library: libGraf #include "TGraph.h"

# TGraph

class description - source file - inheritance tree (.pdf)

## class TGraph : public TNamed, public TAttLine, public TAttFill, public TAttMarker

| Inheritance Chart:

`TObject`

<-

`TNamed`

`TAttLine`

`TAttFill`

`TAttMarker`

<-

`TGraph`

<-

`TCutG` |

`TGraphAsymmErrors` |

`TGraphBentErrors` |

`TGraphErrors` |

        protected:

          virtual Double_t** Allocate(Int_t newsize)
                  Double_t** AllocateArrays(Int_t Narrays, Int_t arraySize)
                virtual void CopyAndRelease(Double_t** newarrays, Int_t ibegin, Int_t iend, Int_t obegin)
              virtual Bool_t CopyPoints(Double_t** newarrays, Int_t ibegin, Int_t iend, Int_t obegin)
                      Bool_t CtorAllocate()
                  Double_t** ExpandAndCopy(Int_t size, Int_t iend)
                virtual void FillZero(Int_t begin, Int_t end, Bool_t from_ctor = kTRUE)
                  Double_t** ShrinkAndCopy(Int_t size, Int_t iend)
                virtual void SwapPoints(Int_t pos1, Int_t pos2)
                 static void SwapValues(Double_t* arr, Int_t pos1, Int_t pos2)

        public:

                            TGraph()
                            TGraph(Int_t n)
                            TGraph(Int_t n, const Int_t* x, const Int_t* y)
                            TGraph(Int_t n, const Float_t* x, const Float_t* y)
                            TGraph(Int_t n, const Double_t* x, const Double_t* y)
                            TGraph(const TGraph& gr)
                            TGraph(const TVector& vx, const TVector& vy)
                            TGraph(const TVectorD& vx, const TVectorD& vy)
                            TGraph(const TH1* h)
                            TGraph(const TF1* f, Option_t* option = "")
                            TGraph(const char* filename, const char* format = "%lg %lg", Option_t* option = "")
                    virtual ~TGraph()
               virtual void Apply(TF1* f)
               virtual void Browse(TBrowser* b)
             static TClass* Class()
              static Bool_t CompareRadius(const TGraph* gr, Int_t left, Int_t right)
              static Bool_t CompareX(const TGraph* gr, Int_t left, Int_t right)
              static Bool_t CompareY(const TGraph* gr, Int_t left, Int_t right)
                       void ComputeLogs(Int_t npoints, Int_t opt)
               virtual void ComputeRange(Double_t& xmin, Double_t& ymin, Double_t& xmax, Double_t& ymax) const
              virtual Int_t DistancetoPrimitive(Int_t px, Int_t py)
               virtual void Draw(Option_t* chopt = "")
               virtual void DrawGraph(Int_t n, const Int_t* x, const Int_t* y, Option_t* option = "")
               virtual void DrawGraph(Int_t n, const Float_t* x, const Float_t* y, Option_t* option = "")
               virtual void DrawGraph(Int_t n, const Double_t* x = 0, const Double_t* y = 0, Option_t* option = "")
               virtual void DrawPanel()
           virtual Double_t Eval(Double_t x, TSpline* spline = 0, Option_t* option = "") const
               virtual void ExecuteEvent(Int_t event, Int_t px, Int_t py)
               virtual void Expand(Int_t newsize)
               virtual void Expand(Int_t newsize, Int_t step)
           virtual TObject* FindObject(const char* name) const
           virtual TObject* FindObject(const TObject* obj) const
              virtual Int_t Fit(const char* formula, Option_t* option = "", Option_t* goption = "", Axis_t xmin = 0, Axis_t xmax = 0)
              virtual Int_t Fit(TF1* f1, Option_t* option = "", Option_t* goption = "", Axis_t xmin = 0, Axis_t xmax = 0)
               virtual void FitPanel()
           virtual Double_t GetCorrelationFactor() const
           virtual Double_t GetCovariance() const
                     Bool_t GetEditable() const
           virtual Double_t GetErrorX(Int_t bin) const
           virtual Double_t GetErrorXhigh(Int_t bin) const
           virtual Double_t GetErrorXlow(Int_t bin) const
           virtual Double_t GetErrorY(Int_t bin) const
           virtual Double_t GetErrorYhigh(Int_t bin) const
           virtual Double_t GetErrorYlow(Int_t bin) const
          virtual Double_t* GetEX() const
          virtual Double_t* GetEXhigh() const
          virtual Double_t* GetEXlow() const
          virtual Double_t* GetEY() const
          virtual Double_t* GetEYhigh() const
          virtual Double_t* GetEYlow() const
                       TF1* GetFunction(const char* name) const
                      TH1F* GetHistogram() const
                     TList* GetListOfFunctions() const
                      Int_t GetMaxSize() const
           virtual Double_t GetMean(Int_t axis = 1) const
                      Int_t GetN() const
               virtual void GetPoint(Int_t i, Double_t& x, Double_t& y) const
           virtual Double_t GetRMS(Int_t axis = 1) const
                  Double_t* GetX() const
                     TAxis* GetXaxis() const
                  Double_t* GetY() const
                     TAxis* GetYaxis() const
               virtual void InitExpo(Double_t xmin = 0, Double_t xmax = 0)
               virtual void InitGaus(Double_t xmin = 0, Double_t xmax = 0)
               virtual void InitPolynom(Double_t xmin = 0, Double_t xmax = 0)
              virtual Int_t InsertPoint()
            virtual TClass* IsA() const
             virtual Bool_t IsEditable() const
               virtual void LeastSquareFit(Int_t m, Double_t* a, Double_t xmin = 0, Double_t xmax = 0)
               virtual void LeastSquareLinearFit(Int_t n, Double_t& a0, Double_t& a1, Int_t& ifail, Double_t xmin = 0, Double_t xmax = 0)
              virtual Int_t Merge(TCollection* list)
                    TGraph& operator=(const TGraph&)
               virtual void Paint(Option_t* chopt = "")
               virtual void PaintFit(TF1* fit)
               virtual void PaintGraph(Int_t npoints, const Double_t* x, const Double_t* y, Option_t* option = "")
               virtual void PaintGrapHist(Int_t npoints, const Double_t* x, const Double_t* y, Option_t* option = "")
               virtual void Print(Option_t* chopt = "") const
              virtual Int_t RemovePoint()
              virtual Int_t RemovePoint(Int_t ipoint)
               virtual void SavePrimitive(ofstream& out, Option_t* option)
               virtual void Set(Int_t n)
               virtual void SetEditable(Bool_t editable = kTRUE)
               virtual void SetHistogram(TH1* h)
               virtual void SetMaximum(Double_t maximum = -1111)
               virtual void SetMinimum(Double_t minimum = -1111)
               virtual void SetPoint(Int_t i, Double_t x, Double_t y)
               virtual void SetTitle(const char* title = "")
               virtual void ShowMembers(TMemberInspector& insp, char* parent)
                       void Smooth(Int_t npoints, Double_t* x, Double_t* y, Int_t drawtype)
               virtual void Sort(Bool_t (*)(const TGraph*, Int_t, Int_t) greater = &TGraph::CompareX, Bool_t ascending = kTRUE, Int_t low = 0, Int_t high = -1111)
               virtual void Streamer(TBuffer& b)
                       void StreamerNVirtual(TBuffer& b)
               virtual void UseCurrentStyle()
                       void Zero(Int_t& k, Double_t AZ, Double_t BZ, Double_t E2, Double_t& X, Double_t& Y, Int_t maxiterations)

### Data Members

        protected:

              Int_t fMaxSize    !Current dimension of arrays fX and fY
              Int_t fNpoints    Number of points <= fMaxSize
          Double_t* fX          [fNpoints] array of X points
          Double_t* fY          [fNpoints] array of Y points
             TList* fFunctions  Pointer to list of functions (fits and user)
              TH1F* fHistogram  Pointer to histogram used for drawing axis
           Double_t fMinimum    Minimum value for plotting along y
           Double_t fMaximum    Maximum value for plotting along y

        public:

          static const enum TGraph:: kClipFrame
          static const enum TGraph:: kNotEditable

## Class Description

       A Graph is a graphics object made of two arrays X and Y
       with npoints each.
       This class supports essentially two graph categories:
         - General case with non equidistant points
         - Special case with equidistant points
       The various format options to draw a Graph are explained in
         TGraph::PaintGraph  and TGraph::PaintGrapHist
       These two functions are derived from the HIGZ routines IGRAPH and IGHIST
       and many modifications.

      The picture below has been generated by the following macro:
    ------------------------------------------------------------------
    {
       TCanvas *c1 = new TCanvas("c1","A Simple Graph Example",200,10,700,500);
       Double_t x[100], y[100];
       Int_t n = 20;
       for (Int_t i=0;i<n;i++) {
         x[i] = i*0.1;
         y[i] = 10*sin(x[i]+0.2);
       }
       gr = new TGraph(n,x,y);
       gr->Draw("AC*");
    }

/* */

TGraph(): TNamed(), TAttLine(), TAttFill(1,1001), TAttMarker()

    *-*-*-*-*-*-*-*-*-*-*Graph default constructor-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
    *-*                  =========================

TGraph(Int_t n) : TNamed("Graph","Graph"), TAttLine(), TAttFill(1,1001), TAttMarker()

     constructor with only the number of points set
     the arrsys x and y will be set later

TGraph(Int_t n, const Int_t *x, const Int_t *y) : TNamed("Graph","Graph"), TAttLine(), TAttFill(1,1001), TAttMarker()

    *-*-*-*-*-*-*-*-*-*-*Graph normal constructor with ints-*-*-*-*-*-*-*-*-*
    *-*                  ==================================

TGraph(Int_t n, const Float_t *x, const Float_t *y) : TNamed("Graph","Graph"), TAttLine(), TAttFill(1,1001), TAttMarker()

    *-*-*-*-*-*-*-*-*-*-*Graph normal constructor with floats-*-*-*-*-*-*-*-*-*
    *-*                  ====================================

TGraph(Int_t n, const Double_t *x, const Double_t *y) : TNamed("Graph","Graph"), TAttLine(), TAttFill(1,1001), TAttMarker()

    *-*-*-*-*-*-*-*-*-*-*Graph normal constructor with doubles-*-*-*-*-*-*-*-*
    *-*                  ========================

TGraph(const TGraph &gr) : TNamed(gr), TAttLine(gr), TAttFill(gr), TAttMarker(gr)

     Copy constructor for this graph

TGraph(const TVector &vx, const TVector &vy) : TNamed("Graph","Graph"), TAttLine(), TAttFill(1,1001), TAttMarker()

     Graph constructor with two vectors of floats in input
     A graph is build with the X coordinates taken from vx and Y coord from vy
     The number of points in the graph is the minimum of number of points
     in vx and vy.

TGraph(const TVectorD &vx, const TVectorD &vy) : TNamed("Graph","Graph"), TAttLine(), TAttFill(1,1001), TAttMarker()

     Graph constructor with two vectors of doubles in input
     A graph is build with the X coordinates taken from vx and Y coord from vy
     The number of points in the graph is the minimum of number of points
     in vx and vy.

TGraph(const TH1 *h) : TNamed("Graph","Graph"), TAttLine(), TAttFill(1,1001), TAttMarker()

     Graph constructor importing its parameters from the TH1 object passed as argument

TGraph(const TF1 *f, Option_t *option) : TNamed("Graph","Graph"), TAttLine(), TAttFill(1,1001), TAttMarker()

     Graph constructor importing its parameters from the TF1 object passed as argument
     if option =="" (default), a TGraph is created with points computed
                    at the fNpx points of f.
     if option =="d", a TGraph is created with points computed with the derivatives
                    at the fNpx points of f.
     if option =="i", a TGraph is created with points computed with the integral
                    at the fNpx points of f.
     if option =="I", a TGraph is created with points computed with the integral
                    at the fNpx+1 points of f and the integral is normalized to 1.

TGraph(const char *filename, const char *format, Option_t *) : TNamed("Graph",filename), TAttLine(), TAttFill(1,1001), TAttMarker()

     Graph constructor reading input from filename
     filename is assumed to contain at least two columns of numbers
     the string format is by default "%lg %lg"

~TGraph()

    *-*-*-*-*-*-*-*-*-*-*Graph default destructor-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
    *-*                  =======================

Double_t** AllocateArrays(Int_t Narrays, Int_t arraySize)

void Apply(TF1 *f)

     apply function f to all the data points
     f may be a 1-D function TF1 or 2-d function TF2
     The Y values of the graph are replaced by the new values computed
     using the function

void Browse(TBrowser *b)

Bool_t CompareX(const TGraph* gr, Int_t left, Int_t right)

     return kTRUE if fX[left] > fX[right]. Can be used by Sort.

Bool_t CompareY(const TGraph* gr, Int_t left, Int_t right)

     return kTRUE if fY[left] > fY[right]. Can be used by Sort.

Bool_t CompareRadius(const TGraph* gr, Int_t left, Int_t right)

     return kTRUE if point number "left"'s distance to origin is bigger than
     that of point number "right". Can be used by Sort.

void ComputeRange(Double_t &, Double_t &, Double_t &, Double_t &) const

     this function is dummy in TGraph, but redefined by TGraphErrors

void CopyAndRelease(Double_t **newarrays, Int_t ibegin, Int_t iend, Int_t obegin)

     Copy points from fX and fY to arrays[0] and arrays[1]
     or to fX and fY if arrays == 0 and ibegin != iend.
     If newarrays is non null, replace fX, fY with pointers from newarrays[0,1].
     Delete newarrays, old fX and fY

Bool_t CopyPoints(Double_t **arrays, Int_t ibegin, Int_t iend, Int_t obegin)

     Copy points from fX and fY to arrays[0] and arrays[1]
     or to fX and fY if arrays == 0 and ibegin != iend.

Bool_t CtorAllocate()

     In constructors set fNpoints than call this method.
     Return kFALSE if the graph will contain no points.

void Draw(Option_t *option)

    *-*-*-*-*-*-*-*-*-*-*Draw this graph with its current attributes*-*-*-*-*-*-*
    *-*                  ==========================================

       Options to draw a graph are described in TGraph::PaintGraph

Int_t DistancetoPrimitive(Int_t px, Int_t py)

    *-*-*-*-*-*-*-*-*-*-*Compute distance from point px,py to a graph*-*-*-*-*-*
    *-*                  ===========================================
      Compute the closest distance of approach from point px,py to this line.
      The distance is computed in pixels units.

void DrawGraph(Int_t n, const Int_t *x, const Int_t *y, Option_t *option)

    *-*-*-*-*-*-*-*-*-*-*Draw this graph with new attributes*-*-*-*-*-*-*-*-*-*
    *-*                  ===================================

void DrawGraph(Int_t n, const Float_t *x, const Float_t *y, Option_t *option)

    *-*-*-*-*-*-*-*-*-*-*Draw this graph with new attributes*-*-*-*-*-*-*-*-*-*
    *-*                  ===================================

void DrawGraph(Int_t n, const Double_t *x, const Double_t *y, Option_t *option)

    *-*-*-*-*-*-*-*-*-*-*Draw this graph with new attributes*-*-*-*-*-*-*-*-*-*
    *-*                  ===================================

void DrawPanel()

    *-*-*-*-*-*-*Display a panel with all graph drawing options*-*-*-*-*-*
    *-*          ==============================================

Double_t Eval(Double_t x, TSpline *spline, Option_t *option) const

     Interpolate points in this graph at x using a TSpline
      -if spline==0 and option="" a linear interpolation between the two points
       close to x is computed. If x is outside the graph range, a linear
       extrapolation is computed.
      -if spline==0 and option="S" a TSpline3 object is created using this graph
       and the interpolated value from the spline is returned.
       the internally created spline is deleted on return.
      -if spline is specified, it is used to return the interpolated value.

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

    *-*-*-*-*-*-*-*-*-*-*Execute action corresponding to one event*-*-*-*
    *-*                  =========================================
      This member function is called when a graph is clicked with the locator

      If Left button clicked on one of the line end points, this point
         follows the cursor until button is released.

      if Middle button clicked, the line is moved parallel to itself
         until the button is released.

void Expand(Int_t newsize)

     if array sizes <= newsize, expand storage to 2*newsize.

void Expand(Int_t newsize, Int_t step)

     If graph capacity is less than newsize points then make array sizes
     equal to least multiple of step to contain newsize points.
     Returns kTRUE if size was altered

Double_t** ExpandAndCopy(Int_t size, Int_t iend)

     if size > fMaxSize allocate new arrays of 2*size points
      and copy oend first points.
     Return pointer to new arrays.

void FillZero(Int_t begin, Int_t end, Bool_t) // Set zero values for point arrays in the range [begin, end) // Should be redefined in descendant classes

TObject* FindObject(const char *name) const

     search object named name in the list of functions

TObject* FindObject(const TObject *obj) const

     search object obj in the list of functions

Int_t Fit(const char *fname, Option_t *option, Option_t *, Axis_t xmin, Axis_t xmax)

    *-*-*-*-*-*Fit this graph with function with name fname*-*-*-*-*-*-*-*-*-*
    *-*        ============================================
      interface to TGraph::Fit(TF1 *f1...

          fname is the name of an already predefined function created by TF1 or TF2
          Predefined functions such as gaus, expo and poln are automatically
          created by ROOT.
          fname can also be a formula, accepted by the linear fitter (linear parts divided
          by "++" sign), for example "x++sin(x)" for fitting "[0]*x+[1]*sin(x)"

Int_t Fit(TF1 *f1, Option_t *option, Option_t *, Axis_t rxmin, Axis_t rxmax)

    *-*-*-*-*-*-*-*-*-*-*Fit this graph with function f1*-*-*-*-*-*-*-*-*-*
    *-*                  ==================================

       f1 is an already predefined function created by TF1.
       Predefined functions such as gaus, expo and poln are automatically
       created by ROOT.

       The list of fit options is given in parameter option.
          option = "W"  Set all errors to 1
                 = "U" Use a User specified fitting algorithm (via SetFCN)
                 = "Q" Quiet mode (minimum printing)
                 = "V" Verbose mode (default is between Q and V)
                 = "B" Use this option when you want to fix one or more parameters
                       and the fitting function is like "gaus","expo","poln","landau".
                 = "R" Use the Range specified in the function range
                 = "N" Do not store the graphics function, do not draw
                 = "0" Do not plot the result of the fit. By default the fitted function
                       is drawn unless the option"N" above is specified.
                 = "+" Add this new fitted function to the list of fitted functions
                       (by default, any previous function is deleted)
                 = "C" In case of linear fitting, not calculate the chisquare
                        (saves time)
                 = "F" If fitting a polN, switch to minuit fitter
                 = "ROB" In case of linear fitting, compute the LTS regression
                         coefficients (robust(resistant) regression), using
                         the default fraction of good points
                   "ROB=0.x" - compute the LTS regression coefficients, using
                               0.x as a fraction of good points

       When the fit is drawn (by default), the parameter goption may be used
       to specify a list of graphics options. See TGraph::Paint for a complete
       list of these options.

       In order to use the Range option, one must first create a function
       with the expression to be fitted. For example, if your graph
       has a defined range between -4 and 4 and you want to fit a gaussian
       only in the interval 1 to 3, you can do:
            TF1 *f1 = new TF1("f1","gaus",1,3);
            graph->Fit("f1","R");

       who is calling this function
       ============================
       Note that this function is called when calling TGraphErrors::Fit
       or TGraphAsymmErrors::Fit ot TGraphBentErrors::Fit
       see the discussion below on the errors calulation.

       Linear fitting
       ============================
       When the fitting function is linear (contains the "++" sign) or the fitting
       function is a polynomial, a linear fitter is initialised.
       To create a linear function, use the following syntaxis: linear parts
       separated by "++" sign.
       Example: to fit the parameters of "[0]*x + [1]*sin(x)", create a
        TF1 *f1=new TF1("f1", "x++sin(x)", xmin, xmax);
       For such a TF1 you don't have to set the initial conditions
       Going via the linear fitter for functions, linear in parameters, gives a considerable
       advantage in speed.

       Setting initial conditions
       ==========================
       Parameters must be initialized before invoking the Fit function.
       The setting of the parameter initial values is automatic for the
       predefined functions : poln, expo, gaus, landau. One can however disable
       this automatic computation by specifying the option "B".
       You can specify boundary limits for some or all parameters via
            f1->SetParLimits(p_number, parmin, parmax);
       if parmin>=parmax, the parameter is fixed
       Note that you are not forced to fix the limits for all parameters.
       For example, if you fit a function with 6 parameters, you can do:
         func->SetParameters(0,3.1,1.e-6,0.1,-8,100);
         func->SetParLimits(4,-10,-4);
         func->SetParLimits(5, 1,1);
       With this setup, parameters 0->3 can vary freely
       Parameter 4 has boundaries [-10,-4] with initial value -8
       Parameter 5 is fixed to 100.

      Fit range
      =========
      The fit range can be specified in two ways:
        - specify rxmax > rxmin (default is rxmin=rxmax=0)
        - specify the option "R". In this case, the function will be taken
          instead of the full graph range.

       Changing the fitting function
       =============================
      By default the fitting function GraphFitChisquare is used.
      To specify a User defined fitting function, specify option "U" and
      call the following functions:
        TVirtualFitter::Fitter(mygraph)->SetFCN(MyFittingFunction)
      where MyFittingFunction is of type:
      extern void MyFittingFunction(Int_t &npar, Double_t *gin, Double_t &f, Double_t *u, Int_t flag);

      How errors are used in the chisquare function (see TFitter GraphFitChisquare)//   Access to the fit results
       ============================================
     In case of a TGraphErrors object, ex, the error along x,  is projected
     along the y-direction by calculating the function at the points x-exlow and
     x+exhigh.

     The chisquare is computed as the sum of the quantity below at each point:

                         (y - f(x))**2
             -----------------------------------
             ey**2 + ((f(x+exhigh) - f(x-exlow))/2)**2

     where x and y are the point coordinates.

     In case the function lies below (above) the data point, ey is ey_low (ey_high).

      thanks to Andy Haas (haas@yahoo.com) for adding the case with TGraphasymmerrors
                University of Washington

     a little different approach to approximating the uncertainty in y because of the
     errors in x, is to make it equal the error in x times the slope of the line.
     The improvement, compared to the first method (f(x+ exhigh) - f(x-exlow))/2
     is of (error of x)**2 order. This approach is called "effective variance method".
     This improvement has been made in version 4.00/08 by Anna Kreshuk.

     Note, that the linear fitter doesn't take into account the errors in x. If errors
     in x are important, go through minuit (use option "F" for polynomial fitting).

       Associated functions
       ====================
      One or more object (typically a TF1*) can be added to the list
      of functions (fFunctions) associated to each graph.
      When TGraph::Fit is invoked, the fitted function is added to this list.
      Given a graph gr, one can retrieve an associated function
      with:  TF1 *myfunc = gr->GetFunction("myfunc");

      If the graph is made persistent, the list of
      associated functions is also persistent. Given a pointer (see above)
      to an associated function myfunc, one can retrieve the function/fit
      parameters with calls such as:
        Double_t chi2 = myfunc->GetChisquare();
        Double_t par0 = myfunc->GetParameter(0); //value of 1st parameter
        Double_t err0 = myfunc->GetParError(0);  //error on first parameter

       Fit Statistics
       ==============
      You can change the statistics box to display the fit parameters with
      the TStyle::SetOptFit(mode) method. This mode has four digits.
      mode = pcev  (default = 0111)
        v = 1;  print name/values of parameters
        e = 1;  print errors (if e=1, v must be 1)
        c = 1;  print Chisquare/Number of degress of freedom
        p = 1;  print Probability

      For example: gStyle->SetOptFit(1011);
      prints the fit probability, parameter names/values, and errors.
      You can change the position of the statistics box with these lines
      (where g is a pointer to the TGraph):

      Root > TPaveStats *st = (TPaveStats*)g->GetListOfFunctions()->FindObject("stats")
      Root > st->SetX1NDC(newx1); //new x start position
      Root > st->SetX2NDC(newx2); //new x end position

void FitPanel()

    *-*-*-*-*-*-*Display a panel with all graph fit options*-*-*-*-*-*
    *-*          ==========================================

       See class TFitPanel for example

Double_t GetCorrelationFactor() const

     Return graph correlation factor

Double_t GetCovariance() const

     Return covariance of vectors x,y

Double_t GetMean(Int_t axis) const

     Return mean value of X (axis=1)  or Y (axis=2)

Double_t GetRMS(Int_t axis) const

     Return RMS of X (axis=1)  or Y (axis=2)

Double_t GetErrorX(Int_t) const

        This function is called by GraphFitChisquare.
        It always returns a negative value. Real implementation in TGraphErrors

Double_t GetErrorY(Int_t) const

        This function is called by GraphFitChisquare.
        It always returns a negative value. Real implementation in TGraphErrors

Double_t GetErrorXhigh(Int_t) const

        This function is called by GraphFitChisquare.
        It always returns a negative value. Real implementation in TGraphErrors
        and TGraphAsymmErrors

Double_t GetErrorXlow(Int_t) const

        This function is called by GraphFitChisquare.
        It always returns a negative value. Real implementation in TGraphErrors
        and TGraphAsymmErrors

Double_t GetErrorYhigh(Int_t) const

        This function is called by GraphFitChisquare.
        It always returns a negative value. Real implementation in TGraphErrors
        and TGraphAsymmErrors

Double_t GetErrorYlow(Int_t) const

        This function is called by GraphFitChisquare.
        It always returns a negative value. Real implementation in TGraphErrors
        and TGraphAsymmErrors

TF1* GetFunction(const char *name) const

    *-*-*-*-*Return pointer to function with name*-*-*-*-*-*-*-*-*-*-*-*-*
    *-*      ===================================

     Functions such as TGraph::Fit store the fitted function in the list of
     functions of this graph.

TH1F* GetHistogram() const

        Returns a pointer to the histogram used to draw the axis
        Takes into account the two following cases.
           1- option 'A' was specified in TGraph::Draw. Return fHistogram
           2- user had called TPad::DrawFrame. return pointer to hframe histogram

void GetPoint(Int_t i, Double_t &x, Double_t &y) const

    *-*-*-*-*-*-*-*-*-*-*Get x and y values for point number i*-*-*-*-*-*-*-*-*
    *-*                  =====================================

TAxis* GetXaxis() const

     Get x axis of the graph.

TAxis* GetYaxis() const

     Get y axis of the graph.

void InitGaus(Double_t xmin, Double_t xmax)

    *-*-*-*-*-*Compute Initial values of parameters for a gaussian*-*-*-*-*-*-*
    *-*        ===================================================

void InitExpo(Double_t xmin, Double_t xmax)

    *-*-*-*-*-*Compute Initial values of parameters for an exponential*-*-*-*-*
    *-*        =======================================================

void InitPolynom(Double_t xmin, Double_t xmax)

    *-*-*-*-*-*Compute Initial values of parameters for a polynom*-*-*-*-*-*-*
    *-*        ===================================================

Int_t InsertPoint()

     Insert a new point at the mouse position

void LeastSquareFit(Int_t m, Double_t *a, Double_t xmin, Double_t xmax)

    *-*-*-*-*-*-*-*Least squares lpolynomial fitting without weights*-*-*-*-*-*-*
    *-*            =================================================

      m     number of parameters
      a     array of parameters
      first 1st point number to fit (default =0)
      last  last point number to fit (default=fNpoints-1)

       based on CERNLIB routine LSQ: Translated to C++ by Rene Brun

void LeastSquareLinearFit(Int_t ndata, Double_t &a0, Double_t &a1, Int_t &ifail, Double_t xmin, Double_t xmax)

    *-*-*-*-*-*-*-*-*-*Least square linear fit without weights*-*-*-*-*-*-*-*-*
    *-*                =======================================

      Fit a straight line (a0 + a1*x) to the data in this graph.
      ndata:  number of points to fit
      first:  first point number to fit
      last:   last point to fit O(ndata should be last-first
      ifail:  return parameter indicating the status of the fit (ifail=0, fit is OK)

       extracted from CERNLIB LLSQ: Translated to C++ by Rene Brun

void Paint(Option_t *option)

    *-*-*-*-*-*-*-*-*-*-*Draw this graph with its current attributes*-*-*-*-*-*-*
    *-*                  ===========================================

void PaintFit(TF1 *fit)

      Paint "stats" box with the fit info

void PaintGraph(Int_t npoints, const Double_t *x, const Double_t *y, Option_t *chopt)

    *-*-*-*-*-*-*-*-*-*-*-*Control function to draw a graph*-*-*-*-*-*-*-*-*-*-*
    *-*                    ================================

      Draws one dimensional graphs. The aspect of the graph is done
      according to the value of the chopt.

      Input parameters:

      npoints : Number of points in X or in Y.
      x[npoints] or x[2] : X coordinates or (XMIN,XMAX) (WC space).
      y[npoints] or y[2] : Y coordinates or (YMIN,YMAX) (WC space).
      chopt : Option.

      chopt='L' :  A simple polyline between every points is drawn

      chopt='F' :  A fill area is drawn ('CF' draw a smooth fill area)

      chopt='A' :  Axis are drawn around the graph

      chopt='C' :  A smooth Curve is drawn

      chopt='*' :  A Star is plotted at each point

      chopt='P' :  Idem with the current marker

      chopt='B' :  A Bar chart is drawn at each point

      chopt='1' :  ylow=rwymin

void PaintGrapHist(Int_t npoints, const Double_t *x, const Double_t *y, Option_t *chopt)

    *-*-*-*-*-*-*-*-*Control function to draw a graphistogram*-*-*-*-*-*-*-*-*-*
    *-*              ========================================

       Draws one dimensional graphs. The aspect of the graph is done
     according to the value of the chopt.

     Input parameters:

      npoints : Number of points in X or in Y.
      X(N) or x[1] : X coordinates or (XMIN,XMAX) (WC space).
      Y(N) or y[1] : Y coordinates or (YMIN,YMAX) (WC space).
      chopt : Option.

      chopt='R' :  Graph is drawn horizontaly, parallel to X axis.
                   (default is vertically, parallel to Y axis)
                   If option R is selected the user must give:
                     2 values for Y (y[0]=YMIN and y[1]=YMAX)
                     N values for X, one for each channel.
                   Otherwise the user must give:
                     N values for Y, one for each channel.
                     2 values for X (x[0]=XMIN and x[1]=XMAX)

      chopt='L' :  A simple polyline beetwen every points is drawn

      chopt='H' :  An Histogram with equidistant bins is drawn
                   as a polyline.

      chopt='F' :  An histogram with equidistant bins is drawn
                   as a fill area. Contour is not drawn unless
                   chopt='H' is also selected..

      chopt='N' :  Non equidistant bins (default is equidistant)
                   If N is the number of channels array X and Y
                   must be dimensionned as follow:
                   If option R is not selected (default) then
                   the user must give:
                     (N+1) values for X (limits of channels).
                      N values for Y, one for each channel.
                   Otherwise the user must give:
                     (N+1) values for Y (limits of channels).
                      N values for X, one for each channel.

      chopt='F1':  Idem as 'F' except that fill area is no more
                   reparted arround axis X=0 or Y=0 .

      chopt='F2':  Draw a Fill area polyline connecting the center of bins

      chopt='C' :  A smooth Curve is drawn.

      chopt='*' :  A Star is plotted at the center of each bin.

      chopt='P' :  Idem with the current marker
      chopt='P0':  Idem with the current marker. Empty bins also drawn

      chopt='B' :  A Bar chart with equidistant bins is drawn as fill
                   areas (Contours are drawn).

      chopt='9' :  Force graph to be drawn in high resolution mode.
                   By default, the graph is drawn in low resolution
                   in case the number of points is greater than the number of pixels
                   in the current pad.

      chopt='][' : "Cutoff" style. When this option is selected together with
                   H option, the first and last vertical lines of the histogram
                   are not drawn.

void ComputeLogs(Int_t npoints, Int_t opt)

    *-*-*-*-*-*-*-*-*-*-*-*Convert WC from Log scales*-*-*-*-*-*-*-*-*-*-*-*
    *-*                    ==========================

       Take the LOG10 of gxwork and gywork according to the value of Options
       and put it in gxworkl and gyworkl.

      npoints : Number of points in gxwork and in gywork.

void Print(Option_t *) const

    *-*-*-*-*-*-*-*-*-*-*Print graph values*-*-*-*-*-*-*-*-*-*-*-*
    *-*                  ==================

Int_t RemovePoint()

     Delete point close to the mouse position

Int_t RemovePoint(Int_t ipoint)

     Delete point number ipoint

void SavePrimitive(ofstream &out, Option_t *option)

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

void Set(Int_t n)

     Set number of points in the graph
     Existing coordinates are preserved
     New coordinates above fNpoints are preset to 0.

Bool_t GetEditable() const

     Return kTRUE if kNotEditable bit is not set, kFALSE otherwise.

void SetEditable(Bool_t editable)

     if editable=kFALSE, the graph cannot be modified with the mouse
      by default a TGraph is editable

void SetMaximum(Double_t maximum)

void SetMinimum(Double_t minimum)

void SetPoint(Int_t i, Double_t x, Double_t y)

    *-*-*-*-*-*-*-*-*-*-*Set x and y values for point number i*-*-*-*-*-*-*-*-*
    *-*                  =====================================

void SetTitle(const char* title)

Double_t** ShrinkAndCopy(Int_t size, Int_t oend)

     if size*2 <= fMaxSize allocate new arrays of size points,
     copy points [0,oend).
     Return newarray (passed or new instance if it was zero
     and allocations are needed)

void Smooth(Int_t npoints, Double_t *x, Double_t *y, Int_t drawtype)

    *-*-*-*-*-*-*-*-*-*-*-*Smooth a curve given by N points*-*-*-*-*-*-*-*-*-*
    *-*                    ================================

       Underlaying routine for Draw based on the CERN GD3 routine TVIPTE

         Author - Marlow etc.   Modified by - P. Ward     Date -  3.10.1973

       This routine draws a smooth tangentially continuous curve through
     the sequence of data points P(I) I=1,N where P(I)=(X(I),Y(I))
     the curve is approximated by a polygonal arc of short vectors .
     the data points can represent open curves, P(1) != P(N) or closed
     curves P(2) == P(N) . If a tangential discontinuity at P(I) is
     required , then set P(I)=P(I+1) . loops are also allowed .

     Reference Marlow and Powell,Harwell report No.R.7092.1972
     MCCONALOGUE,Computer Journal VOL.13,NO4,NOV1970PP392 6

     _Input parameters:

      npoints   : Number of data points.
      x         : Abscissa
      y         : Ordinate

     delta is the accuracy required in constructing the curve.
     if it is zero then the routine calculates a value other-
     wise it uses this value. (default is 0.0)

void Sort(Bool_t (*greaterfunc)(const TGraph*, Int_t, Int_t) /*=TGraph::CompareX()*/, Bool_t ascending /*=kTRUE*/, Int_t low /* =0 */, Int_t high /* =-1111 */)

     Sorts the points of this TGraph using in-place quicksort (see e.g. older glibc).
     To compare two points the function parameter greaterfunc is used (see TGraph::CompareX for an
     example of such a method, which is also the default comparison function for Sort). After
     the sort, greaterfunc(this, i, j) will return kTRUE for all i>j if ascending == kTRUE, and
     kFALSE otherwise.

     The last two parameters are used for the recursive quick sort, stating the range to be sorted

     Examples:
       // sort points along x axis
       graph->Sort();
       // sort points along their distance to origin
       graph->Sort(&TGraph::CompareRadius);

       Bool_t CompareErrors(const TGraph* gr, Int_t i, Int_t j) {
         const TGraphErrors* ge=(const TGraphErrors*)gr;
         return (ge->GetEY()[i]>ge->GetEY()[j]); }
       // sort using the above comparison function, largest errors first
       graph->Sort(&CompareErrors, kFALSE);

void Streamer(TBuffer &b)

     Stream an object of class TGraph.

void SwapPoints(Int_t pos1, Int_t pos2)

void SwapValues(Double_t* arr, Int_t pos1, Int_t pos2)

void UseCurrentStyle()

     Set current style settings in this graph
     This function is called when either TCanvas::UseCurrentStyle
     or TROOT::ForceStyle have been invoked.

void Zero(Int_t &k,Double_t AZ,Double_t BZ,Double_t E2,Double_t &X,Double_t &Y ,Int_t maxiterations)

    *-*-*-*-*-*-*-*-*-*-*-*Find zero of a continuous function*-*-*-*-*-*-*-*-*-*
    *-*                    ==================================

      Underlaying routine for PaintGraph
     This function finds a real zero of the continuous real
     function Y(X) in a given interval (A,B). See accompanying
     notes for details of the argument list and calling sequence

Int_t Merge(TCollection* li)

     Adds all graphs from the collection to this graph.
     Returns the total number of poins in the result or -1 in case of an error.

### Inline Functions

             Double_t** Allocate(Int_t newsize)
                 TList* GetListOfFunctions() const
                  Int_t GetMaxSize() const
                  Int_t GetN() const
              Double_t* GetX() const
              Double_t* GetY() const
              Double_t* GetEX() const
              Double_t* GetEY() const
              Double_t* GetEXhigh() const
              Double_t* GetEXlow() const
              Double_t* GetEYhigh() const
              Double_t* GetEYlow() const
                 Bool_t IsEditable() const
                   void SetHistogram(TH1* h)
                TClass* Class()
                TClass* IsA() const
                   void ShowMembers(TMemberInspector& insp, char* parent)
                   void StreamerNVirtual(TBuffer& b)
                TGraph& operator=(const TGraph&)

Author: Rene Brun, Olivier Couet 12/12/94
Last update: root/graf:$Name: $:$Id: TGraph.cxx,v 1.164 2005/06/23 10:04:08 brun Exp $
Copyright (C) 1995-2000, Rene Brun and Fons Rademakers. *