The Linear Fitter - For fitting functions that are LINEAR IN PARAMETERS.

The Linear Fitter

Linear fitter is used to fit a set of data points with a linear combination of specified functions. Note, that "linear" in the name stands only for the model dependency on parameters, the specified functions can be nonlinear. The general form of this kind of model is

y(x) = a[0] + a[1]*f[1](x)+...a[n]*f[n](x)

Functions f are fixed functions of x. For example, fitting with a polynomial is linear fitting in this sense.

Introduction

The fitting method

The fit is performed using the Normal Equations method with Cholesky decomposition.

Why should it be used?

The linear fitter is considerably faster than general non-linear fitters and doesn't require to set the initial values of parameters.

Using the fitter:

1.Adding the data points:

1.1 To store or not to store the input data?

There are 2 options in the constructor - to store or not store the input data. The advantages of storing the data are that you'll be able to reset the fitting model without adding all the points again, and that for very large sets of points the chisquare is calculated more precisely. The obvious disadvantage is the amount of memory used to keep all the points.
Before you start adding the points, you can change the store/not store option by StoreData() method.

1.2 The data can be added:

simply point by point - AddPoint() method
an array of points at once: If the data is already stored in some arrays, this data can be assigned to the linear fitter without physically coping bytes, thanks to the Use() method of TVector and TMatrix classes - AssignData() method

2.Setting the formula

2.1 The linear formula syntax:

-Additive parts are separated by 2 plus signes "++" –for example "1 ++ x" - for fitting a straight line -All standard functions, undrestood by TFormula, can be used as additive parts –TMath functions can be used too -Functions, used as additive parts, shouldn't have any parameters, even if those parameters are set. –for example, if normalizing a sum of a gaus(0, 1) and a gaus(0, 2), don't use the built-in "gaus" of TFormula, because it has parameters, take TMath::Gaus(x, 0, 1) instead. -Polynomials can be used like "pol3", .."polN" -If fitting a more than 3-dimensional formula, variables should be numbered as follows: – x[0], x[1], x[2]... For example, to fit "1 ++ x[0] ++ x[1] ++ x[2] ++ x[3]*x[3]"

2.2 Setting the formula:

2.2.1 If fitting a 1-2-3-dimensional formula, one can create a

TF123 based on a linear expression and pass this function to the fitter: –Example:

TLinearFitter *lf = new TLinearFitter();
TF2 *f2 = new TF2("f2", "x ++ y ++ x*x*y*y", -2, 2, -2, 2);
lf->SetFormula(f2);

–The results of the fit are then stored in the function, just like when the TH1::Fit or TGraph::Fit is used –A linear function of this kind is by no means different from any other function, it can be drawn, evaluated, etc.

–For multidimensional fitting, TFormulas of the form: x[0]++...++x[n] can be used

2.2.2 There is no need to create the function if you don't want to,

the formula can be set by expression: –Example:

// 2 is the number of dimensions
TLinearFitter *lf = new TLinearFitter(2);
lf->SetFormula("x ++ y ++ x*x*y*y");

2.2.3 The fastest functions to compute are polynomials and hyperplanes.

–Polynomials are set the usual way: "pol1", "pol2",... –Hyperplanes are set by expression "hyp3", "hyp4", ... —The "hypN" expressions only work when the linear fitter is used directly, not through TH1::Fit or TGraph::Fit. To fit a graph or a histogram with a hyperplane, define the function as "1++x++y". —A constant term is assumed for a hyperplane, when using the "hypN" expression, so "hyp3" is in fact fitting with "1++x++y++z" function. –Fitting hyperplanes is much faster than fitting other expressions so if performance is vital, calculate the function values beforehand and give them to the fitter as variables –Example: You want to fit "sin(x)|cos(2*x)" very fast. Calculate sin(x) and cos(2*x) beforehand and store them in array *data. Then: TLinearFitter *lf=new TLinearFitter(2, "hyp2"); lf->AssignData(npoint, 2, data, y);

2.3 Resetting the formula

2.3.1 If the input data is stored (or added via AssignData() function),

the fitting formula can be reset without re-adding all the points. –Example:

TLinearFitter *lf=new TLinearFitter("1++x++x*x");
lf->AssignData(n, 1, x, y, e);
lf->Eval()
//looking at the parameter significance, you see,
// that maybe the fit will improve, if you take out
// the constant term
lf->SetFormula("x++x*x");
lf->Eval();
...

2.3.2 If the input data is not stored, the fitter will have to be

cleared and the data will have to be added again to try a different formula.

3.Accessing the fit results

3.1 There are methods in the fitter to access all relevant information:

–GetParameters, GetCovarianceMatrix, etc –the t-values of parameters and their significance can be reached by GetParTValue() and GetParSignificance() methods

3.2 If fitting with a pre-defined TF123, the fit results are also

written into this function.

4.Robust fitting - Least Trimmed Squares regression (LTS)

Outliers are atypical(by definition), infrequant observations; data points which do not appear to follow the characteristic distribution of the rest of the data. These may reflect genuine properties of the underlying phenomenon(variable), or be due to measurement errors or anomalies which shouldn't be modelled. (StatSoft electronic textbook)

Even a single gross outlier can greatly influence the results of least- squares fitting procedure, and in this case use of robust(resistant) methods is recommended.

The method implemented here is based on the article and algorithm: "Computing LTS Regression for Large Data Sets" by P.J.Rousseeuw and Katrien Van Driessen The idea of the method is to find the fitting coefficients for a subset of h observations (out of n) with the smallest sum of squared residuals. The size of the subset h should lie between (npoints + nparameters +1)/2 and n, and represents the minimal number of good points in the dataset. The default value is set to (npoints + nparameters +1)/2, but of course if you are sure that the data contains less outliers it's better to change h according to your data.

To perform a robust fit, call EvalRobust() function instead of Eval() after adding the points and setting the fitting function. Note, that standard errors on parameters are not computed!

Definition at line 159 of file TLinearFitter.h.

Public Member Functions
	TLinearFitter ()
	default c-tor, input data is stored If you don't want to store the input data, run the function StoreData(kFALSE) after constructor More...

	TLinearFitter (Int_t ndim, const char formula, Option_t opt="D")
	First parameter stands for number of dimensions in the fitting formula Second parameter is the fitting formula: see class description for formula syntax Options: The option is to store or not to store the data If you don't want to store the data, choose "" for the option, or run StoreData(kFalse) member function after the constructor. More...

	TLinearFitter (Int_t ndim)
	The parameter stands for number of dimensions in the fitting formula The input data is stored. More...

	TLinearFitter (TFormula function, Option_t opt="D")
	This constructor uses a linear function. More...

	TLinearFitter (const TLinearFitter &tlf)
	Copy ctor. More...

virtual	~TLinearFitter ()
	Linear fitter cleanup. More...

TLinearFitter &	operator= (const TLinearFitter &tlf)
	Assignment operator. More...

virtual void	Add (TLinearFitter *tlf)
	Add another linear fitter to this linear fitter. More...

virtual void	AddPoint (Double_t *x, Double_t y, Double_t e=1)
	Adds 1 point to the fitter. More...

virtual void	AddTempMatrices ()

virtual void	AssignData (Int_t npoints, Int_t xncols, Double_t x, Double_t y, Double_t *e=0)
	This function is to use when you already have all the data in arrays and don't want to copy them into the fitter. More...

virtual void	Clear (Option_t *option="")
	Clears everything. Used in TH1::Fit and TGraph::Fit(). More...

virtual void	ClearPoints ()
	To be used when different sets of points are fitted with the same formula. More...

virtual void	Chisquare ()
	Calculates the chisquare. More...

virtual Int_t	Eval ()
	Perform the fit and evaluate the parameters Returns 0 if the fit is ok, 1 if there are errors. More...

virtual Int_t	EvalRobust (Double_t h=-1)
	Finds the parameters of the fitted function in case data contains outliers. More...

virtual Int_t	ExecuteCommand (const char command, Double_t args, Int_t nargs)
	To use in TGraph::Fit and TH1::Fit(). More...

virtual void	FixParameter (Int_t ipar)
	Fixes paramter #ipar at its current value. More...

virtual void	FixParameter (Int_t ipar, Double_t parvalue)
	Fixes parameter #ipar at value parvalue. More...

virtual void	GetAtbVector (TVectorD &v)
	Get the Atb vector - a vector, used for internal computations. More...

virtual Double_t	GetChisquare ()
	Get the Chisquare. More...

virtual void	GetConfidenceIntervals (Int_t n, Int_t ndim, const Double_t x, Double_t ci, Double_t cl=0.95)
	Computes point-by-point confidence intervals for the fitted function Parameters: n - number of points ndim - dimensions of points x - points, at which to compute the intervals, for ndim > 1 should be in order: (x0,y0, x1, y1, ... More...

virtual void	GetConfidenceIntervals (TObject *obj, Double_t cl=0.95)
	Computes confidence intervals at level cl. More...

virtual Double_t *	GetCovarianceMatrix () const
	Returns covariance matrix. More...

virtual void	GetCovarianceMatrix (TMatrixD &matr)
	Returns covariance matrix. More...

virtual Double_t	GetCovarianceMatrixElement (Int_t i, Int_t j) const

virtual void	GetDesignMatrix (TMatrixD &matr)
	Returns the internal design matrix. More...

virtual void	GetErrors (TVectorD &vpar)
	Returns parameter errors. More...

virtual Int_t	GetNumberTotalParameters () const

virtual Int_t	GetNumberFreeParameters () const

virtual Int_t	GetNpoints ()

virtual void	GetParameters (TVectorD &vpar)
	Returns parameter values. More...

virtual Double_t	GetParameter (Int_t ipar) const

virtual Int_t	GetParameter (Int_t ipar, char *name, Double_t &value, Double_t &, Double_t &, Double_t &) const
	Returns the value and the name of the parameter #ipar NB: In the calling function the argument name must be set large enough. More...

virtual const char *	GetParName (Int_t ipar) const
	Returns name of parameter #ipar. More...

virtual Double_t	GetParError (Int_t ipar) const
	Returns the error of parameter #ipar. More...

virtual Double_t	GetParTValue (Int_t ipar)
	Returns the t-value for parameter #ipar. More...

virtual Double_t	GetParSignificance (Int_t ipar)
	Returns the significance of parameter #ipar. More...

virtual void	GetFitSample (TBits &bits)
	For robust lts fitting, returns the sample, on which the best fit was based. More...

virtual Double_t	GetY2 () const

virtual Bool_t	IsFixed (Int_t ipar) const

virtual Int_t	Merge (TCollection *list)
	Merge objects in list. More...

virtual void	PrintResults (Int_t level, Double_t amin=0) const
	Level = 3 (to be consistent with minuit) prints parameters and parameter errors. More...

virtual void	ReleaseParameter (Int_t ipar)
	Releases parameter #ipar. More...

virtual void	SetBasisFunctions (TObjArray *functions)
	set the basis functions in case the fitting function is not set directly The TLinearFitter will manage and delete the functions contained in the list More...

virtual void	SetDim (Int_t n)
	set the number of dimensions More...

virtual void	SetFormula (const char *formula)
	Additive parts should be separated by "++". More...

virtual void	SetFormula (TFormula *function)
	Set the fitting function. More...

virtual void	StoreData (Bool_t store)

virtual Bool_t	UpdateMatrix ()
	Update the design matrix after the formula has been changed. More...

virtual Double_t	Chisquare (Int_t, Double_t *) const

virtual Int_t	GetErrors (Int_t, Double_t &, Double_t &, Double_t &, Double_t &) const

virtual Int_t	GetStats (Double_t &, Double_t &, Double_t &, Int_t &, Int_t &) const

virtual Double_t	GetSumLog (Int_t)

virtual void	SetFitMethod (const char *)

virtual Int_t	SetParameter (Int_t, const char *, Double_t, Double_t, Double_t, Double_t)

Public Member Functions inherited from TVirtualFitter
	TVirtualFitter ()

virtual	~TVirtualFitter ()
	Cleanup virtual fitter. More...

virtual FCNFunc_t	GetFCN ()

virtual Foption_t	GetFitOption () const

TMethodCall *	GetMethodCall () const

virtual TObject *	GetObjectFit () const

virtual TObject *	GetUserFunc () const

virtual Int_t	GetXfirst () const

virtual Int_t	GetXlast () const

virtual Int_t	GetYfirst () const

virtual Int_t	GetYlast () const

virtual Int_t	GetZfirst () const

virtual Int_t	GetZlast () const

virtual Double_t *	SetCache (Int_t npoints, Int_t psize)
	Initialize the cache array npoints is the number of points to be stored (or already stored) in the cache psize is the number of elements per point. More...

virtual void	SetFCN (void *fcn)
	To set the address of the minimization objective function. More...

virtual void	SetFCN (void(fcn)(Int_t &, Double_t , Double_t &f, Double_t *, Int_t))
	To set the address of the minimization objective function called by the native compiler (see function below when called by CINT) More...

virtual void	SetFitOption (Foption_t option)

virtual void	SetObjectFit (TObject *obj)

virtual void	SetUserFunc (TObject *userfunc)

virtual void	SetXfirst (Int_t first)

virtual void	SetXlast (Int_t last)

virtual void	SetYfirst (Int_t first)

virtual void	SetYlast (Int_t last)

virtual void	SetZfirst (Int_t first)

virtual void	SetZlast (Int_t last)

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

virtual	~TNamed ()

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	SetName (const char *name)
	Change (i.e. More...

virtual void	SetNameTitle (const char name, const char title)
	Change (i.e. set) all the TNamed parameters (name and title). More...

virtual void	SetTitle (const char *title="")
	Change (i.e. set) the title of the TNamed. More...

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

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

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

Public Member Functions inherited from TObject
	TObject ()

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

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

virtual	~TObject ()
	TObject destructor. 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	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 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 UInt_t	GetUniqueID () const
	Return the unique object id. More...

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

virtual Option_t *	GetOption () const

virtual char *	GetObjectInfo (Int_t px, Int_t py) const
	Returns string containing info about the object at position (px,py). More...

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

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

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

Bool_t	IsOnHeap () const

Bool_t	IsZombie () const

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

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...

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

void *	operator new (size_t sz)

void *	operator new[] (size_t sz)

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

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

void	operator delete (void *ptr)
	Operator delete. More...

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

void	ResetBit (UInt_t f)

Bool_t	TestBit (UInt_t f) const

Int_t	TestBits (UInt_t f) const

void	InvertBit (UInt_t f)

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

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

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

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

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

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...

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

Private Member Functions
void	AddToDesign (Double_t *x, Double_t y, Double_t e)
	Add a point to the AtA matrix and to the Atb vector. More...

void	ComputeTValues ()
	Computes parameters' t-values and significance. More...

Int_t	GraphLinearFitter (Double_t h)
	Used in TGraph::Fit(). More...

Int_t	Graph2DLinearFitter (Double_t h)
	Minimisation function for a TGraph2D. More...

Int_t	HistLinearFitter ()
	Minimization function for H1s using a Chisquare method. More...

Int_t	MultiGraphLinearFitter (Double_t h)
	Minimisation function for a TMultiGraph. More...

Int_t	Partition (Int_t nmini, Int_t *indsubdat)
	divides the elements into approximately equal subgroups number of elements in each subgroup is stored in indsubdat number of subgroups is returned More...

void	RDraw (Int_t subdat, Int_t indsubdat)
	Draws ngroup nonoverlapping subdatasets out of a dataset of size n such that the selected case numbers are uniformly distributed from 1 to n. More...

void	CreateSubset (Int_t ntotal, Int_t h, Int_t *index)
	Creates a p-subset to start ntotal - total number of points from which the subset is chosen. More...

Double_t	CStep (Int_t step, Int_t h, Double_t residuals, Int_t index, Int_t *subdat, Int_t start, Int_t end)
	The CStep procedure, as described in the article. More...

Bool_t	Linf ()

Private Attributes
TVectorD	fParams

TMatrixDSym	fParCovar

TVectorD	fTValues

TVectorD	fParSign

TMatrixDSym	fDesign

TMatrixDSym	fDesignTemp

TMatrixDSym	fDesignTemp2
	temporary matrix, used for num.stability More...

TMatrixDSym	fDesignTemp3

TVectorD	fAtb

TVectorD	fAtbTemp

TVectorD	fAtbTemp2
	temporary vector, used for num.stability More...

TVectorD	fAtbTemp3

TObjArray	fFunctions
	map of basis functions and formula More...

TVectorD	fY

Double_t	fY2

Double_t	fY2Temp

TMatrixD	fX
	temporary variable used for num.stability More...

TVectorD	fE

TFormula *	fInputFunction

Double_t	fVal [1000]

Int_t	fNpoints
	temporary More...

Int_t	fNfunctions

Int_t	fFormulaSize

Int_t	fNdim

Int_t	fNfixed

Int_t	fSpecial

char *	fFormula

Bool_t	fIsSet

Bool_t	fStoreData

Double_t	fChisquare

Int_t	fH

Bool_t	fRobust

TBits	fFitsample

Bool_t *	fFixedParams

Static Private Attributes
static std::map< TString, TFormula * >	fgFormulaMap

Additional Inherited Members
Public Types inherited from TVirtualFitter
typedef void(*	FCNFunc_t )(Int_t &npar, Double_t gin, Double_t &f, Double_t u, Int_t flag)

Public Types inherited from TObject
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) }

enum	{ kIsOnHeap = 0x01000000, kNotDeleted = 0x02000000, kZombie = 0x04000000, kBitMask = 0x00ffffff }

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

Static Public Member Functions inherited from TVirtualFitter
static TVirtualFitter *	GetFitter ()
	static: return the current Fitter More...

static TVirtualFitter *	Fitter (TObject *obj, Int_t maxpar=25)
	Static function returning a pointer to the current fitter. More...

static const char *	GetDefaultFitter ()
	static: return the name of the default fitter More...

static Int_t	GetMaxIterations ()
	static: Return the maximum number of iterations actually max number of function calls More...

static Double_t	GetErrorDef ()
	static: Return the Error Definition More...

static Double_t	GetPrecision ()
	static: Return the fit relative precision More...

static void	SetDefaultFitter (const char *name="")
	static: set name of default fitter More...

static void	SetFitter (TVirtualFitter *fitter, Int_t maxpar=25)
	Static function to set an alternative fitter. More...

static void	SetMaxIterations (Int_t niter=5000)
	static: Set the maximum number of function calls for the minimization algorithm For example for MIGRAD this is the maxcalls value passed as first argument (see http://wwwasdoc.web.cern.ch/wwwasdoc/minuit/node18.html ) More...

static void	SetErrorDef (Double_t errdef=1)
	static: Set the Error Definition (default=1) For Minuit this is the value passed with the "SET ERR" command (see http://wwwasdoc.web.cern.ch/wwwasdoc/minuit/node18.html) More...

static void	SetPrecision (Double_t prec=1e-6)
	static: Set the tolerance used in the minimization algorithm For example for MIGRAD this is tolerance value passed as second argument (see http://wwwasdoc.web.cern.ch/wwwasdoc/minuit/node18.html ) More...

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

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

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

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

Protected Member Functions inherited from TVirtualFitter
	TVirtualFitter (const TVirtualFitter &tvf)
	copy constructor More...

TVirtualFitter &	operator= (const TVirtualFitter &tvf)
	assignment operator More...

Protected Member Functions inherited from TObject
void	MakeZombie ()

virtual void	DoError (int level, const char location, const char fmt, va_list va) const
	Interface to ErrorHandler (protected). More...

Protected Attributes inherited from TVirtualFitter
Foption_t	fOption

Int_t	fXfirst

Int_t	fXlast

Int_t	fYfirst

Int_t	fYlast

Int_t	fZfirst

Int_t	fZlast

Int_t	fNpoints

Int_t	fPointSize

Int_t	fCacheSize

Double_t *	fCache

TObject *	fObjectFit

TObject *	fUserFunc

TMethodCall *	fMethodCall

void(*	fFCN )(Int_t &npar, Double_t gin, Double_t &f, Double_t u, Int_t flag)

Protected Attributes inherited from TNamed
TString	fName

TString	fTitle

#include <TLinearFitter.h>

Inheritance diagram for TLinearFitter:

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Constructor & Destructor Documentation

TLinearFitter::TLinearFitter ( )

default c-tor, input data is stored If you don't want to store the input data, run the function StoreData(kFALSE) after constructor

Definition at line 223 of file TLinearFitter.cxx.

TLinearFitter::TLinearFitter	(	Int_t	ndim,
		const char *	formula,
		Option_t *	opt = `"D"`
	)

First parameter stands for number of dimensions in the fitting formula Second parameter is the fitting formula: see class description for formula syntax Options: The option is to store or not to store the data If you don't want to store the data, choose "" for the option, or run StoreData(kFalse) member function after the constructor.

Definition at line 294 of file TLinearFitter.cxx.

TLinearFitter::TLinearFitter ( Int_t ndim )

The parameter stands for number of dimensions in the fitting formula The input data is stored.

If you don't want to store the input data, run the function StoreData(kFALSE) after constructor

Definition at line 265 of file TLinearFitter.cxx.

TLinearFitter::TLinearFitter	(	TFormula *	function,
		Option_t *	opt = `"D"`
	)

This constructor uses a linear function.

How to create it? TFormula now accepts formulas of the following kind: TFormula("f", "x++y++z++x*x") or TFormula("f", "x[0]++x[1]++x[2]*x[2]"); Other than the look, it's in no way different from the regular formula, it can be evaluated, drawn, etc. The option is to store or not to store the data If you don't want to store the data, choose "" for the option, or run StoreData(kFalse) member function after the constructor

Definition at line 327 of file TLinearFitter.cxx.

TLinearFitter::TLinearFitter ( const TLinearFitter & tlf )

Copy ctor.

Definition at line 360 of file TLinearFitter.cxx.

TLinearFitter::~TLinearFitter ( )

virtual

Linear fitter cleanup.

Definition at line 416 of file TLinearFitter.cxx.

Member Function Documentation

void TLinearFitter::Add ( TLinearFitter * tlf )

virtual

Add another linear fitter to this linear fitter.

Points and Design matrices are added, but the previos fitting results (if any) are deleted. Fitters must have same formulas (this is not checked). Fixed parameters are not changed

Definition at line 507 of file TLinearFitter.cxx.

Referenced by Merge().

void TLinearFitter::AddPoint	(	Double_t *	x,
		Double_t	y,
		Double_t	e = `1`
	)

virtual

Adds 1 point to the fitter.

First parameter stands for the coordinates of the point, where the function is measured Second parameter - the value being fitted Third parameter - weight(measurement error) of this point (=1 by default)

Definition at line 556 of file TLinearFitter.cxx.

Referenced by Graph2DLinearFitter(), GraphLinearFitter(), HistLinearFitter(), MultiGraphLinearFitter(), and TLinearMinimizer::SetFunction().

void TLinearFitter::AddTempMatrices ( )

virtual

Definition at line 718 of file TLinearFitter.cxx.

Referenced by Eval().

void TLinearFitter::AddToDesign	(	Double_t *	x,
		Double_t	y,
		Double_t	e
	)

private

Add a point to the AtA matrix and to the Atb vector.

Definition at line 632 of file TLinearFitter.cxx.

Referenced by AddPoint(), AssignData(), CreateSubset(), CStep(), and UpdateMatrix().

void TLinearFitter::AssignData	(	Int_t	npoints,
		Int_t	xncols,
		Double_t *	x,
		Double_t *	y,
		Double_t *	e = `0`
	)

virtual

This function is to use when you already have all the data in arrays and don't want to copy them into the fitter.

In this function, the Use() method of TVectorD and TMatrixD is used, so no bytes are physically moved around. First parameter - number of points to fit Second parameter - number of variables in the model Third parameter - the variables of the model, stored in the following way: (x0(0), x1(0), x2(0), x3(0), x0(1), x1(1), x2(1), x3(1),...

Definition at line 594 of file TLinearFitter.cxx.

Referenced by fitLinear2().

void TLinearFitter::Chisquare ( )

virtual

Calculates the chisquare.

Definition at line 808 of file TLinearFitter.cxx.

Referenced by GetChisquare().

virtual Double_t TLinearFitter::Chisquare	(	Int_t	,
		Double_t *
	)		const

inlinevirtual

Implements TVirtualFitter.

Definition at line 275 of file TLinearFitter.h.

void TLinearFitter::Clear ( Option_t * option = "" )

virtual

Clears everything. Used in TH1::Fit and TGraph::Fit().

Implements TVirtualFitter.

Definition at line 742 of file TLinearFitter.cxx.

void TLinearFitter::ClearPoints ( )

virtual

To be used when different sets of points are fitted with the same formula.

Definition at line 782 of file TLinearFitter.cxx.

void TLinearFitter::ComputeTValues ( )

private

Computes parameters' t-values and significance.

Definition at line 873 of file TLinearFitter.cxx.

Referenced by GetParSignificance(), and GetParTValue().

void TLinearFitter::CreateSubset	(	Int_t	ntotal,
		Int_t	h,
		Int_t *	index
	)

private

Creates a p-subset to start ntotal - total number of points from which the subset is chosen.

Definition at line 2295 of file TLinearFitter.cxx.

Referenced by EvalRobust().

Double_t TLinearFitter::CStep	(	Int_t	step,
		Int_t	h,
		Double_t *	residuals,
		Int_t *	index,
		Int_t *	subdat,
		Int_t	start,
		Int_t	end
	)

private

The CStep procedure, as described in the article.

Definition at line 2358 of file TLinearFitter.cxx.

Referenced by EvalRobust().

Int_t TLinearFitter::Eval ( )

virtual

Perform the fit and evaluate the parameters Returns 0 if the fit is ok, 1 if there are errors.

Definition at line 885 of file TLinearFitter.cxx.

Referenced by fitLinear2(), Graph2DLinearFitter(), GraphLinearFitter(), HistLinearFitter(), TLinearMinimizer::Minimize(), and MultiGraphLinearFitter().

Int_t TLinearFitter::EvalRobust ( Double_t h = -1 )

virtual

Finds the parameters of the fitted function in case data contains outliers.

Parameter h stands for the minimal fraction of good points in the dataset (h < 1, i.e. for 70% of good points take h=0.7). The default value of h*Npoints is (Npoints + Nparameters+1)/2 If the user provides a value of h smaller than above, default is taken See class description for the algorithm details

Definition at line 2099 of file TLinearFitter.cxx.

Referenced by Graph2DLinearFitter(), GraphLinearFitter(), TLinearMinimizer::Minimize(), and MultiGraphLinearFitter().

Int_t TLinearFitter::ExecuteCommand	(	const char *	command,
		Double_t *	args,
		Int_t	nargs
	)

virtual

To use in TGraph::Fit and TH1::Fit().

Implements TVirtualFitter.

Definition at line 1728 of file TLinearFitter.cxx.

void TLinearFitter::FixParameter ( Int_t ipar )

virtual

Fixes paramter #ipar at its current value.

Implements TVirtualFitter.

Definition at line 1012 of file TLinearFitter.cxx.

Referenced by fitLinear2(), TLinearMinimizer::SetFixedVariable(), and SetFormula().

void TLinearFitter::FixParameter	(	Int_t	ipar,
		Double_t	parvalue
	)

virtual

Fixes parameter #ipar at value parvalue.

Definition at line 1035 of file TLinearFitter.cxx.

void TLinearFitter::GetAtbVector ( TVectorD & v )

virtual

Get the Atb vector - a vector, used for internal computations.

Definition at line 1075 of file TLinearFitter.cxx.

Double_t TLinearFitter::GetChisquare ( )

virtual

Get the Chisquare.

Definition at line 1085 of file TLinearFitter.cxx.

Referenced by Eval(), and fitLinear2().

void TLinearFitter::GetConfidenceIntervals	(	Int_t	n,
		Int_t	ndim,
		const Double_t *	x,
		Double_t *	ci,
		Double_t	cl = `0.95`
	)

virtual

Computes point-by-point confidence intervals for the fitted function Parameters: n - number of points ndim - dimensions of points x - points, at which to compute the intervals, for ndim > 1 should be in order: (x0,y0, x1, y1, ...

xn, yn) ci - computed intervals are returned in this array cl - confidence level, default=0.95

NOTE, that this method can only be used when the fitting function inherits from a TF1, so it's not possible when the fitting function was set as a string or as a pure TFormula

Reimplemented from TVirtualFitter.

Definition at line 1108 of file TLinearFitter.cxx.

Referenced by GetConfidenceIntervals().

void TLinearFitter::GetConfidenceIntervals	(	TObject *	obj,
		Double_t	cl = `0.95`
	)

virtual

Computes confidence intervals at level cl.

Default is 0.95 The TObject parameter can be a TGraphErrors, a TGraph2DErrors or a TH123. For Graphs, confidence intervals are computed for each point, the value of the graph at that point is set to the function value at that point, and the graph y-errors (or z-errors) are set to the value of the confidence interval at that point For Histograms, confidence intervals are computed for each bin center The bin content of this bin is then set to the function value at the bin center, and the bin error is set to the confidence interval value. Allowed combinations: Fitted object Passed object TGraph TGraphErrors, TH1 TGraphErrors, AsymmErrors TGraphErrors, TH1 TH1 TGraphErrors, TH1 TGraph2D TGraph2DErrors, TH2 TGraph2DErrors TGraph2DErrors, TH2 TH2 TGraph2DErrors, TH2 TH3 TH3

Reimplemented from TVirtualFitter.

Definition at line 1159 of file TLinearFitter.cxx.

Double_t * TLinearFitter::GetCovarianceMatrix ( ) const

virtual

Returns covariance matrix.

Implements TVirtualFitter.

Definition at line 1308 of file TLinearFitter.cxx.

Referenced by TLinearMinimizer::Minimize().

void TLinearFitter::GetCovarianceMatrix ( TMatrixD & matr )

virtual

Returns covariance matrix.

Definition at line 1317 of file TLinearFitter.cxx.

virtual Double_t TLinearFitter::GetCovarianceMatrixElement	(	Int_t	i,
		Int_t	j
	)		const

inlinevirtual

Implements TVirtualFitter.

Definition at line 247 of file TLinearFitter.h.

void TLinearFitter::GetDesignMatrix ( TMatrixD & matr )

virtual

Returns the internal design matrix.

Definition at line 1328 of file TLinearFitter.cxx.

void TLinearFitter::GetErrors ( TVectorD & vpar )

virtual

Returns parameter errors.

Definition at line 1339 of file TLinearFitter.cxx.

Referenced by fitLinear2().

virtual Int_t TLinearFitter::GetErrors	(	Int_t	,
		Double_t &	,
		Double_t &	,
		Double_t &	,
		Double_t &
	)		const

inlinevirtual

Implements TVirtualFitter.

Definition at line 276 of file TLinearFitter.h.

void TLinearFitter::GetFitSample ( TBits & bits )

virtual

For robust lts fitting, returns the sample, on which the best fit was based.

Definition at line 1438 of file TLinearFitter.cxx.

virtual Int_t TLinearFitter::GetNpoints ( )

inlinevirtual

Definition at line 252 of file TLinearFitter.h.

virtual Int_t TLinearFitter::GetNumberFreeParameters ( ) const

inlinevirtual

Implements TVirtualFitter.

Definition at line 251 of file TLinearFitter.h.

virtual Int_t TLinearFitter::GetNumberTotalParameters ( ) const

inlinevirtual

Implements TVirtualFitter.

Definition at line 250 of file TLinearFitter.h.

virtual Double_t TLinearFitter::GetParameter ( Int_t ipar ) const

inlinevirtual

Implements TVirtualFitter.

Definition at line 254 of file TLinearFitter.h.

Referenced by TLinearMinimizer::Minimize().

Int_t TLinearFitter::GetParameter	(	Int_t	ipar,
		char *	name,
		Double_t &	value,
		Double_t &	,
		Double_t &	,
		Double_t &
	)		const

virtual

Returns the value and the name of the parameter #ipar NB: In the calling function the argument name must be set large enough.

Implements TVirtualFitter.

Definition at line 1364 of file TLinearFitter.cxx.

void TLinearFitter::GetParameters ( TVectorD & vpar )

virtual

Returns parameter values.

Definition at line 1352 of file TLinearFitter.cxx.

Referenced by fitLinear2().

Double_t TLinearFitter::GetParError ( Int_t ipar ) const

virtual

Returns the error of parameter #ipar.

Implements TVirtualFitter.

Definition at line 1382 of file TLinearFitter.cxx.

Referenced by TLinearMinimizer::Minimize().

const char * TLinearFitter::GetParName ( Int_t ipar ) const

virtual

Returns name of parameter #ipar.

Implements TVirtualFitter.

Definition at line 1396 of file TLinearFitter.cxx.

Double_t TLinearFitter::GetParSignificance ( Int_t ipar )

virtual

Returns the significance of parameter #ipar.

Definition at line 1424 of file TLinearFitter.cxx.

Double_t TLinearFitter::GetParTValue ( Int_t ipar )

virtual

Returns the t-value for parameter #ipar.

Definition at line 1410 of file TLinearFitter.cxx.

virtual Int_t TLinearFitter::GetStats	(	Double_t &	,
		Double_t &	,
		Double_t &	,
		Int_t &	,
		Int_t &
	)		const

inlinevirtual

Implements TVirtualFitter.

Definition at line 278 of file TLinearFitter.h.

virtual Double_t TLinearFitter::GetSumLog ( Int_t )

inlinevirtual

Implements TVirtualFitter.

Definition at line 279 of file TLinearFitter.h.

virtual Double_t TLinearFitter::GetY2 ( ) const

inlinevirtual

Definition at line 261 of file TLinearFitter.h.

Int_t TLinearFitter::Graph2DLinearFitter ( Double_t h )

private

Minimisation function for a TGraph2D.

Definition at line 1834 of file TLinearFitter.cxx.

Referenced by ExecuteCommand().

Int_t TLinearFitter::GraphLinearFitter ( Double_t h )

private

Used in TGraph::Fit().

Definition at line 1772 of file TLinearFitter.cxx.

Referenced by ExecuteCommand().

Int_t TLinearFitter::HistLinearFitter ( )

private

Minimization function for H1s using a Chisquare method.

Definition at line 1978 of file TLinearFitter.cxx.

Referenced by ExecuteCommand().

virtual Bool_t TLinearFitter::IsFixed ( Int_t ipar ) const

inlinevirtual

Implements TVirtualFitter.

Definition at line 262 of file TLinearFitter.h.

Bool_t TLinearFitter::Linf ( )

private

Definition at line 2519 of file TLinearFitter.cxx.

Referenced by CreateSubset(), and CStep().

Int_t TLinearFitter::Merge ( TCollection * list )

virtual

Merge objects in list.

Definition at line 1452 of file TLinearFitter.cxx.

Int_t TLinearFitter::MultiGraphLinearFitter ( Double_t h )

private

Minimisation function for a TMultiGraph.

Definition at line 1907 of file TLinearFitter.cxx.

Referenced by ExecuteCommand().

TLinearFitter & TLinearFitter::operator= ( const TLinearFitter & tlf )

Assignment operator.

Definition at line 436 of file TLinearFitter.cxx.

Int_t TLinearFitter::Partition	(	Int_t	nmini,
		Int_t *	indsubdat
	)

private

divides the elements into approximately equal subgroups number of elements in each subgroup is stored in indsubdat number of subgroups is returned

Definition at line 2558 of file TLinearFitter.cxx.

Referenced by EvalRobust().

void TLinearFitter::PrintResults	(	Int_t	level,
		Double_t	amin = `0`
	)		const

virtual

Level = 3 (to be consistent with minuit) prints parameters and parameter errors.

Implements TVirtualFitter.

Definition at line 1752 of file TLinearFitter.cxx.

void TLinearFitter::RDraw	(	Int_t *	subdat,
		Int_t *	indsubdat
	)

private

Draws ngroup nonoverlapping subdatasets out of a dataset of size n such that the selected case numbers are uniformly distributed from 1 to n.

Definition at line 2610 of file TLinearFitter.cxx.

Referenced by EvalRobust().

void TLinearFitter::ReleaseParameter ( Int_t ipar )

virtual

Releases parameter #ipar.

Implements TVirtualFitter.

Definition at line 1057 of file TLinearFitter.cxx.

void TLinearFitter::SetBasisFunctions ( TObjArray * functions )

virtual

set the basis functions in case the fitting function is not set directly The TLinearFitter will manage and delete the functions contained in the list

Definition at line 1471 of file TLinearFitter.cxx.

Referenced by TLinearMinimizer::SetFunction().

void TLinearFitter::SetDim ( Int_t n )

virtual

set the number of dimensions

Definition at line 1510 of file TLinearFitter.cxx.

Referenced by Graph2DLinearFitter(), GraphLinearFitter(), HistLinearFitter(), and MultiGraphLinearFitter().

virtual void TLinearFitter::SetFitMethod ( const char * )

inlinevirtual

Implements TVirtualFitter.

Definition at line 280 of file TLinearFitter.h.

void TLinearFitter::SetFormula ( const char * formula )

virtual

Additive parts should be separated by "++".

Examples (ai are parameters to fit): 1.fitting function: a0*x0 + a1*x1 + a2*x2 input formula "x[0]++x[1]++x[2]" 2.TMath functions can be used: fitting function: a0*TMath::Gaus(x, 0, 1) + a1*y input formula: "TMath::Gaus(x, 0, 1)++y" fills the array of functions

Definition at line 1531 of file TLinearFitter.cxx.

Referenced by fitLinear2(), Graph2DLinearFitter(), GraphLinearFitter(), HistLinearFitter(), MultiGraphLinearFitter(), and TLinearFitter().