Advanced 2-dimensional spectra fitting functions.

Author: Miroslav Morhac

Class for fitting 2D 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 TSpectrum2Fit.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, kBitMask = 0x00ffffff }

enum	{ kSingleKey = BIT(0), kOverwrite = BIT(1), kWriteDelete = BIT(2) }

enum	EStatusBits { kCanDelete = BIT(0), kMustCleanup = BIT(3), kObjInCanvas = BIT(3), kIsReferenced = BIT(4), kHasUUID = BIT(5), kCannotPick = BIT(6), kNoContextMenu = BIT(8), kInvalidObject = BIT(13) }

Public Member Functions
	TSpectrum2Fit (void)
	Default constructor. More...

	TSpectrum2Fit (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. More...

virtual	~TSpectrum2Fit ()
	Destructor. More...

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

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

void	GetAmplitudeErrors (Double_t amplitudeErrors, Double_t amplitudeErrorsX1, Double_t *amplitudeErrorsY1)
	This function gets the amplitudes of fitted 2D peaks and 1D ridges. More...

void	GetAmplitudes (Double_t amplitudes, Double_t amplitudesX1, Double_t *amplitudesY1)
	This function gets the amplitudes of fitted 2D peaks and 1D ridges. More...

void	GetBackgroundParameters (Double_t &a0, Double_t &a0Err, Double_t &ax, Double_t &axErr, Double_t &ay, Double_t &ayErr)
	This function gets the background parameters and their errors. More...

Double_t	GetChi () const

void	GetPositionErrors (Double_t positionErrorsX, Double_t positionErrorsY, Double_t positionErrorsX1, Double_t positionErrorsY1)
	This function gets the errors of positions of fitted 2D peaks and 1D ridges. More...

void	GetPositions (Double_t positionsX, Double_t positionsY, Double_t positionsX1, Double_t positionsY1)
	This function gets the positions of fitted 2D peaks and 1D ridges. More...

void	GetRo (Double_t &ro, Double_t &roErr)
	This function gets the ro parameter and its error. More...

void	GetSigmaX (Double_t &sigmaX, Double_t &sigmaErrX)
	This function gets the sigma x parameter and its error. More...

void	GetSigmaY (Double_t &sigmaY, Double_t &sigmaErrY)
	This function gets the sigma y parameter and its error. More...

void	GetTailParameters (Double_t &txy, Double_t &txyErr, Double_t &tx, Double_t &txErr, Double_t &ty, Double_t &tyErr, Double_t &bx, Double_t &bxErr, Double_t &by, Double_t &byErr, Double_t &sxy, Double_t &sxyErr, Double_t &sx, Double_t &sxErr, Double_t &sy, Double_t &syErr)
	This function gets the tail parameters and their errors. More...

void	GetVolumeErrors (Double_t *volumeErrors)
	This function gets errors of the volumes of fitted 2D peaks. More...

void	GetVolumes (Double_t *volumes)
	This function gets the volumes of fitted 2D peaks. More...

void	SetBackgroundParameters (Double_t a0Init, Bool_t fixA0, Double_t axInit, Bool_t fixAx, Double_t ayInit, Bool_t fixAy)
	This function sets the following fitting parameters of background: More...

void	SetFitParameters (Int_t xmin, Int_t xmax, Int_t ymin, Int_t ymax, 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: More...

void	SetPeakParameters (Double_t sigmaX, Bool_t fixSigmaX, Double_t sigmaY, Bool_t fixSigmaY, Double_t ro, Bool_t fixRo, const Double_t positionInitX, const Bool_t fixPositionX, const Double_t positionInitY, const Bool_t fixPositionY, const Double_t positionInitX1, const Bool_t fixPositionX1, const Double_t positionInitY1, const Bool_t fixPositionY1, const Double_t ampInit, const Bool_t fixAmp, const Double_t ampInitX1, const Bool_t fixAmpX1, const Double_t ampInitY1, const Bool_t fixAmpY1)
	This function sets the following fitting parameters of peaks: More...

void	SetTailParameters (Double_t tInitXY, Bool_t fixTxy, Double_t tInitX, Bool_t fixTx, Double_t tInitY, Bool_t fixTy, Double_t bInitX, Bool_t fixBx, Double_t bInitY, Bool_t fixBy, Double_t sInitXY, Bool_t fixSxy, Double_t sInitX, Bool_t fixSx, Double_t sInitY, Bool_t fixSy)
	This function sets the following fitting parameters of tails of peaks. More...

Public Member Functions inherited from TNamed
	TNamed ()

	TNamed (const char name, const char title)

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

	TNamed (const TNamed &named)
	TNamed copy ctor. More...

virtual	~TNamed ()

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

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 two TNamed objects. More...

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

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

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

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

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

virtual Bool_t	IsSortable () const

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Bool_t	IsOnHeap () const

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). 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 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...

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...

Protected Member Functions
Double_t	Deramp2 (Double_t x, Double_t y, Double_t x0, Double_t y0, Double_t sigmax, Double_t sigmay, Double_t ro, Double_t txy, Double_t sxy, Double_t bx, Double_t by)
	This function calculates derivative of 2D peaks shape function (see manual) according to amplitude of 2D peak. More...

Double_t	Derampx (Double_t x, Double_t x0, Double_t sigmax, Double_t tx, Double_t sx, Double_t bx)
	This function calculates derivative of 2D peaks shape function (see manual) according to amplitude of the ridge. More...

Double_t	Derbx (Int_t numOfFittedPeaks, Double_t x, Double_t y, const Double_t *parameter, Double_t sigmax, Double_t sigmay, Double_t txy, Double_t tx, Double_t bx, Double_t by)
	This function calculates derivative of peaks shape function (see manual) according to slope bx. More...

Double_t	Derby (Int_t numOfFittedPeaks, Double_t x, Double_t y, const Double_t *parameter, Double_t sigmax, Double_t sigmay, Double_t txy, Double_t ty, Double_t bx, Double_t by)
	This function calculates derivative of peaks shape function (see manual) according to slope by. More...

Double_t	Derderi01 (Double_t x, Double_t ax, Double_t x0, Double_t sigmax)
	This function calculates second derivative of 2D peaks shape function (see manual) according to x position of 1D ridge. More...

Double_t	Derderi02 (Double_t x, Double_t y, Double_t a, Double_t x0, Double_t y0, Double_t sigmax, Double_t sigmay, Double_t ro)
	This function calculates second derivative of 2D peaks shape function (see manual) according to x position of 2D peak. More...

Double_t	Derderj02 (Double_t x, Double_t y, Double_t a, Double_t x0, Double_t y0, Double_t sigmax, Double_t sigmay, Double_t ro)
	This function calculates second derivative of 2D peaks shape function (see manual) according to y position of 2D peak. More...

Double_t	Derdersigmax (Int_t numOfFittedPeaks, Double_t x, Double_t y, const Double_t *parameter, Double_t sigmax, Double_t sigmay, Double_t ro)
	This function calculates second derivative of peaks shape function (see manual) according to sigmax of peaks. More...

Double_t	Derdersigmay (Int_t numOfFittedPeaks, Double_t x, Double_t y, const Double_t *parameter, Double_t sigmax, Double_t sigmay, Double_t ro)
	This function calculates second derivative of peaks shape function (see manual) according to sigmay of peaks. More...

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

Double_t	Deri01 (Double_t x, Double_t ax, Double_t x0, Double_t sigmax, Double_t tx, Double_t sx, Double_t bx)
	This function calculates derivative of 2D peaks shape function (see manual) according to x position of 1D ridge. More...

Double_t	Deri02 (Double_t x, Double_t y, Double_t a, Double_t x0, Double_t y0, Double_t sigmax, Double_t sigmay, Double_t ro, Double_t txy, Double_t sxy, Double_t bx, Double_t by)
	This function calculates derivative of 2D peaks shape function (see manual) according to x position of 2D peak. More...

Double_t	Derj02 (Double_t x, Double_t y, Double_t a, Double_t x0, Double_t y0, Double_t sigmax, Double_t sigmay, Double_t ro, Double_t txy, Double_t sxy, Double_t bx, Double_t by)
	This function calculates derivative of 2D peaks shape function (see manual) according to y position of 2D peak Function parameters: More...

Double_t	Derpa2 (Double_t sx, Double_t sy, Double_t ro)
	This function calculates derivative of the volume of a peak according to amplitude. More...

Double_t	Derpro (Double_t a, Double_t sx, Double_t sy, Double_t ro)
	This function calculates derivative of the volume of a peak according to ro. More...

Double_t	Derpsigmax (Double_t a, Double_t sy, Double_t ro)
	This function calculates derivative of the volume of a peak according to sigmax. More...

Double_t	Derpsigmay (Double_t a, Double_t sx, Double_t ro)
	This function calculates derivative of the volume of a peak according to sigmay. More...

Double_t	Derro (Int_t numOfFittedPeaks, Double_t x, Double_t y, const Double_t *parameter, Double_t sx, Double_t sy, Double_t r)
	This function calculates derivative of peaks shape function (see manual) according to correlation coefficient ro. More...

Double_t	Dersigmax (Int_t numOfFittedPeaks, Double_t x, Double_t y, const Double_t *parameter, Double_t sigmax, Double_t sigmay, Double_t ro, Double_t txy, Double_t sxy, Double_t tx, Double_t sx, Double_t bx, Double_t by)
	This function calculates derivative of peaks shape function (see manual) according to sigmax of peaks. More...

Double_t	Dersigmay (Int_t numOfFittedPeaks, Double_t x, Double_t y, const Double_t *parameter, Double_t sigmax, Double_t sigmay, Double_t ro, Double_t txy, Double_t sxy, Double_t ty, Double_t sy, Double_t bx, Double_t by)
	This function calculates derivative of peaks shape function (see manual) according to sigmax of peaks. More...

Double_t	Dersx (Int_t numOfFittedPeaks, Double_t x, const Double_t *parameter, Double_t sigmax)
	This function calculates derivative of peaks shape function (see manual) according to relative amplitude sx. More...

Double_t	Dersxy (Int_t numOfFittedPeaks, Double_t x, Double_t y, const Double_t *parameter, Double_t sigmax, Double_t sigmay)
	This function calculates derivative of peaks shape function (see manual) according to relative amplitude sxy. More...

Double_t	Dersy (Int_t numOfFittedPeaks, Double_t x, const Double_t *parameter, Double_t sigmax)
	This function calculates derivative of peaks shape function (see manual) according to relative amplitude sy. More...

Double_t	Dertx (Int_t numOfFittedPeaks, Double_t x, const Double_t *parameter, Double_t sigmax, Double_t bx)
	This function calculates derivative of peaks shape function (see manual) according to relative amplitude tx. More...

Double_t	Dertxy (Int_t numOfFittedPeaks, Double_t x, Double_t y, const Double_t *parameter, Double_t sigmax, Double_t sigmay, Double_t bx, Double_t by)
	This function calculates derivative of peaks shape function (see manual) according to relative amplitude txy. More...

Double_t	Derty (Int_t numOfFittedPeaks, Double_t x, const Double_t *parameter, Double_t sigmax, Double_t bx)
	This function calculates derivative of peaks shape function (see manual) according to relative amplitude ty. More...

Double_t	Erfc (Double_t x)
	This function calculates error function of x. More...

Double_t	Ourpowl (Double_t a, Int_t pw)
	power function More...

Double_t	Shape2 (Int_t numOfFittedPeaks, Double_t x, Double_t y, const Double_t *parameter, Double_t sigmax, Double_t sigmay, Double_t ro, Double_t a0, Double_t ax, Double_t ay, Double_t txy, Double_t sxy, Double_t tx, Double_t ty, Double_t sx, Double_t sy, Double_t bx, Double_t by)
	This function calculates 2D peaks shape function (see manual) More...

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

Double_t	Volume (Double_t a, Double_t sx, Double_t sy, Double_t ro)
	This function calculates volume of a peak. More...

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

void	MakeZombie ()

Protected Attributes
Double_t	fA0Calc
	calculated value of background a0 parameter More...

Double_t	fA0Err
	error value of background a0 parameter More...

Double_t	fA0Init
	initial value of background a0 parameter(backgroud is estimated as a0+axx+ayy) More...

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

Int_t	fAlphaOptim
	optimization of convergence algorithm, possible values kFitAlphaHalving, kFitAlphaOptimal More...

Double_t *	fAmpCalc
	[fNPeaks] array of calculated values of amplitudes of 2D peaks, output parameters More...

Double_t *	fAmpCalcX1
	[fNPeaks] array of calculated values of amplitudes of 1D ridges in x direction, output parameters More...

Double_t *	fAmpCalcY1
	[fNPeaks] array of calculated values of amplitudes of 1D ridges in y direction, output parameters More...

Double_t *	fAmpErr
	[fNPeaks] array of amplitudes errors of 2D peaks, output parameters More...

Double_t *	fAmpErrX1
	[fNPeaks] array of amplitudes errors of 1D ridges in x direction, output parameters More...

Double_t *	fAmpErrY1
	[fNPeaks] array of amplitudes errors of 1D ridges in y direction, output parameters More...

Double_t *	fAmpInit
	[fNPeaks] array of initial values of amplitudes of 2D peaks, input parameters More...

Double_t *	fAmpInitX1
	[fNPeaks] array of initial values of amplitudes of 1D ridges in x direction, input parameters More...

Double_t *	fAmpInitY1
	[fNPeaks] array of initial values of amplitudes of 1D ridges in y direction, input parameters More...

Double_t	fAxCalc
	calculated value of background ax parameter More...

Double_t	fAxErr
	error value of background ax parameter More...

Double_t	fAxInit
	initial value of background ax parameter(backgroud is estimated as a0+axx+ayy) More...

Double_t	fAyCalc
	calculated value of background ay parameter More...

Double_t	fAyErr
	error value of background ay parameter More...

Double_t	fAyInit
	initial value of background ay parameter(backgroud is estimated as a0+axx+ayy) More...

Double_t	fBxCalc
	calculated value of b parameter for 1D ridges in x direction More...

Double_t	fBxErr
	error value of b parameter for 1D ridges in x direction More...

Double_t	fBxInit
	initial value of b parameter for 1D ridges in x direction (slope), for details see html manual and references More...

Double_t	fByCalc
	calculated value of b parameter for 1D ridges in y direction More...

Double_t	fByErr
	error value of b parameter for 1D ridges in y direction More...

Double_t	fByInit
	initial value of b parameter for 1D ridges in y direction (slope), for details see html manual and references More...

Double_t	fChi
	here the fitting functions return resulting chi square More...

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

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

Bool_t *	fFixAmp
	[fNPeaks] array of logical values which allow to fix appropriate amplitudes of 2D peaks (not fit). However they are present in the estimated functional More...

Bool_t *	fFixAmpX1
	[fNPeaks] array of logical values which allow to fix appropriate amplitudes of 1D ridges in x direction (not fit). However they are present in the estimated functional More...

Bool_t *	fFixAmpY1
	[fNPeaks] array of logical values which allow to fix appropriate amplitudes of 1D ridges in y direction (not fit). However they are present in the estimated functional More...

Bool_t	fFixAx
	logical value of ax parameter, which allows to fix the parameter (not to fit). More...

Bool_t	fFixAy
	logical value of ay parameter, which allows to fix the parameter (not to fit). More...

Bool_t	fFixBx
	logical value of b parameter for 1D ridges in x direction, which allows to fix the parameter (not to fit). More...

Bool_t	fFixBy
	logical value of b parameter for 1D ridges in y direction, which allows to fix the parameter (not to fit). More...

Bool_t *	fFixPositionX
	[fNPeaks] array of logical values which allow to fix appropriate x positions of 2D peaks (not fit). However they are present in the estimated functional More...

Bool_t *	fFixPositionX1
	[fNPeaks] array of logical values which allow to fix appropriate x positions of 1D ridges (not fit). However they are present in the estimated functional More...

Bool_t *	fFixPositionY
	[fNPeaks] array of logical values which allow to fix appropriate y positions of 2D peaks (not fit). However they are present in the estimated functional More...

Bool_t *	fFixPositionY1
	[fNPeaks] array of logical values which allow to fix appropriate y positions of 1D ridges (not fit). However they are present in the estimated functional More...

Bool_t	fFixRo
	logical value of correlation coefficient, which allows to fix the parameter (not to fit). More...

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

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

Bool_t	fFixSx
	logical value of s parameter for 1D ridges in x direction, which allows to fix the parameter (not to fit). More...

Bool_t	fFixSxy
	logical value of s parameter for 2D peaks, which allows to fix the parameter (not to fit). More...

Bool_t	fFixSy
	logical value of s parameter for 1D ridges in y direction, which allows to fix the parameter (not to fit). More...

Bool_t	fFixTx
	logical value of t parameter for 1D ridges in x direction, which allows to fix the parameter (not to fit). More...

Bool_t	fFixTxy
	logical value of t parameter for 2D peaks, which allows to fix the parameter (not to fit). More...

Bool_t	fFixTy
	logical value of t parameter for 1D ridges in y direction, which allows to fix the parameter (not to fit). More...

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

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

Double_t *	fPositionCalcX
	[fNPeaks] array of calculated values of x positions of 2D peaks, output parameters More...

Double_t *	fPositionCalcX1
	[fNPeaks] array of calculated x positions of 1D ridges, output parameters More...

Double_t *	fPositionCalcY
	[fNPeaks] array of calculated values of y positions of 2D peaks, output parameters More...

Double_t *	fPositionCalcY1
	[fNPeaks] array of calculated y positions of 1D ridges, output parameters More...

Double_t *	fPositionErrX
	[fNPeaks] array of error values of x positions of 2D peaks, output parameters More...

Double_t *	fPositionErrX1
	[fNPeaks] array of x positions errors of 1D ridges, output parameters More...

Double_t *	fPositionErrY
	[fNPeaks] array of error values of y positions of 2D peaks, output parameters More...

Double_t *	fPositionErrY1
	[fNPeaks] array of y positions errors of 1D ridges, output parameters More...

Double_t *	fPositionInitX
	[fNPeaks] array of initial values of x positions of 2D peaks, input parameters More...

Double_t *	fPositionInitX1
	[fNPeaks] array of initial x positions of 1D ridges, input parameters More...

Double_t *	fPositionInitY
	[fNPeaks] array of initial values of y positions of 2D peaks, input parameters More...

Double_t *	fPositionInitY1
	[fNPeaks] array of initial y positions of 1D ridges, input parameters More...

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

Double_t	fRoCalc
	calculated value of correlation coefficient More...

Double_t	fRoErr
	error value of correlation coefficient More...

Double_t	fRoInit
	initial value of correlation coefficient More...

Double_t	fSigmaCalcX
	calculated value of sigma x parameter More...

Double_t	fSigmaCalcY
	calculated value of sigma y parameter More...

Double_t	fSigmaErrX
	error value of sigma x parameter More...

Double_t	fSigmaErrY
	error value of sigma y parameter More...

Double_t	fSigmaInitX
	initial value of sigma x parameter More...

Double_t	fSigmaInitY
	initial value of sigma y parameter More...

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 More...

Double_t	fSxCalc
	calculated value of s parameter for 1D ridges in x direction More...

Double_t	fSxErr
	error value of s parameter for 1D ridges in x direction More...

Double_t	fSxInit
	initial value of s parameter for 1D ridges in x direction (relative amplitude of step), for details see html manual and references More...

Double_t	fSxyCalc
	calculated value of s parameter for 2D peaks More...

Double_t	fSxyErr
	error value of s parameter for 2D peaks More...

Double_t	fSxyInit
	initial value of s parameter for 2D peaks (relative amplitude of step), for details see html manual and references More...

Double_t	fSyCalc
	calculated value of s parameter for 1D ridges in y direction More...

Double_t	fSyErr
	error value of s parameter for 1D ridges in y direction More...

Double_t	fSyInit
	initial value of s parameter for 1D ridges in y direction (relative amplitude of step), for details see html manual and references More...

Double_t	fTxCalc
	calculated value of t parameter for 1D ridges in x direction More...

Double_t	fTxErr
	error value of t parameter for 1D ridges in x direction More...

Double_t	fTxInit
	initial value of t parameter for 1D ridges in x direction (relative amplitude of tail), for details see html manual and references More...

Double_t	fTxyCalc
	calculated value of t parameter for 2D peaks More...

Double_t	fTxyErr
	error value of t parameter for 2D peaks More...

Double_t	fTxyInit
	initial value of t parameter for 2D peaks (relative amplitude of tail), for details see html manual and references More...

Double_t	fTyCalc
	calculated value of t parameter for 1D ridges in y direction More...

Double_t	fTyErr
	error value of t parameter for 1D ridges in y direction More...

Double_t	fTyInit
	initial value of t parameter for 1D ridges in y direction (relative amplitude of tail), for details see html manual and references More...

Double_t *	fVolume
	[fNPeaks] array of calculated volumes of 2D peaks, output parameters More...

Double_t *	fVolumeErr
	[fNPeaks] array of volumes errors of 2D peaks, output parameters More...

Int_t	fXmax
	last fitted channel in x direction More...

Int_t	fXmin
	first fitted channel in x direction More...

Int_t	fYmax
	last fitted channel in y direction More...

Int_t	fYmin
	first fitted channel in y direction More...

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. 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...

#include <TSpectrum2Fit.h>

Inheritance diagram for TSpectrum2Fit:

[legend]

Member Enumeration Documentation

anonymous enum

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

Definition at line 119 of file TSpectrum2Fit.h.

Constructor & Destructor Documentation

TSpectrum2Fit::TSpectrum2Fit ( void )

Default constructor.

Definition at line 35 of file TSpectrum2Fit.cxx.

TSpectrum2Fit::TSpectrum2Fit ( 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 contains the two-dimensional symmetrical Gaussian two one-dimensional symmetrical Gaussian ridges as well as non-symmetrical terms and background.

Definition at line 150 of file TSpectrum2Fit.cxx.

TSpectrum2Fit::~TSpectrum2Fit ( )

virtual

Destructor.

Definition at line 259 of file TSpectrum2Fit.cxx.

Member Function Documentation

Double_t TSpectrum2Fit::Deramp2	(	Double_t	x,
		Double_t	y,
		Double_t	x0,
		Double_t	y0,
		Double_t	sigmax,
		Double_t	sigmay,
		Double_t	ro,
		Double_t	txy,
		Double_t	sxy,
		Double_t	bx,
		Double_t	by
	)

protected

This function calculates derivative of 2D peaks shape function (see manual) according to amplitude of 2D peak.

Function parameters:

x-channel in x-dimension
y-channel in y-dimension
x0-position of peak in x-dimension
y0-position of peak in y-dimension
sigmax-sigmax of peaks
sigmay-sigmay of peaks
ro-correlation coefficient
txy, sxy-relative amplitudes
bx, by-slopes

Definition at line 541 of file TSpectrum2Fit.cxx.

Double_t TSpectrum2Fit::Derampx	(	Double_t	x,
		Double_t	x0,
		Double_t	sigmax,
		Double_t	tx,
		Double_t	sx,
		Double_t	bx
	)

protected

This function calculates derivative of 2D peaks shape function (see manual) according to amplitude of the ridge.

Function parameters:

x-channel in x-dimension
x0-position of peak in x-dimension
y0-position of peak in y-dimension
sigmax-sigmax of peaks
ro-correlation coefficient
tx, sx-relative amplitudes
bx-slope

Definition at line 588 of file TSpectrum2Fit.cxx.

Double_t TSpectrum2Fit::Derbx	(	Int_t	numOfFittedPeaks,
		Double_t	x,
		Double_t	y,
		const Double_t *	parameter,
		Double_t	sigmax,
		Double_t	sigmay,
		Double_t	txy,
		Double_t	tx,
		Double_t	bx,
		Double_t	by
	)

protected

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

Function parameters:

numOfFittedPeaks-number of fitted peaks
x,y-position of channel
parameter-array of peaks parameters (amplitudes and positions)
sigmax-sigmax of peaks
sigmay-sigmay of peaks
txy, tx-relative amplitudes
bx, by-slopes

Definition at line 1420 of file TSpectrum2Fit.cxx.

Double_t TSpectrum2Fit::Derby	(	Int_t	numOfFittedPeaks,
		Double_t	x,
		Double_t	y,
		const Double_t *	parameter,
		Double_t	sigmax,
		Double_t	sigmay,
		Double_t	txy,
		Double_t	ty,
		Double_t	bx,
		Double_t	by
	)

protected

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

Function parameters:

numOfFittedPeaks-number of fitted peaks
x,y-position of channel
parameter-array of peaks parameters (amplitudes and positions)
sigmax-sigmax of peaks
sigmay-sigmay of peaks
txy, ty-relative amplitudes
bx, by-slopes

Definition at line 1476 of file TSpectrum2Fit.cxx.

Double_t TSpectrum2Fit::Derderi01	(	Double_t	x,
		Double_t	ax,
		Double_t	x0,
		Double_t	sigmax
	)

protected

This function calculates second derivative of 2D peaks shape function (see manual) according to x position of 1D ridge.

Function parameters:

x-channel in x-dimension
ax-amplitude of ridge
x0-position of peak in x-dimension
sigmax-sigmax of peaks

Definition at line 865 of file TSpectrum2Fit.cxx.

Double_t TSpectrum2Fit::Derderi02	(	Double_t	x,
		Double_t	y,
		Double_t	a,
		Double_t	x0,
		Double_t	y0,
		Double_t	sigmax,
		Double_t	sigmay,
		Double_t	ro
	)

protected

This function calculates second derivative of 2D peaks shape function (see manual) according to x position of 2D peak.

Function parameters:

x-channel in x-dimension
y-channel in y-dimension
a-amplitude
x0-position of peak in x-dimension
y0-position of peak in y-dimension
sigmax-sigmax of peaks
sigmay-sigmay of peaks
ro-correlation coefficient

Definition at line 690 of file TSpectrum2Fit.cxx.

Double_t TSpectrum2Fit::Derderj02	(	Double_t	x,
		Double_t	y,
		Double_t	a,
		Double_t	x0,
		Double_t	y0,
		Double_t	sigmax,
		Double_t	sigmay,
		Double_t	ro
	)

protected

This function calculates second derivative of 2D peaks shape function (see manual) according to y position of 2D peak.

Function parameters:

x-channel in x-dimension
y-channel in y-dimension
a-amplitude
x0-position of peak in x-dimension
y0-position of peak in y-dimension
sigmax-sigmax of peaks
sigmay-sigmay of peaks
ro-correlation coefficient

Definition at line 785 of file TSpectrum2Fit.cxx.

Double_t TSpectrum2Fit::Derdersigmax	(	Int_t	numOfFittedPeaks,
		Double_t	x,
		Double_t	y,
		const Double_t *	parameter,
		Double_t	sigmax,
		Double_t	sigmay,
		Double_t	ro
	)

protected

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

Function parameters:

numOfFittedPeaks-number of fitted peaks
x,y-position of channel
parameter-array of peaks parameters (amplitudes and positions)
sigmax-sigmax of peaks
sigmay-sigmay of peaks
ro-correlation coefficient

Definition at line 985 of file TSpectrum2Fit.cxx.

Double_t TSpectrum2Fit::Derdersigmay	(	Int_t	numOfFittedPeaks,
		Double_t	x,
		Double_t	y,
		const Double_t *	parameter,
		Double_t	sigmax,
		Double_t	sigmay,
		Double_t	ro
	)

protected

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

Function parameters:

numOfFittedPeaks-number of fitted peaks
x,y-position of channel
parameter-array of peaks parameters (amplitudes and positions)
sigmax-sigmax of peaks
sigmay-sigmay of peaks
ro-correlation coefficient

Definition at line 1132 of file TSpectrum2Fit.cxx.

Double_t TSpectrum2Fit::Derfc ( Double_t x )

protected

This function calculates derivative of error function of x.

Definition at line 322 of file TSpectrum2Fit.cxx.

Double_t TSpectrum2Fit::Deri01	(	Double_t	x,
		Double_t	ax,
		Double_t	x0,
		Double_t	sigmax,
		Double_t	tx,
		Double_t	sx,
		Double_t	bx
	)

protected

This function calculates derivative of 2D peaks shape function (see manual) according to x position of 1D ridge.

Function parameters:

x-channel in x-dimension
ax-amplitude of ridge
x0-position of peak in x-dimension
sigmax-sigmax of peaks
ro-correlation coefficient
tx, sx-relative amplitudes
bx-slope

Definition at line 821 of file TSpectrum2Fit.cxx.

Double_t TSpectrum2Fit::Deri02	(	Double_t	x,
		Double_t	y,
		Double_t	a,
		Double_t	x0,
		Double_t	y0,
		Double_t	sigmax,
		Double_t	sigmay,
		Double_t	ro,
		Double_t	txy,
		Double_t	sxy,
		Double_t	bx,
		Double_t	by
	)

protected

This function calculates derivative of 2D peaks shape function (see manual) according to x position of 2D peak.

Function parameters:

x-channel in x-dimension
y-channel in y-dimension
a-amplitude
x0-position of peak in x-dimension
y0-position of peak in y-dimension
sigmax-sigmax of peaks
sigmay-sigmay of peaks
ro-correlation coefficient
txy, sxy-relative amplitudes
bx, by-slopes

Definition at line 635 of file TSpectrum2Fit.cxx.

Double_t TSpectrum2Fit::Derj02	(	Double_t	x,
		Double_t	y,
		Double_t	a,
		Double_t	x0,
		Double_t	y0,
		Double_t	sigmax,
		Double_t	sigmay,
		Double_t	ro,
		Double_t	txy,
		Double_t	sxy,
		Double_t	bx,
		Double_t	by
	)

protected

This function calculates derivative of 2D peaks shape function (see manual) according to y position of 2D peak Function parameters:

x-channel in x-dimension
y-channel in y-dimension
a-amplitude
x0-position of peak in x-dimension
y0-position of peak in y-dimension
sigmax-sigmax of peaks
sigmay-sigmay of peaks
ro-correlation coefficient
txy, sxy-relative amplitudes
bx, by-slopes

Definition at line 728 of file TSpectrum2Fit.cxx.

Double_t TSpectrum2Fit::Derpa2	(	Double_t	sx,
		Double_t	sy,
		Double_t	ro
	)

protected

This function calculates derivative of the volume of a peak according to amplitude.

Function parameters:

sx,sy-sigmas of peak
ro-correlation coefficient

Definition at line 1549 of file TSpectrum2Fit.cxx.

Double_t TSpectrum2Fit::Derpro	(	Double_t	a,
		Double_t	sx,
		Double_t	sy,
		Double_t	ro
	)

protected

This function calculates derivative of the volume of a peak according to ro.

Function parameters:

a-amplitude of peak
sx,sy-sigmas of peak
ro-correlation coefficient

Definition at line 1618 of file TSpectrum2Fit.cxx.

Double_t TSpectrum2Fit::Derpsigmax	(	Double_t	a,
		Double_t	sy,
		Double_t	ro
	)

protected

This function calculates derivative of the volume of a peak according to sigmax.

Function parameters:

a-amplitude of peak
sy-sigma of peak
ro-correlation coefficient

Definition at line 1572 of file TSpectrum2Fit.cxx.

Double_t TSpectrum2Fit::Derpsigmay	(	Double_t	a,
		Double_t	sx,
		Double_t	ro
	)

protected

This function calculates derivative of the volume of a peak according to sigmay.

Function parameters:

a-amplitude of peak
sx-sigma of peak
ro-correlation coefficient

Definition at line 1595 of file TSpectrum2Fit.cxx.

Double_t TSpectrum2Fit::Derro	(	Int_t	numOfFittedPeaks,
		Double_t	x,
		Double_t	y,
		const Double_t *	parameter,
		Double_t	sx,
		Double_t	sy,
		Double_t	r
	)

protected

This function calculates derivative of peaks shape function (see manual) according to correlation coefficient ro.

Function parameters:

numOfFittedPeaks-number of fitted peaks
x,y-position of channel
parameter-array of peaks parameters (amplitudes and positions)
sx-sigmax of peaks
sy-sigmay of peaks
r-correlation coefficient ro

Definition at line 1190 of file TSpectrum2Fit.cxx.

Double_t TSpectrum2Fit::Dersigmax	(	Int_t	numOfFittedPeaks,
		Double_t	x,
		Double_t	y,
		const Double_t *	parameter,
		Double_t	sigmax,
		Double_t	sigmay,
		Double_t	ro,
		Double_t	txy,
		Double_t	sxy,
		Double_t	tx,
		Double_t	sx,
		Double_t	bx,
		Double_t	by
	)

protected

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

Function parameters:

numOfFittedPeaks-number of fitted peaks
x,y-position of channel
parameter-array of peaks parameters (amplitudes and positions)
sigmax-sigmax of peaks
sigmay-sigmay of peaks
ro-correlation coefficient
txy, sxy, tx, sx-relative amplitudes
bx, by-slopes

Definition at line 898 of file TSpectrum2Fit.cxx.

Double_t TSpectrum2Fit::Dersigmay	(	Int_t	numOfFittedPeaks,
		Double_t	x,
		Double_t	y,
		const Double_t *	parameter,
		Double_t	sigmax,
		Double_t	sigmay,
		Double_t	ro,
		Double_t	txy,
		Double_t	sxy,
		Double_t	ty,
		Double_t	sy,
		Double_t	bx,
		Double_t	by
	)

protected

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

Function parameters:

numOfFittedPeaks-number of fitted peaks
x,y-position of channel
parameter-array of peaks parameters (amplitudes and positions)
sigmax-sigmax of peaks
sigmay-sigmay of peaks
ro-correlation coefficient
txy, sxy, ty, sy-relative amplitudes
bx, by-slopes

Definition at line 1045 of file TSpectrum2Fit.cxx.

Double_t TSpectrum2Fit::Dersx	(	Int_t	numOfFittedPeaks,
		Double_t	x,
		const Double_t *	parameter,
		Double_t	sigmax
	)

protected

This function calculates derivative of peaks shape function (see manual) according to relative amplitude sx.

Function parameters:

numOfFittedPeaks-number of fitted peaks
x-position of channel
parameter-array of peaks parameters (amplitudes and positions)
sigmax-sigma of 1D ridge

Definition at line 1363 of file TSpectrum2Fit.cxx.

Double_t TSpectrum2Fit::Dersxy	(	Int_t	numOfFittedPeaks,
		Double_t	x,
		Double_t	y,
		const Double_t *	parameter,
		Double_t	sigmax,
		Double_t	sigmay
	)

protected

This function calculates derivative of peaks shape function (see manual) according to relative amplitude sxy.

Function parameters:

numOfFittedPeaks-number of fitted peaks
x,y-position of channel
parameter-array of peaks parameters (amplitudes and positions)
sigmax-sigmax of peaks
sigmay-sigmay of peaks

Definition at line 1268 of file TSpectrum2Fit.cxx.

Double_t TSpectrum2Fit::Dersy	(	Int_t	numOfFittedPeaks,
		Double_t	x,
		const Double_t *	parameter,
		Double_t	sigmax
	)

protected

This function calculates derivative of peaks shape function (see manual) according to relative amplitude sy.

Function parameters:

numOfFittedPeaks-number of fitted peaks
x-position of channel
parameter-array of peaks parameters (amplitudes and positions)
sigmax-sigma of 1D ridge

Definition at line 1390 of file TSpectrum2Fit.cxx.

Double_t TSpectrum2Fit::Dertx	(	Int_t	numOfFittedPeaks,
		Double_t	x,
		const Double_t *	parameter,
		Double_t	sigmax,
		Double_t	bx
	)

protected

This function calculates derivative of peaks shape function (see manual) according to relative amplitude tx.

Function parameters:

numOfFittedPeaks-number of fitted peaks
x-position of channel
parameter-array of peaks parameters (amplitudes and positions)
sigmax-sigma of 1D ridge
bx-slope

Definition at line 1298 of file TSpectrum2Fit.cxx.

Double_t TSpectrum2Fit::Dertxy	(	Int_t	numOfFittedPeaks,
		Double_t	x,
		Double_t	y,
		const Double_t *	parameter,
		Double_t	sigmax,
		Double_t	sigmay,
		Double_t	bx,
		Double_t	by
	)

protected

This function calculates derivative of peaks shape function (see manual) according to relative amplitude txy.

Function parameters:

numOfFittedPeaks-number of fitted peaks
x,y-position of channel
parameter-array of peaks parameters (amplitudes and positions)
sigmax-sigmax of peaks
sigmay-sigmay of peaks
bx, by-slopes

Definition at line 1232 of file TSpectrum2Fit.cxx.

Double_t TSpectrum2Fit::Derty	(	Int_t	numOfFittedPeaks,
		Double_t	x,
		const Double_t *	parameter,
		Double_t	sigmax,
		Double_t	bx
	)

protected

This function calculates derivative of peaks shape function (see manual) according to relative amplitude ty.

Function parameters:

numOfFittedPeaks-number of fitted peaks
x-position of channel
parameter-array of peaks parameters (amplitudes and positions)
sigmax-sigma of 1D ridge
bx-slope

Definition at line 1331 of file TSpectrum2Fit.cxx.

Double_t TSpectrum2Fit::Erfc ( Double_t x )

protected

This function calculates error function of x.

Definition at line 298 of file TSpectrum2Fit.cxx.

void TSpectrum2Fit::FitAwmi ( Double_t ** source )

This function fits the source spectrum.

The calling program should fill in input parameters of the TSpectrum2Fit class. The fitted parameters are written into TSpectrum2Fit class output parameters and fitted data are written into source spectrum.

Function parameters:

source-pointer to the matrix 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 semiempirical peak shape function
it contains the two-dimensional symmetrical Gaussian two one-dimensional symmetrical Gaussian ridges as well as non-symmetrical terms and background.

where Txy, Tx, Ty, Sxy, Sx, Sy are relative amplitudes and Bx, By are slopes.
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. Morh, J. Kliman, M. Jandel, 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 1 - script FitAwmi2.c:

Original Fig. 1 two-dimensional spectrum with found peaks (using TSpectrum2 peak searching function). The positions of peaks were used as initial estimates in fitting procedure.

Fig. 2 Fitted (generated from fitted parameters) spectrum of the data from Fig. 1 using Algorithm Without Matrix Inversion. Each peak was represented by 7 parameters, which together with Sigmax, Sigmay and a0 resulted in 38 fitted parameters. The chi-squareafter 1000 iterations was 0.642342.

Script:

Example to illustrate fitting function, algorithm without matrix inversion (AWMI) (class TSpectrumFit2). To execute this example, do

root > .x FitAwmi2.C

void FitAwmi2() {
   Int_t i, j, nfound;
   Int_t nbinsx = 64;
   Int_t nbinsy = 64;
   Int_t xmin = 0;
   Int_t xmax = nbinsx;
   Int_t ymin = 0;
   Int_t ymax = nbinsy;
   Double_t ** source = new float *[nbinsx];
   Double_t ** dest = new float *[nbinsx];
   for (i=0;i<nbinsx;i++)
      source[i]=new float[nbinsy];
   for (i=0;i<nbinsx;i++)
      dest[i]=new float[nbinsy];
   TH2F *search = new TH2F("search","High resolution peak searching",nbinsx,xmin,xmax,nbinsy,ymin,ymax);
   TFile *f = new TFile("TSpectrum2.root");
   search=(TH2F*) f->Get("search4;1");
   TCanvas *Searching = new TCanvas("Searching","Two-dimensional fitting using Algorithm Without Matrix Inversion",10,10,1000,700);
   TSpectrum2 *s = new TSpectrum2();
   for (i = 0; i < nbinsx; i++){
      for (j = 0; j < nbinsy; j++){
         source[i][j] = search->GetBinContent(i + 1,j + 1);
      }
   }
   //searching for candidate peaks positions
   nfound = s->SearchHighRes(source, dest, nbinsx, nbinsy, 2, 5, kTRUE, 3, kFALSE, 3);
   Bool_t *FixPosX = new Bool_t[nfound];
   Bool_t *FixPosY = new Bool_t[nfound];
   Bool_t *FixAmp = new Bool_t[nfound];
   Double_t *PosX = new Double_t[nfound];
   Double_t *PosY = new Double_t[nfound];
   Double_t *Amp = new Double_t[nfound];
   Double_t *AmpXY = new Double_t[nfound];
   PosX = s->GetPositionX();
   PosY = s->GetPositionY();
   printf("Found %d candidate peaks\n",nfound);
   for(i = 0; i< nfound ; i++){
      FixPosX[i] = kFALSE;
      FixPosY[i] = kFALSE;
      FixAmp[i] = kFALSE;
      Amp[i] = source[(Int_t)(PosX[i]+0.5)][(Int_t)(PosY[i]+0.5)]; //initial values of peaks amplitudes, input parameters
      AmpXY[i] = 0;
   }
   //filling in the initial estimates of the input parameters
   TSpectrumFit2 *pfit=new TSpectrumFit2(nfound);
   pfit->SetFitParameters(xmin, xmax-1, ymin, ymax-1, 1000, 0.1, pfit->kFitOptimChiCounts,
   pfit->kFitAlphaHalving, pfit->kFitPower2,
   pfit->kFitTaylorOrderFirst);
   pfit->SetPeakParameters(2, kFALSE, 2, kFALSE, 0, kTRUE, PosX, (Bool_t *)
   FixPosX, PosY, (Bool_t *) FixPosY, PosX, (Bool_t *) FixPosX, PosY, (Bool_t *)
   FixPosY, Amp, (Bool_t *) FixAmp, AmpXY, (Bool_t *) FixAmp, AmpXY, (Bool_t *)
   FixAmp);
   pfit->SetBackgroundParameters(0, kFALSE, 0, kTRUE, 0, kTRUE);
   pfit->FitAwmi(source);
   for (i = 0; i < nbinsx; i++){
      for (j = 0; j < nbinsy; j++){
         search->SetBinContent(i + 1, j + 1,source[i][j]);
       }
   }
search->Draw("SURF");
}

Example 2 - script FitAwmi2.c:

Fig. 3 Original two-dimensional gamma-gamma-ray spectrum with found peaks (using TSpectrum2 peak searching function).

Fig. 4 Fitted (generated from fitted parameters) spectrum of the data from Fig. 3 using Algorithm Without Matrix Inversion. 152 peaks were identified. Each peak was represented by 7 parameters, which together with Sigmax, Sigmay and a0 resulted in 1067 fitted parameters. The chi-square after 1000 iterations was 0.728675. One can observe good correspondence with the original data.

Script:

Example to illustrate fitting function, algorithm without matrix inversion (AWMI) (class TSpectrumFit2). To execute this example, do:

root > .x FitA2.C

void FitA2() {
   Int_t i, j, nfound;
   Int_t nbinsx = 256;
   Int_t nbinsy = 256;
   Int_t xmin = 0;
   Int_t xmax = nbinsx;
   Int_t ymin = 0;
   Int_t ymax = nbinsy;
   Double_t ** source = new float *[nbinsx];
   Double_t ** dest = new float *[nbinsx];
   for (i=0;i<nbinsx;i++)
      source[i]=new
   float[nbinsy];
   for (i=0;i<nbinsx;i++)
      dest[i]=new
   float[nbinsy];
   TH2F *search = new TH2F("search","High resolution peak
   searching",nbinsx,xmin,xmax,nbinsy,ymin,ymax);
   TFile *f = new TFile("TSpectrum2.root");
   search=(TH2F*) f->Get("fit1;1");
   TCanvas *Searching = new TCanvas("Searching","Two-dimensional fitting using Algorithm Without Matrix Inversion",10,10,1000,700);
   TSpectrum2 *s = new TSpectrum2(1000,1);
   for (i = 0; i < nbinsx; i++){
      for (j = 0; j < nbinsy; j++){
         source[i][j] = search->GetBinContent(i + 1,j + 1);
      }
   }
   nfound = s->SearchHighRes(source, dest, nbinsx, nbinsy, 2, 2, kTRUE, 100, kFALSE, 3);
   printf("Found %d candidate peaks\n",nfound);
   Bool_t *FixPosX = new Bool_t[nfound];
   Bool_t *FixPosY = new Bool_t[nfound];
   Bool_t *FixAmp = new Bool_t[nfound];
   Double_t *PosX = new Double_t[nfound];
   Double_t *PosY = new Double_t[nfound];
   Double_t *Amp = new Double_t[nfound];
   Double_t *AmpXY = new Double_t[nfound];
   PosX = s->GetPositionX();
   PosY = s->GetPositionY();
   for(i = 0; i< nfound ; i++){
      FixPosX[i] = kFALSE;
      FixPosY[i] = kFALSE;
      FixAmp[i] = kFALSE;
      Amp[i] = source[(Int_t)(PosX[i]+0.5)][(Int_t)(PosY[i]+0.5)]; //initial values of peaks amplitudes, input parameters
      AmpXY[i] = 0;
   }
   //filling in the initial estimates of the input parameters
   TSpectrumFit2 *pfit=new TSpectrumFit2(nfound);
   pfit->SetFitParameters(xmin, xmax-1, ymin, ymax-1, 1000, 0.1,
   pfit->kFitOptimChiCounts, pfit->kFitAlphaHalving, pfit->kFitPower2,
   pfit->kFitTaylorOrderFirst);
   pfit->SetPeakParameters(2, kFALSE, 2, kFALSE, 0, kTRUE, PosX, (Bool_t *)
   FixPosX, PosY, (Bool_t *) FixPosY, PosX, (Bool_t *) FixPosX, PosY, (Bool_t *)
   FixPosY, Amp, (Bool_t *) FixAmp, AmpXY, (Bool_t *) FixAmp, AmpXY, (Bool_t *)
   FixAmp);
   pfit->SetBackgroundParameters(0, kFALSE, 0, kTRUE, 0, kTRUE);
   pfit->FitAwmi(source);
   for (i = 0; i < nbinsx; i++){
      for (j = 0; j < nbinsy; j++){
         search->SetBinContent(i + 1, j + 1,source[i][j]);
      }
   }
   search->Draw("SURF");
}

Definition at line 1847 of file TSpectrum2Fit.cxx.

void TSpectrum2Fit::FitStiefel ( Double_t ** source )

This function fits the source spectrum.

The calling program should fill in input parameters of the TSpectrum2Fit class. The fitted parameters are written into TSpectrum2Fit class output parameters and fitted data are written into source spectrum.

Function parameters:

source-pointer to the matrix of source spectrum

Stiefel fitting algorithm

This function fits the source spectrum using Stiefel-Hestens method [1]. The calling program should fill in input fitting parameters of the TSpectrumFit2 class using a set of TSpectrumFit2 setters. The fitted parameters are written into the class and the fitted data are written into source spectrum. It converges faster than Awmi method.

Reference:

[1] B. Mihaila: Analysis of complex gamma spectra, Rom. Jorn. Phys., Vol. 39, No. 2, (1994), 139-148.

Example 1 - script FitS.c:

Fig. 1 Original two-dimensional spectrum with found peaks (using TSpectrum2 peak searching function). The positions of peaks were used as initial estimates in fitting procedure.

Fig. 2 Fitted (generated from fitted parameters) spectrum of the data from Fig. 1 using Stiefel-Hestens method. Each peak was represented by 7 parameters, which together with Sigmax, Sigmay and a0 resulted in 38 fitted parameters. The chi-square after 1000 iterations was 0.642157.

Script:

Example to illustrate fitting function, algorithm without matrix inversion (AWMI) (class TSpectrumFit2). To execute this example, do

root > .x FitStiefel2.C

  void FitStiefel2() {
     Int_t i, j, nfound;
     Int_t nbinsx = 64;
     Int_t nbinsy = 64;
     Int_t xmin = 0;
     Int_t xmax = nbinsx;
     Int_t ymin = 0;
     Int_t ymax = nbinsy;
     Double_t ** source = new float *[nbinsx];
     Double_t ** dest = new float *[nbinsx];
     for (i=0;i<nbinsx;i++)
        source[i]=new float[nbinsy];
     for (i=0;i<nbinsx;i++)
        dest[i]=  new float[nbinsy];
     TH2F *search = new TH2F("search","High resolution peak searching",nbinsx,xmin,xmax,nbinsy,ymin,ymax);
     TFile *f = new TFile("TSpectrum2.root");
     search=(TH2F*)f->Get("search4;1");
     TCanvas *Searching = new TCanvas("Searching","Two-dimensional fitting using Stiefel-Hestens method",10,10,1000,700);
     TSpectrum2 *s = new TSpectrum2();
     for (i = 0; i < nbinsx; i++){
        for (j = 0; j < nbinsy; j++){
           source[i][j] = search->GetBinContent(i + 1,j + 1);
        }
     }
     nfound = s->SearchHighRes(source, dest, nbinsx, nbinsy, 2, 5, kTRUE, 3, kFALSE, 3);
     printf("Found %d candidate peaks\n",nfound);
     Bool_t *FixPosX = new Bool_t[nfound];
     Bool_t *FixPosY = new Bool_t[nfound];
     Bool_t *FixAmp = new Bool_t[nfound];
     Double_t *PosX = new Double_t[nfound];
     Double_t *PosY = new Double_t[nfound];
     Double_t *Amp = new Double_t[nfound];
     Double_t *AmpXY = new Double_t[nfound];
     PosX = s->GetPositionX();
     PosY = s->GetPositionY();
     for(i = 0; i< nfound ; i++){
        FixPosX[i] = kFALSE;
        FixPosY[i] = kFALSE;
        FixAmp[i] = kFALSE;
        Amp[i] = source[(Int_t)(PosX[i]+0.5)][(Int_t)(PosY[i]+0.5)]; //initial values of peaks amplitudes, input parameters
        AmpXY[i] = 0;
     }
     //filling in the initial estimates of the input parameters
     TSpectrumFit2 *pfit=new
     TSpectrumFit2(nfound);
     pfit->SetFitParameters(xmin, xmax-1, ymin, ymax-1, 1000, 0.1,
     pfit->kFitOptimChiCounts, pfit->kFitAlphaHalving, pfit->kFitPower2,
     pfit->kFitTaylorOrderFirst);
     pfit->SetPeakParameters(2, kFALSE, 2, kFALSE, 0, kTRUE, PosX, (Bool_t *)
     FixPosX, PosY, (Bool_t *) FixPosY, PosX, (Bool_t *) FixPosX, PosY, (Bool_t *)
     FixPosY, Amp, (Bool_t *) FixAmp, AmpXY, (Bool_t *) FixAmp, AmpXY, (Bool_t *)
     FixAmp);
     pfit->SetBackgroundParameters(0, kFALSE, 0, kTRUE, 0, kTRUE);
     pfit->FitStiefel(source);
     for (i = 0; i < nbinsx; i++){
        for (j = 0; j < nbinsy; j++){
           search->SetBinContent(i + 1, j + 1,source[i][j]);
        }
     }
     search->Draw("SURF");
}

Definition at line 3942 of file TSpectrum2Fit.cxx.

void TSpectrum2Fit::GetAmplitudeErrors	(	Double_t *	amplitudeErrors,
		Double_t *	amplitudeErrorsX1,
		Double_t *	amplitudeErrorsY1
	)

This function gets the amplitudes of fitted 2D peaks and 1D ridges.

amplitudeErrors - gets vector of amplitudes errors of 2D peaks
amplitudeErrorsX1 - gets vector of amplitudes errors of 1D ridges in x direction
amplitudesErrorY1 - gets vector of amplitudes errors of 1D ridges in y direction

Definition at line 5754 of file TSpectrum2Fit.cxx.

void TSpectrum2Fit::GetAmplitudes	(	Double_t *	amplitudes,
		Double_t *	amplitudesX1,
		Double_t *	amplitudesY1
	)

This function gets the amplitudes of fitted 2D peaks and 1D ridges.

amplitudes - gets vector of amplitudes of 2D peaks
amplitudesX1 - gets vector of amplitudes of 1D ridges in x direction
amplitudesY1 - gets vector of amplitudes of 1D ridges in y direction

Definition at line 5739 of file TSpectrum2Fit.cxx.

void TSpectrum2Fit::GetBackgroundParameters	(	Double_t &	a0,
		Double_t &	a0Err,
		Double_t &	ax,
		Double_t &	axErr,
		Double_t &	ay,
		Double_t &	ayErr
	)

This function gets the background parameters and their errors.

a0 - gets the fitted value of a0 parameter
a0Err - gets error value of a0 parameter
ax - gets the fitted value of ax parameter
axErr - gets error value of ax parameter
ay - gets the fitted value of ay parameter
ayErr - gets error value of ay parameter

Definition at line 5827 of file TSpectrum2Fit.cxx.

Double_t TSpectrum2Fit::GetChi ( ) const

inline

Definition at line 178 of file TSpectrum2Fit.h.

void TSpectrum2Fit::GetPositionErrors	(	Double_t *	positionErrorsX,
		Double_t *	positionErrorsY,
		Double_t *	positionErrorsX1,
		Double_t *	positionErrorsY1
	)

This function gets the errors of positions of fitted 2D peaks and 1D ridges.

positionErrorsX - gets vector of errors of x positions of 2D peaks
positionErrorsY - gets vector of errors of y positions of 2D peaks
positionErrorsX1 - gets vector of errors of x positions of 1D ridges
positionErrorsY1 - gets vector of errors of y positions of 1D ridges

Definition at line 5723 of file TSpectrum2Fit.cxx.

void TSpectrum2Fit::GetPositions	(	Double_t *	positionsX,
		Double_t *	positionsY,
		Double_t *	positionsX1,
		Double_t *	positionsY1
	)

This function gets the positions of fitted 2D peaks and 1D ridges.

positionX - gets vector of x positions of 2D peaks
positionY - gets vector of y positions of 2D peaks
positionX1 - gets vector of x positions of 1D ridges
positionY1 - gets vector of y positions of 1D ridges

Definition at line 5706 of file TSpectrum2Fit.cxx.

void TSpectrum2Fit::GetRo	(	Double_t &	ro,
		Double_t &	roErr
	)

This function gets the ro parameter and its error.

ro - gets the fitted value of ro parameter
roErr - gets error value of ro parameter

Definition at line 5812 of file TSpectrum2Fit.cxx.

void TSpectrum2Fit::GetSigmaX	(	Double_t &	sigmaX,
		Double_t &	sigmaErrX
	)

This function gets the sigma x parameter and its error.

sigmaX - gets the fitted value of sigma x parameter
sigmaErrX - gets error value of sigma x parameter

Definition at line 5790 of file TSpectrum2Fit.cxx.

void TSpectrum2Fit::GetSigmaY	(	Double_t &	sigmaY,
		Double_t &	sigmaErrY
	)

This function gets the sigma y parameter and its error.

sigmaY - gets the fitted value of sigma y parameter
sigmaErrY - gets error value of sigma y parameter

Definition at line 5801 of file TSpectrum2Fit.cxx.

void TSpectrum2Fit::GetTailParameters	(	Double_t &	txy,
		Double_t &	txyErr,
		Double_t &	tx,
		Double_t &	txErr,
		Double_t &	ty,
		Double_t &	tyErr,
		Double_t &	bx,
		Double_t &	bxErr,
		Double_t &	by,
		Double_t &	byErr,
		Double_t &	sxy,
		Double_t &	sxyErr,
		Double_t &	sx,
		Double_t &	sxErr,
		Double_t &	sy,
		Double_t &	syErr
	)

This function gets the tail parameters and their errors.

txy - gets the fitted value of txy parameter
txyErr - gets error value of txy parameter
tx - gets the fitted value of tx parameter
txErr - gets error value of tx parameter
ty - gets the fitted value of ty parameter
tyErr - gets error value of ty parameter
bx - gets the fitted value of bx parameter
bxErr - gets error value of bx parameter
by - gets the fitted value of by parameter
byErr - gets error value of by parameter
sxy - gets the fitted value of sxy parameter
sxyErr - gets error value of sxy parameter
sx - gets the fitted value of sx parameter
sxErr - gets error value of sx parameter
sy - gets the fitted value of sy parameter
syErr - gets error value of sy parameter

Definition at line 5856 of file TSpectrum2Fit.cxx.

void TSpectrum2Fit::GetVolumeErrors ( Double_t * volumeErrors )

This function gets errors of the volumes of fitted 2D peaks.

volumeErrors - gets vector of volumes errors of 2D peaks

Definition at line 5778 of file TSpectrum2Fit.cxx.

void TSpectrum2Fit::GetVolumes ( Double_t * volumes )

This function gets the volumes of fitted 2D peaks.

volumes - gets vector of volumes of 2D peaks

Definition at line 5767 of file TSpectrum2Fit.cxx.

Double_t TSpectrum2Fit::Ourpowl	(	Double_t	a,
		Int_t	pw
	)

protected

power function

Definition at line 345 of file TSpectrum2Fit.cxx.

void TSpectrum2Fit::SetBackgroundParameters	(	Double_t	a0Init,
		Bool_t	fixA0,
		Double_t	axInit,
		Bool_t	fixAx,
		Double_t	ayInit,
		Bool_t	fixAy
	)

This function sets the following fitting parameters of background:

a0Init - initial value of a0 parameter (background is estimated as a0+ax*x+ay*y)
fixA0 - logical value of a0 parameter, which allows to fix the parameter (not to fit)
axInit - initial value of ax parameter
fixAx - logical value of ax parameter, which allows to fix the parameter (not to fit)
ayInit - initial value of ay parameter
fixAy - logical value of ay parameter, which allows to fix the parameter (not to fit)

Definition at line 5650 of file TSpectrum2Fit.cxx.

void TSpectrum2Fit::SetFitParameters	(	Int_t	xmin,
		Int_t	xmax,
		Int_t	ymin,
		Int_t	ymax,
		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, ymin, ymax - 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 5523 of file TSpectrum2Fit.cxx.

void TSpectrum2Fit::SetPeakParameters	(	Double_t	sigmaX,
		Bool_t	fixSigmaX,
		Double_t	sigmaY,
		Bool_t	fixSigmaY,
		Double_t	ro,
		Bool_t	fixRo,
		const Double_t *	positionInitX,
		const Bool_t *	fixPositionX,
		const Double_t *	positionInitY,
		const Bool_t *	fixPositionY,
		const Double_t *	positionInitX1,
		const Bool_t *	fixPositionX1,
		const Double_t *	positionInitY1,
		const Bool_t *	fixPositionY1,
		const Double_t *	ampInit,
		const Bool_t *	fixAmp,
		const Double_t *	ampInitX1,
		const Bool_t *	fixAmpX1,
		const Double_t *	ampInitY1,
		const Bool_t *	fixAmpY1
	)

This function sets the following fitting parameters of peaks:

sigmaX - initial value of sigma x parameter
fixSigmaX - logical value of sigma x parameter, which allows to fix the parameter (not to fit)
sigmaY - initial value of sigma y parameter
fixSigmaY - logical value of sigma y parameter, which allows to fix the parameter (not to fit)
ro - initial value of ro parameter (correlation coefficient)
fixRo - logical value of ro parameter, which allows to fix the parameter (not to fit)
positionInitX - array of initial values of peaks x positions
fixPositionX - array of logical values which allow to fix appropriate x positions (not fit). However they are present in the estimated functional.
positionInitY - array of initial values of peaks y positions
fixPositionY - array of logical values which allow to fix appropriate y positions (not fit). However they are present in the estimated functional.
ampInit - array of initial values of 2D peaks amplitudes
fixAmp - array of logical values which allow to fix appropriate amplitudes of 2D peaks (not fit). However they are present in the estimated functional
ampInitX1 - array of initial values of amplitudes of 1D ridges in x direction
fixAmpX1 - array of logical values which allow to fix appropriate amplitudes of 1D ridges in x direction (not fit). However they are present in the estimated functional
ampInitY1 - array of initial values of amplitudes of 1D ridges in y direction
fixAmpY1 - array of logical values which allow to fix appropriate amplitudes of 1D ridges in y direction (not fit). However they are present in the estimated functional

Definition at line 5581 of file TSpectrum2Fit.cxx.

void TSpectrum2Fit::SetTailParameters	(	Double_t	tInitXY,
		Bool_t	fixTxy,
		Double_t	tInitX,
		Bool_t	fixTx,
		Double_t	tInitY,
		Bool_t	fixTy,
		Double_t	bInitX,
		Bool_t	fixBx,
		Double_t	bInitY,
		Bool_t	fixBy,
		Double_t	sInitXY,
		Bool_t	fixSxy,
		Double_t	sInitX,
		Bool_t	fixSx,
		Double_t	sInitY,
		Bool_t	fixSy
	)

This function sets the following fitting parameters of tails of peaks.

tInitXY - initial value of txy parameter
fixTxy - logical value of txy parameter, which allows to fix the parameter (not to fit)
tInitX - initial value of tx parameter
fixTx - logical value of tx parameter, which allows to fix the parameter (not to fit)
tInitY - initial value of ty parameter
fixTy - logical value of ty parameter, which allows to fix the parameter (not to fit)
bInitX - initial value of bx parameter
fixBx - logical value of bx parameter, which allows to fix the parameter (not to fit)
bInitY - initial value of by parameter
fixBy - logical value of by parameter, which allows to fix the parameter (not to fit)
sInitXY - initial value of sxy parameter
fixSxy - logical value of sxy parameter, which allows to fix the parameter (not to fit)
sInitX - initial value of sx parameter
fixSx - logical value of sx parameter, which allows to fix the parameter (not to fit)
sInitY - initial value of sy parameter
fixSy - logical value of sy parameter, which allows to fix the parameter (not to fit)

Definition at line 5679 of file TSpectrum2Fit.cxx.

Double_t TSpectrum2Fit::Shape2	(	Int_t	numOfFittedPeaks,
		Double_t	x,
		Double_t	y,
		const Double_t *	parameter,
		Double_t	sigmax,
		Double_t	sigmay,
		Double_t	ro,
		Double_t	a0,
		Double_t	ax,
		Double_t	ay,
		Double_t	txy,
		Double_t	sxy,
		Double_t	tx,
		Double_t	ty,
		Double_t	sx,
		Double_t	sy,
		Double_t	bx,
		Double_t	by
	)

protected

This function calculates 2D peaks shape function (see manual)

Function parameters:

numOfFittedPeaks-number of fitted peaks
x-channel in x-dimension
y-channel in y-dimension
parameter-array of peaks parameters (amplitudes and positions)
sigmax-sigmax of peaks
sigmay-sigmay of peaks
ro-correlation coefficient
a0,ax,ay-bac kground coefficients
txy,tx,ty, sxy,sy,sx-relative amplitudes
bx, by-slopes

Definition at line 435 of file TSpectrum2Fit.cxx.

void TSpectrum2Fit::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 372 of file TSpectrum2Fit.cxx.

Double_t TSpectrum2Fit::Volume	(	Double_t	a,
		Double_t	sx,
		Double_t	sy,
		Double_t	ro
	)

protected

This function calculates volume of a peak.

Function parameters:

a-amplitude of the peak
sx,sy-sigmas of peak
ro-correlation coefficient

Definition at line 1527 of file TSpectrum2Fit.cxx.

Member Data Documentation

Double_t TSpectrum2Fit::fA0Calc

protected

calculated value of background a0 parameter

Definition at line 89 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fA0Err

protected

error value of background a0 parameter

Definition at line 90 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fA0Init

protected

initial value of background a0 parameter(backgroud is estimated as a0+ax*x+ay*y)

Definition at line 88 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fAlpha

protected

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

Definition at line 30 of file TSpectrum2Fit.h.

Int_t TSpectrum2Fit::fAlphaOptim

protected

optimization of convergence algorithm, possible values kFitAlphaHalving, kFitAlphaOptimal

Definition at line 27 of file TSpectrum2Fit.h.

Double_t* TSpectrum2Fit::fAmpCalc

protected

[fNPeaks] array of calculated values of amplitudes of 2D peaks, output parameters

Definition at line 45 of file TSpectrum2Fit.h.

Double_t* TSpectrum2Fit::fAmpCalcX1

protected

[fNPeaks] array of calculated values of amplitudes of 1D ridges in x direction, output parameters

Definition at line 48 of file TSpectrum2Fit.h.

Double_t* TSpectrum2Fit::fAmpCalcY1

protected

[fNPeaks] array of calculated values of amplitudes of 1D ridges in y direction, output parameters

Definition at line 51 of file TSpectrum2Fit.h.

Double_t* TSpectrum2Fit::fAmpErr

protected

[fNPeaks] array of amplitudes errors of 2D peaks, output parameters

Definition at line 46 of file TSpectrum2Fit.h.

Double_t* TSpectrum2Fit::fAmpErrX1

protected

[fNPeaks] array of amplitudes errors of 1D ridges in x direction, output parameters

Definition at line 49 of file TSpectrum2Fit.h.

Double_t* TSpectrum2Fit::fAmpErrY1

protected

[fNPeaks] array of amplitudes errors of 1D ridges in y direction, output parameters

Definition at line 52 of file TSpectrum2Fit.h.

Double_t* TSpectrum2Fit::fAmpInit

protected

[fNPeaks] array of initial values of amplitudes of 2D peaks, input parameters

Definition at line 44 of file TSpectrum2Fit.h.

Double_t* TSpectrum2Fit::fAmpInitX1

protected

[fNPeaks] array of initial values of amplitudes of 1D ridges in x direction, input parameters

Definition at line 47 of file TSpectrum2Fit.h.

Double_t* TSpectrum2Fit::fAmpInitY1

protected

[fNPeaks] array of initial values of amplitudes of 1D ridges in y direction, input parameters

Definition at line 50 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fAxCalc

protected

calculated value of background ax parameter

Definition at line 92 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fAxErr

protected

error value of background ax parameter

Definition at line 93 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fAxInit

protected

initial value of background ax parameter(backgroud is estimated as a0+ax*x+ay*y)

Definition at line 91 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fAyCalc

protected

calculated value of background ay parameter

Definition at line 95 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fAyErr

protected

error value of background ay parameter

Definition at line 96 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fAyInit

protected

initial value of background ay parameter(backgroud is estimated as a0+ax*x+ay*y)

Definition at line 94 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fBxCalc

protected

calculated value of b parameter for 1D ridges in x direction

Definition at line 83 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fBxErr

protected

error value of b parameter for 1D ridges in x direction

Definition at line 84 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fBxInit

protected

initial value of b parameter for 1D ridges in x direction (slope), for details see html manual and references

Definition at line 82 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fByCalc

protected

calculated value of b parameter for 1D ridges in y direction

Definition at line 86 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fByErr

protected

error value of b parameter for 1D ridges in y direction

Definition at line 87 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fByInit

protected

initial value of b parameter for 1D ridges in y direction (slope), for details see html manual and references

Definition at line 85 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fChi

protected

here the fitting functions return resulting chi square

Definition at line 31 of file TSpectrum2Fit.h.

Int_t TSpectrum2Fit::fFitTaylor

protected

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

Definition at line 29 of file TSpectrum2Fit.h.

Bool_t TSpectrum2Fit::fFixA0

protected

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

Definition at line 115 of file TSpectrum2Fit.h.

Bool_t* TSpectrum2Fit::fFixAmp

protected

[fNPeaks] array of logical values which allow to fix appropriate amplitudes of 2D peaks (not fit). However they are present in the estimated functional

Definition at line 101 of file TSpectrum2Fit.h.

Bool_t* TSpectrum2Fit::fFixAmpX1

protected

[fNPeaks] array of logical values which allow to fix appropriate amplitudes of 1D ridges in x direction (not fit). However they are present in the estimated functional

Definition at line 102 of file TSpectrum2Fit.h.

Bool_t* TSpectrum2Fit::fFixAmpY1

protected

[fNPeaks] array of logical values which allow to fix appropriate amplitudes of 1D ridges in y direction (not fit). However they are present in the estimated functional

Definition at line 103 of file TSpectrum2Fit.h.

Bool_t TSpectrum2Fit::fFixAx

protected

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

Definition at line 116 of file TSpectrum2Fit.h.

Bool_t TSpectrum2Fit::fFixAy

protected

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

Definition at line 117 of file TSpectrum2Fit.h.

Bool_t TSpectrum2Fit::fFixBx

protected

logical value of b parameter for 1D ridges in x direction, which allows to fix the parameter (not to fit).

Definition at line 113 of file TSpectrum2Fit.h.

Bool_t TSpectrum2Fit::fFixBy

protected

logical value of b parameter for 1D ridges in y direction, which allows to fix the parameter (not to fit).

Definition at line 114 of file TSpectrum2Fit.h.

Bool_t* TSpectrum2Fit::fFixPositionX

protected

[fNPeaks] array of logical values which allow to fix appropriate x positions of 2D peaks (not fit). However they are present in the estimated functional

Definition at line 97 of file TSpectrum2Fit.h.

Bool_t* TSpectrum2Fit::fFixPositionX1

protected

[fNPeaks] array of logical values which allow to fix appropriate x positions of 1D ridges (not fit). However they are present in the estimated functional

Definition at line 99 of file TSpectrum2Fit.h.

Bool_t* TSpectrum2Fit::fFixPositionY

protected

[fNPeaks] array of logical values which allow to fix appropriate y positions of 2D peaks (not fit). However they are present in the estimated functional

Definition at line 98 of file TSpectrum2Fit.h.

Bool_t* TSpectrum2Fit::fFixPositionY1

protected

[fNPeaks] array of logical values which allow to fix appropriate y positions of 1D ridges (not fit). However they are present in the estimated functional

Definition at line 100 of file TSpectrum2Fit.h.

Bool_t TSpectrum2Fit::fFixRo

protected

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

Definition at line 106 of file TSpectrum2Fit.h.

Bool_t TSpectrum2Fit::fFixSigmaX

protected

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

Definition at line 104 of file TSpectrum2Fit.h.

Bool_t TSpectrum2Fit::fFixSigmaY

protected

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

Definition at line 105 of file TSpectrum2Fit.h.

Bool_t TSpectrum2Fit::fFixSx

protected

logical value of s parameter for 1D ridges in x direction, which allows to fix the parameter (not to fit).

Definition at line 111 of file TSpectrum2Fit.h.

Bool_t TSpectrum2Fit::fFixSxy

protected

logical value of s parameter for 2D peaks, which allows to fix the parameter (not to fit).

Definition at line 108 of file TSpectrum2Fit.h.

Bool_t TSpectrum2Fit::fFixSy

protected

logical value of s parameter for 1D ridges in y direction, which allows to fix the parameter (not to fit).

Definition at line 112 of file TSpectrum2Fit.h.

Bool_t TSpectrum2Fit::fFixTx

protected

logical value of t parameter for 1D ridges in x direction, which allows to fix the parameter (not to fit).

Definition at line 109 of file TSpectrum2Fit.h.

Bool_t TSpectrum2Fit::fFixTxy

protected

logical value of t parameter for 2D peaks, which allows to fix the parameter (not to fit).

Definition at line 107 of file TSpectrum2Fit.h.

Bool_t TSpectrum2Fit::fFixTy

protected

logical value of t parameter for 1D ridges in y direction, which allows to fix the parameter (not to fit).

Definition at line 110 of file TSpectrum2Fit.h.

Int_t TSpectrum2Fit::fNPeaks

protected

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

Definition at line 20 of file TSpectrum2Fit.h.

Int_t TSpectrum2Fit::fNumberIterations

protected

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

Definition at line 21 of file TSpectrum2Fit.h.

Double_t* TSpectrum2Fit::fPositionCalcX

protected

[fNPeaks] array of calculated values of x positions of 2D peaks, output parameters

Definition at line 33 of file TSpectrum2Fit.h.

Double_t* TSpectrum2Fit::fPositionCalcX1

protected

[fNPeaks] array of calculated x positions of 1D ridges, output parameters

Definition at line 39 of file TSpectrum2Fit.h.

Double_t* TSpectrum2Fit::fPositionCalcY

protected

[fNPeaks] array of calculated values of y positions of 2D peaks, output parameters

Definition at line 36 of file TSpectrum2Fit.h.

Double_t* TSpectrum2Fit::fPositionCalcY1

protected

[fNPeaks] array of calculated y positions of 1D ridges, output parameters

Definition at line 42 of file TSpectrum2Fit.h.

Double_t* TSpectrum2Fit::fPositionErrX

protected

[fNPeaks] array of error values of x positions of 2D peaks, output parameters

Definition at line 34 of file TSpectrum2Fit.h.

Double_t* TSpectrum2Fit::fPositionErrX1

protected

[fNPeaks] array of x positions errors of 1D ridges, output parameters

Definition at line 40 of file TSpectrum2Fit.h.

Double_t* TSpectrum2Fit::fPositionErrY

protected

[fNPeaks] array of error values of y positions of 2D peaks, output parameters

Definition at line 37 of file TSpectrum2Fit.h.

Double_t* TSpectrum2Fit::fPositionErrY1

protected

[fNPeaks] array of y positions errors of 1D ridges, output parameters

Definition at line 43 of file TSpectrum2Fit.h.

Double_t* TSpectrum2Fit::fPositionInitX

protected

[fNPeaks] array of initial values of x positions of 2D peaks, input parameters

Definition at line 32 of file TSpectrum2Fit.h.

Double_t* TSpectrum2Fit::fPositionInitX1

protected

[fNPeaks] array of initial x positions of 1D ridges, input parameters

Definition at line 38 of file TSpectrum2Fit.h.

Double_t* TSpectrum2Fit::fPositionInitY

protected

[fNPeaks] array of initial values of y positions of 2D peaks, input parameters

Definition at line 35 of file TSpectrum2Fit.h.

Double_t* TSpectrum2Fit::fPositionInitY1

protected

[fNPeaks] array of initial y positions of 1D ridges, input parameters

Definition at line 41 of file TSpectrum2Fit.h.

Int_t TSpectrum2Fit::fPower

protected

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

Definition at line 28 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fRoCalc

protected

calculated value of correlation coefficient

Definition at line 62 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fRoErr

protected

error value of correlation coefficient

Definition at line 63 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fRoInit

protected

initial value of correlation coefficient

Definition at line 61 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fSigmaCalcX

protected

calculated value of sigma x parameter

Definition at line 56 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fSigmaCalcY

protected

calculated value of sigma y parameter

Definition at line 59 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fSigmaErrX

protected

error value of sigma x parameter

Definition at line 57 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fSigmaErrY

protected

error value of sigma y parameter

Definition at line 60 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fSigmaInitX

protected

initial value of sigma x parameter

Definition at line 55 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fSigmaInitY

protected

initial value of sigma y parameter

Definition at line 58 of file TSpectrum2Fit.h.

Int_t TSpectrum2Fit::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 26 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fSxCalc

protected

calculated value of s parameter for 1D ridges in x direction

Definition at line 77 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fSxErr

protected

error value of s parameter for 1D ridges in x direction

Definition at line 78 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fSxInit

protected

initial value of s parameter for 1D ridges in x direction (relative amplitude of step), for details see html manual and references

Definition at line 76 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fSxyCalc

protected

calculated value of s parameter for 2D peaks

Definition at line 68 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fSxyErr

protected

error value of s parameter for 2D peaks

Definition at line 69 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fSxyInit

protected

initial value of s parameter for 2D peaks (relative amplitude of step), for details see html manual and references

Definition at line 67 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fSyCalc

protected

calculated value of s parameter for 1D ridges in y direction

Definition at line 80 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fSyErr

protected

error value of s parameter for 1D ridges in y direction

Definition at line 81 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fSyInit

protected

initial value of s parameter for 1D ridges in y direction (relative amplitude of step), for details see html manual and references

Definition at line 79 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fTxCalc

protected

calculated value of t parameter for 1D ridges in x direction

Definition at line 71 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fTxErr

protected

error value of t parameter for 1D ridges in x direction

Definition at line 72 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fTxInit

protected

initial value of t parameter for 1D ridges in x direction (relative amplitude of tail), for details see html manual and references

Definition at line 70 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fTxyCalc

protected

calculated value of t parameter for 2D peaks

Definition at line 65 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fTxyErr

protected

error value of t parameter for 2D peaks

Definition at line 66 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fTxyInit

protected

initial value of t parameter for 2D peaks (relative amplitude of tail), for details see html manual and references

Definition at line 64 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fTyCalc

protected

calculated value of t parameter for 1D ridges in y direction

Definition at line 74 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fTyErr

protected

error value of t parameter for 1D ridges in y direction

Definition at line 75 of file TSpectrum2Fit.h.

Double_t TSpectrum2Fit::fTyInit

protected

initial value of t parameter for 1D ridges in y direction (relative amplitude of tail), for details see html manual and references

Definition at line 73 of file TSpectrum2Fit.h.

Double_t* TSpectrum2Fit::fVolume

protected

[fNPeaks] array of calculated volumes of 2D peaks, output parameters

Definition at line 53 of file TSpectrum2Fit.h.

Double_t* TSpectrum2Fit::fVolumeErr

protected

[fNPeaks] array of volumes errors of 2D peaks, output parameters

Definition at line 54 of file TSpectrum2Fit.h.

Int_t TSpectrum2Fit::fXmax

protected

last fitted channel in x direction

Definition at line 23 of file TSpectrum2Fit.h.

Int_t TSpectrum2Fit::fXmin

protected

first fitted channel in x direction

Definition at line 22 of file TSpectrum2Fit.h.

Int_t TSpectrum2Fit::fYmax

protected

last fitted channel in y direction

Definition at line 25 of file TSpectrum2Fit.h.

Int_t TSpectrum2Fit::fYmin

protected

first fitted channel in y direction

Definition at line 24 of file TSpectrum2Fit.h.

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

hist/spectrum/inc/TSpectrum2Fit.h
hist/spectrum/src/TSpectrum2Fit.cxx

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Fitting

References:

Example 1 - script FitAwmi2.c:

Script:

Example 2 - script FitAwmi2.c:

Script:

Stiefel fitting algorithm

Reference:

Script:

Member Data Documentation