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TLinearFitter Class Reference

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 + a*f(x)+...a[n]*f[n](x)
#define f(i)
Definition RSha256.hxx:104
#define a(i)
Definition RSha256.hxx:99
Double_t y[n]
Definition legend1.C:17
Double_t x[n]
Definition legend1.C:17
const Int_t n
Definition legend1.C:16

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:

#### 1.1 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, x, x... For example, to fit "1 ++ x ++ x ++ x ++ x*x"

#### 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:

TF2 *f2 = new TF2("f2", "x ++ y ++ x*x*y*y", -2, 2, -2, 2);
lf->SetFormula(f2);
A 2-Dim function with parameters.
Definition TF2.h:29
The Linear Fitter - For fitting functions that are LINEAR IN PARAMETERS.
TLinearFitter()
default c-tor, input data is stored If you don't want to store the input data, run the function Store...
virtual void SetFormula(const char *formula)
Additive parts should be separated by "++".

–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++...++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
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();
...
#define e(i)
Definition RSha256.hxx:103
virtual Int_t Eval()
Perform the fit and evaluate the parameters Returns 0 if the fit is ok, 1 if there are errors.
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...
##### 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 153 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

TLinearFitter (const TLinearFitter &tlf)
Copy ctor.

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

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.

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

virtual ~TLinearFitter ()
Linear fitter cleanup.

Add another linear fitter to this linear fitter.

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

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.

virtual void Chisquare ()
Calculates the chisquare.

virtual Double_t Chisquare (Int_t, Double_t *) const

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

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

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

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

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

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

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

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

virtual Double_t GetChisquare ()
Get the Chisquare.

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

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

virtual Double_tGetCovarianceMatrix () const
Returns covariance matrix.

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

virtual Double_t GetCovarianceMatrixElement (Int_t i, Int_t j) const

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

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

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

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

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.

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

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

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

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

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

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.

TLinearFitteroperator= (const TLinearFitter &tlf)
Assignment operator.

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

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

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

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

virtual void SetFitMethod (const char *)

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

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

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. Public Member Functions inherited from TVirtualFitter
TVirtualFitter ()
Default constructor.

virtual ~TVirtualFitter ()
Cleanup virtual fitter.

virtual FCNFunc_t GetFCN ()

virtual Foption_t GetFitOption () const

TMethodCallGetMethodCall () const

virtual TObjectGetObjectFit () const

virtual TObjectGetUserFunc () 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_tSetCache (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.

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)

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 TNamed &named)
TNamed copy ctor.

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

virtual ~TNamed ()
TNamed destructor.

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

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

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

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

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

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

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

virtual Bool_t IsSortable () const

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

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

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

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

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

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

virtual Int_t Sizeof () const
Return size of the TNamed part of the TObject. Public Member Functions inherited from TObject
TObject ()
TObject constructor.

TObject (const TObject &object)
TObject copy ctor.

virtual ~TObject ()
TObject destructor.

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

Append graphics object to current pad.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

virtual Option_tGetOption () const

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

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

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

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

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

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

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

void InvertBit (UInt_t f)

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

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

R__ALWAYS_INLINE Bool_t IsOnHeap () const

R__ALWAYS_INLINE Bool_t IsZombie () const

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

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

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

void operator delete (void *ptr)
Operator delete.

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

voidoperator new (size_t sz)

voidoperator new (size_t sz, void *vp)

voidoperator new[] (size_t sz)

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

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

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

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

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

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

void ResetBit (UInt_t f)

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

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

void SetBit (UInt_t f)

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

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

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

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

R__ALWAYS_INLINE Bool_t TestBit (UInt_t f) const

Int_t TestBits (UInt_t f) const

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

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

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

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

## 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.

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

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.

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.

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

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

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

Bool_t Linf ()

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

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

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.

## Private Attributes

TVectorD fAtb

TVectorD fAtbTemp

TVectorD fAtbTemp2
temporary vector, used for num.stability

TVectorD fAtbTemp3

Double_t fChisquare

TMatrixDSym fDesign

TMatrixDSym fDesignTemp

TMatrixDSym fDesignTemp2
temporary matrix, used for num.stability

TMatrixDSym fDesignTemp3

TVectorD fE

TBits fFitsample

Bool_tfFixedParams

char * fFormula

Int_t fFormulaSize

TObjArray fFunctions
map of basis functions and formula

Int_t fH

TFormulafInputFunction

Bool_t fIsSet

Int_t fNdim

Int_t fNfixed

Int_t fNfunctions

Int_t fNpoints
temporary

TVectorD fParams

TMatrixDSym fParCovar

TVectorD fParSign

Bool_t fRobust

Int_t fSpecial

Bool_t fStoreData

TVectorD fTValues

Double_t fVal 

TMatrixD fX
temporary variable used for num.stability

TVectorD fY

Double_t fY2

Double_t fY2Temp

## Static Private Attributes

static std::map< TString, TFormula * > fgFormulaMap 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  {
kIsOnHeap = 0x01000000 , kNotDeleted = 0x02000000 , kZombie = 0x04000000 , kInconsistent = 0x08000000 ,
}

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

enum  EDeprecatedStatusBits { kObjInCanvas = BIT(3) }

enum  EStatusBits {
kCanDelete = BIT(0) , kMustCleanup = BIT(3) , kIsReferenced = BIT(4) , kHasUUID = BIT(5) ,
kCannotPick = BIT(6) , kNoContextMenu = BIT(8) , kInvalidObject = BIT(13)
} Static Public Member Functions inherited from TVirtualFitter
static TVirtualFitterFitter (TObject *obj, Int_t maxpar=25)
Static function returning a pointer to the current fitter.

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

static Double_t GetErrorDef ()
static: Return the Error Definition

static TVirtualFitterGetFitter ()
static: return the current Fitter

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

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

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

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 https://cern-tex.web.cern.ch/cern-tex/minuit/node18.html)

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

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 https://cern-tex.web.cern.ch/cern-tex/minuit/node18.html )

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 https://cern-tex.web.cern.ch/cern-tex/minuit/node18.html ) Static Public Member Functions inherited from TObject
static Long_t GetDtorOnly ()
Return destructor only flag.

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

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

static void SetObjectStat (Bool_t stat)
Turn on/off tracking of objects in the TObjectTable. Protected Types inherited from TObject
enum  { kOnlyPrepStep = BIT(3) } Protected Member Functions inherited from TVirtualFitter
TVirtualFitter (const TVirtualFitter &tvf)
copy constructor

TVirtualFitteroperator= (const TVirtualFitter &tvf)
assignment operator Protected Member Functions inherited from TObject
virtual void DoError (int level, const char *location, const char *fmt, va_list va) const
Interface to ErrorHandler (protected).

void MakeZombie () Protected Attributes inherited from TVirtualFitter
Double_tfCache

Int_t fCacheSize

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

TMethodCallfMethodCall

Int_t fNpoints

TObjectfObjectFit

Foption_t fOption

Int_t fPointSize

TObjectfUserFunc

Int_t fXfirst

Int_t fXlast

Int_t fYfirst

Int_t fYlast

Int_t fZfirst

Int_t fZlast Protected Attributes inherited from TNamed
TString fName

TString fTitle

#include <TLinearFitter.h>

Inheritance diagram for TLinearFitter:
[legend]

## ◆ 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 226 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 297 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 268 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++x++x*x"); 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 330 of file TLinearFitter.cxx.

## ◆ TLinearFitter() [5/5]

 TLinearFitter::TLinearFitter ( const TLinearFitter & tlf )

Copy ctor.

Definition at line 363 of file TLinearFitter.cxx.

## ◆ ~TLinearFitter()

 TLinearFitter::~TLinearFitter ( )
virtual

Linear fitter cleanup.

Definition at line 419 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 510 of file TLinearFitter.cxx.

 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 559 of file TLinearFitter.cxx.

virtual

Definition at line 721 of file TLinearFitter.cxx.

 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 635 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 597 of file TLinearFitter.cxx.

## ◆ Chisquare() [1/2]

 void TLinearFitter::Chisquare ( )
virtual

Calculates the chisquare.

Definition at line 811 of file TLinearFitter.cxx.

## ◆ Chisquare() [2/2]

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

Implements TVirtualFitter.

Definition at line 269 of file TLinearFitter.h.

## ◆ Clear()

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

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

Implements TVirtualFitter.

Definition at line 745 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 785 of file TLinearFitter.cxx.

## ◆ ComputeTValues()

 void TLinearFitter::ComputeTValues ( )
private

Computes parameters' t-values and significance.

Definition at line 876 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 2305 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 2368 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 888 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 2109 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().

Implements TVirtualFitter.

Definition at line 1738 of file TLinearFitter.cxx.

## ◆ FixParameter() [1/2]

 void TLinearFitter::FixParameter ( Int_t ipar )
virtual

Fixes paramter #ipar at its current value.

Implements TVirtualFitter.

Definition at line 1015 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 1038 of file TLinearFitter.cxx.

## ◆ GetAtbVector()

 void TLinearFitter::GetAtbVector ( TVectorD & v )
virtual

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

Definition at line 1078 of file TLinearFitter.cxx.

## ◆ GetChisquare()

 Double_t TLinearFitter::GetChisquare ( )
virtual

Get the Chisquare.

Definition at line 1088 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

Reimplemented from TVirtualFitter.

Definition at line 1111 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

Reimplemented from TVirtualFitter.

Definition at line 1162 of file TLinearFitter.cxx.

## ◆ GetCovarianceMatrix() [1/2]

 Double_t * TLinearFitter::GetCovarianceMatrix ( ) const
virtual

Returns covariance matrix.

Implements TVirtualFitter.

Definition at line 1311 of file TLinearFitter.cxx.

## ◆ GetCovarianceMatrix() [2/2]

 void TLinearFitter::GetCovarianceMatrix ( TMatrixD & matr )
virtual

Returns covariance matrix.

Definition at line 1320 of file TLinearFitter.cxx.

## ◆ GetCovarianceMatrixElement()

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

Implements TVirtualFitter.

Definition at line 241 of file TLinearFitter.h.

## ◆ GetDesignMatrix()

 void TLinearFitter::GetDesignMatrix ( TMatrixD & matr )
virtual

Returns the internal design matrix.

Definition at line 1331 of file TLinearFitter.cxx.

## ◆ GetErrors() [1/2]

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

Implements TVirtualFitter.

Definition at line 270 of file TLinearFitter.h.

## ◆ GetErrors() [2/2]

 void TLinearFitter::GetErrors ( TVectorD & vpar )
virtual

Returns parameter errors.

Definition at line 1342 of file TLinearFitter.cxx.

## ◆ GetFitSample()

 void TLinearFitter::GetFitSample ( TBits & bits )
virtual

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

Definition at line 1441 of file TLinearFitter.cxx.

## ◆ GetNpoints()

 virtual Int_t TLinearFitter::GetNpoints ( )
inlinevirtual

Definition at line 246 of file TLinearFitter.h.

## ◆ GetNumberFreeParameters()

 virtual Int_t TLinearFitter::GetNumberFreeParameters ( ) const
inlinevirtual

Implements TVirtualFitter.

Definition at line 245 of file TLinearFitter.h.

## ◆ GetNumberTotalParameters()

 virtual Int_t TLinearFitter::GetNumberTotalParameters ( ) const
inlinevirtual

Implements TVirtualFitter.

Definition at line 244 of file TLinearFitter.h.

## ◆ GetParameter() [1/2]

 virtual Double_t TLinearFitter::GetParameter ( Int_t ipar ) const
inlinevirtual

Implements TVirtualFitter.

Definition at line 248 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.

Implements TVirtualFitter.

Definition at line 1367 of file TLinearFitter.cxx.

## ◆ GetParameters()

 void TLinearFitter::GetParameters ( TVectorD & vpar )
virtual

Returns parameter values.

Definition at line 1355 of file TLinearFitter.cxx.

## ◆ GetParError()

 Double_t TLinearFitter::GetParError ( Int_t ipar ) const
virtual

Returns the error of parameter #ipar.

Implements TVirtualFitter.

Definition at line 1385 of file TLinearFitter.cxx.

## ◆ GetParName()

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

Returns name of parameter #ipar.

Implements TVirtualFitter.

Definition at line 1399 of file TLinearFitter.cxx.

## ◆ GetParSignificance()

 Double_t TLinearFitter::GetParSignificance ( Int_t ipar )
virtual

Returns the significance of parameter #ipar.

Definition at line 1427 of file TLinearFitter.cxx.

## ◆ GetParTValue()

 Double_t TLinearFitter::GetParTValue ( Int_t ipar )
virtual

Returns the t-value for parameter #ipar.

Definition at line 1413 of file TLinearFitter.cxx.

## ◆ GetStats()

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

Implements TVirtualFitter.

Definition at line 272 of file TLinearFitter.h.

## ◆ GetSumLog()

 virtual Double_t TLinearFitter::GetSumLog ( Int_t )
inlinevirtual

Implements TVirtualFitter.

Definition at line 273 of file TLinearFitter.h.

## ◆ GetY2()

 virtual Double_t TLinearFitter::GetY2 ( ) const
inlinevirtual

Definition at line 255 of file TLinearFitter.h.

## ◆ Graph2DLinearFitter()

 Int_t TLinearFitter::Graph2DLinearFitter ( Double_t h )
private

Minimisation function for a TGraph2D.

Definition at line 1844 of file TLinearFitter.cxx.

## ◆ GraphLinearFitter()

 Int_t TLinearFitter::GraphLinearFitter ( Double_t h )
private

Used in TGraph::Fit().

Definition at line 1782 of file TLinearFitter.cxx.

## ◆ HistLinearFitter()

 Int_t TLinearFitter::HistLinearFitter ( )
private

Minimization function for H1s using a Chisquare method.

Definition at line 1988 of file TLinearFitter.cxx.

## ◆ IsFixed()

 virtual Bool_t TLinearFitter::IsFixed ( Int_t ipar ) const
inlinevirtual

Implements TVirtualFitter.

Definition at line 256 of file TLinearFitter.h.

## ◆ Linf()

 Bool_t TLinearFitter::Linf ( )
private

Definition at line 2529 of file TLinearFitter.cxx.

## ◆ Merge()

 Int_t TLinearFitter::Merge ( TCollection * list )
virtual

Merge objects in list.

Definition at line 1455 of file TLinearFitter.cxx.

## ◆ MultiGraphLinearFitter()

 Int_t TLinearFitter::MultiGraphLinearFitter ( Double_t h )
private

Minimisation function for a TMultiGraph.

Definition at line 1917 of file TLinearFitter.cxx.

## ◆ operator=()

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

Assignment operator.

Definition at line 439 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 2568 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.

Implements TVirtualFitter.

Definition at line 1762 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 2620 of file TLinearFitter.cxx.

## ◆ ReleaseParameter()

 void TLinearFitter::ReleaseParameter ( Int_t ipar )
virtual

Releases parameter #ipar.

Implements TVirtualFitter.

Definition at line 1060 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 1474 of file TLinearFitter.cxx.

## ◆ SetDim()

 void TLinearFitter::SetDim ( Int_t n )
virtual

set the number of dimensions

Definition at line 1514 of file TLinearFitter.cxx.

## ◆ SetFitMethod()

 virtual void TLinearFitter::SetFitMethod ( const char * )
inlinevirtual

Implements TVirtualFitter.

Definition at line 274 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++x++x" 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 1535 of file TLinearFitter.cxx.

## ◆ SetFormula() [2/2]

 void TLinearFitter::SetFormula ( TFormula * function )
virtual

Set the fitting function.

Definition at line 1656 of file TLinearFitter.cxx.

## ◆ SetParameter()

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

Implements TVirtualFitter.

Definition at line 275 of file TLinearFitter.h.

## ◆ StoreData()

 virtual void TLinearFitter::StoreData ( Bool_t store )
inlinevirtual

Definition at line 264 of file TLinearFitter.h.

## ◆ UpdateMatrix()

 Bool_t TLinearFitter::UpdateMatrix ( )
virtual

Update the design matrix after the formula has been changed.

Definition at line 1723 of file TLinearFitter.cxx.

## ◆ fAtb

 TVectorD TLinearFitter::fAtb
private

Definition at line 165 of file TLinearFitter.h.

## ◆ fAtbTemp

 TVectorD TLinearFitter::fAtbTemp
private

Definition at line 166 of file TLinearFitter.h.

## ◆ fAtbTemp2

 TVectorD TLinearFitter::fAtbTemp2
private

temporary vector, used for num.stability

Definition at line 167 of file TLinearFitter.h.

## ◆ fAtbTemp3

 TVectorD TLinearFitter::fAtbTemp3
private

Definition at line 168 of file TLinearFitter.h.

## ◆ fChisquare

 Double_t TLinearFitter::fChisquare
private

Definition at line 190 of file TLinearFitter.h.

## ◆ fDesign

 TMatrixDSym TLinearFitter::fDesign
private

Definition at line 160 of file TLinearFitter.h.

## ◆ fDesignTemp

 TMatrixDSym TLinearFitter::fDesignTemp
private

Definition at line 161 of file TLinearFitter.h.

## ◆ fDesignTemp2

 TMatrixDSym TLinearFitter::fDesignTemp2
private

temporary matrix, used for num.stability

Definition at line 162 of file TLinearFitter.h.

## ◆ fDesignTemp3

 TMatrixDSym TLinearFitter::fDesignTemp3
private

Definition at line 163 of file TLinearFitter.h.

## ◆ fE

 TVectorD TLinearFitter::fE
private

Definition at line 176 of file TLinearFitter.h.

## ◆ fFitsample

 TBits TLinearFitter::fFitsample
private

Definition at line 194 of file TLinearFitter.h.

## ◆ fFixedParams

 Bool_t* TLinearFitter::fFixedParams
private

Definition at line 196 of file TLinearFitter.h.

## ◆ fFormula

 char* TLinearFitter::fFormula
private

Definition at line 187 of file TLinearFitter.h.

## ◆ fFormulaSize

 Int_t TLinearFitter::fFormulaSize
private

Definition at line 182 of file TLinearFitter.h.

## ◆ fFunctions

 TObjArray TLinearFitter::fFunctions
private

map of basis functions and formula

Definition at line 171 of file TLinearFitter.h.

## ◆ fgFormulaMap

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

Definition at line 170 of file TLinearFitter.h.

## ◆ fH

 Int_t TLinearFitter::fH
private

Definition at line 192 of file TLinearFitter.h.

## ◆ fInputFunction

 TFormula* TLinearFitter::fInputFunction
private

Definition at line 177 of file TLinearFitter.h.

## ◆ fIsSet

 Bool_t TLinearFitter::fIsSet
private

Definition at line 188 of file TLinearFitter.h.

## ◆ fNdim

 Int_t TLinearFitter::fNdim
private

Definition at line 183 of file TLinearFitter.h.

## ◆ fNfixed

 Int_t TLinearFitter::fNfixed
private

Definition at line 184 of file TLinearFitter.h.

## ◆ fNfunctions

 Int_t TLinearFitter::fNfunctions
private

Definition at line 181 of file TLinearFitter.h.

## ◆ fNpoints

 Int_t TLinearFitter::fNpoints
private

temporary

Definition at line 180 of file TLinearFitter.h.

## ◆ fParams

 TVectorD TLinearFitter::fParams
private

Definition at line 156 of file TLinearFitter.h.

## ◆ fParCovar

 TMatrixDSym TLinearFitter::fParCovar
private

Definition at line 157 of file TLinearFitter.h.

## ◆ fParSign

 TVectorD TLinearFitter::fParSign
private

Definition at line 159 of file TLinearFitter.h.

## ◆ fRobust

 Bool_t TLinearFitter::fRobust
private

Definition at line 193 of file TLinearFitter.h.

## ◆ fSpecial

 Int_t TLinearFitter::fSpecial
private

Definition at line 185 of file TLinearFitter.h.

## ◆ fStoreData

 Bool_t TLinearFitter::fStoreData
private

Definition at line 189 of file TLinearFitter.h.

## ◆ fTValues

 TVectorD TLinearFitter::fTValues
private

Definition at line 158 of file TLinearFitter.h.

## ◆ fVal

 Double_t TLinearFitter::fVal
private

Definition at line 178 of file TLinearFitter.h.

## ◆ fX

 TMatrixD TLinearFitter::fX
private

temporary variable used for num.stability

Definition at line 175 of file TLinearFitter.h.

## ◆ fY

 TVectorD TLinearFitter::fY
private

Definition at line 172 of file TLinearFitter.h.

## ◆ fY2

 Double_t TLinearFitter::fY2
private

Definition at line 173 of file TLinearFitter.h.

## ◆ fY2Temp

 Double_t TLinearFitter::fY2Temp
private

Definition at line 174 of file TLinearFitter.h.

Libraries for TLinearFitter: [legend]

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