ROOT » HIST » HIST » TF1

class TF1: public TFormula, public TAttLine, public TAttFill, public TAttMarker


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 (see TFormula) or a precompiled user function.
The function may have associated parameters.
TF1 graphics function is via the TH1/TGraph drawing functions.

The following types of functions can be created:

A - 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();
output of htmldoc/MACRO_TF1_1.gif

Case 2: inline expression using TMath functions without parameters

   TF1 *fa2 = new TF1("fa2","TMath::DiLog(x)",0,10);
   fa2->Draw();
output of htmldoc/MACRO_TF1_3.gif

Case 3: inline expression using a CINT function by name

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

B - 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();
output of htmldoc/MACRO_TF1_5.gif

C - 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 > myfunc();
   Root > myfit();
TF1 objects can reference other TF1 objects (thanks John
Odonnell) of type A or B defined above. This excludes CINT interpreted functions
and 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");
   }

D - 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 it can have a state and reference therefore what-ever other object. In this way the user can customize their 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 = new MyFunctionObject(....);       // create the function object
   TF1 * f = new TF1("f",fobj,0,1,npar,"MyFunctionObject");    // create TF1 class.
   .....
}
When constructing the TF1 class, the name of the function object class is required only if running in CINT and it is not needed in compiled C++ mode. In addition in compiled mode the cfnution object can be passed to TF1 by value. See also the tutorial math/exampleFunctor.C for a running example.

E - 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.
   .....
}
When constructing the TF1 class, the name of the function class and of the member function are required only if running in CINT and they are not need in compiled C++ mode. See also the tutorial math/exampleFunctor.C for a running example.
 

Function Members (Methods)

public:
virtual~TF1()
voidTObject::AbstractMethod(const char* method) const
static voidAbsValue(Bool_t reject = kTRUE)
virtual voidTFormula::Analyze(const char* schain, Int_t& err, Int_t offset = 0)
virtual Bool_tTFormula::AnalyzeFunction(TString& chaine, Int_t& err, Int_t offset = 0)
virtual voidTObject::AppendPad(Option_t* option = "")
virtual voidBrowse(TBrowser* b)
static voidCalcGaussLegendreSamplingPoints(Int_t num, Double_t* x, Double_t* w, Double_t eps = 3.0E-11)
virtual Double_tCentralMoment(Double_t n, Double_t a, Double_t b, const Double_t* params = 0, Double_t epsilon = 9.9999999999999995E-7)
static TClass*Class()
virtual const char*TObject::ClassName() const
virtual voidTFormula::Clear(Option_t* option = "")
virtual TObject*TNamed::Clone(const char* newname = "") const
virtual Int_tTNamed::Compare(const TObject* obj) const
virtual Int_tTFormula::Compile(const char* expression = "")
virtual voidCopy(TObject& f1) const
virtual char*TFormula::DefinedString(Int_t code)
virtual Double_tTFormula::DefinedValue(Int_t code)
virtual Int_tTFormula::DefinedVariable(TString& variable, Int_t& action)
virtual voidTObject::Delete(Option_t* option = "")MENU
virtual Double_tDerivative(Double_t x, Double_t* params = 0, Double_t epsilon = 0.001) const
virtual Double_tDerivative2(Double_t x, Double_t* params = 0, Double_t epsilon = 0.001) const
virtual Double_tDerivative3(Double_t x, Double_t* params = 0, Double_t epsilon = 0.001) const
static Double_tDerivativeError()
Int_tTAttLine::DistancetoLine(Int_t px, Int_t py, Double_t xp1, Double_t yp1, Double_t xp2, Double_t yp2)
virtual Int_tDistancetoPrimitive(Int_t px, Int_t py)
virtual voidDraw(Option_t* option = "")
virtual voidTObject::DrawClass() constMENU
virtual TObject*TObject::DrawClone(Option_t* option = "") constMENU
virtual TF1*DrawCopy(Option_t* option = "") const
virtual TObject*DrawDerivative(Option_t* option = "al")MENU
virtual voidDrawF1(const char* formula, Double_t xmin, Double_t xmax, Option_t* option = "")
virtual TObject*DrawIntegral(Option_t* option = "al")MENU
virtual voidTObject::Dump() constMENU
virtual voidTObject::Error(const char* method, const char* msgfmt) const
virtual Double_tEval(Double_t x, Double_t y = 0, Double_t z = 0, Double_t t = 0) const
virtual Double_tEvalPar(const Double_t* x, const Double_t* params = 0)
virtual Double_tTFormula::EvalParOld(const Double_t* x, const Double_t* params = 0)
virtual voidTObject::Execute(const char* method, const char* params, Int_t* error = 0)
virtual voidTObject::Execute(TMethod* method, TObjArray* params, Int_t* error = 0)
virtual voidExecuteEvent(Int_t event, Int_t px, Int_t py)
virtual voidTObject::Fatal(const char* method, const char* msgfmt) const
virtual voidTNamed::FillBuffer(char*& buffer)
virtual TObject*TObject::FindObject(const char* name) const
virtual TObject*TObject::FindObject(const TObject* obj) const
virtual voidFixParameter(Int_t ipar, Double_t value)
Double_tGetChisquare() const
static TF1*GetCurrent()
virtual Option_t*TObject::GetDrawOption() const
static Long_tTObject::GetDtorOnly()
virtual TStringTFormula::GetExpFormula(Option_t* option = "") const
virtual Color_tTAttFill::GetFillColor() const
virtual Style_tTAttFill::GetFillStyle() const
TH1*GetHistogram() const
virtual const char*TObject::GetIconName() const
virtual const TObject*TFormula::GetLinearPart(Int_t i)
virtual Color_tTAttLine::GetLineColor() const
virtual Style_tTAttLine::GetLineStyle() const
virtual Width_tTAttLine::GetLineWidth() const
virtual Color_tTAttMarker::GetMarkerColor() const
virtual Size_tTAttMarker::GetMarkerSize() const
virtual Style_tTAttMarker::GetMarkerStyle() const
virtual Double_tGetMaximum(Double_t xmin = 0, Double_t xmax = 0, Double_t epsilon = 1.0E-10, Int_t maxiter = 100, Bool_t logx = false) const
virtual Double_tGetMaximumX(Double_t xmin = 0, Double_t xmax = 0, Double_t epsilon = 1.0E-10, Int_t maxiter = 100, Bool_t logx = false) const
TMethodCall*GetMethodCall() const
virtual Double_tGetMinimum(Double_t xmin = 0, Double_t xmax = 0, Double_t epsilon = 1.0E-10, Int_t maxiter = 100, Bool_t logx = false) const
virtual Double_tGetMinimumX(Double_t xmin = 0, Double_t xmax = 0, Double_t epsilon = 1.0E-10, Int_t maxiter = 100, Bool_t logx = false) const
virtual const char*TNamed::GetName() const
virtual Int_tGetNDF() const
virtual Int_tTFormula::GetNdim() const
virtual Int_tTFormula::GetNpar() const
virtual Int_tGetNpx() const
virtual Int_tTFormula::GetNumber() const
virtual Int_tGetNumberFitPoints() const
virtual Int_tGetNumberFreeParameters() const
virtual char*GetObjectInfo(Int_t px, Int_t py) const
static Bool_tTObject::GetObjectStat()
virtual Option_t*TObject::GetOption() const
Double_tTFormula::GetParameter(Int_t ipar) const
Double_tTFormula::GetParameter(const char* name) const
virtual Double_t*TFormula::GetParameters() const
virtual voidTFormula::GetParameters(Double_t* params)
TObject*GetParent() const
virtual Double_tGetParError(Int_t ipar) const
virtual Double_t*GetParErrors() const
virtual voidGetParLimits(Int_t ipar, Double_t& parmin, Double_t& parmax) const
virtual const char*TFormula::GetParName(Int_t ipar) const
virtual Int_tTFormula::GetParNumber(const char* name) const
virtual Double_tGetProb() const
virtual Int_tGetQuantiles(Int_t nprobSum, Double_t* q, const Double_t* probSum)
virtual Double_tGetRandom()
virtual Double_tGetRandom(Double_t xmin, Double_t xmax)
virtual voidGetRange(Double_t& xmin, Double_t& xmax) const
virtual voidGetRange(Double_t& xmin, Double_t& ymin, Double_t& xmax, Double_t& ymax) const
virtual voidGetRange(Double_t& xmin, Double_t& ymin, Double_t& zmin, Double_t& xmax, Double_t& ymax, Double_t& zmax) const
virtual Double_tGetSave(const Double_t* x)
virtual const char*TNamed::GetTitle() const
virtual UInt_tTObject::GetUniqueID() const
virtual Double_tGetX(Double_t y, Double_t xmin = 0, Double_t xmax = 0, Double_t epsilon = 1.0E-10, Int_t maxiter = 100, Bool_t logx = false) const
TAxis*GetXaxis() const
virtual Double_tGetXmax() const
virtual Double_tGetXmin() const
TAxis*GetYaxis() const
TAxis*GetZaxis() const
virtual Double_tGradientPar(Int_t ipar, const Double_t* x, Double_t eps = 0.01)
virtual voidGradientPar(const Double_t* x, Double_t* grad, Double_t eps = 0.01)
virtual Bool_tTObject::HandleTimer(TTimer* timer)
virtual ULong_tTNamed::Hash() const
virtual voidTObject::Info(const char* method, const char* msgfmt) const
virtual Bool_tTObject::InheritsFrom(const char* classname) const
virtual Bool_tTObject::InheritsFrom(const TClass* cl) const
virtual voidInitArgs(const Double_t* x, const Double_t* params)
static voidInitStandardFunctions()
virtual voidTObject::Inspect() constMENU
virtual Double_tIntegral(Double_t a, Double_t b, Double_t epsrel = 9.9999999999999998E-13)
virtual Double_tIntegralError(Double_t a, Double_t b, const Double_t* params = 0, const Double_t* covmat = 0, Double_t epsilon = 0.01)
virtual Double_tIntegralError(Int_t n, const Double_t* a, const Double_t* b, const Double_t* params = 0, const Double_t* covmat = 0, Double_t epsilon = 0.01)
virtual Double_tIntegralFast(Int_t num, Double_t* x, Double_t* w, Double_t a, Double_t b, Double_t* params = 0, Double_t epsilon = 9.9999999999999998E-13)
virtual Double_tIntegralMultiple(Int_t n, const Double_t* a, const Double_t* b, Double_t epsrel, Double_t& relerr)
virtual Double_tIntegralMultiple(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 Double_tIntegralMultiple(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_tIntegralOneDim(Double_t a, Double_t b, Double_t epsrel, Double_t epsabs, Double_t& err)
voidTObject::InvertBit(UInt_t f)
virtual TClass*IsA() const
virtual Bool_tTObject::IsEqual(const TObject* obj) const
virtual Bool_tTObject::IsFolder() const
virtual Bool_tIsInside(const Double_t* x) const
virtual Bool_tTFormula::IsLinear() const
virtual Bool_tTFormula::IsNormalized() const
Bool_tTObject::IsOnHeap() const
virtual Bool_tTNamed::IsSortable() const
virtual Bool_tTAttFill::IsTransparent() const
Bool_tTObject::IsZombie() const
virtual voidTNamed::ls(Option_t* option = "") const
voidTObject::MayNotUse(const char* method) const
virtual Double_tMean(Double_t a, Double_t b, const Double_t* params = 0, Double_t epsilon = 9.9999999999999995E-7)
virtual voidTAttLine::Modify()
virtual Double_tMoment(Double_t n, Double_t a, Double_t b, const Double_t* params = 0, Double_t epsilon = 9.9999999999999995E-7)
virtual Bool_tTObject::Notify()
voidTObject::Obsolete(const char* method, const char* asOfVers, const char* removedFromVers) const
voidTObject::operator delete(void* ptr)
voidTObject::operator delete(void* ptr, void* vp)
voidTObject::operator delete[](void* ptr)
voidTObject::operator delete[](void* ptr, void* vp)
void*TObject::operator new(size_t sz)
void*TObject::operator new(size_t sz, void* vp)
void*TObject::operator new[](size_t sz)
void*TObject::operator new[](size_t sz, void* vp)
virtual Double_toperator()(const Double_t* x, const Double_t* params = 0)
virtual Double_toperator()(Double_t x, Double_t y = 0, Double_t z = 0, Double_t t = 0) const
TF1&operator=(const TF1& rhs)
voidTFormula::Optimize()
virtual voidPaint(Option_t* option = "")
virtual voidTObject::Pop()
virtual voidPrint(Option_t* option = "") const
virtual voidTFormula::ProcessLinear(TString& replaceformula)
virtual Int_tTObject::Read(const char* name)
virtual voidTObject::RecursiveRemove(TObject* obj)
static Bool_tRejectedPoint()
static voidRejectPoint(Bool_t reject = kTRUE)
virtual voidReleaseParameter(Int_t ipar)
virtual voidTAttFill::ResetAttFill(Option_t* option = "")
virtual voidTAttLine::ResetAttLine(Option_t* option = "")
virtual voidTAttMarker::ResetAttMarker(Option_t* toption = "")
voidTObject::ResetBit(UInt_t f)
virtual voidSave(Double_t xmin, Double_t xmax, Double_t ymin, Double_t ymax, Double_t zmin, Double_t zmax)
virtual voidTObject::SaveAs(const char* filename = "", Option_t* option = "") constMENU
virtual voidTAttFill::SaveFillAttributes(ostream& out, const char* name, Int_t coldef = 1, Int_t stydef = 1001)
virtual voidTAttLine::SaveLineAttributes(ostream& out, const char* name, Int_t coldef = 1, Int_t stydef = 1, Int_t widdef = 1)
virtual voidTAttMarker::SaveMarkerAttributes(ostream& out, const char* name, Int_t coldef = 1, Int_t stydef = 1, Int_t sizdef = 1)
virtual voidSavePrimitive(ostream& out, Option_t* option = "")
voidTObject::SetBit(UInt_t f)
voidTObject::SetBit(UInt_t f, Bool_t set)
virtual voidSetChisquare(Double_t chi2)
static voidSetCurrent(TF1* f1)
virtual voidTObject::SetDrawOption(Option_t* option = "")MENU
static voidTObject::SetDtorOnly(void* obj)
virtual voidTAttFill::SetFillAttributes()MENU
virtual voidTAttFill::SetFillColor(Color_t fcolor)
virtual voidTAttFill::SetFillColorAlpha(Color_t fcolor, Float_t falpha)
virtual voidTAttFill::SetFillStyle(Style_t fstyle)
virtual voidSetFitResult(const ROOT::Fit::FitResult& result, const Int_t* indpar = 0)
virtual voidTAttLine::SetLineAttributes()MENU
virtual voidTAttLine::SetLineColor(Color_t lcolor)
virtual voidTAttLine::SetLineColorAlpha(Color_t lcolor, Float_t lalpha)
virtual voidTAttLine::SetLineStyle(Style_t lstyle)
virtual voidTAttLine::SetLineWidth(Width_t lwidth)
virtual voidTAttMarker::SetMarkerAttributes()MENU
virtual voidTAttMarker::SetMarkerColor(Color_t mcolor = 1)
virtual voidTAttMarker::SetMarkerColorAlpha(Color_t mcolor, Float_t malpha)
virtual voidTAttMarker::SetMarkerSize(Size_t msize = 1)
virtual voidTAttMarker::SetMarkerStyle(Style_t mstyle = 1)
static voidTFormula::SetMaxima(Int_t maxop = 1000, Int_t maxpar = 1000, Int_t maxconst = 1000)
virtual voidSetMaximum(Double_t maximum = -1111)MENU
virtual voidSetMinimum(Double_t minimum = -1111)MENU
virtual voidTNamed::SetName(const char* name)MENU
virtual voidTNamed::SetNameTitle(const char* name, const char* title)
virtual voidSetNDF(Int_t ndf)
virtual voidSetNpx(Int_t npx = 100)MENU
virtual voidTFormula::SetNumber(Int_t number)
virtual voidSetNumberFitPoints(Int_t npfits)
static voidTObject::SetObjectStat(Bool_t stat)
virtual voidTFormula::SetParameter(const char* name, Double_t parvalue)
virtual voidTFormula::SetParameter(Int_t ipar, Double_t parvalue)
virtual voidTFormula::SetParameters(const Double_t* params)
virtual voidTFormula::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)MENU
virtual voidSetParent(TObject* p = 0)
virtual voidSetParError(Int_t ipar, Double_t error)
virtual voidSetParErrors(const Double_t* errors)
virtual voidSetParLimits(Int_t ipar, Double_t parmin, Double_t parmax)
virtual voidTFormula::SetParName(Int_t ipar, const char* name)
virtual voidTFormula::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")MENU
virtual voidSetRange(Double_t xmin, Double_t xmax)MENU
virtual voidSetRange(Double_t xmin, Double_t ymin, Double_t xmax, Double_t ymax)
virtual voidSetRange(Double_t xmin, Double_t ymin, Double_t zmin, Double_t xmax, Double_t ymax, Double_t zmax)
virtual voidSetSavedPoint(Int_t point, Double_t value)
virtual voidSetTitle(const char* title = "")MENU
virtual voidTObject::SetUniqueID(UInt_t uid)
virtual voidShowMembers(TMemberInspector& insp) const
virtual Int_tTNamed::Sizeof() const
virtual voidStreamer(TBuffer&)
voidStreamerNVirtual(TBuffer& ClassDef_StreamerNVirtual_b)
virtual voidTObject::SysError(const char* method, const char* msgfmt) const
Bool_tTObject::TestBit(UInt_t f) const
Int_tTObject::TestBits(UInt_t f) const
TF1()
TF1(const TF1& f1)
TF1(const char* name, const char* formula, Double_t xmin = 0, Double_t xmax = 1)
TF1(const char* name, Double_t xmin, Double_t xmax, Int_t npar)
TF1(const char* name, Double_t(*)(Double_t*,Double_t*) fcn, Double_t xmin = 0, Double_t xmax = 1, Int_t npar = 0)
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)
TF1(const char* name, ROOT::Math::ParamFunctor f, Double_t xmin = 0, Double_t xmax = 1, Int_t npar = 0)
virtual voidUpdate()
virtual voidTObject::UseCurrentStyle()
virtual Double_tVariance(Double_t a, Double_t b, const Double_t* params = 0, Double_t epsilon = 9.9999999999999995E-7)
virtual voidTObject::Warning(const char* method, const char* msgfmt) const
virtual Int_tTObject::Write(const char* name = 0, Int_t option = 0, Int_t bufsize = 0)
virtual Int_tTObject::Write(const char* name = 0, Int_t option = 0, Int_t bufsize = 0) const
protected:
virtual Bool_tTFormula::CheckOperands(Int_t operation, Int_t& err)
virtual Bool_tTFormula::CheckOperands(Int_t leftoperand, Int_t rightoperartion, Int_t& err)
voidTFormula::ClearFormula(Option_t* option = "")
virtual voidTFormula::Convert(UInt_t fromVersion)
voidCreateFromFunctor(const char* name, Int_t npar)
virtual voidTObject::DoError(int level, const char* location, const char* fmt, va_list va) const
Double_tTFormula::EvalParFast(const Double_t* x, const Double_t* params)
Double_tTFormula::EvalPrimitive(const Double_t* x, const Double_t* params)
Double_tTFormula::EvalPrimitive0(const Double_t* x, const Double_t* params)
Double_tTFormula::EvalPrimitive1(const Double_t* x, const Double_t* params)
Double_tTFormula::EvalPrimitive2(const Double_t* x, const Double_t* params)
Double_tTFormula::EvalPrimitive3(const Double_t* x, const Double_t* params)
Double_tTFormula::EvalPrimitive4(const Double_t* x, const Double_t* params)
Short_tTFormula::GetAction(Int_t code) const
Short_tTFormula::GetActionOptimized(Int_t code) const
Int_tTFormula::GetActionParam(Int_t code) const
Int_tTFormula::GetActionParamOptimized(Int_t code) const
virtual Double_tGetMinMaxNDim(Double_t* x, Bool_t findmax, Double_t epsilon = 0, Int_t maxiter = 0) const
Int_t*TFormula::GetOper() const
Int_t*TFormula::GetOperOptimized() const
virtual voidGetRange(Double_t* xmin, Double_t* xmax) const
virtual Bool_tTFormula::IsString(Int_t oper) const
voidTFormula::MakePrimitive(const char* expr, Int_t pos)
voidTObject::MakeZombie()
Int_tTFormula::PreCompile()
voidTFormula::SetAction(Int_t code, Int_t value, Int_t param = 0)
voidTFormula::SetActionOptimized(Int_t code, Int_t value, Int_t param = 0)
virtual Bool_tTFormula::StringToNumber(Int_t code)

Data Members

public:
static TObject::(anonymous)TObject::kBitMask
static TObject::EStatusBitsTObject::kCanDelete
static TObject::EStatusBitsTObject::kCannotPick
static TObject::EStatusBitsTObject::kHasUUID
static TObject::EStatusBitsTObject::kInvalidObject
static TObject::(anonymous)TObject::kIsOnHeap
static TObject::EStatusBitsTObject::kIsReferenced
static TFormula::(anonymous)TFormula::kLinear
static TObject::EStatusBitsTObject::kMustCleanup
static TObject::EStatusBitsTObject::kNoContextMenu
static TFormula::(anonymous)TFormula::kNormalized
static TObject::(anonymous)TObject::kNotDeleted
static TF1::(anonymous)kNotDraw
static TFormula::(anonymous)TFormula::kNotGlobal
static TObject::EStatusBitsTObject::kObjInCanvas
static TObject::(anonymous)TObject::kOverwrite
static TObject::(anonymous)TObject::kSingleKey
static TObject::(anonymous)TObject::kWriteDelete
static TObject::(anonymous)TObject::kZombie
protected:
Double_t*fAlpha!Array alpha. for each bin in x the deconvolution r of fIntegral
TBitsTFormula::fAlreadyFound! cache for information
Double_t*fBeta!Array beta. is approximated by x = alpha +beta*r *gamma*r**2
Double_tfChisquareFunction fit chisquare
Double_t*TFormula::fConst[fNconst] Array of fNconst formula constants
TString*TFormula::fExpr[fNoper] List of expressions
TString*TFormula::fExprOptimized![fNOperOptimized] List of expressions
Color_tTAttFill::fFillColorfill area color
Style_tTAttFill::fFillStylefill area style
TObjArrayTFormula::fFunctionsArray of function calls to make
ROOT::Math::ParamFunctorfFunctor! Functor object to wrap any C++ callable object
Double_t*fGamma!Array gamma.
TH1*fHistogram!Pointer to histogram used for visualisation
Double_t*fIntegral![fNpx] Integral of function binned on fNpx bins
Color_tTAttLine::fLineColorline color
Style_tTAttLine::fLineStyleline style
Width_tTAttLine::fLineWidthline width
TObjArrayTFormula::fLinearPartsLinear parts if the formula is linear (contains '|' or "++")
Color_tTAttMarker::fMarkerColorMarker color index
Size_tTAttMarker::fMarkerSizeMarker size
Style_tTAttMarker::fMarkerStyleMarker style
Double_tfMaximumMaximum value for plotting
TMethodCall*fMethodCall!Pointer to MethodCall in case of interpreted function
Double_tfMinimumMinimum value for plotting
Int_tfNDFNumber of degrees of freedom in the fit
Int_tTFormula::fNOperOptimized!Number of operators after optimization
TStringTNamed::fNameobject identifier
TString*TFormula::fNames[fNpar] Array of parameter names
Int_tTFormula::fNconstNumber of constants
Int_tTFormula::fNdimDimension of function (1=1-Dim, 2=2-Dim,etc)
Int_tTFormula::fNoperNumber of operators
Int_tTFormula::fNparNumber of parameters
Int_tfNpfitsNumber of points used in the fit
Int_tfNpxNumber of points used for the graphical representation
Int_tfNsaveNumber of points used to fill array fSave
Int_tTFormula::fNstringNumber of different constants character strings
Int_tTFormula::fNumberformula number identifier
Int_tTFormula::fNvalNumber of different variables in expression
TOperOffset*TFormula::fOperOffset![fNOperOptimized] Offsets of operrands
Int_t*TFormula::fOperOptimized![fNOperOptimized] List of operators. (See documentation for changes made at version 7)
TFormula::TFuncGTFormula::fOptimal!pointer to optimal function
Double_t*fParErrors[fNpar] Array of errors of the fNpar parameters
Double_t*fParMax[fNpar] Array of upper limits of the fNpar parameters
Double_t*fParMin[fNpar] Array of lower limits of the fNpar parameters
Double_t*TFormula::fParams[fNpar] Array of fNpar parameters
TObject*fParent!Parent object hooking this function (if one)
TFormulaPrimitive**TFormula::fPredefined![fNPar] predefined function
Double_t*fSave[fNsave] Array of fNsave function values
TStringTNamed::fTitleobject title
Int_tfType(=0 for standard functions, 1 if pointer to function)
Double_tfXmaxUpper bounds for the range
Double_tfXminLower bounds for the range
static Bool_tfgAbsValueuse absolute value of function when computing integral
static TF1*fgCurrentpointer to current function being processed
static Bool_tfgRejectPointTrue if point must be rejected in a fit
static TFormula::(anonymous)TFormula::kAdd
static TFormula::(anonymous)TFormula::kAnd
static TFormula::(anonymous)TFormula::kBinary
static TFormula::(anonymous)TFormula::kBitAnd
static TFormula::(anonymous)TFormula::kBitOr
static TFormula::(anonymous)TFormula::kBoolOptimize
static TFormula::(anonymous)TFormula::kBoolOptimizeAnd
static TFormula::(anonymous)TFormula::kBoolOptimizeOr
static TFormula::(anonymous)TFormula::kBoolSet
static TFormula::(anonymous)TFormula::kConstant
static TFormula::(anonymous)TFormula::kData
static TFormula::(anonymous)TFormula::kDefinedString
static TFormula::(anonymous)TFormula::kDefinedVariable
static TFormula::(anonymous)TFormula::kDivide
static TFormula::(anonymous)TFormula::kEnd
static TFormula::(anonymous)TFormula::kEqual
static TFormula::(anonymous)TFormula::kFD0
static TFormula::(anonymous)TFormula::kFD1
static TFormula::(anonymous)TFormula::kFD2
static TFormula::(anonymous)TFormula::kFD3
static TFormula::(anonymous)TFormula::kFDM
static TFormula::(anonymous)TFormula::kFunctionCall
static TFormula::(anonymous)TFormula::kGreater
static TFormula::(anonymous)TFormula::kGreaterThan
static TFormula::(anonymous)TFormula::kJump
static TFormula::(anonymous)TFormula::kJumpIf
static TFormula::(anonymous)TFormula::kLeftShift
static TFormula::(anonymous)TFormula::kLess
static TFormula::(anonymous)TFormula::kLessThan
static TFormula::(anonymous)TFormula::kModulo
static TFormula::(anonymous)TFormula::kMultD
static TFormula::(anonymous)TFormula::kMultDD
static TFormula::(anonymous)TFormula::kMultiply
static TFormula::(anonymous)TFormula::kNot
static TFormula::(anonymous)TFormula::kNotEqual
static TFormula::(anonymous)TFormula::kOr
static TFormula::(anonymous)TFormula::kParameter
static TFormula::(anonymous)TFormula::kPlusD
static TFormula::(anonymous)TFormula::kPlusDD
static TFormula::(anonymous)TFormula::kRightShift
static TFormula::(anonymous)TFormula::kSignInv
static TFormula::(anonymous)TFormula::kStringConst
static TFormula::(anonymous)TFormula::kStringEqual
static TFormula::(anonymous)TFormula::kStringNotEqual
static TFormula::(anonymous)TFormula::kSubstract
static TFormula::(anonymous)TFormula::kThree
static TFormula::(anonymous)TFormula::kUnary
static TFormula::(anonymous)TFormula::kVariable
static TFormula::(anonymous)TFormula::kabs
static TFormula::(anonymous)TFormula::kacos
static TFormula::(anonymous)TFormula::kacosh
static TFormula::(anonymous)TFormula::kasin
static TFormula::(anonymous)TFormula::kasinh
static TFormula::(anonymous)TFormula::katan
static TFormula::(anonymous)TFormula::katan2
static TFormula::(anonymous)TFormula::katanh
static TFormula::(anonymous)TFormula::kcos
static TFormula::(anonymous)TFormula::kcosh
static TFormula::(anonymous)TFormula::kexp
static TFormula::(anonymous)TFormula::kexpo
static TFormula::(anonymous)TFormula::kfmod
static TFormula::(anonymous)TFormula::kgaus
static TFormula::(anonymous)TFormula::kint
static TFormula::(anonymous)TFormula::klandau
static TFormula::(anonymous)TFormula::klog
static TFormula::(anonymous)TFormula::klog10
static TFormula::(anonymous)TFormula::kmax
static TFormula::(anonymous)TFormula::kmin
static TFormula::(anonymous)TFormula::kpi
static TFormula::(anonymous)TFormula::kpol
static TFormula::(anonymous)TFormula::kpow
static TFormula::(anonymous)TFormula::krndm
static TFormula::(anonymous)TFormula::ksign
static TFormula::(anonymous)TFormula::ksin
static TFormula::(anonymous)TFormula::ksinh
static TFormula::(anonymous)TFormula::ksq
static TFormula::(anonymous)TFormula::ksqrt
static TFormula::(anonymous)TFormula::kstrstr
static TFormula::(anonymous)TFormula::ktan
static TFormula::(anonymous)TFormula::ktanh
static TFormula::(anonymous)TFormula::kxexpo
static TFormula::(anonymous)TFormula::kxgaus
static TFormula::(anonymous)TFormula::kxlandau
static TFormula::(anonymous)TFormula::kxpol
static TFormula::(anonymous)TFormula::kxyexpo
static TFormula::(anonymous)TFormula::kxygaus
static TFormula::(anonymous)TFormula::kxylandau
static TFormula::(anonymous)TFormula::kyexpo
static TFormula::(anonymous)TFormula::kygaus
static TFormula::(anonymous)TFormula::kylandau
static TFormula::(anonymous)TFormula::kypol
static TFormula::(anonymous)TFormula::kzexpo
static TFormula::(anonymous)TFormula::kzgaus
static TFormula::(anonymous)TFormula::kzlandau
static TFormula::(anonymous)TFormula::kzpol

Class Charts

Class Charts

Function documentation

TF1()
 F1 default constructor.
TF1(const char* name, const char* formula, Double_t xmin = 0, Double_t xmax = 1)
 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.
TF1(const char* name, Double_t xmin, Double_t xmax, Int_t npar)
 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.
TF1(const char *name,Double_t (*fcn)(Double_t *, Double_t *), Double_t xmin, Double_t xmax, Int_t npar)
 F1 constructor using a pointer to a real function.

   npar is the number of free parameters used by the function

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

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

 WARNING! A function created with this constructor cannot be Cloned.
TF1(const char *name,Double_t (*fcn)(const Double_t *, const Double_t *), Double_t xmin, Double_t xmax, Int_t npar)
 F1 constructor using a pointer to real function.

   npar is the number of free parameters used by the function

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

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

 WARNING! A function created with this constructor cannot be Cloned.
TF1(const char* name, ROOT::Math::ParamFunctor f, Double_t xmin = 0, Double_t xmax = 1, Int_t npar = 0)
 F1 constructor using the Functor class.

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

   This constructor can be used only in compiled code

 WARNING! A function created with this constructor cannot be Cloned.
void CreateFromFunctor(const char* name, Int_t npar)
 Internal Function to Create a TF1  using a Functor.

          Used by the template constructors
TF1& operator=(const TF1& rhs)
 Operator =
~TF1()
 TF1 default destructor.
TF1(const TF1& f1)
 Constuctor.
void AbsValue(Bool_t reject = kTRUE)
 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.
void Copy(TObject& f1) const
 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)
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"

 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
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"

 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
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"

 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
Double_t DerivativeError()
 Static function returning the error of the last call to the of Derivative's
 functions
Int_t DistancetoPrimitive(Int_t px, Int_t py)
 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.
void Draw(Option_t* option = "")
 Draw this function with its current attributes.

 Possible option values are:
   "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.
TF1 * DrawCopy(Option_t* option = "") const
 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:
   "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"
TObject * DrawDerivative(Option_t* option = "al")
 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.
TObject * DrawIntegral(Option_t* option = "al")
 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.
void DrawF1(const char* formula, Double_t xmin, Double_t xmax, Option_t* option = "")
 Draw formula between xmin and xmax.
Double_t Eval(Double_t x, Double_t y = 0, Double_t z = 0, Double_t t = 0) const
 Evaluate this formula.

   Computes the value of this function (general case for a 3-d function)
   at point x,y,z.
   For a 1-d function give y=0 and z=0
   The current value of variables x,y,z is passed through x, y and z.
   The parameters used will be the ones in the array params if params is given
    otherwise parameters will be taken from the stored data members fParams
Double_t EvalPar(const Double_t* x, const Double_t* params = 0)
 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.
void ExecuteEvent(Int_t event, Int_t px, Int_t py)
 Execute action corresponding to one event.

  This member function is called when a F1 is clicked with the locator
void FixParameter(Int_t ipar, Double_t value)
 Fix the value of a parameter
 The specified value will be used in a fit operation
TF1 * GetCurrent()
 Static function returning the current function being processed
TH1 * GetHistogram() const
 Return a pointer to the histogram used to vusualize the function
Double_t GetMaximum(Double_t xmin = 0, Double_t xmax = 0, Double_t epsilon = 1.0E-10, Int_t maxiter = 100, Bool_t logx = false) const
 Return 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
Double_t GetMaximumX(Double_t xmin = 0, Double_t xmax = 0, Double_t epsilon = 1.0E-10, Int_t maxiter = 100, Bool_t logx = false) const
 Return 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
Double_t GetMinimum(Double_t xmin = 0, Double_t xmax = 0, Double_t epsilon = 1.0E-10, Int_t maxiter = 100, Bool_t logx = false) const
 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
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.
 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
Double_t GetMinimumX(Double_t xmin = 0, Double_t xmax = 0, Double_t epsilon = 1.0E-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
 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
Double_t GetX(Double_t y, Double_t xmin = 0, Double_t xmax = 0, Double_t epsilon = 1.0E-10, Int_t maxiter = 100, Bool_t logx = false) const
 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
Int_t GetNDF() const
 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.
Int_t GetNumberFreeParameters() const
 Return the number of free parameters
char * GetObjectInfo(Int_t px, Int_t py) const
 Redefines TObject::GetObjectInfo.
 Displays the function info (x, function value)
 corresponding to cursor position px,py
Double_t GetParError(Int_t ipar) const
 Return value of parameter number ipar
void GetParLimits(Int_t ipar, Double_t& parmin, Double_t& parmax) const
 Return limits for parameter ipar.
Double_t GetProb() const
 Return the fit probability
Int_t GetQuantiles(Int_t nprobSum, Double_t* q, const Double_t* probSum)
  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

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

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

     TGraph *gr = new TGraph(nprob);
     f1->GetQuantiles(nprob,gr->GetX());
     f2->GetQuantiles(nprob,gr->GetY());
     gr->Draw("alp");
Double_t GetRandom()
 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.
Double_t GetRandom(Double_t xmin, Double_t xmax)
 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.
void GetRange(Double_t* xmin, Double_t* xmax) const
 Return range of a generic N-D function.
void GetRange(Double_t& xmin, Double_t& xmax) const
 Return range of a 1-D function.
void GetRange(Double_t& xmin, Double_t& ymin, Double_t& xmax, Double_t& ymax) const
 Return range of a 2-D function.
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.
Double_t GetSave(const Double_t* x)
 Get value corresponding to X in array of fSave values
TAxis * GetXaxis() const
 Get x axis of the function.
TAxis * GetYaxis() const
 Get y axis of the function.
TAxis * GetZaxis() const
 Get z axis of the function. (In case this object is a TF2 or TF3)
Double_t GradientPar(Int_t ipar, const Double_t* x, Double_t eps = 0.01)
 Compute the gradient (derivative) wrt a parameter ipar
 Parameters:
 ipar - index of parameter for which the derivative is computed
 x - point, where the derivative is computed
 eps - if the errors of parameters have been computed, the step used in
 numerical differentiation is eps*parameter_error.
 if the errors have not been computed, step=eps is used
 default value of eps = 0.01
 Method is the same as in Derivative() function

 If a paramter is fixed, the gradient on this parameter = 0
void GradientPar(const Double_t* x, Double_t* grad, Double_t eps = 0.01)
 Compute the gradient wrt parameters
 Parameters:
 x - point, were the gradient is computed
 grad - used to return the computed gradient, assumed to be of at least fNpar size
 eps - if the errors of parameters have been computed, the step used in
 numerical differentiation is eps*parameter_error.
 if the errors have not been computed, step=eps is used
 default value of eps = 0.01
 Method is the same as in Derivative() function

 If a paramter is fixed, the gradient on this parameter = 0
void InitArgs(const Double_t* x, const Double_t* params)
 Initialize parameters addresses.
void InitStandardFunctions()
 Create the basic function objects
Double_t Integral(Double_t a, Double_t b, Double_t epsrel = 9.9999999999999998E-13)
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.
 The default integrator defined in ROOT::Math::IntegratorOneDimOptions::DefaultIntegrator() is used
 If ROOT contains the MathMore library the default integrator is set to be
 the adaptive ROOT::Math::GSLIntegrator (based on QUADPACK) or otherwise the
 ROOT::Math::GaussIntegrator is used
 See the reference documentation of these classes for more information about the
 integration algorithms
 To change integration algorithm just do :
 ROOT::Math::IntegratorOneDimOptions::SetDefaultIntegrator(IntegratorName);
 Valid integrator names are:
   - Gauss  :               for ROOT::Math::GaussIntegrator
   - GaussLegendre    :     for ROOT::Math::GaussLegendreIntegrator
   - Adaptive         :     for ROOT::Math::GSLIntegrator adaptive method (QAG)
   - AdaptiveSingular :     for ROOT::Math::GSLIntegrator adaptive singular method (QAGS)
   - NonAdaptive      :     for ROOT::Math::GSLIntegrator non adaptive (QNG)

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

 Note 1:
   Values of the function f(x) at the interval end-points A and B are not
   required. The subprogram may therefore be used when these values are
   undefined.

 Note 2:
   Instead of TF1::Integral, you may want to use the combination of
   TF1::CalcGaussLegendreSamplingPoints and TF1::IntegralFast.
   See an example with the following script:

   void gint() {
      TF1 *g = new TF1("g","gaus",-5,5);
      g->SetParameters(1,0,1);
      //default gaus integration method uses 6 points
      //not suitable to integrate on a large domain
      double r1 = g->Integral(0,5);
      double r2 = g->Integral(0,1000);

      //try with user directives computing more points
      Int_t np = 1000;
      double *x=new double[np];
      double *w=new double[np];
      g->CalcGaussLegendreSamplingPoints(np,x,w,1e-15);
      double r3 = g->IntegralFast(np,x,w,0,5);
      double r4 = g->IntegralFast(np,x,w,0,1000);
      double r5 = g->IntegralFast(np,x,w,0,10000);
      double r6 = g->IntegralFast(np,x,w,0,100000);
      printf("g->Integral(0,5)               = %g\n",r1);
      printf("g->Integral(0,1000)            = %g\n",r2);
      printf("g->IntegralFast(n,x,w,0,5)     = %g\n",r3);
      printf("g->IntegralFast(n,x,w,0,1000)  = %g\n",r4);
      printf("g->IntegralFast(n,x,w,0,10000) = %g\n",r5);
      printf("g->IntegralFast(n,x,w,0,100000)= %g\n",r6);
      delete [] x;
      delete [] w;
   }

   This example produces the following results:

      g->Integral(0,5)               = 1.25331
      g->Integral(0,1000)            = 1.25319
      g->IntegralFast(n,x,w,0,5)     = 1.25331
      g->IntegralFast(n,x,w,0,1000)  = 1.25331
      g->IntegralFast(n,x,w,0,10000) = 1.25331
      g->IntegralFast(n,x,w,0,100000)= 1.253
Double_t IntegralError(Double_t a, Double_t b, const Double_t* params = 0, const Double_t* covmat = 0, Double_t epsilon = 0.01)
 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() );
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 = 0.01)
 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() );
Double_t IntegralFast(const TGraph *g, Double_t a, Double_t b, Double_t *params)
 Gauss-Legendre integral, see CalcGaussLegendreSamplingPoints
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.
  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
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

 Input parameters:

    n     : Number of dimensions [2,15]
    a,b   : One-dimensional arrays of length >= N . On entry A[i],  and  B[i],
            contain the lower and upper limits of integration, respectively.
    maxpts: Maximum number of function evaluations to be allowed.
            maxpts >= 2^n +2*n*(n+1) +1
            if maxpts<minpts, maxpts is set to 10*minpts
    epsrel   : Specified relative accuracy.
    epsabs   : Specified 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

 Output parameters:

    relerr : Contains, on exit, an estimation of the relative accuracy of the result.
    nfnevl : number of function evaluations performed.
    ifail  :
        0 Normal exit.  . At least minpts and at most maxpts calls to the function were performed.
        1 maxpts is too small for the specified accuracy eps.
          The result and relerr contain the values obtainable for the
          specified value of maxpts.
        3 n<2 or n>15

 Method:

    The default method used is the Genz-Mallik adaptive multidimensional algorithm
    using the class ROOT::Math::AdaptiveIntegratorMultiDim
    (see the reference documentation of the class)
   Other methods can be used by setting ROOT::Math::IntegratorMultiDimOptions::SetDefaultIntegrator()
   to different integrators.
   Other possible integrators are MC integrators based on the ROOT::Math::GSLMCIntegrator class
   Possible methods are : Vegas, Miser or Plain
   IN case of MC integration the accuracy is determined by the number of function calls, one should be
   careful not to use a too large value of maxpts
Bool_t IsInside(const Double_t* x) const
 Return kTRUE if the point is inside the function range
void Paint(Option_t* option = "")
 Paint this function with its current attributes.
void Print(Option_t* option = "") const
 Dump this function with its attributes.
void ReleaseParameter(Int_t ipar)
 Release parameter number ipar If used in a fit, the parameter
 can vary freely. The parameter limits are reset to 0,0.
void Save(Double_t xmin, Double_t xmax, Double_t ymin, Double_t ymax, Double_t zmin, Double_t zmax)
 Save values of function in array fSave
void SavePrimitive(ostream& out, Option_t* option = "")
 Save primitive as a C++ statement(s) on output stream out
void SetCurrent(TF1* f1)
 Static function setting the current function.
 the current function may be accessed in static C-like functions
 when fitting or painting a function.
void SetFitResult(const ROOT::Fit::FitResult& result, const Int_t* indpar = 0)
 Set the result from the fit
 parameter values, errors, chi2, etc...
 Optionally a pointer to a vector (with size fNpar) of the parameter indices in the FitResult can be passed
 This is useful in the case of a combined fit with different functions, and the FitResult contains the global result
 By default it is assume that indpar = {0,1,2,....,fNpar-1}.
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
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
void SetNDF(Int_t ndf)
 Set the number of degrees of freedom
 ndf should be the number of points used in a fit - the number of free parameters
void SetNpx(Int_t npx = 100)
 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
void SetParError(Int_t ipar, Double_t error)
 Set error for parameter number ipar
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
void SetParLimits(Int_t ipar, Double_t parmin, Double_t parmax)
 Set limits for parameter ipar.

 The specified limits will be used in a fit operation
 when the option "B" is specified (Bounds).
 To fix a parameter, use TF1::FixParameter
void SetRange(Double_t xmin, Double_t xmax)
 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.
void SetSavedPoint(Int_t point, Double_t value)
 Restore value of function saved at point
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.
void Streamer(TBuffer& )
 Stream a class object.
void Update()
 Called by functions such as SetRange, SetNpx, SetParameters
 to force the deletion of the associated histogram or Integral
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.
 This flag can be set by a user in a fitting function.
 The fgRejectPoint flag is reset by the TH1 and TGraph fitting functions.
Double_t Moment(Double_t n, Double_t a, Double_t b, const Double_t* params = 0, Double_t epsilon = 9.9999999999999995E-7)
 Return nth moment of function between a and b

 See TF1::Integral() for parameter definitions
Double_t CentralMoment(Double_t n, Double_t a, Double_t b, const Double_t* params = 0, Double_t epsilon = 9.9999999999999995E-7)
 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@bnl.gov>
void CalcGaussLegendreSamplingPoints(TGraph *g, Double_t eps)
 Type safe interface (static method)
 The number of sampling points are taken from the TGraph
Double_t operator()(Double_t x, Double_t y = 0, Double_t z = 0, Double_t t = 0) const
{ return Eval(x,y,z,t); }
Double_t operator()(const Double_t* x, const Double_t* params = 0)
void SetRange(Double_t xmin, Double_t ymin, Double_t xmax, Double_t ymax)
{ TF1::SetRange(xmin, xmax); }
void SetRange(Double_t xmin, Double_t ymin, Double_t zmin, Double_t xmax, Double_t ymax, Double_t zmax)
{ TF1::SetRange(xmin, xmax); }
Double_t GetChisquare() const
{return fChisquare;}
Int_t GetNpx() const
{return fNpx;}
Int_t GetNumberFitPoints() const
{return fNpfits;}
TObject * GetParent() const
{return fParent;}
Double_t * GetParErrors() const
{return fParErrors;}
Double_t GetXmin() const
{return fXmin;}
Double_t GetXmax() const
{return fXmax;}
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)
 for backward compatibility
void SetChisquare(Double_t chi2)
{fChisquare = chi2;}
void SetNumberFitPoints(Int_t npfits)
{fNpfits = npfits;}
void SetParent(TObject* p = 0)
{fParent = p;}
Double_t Mean(Double_t a, Double_t b, const Double_t* params = 0, Double_t epsilon = 9.9999999999999995E-7)
{return Moment(1,a,b,params,epsilon);}
Double_t Variance(Double_t a, Double_t b, const Double_t* params = 0, Double_t epsilon = 9.9999999999999995E-7)
{return CentralMoment(2,a,b,params,epsilon);}