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 151 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...

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	Chisquare ()
	Calculates the chisquare. More...

virtual Double_t	Chisquare (Int_t, Double_t *) const

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

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

virtual Int_t	GetNpoints ()

virtual Int_t	GetNumberFreeParameters () const

virtual Int_t	GetNumberTotalParameters () const

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

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

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

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

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

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

virtual Double_t	GetSumLog (Int_t)

virtual Double_t	GetY2 () const

virtual Bool_t	IsFixed (Int_t ipar) const

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

TLinearFitter &	operator= (const TLinearFitter &tlf)
	Assignment operator. 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	SetFitMethod (const char *)

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

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

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

virtual void	StoreData (Bool_t store)

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

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...

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

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

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

Bool_t	Linf ()

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...

Private Attributes
TVectorD	fAtb

TVectorD	fAtbTemp

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

TVectorD	fAtbTemp3

Double_t	fChisquare

TMatrixDSym	fDesign

TMatrixDSym	fDesignTemp

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

TMatrixDSym	fDesignTemp3

TVectorD	fE

TBits	fFitsample

Bool_t *	fFixedParams

char *	fFormula

Int_t	fFormulaSize

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

Int_t	fH

TFormula *	fInputFunction

Bool_t	fIsSet

Int_t	fNdim

Int_t	fNfixed

Int_t	fNfunctions

Int_t	fNpoints
	temporary More...

TVectorD	fParams

TMatrixDSym	fParCovar

TVectorD	fParSign

Bool_t	fRobust

Int_t	fSpecial

Bool_t	fStoreData

TVectorD	fTValues

Double_t	fVal [1000]

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

TVectorD	fY

Double_t	fY2

Double_t	fY2Temp

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

#include <TLinearFitter.h>

Inheritance diagram for TLinearFitter:

[legend]

Constructor & Destructor Documentation

◆ TLinearFitter() [1/5]

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() [2/5]

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() [3/5]

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() [4/5]

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() [5/5]

TLinearFitter::TLinearFitter ( const TLinearFitter & tlf )

Copy ctor.

Definition at line 360 of file TLinearFitter.cxx.

◆ ~TLinearFitter()

TLinearFitter::~TLinearFitter ( )

virtual

Linear fitter cleanup.

Definition at line 416 of file TLinearFitter.cxx.

Member Function Documentation

◆ Add()

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.

◆ AddPoint()

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.

◆ AddTempMatrices()

void TLinearFitter::AddTempMatrices ( )

virtual

Definition at line 718 of file TLinearFitter.cxx.

◆ AddToDesign()

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.

◆ AssignData()

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.

◆ Chisquare() [1/2]

void TLinearFitter::Chisquare ( )

virtual

Calculates the chisquare.

Definition at line 808 of file TLinearFitter.cxx.

◆ Chisquare() [2/2]

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

inlinevirtual

Definition at line 267 of file TLinearFitter.h.

◆ Clear()

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

virtual

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

Definition at line 742 of file TLinearFitter.cxx.

◆ ClearPoints()

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.

◆ ComputeTValues()

void TLinearFitter::ComputeTValues ( )

private

Computes parameters' t-values and significance.

Definition at line 873 of file TLinearFitter.cxx.

◆ CreateSubset()

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 2300 of file TLinearFitter.cxx.

◆ CStep()

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 2363 of file TLinearFitter.cxx.

◆ Eval()

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.

◆ EvalRobust()

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 2104 of file TLinearFitter.cxx.

◆ ExecuteCommand()

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

virtual

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

Definition at line 1733 of file TLinearFitter.cxx.

◆ FixParameter() [1/2]

void TLinearFitter::FixParameter ( Int_t ipar )

virtual

Fixes paramter #ipar at its current value.

Definition at line 1012 of file TLinearFitter.cxx.

◆ FixParameter() [2/2]

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

virtual

Fixes parameter #ipar at value parvalue.

Definition at line 1035 of file TLinearFitter.cxx.

◆ GetAtbVector()

void TLinearFitter::GetAtbVector ( TVectorD & v )

virtual

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

Definition at line 1075 of file TLinearFitter.cxx.

◆ GetChisquare()

Double_t TLinearFitter::GetChisquare ( )

virtual

Get the Chisquare.

Definition at line 1085 of file TLinearFitter.cxx.

◆ GetConfidenceIntervals() [1/2]

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

Definition at line 1108 of file TLinearFitter.cxx.

◆ GetConfidenceIntervals() [2/2]

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

Definition at line 1159 of file TLinearFitter.cxx.

◆ GetCovarianceMatrix() [1/2]

Double_t * TLinearFitter::GetCovarianceMatrix ( ) const

virtual

Returns covariance matrix.

Definition at line 1308 of file TLinearFitter.cxx.

◆ GetCovarianceMatrix() [2/2]

void TLinearFitter::GetCovarianceMatrix ( TMatrixD & matr )

virtual

Returns covariance matrix.

Definition at line 1317 of file TLinearFitter.cxx.

◆ GetCovarianceMatrixElement()

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

inlinevirtual

Definition at line 239 of file TLinearFitter.h.

◆ GetDesignMatrix()

void TLinearFitter::GetDesignMatrix ( TMatrixD & matr )

virtual

Returns the internal design matrix.

Definition at line 1328 of file TLinearFitter.cxx.

◆ GetErrors() [1/2]

void TLinearFitter::GetErrors ( TVectorD & vpar )

virtual

Returns parameter errors.

Definition at line 1339 of file TLinearFitter.cxx.

◆ GetErrors() [2/2]

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

inlinevirtual

Definition at line 268 of file TLinearFitter.h.

◆ GetFitSample()

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.

◆ GetNpoints()

virtual Int_t TLinearFitter::GetNpoints ( )

inlinevirtual

Definition at line 244 of file TLinearFitter.h.

◆ GetNumberFreeParameters()

virtual Int_t TLinearFitter::GetNumberFreeParameters ( ) const

inlinevirtual

Definition at line 243 of file TLinearFitter.h.

◆ GetNumberTotalParameters()

virtual Int_t TLinearFitter::GetNumberTotalParameters ( ) const

inlinevirtual

Definition at line 242 of file TLinearFitter.h.

◆ GetParameter() [1/2]

virtual Double_t TLinearFitter::GetParameter ( Int_t ipar ) const

inlinevirtual

Definition at line 246 of file TLinearFitter.h.

◆ GetParameter() [2/2]

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.

Definition at line 1364 of file TLinearFitter.cxx.

◆ GetParameters()

void TLinearFitter::GetParameters ( TVectorD & vpar )

virtual

Returns parameter values.

Definition at line 1352 of file TLinearFitter.cxx.

◆ GetParError()

Double_t TLinearFitter::GetParError ( Int_t ipar ) const

virtual

Returns the error of parameter #ipar.

Definition at line 1382 of file TLinearFitter.cxx.

◆ GetParName()

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

virtual

Returns name of parameter #ipar.

Definition at line 1396 of file TLinearFitter.cxx.

◆ GetParSignificance()

Double_t TLinearFitter::GetParSignificance ( Int_t ipar )

virtual

Returns the significance of parameter #ipar.

Definition at line 1424 of file TLinearFitter.cxx.

◆ GetParTValue()

Double_t TLinearFitter::GetParTValue ( Int_t ipar )

virtual

Returns the t-value for parameter #ipar.

Definition at line 1410 of file TLinearFitter.cxx.

◆ GetStats()

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

inlinevirtual

Definition at line 270 of file TLinearFitter.h.

◆ GetSumLog()

virtual Double_t TLinearFitter::GetSumLog ( Int_t )

inlinevirtual

Definition at line 271 of file TLinearFitter.h.

◆ GetY2()

virtual Double_t TLinearFitter::GetY2 ( ) const

inlinevirtual

Definition at line 253 of file TLinearFitter.h.

◆ Graph2DLinearFitter()

Int_t TLinearFitter::Graph2DLinearFitter ( Double_t h )

private

Minimisation function for a TGraph2D.

Definition at line 1839 of file TLinearFitter.cxx.

◆ GraphLinearFitter()

Int_t TLinearFitter::GraphLinearFitter ( Double_t h )

private

Used in TGraph::Fit().

Definition at line 1777 of file TLinearFitter.cxx.

◆ HistLinearFitter()

Int_t TLinearFitter::HistLinearFitter ( )

private

Minimization function for H1s using a Chisquare method.

Definition at line 1983 of file TLinearFitter.cxx.

◆ IsFixed()

virtual Bool_t TLinearFitter::IsFixed ( Int_t ipar ) const

inlinevirtual

Definition at line 254 of file TLinearFitter.h.

◆ Linf()

Bool_t TLinearFitter::Linf ( )

private

Definition at line 2524 of file TLinearFitter.cxx.

◆ Merge()

Int_t TLinearFitter::Merge ( TCollection * list )

virtual

Merge objects in list.

Definition at line 1452 of file TLinearFitter.cxx.

◆ MultiGraphLinearFitter()

Int_t TLinearFitter::MultiGraphLinearFitter ( Double_t h )

private

Minimisation function for a TMultiGraph.

Definition at line 1912 of file TLinearFitter.cxx.

◆ operator=()

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

Assignment operator.

Definition at line 436 of file TLinearFitter.cxx.

◆ Partition()

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 2563 of file TLinearFitter.cxx.

◆ PrintResults()

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

virtual

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

Definition at line 1757 of file TLinearFitter.cxx.

◆ RDraw()

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 2615 of file TLinearFitter.cxx.

◆ ReleaseParameter()

void TLinearFitter::ReleaseParameter ( Int_t ipar )

virtual

Releases parameter #ipar.

Definition at line 1057 of file TLinearFitter.cxx.

◆ SetBasisFunctions()

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.

◆ SetDim()

void TLinearFitter::SetDim ( Int_t n )

virtual

set the number of dimensions

Definition at line 1511 of file TLinearFitter.cxx.

◆ SetFitMethod()

virtual void TLinearFitter::SetFitMethod ( const char * )

inlinevirtual

Definition at line 272 of file TLinearFitter.h.

◆ SetFormula() [1/2]

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 1532 of file TLinearFitter.cxx.

◆ SetFormula() [2/2]

void TLinearFitter::SetFormula ( TFormula * function )

virtual

Set the fitting function.

Definition at line 1651 of file TLinearFitter.cxx.

◆ SetParameter()

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

inlinevirtual

Definition at line 273 of file TLinearFitter.h.

◆ StoreData()

virtual void TLinearFitter::StoreData ( Bool_t store )

inlinevirtual

Definition at line 262 of file TLinearFitter.h.

◆ UpdateMatrix()

Bool_t TLinearFitter::UpdateMatrix ( )

virtual

Update the design matrix after the formula has been changed.

Definition at line 1718 of file TLinearFitter.cxx.

Member Data Documentation

◆ fAtb

TVectorD TLinearFitter::fAtb

private

Definition at line 163 of file TLinearFitter.h.

◆ fAtbTemp

TVectorD TLinearFitter::fAtbTemp

private

Definition at line 164 of file TLinearFitter.h.

◆ fAtbTemp2

TVectorD TLinearFitter::fAtbTemp2

private

temporary vector, used for num.stability

Definition at line 165 of file TLinearFitter.h.

◆ fAtbTemp3

TVectorD TLinearFitter::fAtbTemp3

private

Definition at line 166 of file TLinearFitter.h.

◆ fChisquare

Double_t TLinearFitter::fChisquare

private

Definition at line 188 of file TLinearFitter.h.

◆ fDesign

TMatrixDSym TLinearFitter::fDesign

private

Definition at line 158 of file TLinearFitter.h.

◆ fDesignTemp

TMatrixDSym TLinearFitter::fDesignTemp

private

Definition at line 159 of file TLinearFitter.h.

◆ fDesignTemp2

TMatrixDSym TLinearFitter::fDesignTemp2

private

temporary matrix, used for num.stability

Definition at line 160 of file TLinearFitter.h.

◆ fDesignTemp3

TMatrixDSym TLinearFitter::fDesignTemp3

private

Definition at line 161 of file TLinearFitter.h.

◆ fE

TVectorD TLinearFitter::fE

private

Definition at line 174 of file TLinearFitter.h.

◆ fFitsample

TBits TLinearFitter::fFitsample

private

Definition at line 192 of file TLinearFitter.h.

◆ fFixedParams

Bool_t* TLinearFitter::fFixedParams

private

Definition at line 194 of file TLinearFitter.h.

◆ fFormula

char* TLinearFitter::fFormula

private

Definition at line 185 of file TLinearFitter.h.

◆ fFormulaSize

Int_t TLinearFitter::fFormulaSize

private

Definition at line 180 of file TLinearFitter.h.

◆ fFunctions

TObjArray TLinearFitter::fFunctions

private

map of basis functions and formula

Definition at line 169 of file TLinearFitter.h.

◆ fgFormulaMap

std::map< TString, TFormula * > TLinearFitter::fgFormulaMap

staticprivate

Definition at line 168 of file TLinearFitter.h.

◆ fH

Int_t TLinearFitter::fH

private

Definition at line 190 of file TLinearFitter.h.

◆ fInputFunction

TFormula* TLinearFitter::fInputFunction

private

Definition at line 175 of file TLinearFitter.h.

◆ fIsSet

Bool_t TLinearFitter::fIsSet

private

Definition at line 186 of file TLinearFitter.h.

◆ fNdim

Int_t TLinearFitter::fNdim

private

Definition at line 181 of file TLinearFitter.h.

◆ fNfixed

Int_t TLinearFitter::fNfixed

private

Definition at line 182 of file TLinearFitter.h.

◆ fNfunctions

Int_t TLinearFitter::fNfunctions

private

Definition at line 179 of file TLinearFitter.h.

◆ fNpoints

Int_t TLinearFitter::fNpoints

private

temporary

Definition at line 178 of file TLinearFitter.h.

◆ fParams

TVectorD TLinearFitter::fParams

private

Definition at line 154 of file TLinearFitter.h.

◆ fParCovar

TMatrixDSym TLinearFitter::fParCovar

private

Definition at line 155 of file TLinearFitter.h.

◆ fParSign

TVectorD TLinearFitter::fParSign

private

Definition at line 157 of file TLinearFitter.h.

◆ fRobust

Bool_t TLinearFitter::fRobust

private

Definition at line 191 of file TLinearFitter.h.

◆ fSpecial

Int_t TLinearFitter::fSpecial

private

Definition at line 183 of file TLinearFitter.h.

◆ fStoreData

Bool_t TLinearFitter::fStoreData

private

Definition at line 187 of file TLinearFitter.h.

◆ fTValues

TVectorD TLinearFitter::fTValues

private

Definition at line 156 of file TLinearFitter.h.

◆ fVal

Double_t TLinearFitter::fVal[1000]

private

Definition at line 176 of file TLinearFitter.h.

◆ fX

TMatrixD TLinearFitter::fX

private

temporary variable used for num.stability

Definition at line 173 of file TLinearFitter.h.

◆ fY

TVectorD TLinearFitter::fY

private

Definition at line 170 of file TLinearFitter.h.

◆ fY2

Double_t TLinearFitter::fY2

private

Definition at line 171 of file TLinearFitter.h.

◆ fY2Temp

Double_t TLinearFitter::fY2Temp

private

Definition at line 172 of file TLinearFitter.h.

Libraries for TLinearFitter:

[legend]

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

math/minuit/inc/TLinearFitter.h
math/minuit/src/TLinearFitter.cxx

The Linear Fitter

Introduction

The fitting method

Why should it be used?

Using the fitter:

1.Adding the data points:

1.1 To store or not to store the input data?

1.2 The data can be added:

2.Setting the formula

2.1 The linear formula syntax:

2.2 Setting the formula:

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

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

2.2.3 The fastest functions to compute are polynomials and hyperplanes.

2.3 Resetting the formula

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

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

3.Accessing the fit results

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

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

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

Public Member Functions

Private Member Functions

Private Attributes

Static Private Attributes

Constructor & Destructor Documentation

◆ TLinearFitter() [1/5]

◆ TLinearFitter() [2/5]

◆ TLinearFitter() [3/5]

◆ TLinearFitter() [4/5]

◆ TLinearFitter() [5/5]

◆ ~TLinearFitter()

Member Function Documentation

◆ Add()

◆ AddPoint()

◆ AddTempMatrices()

◆ AddToDesign()

◆ AssignData()

◆ Chisquare() [1/2]

◆ Chisquare() [2/2]

◆ Clear()

◆ ClearPoints()

◆ ComputeTValues()

◆ CreateSubset()

◆ CStep()

◆ Eval()

◆ EvalRobust()

◆ ExecuteCommand()

◆ FixParameter() [1/2]

◆ FixParameter() [2/2]

◆ GetAtbVector()

◆ GetChisquare()

◆ GetConfidenceIntervals() [1/2]

◆ GetConfidenceIntervals() [2/2]

◆ GetCovarianceMatrix() [1/2]

◆ GetCovarianceMatrix() [2/2]

◆ GetCovarianceMatrixElement()

◆ GetDesignMatrix()

◆ GetErrors() [1/2]

◆ GetErrors() [2/2]

◆ GetFitSample()

◆ GetNpoints()

◆ GetNumberFreeParameters()

◆ GetNumberTotalParameters()

◆ GetParameter() [1/2]

◆ GetParameter() [2/2]

◆ GetParameters()

◆ GetParError()

◆ GetParName()

◆ GetParSignificance()

◆ GetParTValue()

◆ GetStats()

◆ GetSumLog()

◆ GetY2()

◆ Graph2DLinearFitter()

◆ GraphLinearFitter()

◆ HistLinearFitter()

◆ IsFixed()

◆ Linf()

◆ Merge()