ROOT   6.17/01 Reference Guide

1-Dim function class

## TF1: 1-Dim function class

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

The following types of functions can be created:

### 1 - Expression using variable x and no parameters

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

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

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

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

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

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

### 2 - Expression using variable x with parameters

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

Example a:

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

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

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

Parameters may be given a name:

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

Example b:

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

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

#### Case 2: inline expression using TMath functions with parameters

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

### 3 - A lambda expression with variables and parameters

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

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

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

### 4 - A general C function with parameters

Consider the macro myfunc.C below:

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

In an interactive session you can do:

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

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

Example:

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

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

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

Example:

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

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

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

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

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

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

Example:

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

Definition at line 211 of file TF1.h.

## Classes

struct  TF1FunctorPointer

struct  TF1FunctorPointerImpl

## Public Types

enum  EStatusBits { kNotGlobal = BIT(10), kNotDraw = BIT(9) }

Public Types inherited from TObject
enum  {
kIsOnHeap = 0x01000000, kNotDeleted = 0x02000000, kZombie = 0x04000000, kInconsistent = 0x08000000,
}

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

enum  EDeprecatedStatusBits { kObjInCanvas = BIT(3) }

enum  EStatusBits {
kCanDelete = BIT(0), kMustCleanup = BIT(3), kIsReferenced = BIT(4), kHasUUID = BIT(5),
kCannotPick = BIT(6), kNoContextMenu = BIT(8), kInvalidObject = BIT(13)
}

## Public Member Functions

TF1 ()
TF1 default constructor.

F1 constructor using a formula definition. More...

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

F1 constructor using name of an interpreted function. More...

TF1 (const char *name, Double_t(*fcn)(Double_t *, Double_t *), Double_t xmin=0, Double_t xmax=1, Int_t npar=0, Int_t ndim=1, EAddToList addToGlobList=EAddToList::kDefault)
Constructor using a pointer to a real function. More...

TF1 (const char *name, Double_t(*fcn)(const Double_t *, const Double_t *), Double_t xmin=0, Double_t xmax=1, Int_t npar=0, Int_t ndim=1, EAddToList addToGlobList=EAddToList::kDefault)
Constructor using a pointer to real function. More...

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

template<class T >
TF1 (const char *name, T(*fcn)(const T *, const Double_t *), Double_t xmin=0, Double_t xmax=1, Int_t npar=0, Int_t ndim=1, EAddToList addToGlobList=EAddToList::kDefault)
Constructor using a pointer to function. More...

Constructor using the Functor class. More...

template<typename Func >

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<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)

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)

TF1 (const TF1 &f1)

virtual ~TF1 ()
TF1 default destructor.

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

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

virtual void Browse (TBrowser *b)
Browse.

virtual Double_t CentralMoment (Double_t n, Double_t a, Double_t b, const Double_t *params=0, Double_t epsilon=0.000001)
Return nth central moment of function between a and b (i.e the n-th moment around the mean value) More...

virtual void Copy (TObject &f1) const
Copy this F1 to a new F1. More...

virtual TH1CreateHistogram ()

virtual Double_t Derivative (Double_t x, Double_t *params=0, Double_t epsilon=0.001) const
Returns the first derivative of the function at point x, computed by Richardson's extrapolation method (use 2 derivative estimates to compute a third, more accurate estimation) first, derivatives with steps h and h/2 are computed by central difference formulas

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

the final estimate

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

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

virtual Double_t Derivative2 (Double_t x, Double_t *params=0, Double_t epsilon=0.001) const
Returns the second derivative of the function at point x, computed by Richardson's extrapolation method (use 2 derivative estimates to compute a third, more accurate estimation) first, derivatives with steps h and h/2 are computed by central difference formulas

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

the final estimate

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

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

virtual Double_t Derivative3 (Double_t x, Double_t *params=0, Double_t epsilon=0.001) const
Returns the third derivative of the function at point x, computed by Richardson's extrapolation method (use 2 derivative estimates to compute a third, more accurate estimation) first, derivatives with steps h and h/2 are computed by central difference formulas

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

the final estimate

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

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

virtual Int_t DistancetoPrimitive (Int_t px, Int_t py)
Compute distance from point px,py to a function. More...

virtual TH1DoCreateHistogram (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.

Common initialization of the TF1. More...

virtual void Draw (Option_t *option="")
Draw this function with its current attributes. More...

virtual TF1DrawCopy (Option_t *option="") const
Draw a copy of this function with its current attributes. More...

virtual TObjectDrawDerivative (Option_t *option="al")
Draw derivative of this function. More...

virtual void DrawF1 (Double_t xmin, Double_t xmax, Option_t *option="")
Draw function between xmin and xmax.

virtual TObjectDrawIntegral (Option_t *option="al")
Draw integral of this function. More...

virtual Double_t Eval (Double_t x, Double_t y=0, Double_t z=0, Double_t t=0) const
Evaluate this function. More...

virtual Double_t EvalPar (const Double_t *x, const Double_t *params=0)
Evaluate function with given coordinates and parameters. More...

template<class T >
EvalPar (const T *x, const Double_t *params=0)
EvalPar for vectorized.

virtual void ExecuteEvent (Int_t event, Int_t px, Int_t py)
Execute action corresponding to one event. More...

virtual void FixParameter (Int_t ipar, Double_t value)
Fix the value of a parameter The specified value will be used in a fit operation.

Double_t GetChisquare () const

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

virtual TFormulaGetFormula ()

virtual const TFormulaGetFormula () const

virtual TH1GetHistogram () const
Return a pointer to the histogram used to visualise the function.

virtual const TObjectGetLinearPart (Int_t i) const

virtual Double_t GetMaximum (Double_t xmin=0, Double_t xmax=0, Double_t epsilon=1.E-10, Int_t maxiter=100, Bool_t logx=false) const
Returns the maximum value of the function. More...

virtual Double_t GetMaximumStored () const

virtual Double_t GetMaximumX (Double_t xmin=0, Double_t xmax=0, Double_t epsilon=1.E-10, Int_t maxiter=100, Bool_t logx=false) const
Returns the X value corresponding to the maximum value of the function. More...

TMethodCallGetMethodCall () const

virtual Double_t GetMinimum (Double_t xmin=0, Double_t xmax=0, Double_t epsilon=1.E-10, Int_t maxiter=100, Bool_t logx=false) const
Returns the minimum value of the function on the (xmin, xmax) interval. More...

virtual Double_t GetMinimumStored () const

virtual Double_t GetMinimumX (Double_t xmin=0, Double_t xmax=0, Double_t epsilon=1.E-10, Int_t maxiter=100, Bool_t logx=false) const
Returns the X value corresponding to the minimum value of the function on the (xmin, xmax) interval. More...

virtual Double_t GetMinMaxNDim (Double_t *x, Bool_t findmax, Double_t epsilon=0, Int_t maxiter=0) const
Find the minimum of a function of whatever dimension. More...

virtual Int_t GetNDF () const
Return the number of degrees of freedom in the fit the fNDF parameter has been previously computed during a fit. More...

virtual Int_t GetNdim () const

virtual Int_t GetNpar () const

virtual Int_t GetNpx () const

virtual Int_t GetNumber () const

virtual Int_t GetNumberFitPoints () const

virtual Int_t GetNumberFreeParameters () const
Return the number of free parameters.

virtual char * GetObjectInfo (Int_t px, Int_t py) const
Redefines TObject::GetObjectInfo. More...

virtual Double_t GetParameter (Int_t ipar) const

virtual Double_t GetParameter (const TString &name) const

virtual Double_t * GetParameters () const

virtual void GetParameters (Double_t *params)

TObjectGetParent () 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 nprobSum, Double_t *q, const Double_t *probSum)
Compute Quantiles for density distribution of this function. More...

virtual Double_t GetRandom ()
Return a random number following this function shape. More...

virtual Double_t GetRandom (Double_t xmin, Double_t xmax)
Return a random number following this function shape in [xmin,xmax]. More...

virtual void GetRange (Double_t *xmin, Double_t *xmax) const
Return range of a generic N-D function.

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). More...

TAxisGetXaxis () const
Get x axis of the function.

virtual Double_t GetXmax () const

virtual Double_t GetXmin () const

TAxisGetYaxis () const
Get y axis of the function.

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

virtual Double_t GradientPar (Int_t ipar, const Double_t *x, Double_t eps=0.01)
Compute the gradient (derivative) wrt a parameter ipar. More...

template<class T >
GradientPar (Int_t ipar, const T *x, Double_t eps=0.01)

Compute the gradient wrt parameters. More...

template<class T >

template<class T >
GradientParTempl (Int_t ipar, const T *x, Double_t eps=0.01)

template<class T >

virtual void InitArgs (const Double_t *x, const Double_t *params)

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=0, const Double_t *covmat=0, Double_t epsilon=1.E-2)
Return Error on Integral of a parametric function between a and b due to the parameter uncertainties. More...

virtual Double_t IntegralError (Int_t n, const Double_t *a, const Double_t *b, const Double_t *params=0, const Double_t *covmat=0, Double_t epsilon=1.E-2)
Return Error on Integral of a parametric function with dimension larger tan one between a[] and b[] due to the parameters uncertainties. More...

virtual Double_t IntegralFast (Int_t num, Double_t *x, Double_t *w, Double_t a, Double_t b, Double_t *params=0, Double_t epsilon=1e-12)
Gauss-Legendre integral, see CalcGaussLegendreSamplingPoints.

virtual Double_t IntegralMultiple (Int_t n, const Double_t *a, const Double_t *b, Int_t maxpts, Double_t epsrel, Double_t epsabs, Double_t &relerr, Int_t &nfnevl, Int_t &ifail)
This function computes, to an attempted specified accuracy, the value of the integral. More...

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

virtual Double_t IntegralMultiple (Int_t n, const Double_t *a, const Double_t *b, Double_t epsrel, Double_t &relerr)
See more general prototype below. More...

virtual Double_t IntegralOneDim (Double_t a, Double_t b, Double_t epsrel, Double_t epsabs, Double_t &err)
Return Integral of function between a and b using the given parameter values and relative and absolute tolerance. More...

void IntegrateForNormalization ()

virtual Bool_t IsEvalNormalized () const

virtual Bool_t IsInside (const Double_t *x) const
return kTRUE if the point is inside the function range

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=0, Double_t epsilon=0.000001)

virtual Double_t Moment (Double_t n, Double_t a, Double_t b, const Double_t *params=0, Double_t epsilon=0.000001)
Return nth moment of function between a and b. More...

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

template<class T >
operator() (const T *x, const Double_t *params=nullptr)

TF1operator= (const TF1 &rhs)
Operator =.

virtual void Paint (Option_t *option="")
Paint this function with its current attributes. More...

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

virtual void ReleaseParameter (Int_t ipar)
Release parameter number ipar If used in a fit, the parameter can vary freely. More...

virtual void Save (Double_t xmin, Double_t xmax, Double_t ymin, Double_t ymax, Double_t zmin, Double_t zmax)
Save values of function in array fSave.

virtual void SavePrimitive (std::ostream &out, Option_t *option="")
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=0)
Set the result from the fit parameter values, errors, chi2, etc... More...

template<class PtrObj , typename MemFn >
void SetFunction (PtrObj &p, MemFn memFn)

template<typename Func >
void SetFunction (Func f)

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.

virtual void SetNormalized (Bool_t flag)

virtual void SetNpx (Int_t npx=100)
Set the number of points used to draw the function. More...

virtual void SetNumberFitPoints (Int_t npfits)

virtual void SetParameter (Int_t param, Double_t value)

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

virtual void SetParameters (const Double_t *params)

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

virtual void SetParent (TObject *p=0)

virtual void SetParError (Int_t ipar, Double_t error)
Set error for parameter number ipar.

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 limits for parameter ipar. More...

virtual void SetParName (Int_t ipar, const char *name)
Set name of parameter number ipar.

virtual void SetParNames (const char *name0="p0", const char *name1="p1", const char *name2="p2", const char *name3="p3", const char *name4="p4", const char *name5="p5", const char *name6="p6", const char *name7="p7", const char *name8="p8", const char *name9="p9", const char *name10="p10")
Set up to 10 parameter names.

virtual void SetRange (Double_t xmin, Double_t xmax)
Initialize the upper and lower bounds to draw the function. More...

virtual void SetRange (Double_t xmin, Double_t ymin, Double_t xmax, Double_t ymax)

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

virtual void SetSavedPoint (Int_t point, Double_t value)
Restore value of function saved at point.

virtual void SetTitle (const char *title="")
Set function title if title has the form "fffffff;xxxx;yyyy", it is assumed that the function title is "fffffff" and "xxxx" and "yyyy" are the titles for the X and Y axis respectively. More...

virtual void SetVectorized (Bool_t vectorized)

virtual void Update ()
Called by functions such as SetRange, SetNpx, SetParameters to force the deletion of the associated histogram or Integral.

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

Public Member Functions inherited from TNamed
TNamed (const char *name, const char *title)

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

TNamed (const TNamed &named)
TNamed copy ctor.

virtual ~TNamed ()
TNamed destructor.

virtual void Clear (Option_t *option="")
Set name and title to empty strings ("").

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

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

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

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

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

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

virtual Bool_t IsSortable () const

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

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

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

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

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

Public Member Functions inherited from TObject
TObject ()
TObject constructor. More...

TObject (const TObject &object)
TObject copy ctor.

virtual ~TObject ()
TObject destructor. More...

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

Append graphics object to current pad. More...

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

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

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

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

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

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

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

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

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

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

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

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

virtual Option_t * GetDrawOption () const
Get option used by the graphics system to draw this object. More...

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

virtual 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. More...

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

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

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

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. More...

void InvertBit (UInt_t f)

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

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

R__ALWAYS_INLINE Bool_t IsOnHeap () const

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). More...

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

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

void operator delete (void *ptr)
Operator delete.

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

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)

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

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

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

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

void ResetBit (UInt_t f)

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

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

void SetBit (UInt_t f)

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

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

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

R__ALWAYS_INLINE Bool_t TestBit (UInt_t f) const

Int_t TestBits (UInt_t f) const

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

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

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

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

Public Member Functions inherited from TAttLine
TAttLine ()
AttLine default constructor.

TAttLine (Color_t lcolor, Style_t lstyle, Width_t lwidth)
AttLine normal constructor. More...

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. More...

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. More...

virtual void SetLineStyle (Style_t lstyle)
Set the line style.

virtual void SetLineWidth (Width_t lwidth)
Set the line width.

Public Member Functions inherited from TAttFill
TAttFill ()
AttFill default constructor. More...

TAttFill (Color_t fcolor, Style_t fstyle)
AttFill normal constructor. More...

virtual ~TAttFill ()
AttFill destructor.

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. More...

virtual void SetFillStyle (Style_t fstyle)
Set the fill area style.

Public Member Functions inherited from TAttMarker
TAttMarker ()
TAttMarker default constructor. More...

TAttMarker (Color_t color, Style_t style, Size_t msize)
TAttMarker normal constructor. More...

virtual ~TAttMarker ()
TAttMarker destructor.

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. More...

virtual void SetMarkerSize (Size_t msize=1)
Set the marker size.

virtual void SetMarkerStyle (Style_t mstyle=1)
Set the marker style.

## Static Public Member Functions

static void AbsValue (Bool_t reject=kTRUE)
Static function: set the fgAbsValue flag. More...

static void CalcGaussLegendreSamplingPoints (Int_t num, Double_t *x, Double_t *w, Double_t eps=3.0e-11)
Type safe interface (static method) The number of sampling points are taken from the TGraph. More...

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

static Double_t DerivativeError ()
Static function returning the error of the last call to the of Derivative's functions.

static TF1GetCurrent ()
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. More...

static void SetCurrent (TF1 *f1)
Static function setting the current function. More...

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

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 Attributes

static std::atomic< Bool_t > fgAbsValue

static TF1fgCurrent = 0

static Bool_t fgRejectPoint = kFALSE

## Protected Types

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

## Protected Member Functions

TF1 (EFType functionType, const char *name, Double_t xmin, Double_t xmax, Int_t npar, Int_t ndim, EAddToList addToGlobList, TF1Parameters *params=nullptr, TF1FunctorPointer *functor=nullptr)
General constructor for TF1. Most of the other constructors delegate on it.

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
Integral of function binned on fNpx bins.

std::vector< Double_t > fBeta
Array alpha. for each bin in x the deconvolution r of fIntegral.

Double_t fChisquare {}

std::unique_ptr< TF1AbsCompositionfComposition

TF1AbsCompositionfComposition_ptr {nullptr}
Pointer to composition (NSUM or CONV)

TFormulafFormula {nullptr}
Functor object to wrap any C++ callable object.

TF1FunctorPointerfFunctor {nullptr}

std::vector< Double_t > fGamma
Array beta. is approximated by x = alpha +beta*r *gamma*r**2.

TH1fHistogram {nullptr}
Parent object hooking this function (if one)

std::vector< Double_t > fIntegral

Double_t fMaximum {-1111}

TMethodCallfMethodCall {nullptr}
Pointer to histogram used for visualisation.

Double_t fMinimum {-1111}

Int_t fNDF {}

Int_t fNdim {}

Bool_t fNormalized {false}
Pointer to MethodCall in case of interpreted function.

Double_t fNormIntegral {}

Int_t fNpar {}

Int_t fNpfits {}

Int_t fNpx {100}

TF1ParametersfParams {nullptr}

TObjectfParent {nullptr}
Array gamma.

std::vector< Double_t > fParErrors

std::vector< Double_t > fParMax

std::vector< Double_t > fParMin

std::vector< Double_t > fSave

EFType fType {EFType::kTemplScalar}

Double_t fXmax {-1111}

Double_t fXmin {-1111}

Protected Attributes inherited from TNamed
TString fName

TString fTitle

Protected Attributes inherited from TAttLine
Color_t fLineColor
Line color.

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.

## 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 >
EvalParTempl (const T *data, const Double_t *params=0)
Eval for vectorized functions.

int TermCoeffLength (TString &term)

## Friends

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

Inheritance diagram for TF1:
[legend]

## ◆ TF1() [1/6]

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

F1 constructor using a formula definition.

See TFormula constructor for explanation of the formula syntax.

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

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

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

Definition at line 425 of file TF1.cxx.

## ◆ TF1() [2/6]

 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 625 of file TF1.cxx.

## ◆ TF1() [3/6]

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

Constructor using a pointer to a real function.

Parameters
 npar is the number of free parameters used by the function

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

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

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

Definition at line 659 of file TF1.cxx.

## ◆ TF1() [4/6]

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

Constructor using a pointer to real function.

Parameters
 npar is the number of free parameters used by the function

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

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

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

Definition at line 676 of file TF1.cxx.

## ◆ TF1() [5/6]

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

Constructor using a pointer to function.

Parameters
 npar is the number of free parameters used by the function

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

WARNING! A function created with this constructor cannot be Cloned

Definition at line 341 of file TF1.h.

## ◆ TF1() [6/6]

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

Constructor using the Functor class.

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

This constructor can be used only in compiled code

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

Definition at line 691 of file TF1.cxx.

## ◆ 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 885 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:

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

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 3753 of file TF1.cxx.

## ◆ CentralMoment()

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

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

See TF1::Integral() for parameter definitions

Definition at line 3666 of file TF1.cxx.

## ◆ Copy()

 void TF1::Copy ( TObject & obj ) const
virtual

Copy this F1 to a new F1.

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

Reimplemented from TNamed.

Reimplemented in TF2, TF3, and TF12.

Definition at line 906 of file TF1.cxx.

 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 735 of file TF1.cxx.

## ◆ Derivative()

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

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

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

the final estimate

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

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

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

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

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

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

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

Definition at line 1004 of file TF1.cxx.

## ◆ Derivative2()

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

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

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

the final estimate

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

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

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

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

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

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

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

Definition at line 1069 of file TF1.cxx.

## ◆ Derivative3()

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

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

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

the final estimate

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

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

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

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

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

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

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

Definition at line 1134 of file TF1.cxx.

## ◆ DistancetoPrimitive()

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

Compute distance from point px,py to a function.

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

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

Reimplemented from TObject.

Reimplemented in TF2, and TF3.

Definition at line 1184 of file TF1.cxx.

## ◆ DoInitialize()

Common initialization of the TF1.

Add to the global list and set the default style

Definition at line 699 of file TF1.cxx.

## ◆ Draw()

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

Draw this function with its current attributes.

Possible option values are:

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

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

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

Reimplemented from TObject.

Reimplemented in TF2, and TF3.

Definition at line 1224 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 TF2, and TF12.

Definition at line 1254 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 1276 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 1301 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 1336 of file TF1.cxx.

## ◆ EvalPar()

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

Evaluate function with given coordinates and parameters.

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

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

Reimplemented in TF12.

Definition at line 1365 of file TF1.cxx.

## ◆ ExecuteEvent()

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

Execute action corresponding to one event.

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

Reimplemented from TObject.

Reimplemented in TF2, and TF3.

Definition at line 1433 of file TF1.cxx.

## ◆ 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

Definition at line 1501 of file TF1.cxx.

## ◆ 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

Definition at line 1542 of file TF1.cxx.

## ◆ 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

Definition at line 1583 of file TF1.cxx.

## ◆ 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

Definition at line 1710 of file TF1.cxx.

## ◆ GetMinMaxNDim()

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

Find the minimum of a function of whatever dimension.

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

Definition at line 1610 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 1776 of file TF1.cxx.

## ◆ GetObjectInfo()

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

Redefines TObject::GetObjectInfo.

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

Reimplemented from TObject.

Reimplemented in TF2.

Definition at line 1805 of file TF1.cxx.

## ◆ GetQuantiles()

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

Compute Quantiles for density distribution of this function.

Quantile x_q of a probability distribution Function F is defined as

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

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

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

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

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

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


Definition at line 1880 of file TF1.cxx.

## ◆ GetRandom() [1/2]

 Double_t TF1::GetRandom ( )
virtual

Return a random number following this function shape.

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

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

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

Reimplemented in TF2.

Definition at line 1981 of file TF1.cxx.

## ◆ GetRandom() [2/2]

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

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

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

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

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

IMPORTANT NOTE

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

Reimplemented in TF2.

Definition at line 2093 of file TF1.cxx.

## ◆ 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

Definition at line 1750 of file TF1.cxx.

 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 2334 of file TF1.cxx.

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

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 2353 of file TF1.cxx.

## ◆ IntegralError() [1/2]

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

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

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

IMPORTANT NOTE1:

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

IMPORTANT NOTE2:

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

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

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

Definition at line 2596 of file TF1.cxx.

## ◆ IntegralError() [2/2]

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

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

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

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

IMPORTANT NOTE1:

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

IMPORTANT NOTE2:

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

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

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

Definition at line 2635 of file TF1.cxx.

## ◆ IntegralMultiple() [1/2]

 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 maxpts15

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 2728 of file TF1.cxx.

## ◆ IntegralMultiple() [2/2]

 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 2675 of file TF1.cxx.

## ◆ 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:

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 2499 of file TF1.cxx.

## ◆ Moment()

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

Return nth moment of function between a and b.

See TF1::Integral() for parameter definitions

Definition at line 3629 of file TF1.cxx.

## ◆ Paint()

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

Paint this function with its current attributes.

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

Reimplemented from TObject.

Reimplemented in TF2, and TF3.

Definition at line 2830 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 3610 of file TF1.cxx.

## ◆ ReleaseParameter()

 void TF1::ReleaseParameter ( Int_t ipar )
virtual

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

The parameter limits are reset to 0,0.

Definition at line 3030 of file TF1.cxx.

## ◆ 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 3249 of file TF1.cxx.

## ◆ SetFitResult()

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

Set the result from the fit parameter values, errors, chi2, etc...

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

Definition at line 3261 of file TF1.cxx.

## ◆ 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 3339 of file TF1.cxx.

## ◆ SetParLimits()

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

Set limits for parameter ipar.

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

Definition at line 3404 of file TF1.cxx.

## ◆ SetRange()

 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 3425 of file TF1.cxx.

## ◆ SetTitle()

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

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

Reimplemented from TNamed.

Definition at line 3455 of file TF1.cxx.

Libraries for TF1:
[legend]

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