TF1 Class Reference

1-Dim function class

Python interface

The TF1 class has several additions for its use from Python, which are also available in its subclasses TF2 and TF3.

First, TF1 instance can be initialized with user-defined Python functions. Given a generic Python callable, the following can performed:

def func(x: numpy.ndarray, pars: numpy.ndarray) -> float:
    return pars[0] * x[0] * x[0] + x[1] * pars[0]
 
my_func = ROOT.TF1("my_func", func, -10, 10, npar=2, ndim=2)

Second, after performing the initialisation with a Python functor, the TF1 instance can be evaluated using the Pythonized TF1.EvalPar function. The pythonization allows passing in 1D(single set of x variables) or 2D(a dataset) NumPy arrays.

The following example shows how we can create a TF1 instance with a Python function and evaluate it on a dataset:

import ROOT
import math
import numpy as np
 
def pyf_tf1_coulomb(x, p):
    return p[1] * x[0] * x[1] / (p[0]**2) * math.exp(-p[2] / p[0])
 
rtf1_coulomb = ROOT.TF1("my_func", pyf_tf1_coulomb, -10, 10, ndims = 2, npars = 3)
 
# x dataset: 5 pairs of particle charges
x = np.array([
    [1.0, 10, 2.0],
    [1.5, 10, 2.5],
    [2.0, 10, 3.0],
    [2.5, 10, 3.5],
    [3.0, 10, 4.0]
])
 
params = np.array([
    [1.0],       # Distance between charges r
    [8.99e9],    # Coulomb constant k (in N·m²/C²)
    [0.1]        # Additional factor for modulation
])
 
# Slice to avoid the dummy column of 10's
res = rtf1_coulomb.EvalPar(x[:, ::2], params)

The below example defines a TF1 instance using the ROOT constructor, and sets its parameters using the Pythonized TF1.SetParameters function (i.e. without evaluating).

import numpy as np
 
# for illustration, a sinusoidal function with six parameters
myFunction = ROOT.TF1("myExampleFunction", "[0] + [1] * x + [2]*sin([3] * x) + [4]*cos([5] * x)", -5, 5)
 
# declare the parameters as a numpy.array or array.array 
myParams = np.array([0.04, 0.4, 3.0, 3.14, 1.5, 3.14])
 
# note: the following line would also work by setting all six parameters equal to 3.0
# myParams = np.array([3.0] * 6) 
 
myFunction.SetParameters(myParams)

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

{
   auto 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

{
   auto 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); }
....
auto 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:

auto 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:

auto 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

{
    auto 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()
{
   auto f1 = new TF1("myfunc",myfunction,0,10,2);
   f1->SetParameters(2,1);
   f1->SetParNames("constant","coefficient");
   f1->Draw();
}
void myfit()
{
   auto 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:

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

auto g = new TGraph(npointx, xvec, yvec);
auto 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
   auto 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 233 of file TF1.h.

Classes
struct	TF1FunctorPointer
struct	TF1FunctorPointerImpl

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

Public Member Functions
	TF1 ()
	TF1 default constructor.
	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.
	TF1 (const char *name, const char *formula, Double_t xmin=0, Double_t xmax=1, EAddToList addToGlobList=EAddToList::kDefault, bool vectorize=false)
	TF1 constructor using a formula definition.
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.
	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 (const) real function.
	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.
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.
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.
	TF1 (const TF1 &f1)
	~TF1 () override
	TF1 default destructor.
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)
void	Browse (TBrowser *b) override
	Browse.
virtual Double_t	CentralMoment (Double_t n, Double_t a, Double_t b, const Double_t *params=nullptr, 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)
TObject *	Clone (const char *newname=nullptr) const override
	Make a complete copy of the underlying object.
void	Copy (TObject &f1) const override
	Copy this F1 to a new F1.
virtual TH1 *	CreateHistogram ()
virtual Double_t	Derivative (Double_t x, Double_t *params=nullptr, 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.
virtual Double_t	Derivative2 (Double_t x, Double_t *params=nullptr, 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.
virtual Double_t	Derivative3 (Double_t x, Double_t *params=nullptr, 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.
Int_t	DistancetoPrimitive (Int_t px, Int_t py) override
	Compute distance from point px,py to a function.
void	Draw (Option_t *option="") override
	Draw this function with its current attributes.
virtual TF1 *	DrawCopy (Option_t *option="") const
	Draw a copy of this function with its current attributes.
virtual TObject *	DrawDerivative (Option_t *option="al")
	Draw derivative of this function.
virtual void	DrawF1 (Double_t xmin, Double_t xmax, Option_t *option="")
	Draw function between xmin and xmax.
virtual TObject *	DrawIntegral (Option_t *option="al")
	Draw integral of this function.
virtual Double_t	Eval (Double_t x, Double_t y=0, Double_t z=0, Double_t t=0) const
	Evaluate this function.
virtual Double_t	EvalPar (const Double_t *x, const Double_t *params=nullptr)
	Evaluate function with given coordinates and parameters.
template<class T >
T	EvalPar (const T *x, const Double_t *params=nullptr)
	EvalPar for vectorized.
void	ExecuteEvent (Int_t event, Int_t px, Int_t py) override
	Execute action corresponding to one event.
virtual void	FixParameter (Int_t ipar, Double_t value)
	Fix the value of a parameter for a fit operation The specified value will be used in the fit and the parameter will be constant (nor varying) during fitting Note that when using pre-defined functions (e.g gaus), one needs to use the fit option 'B' to have the fix of the paramter effective.
Double_t	GetChisquare () const
	Return the Chisquare after fitting. See ROOT::Fit::FitResult::Chi2()
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 Note that this histogram is managed by the function and in same case it is automatically deleted when some TF1 functions are called such as TF1::SetParameters, TF1::SetNpx, TF1::SetRange It is then reccomended either to clone the return object or calling again teh GetHistogram function whenever is needed.
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.
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.
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.
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.
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.
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.
char *	GetObjectInfo (Int_t px, Int_t py) const override
	Redefines TObject::GetObjectInfo.
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.
virtual const Double_t *	GetParErrors () const
virtual void	GetParLimits (Int_t ipar, Double_t &parmin, Double_t &parmax) const
	Return limits for parameter ipar.
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.
virtual Int_t	GetQuantiles (Int_t n, Double_t *xp, const Double_t *p)
	Compute Quantiles for density distribution of this function.
virtual Double_t	GetRandom (Double_t xmin, Double_t xmax, TRandom *rng=nullptr, Option_t *opt=nullptr)
	Return a random number following this function shape in [xmin,xmax].
virtual Double_t	GetRandom (TRandom *rng=nullptr, Option_t *opt=nullptr)
	Return a random number following this function shape.
virtual void	GetRange (Double_t &xmin, Double_t &xmax) const
	Return range of a 1-D function.
virtual void	GetRange (Double_t &xmin, Double_t &ymin, Double_t &xmax, Double_t &ymax) const
	Return range of a 2-D function.
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.
virtual Double_t	GetSave (const Double_t *x)
	Get value corresponding to X in array of fSave values.
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).
TAxis *	GetXaxis () const
	Get x axis of the function.
virtual Double_t	GetXmax () const
virtual Double_t	GetXmin () const
TAxis *	GetYaxis () const
	Get y axis of the function.
TAxis *	GetZaxis () const
	Get z axis of the function. (In case this object is a TF2 or TF3)
virtual void	GradientPar (const Double_t *x, Double_t *grad, Double_t eps=0.01)
	Compute the gradient wrt parameters If the TF1 object is based on a formula expression (TFormula) and TFormula::GenerateGradientPar() has been successfully called automatic differentiation using CLAD is used instead of the default numerical differentiation.
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.
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)
Bool_t	HasSave () const
	Return true if function has data in fSave buffer.
virtual void	InitArgs (const Double_t *x, const Double_t *params)
	Initialize parameters addresses.
virtual Double_t	Integral (Double_t a, Double_t b, Double_t epsrel=1.e-12)
	IntegralOneDim or analytical integral.
virtual Double_t	IntegralError (Double_t a, Double_t b, const Double_t *params=nullptr, const Double_t *covmat=nullptr, Double_t epsilon=1.E-2)
	Return Error on Integral of a parametric function between a and b due to the parameter uncertainties and their covariance matrix from the fit.
virtual Double_t	IntegralError (Int_t n, const Double_t *a, const Double_t *b, const Double_t *params=nullptr, const Double_t *covmat=nullptr, Double_t epsilon=1.E-2)
	Return Error on Integral of a parametric function with dimension larger than one between a[] and b[] due to the parameters uncertainties.
virtual Double_t	IntegralFast (Int_t num, Double_t *x, Double_t *w, Double_t a, Double_t b, Double_t *params=nullptr, Double_t epsilon=1e-12)
	Gauss-Legendre integral, see CalcGaussLegendreSamplingPoints.
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.
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.
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.
TClass *	IsA () const override
virtual Bool_t	IsEvalNormalized () const
virtual Bool_t	IsInside (const Double_t *x) const
	return kTRUE if the point is inside the function range
virtual Bool_t	IsLinear () const
virtual Bool_t	IsValid () const
	Return kTRUE if the function is valid.
bool	IsVectorized ()
virtual Double_t	Mean (Double_t a, Double_t b, const Double_t *params=nullptr, Double_t epsilon=0.000001)
virtual Double_t	Moment (Double_t n, Double_t a, Double_t b, const Double_t *params=nullptr, Double_t epsilon=0.000001)
	Return nth moment of function between a and b.
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 =.
void	Paint (Option_t *option="") override
	Paint this function with its current attributes.
void	Print (Option_t *option="") const override
	This method must be overridden when a class wants to print itself.
virtual void	ReleaseParameter (Int_t ipar)
	Release parameter number ipar during a fit operation.
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.
void	SavePrimitive (std::ostream &out, Option_t *option="") override
	Save primitive as a C++ statement(s) on output stream out.
virtual void	SetChisquare (Double_t chi2)
virtual void	SetFitResult (const ROOT::Fit::FitResult &result, const Int_t *indpar=nullptr)
	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}.
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.
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.
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.
void	SetNdim (Int_t ndim)
virtual void	SetNormalized (Bool_t flag)
virtual void	SetNpx (Int_t npx=100)
	Set the number of points used to draw the function.
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 p0, double p1=TMath::QuietNaN(), double p2=TMath::QuietNaN(), double p3=TMath::QuietNaN(), double p4=TMath::QuietNaN(), double p5=TMath::QuietNaN(), double p6=TMath::QuietNaN(), double p7=TMath::QuietNaN(), double p8=TMath::QuietNaN(), double p9=TMath::QuietNaN(), double p10=TMath::QuietNaN())
	Set parameter values.
virtual void	SetParent (TObject *p=nullptr)
virtual void	SetParError (Int_t ipar, Double_t error)
	Set error for parameter number ipar.
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.
virtual void	SetParLimits (Int_t ipar, Double_t parmin, Double_t parmax)
	Set lower and upper limits for parameter ipar.
virtual void	SetParName (Int_t ipar, const char *name)
	Set name of parameter number ipar.
virtual void	SetParNames (const char *name0="", const char *name1="", const char *name2="", const char *name3="", const char *name4="", const char *name5="", const char *name6="", const char *name7="", const char *name8="", const char *name9="", const char *name10="")
	Set up to 10 parameter names.
virtual void	SetRange (Double_t xmin, Double_t xmax)
	Initialize the upper and lower bounds to draw the function.
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.
void	SetTitle (const char *title="") override
	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.
virtual void	SetVectorized (Bool_t vectorized)
void	Streamer (TBuffer &) override
	Stream a class object.
void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)
virtual void	Update ()
	Called by functions such as SetRange, SetNpx, SetParameters to force the deletion of the associated histogram or Integral.
virtual Double_t	Variance (Double_t a, Double_t b, const Double_t *params=nullptr, 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.
	TNamed (const TString &name, const TString &title)
virtual	~TNamed ()
	TNamed destructor.
void	Clear (Option_t *option="") override
	Set name and title to empty strings ("").
TObject *	Clone (const char *newname="") const override
	Make a clone of an object using the Streamer facility.
Int_t	Compare (const TObject *obj) const override
	Compare two TNamed objects.
void	Copy (TObject &named) const override
	Copy this to obj.
virtual void	FillBuffer (char *&buffer)
	Encode TNamed into output buffer.
const char *	GetName () const override
	Returns name of object.
const char *	GetTitle () const override
	Returns title of object.
ULong_t	Hash () const override
	Return hash value for this object.
TClass *	IsA () const override
Bool_t	IsSortable () const override
void	ls (Option_t *option="") const override
	List TNamed name and title.
TNamed &	operator= (const TNamed &rhs)
	TNamed assignment operator.
void	Print (Option_t *option="") const override
	Print TNamed name and title.
virtual void	SetName (const char *name)
	Set the name of the TNamed.
virtual void	SetNameTitle (const char *name, const char *title)
	Set all the TNamed parameters (name and title).
virtual Int_t	Sizeof () const
	Return size of the TNamed part of the TObject.
void	Streamer (TBuffer &) override
	Stream an object of class TObject.
void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)
Public Member Functions inherited from TObject
	TObject ()
	TObject constructor.
	TObject (const TObject &object)
	TObject copy ctor.
virtual	~TObject ()
	TObject destructor.
void	AbstractMethod (const char *method) const
	Use this method to implement an "abstract" method that you don't want to leave purely abstract.
virtual void	AppendPad (Option_t *option="")
	Append graphics object to current pad.
ULong_t	CheckedHash ()
	Check and record whether this class has a consistent Hash/RecursiveRemove setup (*) and then return the regular Hash value for this object.
virtual const char *	ClassName () const
	Returns name of class to which the object belongs.
virtual void	Delete (Option_t *option="")
	Delete this object.
virtual void	DrawClass () const
	Draw class inheritance tree of the class to which this object belongs.
virtual TObject *	DrawClone (Option_t *option="") const
	Draw a clone of this object in the current selected pad with: gROOT->SetSelectedPad(c1).
virtual void	Dump () const
	Dump contents of object on stdout.
virtual void	Error (const char *method, const char *msgfmt,...) const
	Issue error message.
virtual void	Execute (const char *method, const char *params, Int_t *error=nullptr)
	Execute method on this object with the given parameter string, e.g.
virtual void	Execute (TMethod *method, TObjArray *params, Int_t *error=nullptr)
	Execute method on this object with parameters stored in the TObjArray.
virtual void	Fatal (const char *method, const char *msgfmt,...) const
	Issue fatal error message.
virtual TObject *	FindObject (const char *name) const
	Must be redefined in derived classes.
virtual TObject *	FindObject (const TObject *obj) const
	Must be redefined in derived classes.
virtual Option_t *	GetDrawOption () const
	Get option used by the graphics system to draw this object.
virtual const char *	GetIconName () const
	Returns mime type name of object.
virtual Option_t *	GetOption () const
virtual UInt_t	GetUniqueID () const
	Return the unique object id.
virtual Bool_t	HandleTimer (TTimer *timer)
	Execute action in response of a timer timing out.
Bool_t	HasInconsistentHash () const
	Return true is the type of this object is known to have an inconsistent setup for Hash and RecursiveRemove (i.e.
virtual void	Info (const char *method, const char *msgfmt,...) const
	Issue info message.
virtual Bool_t	InheritsFrom (const char *classname) const
	Returns kTRUE if object inherits from class "classname".
virtual Bool_t	InheritsFrom (const TClass *cl) const
	Returns kTRUE if object inherits from TClass cl.
virtual void	Inspect () const
	Dump contents of this object in a graphics canvas.
void	InvertBit (UInt_t f)
Bool_t	IsDestructed () const
	IsDestructed.
virtual Bool_t	IsEqual (const TObject *obj) const
	Default equal comparison (objects are equal if they have the same address in memory).
virtual Bool_t	IsFolder () const
	Returns kTRUE in case object contains browsable objects (like containers or lists of other objects).
R__ALWAYS_INLINE Bool_t	IsOnHeap () const
R__ALWAYS_INLINE Bool_t	IsZombie () const
void	MayNotUse (const char *method) const
	Use this method to signal that a method (defined in a base class) may not be called in a derived class (in principle against good design since a child class should not provide less functionality than its parent, however, sometimes it is necessary).
virtual Bool_t	Notify ()
	This method must be overridden to handle object notification (the base implementation is no-op).
void	Obsolete (const char *method, const char *asOfVers, const char *removedFromVers) const
	Use this method to declare a method obsolete.
void	operator delete (void *ptr)
	Operator delete.
void	operator delete (void *ptr, void *vp)
	Only called by placement new when throwing an exception.
void	operator delete[] (void *ptr)
	Operator delete [].
void	operator delete[] (void *ptr, void *vp)
	Only called by placement new[] when throwing an exception.
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.
virtual void	Pop ()
	Pop on object drawn in a pad to the top of the display list.
virtual Int_t	Read (const char *name)
	Read contents of object with specified name from the current directory.
virtual void	RecursiveRemove (TObject *obj)
	Recursively remove this object from a list.
void	ResetBit (UInt_t f)
virtual void	SaveAs (const char *filename="", Option_t *option="") const
	Save this object in the file specified by filename.
void	SetBit (UInt_t f)
void	SetBit (UInt_t f, Bool_t set)
	Set or unset the user status bits as specified in f.
virtual void	SetDrawOption (Option_t *option="")
	Set drawing option for object.
virtual void	SetUniqueID (UInt_t uid)
	Set the unique object id.
void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)
virtual void	SysError (const char *method, const char *msgfmt,...) const
	Issue system error message.
R__ALWAYS_INLINE Bool_t	TestBit (UInt_t f) const
Int_t	TestBits (UInt_t f) const
virtual void	UseCurrentStyle ()
	Set current style settings in this object This function is called when either TCanvas::UseCurrentStyle or TROOT::ForceStyle have been invoked.
virtual void	Warning (const char *method, const char *msgfmt,...) const
	Issue warning message.
virtual Int_t	Write (const char *name=nullptr, Int_t option=0, Int_t bufsize=0)
	Write this object to the current directory.
virtual Int_t	Write (const char *name=nullptr, Int_t option=0, Int_t bufsize=0) const
	Write this object to the current directory.
Public Member Functions inherited from TAttLine
	TAttLine ()
	AttLine default constructor.
	TAttLine (Color_t lcolor, Style_t lstyle, Width_t lwidth)
	AttLine normal constructor.
virtual	~TAttLine ()
	AttLine destructor.
void	Copy (TAttLine &attline) const
	Copy this line attributes to a new TAttLine.
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.
virtual Color_t	GetLineColor () const
	Return the line color.
virtual Style_t	GetLineStyle () const
	Return the line style.
virtual Width_t	GetLineWidth () const
	Return the line width.
virtual void	Modify ()
	Change current line attributes if necessary.
virtual void	ResetAttLine (Option_t *option="")
	Reset this line attributes to default values.
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.
virtual void	SetLineAttributes ()
	Invoke the DialogCanvas Line attributes.
virtual void	SetLineColor (Color_t lcolor)
	Set the line color.
virtual void	SetLineColorAlpha (Color_t lcolor, Float_t lalpha)
	Set a transparent line color.
virtual void	SetLineStyle (Style_t lstyle)
	Set the line style.
virtual void	SetLineWidth (Width_t lwidth)
	Set the line width.
void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)
Public Member Functions inherited from TAttFill
	TAttFill ()
	AttFill default constructor.
	TAttFill (Color_t fcolor, Style_t fstyle)
	AttFill normal constructor.
virtual	~TAttFill ()
	AttFill destructor.
void	Copy (TAttFill &attfill) const
	Copy this fill attributes to a new TAttFill.
virtual Color_t	GetFillColor () const
	Return the fill area color.
virtual Style_t	GetFillStyle () const
	Return the fill area style.
virtual Bool_t	IsTransparent () const
virtual void	Modify ()
	Change current fill area attributes if necessary.
virtual void	ResetAttFill (Option_t *option="")
	Reset this fill attributes to default values.
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.
virtual void	SetFillAttributes ()
	Invoke the DialogCanvas Fill attributes.
virtual void	SetFillColor (Color_t fcolor)
	Set the fill area color.
virtual void	SetFillColorAlpha (Color_t fcolor, Float_t falpha)
	Set a transparent fill color.
virtual void	SetFillStyle (Style_t fstyle)
	Set the fill area style.
void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)
Public Member Functions inherited from TAttMarker
	TAttMarker ()
	TAttMarker default constructor.
	TAttMarker (Color_t color, Style_t style, Size_t msize)
	TAttMarker normal constructor.
virtual	~TAttMarker ()
	TAttMarker destructor.
void	Copy (TAttMarker &attmarker) const
	Copy this marker attributes to a new TAttMarker.
virtual Color_t	GetMarkerColor () const
	Return the marker color.
virtual Size_t	GetMarkerSize () const
	Return the marker size.
virtual Style_t	GetMarkerStyle () const
	Return the marker style.
virtual void	Modify ()
	Change current marker attributes if necessary.
virtual void	ResetAttMarker (Option_t *toption="")
	Reset this marker attributes to the default values.
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.
virtual void	SetMarkerAttributes ()
	Invoke the DialogCanvas Marker attributes.
virtual void	SetMarkerColor (Color_t mcolor=1)
	Set the marker color.
virtual void	SetMarkerColorAlpha (Color_t mcolor, Float_t malpha)
	Set a transparent marker color.
virtual void	SetMarkerSize (Size_t msize=1)
	Set the marker size.
virtual void	SetMarkerStyle (Style_t mstyle=1)
	Set the marker style.
void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

Static Public Member Functions
static void	AbsValue (Bool_t reject=kTRUE)
	Static function: set the fgAbsValue flag.
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.
static TClass *	Class ()
static const char *	Class_Name ()
static constexpr Version_t	Class_Version ()
static const char *	DeclFileName ()
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.
static Double_t	DerivativeError ()
	Static function returning the error of the last call to the of Derivative's functions.
static TF1 *	GetCurrent ()
	Static function returning the current function being processed.
static void	InitStandardFunctions ()
	Create the basic function objects.
static Bool_t	RejectedPoint ()
	See TF1::RejectPoint above.
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.
static void	SetCurrent (TF1 *f1)
	Static function setting the current function.
Static Public Member Functions inherited from TNamed
static TClass *	Class ()
static const char *	Class_Name ()
static constexpr Version_t	Class_Version ()
static const char *	DeclFileName ()
Static Public Member Functions inherited from TObject
static TClass *	Class ()
static const char *	Class_Name ()
static constexpr Version_t	Class_Version ()
static const char *	DeclFileName ()
static Longptr_t	GetDtorOnly ()
	Return destructor only flag.
static Bool_t	GetObjectStat ()
	Get status of object stat flag.
static void	SetDtorOnly (void *obj)
	Set destructor only flag.
static void	SetObjectStat (Bool_t stat)
	Turn on/off tracking of objects in the TObjectTable.
Static Public Member Functions inherited from TAttLine
static TClass *	Class ()
static const char *	Class_Name ()
static constexpr Version_t	Class_Version ()
static const char *	DeclFileName ()
Static Public Member Functions inherited from TAttFill
static TClass *	Class ()
static const char *	Class_Name ()
static constexpr Version_t	Class_Version ()
static const char *	DeclFileName ()
Static Public Member Functions inherited from TAttMarker
static TClass *	Class ()
static const char *	Class_Name ()
static constexpr Version_t	Class_Version ()
static const char *	DeclFileName ()
static Width_t	GetMarkerLineWidth (Style_t style)
	Internal helper function that returns the line width of the given marker style (0 = filled marker)
static Style_t	GetMarkerStyleBase (Style_t style)
	Internal helper function that returns the corresponding marker style with line width 1 for the given style.

Protected Types
enum	EFType {   kFormula = 0 , kPtrScalarFreeFcn , kInterpreted , kTemplVec ,   kTemplScalar , kCompositionFcn }
Protected Types inherited from TObject
enum	{ kOnlyPrepStep = (1ULL << ( 3 )) }

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.
Bool_t	ComputeCdfTable (Option_t *opt)
	Compute the cumulative function at fNpx points between fXmin and fXmax.
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.
void	DoInitialize (EAddToList addToGlobList)
	Common initialization of the TF1.
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.
virtual void	GetRange (Double_t *xmin, Double_t *xmax) const
	Return range of a generic N-D function.
void	IntegrateForNormalization ()
Protected Member Functions inherited from TObject
virtual void	DoError (int level, const char *location, const char *fmt, va_list va) const
	Interface to ErrorHandler (protected).
void	MakeZombie ()

Protected Attributes
std::vector< Double_t >	fAlpha
	! Array alpha. for each bin in x the deconvolution r of fIntegral
std::vector< Double_t >	fBeta
	! Array beta. is approximated by x = alpha +beta*r *gamma*r**2
Double_t	fChisquare {}
	Function fit chisquare.
std::unique_ptr< TF1AbsComposition >	fComposition
	Pointer to composition (NSUM or CONV)
std::unique_ptr< TFormula >	fFormula
	Pointer to TFormula in case when user define formula.
std::unique_ptr< TF1FunctorPointer >	fFunctor
	! Functor object to wrap any C++ callable object
std::vector< Double_t >	fGamma
	! Array gamma.
TH1 *	fHistogram {nullptr}
	! Pointer to histogram used for visualisation
std::vector< Double_t >	fIntegral
	! Integral of function binned on fNpx bins
Double_t	fMaximum {-1111}
	Maximum value for plotting.
std::unique_ptr< TMethodCall >	fMethodCall
	! Pointer to MethodCall in case of interpreted function
Double_t	fMinimum {-1111}
	Minimum value for plotting.
Int_t	fNDF {}
	Number of degrees of freedom in the fit.
Int_t	fNdim {}
	Function dimension.
Bool_t	fNormalized {false}
	Normalization option (false by default)
Double_t	fNormIntegral {}
	Integral of the function before being normalized.
Int_t	fNpar {}
	Number of parameters.
Int_t	fNpfits {}
	Number of points used in the fit.
Int_t	fNpx {100}
	Number of points used for the graphical representation.
std::unique_ptr< TF1Parameters >	fParams
	Pointer to Function parameters object (exists only for not-formula functions)
TObject *	fParent {nullptr}
	! Parent object hooking this function (if one)
std::vector< Double_t >	fParErrors
	Array of errors of the fNpar parameters.
std::vector< Double_t >	fParMax
	Array of upper limits of the fNpar parameters.
std::vector< Double_t >	fParMin
	Array of lower limits of the fNpar parameters.
std::vector< Double_t >	fSave
	Array of fNsave function values.
EFType	fType {EFType::kTemplScalar}
Double_t	fXmax {-1111}
	Upper bounds for the range.
Double_t	fXmin {-1111}
	Lower bounds for the range.
Protected Attributes inherited from TNamed
TString	fName
TString	fTitle
Protected Attributes inherited from TAttLine
Color_t	fLineColor
	Line color.
Style_t	fLineStyle
	Line style.
Width_t	fLineWidth
	Line width.
Protected Attributes inherited from TAttFill
Color_t	fFillColor
	Fill area color.
Style_t	fFillStyle
	Fill area style.
Protected Attributes inherited from TAttMarker
Color_t	fMarkerColor
	Marker color.
Size_t	fMarkerSize
	Marker size.
Style_t	fMarkerStyle
	Marker style.

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

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.
template<class T >
T	EvalParTempl (const T *data, const Double_t *params=nullptr)
	Eval for vectorized functions.
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

Add to list behavior.

Enumerator
kDefault
kAdd
kNo

Definition at line 240 of file TF1.h.

EFType

enum TF1::EFType

protected

Enumerator
kFormula	Formula functions which can be stored,.
kPtrScalarFreeFcn	Pointer to scalar free function,.
kInterpreted	Interpreted functions constructed by name,.
kTemplVec	Vectorized free functions or TemplScalar functors evaluating on vectorized parameters,.
kTemplScalar	TemplScalar functors evaluating on scalar parameters.
kCompositionFcn

Definition at line 254 of file TF1.h.

EStatusBits

enum TF1::EStatusBits

Enumerator
kNotGlobal
kNotDraw

Definition at line 344 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 293 of file TF1.h.

TF1() [2/15]

TF1::TF1

(

)

TF1 default constructor.

Definition at line 489 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
	)

TF1 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 509 of file TF1.cxx.

TF1() [4/15]

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

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 714 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

[in]	name	object name
[in]	fcn	pointer to function
[in]	xmin,xmax	x axis limits
[in]	npar	is the number of free parameters used by the function
[in]	ndim	number of dimensions
[in]	addToGlobList	boolean marking if it should be added to global list

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 753 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 (const) real function.

Parameters

[in]	name	object name
[in]	fcn	pointer to function
[in]	xmin,xmax	x axis limits
[in]	npar	is the number of free parameters used by the function
[in]	ndim	number of dimensions
[in]	addToGlobList	boolean marking if it should be added to global list

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 775 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 357 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

[in]	name	object name
[in]	fcn	pointer to function
[in]	xmin,xmax	x axis limits
[in]	npar	is the number of free parameters used by the function
[in]	ndim	number of dimensions
[in]	addToGlobList	boolean marking if it should be added to global list

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 381 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

[in]	name	object name
	f	parameterized functor
	xmin	and
	xmax	define the plotting range of the function
[in]	npar	is the number of free parameters used by the function
[in]	ndim	number of dimensions
[in]	addToGlobList	boolean marking if it should be added to global list

This constructor can be used only in compiled code

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

Definition at line 794 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 397 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 406 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 422 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 428 of file TF1.h.

TF1() [15/15]

TF1::TF1

(

const TF1 &

f1

)

Definition at line 970 of file TF1.cxx.

~TF1()

TF1::~TF1 ( )

override

TF1 default destructor.

Definition at line 953 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 984 of file TF1.cxx.

AddParameter()

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

inlinevirtual

Definition at line 435 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 847 of file TF1.cxx.

Browse()

void TF1::Browse ( TBrowser *  b )

overridevirtual

Browse.

Reimplemented from TObject.

Definition at line 993 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 3826 of file TF1.cxx.

CentralMoment()

Double_t TF1::CentralMoment ( Double_t  n, Double_t  a, Double_t  b, const Double_t *  params = nullptr, 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 3739 of file TF1.cxx.

Class()

static TClass * TF1::Class ( )

static

Returns

TClass describing this class

Class_Name()

static const char * TF1::Class_Name ( )

static

Returns

Name of this class

Class_Version()

static constexpr Version_t TF1::Class_Version ( )

inlinestaticconstexpr

Returns

Version of this class

Definition at line 755 of file TF1.h.

Clone()

TObject * TF1::Clone ( const char *  newname = nullptr ) const

overridevirtual

Make a complete copy of the underlying object.

If 'newname' is set, the copy's name will be set to that name.

Reimplemented from TObject.

Definition at line 1064 of file TF1.cxx.

ComputeCdfTable()

Bool_t TF1::ComputeCdfTable ( Option_t *  option )

protected

Compute the cumulative function at fNpx points between fXmin and fXmax.

Option can be used to force a log scale (option = "log"), linear (option = "lin") or automatic if empty.

Definition at line 2081 of file TF1.cxx.

Copy()

void TF1::Copy ( TObject &  obj ) const

overridevirtual

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 TObject.

Reimplemented in TF12, TF2, and TF3.

Definition at line 1005 of file TF1.cxx.

CreateHistogram()

virtual TH1 * TF1::CreateHistogram ( )

inlinevirtual

Reimplemented in TF2, and TF3.

Definition at line 477 of file TF1.h.

DeclFileName()

static const char * TF1::DeclFileName ( )

inlinestatic

Returns

Name of the file containing the class declaration

Definition at line 755 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 838 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 883 of file TF1.cxx.

Derivative()

Double_t TF1::Derivative ( Double_t  x, Double_t *  params = nullptr, 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 1113 of file TF1.cxx.

Derivative2()

Double_t TF1::Derivative2 ( Double_t  x, Double_t *  params = nullptr, 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 1178 of file TF1.cxx.

Derivative3()

Double_t TF1::Derivative3 ( Double_t  x, Double_t *  params = nullptr, 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 1243 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 1277 of file TF1.cxx.

DistancetoPrimitive()

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

overridevirtual

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 1293 of file TF1.cxx.

DoCreateHistogram()

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

protectedvirtual

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 3048 of file TF1.cxx.

DoInitialize()

void TF1::DoInitialize ( EAddToList  addToGlobalList )

protected

Common initialization of the TF1.

Add to the global list and set the default style

Definition at line 802 of file TF1.cxx.

Draw()

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

overridevirtual

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 1333 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 1363 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 1385 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 1420 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 1407 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 1439 of file TF1.cxx.

EvalPar() [1/2]

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

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 1468 of file TF1.cxx.

EvalPar() [2/2]

template<class T >

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

EvalPar for vectorized.

Definition at line 819 of file TF1.h.

EvalParTempl()

template<class T >

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

inlineprivate

Eval for vectorized functions.

Definition at line 844 of file TF1.h.

ExecuteEvent()

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

overridevirtual

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 1536 of file TF1.cxx.

FixParameter()

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

virtual

Fix the value of a parameter for a fit operation The specified value will be used in the fit and the parameter will be constant (nor varying) during fitting Note that when using pre-defined functions (e.g gaus), one needs to use the fit option 'B' to have the fix of the paramter effective.

See TH1::Fit(TF1*, Option_t *, Option_t *, Double_t, Double_t) for the fitting documentation and the fitting options.

Definition at line 1557 of file TF1.cxx.

GetChisquare()

Double_t TF1::GetChisquare ( ) const

inline

Return the Chisquare after fitting. See ROOT::Fit::FitResult::Chi2()

Definition at line 472 of file TF1.h.

GetCurrent()

TF1 * TF1::GetCurrent ( )

static

Static function returning the current function being processed.

Definition at line 1569 of file TF1.cxx.

GetExpFormula()

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

inlinevirtual

Definition at line 489 of file TF1.h.

GetFormula() [1/2]

virtual TFormula * TF1::GetFormula ( )

inlinevirtual

Definition at line 481 of file TF1.h.

GetFormula() [2/2]

virtual const TFormula * TF1::GetFormula ( ) const

inlinevirtual

Definition at line 485 of file TF1.h.

GetHistogram()

TH1 * TF1::GetHistogram ( ) const

virtual

Return a pointer to the histogram used to visualise the function Note that this histogram is managed by the function and in same case it is automatically deleted when some TF1 functions are called such as TF1::SetParameters, TF1::SetNpx, TF1::SetRange It is then reccomended either to clone the return object or calling again teh GetHistogram function whenever is needed.

Definition at line 1584 of file TF1.cxx.

GetLinearPart()

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

inlinevirtual

Definition at line 493 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 1614 of file TF1.cxx.

GetMaximumStored()

virtual Double_t TF1::GetMaximumStored ( ) const

inlinevirtual

Definition at line 501 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 1655 of file TF1.cxx.

GetMethodCall()

TMethodCall * TF1::GetMethodCall ( ) const

inline

Definition at line 522 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 1696 of file TF1.cxx.

GetMinimumStored()

virtual Double_t TF1::GetMinimumStored ( ) const

inlinevirtual

Definition at line 505 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 1823 of file TF1.cxx.

GetMinMaxNDim()

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

protectedvirtual

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 1723 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 1889 of file TF1.cxx.

GetNdim()

virtual Int_t TF1::GetNdim ( ) const

inlinevirtual

Definition at line 513 of file TF1.h.

GetNpar()

virtual Int_t TF1::GetNpar ( ) const

inlinevirtual

Definition at line 509 of file TF1.h.

GetNpx()

virtual Int_t TF1::GetNpx ( ) const

inlinevirtual

Definition at line 518 of file TF1.h.

GetNumber()

virtual Int_t TF1::GetNumber ( ) const

inlinevirtual

Definition at line 526 of file TF1.h.

GetNumberFitPoints()

virtual Int_t TF1::GetNumberFitPoints ( ) const

inlinevirtual

Definition at line 531 of file TF1.h.

GetNumberFreeParameters()

Int_t TF1::GetNumberFreeParameters ( ) const

virtual

Return the number of free parameters.

Definition at line 1900 of file TF1.cxx.

GetObjectInfo()

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

overridevirtual

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 1918 of file TF1.cxx.

GetParameter() [1/2]

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

inlinevirtual

Definition at line 544 of file TF1.h.

GetParameter() [2/2]

virtual Double_t TF1::GetParameter ( Int_t  ipar ) const

inlinevirtual

Definition at line 540 of file TF1.h.

GetParameters() [1/2]

virtual Double_t * TF1::GetParameters ( ) const

inlinevirtual

Definition at line 548 of file TF1.h.

GetParameters() [2/2]

virtual void TF1::GetParameters ( Double_t *  params )

inlinevirtual

Definition at line 552 of file TF1.h.

GetParent()

TObject * TF1::GetParent ( ) const

inline

Definition at line 536 of file TF1.h.

GetParError()

Double_t TF1::GetParError ( Int_t  ipar ) const

virtual

Return value of parameter number ipar.

Definition at line 1930 of file TF1.cxx.

GetParErrors()

virtual const Double_t * TF1::GetParErrors ( ) const

inlinevirtual

Definition at line 566 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 1940 of file TF1.cxx.

GetParName()

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

inlinevirtual

Definition at line 557 of file TF1.h.

GetParNumber()

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

inlinevirtual

Definition at line 561 of file TF1.h.

GetProb()

Double_t TF1::GetProb ( ) const

virtual

Return the fit probability.

Definition at line 1955 of file TF1.cxx.

GetQuantiles()

Int_t TF1::GetQuantiles ( Int_t  n, Double_t *  xp, const Double_t *  p  )

virtual

Compute Quantiles for density distribution of this function.

Quantile x_p of a probability distribution Function F is defined as

\[ F(x_{p}) = \int_{xmin}^{x_{p}} f dx = p with 0 <= p <= 1. \]

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]	n	maximum size of array xp and size of array p
[out]	xp	array filled with n quantiles evaluated at p. Memory has to be preallocated by caller.
[in]	p	array of cumulative probabilities where quantiles should be evaluated. It is assumed to contain at least n values.

Returns

n, the number of quantiles computed (same as input argument n)

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(),p);
f2->GetQuantiles(nprob,gr->GetY(),p);
gr->Draw("alp");

Author

Eddy Offermann

Warning

Function leads to undefined behavior if xp or p are null or their size does not match with n

Definition at line 1994 of file TF1.cxx.

GetRandom() [1/2]

Double_t TF1::GetRandom ( Double_t  xmin, Double_t  xmax, TRandom *  rng = nullptr, Option_t *  option = nullptr  )

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.

Parameters

xmin	minimum value for generated random numbers
xmax	maximum value for generated random numbers
rng	(optional) random number generator pointer
option	(optional) : LOG or LIN to force the usage of a log or linear scale for computing the cumulative integral table

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 2245 of file TF1.cxx.

GetRandom() [2/2]

Double_t TF1::GetRandom ( TRandom *  rng = nullptr, Option_t *  option = nullptr  )

virtual

Return a random number following this function shape.

Parameters

rng	Random number generator. By default (or when passing a nullptr) the global gRandom is used
option	Option string which controls the binning used to compute the integral. Default mode is automatic depending of xmax, xmin and Npx (function points). Possible values are: "LOG" to force usage of log scale for tabulating the integral "LIN" to force usage of linear scale when tabulating the integral

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 user can provide as optional parameter a Random number generator. By default gRandom is used

If the ratio fXmax/fXmin > fNpx the integral is tabulated in log scale in x A log scale for the intergral is also always used if a user specifies the "LOG" option Instead if a user requestes a "LIN" option the integral binning is never done in log scale whatever the fXmax/fXmin ratio is

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

Reimplemented in TF2.

Definition at line 2192 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 2308 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, TF3, TF2, and TF3.

Definition at line 2318 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, TF3, TF2, and TF3.

Definition at line 2330 of file TF1.cxx.

GetRange() [4/4]

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

protectedvirtual

Return range of a generic N-D function.

Reimplemented in TF2, and TF3.

Definition at line 2281 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 2344 of file TF1.cxx.

GetVariable()

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

inlinevirtual

Definition at line 591 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 1863 of file TF1.cxx.

GetXaxis()

TAxis * TF1::GetXaxis

(

)

const

Get x axis of the function.

Definition at line 2400 of file TF1.cxx.

GetXmax()

virtual Double_t TF1::GetXmax ( ) const

inlinevirtual

Definition at line 584 of file TF1.h.

GetXmin()

virtual Double_t TF1::GetXmin ( ) const

inlinevirtual

Definition at line 580 of file TF1.h.

GetYaxis()

TAxis * TF1::GetYaxis

(

)

const

Get y axis of the function.

Definition at line 2411 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 2422 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 If the TF1 object is based on a formula expression (TFormula) and TFormula::GenerateGradientPar() has been successfully called automatic differentiation using CLAD is used instead of the default numerical differentiation.

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 2468 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 970 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 2445 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 903 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 979 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 912 of file TF1.h.

HasSave()

Bool_t TF1::HasSave ( ) const

inline

Return true if function has data in fSave buffer.

Definition at line 466 of file TF1.h.

InitArgs()

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

virtual

Initialize parameters addresses.

Definition at line 2482 of file TF1.cxx.

InitStandardFunctions()

void TF1::InitStandardFunctions ( )

static

Create the basic function objects.

Definition at line 2497 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 2531 of file TF1.cxx.

IntegralError() [1/2]

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

virtual

Return Error on Integral of a parametric function between a and b due to the parameter uncertainties and their covariance matrix from the fit.

In addition to the integral limits, this method takes as input a pointer to the fitted parameter values and a pointer the covariance matrix from the fit. These pointers should be retrieved from the previously performed fit using the TFitResult class. Note that to get the TFitResult, te fit should be done using the fit option S. Example:

TFitResultPtr r = histo->Fit(func, "S");
func->IntegralError(x1,x2,r->GetParams(), r->GetCovarianceMatrix()->GetMatrixArray() );

IMPORTANT NOTE1:

A null pointer to the parameter values vector and to the covariance matrix can be passed. In this case, when the parameter values pointer is null, the parameter values stored in this TF1 function object are used in the integral error computation. When the poassed pointer to the covariance matrix is null, a covariance matrix from the last fit is retrieved from a global fitter instance when it exists. Note that the global fitter instance esists only when ROOT is not running with multi-threading enabled (ROOT::IsImplicitMTEnabled() == True). When the ovariance matrix from the last fit cannot be retrieved, an error message is printed and a zero value is returned.

IMPORTANT NOTE2:

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 NOTE3:

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. The covariance matrix must be retrieved from the TFitResult class as shown above and not from TVirtualFitter::GetCovarianceMatrix() function.

Definition at line 2708 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 = nullptr, const Double_t *  covmat = nullptr, Double_t  epsilon = 1.E-2  )

virtual

Return Error on Integral of a parametric function with dimension larger than 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

In addition to the integral limits, this method takes as input a pointer to the fitted parameter values and a pointer the covariance matrix from the fit. These pointers should be retrieved from the previously performed fit using the TFitResult class. Note that to get the TFitResult, te fit should be done using the fit option S. Example:

TFitResultPtr r = histo2d->Fit(func2, "S");
func2->IntegralError(a,b,r->GetParams(), r->GetCovarianceMatrix()->GetMatrixArray() );

IMPORTANT NOTE1:

A null pointer to the parameter values vector and to the covariance matrix can be passed. In this case, when the parameter values pointer is null, the parameter values stored in this TF1 function object are used in the integral error computation. When the poassed pointer to the covariance matrix is null, a covariance matrix from the last fit is retrieved from a global fitter instance when it exists. Note that the global fitter instance esists only when ROOT is not running with multi-threading enabled (ROOT::IsImplicitMTEnabled() == True). When the ovariance matrix from the last fit cannot be retrieved, an error message is printed and a zero value is returned.

IMPORTANT NOTE2:

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 NOTE3:

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. The covariance matrix must be retrieved from the TFitResult class as shown above and not from TVirtualFitter::GetCovarianceMatrix() function.

Definition at line 2758 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 = nullptr, Double_t  epsilon = 1e-12  )

virtual

Gauss-Legendre integral, see CalcGaussLegendreSamplingPoints.

Definition at line 2778 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 2798 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 2851 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 616 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 2621 of file TF1.cxx.

IntegrateForNormalization()

void TF1::IntegrateForNormalization ( )

protected

IsA()

TClass * TF1::IsA ( ) const

inlineoverridevirtual

Returns

TClass describing current object

Reimplemented from TObject.

Reimplemented in TF12, TF2, and TF3.

Definition at line 755 of file TF1.h.

IsEvalNormalized()

virtual Bool_t TF1::IsEvalNormalized ( ) const

inlinevirtual

Definition at line 621 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 626 of file TF1.h.

IsLinear()

virtual Bool_t TF1::IsLinear ( ) const

inlinevirtual

Definition at line 630 of file TF1.h.

IsValid()

Bool_t TF1::IsValid ( ) const

virtual

Return kTRUE if the function is valid.

Definition at line 2882 of file TF1.cxx.

IsVectorized()

bool TF1::IsVectorized ( )

inline

Definition at line 467 of file TF1.h.

Mean()

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

inlinevirtual

Definition at line 733 of file TF1.h.

Moment()

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

virtual

Return nth moment of function between a and b.

See TF1::Integral() for parameter definitions

Definition at line 3702 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 811 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 805 of file TF1.h.

operator=()

TF1 & TF1::operator=

(

const TF1 &

rhs

)

Operator =.

Definition at line 942 of file TF1.cxx.

Paint()

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

overridevirtual

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 2953 of file TF1.cxx.

Print()

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

overridevirtual

This method must be overridden when a class wants to print itself.

Reimplemented from TObject.

Definition at line 2897 of file TF1.cxx.

RejectedPoint()

Bool_t TF1::RejectedPoint ( )

static

See TF1::RejectPoint above.

Definition at line 3692 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 3683 of file TF1.cxx.

ReleaseParameter()

void TF1::ReleaseParameter ( Int_t  ipar )

virtual

Release parameter number ipar during a fit operation.

After releasing it, the parameter can vary freely in the fit. The parameter limits are reset to 0,0.

Definition at line 3151 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 3161 of file TF1.cxx.

SavePrimitive()

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

overridevirtual

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

Reimplemented from TObject.

Reimplemented in TF12, TF2, and TF3.

Definition at line 3218 of file TF1.cxx.

SetChisquare()

virtual void TF1::SetChisquare ( Double_t  chi2 )

inlinevirtual

Definition at line 640 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 3343 of file TF1.cxx.

SetFitResult()

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

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 3355 of file TF1.cxx.

SetFunction() [1/2]

template<typename Func >

void TF1::SetFunction

(

Func

f

)

Definition at line 888 of file TF1.h.

SetFunction() [2/2]

template<class PtrObj , typename MemFn >

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

Definition at line 895 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 3394 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 3407 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 3419 of file TF1.cxx.

SetNdim()

void TF1::SetNdim ( Int_t  ndim )

inline

Definition at line 661 of file TF1.h.

SetNormalized()

virtual void TF1::SetNormalized ( Bool_t  flag )

inlinevirtual

Definition at line 656 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 3433 of file TF1.cxx.

SetNumberFitPoints()

virtual void TF1::SetNumberFitPoints ( Int_t  npfits )

inlinevirtual

Definition at line 652 of file TF1.h.

SetParameter() [1/2]

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

inlinevirtual

Definition at line 672 of file TF1.h.

SetParameter() [2/2]

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

inlinevirtual

Definition at line 667 of file TF1.h.

SetParameters() [1/2]

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

inlinevirtual

Definition at line 677 of file TF1.h.

SetParameters() [2/2]

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

inlinevirtual

Set parameter values.

NaN values will be skipped, meaning that the corresponding parameters will not be changed.

Definition at line 684 of file TF1.h.

SetParent()

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

inlinevirtual

Definition at line 706 of file TF1.h.

SetParError()

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

virtual

Set error for parameter number ipar.

Definition at line 3479 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 3490 of file TF1.cxx.

SetParLimits()

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

virtual

Set lower and upper limits for parameter ipar.

The specified limits will be used in a fit operation. Note that when this function is a pre-defined function (e.g. gaus) one needs to use the fit option "B" to have the limits used in the fit. See TH1::Fit(TF1*, Option_t *, Option_t *, Double_t, Double_t) for the fitting documentation and the fitting options

To fix a parameter, use TF1::FixParameter

Definition at line 3507 of file TF1.cxx.

SetParName()

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

virtual

Set name of parameter number ipar.

Definition at line 3450 of file TF1.cxx.

SetParNames()

void TF1::SetParNames ( const char *  name0 = "", const char *  name1 = "", const char *  name2 = "", const char *  name3 = "", const char *  name4 = "", const char *  name5 = "", const char *  name6 = "", const char *  name7 = "", const char *  name8 = "", const char *  name9 = "", const char *  name10 = ""  )

virtual

Set up to 10 parameter names.

Empty strings will be skipped, meaning that the corresponding name will not be changed.

Definition at line 3463 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 3528 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 878 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 882 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 3542 of file TF1.cxx.

SetTitle()

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

overridevirtual

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 3558 of file TF1.cxx.

SetVectorized()

virtual void TF1::SetVectorized ( Bool_t  vectorized )

inlinevirtual

Definition at line 715 of file TF1.h.

Streamer()

void TF1::Streamer ( TBuffer &  b )

overridevirtual

Stream a class object.

Reimplemented from TObject.

Reimplemented in TF12, TF2, and TF3.

Definition at line 3571 of file TF1.cxx.

StreamerNVirtual()

void TF1::StreamerNVirtual ( TBuffer &  ClassDef_StreamerNVirtual_b )

inline

Definition at line 755 of file TF1.h.

TermCoeffLength()

int TF1::TermCoeffLength ( TString &  term )

private

Definition at line 924 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 3619 of file TF1.cxx.

Variance()

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

inlinevirtual

Definition at line 737 of file TF1.h.

Friends And Related Symbol Documentation

ROOT::Internal::TF1Builder

template<class Func >

friend struct ROOT::Internal::TF1Builder

friend

Definition at line 236 of file TF1.h.

Member Data Documentation

fAlpha

std::vector<Double_t> TF1::fAlpha

protected

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

Definition at line 279 of file TF1.h.

fBeta

std::vector<Double_t> TF1::fBeta

protected

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

Definition at line 280 of file TF1.h.

fChisquare

Double_t TF1::fChisquare {}

protected

Function fit chisquare.

Definition at line 271 of file TF1.h.

fComposition

std::unique_ptr<TF1AbsComposition> TF1::fComposition

protected

Pointer to composition (NSUM or CONV)

Definition at line 290 of file TF1.h.

fFormula

std::unique_ptr<TFormula> TF1::fFormula

protected

Pointer to TFormula in case when user define formula.

Definition at line 288 of file TF1.h.

fFunctor

std::unique_ptr<TF1FunctorPointer> TF1::fFunctor

protected

! Functor object to wrap any C++ callable object

Definition at line 287 of file TF1.h.

fgAbsValue

std::atomic< Bool_t > TF1::fgAbsValue

staticprotected

Definition at line 324 of file TF1.h.

fgAddToGlobList

std::atomic< Bool_t > TF1::fgAddToGlobList

staticprotected

Definition at line 326 of file TF1.h.

fGamma

std::vector<Double_t> TF1::fGamma

protected

! Array gamma.

Definition at line 281 of file TF1.h.

fgCurrent

TF1 * TF1::fgCurrent = nullptr

staticprotected

Definition at line 327 of file TF1.h.

fgRejectPoint

Bool_t TF1::fgRejectPoint = kFALSE

staticprotected

Definition at line 325 of file TF1.h.

fHistogram

TH1* TF1::fHistogram {nullptr}

protected

! Pointer to histogram used for visualisation

Definition at line 283 of file TF1.h.

fIntegral

std::vector<Double_t> TF1::fIntegral

protected

! Integral of function binned on fNpx bins

Definition at line 278 of file TF1.h.

fMaximum

Double_t TF1::fMaximum {-1111}

protected

Maximum value for plotting.

Definition at line 273 of file TF1.h.

fMethodCall

std::unique_ptr<TMethodCall> TF1::fMethodCall

protected

! Pointer to MethodCall in case of interpreted function

Definition at line 284 of file TF1.h.

fMinimum

Double_t TF1::fMinimum {-1111}

protected

Minimum value for plotting.

Definition at line 272 of file TF1.h.

fNDF

Int_t TF1::fNDF {}

protected

Number of degrees of freedom in the fit.

Definition at line 270 of file TF1.h.

fNdim

Int_t TF1::fNdim {}

protected

Function dimension.

Definition at line 266 of file TF1.h.

fNormalized

Bool_t TF1::fNormalized {false}

protected

Normalization option (false by default)

Definition at line 285 of file TF1.h.

fNormIntegral

Double_t TF1::fNormIntegral {}

protected

Integral of the function before being normalized.

Definition at line 286 of file TF1.h.

fNpar

Int_t TF1::fNpar {}

protected

Number of parameters.

Definition at line 265 of file TF1.h.

fNpfits

Int_t TF1::fNpfits {}

protected

Number of points used in the fit.

Definition at line 269 of file TF1.h.

fNpx

Int_t TF1::fNpx {100}

protected

Number of points used for the graphical representation.

Definition at line 267 of file TF1.h.

fParams

std::unique_ptr<TF1Parameters> TF1::fParams

protected

Pointer to Function parameters object (exists only for not-formula functions)

Definition at line 289 of file TF1.h.

fParent

TObject* TF1::fParent {nullptr}

protected

! Parent object hooking this function (if one)

Definition at line 282 of file TF1.h.

fParErrors

std::vector<Double_t> TF1::fParErrors

protected

Array of errors of the fNpar parameters.

Definition at line 274 of file TF1.h.

fParMax

std::vector<Double_t> TF1::fParMax

protected

Array of upper limits of the fNpar parameters.

Definition at line 276 of file TF1.h.

fParMin

std::vector<Double_t> TF1::fParMin

protected

Array of lower limits of the fNpar parameters.

Definition at line 275 of file TF1.h.

fSave

std::vector<Double_t> TF1::fSave

protected

Array of fNsave function values.

Definition at line 277 of file TF1.h.

fType

EFType TF1::fType {EFType::kTemplScalar}

protected

Definition at line 268 of file TF1.h.

fXmax

Double_t TF1::fXmax {-1111}

protected

Upper bounds for the range.

Definition at line 264 of file TF1.h.

fXmin

Double_t TF1::fXmin {-1111}

protected

Lower bounds for the range.

Definition at line 263 of file TF1.h.

Libraries for TF1:

---

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

• hist/hist/inc/TF1.h
• hist/hist/src/TF1.cxx