ROOT  6.06/09
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TF1 Class Reference

1-Dim function class

TF1: 1-Dim function class

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

The following types of functions can be created:

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

1 - Expression using variable x and no parameters

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

{
TF1 *fa1 = new TF1("fa1","sin(x)/x",0,10);
fa1->Draw();
}
TF1_001.png

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();
}
TF1_002.png

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

Double_t myFunc(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();
{
TCanvas *c = new TCanvas("c","c",0,0,500,300);
TF1 *fb2 = new TF1("fa3","TMath::Landau(x,[0],[1],0)",-5,10);
fb2->SetParameters(0.2,1.3); fb2->Draw();
return c;
}
TF1_003.png

3 - A lambda expression with variables and parameters **(NEW)**

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

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=gROOT->GetFunction("myfunc");
f1->SetParameters(800,1);
h1->Fit("myfunc");
}

In an interactive session you can do:

Root > .L myfunc.C
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 a sfunction parameter the graph normalization.

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

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

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

Example:

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

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

Definition at line 149 of file TF1.h.

Public Types

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

Public Member Functions

 TF1 ()
 TF1 default constructor. More...
 
 TF1 (const char *name, const char *formula, Double_t xmin=0, Double_t xmax=1, EAddToList addToGlobList=EAddToList::kDefault)
 F1 constructor using a formula definition. More...
 
 TF1 (const char *name, Double_t xmin, Double_t xmax, Int_t npar, Int_t ndim=1, EAddToList addToGlobList=EAddToList::kDefault)
 F1 constructor using name of an interpreted function. More...
 
 TF1 (const char *name, Double_t(*fcn)(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...
 
 TF1 (const char *name, ROOT::Math::ParamFunctor f, Double_t xmin=0, Double_t xmax=1, Int_t npar=0, Int_t ndim=1, EAddToList addToGlobList=EAddToList::kDefault)
 Constructor using the Functor class. More...
 
template<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)
 ctor implementation More...
 
template<typename Func >
 TF1 (const char *name, Func f, Double_t xmin, Double_t xmax, Int_t npar, const char *, EAddToList addToGlobList=EAddToList::kDefault)
 
template<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)
 
TF1operator= (const TF1 &rhs)
 Operator =. More...
 
virtual ~TF1 ()
 TF1 default destructor. More...
 
virtual void AddParameter (const TString &name, Double_t value)
 
virtual Bool_t AddToGlobalList (Bool_t on=kTRUE)
 Add to global list of functions (gROOT->GetListOfFunctions() ) return previous status (true if the function was already in the list false if not) More...
 
virtual void Browse (TBrowser *b)
 Browse. More...
 
virtual void Copy (TObject &f1) const
 Copy this F1 to a new F1. More...
 
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 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 TObjectDrawIntegral (Option_t *option="al")
 Draw integral of this function. More...
 
virtual void DrawF1 (Double_t xmin, Double_t xmax, Option_t *option="")
 Draw function between xmin and xmax. 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...
 
virtual Double_t operator() (Double_t x, Double_t y=0, Double_t z=0, Double_t t=0) const
 
virtual Double_t operator() (const Double_t *x, const Double_t *params=0)
 
virtual void ExecuteEvent (Int_t event, Int_t px, Int_t py)
 Execute action corresponding to one event. More...
 
virtual void FixParameter (Int_t ipar, Double_t value)
 Fix the value of a parameter The specified value will be used in a fit operation. More...
 
Double_t GetChisquare () const
 
virtual TH1GetHistogram () const
 Return a pointer to the histogram used to vusualize the function. More...
 
virtual TH1CreateHistogram ()
 
virtual TFormulaGetFormula ()
 
virtual const TFormulaGetFormula () const
 
virtual TString GetExpFormula (Option_t *option="") const
 
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 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 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...
 
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 GetMaximumStored () const
 
virtual Double_t GetMinimumStored () const
 
virtual Int_t GetNpar () const
 
virtual Int_t GetNdim () const
 
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 GetNpx () const
 
TMethodCallGetMethodCall () const
 
virtual Int_t GetNumber () const
 
virtual Int_t GetNumberFreeParameters () const
 Return the number of free parameters. More...
 
virtual Int_t GetNumberFitPoints () const
 
virtual char * GetObjectInfo (Int_t px, Int_t py) const
 Redefines TObject::GetObjectInfo. More...
 
TObjectGetParent () const
 
virtual Double_t GetParameter (Int_t ipar) const
 
virtual Double_t GetParameter (const TString &name) const
 
virtual Double_tGetParameters () const
 
virtual void GetParameters (Double_t *params)
 
virtual const char * GetParName (Int_t ipar) const
 
virtual Int_t GetParNumber (const char *name) const
 
virtual Double_t GetParError (Int_t ipar) const
 Return value of parameter number ipar. More...
 
virtual const Double_tGetParErrors () const
 
virtual void GetParLimits (Int_t ipar, Double_t &parmin, Double_t &parmax) const
 Return limits for parameter ipar. More...
 
virtual Double_t GetProb () const
 Return the fit probability. More...
 
virtual Int_t GetQuantiles (Int_t nprobSum, Double_t *q, const Double_t *probSum)
 Compute Quantiles for density distribution of this function. More...
 
virtual Double_t GetRandom ()
 Return a random number following this function shape. More...
 
virtual Double_t GetRandom (Double_t xmin, Double_t xmax)
 Return a random number following this function shape in [xmin,xmax]. More...
 
virtual void GetRange (Double_t &xmin, Double_t &xmax) const
 Return range of a 1-D function. More...
 
virtual void GetRange (Double_t &xmin, Double_t &ymin, Double_t &xmax, Double_t &ymax) const
 Return range of a 2-D function. More...
 
virtual void GetRange (Double_t &xmin, Double_t &ymin, Double_t &zmin, Double_t &xmax, Double_t &ymax, Double_t &zmax) const
 Return range of function. More...
 
virtual Double_t GetSave (const Double_t *x)
 Get value corresponding to X in array of fSave values. More...
 
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...
 
virtual Double_t GetXmin () const
 
virtual Double_t GetXmax () const
 
TAxisGetXaxis () const
 Get x axis of the function. More...
 
TAxisGetYaxis () const
 Get y axis of the function. More...
 
TAxisGetZaxis () const
 Get z axis of the function. (In case this object is a TF2 or TF3) More...
 
virtual Double_t GetVariable (const TString &name)
 
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...
 
virtual void GradientPar (const Double_t *x, Double_t *grad, Double_t eps=0.01)
 Compute the gradient wrt parameters. More...
 
virtual void InitArgs (const Double_t *x, const Double_t *params)
 Initialize parameters addresses. More...
 
virtual Double_t Integral (Double_t a, Double_t b, Double_t epsrel=1.e-12)
 IntegralOneDim or analytical integral. More...
 
virtual Double_t 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...
 
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 parameteric 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 parameteric function with dimension larger tan one between a[] and b[] due to the parameters uncertainties. More...
 
virtual Double_t IntegralFast (Int_t num, Double_t *x, Double_t *w, Double_t a, Double_t b, Double_t *params=0, Double_t epsilon=1e-12)
 Gauss-Legendre integral, see CalcGaussLegendreSamplingPoints. More...
 
virtual Double_t IntegralMultiple (Int_t n, const Double_t *a, const Double_t *b, 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 Bool_t IsEvalNormalized () const
 
virtual Bool_t IsInside (const Double_t *x) const
 return kTRUE if the point is inside the function range More...
 
virtual Bool_t IsLinear () const
 
virtual Bool_t IsValid () const
 Return kTRUE if the function is valid. More...
 
virtual void Print (Option_t *option="") const
 Print TNamed name and title. More...
 
virtual void Paint (Option_t *option="")
 Paint this function with its current attributes. More...
 
virtual void ReleaseParameter (Int_t ipar)
 Release parameter number ipar If used in a fit, the parameter can vary freely. More...
 
virtual void Save (Double_t xmin, Double_t xmax, Double_t ymin, Double_t ymax, Double_t zmin, Double_t zmax)
 Save values of function in array fSave. More...
 
virtual void SavePrimitive (std::ostream &out, Option_t *option="")
 Save primitive as a C++ statement(s) on output stream out. More...
 
virtual void SetChisquare (Double_t chi2)
 
virtual void SetFitResult (const ROOT::Fit::FitResult &result, const Int_t *indpar=0)
 Set the result from the fit parameter values, errors, chi2, etc... 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. More...
 
virtual void SetMinimum (Double_t minimum=-1111)
 Set the minimum value along Y for this function In case the function is already drawn, set also the minimum in the helper histogram. More...
 
virtual void SetNDF (Int_t ndf)
 Set the number of degrees of freedom ndf should be the number of points used in a fit - the number of free parameters. More...
 
virtual void SetNumberFitPoints (Int_t npfits)
 
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 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 SetParName (Int_t ipar, const char *name)
 Set name of parameter number ipar. More...
 
virtual void SetParNames (const char *name0="p0", const char *name1="p1", const char *name2="p2", const char *name3="p3", const char *name4="p4", const char *name5="p5", const char *name6="p6", const char *name7="p7", const char *name8="p8", const char *name9="p9", const char *name10="p10")
 Set up to 10 parameter names. More...
 
virtual void SetParError (Int_t ipar, Double_t error)
 Set error for parameter number ipar. More...
 
virtual void SetParErrors (const Double_t *errors)
 Set errors for all active parameters when calling this function, the array errors must have at least fNpar values. More...
 
virtual void SetParLimits (Int_t ipar, Double_t parmin, Double_t parmax)
 Set limits for parameter ipar. More...
 
virtual void SetParent (TObject *p=0)
 
virtual void SetRange (Double_t xmin, Double_t xmax)
 Initialize the upper and lower bounds to draw the function. More...
 
virtual void SetRange (Double_t xmin, Double_t ymin, Double_t xmax, Double_t ymax)
 
virtual void SetRange (Double_t xmin, Double_t ymin, Double_t zmin, Double_t xmax, Double_t ymax, Double_t zmax)
 
virtual void SetSavedPoint (Int_t point, Double_t value)
 Restore value of function saved at point. More...
 
virtual void SetTitle (const char *title="")
 Set function title if title has the form "fffffff;xxxx;yyyy", it is assumed that the function title is "fffffff" and "xxxx" and "yyyy" are the titles for the X and Y axis respectively. More...
 
virtual void Update ()
 Called by functions such as SetRange, SetNpx, SetParameters to force the deletion of the associated histogram or Integral. More...
 
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 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 Double_t Mean (Double_t a, Double_t b, const Double_t *params=0, Double_t epsilon=0.000001)
 
virtual Double_t Variance (Double_t a, Double_t b, const Double_t *params=0, Double_t epsilon=0.000001)
 
- Public Member Functions inherited from TNamed
 TNamed ()
 
 TNamed (const char *name, const char *title)
 
 TNamed (const TString &name, const TString &title)
 
 TNamed (const TNamed &named)
 
TNamedoperator= (const TNamed &rhs)
 TNamed assignment operator. More...
 
virtual ~TNamed ()
 
virtual void Clear (Option_t *option="")
 Set name and title to empty strings (""). More...
 
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. More...
 
virtual const char * GetName () const
 Returns name of object. More...
 
virtual const char * GetTitle () const
 Returns title of object. More...
 
virtual ULong_t Hash () const
 Return hash value for this object. More...
 
virtual Bool_t IsSortable () const
 
virtual void SetName (const char *name)
 Change (i.e. More...
 
virtual void SetNameTitle (const char *name, const char *title)
 Change (i.e. set) all the TNamed parameters (name and title). More...
 
virtual void ls (Option_t *option="") const
 List TNamed name and title. More...
 
virtual Int_t Sizeof () const
 Return size of the TNamed part of the TObject. More...
 
- Public Member Functions inherited from TObject
 TObject ()
 
 TObject (const TObject &object)
 TObject copy ctor. More...
 
TObjectoperator= (const TObject &rhs)
 TObject assignment operator. More...
 
virtual ~TObject ()
 TObject destructor. More...
 
virtual void AppendPad (Option_t *option="")
 Append graphics object to current pad. More...
 
virtual const char * ClassName () const
 Returns name of class to which the object belongs. More...
 
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 pad. More...
 
virtual void Dump () const
 Dump contents of object on stdout. 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 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_tGetDrawOption () const
 Get option used by the graphics system to draw this object. More...
 
virtual UInt_t GetUniqueID () const
 Return the unique object id. More...
 
virtual const char * GetIconName () const
 Returns mime type name of object. More...
 
virtual Option_tGetOption () const
 
virtual Bool_t HandleTimer (TTimer *timer)
 Execute action in response of a timer timing out. More...
 
virtual Bool_t InheritsFrom (const char *classname) const
 Returns kTRUE if object inherits from class "classname". More...
 
virtual Bool_t InheritsFrom (const TClass *cl) const
 Returns kTRUE if object inherits from TClass cl. More...
 
virtual void Inspect () const
 Dump contents of this object in a graphics canvas. More...
 
virtual Bool_t IsFolder () const
 Returns kTRUE in case object contains browsable objects (like containers or lists of other objects). More...
 
virtual Bool_t IsEqual (const TObject *obj) const
 Default equal comparison (objects are equal if they have the same address in memory). More...
 
Bool_t IsOnHeap () const
 
Bool_t IsZombie () const
 
virtual Bool_t Notify ()
 This method must be overridden to handle object notification. More...
 
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...
 
virtual void SaveAs (const char *filename="", Option_t *option="") const
 Save this object in the file specified by filename. More...
 
virtual void SetDrawOption (Option_t *option="")
 Set drawing option for object. More...
 
virtual void SetUniqueID (UInt_t uid)
 Set the unique object id. More...
 
virtual void UseCurrentStyle ()
 Set current style settings in this object This function is called when either TCanvas::UseCurrentStyle or TROOT::ForceStyle have been invoked. 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...
 
voidoperator new (size_t sz)
 
voidoperator new[] (size_t sz)
 
voidoperator new (size_t sz, void *vp)
 
voidoperator new[] (size_t sz, void *vp)
 
void operator delete (void *ptr)
 Operator delete. More...
 
void operator delete[] (void *ptr)
 Operator delete []. More...
 
void SetBit (UInt_t f, Bool_t set)
 Set or unset the user status bits as specified in f. More...
 
void SetBit (UInt_t f)
 
void ResetBit (UInt_t f)
 
Bool_t TestBit (UInt_t f) const
 
Int_t TestBits (UInt_t f) const
 
void InvertBit (UInt_t f)
 
virtual void Info (const char *method, const char *msgfmt,...) const
 Issue info message. More...
 
virtual void Warning (const char *method, const char *msgfmt,...) const
 Issue warning message. More...
 
virtual void Error (const char *method, const char *msgfmt,...) const
 Issue error message. More...
 
virtual void SysError (const char *method, const char *msgfmt,...) const
 Issue system error message. More...
 
virtual void Fatal (const char *method, const char *msgfmt,...) const
 Issue fatal error message. 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...
 
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...
 
void Obsolete (const char *method, const char *asOfVers, const char *removedFromVers) const
 Use this method to declare a method obsolete. More...
 
- Public Member Functions inherited from TAttLine
 TAttLine ()
 AttLine default constructor. More...
 
 TAttLine (Color_t lcolor, Style_t lstyle, Width_t lwidth)
 AttLine normal constructor. More...
 
virtual ~TAttLine ()
 AttLine destructor. More...
 
void Copy (TAttLine &attline) const
 Copy this line attributes to a new TAttLine. More...
 
Int_t DistancetoLine (Int_t px, Int_t py, Double_t xp1, Double_t yp1, Double_t xp2, Double_t yp2)
 Compute distance from point px,py to a line. More...
 
virtual Color_t GetLineColor () const
 
virtual Style_t GetLineStyle () const
 
virtual Width_t GetLineWidth () const
 
virtual void Modify ()
 Change current line attributes if necessary. More...
 
virtual void ResetAttLine (Option_t *option="")
 Reset this line attributes to default values. More...
 
virtual void SaveLineAttributes (std::ostream &out, const char *name, Int_t coldef=1, Int_t stydef=1, Int_t widdef=1)
 Save line attributes as C++ statement(s) on output stream out. More...
 
virtual void SetLineAttributes ()
 Invoke the DialogCanvas Line attributes. More...
 
virtual void SetLineColor (Color_t lcolor)
 
virtual void SetLineColorAlpha (Color_t lcolor, Float_t lalpha)
 Set a transparent line color. More...
 
virtual void SetLineStyle (Style_t lstyle)
 
virtual void SetLineWidth (Width_t lwidth)
 
 ClassDef (TAttLine, 2)
 
- Public Member Functions inherited from TAttFill
 TAttFill ()
 
 TAttFill (Color_t fcolor, Style_t fstyle)
 AttFill normal constructor. More...
 
virtual ~TAttFill ()
 AttFill destructor. More...
 
void Copy (TAttFill &attfill) const
 Copy this fill attributes to a new TAttFill. More...
 
virtual Color_t GetFillColor () const
 
virtual Style_t GetFillStyle () const
 
virtual Bool_t IsTransparent () const
 
virtual void Modify ()
 Change current fill area attributes if necessary. More...
 
virtual void ResetAttFill (Option_t *option="")
 Reset this fill attributes to default values. More...
 
virtual void SaveFillAttributes (std::ostream &out, const char *name, Int_t coldef=1, Int_t stydef=1001)
 Save fill attributes as C++ statement(s) on output stream out. More...
 
virtual void SetFillAttributes ()
 Invoke the DialogCanvas Fill attributes. More...
 
virtual void SetFillColor (Color_t fcolor)
 
virtual void SetFillColorAlpha (Color_t fcolor, Float_t falpha)
 Set a transparent fill color. More...
 
virtual void SetFillStyle (Style_t fstyle)
 
- Public Member Functions inherited from TAttMarker
 TAttMarker ()
 
 TAttMarker (Color_t color, Style_t style, Size_t msize)
 TAttMarker normal constructor. More...
 
virtual ~TAttMarker ()
 TAttMarker destructor. More...
 
void Copy (TAttMarker &attmarker) const
 Copy this marker attributes to a new TAttMarker. More...
 
virtual Color_t GetMarkerColor () const
 
virtual Style_t GetMarkerStyle () const
 
virtual Size_t GetMarkerSize () const
 
virtual void Modify ()
 Change current marker attributes if necessary. More...
 
virtual void ResetAttMarker (Option_t *toption="")
 Reset this marker attributes to the default values. More...
 
virtual void SaveMarkerAttributes (std::ostream &out, const char *name, Int_t coldef=1, Int_t stydef=1, Int_t sizdef=1)
 Save line attributes as C++ statement(s) on output stream out. More...
 
virtual void SetMarkerAttributes ()
 Invoke the DialogCanvas Marker attributes. More...
 
virtual void SetMarkerColor (Color_t mcolor=1)
 
virtual void SetMarkerColorAlpha (Color_t mcolor, Float_t malpha)
 Set a transparent marker color. More...
 
virtual void SetMarkerStyle (Style_t mstyle=1)
 
virtual void SetMarkerSize (Size_t msize=1)
 
 ClassDef (TAttMarker, 2)
 

Static Public Member Functions

static Bool_t DefaultAddToGlobalList (Bool_t on=kTRUE)
 Static method to add/avoid to add automatically functions to the global list (gROOT->GetListOfFunctions() ) After having called this static method, all the functions created afterwards will follow the desired behaviour. More...
 
static Double_t DerivativeError ()
 Static function returning the error of the last call to the of Derivative's functions. More...
 
static void InitStandardFunctions ()
 Create the basic function objects. More...
 
static TF1GetCurrent ()
 Static function returning the current function being processed. More...
 
static void AbsValue (Bool_t reject=kTRUE)
 Static function: set the fgAbsValue flag. More...
 
static void RejectPoint (Bool_t reject=kTRUE)
 Static function to set the global flag to reject points the fgRejectPoint global flag is tested by all fit functions if TRUE the point is not included in the fit. More...
 
static Bool_t RejectedPoint ()
 See TF1::RejectPoint above. More...
 
static void SetCurrent (TF1 *f1)
 Static function setting the current function. 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 Public Member Functions inherited from TObject
static Long_t GetDtorOnly ()
 Return destructor only flag. More...
 
static void SetDtorOnly (void *obj)
 Set destructor only flag. More...
 
static Bool_t GetObjectStat ()
 Get status of object stat flag. More...
 
static void SetObjectStat (Bool_t stat)
 Turn on/off tracking of objects in the TObjectTable. More...
 

Protected Types

enum  { kNotGlobal = BIT(10) }
 

Protected Member Functions

void DoInitialize (EAddToList addToGlobList)
 Common initialization of the TF1. More...
 
void IntegrateForNormalization ()
 
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 void GetRange (Double_t *xmin, Double_t *xmax) const
 Return range of a generic N-D 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. More...
 
- Protected Member Functions inherited from TObject
void MakeZombie ()
 
virtual void DoError (int level, const char *location, const char *fmt, va_list va) const
 Interface to ErrorHandler (protected). More...
 

Protected Attributes

Double_t fXmin
 
Double_t fXmax
 
Int_t fNpar
 
Int_t fNdim
 
Int_t fNpx
 
Int_t fType
 
Int_t fNpfits
 
Int_t fNDF
 
Double_t fChisquare
 
Double_t fMinimum
 
Double_t fMaximum
 
std::vector< Double_tfParErrors
 
std::vector< Double_tfParMin
 
std::vector< Double_tfParMax
 
std::vector< Double_tfSave
 
std::vector< Double_tfIntegral
 
std::vector< Double_tfAlpha
 Integral of function binned on fNpx bins. More...
 
std::vector< Double_tfBeta
 Array alpha. for each bin in x the deconvolution r of fIntegral. More...
 
std::vector< Double_tfGamma
 Array beta. is approximated by x = alpha +beta*r *gamma*r**2. More...
 
TObjectfParent
 Array gamma. More...
 
TH1fHistogram
 Parent object hooking this function (if one) More...
 
TMethodCallfMethodCall
 Pointer to histogram used for visualisation. More...
 
Bool_t fNormalized
 Pointer to MethodCall in case of interpreted function. More...
 
Double_t fNormIntegral
 
ROOT::Math::ParamFunctor fFunctor
 
TFormulafFormula
 Functor object to wrap any C++ callable object. More...
 
TF1ParametersfParams
 
- Protected Attributes inherited from TNamed
TString fName
 
TString fTitle
 
- Protected Attributes inherited from TAttLine
Color_t fLineColor
 
Style_t fLineStyle
 
Width_t fLineWidth
 
- Protected Attributes inherited from TAttFill
Color_t fFillColor
 
Style_t fFillStyle
 
- Protected Attributes inherited from TAttMarker
Color_t fMarkerColor
 
Style_t fMarkerStyle
 
Size_t fMarkerSize
 

Static Protected Attributes

static std::atomic< Bool_tfgAbsValue
 
static Bool_t fgRejectPoint = kFALSE
 
static std::atomic< Bool_tfgAddToGlobList
 
static TF1fgCurrent = 0
 

Friends

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

#include <TF1.h>

+ Inheritance diagram for TF1:
+ Collaboration diagram for TF1:

Member Enumeration Documentation

anonymous enum
protected
Enumerator
kNotGlobal 

Definition at line 206 of file TF1.h.

anonymous enum
Enumerator
kNotDraw 

Definition at line 212 of file TF1.h.

enum TF1::EAddToList
strong
Enumerator
kDefault 
kAdd 
kNo 

Definition at line 156 of file TF1.h.

Constructor & Destructor Documentation

TF1::TF1 ( )

TF1 default constructor.

Definition at line 392 of file TF1.cxx.

Referenced by InitStandardFunctions().

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

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 420 of file TF1.cxx.

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 CINT cunction. 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 CINT.

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

Definition at line 466 of file TF1.cxx.

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
nparis 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 515 of file TF1.cxx.

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
nparis 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 549 of file TF1.cxx.

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
xminand
xmaxdefine the plotting range of the function
nparis 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 581 of file TF1.cxx.

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 
)

ctor implementation

Definition at line 488 of file TF1.h.

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 238 of file TF1.h.

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 268 of file TF1.h.

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 289 of file TF1.h.

TF1::TF1 ( const TF1 f1)

Definition at line 717 of file TF1.cxx.

TF1::~TF1 ( )
virtual

TF1 default destructor.

Definition at line 697 of file TF1.cxx.

Member Function Documentation

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 738 of file TF1.cxx.

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

Definition at line 312 of file TF1.h.

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 649 of file TF1.cxx.

Referenced by copyTF1(), and HFit::StoreAndDrawFitFunction().

void TF1::Browse ( TBrowser b)
virtual

Browse.

Reimplemented from TObject.

Definition at line 747 of file TF1.cxx.

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 3532 of file TF1.cxx.

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

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

See TF1::Integral() for parameter definitions Author: Gene Van Buren gene@.nosp@m.bnl..nosp@m.gov

Definition at line 3445 of file TF1.cxx.

Referenced by Variance().

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 759 of file TF1.cxx.

Referenced by TF12::Copy(), TF2::Copy(), copyTF1(), DrawCopy(), GAMinTutorial(), TFitEditor::GetFitFunction(), TF1Convolution::InitializeDataMembers(), operator=(), ROOT::Math::WrappedMultiTF1::SetAndCopyFunction(), HFit::StoreAndDrawFitFunction(), TF12::TF12(), TF1NormSum::TF1NormSum(), and TF2::TF2().

virtual TH1* TF1::CreateHistogram ( )
inlinevirtual

Reimplemented in TF2, and TF3.

Definition at line 338 of file TF1.h.

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

Definition at line 640 of file TF1.cxx.

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

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

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

the final estimate

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

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

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

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

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

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

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

Author: Anna Kreshuk

Definition at line 852 of file TF1.cxx.

Referenced by RooStats::HypoTestInverterResult::CalculateEstimatedError(), ROOT::Math::WrappedTF1::DoDerivative(), TProofBench::DrawCPU(), TProofBench::DrawDataSet(), GraphFitChisquare(), GraphFitChisquareFumili(), MultiGraphFitChisquare(), and TestDerivative().

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

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

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

the final estimate

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

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

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

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

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

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

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

Author: Anna Kreshuk

Definition at line 918 of file TF1.cxx.

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: Begin_Latex err = k::sqrt{f(x)^{2} + x^{2}deriv^{2}}sqrt{#sum ai^{2}}, End_Latex 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 984 of file TF1.cxx.

Double_t TF1::DerivativeError ( )
static

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

Definition at line 1019 of file TF1.cxx.

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 1035 of file TF1.cxx.

Referenced by TF3::DistancetoPrimitive().

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 2750 of file TF1.cxx.

Referenced by CreateHistogram(), and Paint().

void TF1::DoInitialize ( EAddToList  addToGlobalList)
protected

Common initialization of the TF1.

Add to the global list and set the default style

Definition at line 606 of file TF1.cxx.

Referenced by TF1().

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 1075 of file TF1.cxx.

Referenced by ApplicationWindow::ApplicationWindow(), Browse(), doFit(), TFitEditor::DoFit(), TF1Editor::DoSliderXMoved(), TF1Editor::DoSliderXPressed(), TF1Editor::DoSliderXReleased(), RooStats::LikelihoodIntervalPlot::Draw(), TKDE::Draw(), TGeoPainter::DrawBatemanSol(), TKDE::DrawConfidenceInterval(), DrawF1(), TFitParametersDialog::DrawFunction(), GAMinTutorial(), RooStats::HybridPlot::GetHistoCenter(), TFunctionParametersDialog::RedrawFunction(), RooStats::HypoTestInverter::RunLimit(), and testAnalyticalIntegrals().

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 1103 of file TF1.cxx.

Referenced by GAMinTutorial().

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 1125 of file TF1.cxx.

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

Draw function between xmin and xmax.

Definition at line 1166 of file TF1.cxx.

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 1150 of file TF1.cxx.

Double_t TF1::Eval ( Double_t  x,
Double_t  y = 0,
Double_t  z = 0,
Double_t  t = 0 
) const
virtual
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-dimemsional 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 responsability 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 everytime these addresses change.

Reimplemented in TF12.

Definition at line 1215 of file TF1.cxx.

Referenced by TH1::Add(), TLinearFitter::AddToDesign(), TF2::CreateHistogram(), TLinearFitter::CStep(), TH1::Divide(), DoCreateHistogram(), ROOT::Math::WrappedTF1::DoEval(), ROOT::Math::WrappedMultiTF1::DoEval(), ROOT::Math::WrappedTF1::DoEvalPar(), ROOT::Math::WrappedMultiTF1::DoEvalPar(), TF12::EvalPar(), TFumili::EvalTFN(), F2Fit(), F3Fit(), fillSparse(), TFitter::FitChisquare(), TFumili::FitChisquare(), TFitter::FitLikelihood(), TFumili::FitLikelihood(), TUnfoldBinning::GetBinFactor(), TFitter::GetConfidenceIntervals(), TF3::GetRandom3(), GradientPar(), Graph2DFitChisquare(), GraphFitChisquare(), GraphFitChisquareFumili(), TLinearFitter::HistLinearFitter(), MultiGraphFitChisquare(), TProfile::Multiply(), THnBase::Multiply(), TH1::Multiply(), operator()(), TF2::Paint(), TF3::Save(), TF2::Save(), Save(), SavePrimitive(), and TestTimeTF1().

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 1260 of file TF1.cxx.

Referenced by TF3::ExecuteEvent(), and TF2::ExecuteEvent().

void TF1::FixParameter ( Int_t  ipar,
Double_t  value 
)
virtual
Double_t TF1::GetChisquare ( ) const
inline
TF1 * TF1::GetCurrent ( )
static

Static function returning the current function being processed.

Definition at line 1288 of file TF1.cxx.

Referenced by rr_ctf1_fcn(), and rr_ctf2_fcn().

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

Definition at line 340 of file TF1.h.

TH1 * TF1::GetHistogram ( ) const
virtual
virtual const TObject* TF1::GetLinearPart ( Int_t  i) const
inlinevirtual
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

Definition at line 1327 of file TF1.cxx.

virtual Double_t TF1::GetMaximumStored ( ) const
inlinevirtual

Definition at line 347 of file TF1.h.

Referenced by THistPainter::PaintInit().

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 1365 of file TF1.cxx.

Referenced by TestMaxMin().

TMethodCall* TF1::GetMethodCall ( ) const
inline
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

Definition at line 1403 of file TF1.cxx.

virtual Double_t TF1::GetMinimumStored ( ) const
inlinevirtual

Definition at line 348 of file TF1.h.

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 1531 of file TF1.cxx.

Referenced by TestMaxMin().

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 1427 of file TF1.cxx.

Referenced by TF3::FindMinMax(), and TF2::FindMinMax().

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 1591 of file TF1.cxx.

Referenced by TFitter::GetConfidenceIntervals(), THistPainter::PaintStat(), THistPainter::PaintStat2(), THistPainter::PaintStat3(), TGraphPainter::PaintStats(), SavePrimitive(), testHisto1DFit(), unuranDistr(), and unuranSimple().

virtual Int_t TF1::GetNdim ( ) const
inlinevirtual
virtual Int_t TF1::GetNpar ( ) const
inlinevirtual
virtual Int_t TF1::GetNpx ( ) const
inlinevirtual
virtual Int_t TF1::GetNumber ( ) const
inlinevirtual
virtual Int_t TF1::GetNumberFitPoints ( ) const
inlinevirtual

Definition at line 356 of file TF1.h.

Referenced by TH2::DoFitSlices(), TBinomialEfficiencyFitter::Fit(), and TH3::FitSlicesZ().

Int_t TF1::GetNumberFreeParameters ( ) const
virtual

Return the number of free parameters.

Definition at line 1602 of file TF1.cxx.

Referenced by TFitter::GetConfidenceIntervals(), and THistPainter::PaintStat().

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 1619 of file TF1.cxx.

virtual Double_t TF1::GetParameter ( Int_t  ipar) const
inlinevirtual
virtual Double_t TF1::GetParameter ( const TString name) const
inlinevirtual

Definition at line 362 of file TF1.h.

virtual Double_t* TF1::GetParameters ( ) const
inlinevirtual
virtual void TF1::GetParameters ( Double_t params)
inlinevirtual

Definition at line 368 of file TF1.h.

TObject* TF1::GetParent ( ) const
inline

Definition at line 358 of file TF1.h.

Double_t TF1::GetParError ( Int_t  ipar) const
virtual
virtual const Double_t* TF1::GetParErrors ( ) const
inlinevirtual

Definition at line 377 of file TF1.h.

void TF1::GetParLimits ( Int_t  ipar,
Double_t parmin,
Double_t parmax 
) const
virtual
virtual const char* TF1::GetParName ( Int_t  ipar) const
inlinevirtual
virtual Int_t TF1::GetParNumber ( const char *  name) const
inlinevirtual

Definition at line 373 of file TF1.h.

Double_t TF1::GetProb ( ) const
virtual

Return the fit probability.

Definition at line 1656 of file TF1.cxx.

Referenced by unuranDistr(), and unuranSimple().

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:

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

code from Eddy Offermann, Renaissance

Parameters
[in]thisTF1 function
[in]nprobSummaximum size of array q and size of array probSum
[in]probSumarray of positions where quantiles will be computed. It is assumed to contain at least nprobSum values.
[out]returnvalue nq (<=nprobSum) with the number of quantiles computed
[out]arrayq 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 1692 of file TF1.cxx.

Referenced by RooStats::BayesianCalculator::ComputeIntervalFromApproxPosterior(), TGraphQQ::MakeFunctionQuantiles(), and TGraphQQ::Quartiles().

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 1785 of file TF1.cxx.

Referenced by GAMinTutorial(), testHisto1DPolFit(), testPolyFit(), and unuranDistr().

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 1898 of file TF1.cxx.

void TF1::GetRange ( Double_t xmin,
Double_t xmax 
) const
protectedvirtual
void TF1::GetRange ( Double_t xmin,
Double_t xmax 
) const
virtual

Return range of a 1-D function.

Reimplemented in TF3.

Definition at line 2003 of file TF1.cxx.

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, and TF3.

Definition at line 2013 of file TF1.cxx.

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, and TF3.

Definition at line 2025 of file TF1.cxx.

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 2039 of file TF1.cxx.

Referenced by EvalPar().

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

Definition at line 393 of file TF1.h.

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 1568 of file TF1.cxx.

Referenced by RooStats::LikelihoodIntervalPlot::Draw(), runTest(), and TestRoot().

TAxis * TF1::GetXaxis ( ) const

Get x axis of the function.

Definition at line 2095 of file TF1.cxx.

Referenced by RooStats::LikelihoodIntervalPlot::Draw(), SavePrimitive(), and Rgl::Mc::TF3Adapter::SetDataSource().

virtual Double_t TF1::GetXmax ( ) const
inlinevirtual
virtual Double_t TF1::GetXmin ( ) const
inlinevirtual
TAxis * TF1::GetYaxis ( ) const

Get y axis of the function.

Definition at line 2106 of file TF1.cxx.

Referenced by RooStats::LikelihoodIntervalPlot::Draw(), SavePrimitive(), and Rgl::Mc::TF3Adapter::SetDataSource().

TAxis * TF1::GetZaxis ( ) const

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

Definition at line 2117 of file TF1.cxx.

Referenced by Rgl::Mc::TF3Adapter::SetDataSource().

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
iparindex of parameter for which the derivative is computed
xpoint, 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 2140 of file TF1.cxx.

Referenced by ROOT::Math::WrappedTF1::DoParameterDerivative(), ROOT::Math::WrappedMultiTF1::DoParameterDerivative(), TFitter::GetConfidenceIntervals(), GradientPar(), ROOT::TF1Helper::TGradientParFunction::operator()(), ROOT::Math::WrappedTF1::ParameterGradient(), and ROOT::Math::WrappedMultiTF1::ParameterGradient().

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

Compute the gradient wrt parameters.

Parameters
xpoint, were the gradient is computed
gradused to return the computed gradient, assumed to be of at least fNpar size
epsif 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 paramter is fixed, the gradient on this parameter = 0

Definition at line 2206 of file TF1.cxx.

void TF1::InitArgs ( const Double_t x,
const Double_t params 
)
virtual
void TF1::InitStandardFunctions ( )
static

Create the basic function objects.

Definition at line 2236 of file TF1.cxx.

Referenced by TF1Convolution::TF1Convolution(), and TF1NormSum::TF1NormSum().

Double_t TF1::Integral ( Double_t  a,
Double_t  b,
Double_t  epsrel = 1.e-12 
)
virtual
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 parameteric 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 2445 of file TF1.cxx.

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 parameteric 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 2484 of file TF1.cxx.

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

Gauss-Legendre integral, see CalcGaussLegendreSamplingPoints.

Definition at line 2504 of file TF1.cxx.

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.

Input parameters:

Parameters
[in]nNumber of dimensions [2,15]
[in]a,bOne-dimensional arrays of length >= N . On entry A[i], and B[i], contain the lower and upper limits of integration, respectively.
[in]maxptsMaximum 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]epsrelSpecified relative accuracy.
[in]epsabsSpecified absolute accuracy. The integration algorithm will attempt to reach either the relative or the absolute accuracy. In case the maximum funcion called is reached the algorithm will stop earlier without having reached the desired accuracy
[out]relerrContains, on exit, an estimation of the relative accuracy of the result.
[out]nfnevlnumber 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 defult 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 2579 of file TF1.cxx.

Referenced by TF3::Integral(), TF2::Integral(), ROOT::TF1Helper::IntegralError(), and IntegralMultiple().

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 405 of file TF1.h.

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 reccomended to use the other interface where one can specify also epsabs and the maximum number of points

Definition at line 2524 of file TF1.cxx.

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 defult 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];
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 2353 of file TF1.cxx.

Referenced by Integral(), and ROOT::TF1Helper::IntegralError().

void TF1::IntegrateForNormalization ( )
protected
virtual Bool_t TF1::IsEvalNormalized ( ) const
inlinevirtual

Definition at line 409 of file TF1.h.

virtual Bool_t TF1::IsInside ( const Double_t x) const
inlinevirtual
virtual Bool_t TF1::IsLinear ( ) const
inlinevirtual
Bool_t TF1::IsValid ( ) const
virtual

Return kTRUE if the function is valid.

Definition at line 2609 of file TF1.cxx.

Referenced by TFitEditor::CheckFunctionString().

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

Definition at line 475 of file TF1.h.

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 3409 of file TF1.cxx.

Referenced by Mean().

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

Definition at line 538 of file TF1.h.

Double_t TF1::operator() ( const Double_t x,
const Double_t params = 0 
)
inlinevirtual

Definition at line 540 of file TF1.h.

TF1 & TF1::operator= ( const TF1 rhs)

Operator =.

Definition at line 685 of file TF1.cxx.

void TF1::Paint ( Option_t option = "")
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 2672 of file TF1.cxx.

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

Print TNamed name and title.

Reimplemented from TNamed.

Definition at line 2623 of file TF1.cxx.

Referenced by TProofBench::DrawCPU(), and TProofBench::DrawDataSet().

Bool_t TF1::RejectedPoint ( )
static
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 3390 of file TF1.cxx.

Referenced by TH1::Add(), TH1::Divide(), ROOT::Fit::DoFillData(), ROOT::Fit::FillData(), TFitter::FitChisquare(), TFumili::FitChisquare(), TFitter::FitChisquareI(), TFumili::FitChisquareI(), TFitter::FitLikelihood(), TFumili::FitLikelihood(), TFitter::FitLikelihoodI(), TFumili::FitLikelihoodI(), Graph2DFitChisquare(), GraphFitChisquare(), GraphFitChisquareFumili(), MultiGraphFitChisquare(), TProfile::Multiply(), THnBase::Multiply(), and TH1::Multiply().

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 2843 of file TF1.cxx.

Referenced by TFitParametersDialog::DoParBound(), TFitParametersDialog::DoParValue(), and TFitParametersDialog::SetParameters().

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 2853 of file TF1.cxx.

Referenced by copyTF1(), and HFit::StoreAndDrawFitFunction().

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

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

Reimplemented from TObject.

Reimplemented in TF2, TF3, and TF12.

Definition at line 2904 of file TF1.cxx.

virtual void TF1::SetChisquare ( Double_t  chi2)
inlinevirtual
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 3049 of file TF1.cxx.

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 3061 of file TF1.cxx.

template<class PtrObj , typename MemFn >
void TF1::SetFunction ( PtrObj &  p,
MemFn  memFn 
)

Definition at line 560 of file TF1.h.

template<typename Func >
void TF1::SetFunction ( Func  f)

Definition at line 554 of file TF1.h.

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 3100 of file TF1.cxx.

Referenced by RooStats::LikelihoodIntervalPlot::Draw(), TGeoPainter::DrawBatemanSol(), and THistPainter::PaintFunction().

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 3113 of file TF1.cxx.

Referenced by TGeoPainter::DrawBatemanSol(), and THistPainter::PaintFunction().

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 3125 of file TF1.cxx.

Referenced by TBinomialEfficiencyFitter::Fit(), HFit::Fit(), SetFitResult(), and ROOT::Fit::UnBinFit().

virtual void TF1::SetNormalized ( Bool_t  flag)
inlinevirtual

Definition at line 429 of file TF1.h.

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 3139 of file TF1.cxx.

Referenced by RooStats::BayesianCalculator::ApproximatePosterior(), TF1Editor::DoSliderXMoved(), TF1Editor::DoSliderXPressed(), TF1Editor::DoSliderXReleased(), TF1Editor::DoXPoints(), RooStats::LikelihoodIntervalPlot::Draw(), TKDE::GetKDEApproximateBias(), TKDE::GetKDEFunction(), TKDE::GetPDFLowerConfidenceInterval(), TKDE::GetPDFUpperConfidenceInterval(), unuranMulti2D(), and unuranMultiDim().

virtual void TF1::SetNumberFitPoints ( Int_t  npfits)
inlinevirtual
virtual void TF1::SetParameter ( Int_t  param,
Double_t  value 
)
inlinevirtual
virtual void TF1::SetParameter ( const TString name,
Double_t  value 
)
inlinevirtual

Definition at line 435 of file TF1.h.

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

Definition at line 443 of file TF1.h.

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

Definition at line 458 of file TF1.h.

Referenced by copyTF1(), and HFit::StoreAndDrawFitFunction().

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

Set error for parameter number ipar.

Definition at line 3181 of file TF1.cxx.

Referenced by TFunctionParametersDialog::DoReset(), and TFitParametersDialog::DoReset().

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 3192 of file TF1.cxx.

Referenced by TBinomialEfficiencyFitter::Fit(), HFit::Fit(), and ROOT::Fit::UnBinFit().

void TF1::SetParLimits ( Int_t  ipar,
Double_t  parmin,
Double_t  parmax 
)
virtual
void TF1::SetParName ( Int_t  ipar,
const char *  name 
)
virtual

Set name of parameter number ipar.

Definition at line 3157 of file TF1.cxx.

Referenced by RooAbsReal::asTF().

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

Set up to 10 parameter names.

Definition at line 3170 of file TF1.cxx.

Referenced by TProofBench::AssertFittingFun().

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 3223 of file TF1.cxx.

Referenced by copyTF1(), TH2::DoFitSlices(), TFunctionParametersDialog::DoOK(), TF1Editor::DoXPoints(), RooStats::LikelihoodIntervalPlot::Draw(), DrawF1(), TH3::FitSlicesZ(), TFunctionParametersDialog::RedrawFunction(), RooStats::HypoTestInverter::RunLimit(), TFitParametersDialog::SetParameters(), TF2::SetRange(), SetRange(), HFit::StoreAndDrawFitFunction(), and unuranDistr().

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

Reimplemented in TF2, and TF3.

Definition at line 548 of file TF1.h.

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 550 of file TF1.h.

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

Restore value of function saved at point.

Definition at line 3234 of file TF1.cxx.

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 3250 of file TF1.cxx.

Referenced by ROOT::Internal::TF1Builder< const char * >::Build(), RooStats::LikelihoodIntervalPlot::Draw(), TGeoPainter::DrawBatemanSol(), TKDE::GetKDEFunction(), and TF12::SetXY().

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 3360 of file TF1.cxx.

Referenced by SetFitResult(), SetNormalized(), SetNpx(), TF2::SetNpy(), TF3::SetNpz(), SetParameter(), SetParameters(), TF3::SetRange(), TF2::SetRange(), and SetRange().

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

Definition at line 476 of file TF1.h.

Friends And Related Function Documentation

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

Definition at line 152 of file TF1.h.

Member Data Documentation

std::vector<Double_t> TF1::fAlpha
protected

Integral of function binned on fNpx bins.

Definition at line 179 of file TF1.h.

Referenced by GetRandom(), and Update().

std::vector<Double_t> TF1::fBeta
protected

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

Definition at line 180 of file TF1.h.

Referenced by GetRandom(), and Update().

Double_t TF1::fChisquare
protected

Definition at line 171 of file TF1.h.

Referenced by Copy(), GetChisquare(), and GetProb().

TFormula* TF1::fFormula
protected

Functor object to wrap any C++ callable object.

Definition at line 188 of file TF1.h.

Referenced by ROOT::Internal::TF1Builder< const char * >::Build(), Copy(), Eval(), EvalPar(), GetFormula(), IsValid(), Print(), SetParameter(), SetParameters(), SetParName(), SetParNames(), TF1(), and ~TF1().

ROOT::Math::ParamFunctor TF1::fFunctor
protected

Definition at line 187 of file TF1.h.

Referenced by ROOT::Internal::TF1Builder< Func >::Build(), Copy(), EvalPar(), IsValid(), and Print().

std::atomic< Bool_t > TF1::fgAbsValue
staticprotected

Definition at line 191 of file TF1.h.

Referenced by AbsValue(), and IntegralOneDim().

std::atomic< Bool_t > TF1::fgAddToGlobList
staticprotected

Definition at line 193 of file TF1.h.

Referenced by DefaultAddToGlobalList(), and DoInitialize().

std::vector<Double_t> TF1::fGamma
protected

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

Definition at line 181 of file TF1.h.

Referenced by GetRandom(), and Update().

TF1 * TF1::fgCurrent = 0
staticprotected

Definition at line 194 of file TF1.h.

Referenced by EvalPar(), GetCurrent(), Paint(), and SetCurrent().

Bool_t TF1::fgRejectPoint = kFALSE
staticprotected

Definition at line 192 of file TF1.h.

Referenced by RejectedPoint(), and RejectPoint().

TH1* TF1::fHistogram
protected
std::vector<Double_t> TF1::fIntegral
protected

Definition at line 178 of file TF1.h.

Referenced by GetRandom(), TF2::GetRandom2(), TF3::GetRandom3(), and Update().

Double_t TF1::fMaximum
protected
TMethodCall* TF1::fMethodCall
protected

Pointer to histogram used for visualisation.

Definition at line 184 of file TF1.h.

Referenced by Copy(), EvalPar(), GetMethodCall(), InitArgs(), IsValid(), TF3::SavePrimitive(), TF2::SavePrimitive(), TF1(), and ~TF1().

Double_t TF1::fMinimum
protected
Int_t TF1::fNDF
protected

Definition at line 170 of file TF1.h.

Referenced by Copy(), GetNDF(), GetProb(), and SetNDF().

Int_t TF1::fNdim
protected

Definition at line 166 of file TF1.h.

Referenced by ROOT::Internal::TF1Builder< const char * >::Build(), Copy(), GetNdim(), and TF1().

Bool_t TF1::fNormalized
protected

Pointer to MethodCall in case of interpreted function.

Definition at line 185 of file TF1.h.

Referenced by Copy(), EvalPar(), IsEvalNormalized(), and Update().

Double_t TF1::fNormIntegral
protected

Definition at line 186 of file TF1.h.

Referenced by Copy(), EvalPar(), and Update().

Int_t TF1::fNpar
protected
Int_t TF1::fNpfits
protected

Definition at line 169 of file TF1.h.

Referenced by Copy(), GetNDF(), and GetNumberFitPoints().

Int_t TF1::fNpx
protected
TF1Parameters* TF1::fParams
protected
TObject* TF1::fParent
protected

Array gamma.

Definition at line 182 of file TF1.h.

Referenced by Copy(), GetParent(), GetSave(), Save(), and ~TF1().

std::vector<Double_t> TF1::fParErrors
protected

Definition at line 174 of file TF1.h.

Referenced by Copy(), GetParError(), SetFitResult(), SetParError(), SetParErrors(), and TF1().

std::vector<Double_t> TF1::fParMax
protected

Definition at line 176 of file TF1.h.

Referenced by Copy(), GetParLimits(), SetParLimits(), and TF1().

std::vector<Double_t> TF1::fParMin
protected

Definition at line 175 of file TF1.h.

Referenced by Copy(), GetParLimits(), SetParLimits(), and TF1().

std::vector<Double_t> TF1::fSave
protected
Int_t TF1::fType
protected
Double_t TF1::fXmax
protected
Double_t TF1::fXmin
protected

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