigma, Double_t t, Double_t b)
	This function calculates derivative of the area of peak according to b parameter.

Double_t	Derpsigma (Double_t a, Double_t t, Double_t b)
	This function calculates derivative of the area of peak according to sigma of peaks.

Double_t	Derpt (Double_t a, Double_t sigma, Double_t b)
	This function calculates derivative of the area of peak according to t parameter.

Double_t	Ders (Int_t num_of_fitted_peaks, Double_t i, const Double_t *parameter, Double_t sigma)
	This function calculates derivative of peaks shape function (see manual) according to relative amplitude s.

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)
	This function calculates derivative of peaks shape function (see manual) according to sigma of peaks.

Double_t	Dert (Int_t num_of_fitted_peaks, Double_t i, const Double_t *parameter, Double_t sigma, Double_t b)
	This function calculates derivative of peaks shape function (see manual) according to relative amplitude t.

Double_t	Erfc (Double_t x)

Double_t	Ourpowl (Double_t a, Int_t pw)
	Power function.

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)
	This function calculates peaks shape function (see manual) Function parameters:

void	StiefelInversion (Double_t **a, Int_t rozmer)
	This function calculates solution of the system of linear equations.

Protected Member Functions inherited from TObject
virtual void	DoError (int level, const char location, const char fmt, va_list va) const
	Interface to ErrorHandler (protected).

void	MakeZombie ()

Protected Attributes
Double_t	fA0Calc
	calculated value of background a0 parameter

Double_t	fA0Err
	error value of background a0 parameter

Double_t	fA0Init
	initial value of background a0 parameter(backgroud is estimated as a0+a1x+a2x*x)

Double_t	fA1Calc
	calculated value of background a1 parameter

Double_t	fA1Err
	error value of background a1 parameter

Double_t	fA1Init
	initial value of background a1 parameter(backgroud is estimated as a0+a1x+a2x*x)

Double_t	fA2Calc
	calculated value of background a2 parameter

Double_t	fA2Err
	error value of background a2 parameter

Double_t	fA2Init
	initial value of background a2 parameter(backgroud is estimated as a0+a1x+a2x*x)

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

Int_t	fAlphaOptim
	optimization 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_t	fBCalc
	calculated value of b parameter

Double_t	fBErr
	error value of b parameter

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

Double_t	fChi
	here the fitting functions return resulting chi square

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

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).

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	fFixB
	logical 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_t	fFixS
	logical value of s parameter, which allows to fix the parameter (not to fit).

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).

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

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

Double_t	fSCalc
	calculated value of s parameter

Double_t	fSErr
	error value of s parameter

Double_t	fSigmaCalc
	calculated value of sigma parameter

Double_t	fSigmaErr
	error value of sigma parameter

Double_t	fSigmaInit
	initial value of sigma parameter

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

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

Double_t	fTCalc
	calculated value of t parameter

Double_t	fTErr
	error value of t parameter

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

Int_t	fXmax
	last fitted channel

Int_t	fXmin
	first fitted channel

Protected Attributes inherited from TNamed
TString	fName

TString	fTitle

Additional Inherited Members
Static Public Member Functions inherited from TObject
static Long_t	GetDtorOnly ()
	Return destructor only flag.

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

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

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

Protected Types inherited from TObject
enum	{ kOnlyPrepStep = BIT(3) }

#include <TSpectrumFit.h>

Inheritance diagram for TSpectrumFit:

[legend]

Member Enumeration Documentation

◆ anonymous enum

anonymous enum

Enumerator
kFitOptimChiCounts
kFitOptimChiFuncValues
kFitOptimMaxLikelihood
kFitAlphaHalving
kFitAlphaOptimal
kFitPower2
kFitPower4
kFitPower6
kFitPower8
kFitPower10
kFitPower12
kFitTaylorOrderFirst
kFitTaylorOrderSecond
kFitNumRegulCycles

Definition at line 70 of file TSpectrumFit.h.

Constructor & Destructor Documentation

◆ TSpectrumFit() [1/2]

TSpectrumFit::TSpectrumFit ( void )

Default constructor.

Definition at line 35 of file TSpectrumFit.cxx.

◆ TSpectrumFit() [2/2]

TSpectrumFit::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).

Definition at line 101 of file TSpectrumFit.cxx.

◆ ~TSpectrumFit()

TSpectrumFit::~TSpectrumFit ( )

virtual

Destructor.

Definition at line 160 of file TSpectrumFit.cxx.

Member Function Documentation

◆ Area()

Double_t TSpectrumFit::Area	(	Double_t	a,
		Double_t	sigma,
		Double_t	t,
		Double_t	b
	)

protected

This function calculates area of a peak Function parameters:

a-amplitude of the peak
sigma-sigma of peak
t-relative amplitude
b-slope

Definition at line 569 of file TSpectrumFit.cxx.

◆ Dera1()

Double_t TSpectrumFit::Dera1 ( Double_t i )

protected

Derivative of background according to a1.

Definition at line 492 of file TSpectrumFit.cxx.

◆ Dera2()

Double_t TSpectrumFit::Dera2 ( Double_t i )

protected

Derivative of background according to a2.

Definition at line 500 of file TSpectrumFit.cxx.

◆ Deramp()

Double_t TSpectrumFit::Deramp	(	Double_t	i,
		Double_t	i0,
		Double_t	sigma,
		Double_t	t,
		Double_t	s,
		Double_t	b
	)

protected

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

Definition at line 229 of file TSpectrumFit.cxx.

◆ Derb()

Double_t TSpectrumFit::Derb	(	Int_t	num_of_fitted_peaks,
		Double_t	i,
		const Double_t *	parameter,
		Double_t	sigma,
		Double_t	t,
		Double_t	b
	)

protected

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

Definition at line 463 of file TSpectrumFit.cxx.

◆ Derderi0()

Double_t TSpectrumFit::Derderi0	(	Double_t	i,
		Double_t	amp,
		Double_t	i0,
		Double_t	sigma
	)

protected

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

Definition at line 303 of file TSpectrumFit.cxx.

◆ Derdersigma()

Double_t TSpectrumFit::Derdersigma	(	Int_t	num_of_fitted_peaks,
		Double_t	i,
		const Double_t *	parameter,
		Double_t	sigma
	)

protected

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

Definition at line 376 of file TSpectrumFit.cxx.

◆ Derfc()

Double_t TSpectrumFit::Derfc ( Double_t x )

protected

This function calculates derivative of error function of x.

Definition at line 200 of file TSpectrumFit.cxx.

◆ Deri0()

Double_t TSpectrumFit::Deri0	(	Double_t	i,
		Double_t	amp,
		Double_t	i0,
		Double_t	sigma,
		Double_t	t,
		Double_t	s,
		Double_t	b
	)

protected

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

Definition at line 266 of file TSpectrumFit.cxx.

◆ Derpa()

Double_t TSpectrumFit::Derpa	(	Double_t	sigma,
		Double_t	t,
		Double_t	b
	)

protected

This function calculates derivative of the area of peak according to its amplitude.

Function parameters:

sigma-sigma of peak
t-relative amplitudes
b-slope

Definition at line 592 of file TSpectrumFit.cxx.

◆ Derpb()

Double_t TSpectrumFit::Derpb	(	Double_t	a,
		Double_t	sigma,
		Double_t	t,
		Double_t	b
	)

protected

This function calculates derivative of the area of peak according to b parameter.

Function parameters:

sigma-sigma of peak
t-relative amplitudes
b-slope

Definition at line 658 of file TSpectrumFit.cxx.

◆ Derpsigma()

Double_t TSpectrumFit::Derpsigma	(	Double_t	a,
		Double_t	t,
		Double_t	b
	)

protected

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

Definition at line 614 of file TSpectrumFit.cxx.

◆ Derpt()

Double_t TSpectrumFit::Derpt	(	Double_t	a,
		Double_t	sigma,
		Double_t	b
	)

protected

This function calculates derivative of the area of peak according to t parameter.

Function parameters:

sigma-sigma of peak
t-relative amplitudes
b-slope

Definition at line 636 of file TSpectrumFit.cxx.

◆ Ders()

Double_t TSpectrumFit::Ders	(	Int_t	num_of_fitted_peaks,
		Double_t	i,
		const Double_t *	parameter,
		Double_t	sigma
	)

protected

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

Definition at line 437 of file TSpectrumFit.cxx.

◆ Dersigma()

Double_t TSpectrumFit::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
	)

protected

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

Definition at line 331 of file TSpectrumFit.cxx.

◆ Dert()

Double_t TSpectrumFit::Dert	(	Int_t	num_of_fitted_peaks,
		Double_t	i,
		const Double_t *	parameter,
		Double_t	sigma,
		Double_t	b
	)

protected

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

Definition at line 409 of file TSpectrumFit.cxx.

◆ Erfc()

Double_t TSpectrumFit::Erfc ( Double_t x )

protected

Definition at line 177 of file TSpectrumFit.cxx.

◆ FitAwmi()

void TSpectrumFit::FitAwmi ( Double_t * source )

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 neighbouring 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 non-symmetrical semi-empirical peak shape function [1]
it contains the symmetrical Gaussian as well as non-symmetrical 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].

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. Morhac, J. Kliman, M. Jandel, L. Krupa, V. Matouoek: 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);
}

Definition at line 820 of file TSpectrumFit.cxx.

◆ FitStiefel()

void TSpectrumFit::FitStiefel ( Double_t * source )

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

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("SAMEL");
   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);
}

Definition at line 1857 of file TSpectrumFit.cxx.

◆ GetAmplitudes()

Double_t * TSpectrumFit::GetAmplitudes ( ) const

inline

Definition at line 116 of file TSpectrumFit.h.

◆ GetAmplitudesErrors()

Double_t * TSpectrumFit::GetAmplitudesErrors ( ) const

inline

Definition at line 117 of file TSpectrumFit.h.

◆ GetAreas()

Double_t * TSpectrumFit::GetAreas ( ) const

inline

Definition at line 118 of file TSpectrumFit.h.

◆ GetAreasErrors()

Double_t * TSpectrumFit::GetAreasErrors ( ) const

inline

Definition at line 119 of file TSpectrumFit.h.

◆ GetBackgroundParameters()

void TSpectrumFit::GetBackgroundParameters	(	Double_t &	a0,
		Double_t &	a0Err,
		Double_t &	a1,
		Double_t &	a1Err,
		Double_t &	a2,
		Double_t &	a2Err
	)

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

Definition at line 2740 of file TSpectrumFit.cxx.

◆ GetChi()

Double_t TSpectrumFit::GetChi ( ) const

inline

Definition at line 121 of file TSpectrumFit.h.

◆ GetPositions()

Double_t * TSpectrumFit::GetPositions ( ) const

inline

Definition at line 122 of file TSpectrumFit.h.

◆ GetPositionsErrors()

Double_t * TSpectrumFit::GetPositionsErrors ( ) const

inline

Definition at line 123 of file TSpectrumFit.h.

◆ GetSigma()

void TSpectrumFit::GetSigma	(	Double_t &	sigma,
		Double_t &	sigmaErr
	)

This function gets the sigma parameter and its error.

sigma - gets the fitted value of sigma parameter
sigmaErr - gets error value of sigma parameter

Definition at line 2725 of file TSpectrumFit.cxx.

◆ GetTailParameters()

void TSpectrumFit::GetTailParameters	(	Double_t &	t,
		Double_t &	tErr,
		Double_t &	b,
		Double_t &	bErr,
		Double_t &	s,
		Double_t &	sErr
	)

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

Definition at line 2760 of file TSpectrumFit.cxx.

◆ Ourpowl()

Double_t TSpectrumFit::Ourpowl	(	Double_t	a,
		Int_t	pw
	)

protected

Power function.

Definition at line 674 of file TSpectrumFit.cxx.

◆ SetBackgroundParameters()

void TSpectrumFit::SetBackgroundParameters	(	Double_t	a0Init,
		Bool_t	fixA0,
		Double_t	a1Init,
		Bool_t	fixA1,
		Double_t	a2Init,
		Bool_t	fixA2
	)

This function sets the following fitting parameters of background:

a0Init - initial value of a0 parameter (background 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)

Definition at line 2691 of file TSpectrumFit.cxx.

◆ SetFitParameters()

void TSpectrumFit::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
	)

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.

Definition at line 2608 of file TSpectrumFit.cxx.

◆ SetPeakParameters()

void TSpectrumFit::SetPeakParameters	(	Double_t	sigma,
		Bool_t	fixSigma,
		const Double_t *	positionInit,
		const Bool_t *	fixPosition,
		const Double_t *	ampInit,
		const Bool_t *	fixAmp
	)

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 - array 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 - array of initial values of peaks amplitudes
fixAmp - array of logical values which allow to fix appropriate amplitudes (not fit). However they are present in the estimated functional

Definition at line 2656 of file TSpectrumFit.cxx.

◆ SetTailParameters()

void TSpectrumFit::SetTailParameters	(	Double_t	tInit,
		Bool_t	fixT,
		Double_t	bInit,
		Bool_t	fixB,
		Double_t	sInit,
		Bool_t	fixS
	)

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)

Definition at line 2710 of file TSpectrumFit.cxx.

◆ Shape()

Double_t TSpectrumFit::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
	)

protected

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

Definition at line 516 of file TSpectrumFit.cxx.

◆ StiefelInversion()

void TSpectrumFit::StiefelInversion	(	Double_t **	a,
		Int_t	size
	)

protected

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

Definition at line 1721 of file TSpectrumFit.cxx.

Member Data Documentation

◆ fA0Calc

Double_t TSpectrumFit::fA0Calc

protected

calculated value of background a0 parameter

Definition at line 51 of file TSpectrumFit.h.

◆ fA0Err

Double_t TSpectrumFit::fA0Err

protected

error value of background a0 parameter

Definition at line 52 of file TSpectrumFit.h.

◆ fA0Init

Double_t TSpectrumFit::fA0Init

protected

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

Definition at line 50 of file TSpectrumFit.h.

◆ fA1Calc

Double_t TSpectrumFit::fA1Calc

protected

calculated value of background a1 parameter

Definition at line 54 of file TSpectrumFit.h.

◆ fA1Err

Double_t TSpectrumFit::fA1Err

protected

error value of background a1 parameter

Definition at line 55 of file TSpectrumFit.h.

◆ fA1Init

Double_t TSpectrumFit::fA1Init

protected

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

Definition at line 53 of file TSpectrumFit.h.

◆ fA2Calc

Double_t TSpectrumFit::fA2Calc

protected

calculated value of background a2 parameter

Definition at line 57 of file TSpectrumFit.h.

◆ fA2Err

Double_t TSpectrumFit::fA2Err

protected

error value of background a2 parameter

Definition at line 58 of file TSpectrumFit.h.

◆ fA2Init

Double_t TSpectrumFit::fA2Init

protected

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

Definition at line 56 of file TSpectrumFit.h.

◆ fAlpha

Double_t TSpectrumFit::fAlpha

protected

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

Definition at line 28 of file TSpectrumFit.h.

◆ fAlphaOptim

Int_t TSpectrumFit::fAlphaOptim

protected

optimization of convergence algorithm, possible values kFitAlphaHalving, kFitAlphaOptimal

Definition at line 25 of file TSpectrumFit.h.

◆ fAmpCalc

Double_t* TSpectrumFit::fAmpCalc

protected

[fNPeaks] array of calculated values of fitted amplitudes, output parameters

Definition at line 34 of file TSpectrumFit.h.

◆ fAmpErr

Double_t* TSpectrumFit::fAmpErr

protected

[fNPeaks] array of amplitude errors

Definition at line 35 of file TSpectrumFit.h.

◆ fAmpInit

Double_t* TSpectrumFit::fAmpInit

protected

[fNPeaks] array of initial values of peaks amplitudes, input parameters

Definition at line 33 of file TSpectrumFit.h.

◆ fArea

Double_t* TSpectrumFit::fArea

protected

[fNPeaks] array of calculated areas of peaks

Definition at line 36 of file TSpectrumFit.h.

◆ fAreaErr

Double_t* TSpectrumFit::fAreaErr

protected

[fNPeaks] array of errors of peak areas

Definition at line 37 of file TSpectrumFit.h.

◆ fBCalc

Double_t TSpectrumFit::fBCalc

protected

calculated value of b parameter

Definition at line 45 of file TSpectrumFit.h.

◆ fBErr

Double_t TSpectrumFit::fBErr

protected

error value of b parameter

Definition at line 46 of file TSpectrumFit.h.

◆ fBInit

Double_t TSpectrumFit::fBInit

protected

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

Definition at line 44 of file TSpectrumFit.h.

◆ fChi

Double_t TSpectrumFit::fChi

protected

here the fitting functions return resulting chi square

Definition at line 29 of file TSpectrumFit.h.

◆ fFitTaylor

Int_t TSpectrumFit::fFitTaylor

protected

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

Definition at line 27 of file TSpectrumFit.h.

◆ fFixA0

Bool_t TSpectrumFit::fFixA0

protected

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

Definition at line 65 of file TSpectrumFit.h.

◆ fFixA1

Bool_t TSpectrumFit::fFixA1

protected

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

Definition at line 66 of file TSpectrumFit.h.

◆ fFixA2

Bool_t TSpectrumFit::fFixA2

protected

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

Definition at line 67 of file TSpectrumFit.h.

◆ fFixAmp

Bool_t* TSpectrumFit::fFixAmp

protected

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

Definition at line 60 of file TSpectrumFit.h.

◆ fFixB

Bool_t TSpectrumFit::fFixB

protected

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

Definition at line 63 of file TSpectrumFit.h.

◆ fFixPosition

Bool_t* TSpectrumFit::fFixPosition

protected

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

Definition at line 59 of file TSpectrumFit.h.

◆ fFixS

Bool_t TSpectrumFit::fFixS

protected

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

Definition at line 64 of file TSpectrumFit.h.

◆ fFixSigma

Bool_t TSpectrumFit::fFixSigma

protected

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

Definition at line 61 of file TSpectrumFit.h.

◆ fFixT

Bool_t TSpectrumFit::fFixT

protected

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

Definition at line 62 of file TSpectrumFit.h.

◆ fNPeaks

Int_t TSpectrumFit::fNPeaks

protected

number of peaks present in fit, input parameter, it should be > 0

Definition at line 20 of file TSpectrumFit.h.

◆ fNumberIterations

Int_t TSpectrumFit::fNumberIterations

protected

number of iterations in fitting procedure, input parameter, it should be > 0

Definition at line 21 of file TSpectrumFit.h.

◆ fPositionCalc

Double_t* TSpectrumFit::fPositionCalc

protected

[fNPeaks] array of calculated values of fitted positions, output parameters

Definition at line 31 of file TSpectrumFit.h.

◆ fPositionErr

Double_t* TSpectrumFit::fPositionErr

protected

[fNPeaks] array of position errors

Definition at line 32 of file TSpectrumFit.h.

◆ fPositionInit

Double_t* TSpectrumFit::fPositionInit

protected

[fNPeaks] array of initial values of peaks positions, input parameters

Definition at line 30 of file TSpectrumFit.h.

◆ fPower

Int_t TSpectrumFit::fPower

protected

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

Definition at line 26 of file TSpectrumFit.h.

◆ fSCalc

Double_t TSpectrumFit::fSCalc

protected

calculated value of s parameter

Definition at line 48 of file TSpectrumFit.h.

◆ fSErr

Double_t TSpectrumFit::fSErr

protected

error value of s parameter

Definition at line 49 of file TSpectrumFit.h.

◆ fSigmaCalc

Double_t TSpectrumFit::fSigmaCalc

protected

calculated value of sigma parameter

Definition at line 39 of file TSpectrumFit.h.

◆ fSigmaErr

Double_t TSpectrumFit::fSigmaErr

protected

error value of sigma parameter

Definition at line 40 of file TSpectrumFit.h.

◆ fSigmaInit

Double_t TSpectrumFit::fSigmaInit

protected

initial value of sigma parameter

Definition at line 38 of file TSpectrumFit.h.

◆ fSInit

Double_t TSpectrumFit::fSInit

protected

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

Definition at line 47 of file TSpectrumFit.h.

◆ fStatisticType

Int_t TSpectrumFit::fStatisticType

protected

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

Definition at line 24 of file TSpectrumFit.h.

◆ fTCalc

Double_t TSpectrumFit::fTCalc

protected

calculated value of t parameter

Definition at line 42 of file TSpectrumFit.h.

◆ fTErr

Double_t TSpectrumFit::fTErr

protected

error value of t parameter

Definition at line 43 of file TSpectrumFit.h.

◆ fTInit

Double_t TSpectrumFit::fTInit

protected

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

Definition at line 41 of file TSpectrumFit.h.

◆ fXmax

Int_t TSpectrumFit::fXmax

protected

last fitted channel

Definition at line 23 of file TSpectrumFit.h.

◆ fXmin

Int_t TSpectrumFit::fXmin

protected

first fitted channel

Definition at line 22 of file TSpectrumFit.h.

Libraries for TSpectrumFit:

[legend]

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

hist/spectrum/inc/TSpectrumFit.h
hist/spectrum/src/TSpectrumFit.cxx

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ TSpectrumFit() [1/2]

◆ TSpectrumFit() [2/2]

◆ ~TSpectrumFit()

Member Function Documentation

◆ Area()

◆ Dera1()

◆ Dera2()

◆ Deramp()

◆ Derb()

◆ Derderi0()

◆ Derdersigma()

◆ Derfc()

◆ Deri0()

◆ Derpa()

◆ Derpb()

◆ Derpsigma()

◆ Derpt()

◆ Ders()

◆ Dersigma()

◆ Dert()

◆ Erfc()

◆ FitAwmi()

Fitting

References:

Example - script FitAwmi.c:

Script:

◆ FitStiefel()

Example - script FitStiefel.c:

Script:

◆ GetAmplitudes()

◆ GetAmplitudesErrors()

◆ GetAreas()

◆ GetAreasErrors()

◆ GetBackgroundParameters()

◆ GetChi()

◆ GetPositions()

◆ GetPositionsErrors()

◆ GetSigma()

◆ GetTailParameters()

◆ Ourpowl()

◆ SetBackgroundParameters()

◆ SetFitParameters()

◆ SetPeakParameters()

◆ SetTailParameters()

◆ Shape()

◆ StiefelInversion()

Member Data Documentation

◆ fA0Calc

◆ fA0Err

◆ fA0Init

◆ fA1Calc

◆ fA1Err

◆ fA1Init

◆ fA2Calc

◆ fA2Err

◆ fA2Init

◆ fAlpha

◆ fAlphaOptim

◆ fAmpCalc

◆ fAmpErr

◆ fAmpInit

◆ fArea

◆ fAreaErr

◆ fBCalc

◆ fBErr

◆ fBInit

◆ fChi

◆ fFitTaylor

◆ fFixA0

◆ fFixA1

◆ fFixA2

◆ fFixAmp