TF1 Class Reference

1-Dim function class

TF1: 1-Dim function class

A TF1 object is a 1-Dim function defined between a lower and upper limit. The function may be a simple function based on a TFormula expression or a precompiled user function. The function may have associated parameters. TF1 graphics function is via the TH1 and TGraph drawing functions.

The following types of functions can be created:

1. Expression using variable x and no parameters
2. Expression using variable x with parameters
3. Lambda Expression with variable x and parameters
4. A general C function with parameters
5. A general C++ function object (functor) with parameters
6. A member function with parameters of a general C++ class

1 - Expression using variable x and no parameters

Case 1: inline expression using standard C++ functions/operators

{
   TF1 *fa1 = new TF1("fa1","sin(x)/x",0,10);
   fa1->Draw();
}

Case 2: inline expression using a ROOT function (e.g. from TMath) without parameters

{
   TF1 *fa2 = new TF1("fa2","TMath::DiLog(x)",0,10);
   fa2->Draw();
}

Case 3: inline expression using a user defined CLING function by name

Double_t myFunc(double x) { return x+sin(x); }
....
TF1 *fa3 = new TF1("fa3","myFunc(x)",-3,5);
fa3->Draw();

2 - Expression using variable x with parameters

Case 1: inline expression using standard C++ functions/operators

Example a:

TF1 *fa = new TF1("fa","[0]*x*sin([1]*x)",-3,3);

This creates a function of variable x with 2 parameters. The parameters must be initialized via:

fa->SetParameter(0,value_first_parameter);
fa->SetParameter(1,value_second_parameter);

Parameters may be given a name:

fa->SetParName(0,"Constant");

Example b:

TF1 *fb = new TF1("fb","gaus(0)*expo(3)",0,10);

gaus(0) is a substitute for [0]*exp(-0.5*((x-[1])/[2])**2) and (0) means start numbering parameters at 0. expo(3) is a substitute for exp([3]+[4]*x).

Case 2: inline expression using TMath functions with parameters

TF1 *fb2 = new TF1("fa3","TMath::Landau(x,[0],[1],0)",-5,10);
fb2->SetParameters(0.2,1.3);
fb2->Draw();

3 - A lambda expression with variables and parameters

Since

6.00/00: TF1 supports using lambda expressions in the formula. This allows, by using a full C++ syntax the full power of lambda functions and still maintain the capability of storing the function in a file which cannot be done with function pointer or lambda written not as expression, but as code (see items below).

Example on how using lambda to define a sum of two functions. Note that is necessary to provide the number of parameters

TF1 f1("f1","sin(x)",0,10);
TF1 f2("f2","cos(x)",0,10);
TF1 fsum("f1","[&](double *x, double *p){ return p[0]*f1(x) + p[1]*f2(x); }",0,10,2);

4 - A general C function with parameters

Consider the macro myfunc.C below:

// Macro myfunc.C
Double_t myfunction(Double_t *x, Double_t *par)
{
   Float_t xx =x[0];
   Double_t f = TMath::Abs(par[0]*sin(par[1]*xx)/xx);
   return f;
}
void myfunc()
{
   TF1 *f1 = new TF1("myfunc",myfunction,0,10,2);
   f1->SetParameters(2,1);
   f1->SetParNames("constant","coefficient");
   f1->Draw();
}
void myfit()
{
   TH1F *h1=new TH1F("h1","test",100,0,10);
   h1->FillRandom("myfunc",20000);
   TF1 *f1 = (TF1 *)gROOT->GetFunction("myfunc");
   f1->SetParameters(800,1);
   h1->Fit("myfunc");
}

In an interactive session you can do:

Root > .L myfunc.C
Root > myfunc();
Root > myfit();

TF1 objects can reference other TF1 objects of type A or B defined above. This excludes CLing or compiled functions. However, there is a restriction. A function cannot reference a basic function if the basic function is a polynomial polN.

Example:

{
      TF1 *fcos = new TF1 ("fcos", "[0]*cos(x)", 0., 10.);
      fcos->SetParNames( "cos");
      fcos->SetParameter( 0, 1.1);
 
      TF1 *fsin = new TF1 ("fsin", "[0]*sin(x)", 0., 10.);
      fsin->SetParNames( "sin");
      fsin->SetParameter( 0, 2.1);
 
      TF1 *fsincos = new TF1 ("fsc", "fcos+fsin");
 
      TF1 *fs2 = new TF1 ("fs2", "fsc+fsc");
}

5 - A general C++ function object (functor) with parameters

A TF1 can be created from any C++ class implementing the operator()(double *x, double *p). The advantage of the function object is that he can have a state and reference therefore what-ever other object. In this way the user can customize his function.

Example:

class  MyFunctionObject {
 public:
   // use constructor to customize your function object
 
   double operator() (double *x, double *p) {
      // function implementation using class data members
   }
};
{
    ....
   MyFunctionObject fobj;
   TF1 * f = new TF1("f",fobj,0,1,npar);    // create TF1 class.
   .....
}

Using a lambda function as a general C++ functor object

From C++11 we can use both std::function or even better lambda functions to create the TF1. As above the lambda must have the right signature but can capture whatever we want. For example we can make a TF1 from the TGraph::Eval function as shown below where we use as function parameter the graph normalization.

TGraph * g = new TGraph(npointx, xvec, yvec);
TF1 * f = new TF1("f",[&](double*x, double *p){ return p[0]*g->Eval(x[0]); }, xmin, xmax, 1);

6 - A member function with parameters of a general C++ class

A TF1 can be created in this case from any member function of a class which has the signature of (double * , double *) and returning a double.

Example:

class  MyFunction {
 public:
   ...
   double Evaluate() (double *x, double *p) {
      // function implementation
   }
};
{
    ....
   MyFunction * fptr = new MyFunction(....);  // create the user function class
   TF1 * f = new TF1("f",fptr,&MyFunction::Evaluate,0,1,npar,"MyFunction","Evaluate");   // create TF1 class.
 
   .....
}

See also the tutorial math/exampleFunctor.C for a running example.

Definition at line 211 of file TF1.h.

Classes
struct	TF1FunctorPointer
struct	TF1FunctorPointerImpl

Public Types
enum class	EAddToList { kDefault , kAdd , kNo }
enum	EStatusBits { kNotGlobal = BIT(10) , kNotDraw = BIT(9) }
Public Types inherited from TObject
enum	{   kIsOnHeap = 0x01000000 , kNotDeleted = 0x02000000 , kZombie = 0x04000000 , kInconsistent = 0x08000000 ,   kBitMask = 0x00ffffff }
enum	{ kSingleKey = BIT(0) , kOverwrite = BIT(1) , kWriteDelete = BIT(2) }
enum	EDeprecatedStatusBits { kObjInCanvas = BIT(3) }
enum	EStatusBits {   kCanDelete = BIT(0) , kMustCleanup = BIT(3) , kIsReferenced = BIT(4) , kHasUUID = BIT(5) ,   kCannotPick = BIT(6) , kNoContextMenu = BIT(8) , kInvalidObject = BIT(13) }

Public Member Functions
	TF1 ()
	TF1 default constructor. More...
	TF1 (const char *name, const char *formula, Double_t xmin, Double_t xmax, Option_t *option)
	Same constructor as above (for TFormula based function) but passing an option strings available options VEC - vectorize the formula expressions (not possible for lambda based expressions) NL - function is not stores in the global list of functions GL - function will be always stored in the global list of functions , independently of the global setting of TF1::DefaultAddToGlobalList. More...
	TF1 (const char *name, const char *formula, Double_t xmin=0, Double_t xmax=1, EAddToList addToGlobList=EAddToList::kDefault, bool vectorize=false)
	F1 constructor using a formula definition. More...
template<class PtrObj , typename MemFn >
	TF1 (const char *name, const PtrObj &p, MemFn memFn, Double_t xmin, Double_t xmax, Int_t npar, const char *, const char *, EAddToList addToGlobList=EAddToList::kDefault)
template<class PtrObj , typename MemFn >
	TF1 (const char *name, const PtrObj &p, MemFn memFn, Double_t xmin, Double_t xmax, Int_t npar, Int_t ndim=1, EAddToList addToGlobList=EAddToList::kDefault)
	TF1 (const char *name, Double_t xmin, Double_t xmax, Int_t npar, Int_t ndim=1, EAddToList addToGlobList=EAddToList::kDefault)
	F1 constructor using name of an interpreted function. More...
	TF1 (const char *name, Double_t(*fcn)(const Double_t *, const Double_t *), Double_t xmin=0, Double_t xmax=1, Int_t npar=0, Int_t ndim=1, EAddToList addToGlobList=EAddToList::kDefault)
	Constructor using a pointer to real function. More...
	TF1 (const char *name, Double_t(*fcn)(Double_t *, Double_t *), Double_t xmin=0, Double_t xmax=1, Int_t npar=0, Int_t ndim=1, EAddToList addToGlobList=EAddToList::kDefault)
	Constructor using a pointer to a real function. More...
template<typename Func >
	TF1 (const char *name, Func f, Double_t xmin, Double_t xmax, Int_t npar, const char *, EAddToList addToGlobList=EAddToList::kDefault)
template<typename Func >
	TF1 (const char *name, Func f, Double_t xmin, Double_t xmax, Int_t npar, Int_t ndim=1, EAddToList addToGlobList=EAddToList::kDefault)
	TF1 (const char *name, ROOT::Math::ParamFunctor f, Double_t xmin=0, Double_t xmax=1, Int_t npar=0, Int_t ndim=1, EAddToList addToGlobList=EAddToList::kDefault)
	Constructor using the Functor class. More...
template<class T >
	TF1 (const char *name, std::function< T(const T *data, const Double_t *param)> &fcn, Double_t xmin=0, Double_t xmax=1, Int_t npar=0, Int_t ndim=1, EAddToList addToGlobList=EAddToList::kDefault)
template<class T >
	TF1 (const char *name, T(*fcn)(const T *, const Double_t *), Double_t xmin=0, Double_t xmax=1, Int_t npar=0, Int_t ndim=1, EAddToList addToGlobList=EAddToList::kDefault)
	Constructor using a pointer to function. More...
	TF1 (const TF1 &f1)
virtual	~TF1 ()
	TF1 default destructor. More...
virtual void	AddParameter (const TString &name, Double_t value)
virtual Bool_t	AddToGlobalList (Bool_t on=kTRUE)
	Add to global list of functions (gROOT->GetListOfFunctions() ) return previous status (true if the function was already in the list false if not) More...
virtual void	Browse (TBrowser *b)
	Browse. More...
virtual Double_t	CentralMoment (Double_t n, Double_t a, Double_t b, const Double_t *params=0, Double_t epsilon=0.000001)
	Return nth central moment of function between a and b (i.e the n-th moment around the mean value) More...
virtual void	Copy (TObject &f1) const
	Copy this F1 to a new F1. More...
virtual TH1 *	CreateHistogram ()
virtual Double_t	Derivative (Double_t x, Double_t *params=0, Double_t epsilon=0.001) const
	Returns the first derivative of the function at point x, computed by Richardson's extrapolation method (use 2 derivative estimates to compute a third, more accurate estimation) first, derivatives with steps h and h/2 are computed by central difference formulas. More...
virtual Double_t	Derivative2 (Double_t x, Double_t *params=0, Double_t epsilon=0.001) const
	Returns the second derivative of the function at point x, computed by Richardson's extrapolation method (use 2 derivative estimates to compute a third, more accurate estimation) first, derivatives with steps h and h/2 are computed by central difference formulas. More...
virtual Double_t	Derivative3 (Double_t x, Double_t *params=0, Double_t epsilon=0.001) const
	Returns the third derivative of the function at point x, computed by Richardson's extrapolation method (use 2 derivative estimates to compute a third, more accurate estimation) first, derivatives with steps h and h/2 are computed by central difference formulas. More...
virtual Int_t	DistancetoPrimitive (Int_t px, Int_t py)
	Compute distance from point px,py to a function. More...
virtual TH1 *	DoCreateHistogram (Double_t xmin, Double_t xmax, Bool_t recreate=kFALSE)
	Create histogram with bin content equal to function value computed at the bin center This histogram will be used to paint the function A re-creation is forced and a new histogram is done if recreate=true. More...
void	DoInitialize (EAddToList addToGlobList)
	Common initialization of the TF1. More...
virtual void	Draw (Option_t *option="")
	Draw this function with its current attributes. More...
virtual TF1 *	DrawCopy (Option_t *option="") const
	Draw a copy of this function with its current attributes. More...
virtual TObject *	DrawDerivative (Option_t *option="al")
	Draw derivative of this function. More...
virtual void	DrawF1 (Double_t xmin, Double_t xmax, Option_t *option="")
	Draw function between xmin and xmax. More...
virtual TObject *	DrawIntegral (Option_t *option="al")
	Draw integral of this function. More...
virtual Double_t	Eval (Double_t x, Double_t y=0, Double_t z=0, Double_t t=0) const
	Evaluate this function. More...
virtual Double_t	EvalPar (const Double_t *x, const Double_t *params=0)
	Evaluate function with given coordinates and parameters. More...
template<class T >
T	EvalPar (const T *x, const Double_t *params=0)
	EvalPar for vectorized. More...
virtual void	ExecuteEvent (Int_t event, Int_t px, Int_t py)
	Execute action corresponding to one event. More...
virtual void	FixParameter (Int_t ipar, Double_t value)
	Fix the value of a parameter The specified value will be used in a fit operation. More...
Double_t	GetChisquare () const
virtual TString	GetExpFormula (Option_t *option="") const
virtual TFormula *	GetFormula ()
virtual const TFormula *	GetFormula () const
virtual TH1 *	GetHistogram () const
	Return a pointer to the histogram used to visualise the function. More...
virtual const TObject *	GetLinearPart (Int_t i) const
virtual Double_t	GetMaximum (Double_t xmin=0, Double_t xmax=0, Double_t epsilon=1.E-10, Int_t maxiter=100, Bool_t logx=false) const
	Returns the maximum value of the function. More...
virtual Double_t	GetMaximumStored () const
virtual Double_t	GetMaximumX (Double_t xmin=0, Double_t xmax=0, Double_t epsilon=1.E-10, Int_t maxiter=100, Bool_t logx=false) const
	Returns the X value corresponding to the maximum value of the function. More...
TMethodCall *	GetMethodCall () const
virtual Double_t	GetMinimum (Double_t xmin=0, Double_t xmax=0, Double_t epsilon=1.E-10, Int_t maxiter=100, Bool_t logx=false) const
	Returns the minimum value of the function on the (xmin, xmax) interval. More...
virtual Double_t	GetMinimumStored () const
virtual Double_t	GetMinimumX (Double_t xmin=0, Double_t xmax=0, Double_t epsilon=1.E-10, Int_t maxiter=100, Bool_t logx=false) const
	Returns the X value corresponding to the minimum value of the function on the (xmin, xmax) interval. More...
virtual Double_t	GetMinMaxNDim (Double_t *x, Bool_t findmax, Double_t epsilon=0, Int_t maxiter=0) const
	Find the minimum of a function of whatever dimension. More...
virtual Int_t	GetNDF () const
	Return the number of degrees of freedom in the fit the fNDF parameter has been previously computed during a fit. More...
virtual Int_t	GetNdim () const
virtual Int_t	GetNpar () const
virtual Int_t	GetNpx () const
virtual Int_t	GetNumber () const
virtual Int_t	GetNumberFitPoints () const
virtual Int_t	GetNumberFreeParameters () const
	Return the number of free parameters. More...
virtual char *	GetObjectInfo (Int_t px, Int_t py) const
	Redefines TObject::GetObjectInfo. More...
virtual Double_t	GetParameter (const TString &name) const
virtual Double_t	GetParameter (Int_t ipar) const
virtual Double_t *	GetParameters () const
virtual void	GetParameters (Double_t *params)
TObject *	GetParent () const
virtual Double_t	GetParError (Int_t ipar) const
	Return value of parameter number ipar. More...
virtual const Double_t *	GetParErrors () const
virtual void	GetParLimits (Int_t ipar, Double_t &parmin, Double_t &parmax) const
	Return limits for parameter ipar. More...
virtual const char *	GetParName (Int_t ipar) const
virtual Int_t	GetParNumber (const char *name) const
virtual Double_t	GetProb () const
	Return the fit probability. More...
virtual Int_t	GetQuantiles (Int_t nprobSum, Double_t *q, const Double_t *probSum)
	Compute Quantiles for density distribution of this function. More...
virtual Double_t	GetRandom ()
	Return a random number following this function shape. More...
virtual Double_t	GetRandom (Double_t xmin, Double_t xmax)
	Return a random number following this function shape in [xmin,xmax]. More...
virtual void	GetRange (Double_t &xmin, Double_t &xmax) const
	Return range of a 1-D function. More...
virtual void	GetRange (Double_t &xmin, Double_t &ymin, Double_t &xmax, Double_t &ymax) const
	Return range of a 2-D function. More...
virtual void	GetRange (Double_t &xmin, Double_t &ymin, Double_t &zmin, Double_t &xmax, Double_t &ymax, Double_t &zmax) const
	Return range of function. More...
virtual void	GetRange (Double_t *xmin, Double_t *xmax) const
	Return range of a generic N-D function. More...
virtual Double_t	GetSave (const Double_t *x)
	Get value corresponding to X in array of fSave values. More...
virtual Double_t	GetVariable (const TString &name)
virtual Double_t	GetX (Double_t y, Double_t xmin=0, Double_t xmax=0, Double_t epsilon=1.E-10, Int_t maxiter=100, Bool_t logx=false) const
	Returns the X value corresponding to the function value fy for (xmin<x<xmax). More...
TAxis *	GetXaxis () const
	Get x axis of the function. More...
virtual Double_t	GetXmax () const
virtual Double_t	GetXmin () const
TAxis *	GetYaxis () const
	Get y axis of the function. More...
TAxis *	GetZaxis () const
	Get z axis of the function. (In case this object is a TF2 or TF3) More...
virtual void	GradientPar (const Double_t *x, Double_t *grad, Double_t eps=0.01)
	Compute the gradient wrt parameters. More...
template<class T >
void	GradientPar (const T *x, T *grad, Double_t eps=0.01)
virtual Double_t	GradientPar (Int_t ipar, const Double_t *x, Double_t eps=0.01)
	Compute the gradient (derivative) wrt a parameter ipar. More...
template<class T >
T	GradientPar (Int_t ipar, const T *x, Double_t eps=0.01)
template<class T >
void	GradientParTempl (const T *x, T *grad, Double_t eps=0.01)
template<class T >
T	GradientParTempl (Int_t ipar, const T *x, Double_t eps=0.01)
virtual void	InitArgs (const Double_t *x, const Double_t *params)
	Initialize parameters addresses. More...
virtual Double_t	Integral (Double_t a, Double_t b, Double_t epsrel=1.e-12)
	IntegralOneDim or analytical integral. More...
virtual Double_t	IntegralError (Double_t a, Double_t b, const Double_t *params=0, const Double_t *covmat=0, Double_t epsilon=1.E-2)
	Return Error on Integral of a parametric function between a and b due to the parameter uncertainties. More...
virtual Double_t	IntegralError (Int_t n, const Double_t *a, const Double_t *b, const Double_t *params=0, const Double_t *covmat=0, Double_t epsilon=1.E-2)
	Return Error on Integral of a parametric function with dimension larger tan one between a[] and b[] due to the parameters uncertainties. More...
virtual Double_t	IntegralFast (Int_t num, Double_t *x, Double_t *w, Double_t a, Double_t b, Double_t *params=0, Double_t epsilon=1e-12)
	Gauss-Legendre integral, see CalcGaussLegendreSamplingPoints. More...
virtual Double_t	IntegralMultiple (Int_t n, const Double_t *a, const Double_t *b, Double_t epsrel, Double_t &relerr)
	See more general prototype below. More...
virtual Double_t	IntegralMultiple (Int_t n, const Double_t *a, const Double_t *b, Int_t maxpts, Double_t epsrel, Double_t epsabs, Double_t &relerr, Int_t &nfnevl, Int_t &ifail)
	This function computes, to an attempted specified accuracy, the value of the integral. More...
virtual Double_t	IntegralMultiple (Int_t n, const Double_t *a, const Double_t *b, Int_t, Int_t maxpts, Double_t epsrel, Double_t &relerr, Int_t &nfnevl, Int_t &ifail)
virtual Double_t	IntegralOneDim (Double_t a, Double_t b, Double_t epsrel, Double_t epsabs, Double_t &err)
	Return Integral of function between a and b using the given parameter values and relative and absolute tolerance. More...
void	IntegrateForNormalization ()
virtual Bool_t	IsEvalNormalized () const
virtual Bool_t	IsInside (const Double_t *x) const
	return kTRUE if the point is inside the function range More...
virtual Bool_t	IsLinear () const
virtual Bool_t	IsValid () const
	Return kTRUE if the function is valid. More...
bool	IsVectorized ()
virtual Double_t	Mean (Double_t a, Double_t b, const Double_t *params=0, Double_t epsilon=0.000001)
virtual Double_t	Moment (Double_t n, Double_t a, Double_t b, const Double_t *params=0, Double_t epsilon=0.000001)
	Return nth moment of function between a and b. More...
template<class T >
T	operator() (const T *x, const Double_t *params=nullptr)
virtual Double_t	operator() (Double_t x, Double_t y=0, Double_t z=0, Double_t t=0) const
TF1 &	operator= (const TF1 &rhs)
	Operator =. More...
virtual void	Paint (Option_t *option="")
	Paint this function with its current attributes. More...
virtual void	Print (Option_t *option="") const
	Print TNamed name and title. More...
virtual void	ReleaseParameter (Int_t ipar)
	Release parameter number ipar If used in a fit, the parameter can vary freely. More...
virtual void	Save (Double_t xmin, Double_t xmax, Double_t ymin, Double_t ymax, Double_t zmin, Double_t zmax)
	Save values of function in array fSave. More...
virtual void	SavePrimitive (std::ostream &out, Option_t *option="")
	Save primitive as a C++ statement(s) on output stream out. More...
virtual void	SetChisquare (Double_t chi2)
virtual void	SetFitResult (const ROOT::Fit::FitResult &result, const Int_t *indpar=0)
	Set the result from the fit parameter values, errors, chi2, etc... Optionally a pointer to a vector (with size fNpar) of the parameter indices in the FitResult can be passed This is useful in the case of a combined fit with different functions, and the FitResult contains the global result By default it is assume that indpar = {0,1,2,....,fNpar-1}. More...
template<typename Func >
void	SetFunction (Func f)
template<class PtrObj , typename MemFn >
void	SetFunction (PtrObj &p, MemFn memFn)
virtual void	SetMaximum (Double_t maximum=-1111)
	Set the maximum value along Y for this function In case the function is already drawn, set also the maximum in the helper histogram. More...
virtual void	SetMinimum (Double_t minimum=-1111)
	Set the minimum value along Y for this function In case the function is already drawn, set also the minimum in the helper histogram. More...
virtual void	SetNDF (Int_t ndf)
	Set the number of degrees of freedom ndf should be the number of points used in a fit - the number of free parameters. More...
virtual void	SetNormalized (Bool_t flag)
virtual void	SetNpx (Int_t npx=100)
	Set the number of points used to draw the function. More...
virtual void	SetNumberFitPoints (Int_t npfits)
virtual void	SetParameter (const TString &name, Double_t value)
virtual void	SetParameter (Int_t param, Double_t value)
virtual void	SetParameters (const Double_t *params)
virtual void	SetParameters (Double_t p0, Double_t p1, Double_t p2=0, Double_t p3=0, Double_t p4=0, Double_t p5=0, Double_t p6=0, Double_t p7=0, Double_t p8=0, Double_t p9=0, Double_t p10=0)
virtual void	SetParent (TObject *p=0)
virtual void	SetParError (Int_t ipar, Double_t error)
	Set error for parameter number ipar. More...
virtual void	SetParErrors (const Double_t *errors)
	Set errors for all active parameters when calling this function, the array errors must have at least fNpar values. More...
virtual void	SetParLimits (Int_t ipar, Double_t parmin, Double_t parmax)
	Set limits for parameter ipar. More...
virtual void	SetParName (Int_t ipar, const char *name)
	Set name of parameter number ipar. More...
virtual void	SetParNames (const char *name0="p0", const char *name1="p1", const char *name2="p2", const char *name3="p3", const char *name4="p4", const char *name5="p5", const char *name6="p6", const char *name7="p7", const char *name8="p8", const char *name9="p9", const char *name10="p10")
	Set up to 10 parameter names. More...
virtual void	SetRange (Double_t xmin, Double_t xmax)
	Initialize the upper and lower bounds to draw the function. More...
virtual void	SetRange (Double_t xmin, Double_t ymin, Double_t xmax, Double_t ymax)
virtual void	SetRange (Double_t xmin, Double_t ymin, Double_t zmin, Double_t xmax, Double_t ymax, Double_t zmax)
virtual void	SetSavedPoint (Int_t point, Double_t value)
	Restore value of function saved at point. More...
virtual void	SetTitle (const char *title="")
	Set function title if title has the form "fffffff;xxxx;yyyy", it is assumed that the function title is "fffffff" and "xxxx" and "yyyy" are the titles for the X and Y axis respectively. More...
virtual void	SetVectorized (Bool_t vectorized)
virtual void	Update ()
	Called by functions such as SetRange, SetNpx, SetParameters to force the deletion of the associated histogram or Integral. More...
virtual Double_t	Variance (Double_t a, Double_t b, const Double_t *params=0, Double_t epsilon=0.000001)
Public Member Functions inherited from TNamed
	TNamed ()
	TNamed (const char *name, const char *title)
	TNamed (const TNamed &named)
	TNamed copy ctor. More...
	TNamed (const TString &name, const TString &title)
virtual	~TNamed ()
	TNamed destructor. More...
virtual void	Clear (Option_t *option="")
	Set name and title to empty strings (""). More...
virtual TObject *	Clone (const char *newname="") const
	Make a clone of an object using the Streamer facility. More...
virtual Int_t	Compare (const TObject *obj) const
	Compare two TNamed objects. More...
virtual void	Copy (TObject &named) const
	Copy this to obj. More...
virtual void	FillBuffer (char *&buffer)
	Encode TNamed into output buffer. More...
virtual const char *	GetName () const
	Returns name of object. More...
virtual const char *	GetTitle () const
	Returns title of object. More...
virtual ULong_t	Hash () const
	Return hash value for this object. More...
virtual Bool_t	IsSortable () const
virtual void	ls (Option_t *option="") const
	List TNamed name and title. More...
TNamed &	operator= (const TNamed &rhs)
	TNamed assignment operator. More...
virtual void	Print (Option_t *option="") const
	Print TNamed name and title. More...
virtual void	SetName (const char *name)
	Set the name of the TNamed. More...
virtual void	SetNameTitle (const char *name, const char *title)
	Set all the TNamed parameters (name and title). More...
virtual void	SetTitle (const char *title="")
	Set the title of the TNamed. More...
virtual Int_t	Sizeof () const
	Return size of the TNamed part of the TObject. More...
Public Member Functions inherited from TObject
	TObject ()
	TObject constructor. More...
	TObject (const TObject &object)
	TObject copy ctor. More...
virtual	~TObject ()
	TObject destructor. More...
void	AbstractMethod (const char *method) const
	Use this method to implement an "abstract" method that you don't want to leave purely abstract. More...
virtual void	AppendPad (Option_t *option="")
	Append graphics object to current pad. More...
virtual void	Browse (TBrowser *b)
	Browse object. May be overridden for another default action. More...
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. More...
virtual const char *	ClassName () const
	Returns name of class to which the object belongs. More...
virtual void	Clear (Option_t *="")
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 abstract method. More...
virtual void	Copy (TObject &object) const
	Copy this to obj. 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 selected pad for instance with: gROOT->SetSelectedPad(gPad). More...
virtual void	Dump () const
	Dump contents of object on stdout. More...
virtual void	Error (const char *method, const char *msgfmt,...) const
	Issue error message. More...
virtual void	Execute (const char *method, const char *params, Int_t *error=0)
	Execute method on this object with the given parameter string, e.g. More...
virtual void	Execute (TMethod *method, TObjArray *params, Int_t *error=0)
	Execute method on this object with parameters stored in the TObjArray. More...
virtual void	ExecuteEvent (Int_t event, Int_t px, Int_t py)
	Execute action corresponding to an event at (px,py). More...
virtual void	Fatal (const char *method, const char *msgfmt,...) const
	Issue fatal error message. More...
virtual TObject *	FindObject (const char *name) const
	Must be redefined in derived classes. More...
virtual TObject *	FindObject (const TObject *obj) const
	Must be redefined in derived classes. More...
virtual Option_t *	GetDrawOption () const
	Get option used by the graphics system to draw this object. More...
virtual const char *	GetIconName () const
	Returns mime type name of object. More...
virtual const char *	GetName () const
	Returns name of object. More...
virtual char *	GetObjectInfo (Int_t px, Int_t py) const
	Returns string containing info about the object at position (px,py). More...
virtual Option_t *	GetOption () const
virtual const char *	GetTitle () const
	Returns title of object. More...
virtual UInt_t	GetUniqueID () const
	Return the unique object id. More...
virtual Bool_t	HandleTimer (TTimer *timer)
	Execute action in response of a timer timing out. More...
virtual ULong_t	Hash () const
	Return hash value for this object. More...
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. More...
virtual void	Info (const char *method, const char *msgfmt,...) const
	Issue info message. More...
virtual Bool_t	InheritsFrom (const char *classname) const
	Returns kTRUE if object inherits from class "classname". More...
virtual Bool_t	InheritsFrom (const TClass *cl) const
	Returns kTRUE if object inherits from TClass cl. More...
virtual void	Inspect () const
	Dump contents of this object in a graphics canvas. More...
void	InvertBit (UInt_t f)
virtual Bool_t	IsEqual (const TObject *obj) const
	Default equal comparison (objects are equal if they have the same address in memory). More...
virtual Bool_t	IsFolder () const
	Returns kTRUE in case object contains browsable objects (like containers or lists of other objects). More...
R__ALWAYS_INLINE Bool_t	IsOnHeap () const
virtual Bool_t	IsSortable () const
R__ALWAYS_INLINE Bool_t	IsZombie () const
virtual void	ls (Option_t *option="") const
	The ls function lists the contents of a class on stdout. 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...
virtual Bool_t	Notify ()
	This method must be overridden to handle object notification. More...
void	Obsolete (const char *method, const char *asOfVers, const char *removedFromVers) const
	Use this method to declare a method obsolete. More...
void	operator delete (void *ptr)
	Operator delete. More...
void	operator delete[] (void *ptr)
	Operator delete []. More...
void *	operator new (size_t sz)
void *	operator new (size_t sz, void *vp)
void *	operator new[] (size_t sz)
void *	operator new[] (size_t sz, void *vp)
TObject &	operator= (const TObject &rhs)
	TObject assignment operator. More...
virtual void	Paint (Option_t *option="")
	This method must be overridden if a class wants to paint itself. More...
virtual void	Pop ()
	Pop on object drawn in a pad to the top of the display list. More...
virtual void	Print (Option_t *option="") const
	This method must be overridden when a class wants to print itself. More...
virtual Int_t	Read (const char *name)
	Read contents of object with specified name from the current directory. More...
virtual void	RecursiveRemove (TObject *obj)
	Recursively remove this object from a list. More...
void	ResetBit (UInt_t f)
virtual void	SaveAs (const char *filename="", Option_t *option="") const
	Save this object in the file specified by filename. More...
virtual void	SavePrimitive (std::ostream &out, Option_t *option="")
	Save a primitive as a C++ statement(s) on output stream "out". More...
void	SetBit (UInt_t f)
void	SetBit (UInt_t f, Bool_t set)
	Set or unset the user status bits as specified in f. 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	SysError (const char *method, const char *msgfmt,...) const
	Issue system error message. More...
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. More...
virtual void	Warning (const char *method, const char *msgfmt,...) const
	Issue warning message. More...
virtual Int_t	Write (const char *name=0, Int_t option=0, Int_t bufsize=0)
	Write this object to the current directory. More...
virtual Int_t	Write (const char *name=0, Int_t option=0, Int_t bufsize=0) const
	Write this object to the current directory. More...
Public Member Functions inherited from TAttLine
	TAttLine ()
	AttLine default constructor. More...
	TAttLine (Color_t lcolor, Style_t lstyle, Width_t lwidth)
	AttLine normal constructor. More...
virtual	~TAttLine ()
	AttLine destructor. More...
void	Copy (TAttLine &attline) const
	Copy this line attributes to a new TAttLine. More...
Int_t	DistancetoLine (Int_t px, Int_t py, Double_t xp1, Double_t yp1, Double_t xp2, Double_t yp2)
	Compute distance from point px,py to a line. More...
virtual Color_t	GetLineColor () const
	Return the line color. More...
virtual Style_t	GetLineStyle () const
	Return the line style. More...
virtual Width_t	GetLineWidth () const
	Return the line width. More...
virtual void	Modify ()
	Change current line attributes if necessary. More...
virtual void	ResetAttLine (Option_t *option="")
	Reset this line attributes to default values. More...
virtual void	SaveLineAttributes (std::ostream &out, const char *name, Int_t coldef=1, Int_t stydef=1, Int_t widdef=1)
	Save line attributes as C++ statement(s) on output stream out. More...
virtual void	SetLineAttributes ()
	Invoke the DialogCanvas Line attributes. More...
virtual void	SetLineColor (Color_t lcolor)
	Set the line color. More...
virtual void	SetLineColorAlpha (Color_t lcolor, Float_t lalpha)
	Set a transparent line color. More...
virtual void	SetLineStyle (Style_t lstyle)
	Set the line style. More...
virtual void	SetLineWidth (Width_t lwidth)
	Set the line width. More...
Public Member Functions inherited from TAttFill
	TAttFill ()
	AttFill default constructor. More...
	TAttFill (Color_t fcolor, Style_t fstyle)
	AttFill normal constructor. More...
virtual	~TAttFill ()
	AttFill destructor. More...
void	Copy (TAttFill &attfill) const
	Copy this fill attributes to a new TAttFill. More...
virtual Color_t	GetFillColor () const
	Return the fill area color. More...
virtual Style_t	GetFillStyle () const
	Return the fill area style. More...
virtual Bool_t	IsTransparent () const
virtual void	Modify ()
	Change current fill area attributes if necessary. More...
virtual void	ResetAttFill (Option_t *option="")
	Reset this fill attributes to default values. More...
virtual void	SaveFillAttributes (std::ostream &out, const char *name, Int_t coldef=1, Int_t stydef=1001)
	Save fill attributes as C++ statement(s) on output stream out. More...
virtual void	SetFillAttributes ()
	Invoke the DialogCanvas Fill attributes. More...
virtual void	SetFillColor (Color_t fcolor)
	Set the fill area color. More...
virtual void	SetFillColorAlpha (Color_t fcolor, Float_t falpha)
	Set a transparent fill color. More...
virtual void	SetFillStyle (Style_t fstyle)
	Set the fill area style. More...
Public Member Functions inherited from TAttMarker
	TAttMarker ()
	TAttMarker default constructor. More...
	TAttMarker (Color_t color, Style_t style, Size_t msize)
	TAttMarker normal constructor. More...
virtual	~TAttMarker ()
	TAttMarker destructor. More...
void	Copy (TAttMarker &attmarker) const
	Copy this marker attributes to a new TAttMarker. More...
virtual Color_t	GetMarkerColor () const
	Return the marker color. More...
virtual Size_t	GetMarkerSize () const
	Return the marker size. More...
virtual Style_t	GetMarkerStyle () const
	Return the marker style. More...
virtual void	Modify ()
	Change current marker attributes if necessary. More...
virtual void	ResetAttMarker (Option_t *toption="")
	Reset this marker attributes to the default values. More...
virtual void	SaveMarkerAttributes (std::ostream &out, const char *name, Int_t coldef=1, Int_t stydef=1, Int_t sizdef=1)
	Save line attributes as C++ statement(s) on output stream out. More...
virtual void	SetMarkerAttributes ()
	Invoke the DialogCanvas Marker attributes. More...
virtual void	SetMarkerColor (Color_t mcolor=1)
	Set the marker color. More...
virtual void	SetMarkerColorAlpha (Color_t mcolor, Float_t malpha)
	Set a transparent marker color. More...
virtual void	SetMarkerSize (Size_t msize=1)
	Set the marker size. More...
virtual void	SetMarkerStyle (Style_t mstyle=1)
	Set the marker style. More...

Static Public Member Functions
static void	AbsValue (Bool_t reject=kTRUE)
	Static function: set the fgAbsValue flag. More...
static void	CalcGaussLegendreSamplingPoints (Int_t num, Double_t *x, Double_t *w, Double_t eps=3.0e-11)
	Type safe interface (static method) The number of sampling points are taken from the TGraph. More...
static Bool_t	DefaultAddToGlobalList (Bool_t on=kTRUE)
	Static method to add/avoid to add automatically functions to the global list (gROOT->GetListOfFunctions() ) After having called this static method, all the functions created afterwards will follow the desired behaviour. More...
static Double_t	DerivativeError ()
	Static function returning the error of the last call to the of Derivative's functions. More...
static TF1 *	GetCurrent ()
	Static function returning the current function being processed. More...
static void	InitStandardFunctions ()
	Create the basic function objects. More...
static Bool_t	RejectedPoint ()
	See TF1::RejectPoint above. More...
static void	RejectPoint (Bool_t reject=kTRUE)
	Static function to set the global flag to reject points the fgRejectPoint global flag is tested by all fit functions if TRUE the point is not included in the fit. More...
static void	SetCurrent (TF1 *f1)
	Static function setting the current function. More...
Static Public Member Functions inherited from TObject
static Long_t	GetDtorOnly ()
	Return destructor only flag. More...
static Bool_t	GetObjectStat ()
	Get status of object stat flag. More...
static void	SetDtorOnly (void *obj)
	Set destructor only flag. More...
static void	SetObjectStat (Bool_t stat)
	Turn on/off tracking of objects in the TObjectTable. More...

Static Public Attributes
static std::atomic< Bool_t >	fgAbsValue
static std::atomic< Bool_t >	fgAddToGlobList
static TF1 *	fgCurrent = 0
static Bool_t	fgRejectPoint = kFALSE

Protected Types
enum	EFType {   kFormula = 0 , kPtrScalarFreeFcn , kInterpreted , kTemplVec ,   kTemplScalar , kCompositionFcn }

Protected Member Functions
	TF1 (EFType functionType, const char *name, Double_t xmin, Double_t xmax, Int_t npar, Int_t ndim, EAddToList addToGlobList, TF1Parameters *params=nullptr, TF1FunctorPointer *functor=nullptr)
	General constructor for TF1. Most of the other constructors delegate on it. More...
Protected Member Functions inherited from TObject
virtual void	DoError (int level, const char *location, const char *fmt, va_list va) const
	Interface to ErrorHandler (protected). More...
void	MakeZombie ()

Protected Attributes
std::vector< Double_t >	fAlpha
	Integral of function binned on fNpx bins. More...
std::vector< Double_t >	fBeta
	Array alpha. for each bin in x the deconvolution r of fIntegral. More...
Double_t	fChisquare {}
std::unique_ptr< TF1AbsComposition >	fComposition
TF1AbsComposition *	fComposition_ptr {nullptr}
	Pointer to composition (NSUM or CONV) More...
TFormula *	fFormula {nullptr}
	Functor object to wrap any C++ callable object. More...
TF1FunctorPointer *	fFunctor {nullptr}
std::vector< Double_t >	fGamma
	Array beta. is approximated by x = alpha +beta*r *gamma*r**2. More...
TH1 *	fHistogram {nullptr}
	Parent object hooking this function (if one) More...
std::vector< Double_t >	fIntegral
Double_t	fMaximum {-1111}
TMethodCall *	fMethodCall {nullptr}
	Pointer to histogram used for visualisation. More...
Double_t	fMinimum {-1111}
Int_t	fNDF {}
Int_t	fNdim {}
Bool_t	fNormalized {false}
	Pointer to MethodCall in case of interpreted function. More...
Double_t	fNormIntegral {}
Int_t	fNpar {}
Int_t	fNpfits {}
Int_t	fNpx {100}
TF1Parameters *	fParams {nullptr}
TObject *	fParent {nullptr}
	Array gamma. More...
std::vector< Double_t >	fParErrors
std::vector< Double_t >	fParMax
std::vector< Double_t >	fParMin
std::vector< Double_t >	fSave
EFType	fType {EFType::kTemplScalar}
Double_t	fXmax {-1111}
Double_t	fXmin {-1111}
Protected Attributes inherited from TNamed
TString	fName
TString	fTitle
Protected Attributes inherited from TAttLine
Color_t	fLineColor
	Line color. More...
Style_t	fLineStyle
	Line style. More...
Width_t	fLineWidth
	Line width. More...
Protected Attributes inherited from TAttFill
Color_t	fFillColor
	Fill area color. More...
Style_t	fFillStyle
	Fill area style. More...
Protected Attributes inherited from TAttMarker
Color_t	fMarkerColor
	Marker color. More...
Size_t	fMarkerSize
	Marker size. More...
Style_t	fMarkerStyle
	Marker style. More...

Private Member Functions
void	DefineNSUMTerm (TObjArray *newFuncs, TObjArray *coeffNames, TString &fullFormula, TString &formula, int termStart, int termEnd, Double_t xmin, Double_t xmax)
	Helper functions for NSUM parsing. More...
template<class T >
T	EvalParTempl (const T *data, const Double_t *params=0)
	Eval for vectorized functions. More...
int	TermCoeffLength (TString &term)

Friends
template<class Func >
struct	ROOT::Internal::TF1Builder

#include <TF1.h>

Inheritance diagram for TF1:

Member Enumeration Documentation

EAddToList

enum class TF1::EAddToList

strong

Enumerator
kDefault
kAdd
kNo

Definition at line 218 of file TF1.h.

EFType

enum TF1::EFType

protected

Enumerator
kFormula
kPtrScalarFreeFcn
kInterpreted
kTemplVec
kTemplScalar
kCompositionFcn

Definition at line 226 of file TF1.h.

EStatusBits

enum TF1::EStatusBits

Enumerator
kNotGlobal
kNotDraw

Definition at line 309 of file TF1.h.

Constructor & Destructor Documentation

TF1() [1/15]

TF1::TF1 ( EFType  functionType, const char *  name, Double_t  xmin, Double_t  xmax, Int_t  npar, Int_t  ndim, EAddToList  addToGlobList, TF1Parameters *  params = nullptr, TF1FunctorPointer *  functor = nullptr  )

inlineprotected

General constructor for TF1. Most of the other constructors delegate on it.

Definition at line 266 of file TF1.h.

TF1() [2/15]

TF1::TF1

(

)

TF1 default constructor.

Definition at line 491 of file TF1.cxx.

TF1() [3/15]

TF1::TF1	(	const char *	name,
		const char *	formula,
		Double_t	xmin = 0,
		Double_t	xmax = 1,
		EAddToList	addToGlobList = EAddToList::kDefault,
		bool	vectorize = false
	)

F1 constructor using a formula definition.

See TFormula constructor for explanation of the formula syntax.

See tutorials: fillrandom, first, fit1, formula1, multifit for real examples.

Creates a function of type A or B between xmin and xmax

if formula has the form "fffffff;xxxx;yyyy", it is assumed that the formula string is "fffffff" and "xxxx" and "yyyy" are the titles for the X and Y axis respectively.

Definition at line 513 of file TF1.cxx.

TF1() [4/15]

TF1::TF1	(	const char *	name,
		const char *	formula,
		Double_t	xmin,
		Double_t	xmax,
		Option_t *	option
	)

Same constructor as above (for TFormula based function) but passing an option strings available options VEC - vectorize the formula expressions (not possible for lambda based expressions) NL - function is not stores in the global list of functions GL - function will be always stored in the global list of functions , independently of the global setting of TF1::DefaultAddToGlobalList.

Definition at line 688 of file TF1.cxx.

TF1() [5/15]

TF1::TF1	(	const char *	name,
		Double_t	xmin,
		Double_t	xmax,
		Int_t	npar,
		Int_t	ndim = 1,
		EAddToList	addToGlobList = EAddToList::kDefault
	)

F1 constructor using name of an interpreted function.

Creates a function of type C between xmin and xmax. name is the name of an interpreted C++ function. The function is defined with npar parameters fcn must be a function of type:

Double_t fcn(Double_t *x, Double_t *params)

This constructor is called for functions of type C by the C++ interpreter.

WARNING! A function created with this constructor cannot be Cloned.

Definition at line 713 of file TF1.cxx.

TF1() [6/15]

TF1::TF1	(	const char *	name,
		Double_t(*)(Double_t *, Double_t *)	fcn,
		Double_t	xmin = 0,
		Double_t	xmax = 1,
		Int_t	npar = 0,
		Int_t	ndim = 1,
		EAddToList	addToGlobList = EAddToList::kDefault
	)

Constructor using a pointer to a real function.

Parameters

npar	is the number of free parameters used by the function

This constructor creates a function of type C when invoked with the normal C++ compiler.

see test program test/stress.cxx (function stress1) for an example. note the interface with an intermediate pointer.

WARNING! A function created with this constructor cannot be Cloned.

Definition at line 747 of file TF1.cxx.

TF1() [7/15]

TF1::TF1	(	const char *	name,
		Double_t(*)(const Double_t *, const Double_t *)	fcn,
		Double_t	xmin = 0,
		Double_t	xmax = 1,
		Int_t	npar = 0,
		Int_t	ndim = 1,
		EAddToList	addToGlobList = EAddToList::kDefault
	)

Constructor using a pointer to real function.

Parameters

npar	is the number of free parameters used by the function

This constructor creates a function of type C when invoked with the normal C++ compiler.

see test program test/stress.cxx (function stress1) for an example. note the interface with an intermediate pointer.

WARNING! A function created with this constructor cannot be Cloned.

Definition at line 764 of file TF1.cxx.

TF1() [8/15]

template<class T >

TF1::TF1 ( const char *  name, std::function< T(const T *data, const Double_t *param)> &  fcn, Double_t  xmin = 0, Double_t  xmax = 1, Int_t  npar = 0, Int_t  ndim = 1, EAddToList  addToGlobList = EAddToList::kDefault  )

inline

Definition at line 322 of file TF1.h.

TF1() [9/15]

template<class T >

TF1::TF1 ( const char *  name, T(*)(const T *, const Double_t *)  fcn, Double_t  xmin = 0, Double_t  xmax = 1, Int_t  npar = 0, Int_t  ndim = 1, EAddToList  addToGlobList = EAddToList::kDefault  )

inline

Constructor using a pointer to function.

Parameters

npar	is the number of free parameters used by the function

This constructor creates a function of type C when invoked with the normal C++ compiler.

WARNING! A function created with this constructor cannot be Cloned

Definition at line 341 of file TF1.h.

TF1() [10/15]

TF1::TF1	(	const char *	name,
		ROOT::Math::ParamFunctor	f,
		Double_t	xmin = 0,
		Double_t	xmax = 1,
		Int_t	npar = 0,
		Int_t	ndim = 1,
		EAddToList	addToGlobList = EAddToList::kDefault
	)

Constructor using the Functor class.

Parameters

xmin	and
xmax	define the plotting range of the function
npar	is the number of free parameters used by the function

This constructor can be used only in compiled code

WARNING! A function created with this constructor cannot be Cloned.

Definition at line 779 of file TF1.cxx.

TF1() [11/15]

template<typename Func >

TF1::TF1 ( const char *  name, Func  f, Double_t  xmin, Double_t  xmax, Int_t  npar, Int_t  ndim = 1, EAddToList  addToGlobList = EAddToList::kDefault  )

inline

Definition at line 357 of file TF1.h.

TF1() [12/15]

template<typename Func >

TF1::TF1 ( const char *  name, Func  f, Double_t  xmin, Double_t  xmax, Int_t  npar, const char *  , EAddToList  addToGlobList = EAddToList::kDefault  )

inline

Definition at line 366 of file TF1.h.

TF1() [13/15]

template<class PtrObj , typename MemFn >

TF1::TF1 ( const char *  name, const PtrObj &  p, MemFn  memFn, Double_t  xmin, Double_t  xmax, Int_t  npar, Int_t  ndim = 1, EAddToList  addToGlobList = EAddToList::kDefault  )

inline

Definition at line 382 of file TF1.h.

TF1() [14/15]

template<class PtrObj , typename MemFn >

TF1::TF1 ( const char *  name, const PtrObj &  p, MemFn  memFn, Double_t  xmin, Double_t  xmax, Int_t  npar, const char *  , const char *  , EAddToList  addToGlobList = EAddToList::kDefault  )

inline

Definition at line 388 of file TF1.h.

TF1() [15/15]

TF1::TF1

(

const TF1 &

f1

)

Definition at line 959 of file TF1.cxx.

~TF1()

TF1::~TF1 ( )

virtual

TF1 default destructor.

Definition at line 939 of file TF1.cxx.

Member Function Documentation

AbsValue()

void TF1::AbsValue ( Bool_t  flag = kTRUE )

static

Static function: set the fgAbsValue flag.

By default TF1::Integral uses the original function value to compute the integral However, TF1::Moment, CentralMoment require to compute the integral using the absolute value of the function.

Definition at line 973 of file TF1.cxx.

AddParameter()

virtual void TF1::AddParameter ( const TString &  name, Double_t  value  )

inlinevirtual

Definition at line 395 of file TF1.h.

AddToGlobalList()

Bool_t TF1::AddToGlobalList ( Bool_t  on = kTRUE )

virtual

Add to global list of functions (gROOT->GetListOfFunctions() ) return previous status (true if the function was already in the list false if not)

Definition at line 832 of file TF1.cxx.

Browse()

void TF1::Browse ( TBrowser *  b )

virtual

Browse.

Reimplemented from TObject.

Definition at line 982 of file TF1.cxx.

CalcGaussLegendreSamplingPoints()

void TF1::CalcGaussLegendreSamplingPoints ( Int_t  num, Double_t *  x, Double_t *  w, Double_t  eps = 3.0e-11  )

static

Type safe interface (static method) The number of sampling points are taken from the TGraph.

Type: unsafe but fast interface filling the arrays x and w (static method)

Given the number of sampling points this routine fills the arrays x and w of length num, containing the abscissa and weight of the Gauss-Legendre n-point quadrature formula.

Gauss-Legendre:

$$W(x)=1 -1<x<1 \\ (j+1)P_{j+1} = (2j+1)xP_j-jP_{j-1}$$

num is the number of sampling points (>0) x and w are arrays of size num eps is the relative precision

If num<=0 or eps<=0 no action is done.

Reference: Numerical Recipes in C, Second Edition

Definition at line 3787 of file TF1.cxx.

CentralMoment()

Double_t TF1::CentralMoment ( Double_t  n, Double_t  a, Double_t  b, const Double_t *  params = 0, Double_t  epsilon = 0.000001  )

virtual

Return nth central moment of function between a and b (i.e the n-th moment around the mean value)

See TF1::Integral() for parameter definitions

Author

Gene Van Buren gene@.nosp@m.bnl..nosp@m.gov

Definition at line 3700 of file TF1.cxx.

Copy()

void TF1::Copy ( TObject &  obj ) const

virtual

Copy this F1 to a new F1.

Note that the cached integral with its related arrays are not copied (they are also set as transient data members)

Reimplemented from TNamed.

Reimplemented in TF12, TF2, and TF3.

Definition at line 994 of file TF1.cxx.

CreateHistogram()

virtual TH1 * TF1::CreateHistogram ( )

inlinevirtual

Reimplemented in TF2, and TF3.

Definition at line 433 of file TF1.h.

DefaultAddToGlobalList()

Bool_t TF1::DefaultAddToGlobalList ( Bool_t  on = kTRUE )

static

Static method to add/avoid to add automatically functions to the global list (gROOT->GetListOfFunctions() ) After having called this static method, all the functions created afterwards will follow the desired behaviour.

By default the functions are added automatically It returns the previous status (true if the functions are added automatically)

Definition at line 823 of file TF1.cxx.

DefineNSUMTerm()

void TF1::DefineNSUMTerm ( TObjArray *  newFuncs, TObjArray *  coeffNames, TString &  fullFormula, TString &  formula, int  termStart, int  termEnd, Double_t  xmin, Double_t  xmax  )

private

Helper functions for NSUM parsing.

Definition at line 868 of file TF1.cxx.

Derivative()

Double_t TF1::Derivative ( Double_t  x, Double_t *  params = 0, Double_t  eps = 0.001  ) const

virtual

Returns the first derivative of the function at point x, computed by Richardson's extrapolation method (use 2 derivative estimates to compute a third, more accurate estimation) first, derivatives with steps h and h/2 are computed by central difference formulas.

$$D(h) = \frac{f(x+h) - f(x-h)}{2h}$$

the final estimate

$$D = \frac{4D(h/2) - D(h)}{3}$$

"Numerical Methods for Scientists and Engineers", H.M.Antia, 2nd edition"

if the argument params is null, the current function parameters are used, otherwise the parameters in params are used.

the argument eps may be specified to control the step size (precision). the step size is taken as eps*(xmax-xmin). the default value (0.001) should be good enough for the vast majority of functions. Give a smaller value if your function has many changes of the second derivative in the function range.

Getting the error via TF1::DerivativeError: (total error = roundoff error + interpolation error) the estimate of the roundoff error is taken as follows:

$$err = k\sqrt{f(x)^{2} + x^{2}deriv^{2}}\sqrt{\sum ai^{2}},$$

where k is the double precision, ai are coefficients used in central difference formulas interpolation error is decreased by making the step size h smaller.

Author

Anna Kreshuk

Definition at line 1092 of file TF1.cxx.

Derivative2()

Double_t TF1::Derivative2 ( Double_t  x, Double_t *  params = 0, Double_t  eps = 0.001  ) const

virtual

Returns the second derivative of the function at point x, computed by Richardson's extrapolation method (use 2 derivative estimates to compute a third, more accurate estimation) first, derivatives with steps h and h/2 are computed by central difference formulas.

$$D(h) = \frac{f(x+h) - 2f(x) + f(x-h)}{h^{2}}$$

the final estimate

$$D = \frac{4D(h/2) - D(h)}{3}$$

"Numerical Methods for Scientists and Engineers", H.M.Antia, 2nd edition"

if the argument params is null, the current function parameters are used, otherwise the parameters in params are used.

the argument eps may be specified to control the step size (precision). the step size is taken as eps*(xmax-xmin). the default value (0.001) should be good enough for the vast majority of functions. Give a smaller value if your function has many changes of the second derivative in the function range.

Getting the error via TF1::DerivativeError: (total error = roundoff error + interpolation error) the estimate of the roundoff error is taken as follows:

$$err = k\sqrt{f(x)^{2} + x^{2}deriv^{2}}\sqrt{\sum ai^{2}},$$

where k is the double precision, ai are coefficients used in central difference formulas interpolation error is decreased by making the step size h smaller.

Author

Anna Kreshuk

Definition at line 1157 of file TF1.cxx.

Derivative3()

Double_t TF1::Derivative3 ( Double_t  x, Double_t *  params = 0, Double_t  eps = 0.001  ) const

virtual

Returns the third derivative of the function at point x, computed by Richardson's extrapolation method (use 2 derivative estimates to compute a third, more accurate estimation) first, derivatives with steps h and h/2 are computed by central difference formulas.

$$D(h) = \frac{f(x+2h) - 2f(x+h) + 2f(x-h) - f(x-2h)}{2h^{3}}$$

the final estimate

$$D = \frac{4D(h/2) - D(h)}{3}$$

"Numerical Methods for Scientists and Engineers", H.M.Antia, 2nd edition"

if the argument params is null, the current function parameters are used, otherwise the parameters in params are used.

the argument eps may be specified to control the step size (precision). the step size is taken as eps*(xmax-xmin). the default value (0.001) should be good enough for the vast majority of functions. Give a smaller value if your function has many changes of the second derivative in the function range.

Getting the error via TF1::DerivativeError: (total error = roundoff error + interpolation error) the estimate of the roundoff error is taken as follows:

$$err = k\sqrt{f(x)^{2} + x^{2}deriv^{2}}\sqrt{\sum ai^{2}},$$

where k is the double precision, ai are coefficients used in central difference formulas interpolation error is decreased by making the step size h smaller.

Author

Anna Kreshuk

Definition at line 1222 of file TF1.cxx.

DerivativeError()

Double_t TF1::DerivativeError ( )

static

Static function returning the error of the last call to the of Derivative's functions.

Definition at line 1256 of file TF1.cxx.

DistancetoPrimitive()

Int_t TF1::DistancetoPrimitive ( Int_t  px, Int_t  py  )

virtual

Compute distance from point px,py to a function.

Compute the closest distance of approach from point px,py to this function. The distance is computed in pixels units.

Note that px is called with a negative value when the TF1 is in TGraph or TH1 list of functions. In this case there is no point looking at the histogram axis.

Reimplemented from TObject.

Reimplemented in TF2, and TF3.

Definition at line 1272 of file TF1.cxx.

DoCreateHistogram()

TH1 * TF1::DoCreateHistogram ( Double_t  xmin, Double_t  xmax, Bool_t  recreate = kFALSE  )

virtual

Create histogram with bin content equal to function value computed at the bin center This histogram will be used to paint the function A re-creation is forced and a new histogram is done if recreate=true.

Definition at line 3016 of file TF1.cxx.

DoInitialize()

void TF1::DoInitialize

(

EAddToList

addToGlobalList

)

Common initialization of the TF1.

Add to the global list and set the default style

Definition at line 787 of file TF1.cxx.

Draw()

void TF1::Draw ( Option_t *  option = "" )

virtual

Draw this function with its current attributes.

Possible option values are:

option	description
"SAME"	superimpose on top of existing picture
"L"	connect all computed points with a straight line
"C"	connect all computed points with a smooth curve
"FC"	draw a fill area below a smooth curve

Note that the default value is "L". Therefore to draw on top of an existing picture, specify option "LSAME"

NB. You must use DrawCopy if you want to draw several times the same function in the current canvas.

Reimplemented from TObject.

Reimplemented in TF2, and TF3.

Definition at line 1312 of file TF1.cxx.

DrawCopy()

TF1 * TF1::DrawCopy ( Option_t *  option = "" ) const

virtual

Draw a copy of this function with its current attributes.

This function MUST be used instead of Draw when you want to draw the same function with different parameters settings in the same canvas.

Possible option values are:

option	description
"SAME"	superimpose on top of existing picture
"L"	connect all computed points with a straight line
"C"	connect all computed points with a smooth curve
"FC"	draw a fill area below a smooth curve

Note that the default value is "L". Therefore to draw on top of an existing picture, specify option "LSAME"

Reimplemented in TF12, and TF2.

Definition at line 1342 of file TF1.cxx.

DrawDerivative()

TObject * TF1::DrawDerivative ( Option_t *  option = "al" )

virtual

Draw derivative of this function.

An intermediate TGraph object is built and drawn with option. The function returns a pointer to the TGraph object. Do:

TGraph *g = (TGraph*)myfunc.DrawDerivative(option);

The resulting graph will be drawn into the current pad. If this function is used via the context menu, it recommended to create a new canvas/pad before invoking this function.

Reimplemented in TF2, and TF3.

Definition at line 1364 of file TF1.cxx.

DrawF1()

void TF1::DrawF1 ( Double_t  xmin, Double_t  xmax, Option_t *  option = ""  )

virtual

Draw function between xmin and xmax.

Definition at line 1405 of file TF1.cxx.

DrawIntegral()

TObject * TF1::DrawIntegral ( Option_t *  option = "al" )

virtual

Draw integral of this function.

An intermediate TGraph object is built and drawn with option. The function returns a pointer to the TGraph object. Do:

TGraph *g = (TGraph*)myfunc.DrawIntegral(option);

The resulting graph will be drawn into the current pad. If this function is used via the context menu, it recommended to create a new canvas/pad before invoking this function.

Reimplemented in TF2, and TF3.

Definition at line 1389 of file TF1.cxx.

Eval()

Double_t TF1::Eval ( Double_t  x, Double_t  y = 0, Double_t  z = 0, Double_t  t = 0  ) const

virtual

Evaluate this function.

Computes the value of this function (general case for a 3-d function) at point x,y,z. For a 1-d function give y=0 and z=0 The current value of variables x,y,z is passed through x, y and z. The parameters used will be the ones in the array params if params is given otherwise parameters will be taken from the stored data members fParams

Reimplemented in TF12.

Definition at line 1424 of file TF1.cxx.

EvalPar() [1/2]

Double_t TF1::EvalPar ( const Double_t *  x, const Double_t *  params = 0  )

virtual

Evaluate function with given coordinates and parameters.

Compute the value of this function at point defined by array x and current values of parameters in array params. If argument params is omitted or equal 0, the internal values of parameters (array fParams) will be used instead. For a 1-D function only x[0] must be given. In case of a multi-dimensional function, the arrays x must be filled with the corresponding number of dimensions.

WARNING. In case of an interpreted function (fType=2), it is the user's responsibility to initialize the parameters via InitArgs before calling this function. InitArgs should be called at least once to specify the addresses of the arguments x and params. InitArgs should be called every time these addresses change.

Reimplemented in TF12.

Definition at line 1453 of file TF1.cxx.

EvalPar() [2/2]

template<class T >

T TF1::EvalPar	(	const T *	x,
		const Double_t *	params = 0
	)

EvalPar for vectorized.

Definition at line 754 of file TF1.h.

EvalParTempl()

template<class T >

T TF1::EvalParTempl ( const T *  data, const Double_t *  params = 0  )

inlineprivate

Eval for vectorized functions.

Definition at line 779 of file TF1.h.

ExecuteEvent()

void TF1::ExecuteEvent ( Int_t  event, Int_t  px, Int_t  py  )

virtual

Execute action corresponding to one event.

This member function is called when a F1 is clicked with the locator

Reimplemented from TObject.

Reimplemented in TF2, and TF3.

Definition at line 1521 of file TF1.cxx.

FixParameter()

void TF1::FixParameter ( Int_t  ipar, Double_t  value  )

virtual

Fix the value of a parameter The specified value will be used in a fit operation.

Definition at line 1537 of file TF1.cxx.

GetChisquare()

Double_t TF1::GetChisquare ( ) const

inline

Definition at line 428 of file TF1.h.

GetCurrent()

TF1 * TF1::GetCurrent ( )

static

Static function returning the current function being processed.

Definition at line 1549 of file TF1.cxx.

GetExpFormula()

virtual TString TF1::GetExpFormula ( Option_t *  option = "" ) const

inlinevirtual

Definition at line 445 of file TF1.h.

GetFormula() [1/2]

virtual TFormula * TF1::GetFormula ( )

inlinevirtual

Definition at line 437 of file TF1.h.

GetFormula() [2/2]

virtual const TFormula * TF1::GetFormula ( ) const

inlinevirtual

Definition at line 441 of file TF1.h.

GetHistogram()

TH1 * TF1::GetHistogram ( ) const

virtual

Return a pointer to the histogram used to visualise the function.

Definition at line 1559 of file TF1.cxx.

GetLinearPart()

virtual const TObject * TF1::GetLinearPart ( Int_t  i ) const

inlinevirtual

Definition at line 449 of file TF1.h.

GetMaximum()

Double_t TF1::GetMaximum ( Double_t  xmin = 0, Double_t  xmax = 0, Double_t  epsilon = 1.E-10, Int_t  maxiter = 100, Bool_t  logx = false  ) const

virtual

Returns the maximum value of the function.

Method: First, the grid search is used to bracket the maximum with the step size = (xmax-xmin)/fNpx. This way, the step size can be controlled via the SetNpx() function. If the function is unimodal or if its extrema are far apart, setting the fNpx to a small value speeds the algorithm up many times. Then, Brent's method is applied on the bracketed interval epsilon (default = 1.E-10) controls the relative accuracy (if |x| > 1 ) and absolute (if |x| < 1) and maxiter (default = 100) controls the maximum number of iteration of the Brent algorithm If the flag logx is set the grid search is done in log step size This is done automatically if the log scale is set in the current Pad

NOTE: see also TF1::GetMaximumX and TF1::GetX

Reimplemented in TF2.

Definition at line 1589 of file TF1.cxx.

GetMaximumStored()

virtual Double_t TF1::GetMaximumStored ( ) const

inlinevirtual

Definition at line 457 of file TF1.h.

GetMaximumX()

Double_t TF1::GetMaximumX ( Double_t  xmin = 0, Double_t  xmax = 0, Double_t  epsilon = 1.E-10, Int_t  maxiter = 100, Bool_t  logx = false  ) const

virtual

Returns the X value corresponding to the maximum value of the function.

Method: First, the grid search is used to bracket the maximum with the step size = (xmax-xmin)/fNpx. This way, the step size can be controlled via the SetNpx() function. If the function is unimodal or if its extrema are far apart, setting the fNpx to a small value speeds the algorithm up many times. Then, Brent's method is applied on the bracketed interval epsilon (default = 1.E-10) controls the relative accuracy (if |x| > 1 ) and absolute (if |x| < 1) and maxiter (default = 100) controls the maximum number of iteration of the Brent algorithm If the flag logx is set the grid search is done in log step size This is done automatically if the log scale is set in the current Pad

NOTE: see also TF1::GetX

Definition at line 1630 of file TF1.cxx.

GetMethodCall()

TMethodCall * TF1::GetMethodCall ( ) const

inline

Definition at line 478 of file TF1.h.

GetMinimum()

Double_t TF1::GetMinimum ( Double_t  xmin = 0, Double_t  xmax = 0, Double_t  epsilon = 1.E-10, Int_t  maxiter = 100, Bool_t  logx = false  ) const

virtual

Returns the minimum value of the function on the (xmin, xmax) interval.

Method: First, the grid search is used to bracket the maximum with the step size = (xmax-xmin)/fNpx. This way, the step size can be controlled via the SetNpx() function. If the function is unimodal or if its extrema are far apart, setting the fNpx to a small value speeds the algorithm up many times. Then, Brent's method is applied on the bracketed interval epsilon (default = 1.E-10) controls the relative accuracy (if |x| > 1 ) and absolute (if |x| < 1) and maxiter (default = 100) controls the maximum number of iteration of the Brent algorithm If the flag logx is set the grid search is done in log step size This is done automatically if the log scale is set in the current Pad

NOTE: see also TF1::GetMaximumX and TF1::GetX

Reimplemented in TF2.

Definition at line 1671 of file TF1.cxx.

GetMinimumStored()

virtual Double_t TF1::GetMinimumStored ( ) const

inlinevirtual

Definition at line 461 of file TF1.h.

GetMinimumX()

Double_t TF1::GetMinimumX ( Double_t  xmin = 0, Double_t  xmax = 0, Double_t  epsilon = 1.E-10, Int_t  maxiter = 100, Bool_t  logx = false  ) const

virtual

Returns the X value corresponding to the minimum value of the function on the (xmin, xmax) interval.

Method: First, the grid search is used to bracket the maximum with the step size = (xmax-xmin)/fNpx. This way, the step size can be controlled via the SetNpx() function. If the function is unimodal or if its extrema are far apart, setting the fNpx to a small value speeds the algorithm up many times. Then, Brent's method is applied on the bracketed interval epsilon (default = 1.E-10) controls the relative accuracy (if |x| > 1 ) and absolute (if |x| < 1) and maxiter (default = 100) controls the maximum number of iteration of the Brent algorithm If the flag logx is set the grid search is done in log step size This is done automatically if the log scale is set in the current Pad

NOTE: see also TF1::GetX

Definition at line 1798 of file TF1.cxx.

GetMinMaxNDim()

Double_t TF1::GetMinMaxNDim ( Double_t *  x, Bool_t  findmax, Double_t  epsilon = 0, Int_t  maxiter = 0  ) const

virtual

Find the minimum of a function of whatever dimension.

While GetMinimum works only for 1D function , GetMinimumNDim works for all dimensions since it uses the minimizer interface vector x at beginning will contained the initial point, on exit will contain the result

Definition at line 1698 of file TF1.cxx.

GetNDF()

Int_t TF1::GetNDF ( ) const

virtual

Return the number of degrees of freedom in the fit the fNDF parameter has been previously computed during a fit.

The number of degrees of freedom corresponds to the number of points used in the fit minus the number of free parameters.

Definition at line 1863 of file TF1.cxx.

GetNdim()

virtual Int_t TF1::GetNdim ( ) const

inlinevirtual

Definition at line 469 of file TF1.h.

GetNpar()

virtual Int_t TF1::GetNpar ( ) const

inlinevirtual

Definition at line 465 of file TF1.h.

GetNpx()

virtual Int_t TF1::GetNpx ( ) const

inlinevirtual

Definition at line 474 of file TF1.h.

GetNumber()

virtual Int_t TF1::GetNumber ( ) const

inlinevirtual

Definition at line 482 of file TF1.h.

GetNumberFitPoints()

virtual Int_t TF1::GetNumberFitPoints ( ) const

inlinevirtual

Definition at line 487 of file TF1.h.

GetNumberFreeParameters()

Int_t TF1::GetNumberFreeParameters ( ) const

virtual

Return the number of free parameters.

Definition at line 1874 of file TF1.cxx.

GetObjectInfo()

char * TF1::GetObjectInfo ( Int_t  px, Int_t  py  ) const

virtual

Redefines TObject::GetObjectInfo.

Displays the function info (x, function value) corresponding to cursor position px,py

Reimplemented from TObject.

Reimplemented in TF2.

Definition at line 1892 of file TF1.cxx.

GetParameter() [1/2]

virtual Double_t TF1::GetParameter ( const TString &  name ) const

inlinevirtual

Definition at line 500 of file TF1.h.

GetParameter() [2/2]

virtual Double_t TF1::GetParameter ( Int_t  ipar ) const

inlinevirtual

Definition at line 496 of file TF1.h.

GetParameters() [1/2]

virtual Double_t * TF1::GetParameters ( ) const

inlinevirtual

Definition at line 504 of file TF1.h.

GetParameters() [2/2]

virtual void TF1::GetParameters ( Double_t *  params )

inlinevirtual

Definition at line 508 of file TF1.h.

GetParent()

TObject * TF1::GetParent ( ) const

inline

Definition at line 492 of file TF1.h.

GetParError()

Double_t TF1::GetParError ( Int_t  ipar ) const

virtual

Return value of parameter number ipar.

Definition at line 1904 of file TF1.cxx.

GetParErrors()

virtual const Double_t * TF1::GetParErrors ( ) const

inlinevirtual

Definition at line 522 of file TF1.h.

GetParLimits()

void TF1::GetParLimits ( Int_t  ipar, Double_t &  parmin, Double_t &  parmax  ) const

virtual

Return limits for parameter ipar.

Definition at line 1914 of file TF1.cxx.

GetParName()

virtual const char * TF1::GetParName ( Int_t  ipar ) const

inlinevirtual

Definition at line 513 of file TF1.h.

GetParNumber()

virtual Int_t TF1::GetParNumber ( const char *  name ) const

inlinevirtual

Definition at line 517 of file TF1.h.

GetProb()

Double_t TF1::GetProb ( ) const

virtual

Return the fit probability.

Definition at line 1929 of file TF1.cxx.

GetQuantiles()

Int_t TF1::GetQuantiles ( Int_t  nprobSum, Double_t *  q, const Double_t *  probSum  )

virtual

Compute Quantiles for density distribution of this function.

Quantile x_q of a probability distribution Function F is defined as

$$F(x_{q}) = \int_{xmin}^{x_{q}} f dx = q with 0 <= q <= 1.$$

For instance the median $x_{\frac{1}{2}}$ of a distribution is defined as that value of the random variable for which the distribution function equals 0.5:

$$F(x_{\frac{1}{2}}) = \prod(x < x_{\frac{1}{2}}) = \frac{1}{2}$$

Parameters

[in]	this	TF1 function
[in]	nprobSum	maximum size of array q and size of array probSum
[in]	probSum	array of positions where quantiles will be computed. It is assumed to contain at least nprobSum values.
[out]	return	value nq (<=nprobSum) with the number of quantiles computed
[out]	array	q filled with nq quantiles

Getting quantiles from two histograms and storing results in a TGraph, a so-called QQ-plot

TGraph *gr = new TGraph(nprob);
f1->GetQuantiles(nprob,gr->GetX());
f2->GetQuantiles(nprob,gr->GetY());
gr->Draw("alp");

Author

Eddy Offermann

Definition at line 1967 of file TF1.cxx.

GetRandom() [1/2]

Double_t TF1::GetRandom ( )

virtual

Return a random number following this function shape.

The distribution contained in the function fname (TF1) is integrated over the channel contents. It is normalized to 1. For each bin the integral is approximated by a parabola. The parabola coefficients are stored as non persistent data members Getting one random number implies:

• Generating a random number between 0 and 1 (say r1)
• Look in which bin in the normalized integral r1 corresponds to
• Evaluate the parabolic curve in the selected bin to find the corresponding X value.

If the ratio fXmax/fXmin > fNpx the integral is tabulated in log scale in x The parabolic approximation is very good as soon as the number of bins is greater than 50.

Reimplemented in TF2.

Definition at line 2068 of file TF1.cxx.

GetRandom() [2/2]

Double_t TF1::GetRandom ( Double_t  xmin, Double_t  xmax  )

virtual

Return a random number following this function shape in [xmin,xmax].

The distribution contained in the function fname (TF1) is integrated over the channel contents. It is normalized to 1. For each bin the integral is approximated by a parabola. The parabola coefficients are stored as non persistent data members Getting one random number implies:

• Generating a random number between 0 and 1 (say r1)
• Look in which bin in the normalized integral r1 corresponds to
• Evaluate the parabolic curve in the selected bin to find the corresponding X value.

The parabolic approximation is very good as soon as the number of bins is greater than 50.

IMPORTANT NOTE

The integral of the function is computed at fNpx points. If the function has sharp peaks, you should increase the number of points (SetNpx) such that the peak is correctly tabulated at several points.

Reimplemented in TF2.

Definition at line 2180 of file TF1.cxx.

GetRange() [1/4]

void TF1::GetRange ( Double_t &  xmin, Double_t &  xmax  ) const

virtual

Return range of a 1-D function.

Reimplemented in TF2, TF3, and TF3.

Definition at line 2284 of file TF1.cxx.

GetRange() [2/4]

void TF1::GetRange ( Double_t &  xmin, Double_t &  ymin, Double_t &  xmax, Double_t &  ymax  ) const

virtual

Return range of a 2-D function.

Reimplemented in TF2, TF2, TF3, and TF3.

Definition at line 2294 of file TF1.cxx.

GetRange() [3/4]

void TF1::GetRange ( Double_t &  xmin, Double_t &  ymin, Double_t &  zmin, Double_t &  xmax, Double_t &  ymax, Double_t &  zmax  ) const

virtual

Return range of function.

Reimplemented in TF2, TF2, TF3, and TF3.

Definition at line 2306 of file TF1.cxx.

GetRange() [4/4]

void TF1::GetRange ( Double_t *  xmin, Double_t *  xmax  ) const

virtual

Return range of a generic N-D function.

Reimplemented in TF2, and TF3.

Definition at line 2257 of file TF1.cxx.

GetSave()

Double_t TF1::GetSave ( const Double_t *  x )

virtual

Get value corresponding to X in array of fSave values.

Reimplemented in TF2, and TF3.

Definition at line 2320 of file TF1.cxx.

GetVariable()

virtual Double_t TF1::GetVariable ( const TString &  name )

inlinevirtual

Definition at line 547 of file TF1.h.

GetX()

Double_t TF1::GetX ( Double_t  fy, Double_t  xmin = 0, Double_t  xmax = 0, Double_t  epsilon = 1.E-10, Int_t  maxiter = 100, Bool_t  logx = false  ) const

virtual

Returns the X value corresponding to the function value fy for (xmin<x<xmax).

in other words it can find the roots of the function when fy=0 and successive calls by changing the next call to [xmin+eps,xmax] where xmin is the previous root.

Method: First, the grid search is used to bracket the maximum with the step size = (xmax-xmin)/fNpx. This way, the step size can be controlled via the SetNpx() function. If the function is unimodal or if its extrema are far apart, setting the fNpx to a small value speeds the algorithm up many times. Then, Brent's method is applied on the bracketed interval epsilon (default = 1.E-10) controls the relative accuracy (if |x| > 1 ) and absolute (if |x| < 1) and maxiter (default = 100) controls the maximum number of iteration of the Brent algorithm If the flag logx is set the grid search is done in log step size This is done automatically if the log scale is set in the current Pad

NOTE: see also TF1::GetMaximumX, TF1::GetMinimumX

Definition at line 1838 of file TF1.cxx.

GetXaxis()

TAxis * TF1::GetXaxis

(

)

const

Get x axis of the function.

Definition at line 2376 of file TF1.cxx.

GetXmax()

virtual Double_t TF1::GetXmax ( ) const

inlinevirtual

Definition at line 540 of file TF1.h.

GetXmin()

virtual Double_t TF1::GetXmin ( ) const

inlinevirtual

Definition at line 536 of file TF1.h.

GetYaxis()

TAxis * TF1::GetYaxis

(

)

const

Get y axis of the function.

Definition at line 2387 of file TF1.cxx.

GetZaxis()

TAxis * TF1::GetZaxis

(

)

const

Get z axis of the function. (In case this object is a TF2 or TF3)

Definition at line 2398 of file TF1.cxx.

GradientPar() [1/4]

void TF1::GradientPar ( const Double_t *  x, Double_t *  grad, Double_t  eps = 0.01  )

virtual

Compute the gradient wrt parameters.

Parameters

x	point, were the gradient is computed
grad	used to return the computed gradient, assumed to be of at least fNpar size
eps	if the errors of parameters have been computed, the step used in numerical differentiation is eps*parameter_error.

if the errors have not been computed, step=eps is used default value of eps = 0.01 Method is the same as in Derivative() function

If a parameter is fixed, the gradient on this parameter = 0

Definition at line 2440 of file TF1.cxx.

GradientPar() [2/4]

template<class T >

void TF1::GradientPar ( const T *  x, T *  grad, Double_t  eps = 0.01  )

inline

Definition at line 905 of file TF1.h.

GradientPar() [3/4]

Double_t TF1::GradientPar ( Int_t  ipar, const Double_t *  x, Double_t  eps = 0.01  )

virtual

Compute the gradient (derivative) wrt a parameter ipar.

Parameters

ipar	index of parameter for which the derivative is computed
x	point, where the derivative is computed
eps	- if the errors of parameters have been computed, the step used in numerical differentiation is eps*parameter_error.

if the errors have not been computed, step=eps is used default value of eps = 0.01 Method is the same as in Derivative() function

If a parameter is fixed, the gradient on this parameter = 0

Definition at line 2421 of file TF1.cxx.

GradientPar() [4/4]

template<class T >

T TF1::GradientPar ( Int_t  ipar, const T *  x, Double_t  eps = 0.01  )

inline

Definition at line 838 of file TF1.h.

GradientParTempl() [1/2]

template<class T >

void TF1::GradientParTempl ( const T *  x, T *  grad, Double_t  eps = 0.01  )

inline

Definition at line 914 of file TF1.h.

GradientParTempl() [2/2]

template<class T >

T TF1::GradientParTempl ( Int_t  ipar, const T *  x, Double_t  eps = 0.01  )

inline

Definition at line 847 of file TF1.h.

InitArgs()

void TF1::InitArgs ( const Double_t *  x, const Double_t *  params  )

virtual

Initialize parameters addresses.

Definition at line 2448 of file TF1.cxx.

InitStandardFunctions()

void TF1::InitStandardFunctions ( )

static

Create the basic function objects.

Definition at line 2463 of file TF1.cxx.

Integral()

Double_t TF1::Integral ( Double_t  a, Double_t  b, Double_t  epsrel = 1.e-12  )

virtual

IntegralOneDim or analytical integral.

Reimplemented in TF2, and TF3.

Definition at line 2496 of file TF1.cxx.

IntegralError() [1/2]

Double_t TF1::IntegralError ( Double_t  a, Double_t  b, const Double_t *  params = 0, const Double_t *  covmat = 0, Double_t  epsilon = 1.E-2  )

virtual

Return Error on Integral of a parametric function between a and b due to the parameter uncertainties.

A pointer to a vector of parameter values and to the elements of the covariance matrix (covmat) can be optionally passed. By default (i.e. when a zero pointer is passed) the current stored parameter values are used to estimate the integral error together with the covariance matrix from the last fit (retrieved from the global fitter instance)

IMPORTANT NOTE1:

When no covariance matrix is passed and in the meantime a fit is done using another function, the routine will signal an error and it will return zero only when the number of fit parameter is different than the values stored in TF1 (TF1::GetNpar() ). In the case that npar is the same, an incorrect result is returned.

IMPORTANT NOTE2:

The user must pass a pointer to the elements of the full covariance matrix dimensioned with the right size (npar*npar), where npar is the total number of parameters (TF1::GetNpar()), including also the fixed parameters. When there are fixed parameters, the pointer returned from TVirtualFitter::GetCovarianceMatrix() cannot be used. One should use the TFitResult class, as shown in the example below.

To get the matrix and values from an old fit do for example: TFitResultPtr r = histo->Fit(func, "S"); ..... after performing other fits on the same function do

func->IntegralError(x1,x2,r->GetParams(), r->GetCovarianceMatrix()->GetMatrixArray() ); 

Definition at line 2683 of file TF1.cxx.

IntegralError() [2/2]

Double_t TF1::IntegralError ( Int_t  n, const Double_t *  a, const Double_t *  b, const Double_t *  params = 0, const Double_t *  covmat = 0, Double_t  epsilon = 1.E-2  )

virtual

Return Error on Integral of a parametric function with dimension larger tan one between a[] and b[] due to the parameters uncertainties.

For a TF1 with dimension larger than 1 (for example a TF2 or TF3) TF1::IntegralMultiple is used for the integral calculation

A pointer to a vector of parameter values and to the elements of the covariance matrix (covmat) can be optionally passed. By default (i.e. when a zero pointer is passed) the current stored parameter values are used to estimate the integral error together with the covariance matrix from the last fit (retrieved from the global fitter instance).

IMPORTANT NOTE1:

When no covariance matrix is passed and in the meantime a fit is done using another function, the routine will signal an error and it will return zero only when the number of fit parameter is different than the values stored in TF1 (TF1::GetNpar() ). In the case that npar is the same, an incorrect result is returned.

IMPORTANT NOTE2:

The user must pass a pointer to the elements of the full covariance matrix dimensioned with the right size (npar*npar), where npar is the total number of parameters (TF1::GetNpar()), including also the fixed parameters. When there are fixed parameters, the pointer returned from TVirtualFitter::GetCovarianceMatrix() cannot be used. One should use the TFitResult class, as shown in the example below.

To get the matrix and values from an old fit do for example: TFitResultPtr r = histo->Fit(func, "S"); ..... after performing other fits on the same function do

func->IntegralError(x1,x2,r->GetParams(), r->GetCovarianceMatrix()->GetMatrixArray() ); 

Definition at line 2722 of file TF1.cxx.

IntegralFast()

Double_t TF1::IntegralFast ( Int_t  num, Double_t *  x, Double_t *  w, Double_t  a, Double_t  b, Double_t *  params = 0, Double_t  epsilon = 1e-12  )

virtual

Gauss-Legendre integral, see CalcGaussLegendreSamplingPoints.

Definition at line 2742 of file TF1.cxx.

IntegralMultiple() [1/3]

Double_t TF1::IntegralMultiple ( Int_t  n, const Double_t *  a, const Double_t *  b, Double_t  epsrel, Double_t &  relerr  )

virtual

See more general prototype below.

This interface kept for back compatibility It is recommended to use the other interface where one can specify also epsabs and the maximum number of points

Definition at line 2762 of file TF1.cxx.

IntegralMultiple() [2/3]

Double_t TF1::IntegralMultiple ( Int_t  n, const Double_t *  a, const Double_t *  b, Int_t  maxpts, Double_t  epsrel, Double_t  epsabs, Double_t &  relerr, Int_t &  nfnevl, Int_t &  ifail  )

virtual

This function computes, to an attempted specified accuracy, the value of the integral.

Parameters

[in]	n	Number of dimensions [2,15]
[in]	a,b	One-dimensional arrays of length >= N . On entry A[i], and B[i], contain the lower and upper limits of integration, respectively.
[in]	maxpts	Maximum number of function evaluations to be allowed. maxpts >= 2^n +2*n*(n+1) +1 if maxpts<minpts, maxpts is set to 10*minpts
[in]	epsrel	Specified relative accuracy.
[in]	epsabs	Specified absolute accuracy. The integration algorithm will attempt to reach either the relative or the absolute accuracy. In case the maximum function called is reached the algorithm will stop earlier without having reached the desired accuracy
[out]	relerr	Contains, on exit, an estimation of the relative accuracy of the result.
[out]	nfnevl	number of function evaluations performed.
[out]	ifail	0 Normal exit. At least minpts and at most maxpts calls to the function were performed. 1 maxpts is too small for the specified accuracy eps. The result and relerr contain the values obtainable for the specified value of maxpts. 3 n<2 or n>15

Method:

The default method used is the Genz-Mallik adaptive multidimensional algorithm using the class ROOT::Math::AdaptiveIntegratorMultiDim (see the reference documentation of the class)

Other methods can be used by setting ROOT::Math::IntegratorMultiDimOptions::SetDefaultIntegrator() to different integrators. Other possible integrators are MC integrators based on the ROOT::Math::GSLMCIntegrator class Possible methods are : Vegas, Miser or Plain IN case of MC integration the accuracy is determined by the number of function calls, one should be careful not to use a too large value of maxpts

Definition at line 2815 of file TF1.cxx.

IntegralMultiple() [3/3]

virtual Double_t TF1::IntegralMultiple ( Int_t  n, const Double_t *  a, const Double_t *  b, Int_t  , Int_t  maxpts, Double_t  epsrel, Double_t &  relerr, Int_t &  nfnevl, Int_t &  ifail  )

inlinevirtual

Definition at line 572 of file TF1.h.

IntegralOneDim()

Double_t TF1::IntegralOneDim ( Double_t  a, Double_t  b, Double_t  epsrel, Double_t  epsabs, Double_t &  error  )

virtual

Return Integral of function between a and b using the given parameter values and relative and absolute tolerance.

The default integrator defined in ROOT::Math::IntegratorOneDimOptions::DefaultIntegrator() is used If ROOT contains the MathMore library the default integrator is set to be the adaptive ROOT::Math::GSLIntegrator (based on QUADPACK) or otherwise the ROOT::Math::GaussIntegrator is used See the reference documentation of these classes for more information about the integration algorithms To change integration algorithm just do : ROOT::Math::IntegratorOneDimOptions::SetDefaultIntegrator(IntegratorName); Valid integrator names are:

• Gauss : for ROOT::Math::GaussIntegrator
• GaussLegendre : for ROOT::Math::GaussLegendreIntegrator
• Adaptive : for ROOT::Math::GSLIntegrator adaptive method (QAG)
• AdaptiveSingular : for ROOT::Math::GSLIntegrator adaptive singular method (QAGS)
• NonAdaptive : for ROOT::Math::GSLIntegrator non adaptive (QNG)

In order to use the GSL integrators one needs to have the MathMore library installed

Note 1:

Values of the function f(x) at the interval end-points A and B are not required. The subprogram may therefore be used when these values are undefined.

Note 2:

Instead of TF1::Integral, you may want to use the combination of TF1::CalcGaussLegendreSamplingPoints and TF1::IntegralFast. See an example with the following script:

void gint() {
   TF1 *g = new TF1("g","gaus",-5,5);
   g->SetParameters(1,0,1);
   //default gaus integration method uses 6 points
   //not suitable to integrate on a large domain
   double r1 = g->Integral(0,5);
   double r2 = g->Integral(0,1000);
 
   //try with user directives computing more points
   Int_t np = 1000;
   double *x=new double[np];
   double *w=new double[np];
   g->CalcGaussLegendreSamplingPoints(np,x,w,1e-15);
   double r3 = g->IntegralFast(np,x,w,0,5);
   double r4 = g->IntegralFast(np,x,w,0,1000);
   double r5 = g->IntegralFast(np,x,w,0,10000);
   double r6 = g->IntegralFast(np,x,w,0,100000);
   printf("g->Integral(0,5)               = %g\n",r1);
   printf("g->Integral(0,1000)            = %g\n",r2);
   printf("g->IntegralFast(n,x,w,0,5)     = %g\n",r3);
   printf("g->IntegralFast(n,x,w,0,1000)  = %g\n",r4);
   printf("g->IntegralFast(n,x,w,0,10000) = %g\n",r5);
   printf("g->IntegralFast(n,x,w,0,100000)= %g\n",r6);
   delete [] x;
   delete [] w;
}

This example produces the following results:

g->Integral(0,5)               = 1.25331
g->Integral(0,1000)            = 1.25319
g->IntegralFast(n,x,w,0,5)     = 1.25331
g->IntegralFast(n,x,w,0,1000)  = 1.25331
g->IntegralFast(n,x,w,0,10000) = 1.25331
g->IntegralFast(n,x,w,0,100000)= 1.253

Definition at line 2586 of file TF1.cxx.

IntegrateForNormalization()

void TF1::IntegrateForNormalization

(

)

IsEvalNormalized()

virtual Bool_t TF1::IsEvalNormalized ( ) const

inlinevirtual

Definition at line 577 of file TF1.h.

IsInside()

virtual Bool_t TF1::IsInside ( const Double_t *  x ) const

inlinevirtual

return kTRUE if the point is inside the function range

Reimplemented in TF2, and TF3.

Definition at line 582 of file TF1.h.

IsLinear()

virtual Bool_t TF1::IsLinear ( ) const

inlinevirtual

Definition at line 586 of file TF1.h.

IsValid()

Bool_t TF1::IsValid ( ) const

virtual

Return kTRUE if the function is valid.

Definition at line 2846 of file TF1.cxx.

IsVectorized()

bool TF1::IsVectorized ( )

inline

Definition at line 424 of file TF1.h.

Mean()

virtual Double_t TF1::Mean ( Double_t  a, Double_t  b, const Double_t *  params = 0, Double_t  epsilon = 0.000001  )

inlinevirtual

Definition at line 676 of file TF1.h.

Moment()

Double_t TF1::Moment ( Double_t  n, Double_t  a, Double_t  b, const Double_t *  params = 0, Double_t  epsilon = 0.000001  )

virtual

Return nth moment of function between a and b.

See TF1::Integral() for parameter definitions

Definition at line 3663 of file TF1.cxx.

operator()() [1/2]

template<class T >

T TF1::operator() ( const T *  x, const Double_t *  params = nullptr  )

inline

Definition at line 746 of file TF1.h.

operator()() [2/2]

Double_t TF1::operator() ( Double_t  x, Double_t  y = 0, Double_t  z = 0, Double_t  t = 0  ) const

inlinevirtual

Definition at line 740 of file TF1.h.

operator=()

TF1 & TF1::operator=

(

const TF1 &

rhs

)

Operator =.

Definition at line 927 of file TF1.cxx.

Paint()

void TF1::Paint ( Option_t *  choptin = "" )

virtual

Paint this function with its current attributes.

The function is going to be converted in an histogram and the corresponding histogram is painted. The painted histogram can be retrieved calling afterwards the method TF1::GetHistogram()

Reimplemented from TObject.

Reimplemented in TF2, and TF3.

Definition at line 2917 of file TF1.cxx.

Print()

void TF1::Print ( Option_t *  option = "" ) const

virtual

Print TNamed name and title.

Reimplemented from TNamed.

Definition at line 2861 of file TF1.cxx.

RejectedPoint()

Bool_t TF1::RejectedPoint ( )

static

See TF1::RejectPoint above.

Definition at line 3653 of file TF1.cxx.

RejectPoint()

void TF1::RejectPoint ( Bool_t  reject = kTRUE )

static

Static function to set the global flag to reject points the fgRejectPoint global flag is tested by all fit functions if TRUE the point is not included in the fit.

This flag can be set by a user in a fitting function. The fgRejectPoint flag is reset by the TH1 and TGraph fitting functions.

Definition at line 3644 of file TF1.cxx.

ReleaseParameter()

void TF1::ReleaseParameter ( Int_t  ipar )

virtual

Release parameter number ipar If used in a fit, the parameter can vary freely.

The parameter limits are reset to 0,0.

Definition at line 3117 of file TF1.cxx.

Save()

void TF1::Save ( Double_t  xmin, Double_t  xmax, Double_t  ymin, Double_t  ymax, Double_t  zmin, Double_t  zmax  )

virtual

Save values of function in array fSave.

Reimplemented in TF2, and TF3.

Definition at line 3127 of file TF1.cxx.

SavePrimitive()

void TF1::SavePrimitive ( std::ostream &  out, Option_t *  option = ""  )

virtual

Save primitive as a C++ statement(s) on output stream out.

Reimplemented from TObject.

Reimplemented in TF12, TF2, and TF3.

Definition at line 3180 of file TF1.cxx.

SetChisquare()

virtual void TF1::SetChisquare ( Double_t  chi2 )

inlinevirtual

Definition at line 596 of file TF1.h.

SetCurrent()

void TF1::SetCurrent ( TF1 *  f1 )

static

Static function setting the current function.

the current function may be accessed in static C-like functions when fitting or painting a function.

Definition at line 3336 of file TF1.cxx.

SetFitResult()

void TF1::SetFitResult ( const ROOT::Fit::FitResult &  result, const Int_t *  indpar = 0  )

virtual

Set the result from the fit parameter values, errors, chi2, etc... Optionally a pointer to a vector (with size fNpar) of the parameter indices in the FitResult can be passed This is useful in the case of a combined fit with different functions, and the FitResult contains the global result By default it is assume that indpar = {0,1,2,....,fNpar-1}.

Definition at line 3348 of file TF1.cxx.

SetFunction() [1/2]

template<typename Func >

void TF1::SetFunction

(

Func

f

)

Definition at line 823 of file TF1.h.

SetFunction() [2/2]

template<class PtrObj , typename MemFn >

void TF1::SetFunction	(	PtrObj &	p,
		MemFn	memFn
	)

Definition at line 830 of file TF1.h.

SetMaximum()

void TF1::SetMaximum ( Double_t  maximum = -1111 )

virtual

Set the maximum value along Y for this function In case the function is already drawn, set also the maximum in the helper histogram.

Definition at line 3387 of file TF1.cxx.

SetMinimum()

void TF1::SetMinimum ( Double_t  minimum = -1111 )

virtual

Set the minimum value along Y for this function In case the function is already drawn, set also the minimum in the helper histogram.

Definition at line 3400 of file TF1.cxx.

SetNDF()

void TF1::SetNDF ( Int_t  ndf )

virtual

Set the number of degrees of freedom ndf should be the number of points used in a fit - the number of free parameters.

Definition at line 3412 of file TF1.cxx.

SetNormalized()

virtual void TF1::SetNormalized ( Bool_t  flag )

inlinevirtual

Definition at line 612 of file TF1.h.

SetNpx()

void TF1::SetNpx ( Int_t  npx = 100 )

virtual

Set the number of points used to draw the function.

The default number of points along x is 100 for 1-d functions and 30 for 2-d/3-d functions You can increase this value to get a better resolution when drawing pictures with sharp peaks or to get a better result when using TF1::GetRandom the minimum number of points is 4, the maximum is 10000000 for 1-d and 10000 for 2-d/3-d functions

Definition at line 3426 of file TF1.cxx.

SetNumberFitPoints()

virtual void TF1::SetNumberFitPoints ( Int_t  npfits )

inlinevirtual

Definition at line 608 of file TF1.h.

SetParameter() [1/2]

virtual void TF1::SetParameter ( const TString &  name, Double_t  value  )

inlinevirtual

Definition at line 623 of file TF1.h.

SetParameter() [2/2]

virtual void TF1::SetParameter ( Int_t  param, Double_t  value  )

inlinevirtual

Definition at line 618 of file TF1.h.

SetParameters() [1/2]

virtual void TF1::SetParameters ( const Double_t *  params )

inlinevirtual

Definition at line 628 of file TF1.h.

SetParameters() [2/2]

virtual void TF1::SetParameters ( Double_t  p0, Double_t  p1, Double_t  p2 = 0, Double_t  p3 = 0, Double_t  p4 = 0, Double_t  p5 = 0, Double_t  p6 = 0, Double_t  p7 = 0, Double_t  p8 = 0, Double_t  p9 = 0, Double_t  p10 = 0  )

inlinevirtual

Definition at line 633 of file TF1.h.

SetParent()

virtual void TF1::SetParent ( TObject *  p = 0 )

inlinevirtual

Definition at line 649 of file TF1.h.

SetParError()

void TF1::SetParError ( Int_t  ipar, Double_t  error  )

virtual

Set error for parameter number ipar.

Definition at line 3466 of file TF1.cxx.

SetParErrors()

void TF1::SetParErrors ( const Double_t *  errors )

virtual

Set errors for all active parameters when calling this function, the array errors must have at least fNpar values.

Definition at line 3477 of file TF1.cxx.

SetParLimits()

void TF1::SetParLimits ( Int_t  ipar, Double_t  parmin, Double_t  parmax  )

virtual

Set limits for parameter ipar.

The specified limits will be used in a fit operation when the option "B" is specified (Bounds). To fix a parameter, use TF1::FixParameter

Definition at line 3491 of file TF1.cxx.

SetParName()

void TF1::SetParName ( Int_t  ipar, const char *  name  )

virtual

Set name of parameter number ipar.

Definition at line 3443 of file TF1.cxx.

SetParNames()

void TF1::SetParNames ( const char *  name0 = "p0", const char *  name1 = "p1", const char *  name2 = "p2", const char *  name3 = "p3", const char *  name4 = "p4", const char *  name5 = "p5", const char *  name6 = "p6", const char *  name7 = "p7", const char *  name8 = "p8", const char *  name9 = "p9", const char *  name10 = "p10"  )

virtual

Set up to 10 parameter names.

Definition at line 3455 of file TF1.cxx.

SetRange() [1/3]

void TF1::SetRange ( Double_t  xmin, Double_t  xmax  )

virtual

Initialize the upper and lower bounds to draw the function.

The function range is also used in an histogram fit operation when the option "R" is specified.

Reimplemented in TF2, and TF3.

Definition at line 3512 of file TF1.cxx.

SetRange() [2/3]

void TF1::SetRange ( Double_t  xmin, Double_t  ymin, Double_t  xmax, Double_t  ymax  )

inlinevirtual

Reimplemented in TF2, and TF3.

Definition at line 813 of file TF1.h.

SetRange() [3/3]

void TF1::SetRange ( Double_t  xmin, Double_t  ymin, Double_t  zmin, Double_t  xmax, Double_t  ymax, Double_t  zmax  )

inlinevirtual

Reimplemented in TF2, and TF3.

Definition at line 817 of file TF1.h.

SetSavedPoint()

void TF1::SetSavedPoint ( Int_t  point, Double_t  value  )

virtual

Restore value of function saved at point.

Definition at line 3526 of file TF1.cxx.

SetTitle()

void TF1::SetTitle ( const char *  title = "" )

virtual

Set function title if title has the form "fffffff;xxxx;yyyy", it is assumed that the function title is "fffffff" and "xxxx" and "yyyy" are the titles for the X and Y axis respectively.

Reimplemented from TNamed.

Definition at line 3542 of file TF1.cxx.

SetVectorized()

virtual void TF1::SetVectorized ( Bool_t  vectorized )

inlinevirtual

Definition at line 658 of file TF1.h.

TermCoeffLength()

int TF1::TermCoeffLength ( TString &  term )

private

Definition at line 909 of file TF1.cxx.

Update()

void TF1::Update ( )

virtual

Called by functions such as SetRange, SetNpx, SetParameters to force the deletion of the associated histogram or Integral.

Definition at line 3609 of file TF1.cxx.

Variance()

virtual Double_t TF1::Variance ( Double_t  a, Double_t  b, const Double_t *  params = 0, Double_t  epsilon = 0.000001  )

inlinevirtual

Definition at line 680 of file TF1.h.

Friends And Related Function Documentation

ROOT::Internal::TF1Builder

template<class Func >

friend struct ROOT::Internal::TF1Builder

friend

Definition at line 214 of file TF1.h.

Member Data Documentation

fAlpha

std::vector<Double_t> TF1::fAlpha

protected

Integral of function binned on fNpx bins.

Definition at line 251 of file TF1.h.

fBeta

std::vector<Double_t> TF1::fBeta

protected

Array alpha. for each bin in x the deconvolution r of fIntegral.

Definition at line 252 of file TF1.h.

fChisquare

Double_t TF1::fChisquare {}

protected

Definition at line 243 of file TF1.h.

fComposition

std::unique_ptr<TF1AbsComposition> TF1::fComposition

protected

Definition at line 262 of file TF1.h.

fComposition_ptr

TF1AbsComposition* TF1::fComposition_ptr {nullptr}

protected

Pointer to composition (NSUM or CONV)

Definition at line 263 of file TF1.h.

fFormula

TFormula* TF1::fFormula {nullptr}

protected

Functor object to wrap any C++ callable object.

Definition at line 260 of file TF1.h.

fFunctor

TF1FunctorPointer* TF1::fFunctor {nullptr}

protected

Definition at line 259 of file TF1.h.

fgAbsValue

std::atomic< Bool_t > TF1::fgAbsValue

static

Definition at line 293 of file TF1.h.

fgAddToGlobList

std::atomic< Bool_t > TF1::fgAddToGlobList

static

Definition at line 295 of file TF1.h.

fGamma

std::vector<Double_t> TF1::fGamma

protected

Array beta. is approximated by x = alpha +beta*r *gamma*r**2.

Definition at line 253 of file TF1.h.

fgCurrent

TF1 * TF1::fgCurrent = 0

static

Definition at line 296 of file TF1.h.

fgRejectPoint

Bool_t TF1::fgRejectPoint = kFALSE

static

Definition at line 294 of file TF1.h.

fHistogram

TH1* TF1::fHistogram {nullptr}

protected

Parent object hooking this function (if one)

Definition at line 255 of file TF1.h.

fIntegral

std::vector<Double_t> TF1::fIntegral

protected

Definition at line 250 of file TF1.h.

fMaximum

Double_t TF1::fMaximum {-1111}

protected

Definition at line 245 of file TF1.h.

fMethodCall

TMethodCall* TF1::fMethodCall {nullptr}

protected

Pointer to histogram used for visualisation.

Definition at line 256 of file TF1.h.

fMinimum

Double_t TF1::fMinimum {-1111}

protected

Definition at line 244 of file TF1.h.

fNDF

Int_t TF1::fNDF {}

protected

Definition at line 242 of file TF1.h.

fNdim

Int_t TF1::fNdim {}

protected

Definition at line 238 of file TF1.h.

fNormalized

Bool_t TF1::fNormalized {false}

protected

Pointer to MethodCall in case of interpreted function.

Definition at line 257 of file TF1.h.

fNormIntegral

Double_t TF1::fNormIntegral {}

protected

Definition at line 258 of file TF1.h.

fNpar

Int_t TF1::fNpar {}

protected

Definition at line 237 of file TF1.h.

fNpfits

Int_t TF1::fNpfits {}

protected

Definition at line 241 of file TF1.h.

fNpx

Int_t TF1::fNpx {100}

protected

Definition at line 239 of file TF1.h.

fParams

TF1Parameters* TF1::fParams {nullptr}

protected

Definition at line 261 of file TF1.h.

fParent

TObject* TF1::fParent {nullptr}

protected

Array gamma.

Definition at line 254 of file TF1.h.

fParErrors

std::vector<Double_t> TF1::fParErrors

protected

Definition at line 246 of file TF1.h.

fParMax

std::vector<Double_t> TF1::fParMax

protected

Definition at line 248 of file TF1.h.

fParMin

std::vector<Double_t> TF1::fParMin

protected

Definition at line 247 of file TF1.h.

fSave

std::vector<Double_t> TF1::fSave

protected

Definition at line 249 of file TF1.h.

fType

EFType TF1::fType {EFType::kTemplScalar}

protected

Definition at line 240 of file TF1.h.

fXmax

Double_t TF1::fXmax {-1111}

protected

Definition at line 236 of file TF1.h.

fXmin

Double_t TF1::fXmin {-1111}

protected

Definition at line 235 of file TF1.h.

Libraries for TF1:

[legend]