TGraph2D.cxx

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// @(#)root/hist:$Id: TGraph2D.cxx,v 1.00
// Author: Olivier Couet

/*************************************************************************
 * Copyright (C) 1995-2000, Rene Brun and Fons Rademakers.               *
 * All rights reserved.                                                  *
 *                                                                       *
 * For the licensing terms see $ROOTSYS/LICENSE.                         *
 * For the list of contributors see $ROOTSYS/README/CREDITS.             *
 *************************************************************************/

#include "Riostream.h"
#include "TROOT.h"
#include "TMath.h"
#include "TH2.h"
#include "TF2.h"
#include "TList.h"
#include "TGraph2D.h"
#include "TGraphDelaunay.h"
#include "TVirtualPad.h"
#include "TVirtualFitter.h"
#include "TPluginManager.h"
#include "TClass.h"
#include "TSystem.h"
#include <stdlib.h>

#include "HFitInterface.h"
#include "Fit/DataRange.h"
#include "Math/MinimizerOptions.h"

ClassImp(TGraph2D)


//______________________________________________________________________________
/* Begin_Html
<center><h2>Graph 2D class</h2></center>
A Graph2D is a graphics object made of three arrays X, Y and Z with the same
number of points each.
<p>
This class has different constructors:
<ol>
<p><li> With an array's dimension and three arrays x, y, and z:
<pre>
   TGraph2D *g = new TGraph2D(n, x, y, z);
</pre>
    x, y, z arrays can be doubles, floats, or ints.

<p><li> With an array's dimension only:
<pre>
   TGraph2D *g = new TGraph2D(n);
</pre>
   The internal arrays are then filled with SetPoint. The following line
   fills the the internal arrays at the position "i" with the values x,y,z.
<pre>
   g->SetPoint(i, x, y, z);
</pre>
<p><li> Without parameters:
<pre>
   TGraph2D *g = new TGraph2D();
</pre>
   again SetPoint must be used to fill the internal arrays.
<p><li> From a file:
<pre>
   TGraph2D *g = new TGraph2D("graph.dat");
</pre>
   Arrays are read from the ASCII file "graph.dat" according to a specifies
   format. The format's default value is "%lg %lg %lg"
</ol>

Note that in any of these three cases, SetPoint can be used to change a data
point or add a new one. If the data point index (i) is greater than the
current size of the internal arrays, they are automatically extended.
<p>
Specific drawing options can be used to paint a TGraph2D:

<table border=0>

<tr><th valign=top>"TRI"</th><td>
The Delaunay triangles are drawn using filled area.
An hidden surface drawing technique is used. The surface is
painted with the current fill area color. The edges of each
triangles are painted with the current line color.
</td></tr>

<tr><th valign=top>"TRIW</th><td>
The Delaunay triangles are drawn as wire frame
</td></tr>

<tr><th valign=top>"TRI1</th><td>
The Delaunay triangles are painted with color levels. The edges
of each triangles are painted with the current line color.
</td></tr>

<tr><th valign=top>"TRI2</th><td>
the Delaunay triangles are painted with color levels.
</td></tr>

<tr><th valign=top>"P"  </th><td>
Draw a marker at each vertex
</td></tr>

<tr><th valign=top>"P0" </th><td>
Draw a circle at each vertex. Each circle background is white.
</td></tr>

<tr><th valign=top>"PCOL" </th><td>
Draw a marker at each vertex. The color of each marker is
defined according to its Z position.
</td></tr>

<tr><th valign=top>"CONT" </th><td>
Draw contours.
</td></tr>

<tr><th valign=top>"LINE" </th><td>
Draw a 3D polyline.
</td></tr>

</table>

A TGraph2D can be also drawn with ANY options valid to draw a 2D histogram.
<p>
When a TGraph2D is drawn with one of the 2D histogram drawing option,
a intermediate 2D histogram is filled using the Delaunay triangles
technique to interpolate the data set.
<p>
TGraph2D linearly interpolate a Z value for any (X,Y) point given some
existing (X,Y,Z) points. The existing (X,Y,Z) points can be randomly
scattered. The algorithm works by joining the existing points to make
Delaunay triangles in (X,Y). These are then used to define flat planes
in (X,Y,Z) over which to interpolate. The interpolated surface thus takes
the form of tessellating triangles at various angles. Output can take the
form of a 2D histogram or a vector. The triangles found can be drawn in 3D.
<p>
This software cannot be guaranteed to work under all circumstances. They
were originally written to work with a few hundred points in an XY space
with similar X and Y ranges.
<p>
Example:

End_Html
Begin_Macro(source)
{
   TCanvas *c = new TCanvas("c","Graph2D example",0,0,600,400);
   Double_t x, y, z, P = 6.;
   Int_t np = 200;
   TGraph2D *dt = new TGraph2D();
   TRandom *r = new TRandom();
   for (Int_t N=0; N<np; N++) {
      x = 2*P*(r->Rndm(N))-P;
      y = 2*P*(r->Rndm(N))-P;
      z = (sin(x)/x)*(sin(y)/y)+0.2;
      dt->SetPoint(N,x,y,z);
   }
   gStyle->SetPalette(1);
   dt->Draw("surf1");
   return c;
}
End_Macro
Begin_Html

2D graphs can be fitted as shown by the following example:

End_Html
Begin_Macro(source)
../../../tutorials/fit/graph2dfit.C
End_Macro
Begin_Html

Example showing the PCOL option.

End_Html
Begin_Macro(source)
{
   TCanvas *c1 = new TCanvas("c1","Graph2D example",0,0,600,400);
   Double_t P = 5.;
   Int_t npx  = 20 ;
   Int_t npy  = 20 ;
   Double_t x = -P;
   Double_t y = -P;
   Double_t z;
   Int_t k = 0;
   Double_t dx = (2*P)/npx;
   Double_t dy = (2*P)/npy;
   TGraph2D *dt = new TGraph2D(npx*npy);
   dt->SetNpy(41);
   dt->SetNpx(40);
   for (Int_t i=0; i<npx; i++) {
      for (Int_t j=0; j<npy; j++) {
         z = sin(sqrt(x*x+y*y))+1;
         dt->SetPoint(k,x,y,z);
         k++;
         y = y+dx;
      }
      x = x+dx;
      y = -P;
   }
   gStyle->SetPalette(1);
   dt->SetMarkerStyle(20);
   dt->Draw("pcol");
   return c1;
}
End_Macro
Begin_Html

<h3>Definition of Delaunay triangulation (After B. Delaunay)</h3>
For a set S of points in the Euclidean plane, the unique triangulation DT(S)
of S such that no point in S is inside the circumcircle of any triangle in
DT(S). DT(S) is the dual of the Voronoi diagram of S.
If n is the number of points in S, the Voronoi diagram of S is the partitioning
of the plane containing S points into n convex polygons such that each polygon
contains exactly one point and every point in a given polygon is closer to its
central point than to any other. A Voronoi diagram is sometimes also known as
a Dirichlet tessellation.

<img src="gif/dtvd.gif">

<br>
<a href="http://www.cs.cornell.edu/Info/People/chew/Delaunay.html">This applet</a>
gives a nice practical view of Delaunay triangulation and Voronoi diagram.
End_Html */


//______________________________________________________________________________
TGraph2D::TGraph2D()
         : TNamed("Graph2D","Graph2D"), TAttLine(1,1,1), TAttFill(0,1001),
           TAttMarker(), fNpoints(0)
{
   // Graph2D default constructor

   fSize      = 0;
   fMargin    = 0.;
   fNpx       = 40;
   fNpy       = 40;
   fDirectory = 0;
   fHistogram = 0;
   fMaximum   = -1111;
   fMinimum   = -1111;
   fX         = 0;
   fY         = 0;
   fZ         = 0;
   fZout      = 0;
   fMaxIter   = 100000;
   fPainter   = 0;
   fFunctions = new TList;
   fUserHisto = kFALSE;
}


//______________________________________________________________________________
TGraph2D::TGraph2D(Int_t n, Int_t *x, Int_t *y, Int_t *z)
         : TNamed("Graph2D","Graph2D"), TAttLine(1,1,1), TAttFill(0,1001),
           TAttMarker(), fNpoints(n)
{
   // Graph2D constructor with three vectors of ints as input.

   Build(n);

   // Copy the input vectors into local arrays
   for (Int_t i=0; i<fNpoints; ++i) {
      fX[i] = (Double_t)x[i];
      fY[i] = (Double_t)y[i];
      fZ[i] = (Double_t)z[i];
   }
}


//______________________________________________________________________________
TGraph2D::TGraph2D(Int_t n, Float_t *x, Float_t *y, Float_t *z)
         : TNamed("Graph2D","Graph2D"), TAttLine(1,1,1), TAttFill(0,1001),
           TAttMarker(), fNpoints(n)
{
   // Graph2D constructor with three vectors of floats as input.

   Build(n);

   // Copy the input vectors into local arrays
   for (Int_t i=0; i<fNpoints; ++i) {
      fX[i] = x[i];
      fY[i] = y[i];
      fZ[i] = z[i];
   }
}


//______________________________________________________________________________
TGraph2D::TGraph2D(Int_t n, Double_t *x, Double_t *y, Double_t *z)
         : TNamed("Graph2D","Graph2D"), TAttLine(1,1,1), TAttFill(0,1001),
           TAttMarker(), fNpoints(n)
{
   // Graph2D constructor with three vectors of doubles as input.

   Build(n);

   // Copy the input vectors into local arrays
   for (Int_t i=0; i<fNpoints; ++i) {
      fX[i] = x[i];
      fY[i] = y[i];
      fZ[i] = z[i];
   }
}


//______________________________________________________________________________
TGraph2D::TGraph2D(TH2 *h2)
         : TNamed("Graph2D","Graph2D"), TAttLine(1,1,1), TAttFill(0,1001),
           TAttMarker(), fNpoints(0)
{
   // Graph2D constructor with a TH2 (h2) as input.
   // Only the h2's bins within the X and Y axis ranges are used.
   // Empty bins, recognized when both content and errors are zero, are excluded.
   Build(h2->GetNbinsX()*h2->GetNbinsY());

   TString gname = "Graph2D_from_" + TString(h2->GetName() );
   SetName(gname);
   // need to call later because sets title in ref histogram
   SetTitle(h2->GetTitle());



   TAxis *xaxis = h2->GetXaxis();
   TAxis *yaxis = h2->GetYaxis();
   Int_t xfirst = xaxis->GetFirst();
   Int_t xlast  = xaxis->GetLast();
   Int_t yfirst = yaxis->GetFirst();
   Int_t ylast  = yaxis->GetLast();


   Double_t x, y, z;
   Int_t k=0;

   for (Int_t i=xfirst; i<= xlast; i++) {
      for (Int_t j=yfirst; j<= ylast; j++) {
         x = xaxis->GetBinCenter(i);
         y = yaxis->GetBinCenter(j);
         z = h2->GetBinContent(i,j);
         Double_t ez = h2->GetBinError(i,j);
         if (z != 0. || ez != 0) {
            SetPoint(k, x, y, z);
            k++;
         }
      }
   }
}


//______________________________________________________________________________
TGraph2D::TGraph2D(const char *name,const char *title,
                   Int_t n, Double_t *x, Double_t *y, Double_t *z)
         : TNamed(name,title), TAttLine(1,1,1), TAttFill(0,1001),
           TAttMarker(), fNpoints(n)
{
   // Graph2D constructor with name, title and three vectors of doubles as input.
   // name   : name of 2D graph (avoid blanks)
   // title  : 2D graph title
   //          if title is of the form "stringt;stringx;stringy;stringz"
   //          the 2D graph title is set to stringt, the x axis title to stringx,
   //          the y axis title to stringy,etc

   Build(n);

   // Copy the input vectors into local arrays
   for (Int_t i=0; i<fNpoints; ++i) {
      fX[i] = x[i];
      fY[i] = y[i];
      fZ[i] = z[i];
   }
}


//______________________________________________________________________________
TGraph2D::TGraph2D(Int_t n)
         : TNamed("Graph2D","Graph2D"), TAttLine(1,1,1), TAttFill(0,1001),
           TAttMarker(), fNpoints(0)
{
   // Graph2D constructor. The arrays fX, fY and fZ should be filled via
   // calls to SetPoint

   Build(n);
}


//______________________________________________________________________________
TGraph2D::TGraph2D(const char *filename, const char *format, Option_t *)
         : TNamed("Graph2D",filename), TAttLine(1,1,1), TAttFill(0,1001),
           TAttMarker(), fNpoints(0)
{
   // Graph2D constructor reading input from filename
   // filename is assumed to contain at least three columns of numbers

   Build(100);

   Double_t x,y,z;
   FILE *fp = fopen(filename,"r");
   if (!fp) {
      MakeZombie();
      Error("TGraph2D", "Cannot open file: %s, TGraph2D is Zombie",filename);
      return;
   }
   char line[80];
   Int_t np = 0;
   while (fgets(line,80,fp)) {
      sscanf(&line[0],format,&x, &y, &z);
      SetPoint(np,x,y,z);
      np++;
   }

   fclose(fp);
}


//______________________________________________________________________________
TGraph2D::TGraph2D(const TGraph2D &g)
         : TNamed(g), TAttLine(g), TAttFill(g), TAttMarker(g)
{
   // Graph2D copy constructor.

   fNpoints = g.fNpoints;
   Build(fNpoints);

   for (Int_t n=0; n<fNpoints; n++) {
      fX[n] = g.fX[n];
      fY[n] = g.fY[n];
      fZ[n] = g.fZ[n];
   }
}


//______________________________________________________________________________
TGraph2D::~TGraph2D()
{
   // TGraph2D destructor.

   Clear();
}


//______________________________________________________________________________
TGraph2D& TGraph2D::operator=(const TGraph2D &g)
{
   // Graph2D operator "="

   if (this == &g) return *this;

   Clear();

   fNpoints = g.fNpoints;
   Build(fNpoints);

   for (Int_t n=0; n<fNpoints; n++) {
      fX[n] = g.fX[n];
      fY[n] = g.fY[n];
      fZ[n] = g.fZ[n];
   }
   return *this;
}

//______________________________________________________________________________
void TGraph2D::Build(Int_t n)
{
   // Creates the 2D graph basic data structure

   if (n <= 0) {
      Error("TGraph2D", "Invalid number of points (%d)", n);
      return;
   }

   fSize      = n;
   fMargin    = 0.;
   fNpx       = 40;
   fNpy       = 40;
   fDirectory = 0;
   fHistogram = 0;
   fMaximum   = -1111;
   fMinimum   = -1111;
   fX         = new Double_t[fSize];
   fY         = new Double_t[fSize];
   fZ         = new Double_t[fSize];
   fZout      = 0;
   fMaxIter   = 100000;
   fFunctions = new TList;
   fPainter   = 0;
   fUserHisto = kFALSE;

   if (TH1::AddDirectoryStatus()) {
      fDirectory = gDirectory;
      if (fDirectory) {
         fDirectory->Append(this,kTRUE);
      }
   }
}


//______________________________________________________________________________
void TGraph2D::Clear(Option_t * /*option = "" */)
{
   // Free all memory allocated by this object.

   delete [] fX; fX = 0;
   delete [] fY; fY = 0;
   delete [] fZ; fZ = 0;
   delete fHistogram; fHistogram = 0;
   if (fFunctions) {
      fFunctions->SetBit(kInvalidObject);
      fFunctions->Delete();
      delete fFunctions;
      fFunctions = 0;
   }
   if (fDirectory) {
      fDirectory->Remove(this);
      fDirectory = 0;
   }
   delete fPainter;
   fPainter   = 0;
}


//______________________________________________________________________________
void TGraph2D::DirectoryAutoAdd(TDirectory *dir)
{
   // Perform the automatic addition of the graph to the given directory
   //
   // Note this function is called in place when the semantic requires
   // this object to be added to a directory (I.e. when being read from
   // a TKey or being Cloned)

   Bool_t addStatus = TH1::AddDirectoryStatus();
   if (addStatus) {
      SetDirectory(dir);
      if (dir) {
         ResetBit(kCanDelete);
      }
   }
}


//______________________________________________________________________________
Int_t TGraph2D::DistancetoPrimitive(Int_t px, Int_t py)
{
   // Computes distance from point px,py to a graph

   Int_t distance = 9999;
   if (fHistogram) distance = fHistogram->DistancetoPrimitive(px,py);
   return distance;
}


//______________________________________________________________________________
void TGraph2D::Draw(Option_t *option)
{
   // Specific drawing options can be used to paint a TGraph2D:
   //
   //   "TRI"  : The Delaunay triangles are drawn using filled area.
   //            An hidden surface drawing technique is used. The surface is
   //            painted with the current fill area color. The edges of each
   //            triangles are painted with the current line color.
   //   "TRIW" : The Delaunay triangles are drawn as wire frame
   //   "TRI1" : The Delaunay triangles are painted with color levels. The edges
   //            of each triangles are painted with the current line color.
   //   "TRI2" : the Delaunay triangles are painted with color levels.
   //   "P"    : Draw a marker at each vertex
   //   "P0"   : Draw a circle at each vertex. Each circle background is white.
   //   "PCOL" : Draw a marker at each vertex. The color of each marker is
   //            defined according to its Z position.
   //   "CONT" : Draw contours
   //   "LINE" : Draw a 3D polyline
   //
   // A TGraph2D can be also drawn with ANY options valid to draw a 2D histogram.
   //
   // When a TGraph2D is drawn with one of the 2D histogram drawing option,
   // a intermediate 2D histogram is filled using the Delaunay triangles
   // technique to interpolate the data set.

   TString opt = option;
   opt.ToLower();
   if (gPad) {
      if (!gPad->IsEditable()) gROOT->MakeDefCanvas();
      if (!opt.Contains("same")) {
         //the following statement is necessary in case one attempts to draw
         //a temporary histogram already in the current pad
         if (TestBit(kCanDelete)) gPad->GetListOfPrimitives()->Remove(this);
         gPad->Clear();
      }
   }
   AppendPad(opt.Data());
}


//______________________________________________________________________________
void TGraph2D::ExecuteEvent(Int_t event, Int_t px, Int_t py)
{
   // Executes action corresponding to one event

   if (fHistogram) fHistogram->ExecuteEvent(event, px, py);
}


//______________________________________________________________________________
TObject *TGraph2D::FindObject(const char *name) const
{
   // search object named name in the list of functions

   if (fFunctions) return fFunctions->FindObject(name);
   return 0;
}


//______________________________________________________________________________
TObject *TGraph2D::FindObject(const TObject *obj) const
{
   // search object obj in the list of functions

   if (fFunctions) return fFunctions->FindObject(obj);
   return 0;
}


//______________________________________________________________________________
TFitResultPtr TGraph2D::Fit(const char *fname, Option_t *option, Option_t *)
{
   // Fits this graph with function with name fname
   // 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(y)" for fitting "[0]*x+[1]*sin(y)"


   char *linear;
   linear= (char*)strstr(fname, "++");
   TF2 *f2=0;
   if (linear)
      f2=new TF2(fname, fname);
   else{
      f2 = (TF2*)gROOT->GetFunction(fname);
      if (!f2) { Printf("Unknown function: %s",fname); return -1; }
   }
   return Fit(f2,option,"");

}


//______________________________________________________________________________
TFitResultPtr TGraph2D::Fit(TF2 *f2, Option_t *option, Option_t *)
{
   // Fits this 2D graph with function f2
   //
   //  f2 is an already predefined function created by TF2.
   //  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 weights to 1; ignore error bars
   //            = "U" Use a User specified fitting algorithm (via SetFCN)
   //            = "Q" Quiet mode (minimum printing)
   //            = "V" Verbose mode (default is between Q and V)
   //            = "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)
   //            = "EX0" When fitting a TGraphErrors do not consider errors in the coordinate
   //            = "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
   //            = "S"  The result of the fit is returned in the TFitResultPtr
   //                     (see below Access to the Fit Result)
   //
   //  In order to use the Range option, one must first create a function
   //  with the expression to be fitted. For example, if your graph2d
   //  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:
   //       TF2 *f2 = new TF2("f2","gaus",1,3);
   //       graph2d->Fit("f2","R");
   //
   //
   //  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. One can however disable
   //  this automatic computation by specifying the option "B".
   //  You can specify boundary limits for some or all parameters via
   //       f2->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 a chi2 fitting function is used for fitting a TGraph.
   //   The function is implemented in FitUtil::EvaluateChi2.
   //   In case of TGraph2DErrors an effective chi2 is used
   //   (see TGraphErrors fit in TGraph::Fit) and is implemented in
   //   FitUtil::EvaluateChi2Effective
   //   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);
   //
   //  Associated functions
   //  ====================
   //  One or more object (typically a TF2*) 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:  TF2 *myfunc = gr->GetFunction("myfunc");
   //
   //  Access to the fit results
   //  =========================
   //  The function returns a TFitResultPtr which can hold a  pointer to a TFitResult object.
   //  By default the TFitResultPtr contains only the status of the fit and it converts automatically to an
   //  integer. If the option "S" is instead used, TFitResultPtr contains the TFitResult and behaves as a smart
   //  pointer to it. For example one can do:
   //     TFitResultPtr r = graph->Fit("myFunc","S");
   //     TMatrixDSym cov = r->GetCovarianceMatrix();  //  to access the covariance matrix
   //     Double_t par0   = r->Value(0); // retrieve the value for the parameter 0
   //     Double_t err0   = r->Error(0); // retrieve the error for the parameter 0
   //     r->Print("V");     // print full information of fit including covariance matrix
   //     r->Write();        // store the result in a file
   //
   //  The fit parameters, error and chi2 (but not covariance matrix) can be retrieved also
   //  from the fitted function.
   //  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

   // internal graph2D fitting methods
   Foption_t fitOption;
   Option_t *goption = "";
   ROOT::Fit::FitOptionsMake(option,fitOption);

   // create range and minimizer options with default values
   ROOT::Fit::DataRange range(2);
   ROOT::Math::MinimizerOptions minOption;
   return ROOT::Fit::FitObject(this, f2 , fitOption , minOption, goption, range);
}


//______________________________________________________________________________
void TGraph2D::FitPanel()
{
   // Display a GUI panel with all graph fit options.
   //
   //   See class TFitEditor for example
   if (!gPad)
      gROOT->MakeDefCanvas();

   if (!gPad) {
      Error("FitPanel", "Unable to create a default canvas");
      return;
   }

   // use plugin manager to create instance of TFitEditor
   TPluginHandler *handler = gROOT->GetPluginManager()->FindHandler("TFitEditor");
   if (handler && handler->LoadPlugin() != -1) {
      if (handler->ExecPlugin(2, gPad, this) == 0)
         Error("FitPanel", "Unable to crate the FitPanel");
   }
   else
      Error("FitPanel", "Unable to find the FitPanel plug-in");

}


//______________________________________________________________________________
TAxis *TGraph2D::GetXaxis() const
{
   // Get x axis of the graph.

   //if (!gPad) return 0;
   TH1 *h = ((TGraph2D*)this)->GetHistogram();
   if (!h) return 0;
   return h->GetXaxis();
}


//______________________________________________________________________________
TAxis *TGraph2D::GetYaxis() const
{
   // Get y axis of the graph.

   //if (!gPad) return 0;
   TH1 *h = ((TGraph2D*)this)->GetHistogram();
   if (!h) return 0;
   return h->GetYaxis();
}


//______________________________________________________________________________
TAxis *TGraph2D::GetZaxis() const
{
   // Get z axis of the graph.

   //if (!gPad) return 0;
   TH1 *h = ((TGraph2D*)this)->GetHistogram();
   if (!h) return 0;
   return h->GetZaxis();
}


//______________________________________________________________________________
TList *TGraph2D::GetContourList(Double_t contour)
{
   // Returns the X and Y graphs building a contour. A contour level may
   // consist in several parts not connected to each other. This function
   // returns them in a graphs' list.

   if (fNpoints <= 0) {
      Error("GetContourList", "Empty TGraph2D");
      return 0;
   }

   if(!fHistogram) GetHistogram("empty");

   if (!fPainter) fPainter = fHistogram->GetPainter();

   return fPainter->GetContourList(contour);
}


//______________________________________________________________________________
Double_t TGraph2D::GetErrorX(Int_t) const
{
   // This function is called by Graph2DFitChisquare.
   // It always returns a negative value. Real implementation in TGraph2DErrors

   return -1;
}


//______________________________________________________________________________
Double_t TGraph2D::GetErrorY(Int_t) const
{
   // This function is called by Graph2DFitChisquare.
   // It always returns a negative value. Real implementation in TGraph2DErrors

   return -1;
}


//______________________________________________________________________________
Double_t TGraph2D::GetErrorZ(Int_t) const
{
   // This function is called by Graph2DFitChisquare.
   // It always returns a negative value. Real implementation in TGraph2DErrors

   return -1;
}


//______________________________________________________________________________
TH2D *TGraph2D::GetHistogram(Option_t *option)
{
   // By default returns a pointer to the Delaunay histogram. If fHistogram
   // doesn't exist, books the 2D histogram fHistogram with a margin around
   // the hull. Calls TGraphDelaunay::Interpolate at each bin centre to build up
   // an interpolated 2D histogram.
   // If the "empty" option is selected, returns an empty histogram booked with
   // the limits of fX, fY and fZ. This option is used when the data set is
   // drawn with markers only. In that particular case there is no need to
   // find the Delaunay triangles.

   if (fNpoints <= 0) {
      Error("GetHistogram", "Empty TGraph2D");
      return 0;
   }

   TString opt = option;
   opt.ToLower();
   Bool_t empty = opt.Contains("empty");

   if (fHistogram) {
      if (!empty && fHistogram->GetEntries()==0) {
         if (!fUserHisto) {
            delete fHistogram;
            fHistogram = 0;
         }
      } else {
         return fHistogram;
      }
   }

   Double_t hxmax, hymax, hxmin, hymin;

   // Book fHistogram if needed. It is not added in the current directory
   if (!fUserHisto) {
      Bool_t add = TH1::AddDirectoryStatus();
      TH1::AddDirectory(kFALSE);
      Double_t xmax  = GetXmaxE();
      Double_t ymax  = GetYmaxE();
      Double_t xmin  = GetXminE();
      Double_t ymin  = GetYminE();
      hxmin = xmin-fMargin*(xmax-xmin);
      hymin = ymin-fMargin*(ymax-ymin);
      hxmax = xmax+fMargin*(xmax-xmin);
      hymax = ymax+fMargin*(ymax-ymin);
      fHistogram = new TH2D(GetName(),GetTitle(),
                            fNpx ,hxmin, hxmax,
                            fNpy, hymin, hymax);
      TH1::AddDirectory(add);
      fHistogram->SetBit(TH1::kNoStats);
   } else {
      hxmin = fHistogram->GetXaxis()->GetXmin();
      hymin = fHistogram->GetYaxis()->GetXmin();
      hxmax = fHistogram->GetXaxis()->GetXmax();
      hymax = fHistogram->GetYaxis()->GetXmax();
   }

   // Add a TGraphDelaunay in the list of the fHistogram's functions
   TGraphDelaunay *dt = new TGraphDelaunay(this);
   dt->SetMaxIter(fMaxIter);
   dt->SetMarginBinsContent(fZout);
   TList *hl = fHistogram->GetListOfFunctions();
   hl->Add(dt);

   // Option "empty" is selected. An empty histogram is returned.
   if (empty) {
      Double_t hzmax, hzmin;
      if (fMinimum != -1111) {
         hzmin = fMinimum;
      } else {
         hzmin = GetZmin();
///         hzmin = GetZminE();
      }
      if (fMaximum != -1111) {
         hzmax = fMaximum;
      } else {
         hzmax = GetZmax();
///         hzmax = GetZmaxE();
      }
      if (hzmin==hzmax) {
         hzmin = hzmin-0.01*hzmin;
         hzmax = hzmax+0.01*hzmax;
      }
      fHistogram->SetMinimum(hzmin);
      fHistogram->SetMaximum(hzmax);
      return fHistogram;
   }

   Double_t dx = (hxmax-hxmin)/fNpx;
   Double_t dy = (hymax-hymin)/fNpy;

   Double_t x, y, z;
   for (Int_t ix=1; ix<=fNpx; ix++) {
      x  = hxmin+(ix-0.5)*dx;
      for (Int_t iy=1; iy<=fNpy; iy++) {
         y  = hymin+(iy-0.5)*dy;
         z  = dt->ComputeZ(x, y);
         fHistogram->Fill(x, y, z);
      }
   }

   if (fMinimum != -1111) fHistogram->SetMinimum(fMinimum);
   if (fMaximum != -1111) fHistogram->SetMaximum(fMaximum);

   return fHistogram;
}


//______________________________________________________________________________
Double_t TGraph2D::GetXmax() const
{
   // Returns the X maximum

   Double_t v = fX[0];
   for (Int_t i=1; i<fNpoints; i++) if (fX[i]>v) v=fX[i];
   return v;
}


//______________________________________________________________________________
Double_t TGraph2D::GetXmin() const
{
   // Returns the X minimum

   Double_t v = fX[0];
   for (Int_t i=1; i<fNpoints; i++) if (fX[i]<v) v=fX[i];
   return v;
}


//______________________________________________________________________________
Double_t TGraph2D::GetYmax() const
{
   // Returns the Y maximum

   Double_t v = fY[0];
   for (Int_t i=1; i<fNpoints; i++) if (fY[i]>v) v=fY[i];
   return v;
}


//______________________________________________________________________________
Double_t TGraph2D::GetYmin() const
{
   // Returns the Y minimum

   Double_t v = fY[0];
   for (Int_t i=1; i<fNpoints; i++) if (fY[i]<v) v=fY[i];
   return v;
}


//______________________________________________________________________________
Double_t TGraph2D::GetZmax() const
{
   // Returns the Z maximum

   Double_t v = fZ[0];
   for (Int_t i=1; i<fNpoints; i++) if (fZ[i]>v) v=fZ[i];
   return v;
}


//______________________________________________________________________________
Double_t TGraph2D::GetZmin() const
{
   // Returns the Z minimum

   Double_t v = fZ[0];
   for (Int_t i=1; i<fNpoints; i++) if (fZ[i]<v) v=fZ[i];
   return v;
}


//______________________________________________________________________________
Double_t TGraph2D::Interpolate(Double_t x, Double_t y)
{
   // Finds the z value at the position (x,y) thanks to
   // the Delaunay interpolation.

   if (fNpoints <= 0) {
      Error("Interpolate", "Empty TGraph2D");
      return 0;
   }

   TGraphDelaunay *dt;

   if(!fHistogram) GetHistogram("empty");

   TList *hl = fHistogram->GetListOfFunctions();
   dt = (TGraphDelaunay*)hl->FindObject("TGraphDelaunay");

   return dt->ComputeZ(x, y);
}


//______________________________________________________________________________
void TGraph2D::Paint(Option_t *option)
{
   // Paints this 2D graph with its current attributes

   if (fNpoints <= 0) {
      Error("Paint", "Empty TGraph2D");
      return;
   }

   TString opt = option;
   opt.ToLower();
   if (opt.Contains("p") && !opt.Contains("tri")) {
      if (!opt.Contains("pol") &&
          !opt.Contains("sph") &&
          !opt.Contains("psr")) opt.Append("tri0");
   }

   if (opt.Contains("line") && !opt.Contains("tri")) opt.Append("tri0");

   if (opt.Contains("err")  && !opt.Contains("tri")) opt.Append("tri0");

   if (opt.Contains("tri0")) {
      GetHistogram("empty");
   } else {
      GetHistogram();
   }

   fHistogram->SetLineColor(GetLineColor());
   fHistogram->SetLineStyle(GetLineStyle());
   fHistogram->SetLineWidth(GetLineWidth());
   fHistogram->SetFillColor(GetFillColor());
   fHistogram->SetFillStyle(GetFillStyle());
   fHistogram->SetMarkerColor(GetMarkerColor());
   fHistogram->SetMarkerStyle(GetMarkerStyle());
   fHistogram->SetMarkerSize(GetMarkerSize());
   fHistogram->Paint(opt.Data());
}


//______________________________________________________________________________
TH1 *TGraph2D::Project(Option_t *option) const
{
   // Projects a 2-d graph into 1 or 2-d histograms depending on the
   // option parameter
   // option may contain a combination of the characters x,y,z
   // option = "x" return the x projection into a TH1D histogram
   // option = "y" return the y projection into a TH1D histogram
   // option = "xy" return the x versus y projection into a TH2D histogram
   // option = "yx" return the y versus x projection into a TH2D histogram

   if (fNpoints <= 0) {
      Error("Project", "Empty TGraph2D");
      return 0;
   }

   TString opt = option; opt.ToLower();

   Int_t pcase = 0;
   if (opt.Contains("x"))  pcase = 1;
   if (opt.Contains("y"))  pcase = 2;
   if (opt.Contains("xy")) pcase = 3;
   if (opt.Contains("yx")) pcase = 4;

   // Create the projection histogram
   TH1D *h1 = 0;
   TH2D *h2 = 0;
   Int_t nch = strlen(GetName()) +opt.Length() +2;
   char *name = new char[nch];
   snprintf(name,nch,"%s_%s",GetName(),option);
   nch = strlen(GetTitle()) +opt.Length() +2;
   char *title = new char[nch];
   snprintf(title,nch,"%s_%s",GetTitle(),option);

   Double_t hxmin = GetXmin();
   Double_t hxmax = GetXmax();
   Double_t hymin = GetYmin();
   Double_t hymax = GetYmax();

   switch (pcase) {
      case 1:
         // "x"
         h1 = new TH1D(name,title,fNpx,hxmin,hxmax);
         break;
      case 2:
         // "y"
         h1 = new TH1D(name,title,fNpy,hymin,hymax);
         break;
      case 3:
         // "xy"
         h2 = new TH2D(name,title,fNpx,hxmin,hxmax,fNpy,hymin,hymax);
         break;
      case 4:
         // "yx"
         h2 = new TH2D(name,title,fNpy,hymin,hymax,fNpx,hxmin,hxmax);
         break;
   }

   delete [] name;
   delete [] title;
   TH1 *h = h1;
   if (h2) h = h2;
   if (h == 0) return 0;

   // Fill the projected histogram
   Double_t entries = 0;
   for (Int_t n=0; n<fNpoints; n++) {
      switch (pcase) {
         case 1:
            // "x"
            h1->Fill(fX[n], fZ[n]);
            break;
         case 2:
            // "y"
            h1->Fill(fY[n], fZ[n]);
            break;
         case 3:
            // "xy"
            h2->Fill(fX[n], fY[n], fZ[n]);
            break;
         case 4:
            // "yx"
            h2->Fill(fY[n], fX[n], fZ[n]);
            break;
      }
      entries += fZ[n];
   }
   h->SetEntries(entries);
   return h;
}


//______________________________________________________________________________
Int_t TGraph2D::RemovePoint(Int_t ipoint)
{
   // Deletes point number ipoint

   if (ipoint < 0) return -1;
   if (ipoint >= fNpoints) return -1;

   fNpoints--;
   Double_t *newX = new Double_t[fNpoints];
   Double_t *newY = new Double_t[fNpoints];
   Double_t *newZ = new Double_t[fNpoints];
   Int_t j = -1;
   for (Int_t i=0;i<fNpoints+1;i++) {
      if (i == ipoint) continue;
      j++;
      newX[j] = fX[i];
      newY[j] = fY[i];
      newZ[j] = fZ[i];
   }
   delete [] fX;
   delete [] fY;
   delete [] fZ;
   fX = newX;
   fY = newY;
   fZ = newZ;
   fSize = fNpoints;
   if (fHistogram) {delete fHistogram; fHistogram = 0;}
   return ipoint;
}


//______________________________________________________________________________
void TGraph2D::SavePrimitive(ostream &out, Option_t *option /*= ""*/)
{
   // Saves primitive as a C++ statement(s) on output stream out

   char quote = '"';
   out<<"   "<<endl;
   if (gROOT->ClassSaved(TGraph2D::Class())) {
      out<<"   ";
   } else {
      out<<"   TGraph2D *";
   }

   out<<"graph2d = new TGraph2D("<<fNpoints<<");"<<endl;
   out<<"   graph2d->SetName("<<quote<<GetName()<<quote<<");"<<endl;
   out<<"   graph2d->SetTitle("<<quote<<GetTitle()<<quote<<");"<<endl;

   if (fDirectory == 0) {
      out<<"   "<<GetName()<<"->SetDirectory(0);"<<endl;
   }

   SaveFillAttributes(out,"graph2d",0,1001);
   SaveLineAttributes(out,"graph2d",1,1,1);
   SaveMarkerAttributes(out,"graph2d",1,1,1);

   for (Int_t i=0;i<fNpoints;i++) {
      out<<"   graph2d->SetPoint("<<i<<","<<fX[i]<<","<<fY[i]<<","<<fZ[i]<<");"<<endl;
   }

   // save list of functions
   TIter next(fFunctions);
   TObject *obj;
   while ((obj=next())) {
      obj->SavePrimitive(out,"nodraw");
      out<<"   graph2d->GetListOfFunctions()->Add("<<obj->GetName()<<");"<<endl;
      if (obj->InheritsFrom("TPaveStats")) {
         out<<"   ptstats->SetParent(graph2d->GetListOfFunctions());"<<endl;
      }
   }

   out<<"   graph2d->Draw("<<quote<<option<<quote<<");"<<endl;
}


//______________________________________________________________________________
void TGraph2D::Set(Int_t n)
{
   // Set number of points in the 2D graph.
   // Existing coordinates are preserved.
   // New coordinates above fNpoints are preset to 0.

   if (n < 0) n = 0;
   if (n == fNpoints) return;
   if (n >  fNpoints) SetPoint(n,0,0,0);
   fNpoints = n;
}


//______________________________________________________________________________
void TGraph2D::SetDirectory(TDirectory *dir)
{
   // By default when an 2D graph is created, it is added to the list
   // of 2D graph objects in the current directory in memory.
   // Remove reference to this 2D graph from current directory and add
   // reference to new directory dir. dir can be 0 in which case the
   // 2D graph does not belong to any directory.

   if (fDirectory == dir) return;
   if (fDirectory) fDirectory->Remove(this);
   fDirectory = dir;
   if (fDirectory) fDirectory->Append(this);
}


//______________________________________________________________________________
void TGraph2D::SetHistogram(TH2 *h)
{
   // Sets the histogram to be filled

   fUserHisto = kTRUE;
   fHistogram = (TH2D*)h;
   fNpx       = h->GetNbinsX();
   fNpy       = h->GetNbinsY();
}


//______________________________________________________________________________
void TGraph2D::SetMargin(Double_t m)
{
   // Sets the extra space (in %) around interpolated area for the 2D histogram

   if (m<0 || m>1) {
      Warning("SetMargin","The margin must be >= 0 && <= 1, fMargin set to 0.1");
      fMargin = 0.1;
   } else {
      fMargin = m;
   }
   if (fHistogram) {delete fHistogram; fHistogram = 0;}
}


//______________________________________________________________________________
void TGraph2D::SetMarginBinsContent(Double_t z)
{
   // Sets the histogram bin height for points lying outside the TGraphDelaunay
   // convex hull ie: the bins in the margin.

   fZout = z;
   if (fHistogram) {delete fHistogram; fHistogram = 0;}
}


//______________________________________________________________________________
void TGraph2D::SetMaximum(Double_t maximum)
{
   // Set maximum.

   fMaximum = maximum;
   GetHistogram()->SetMaximum(maximum);
}


//______________________________________________________________________________
void TGraph2D::SetMinimum(Double_t minimum)
{
   // Set minimum.

   fMinimum = minimum;
   GetHistogram()->SetMinimum(minimum);
}


//______________________________________________________________________________
void TGraph2D::SetName(const char *name)
{
   // Changes the name of this 2D graph

   //  2D graphs are named objects in a THashList.
   //  We must update the hashlist if we change the name
   if (fDirectory) fDirectory->Remove(this);
   fName = name;
   if (fDirectory) fDirectory->Append(this);
}


//______________________________________________________________________________
void TGraph2D::SetNameTitle(const char *name, const char *title)
{
   // Change the name and title of this 2D graph
   //

   //  2D graphs are named objects in a THashList.
   //  We must update the hashlist if we change the name
   if (fDirectory) fDirectory->Remove(this);
   fName  = name;
   SetTitle(title);
   if (fDirectory) fDirectory->Append(this);
}


//______________________________________________________________________________
void TGraph2D::SetNpx(Int_t npx)
{
   // Sets the number of bins along X used to draw the function

   if (npx < 4) {
      Warning("SetNpx","Number of points must be >4 && < 500, fNpx set to 4");
      fNpx = 4;
   } else if(npx > 500) {
      Warning("SetNpx","Number of points must be >4 && < 500, fNpx set to 500");
      fNpx = 500;
   } else {
      fNpx = npx;
   }
   if (fHistogram) {delete fHistogram; fHistogram = 0;}
}


//______________________________________________________________________________
void TGraph2D::SetNpy(Int_t npy)
{
   // Sets the number of bins along Y used to draw the function

   if (npy < 4) {
      Warning("SetNpy","Number of points must be >4 && < 500, fNpy set to 4");
      fNpy = 4;
   } else if(npy > 500) {
      Warning("SetNpy","Number of points must be >4 && < 500, fNpy set to 500");
      fNpy = 500;
   } else {
      fNpy = npy;
   }
   if (fHistogram) {delete fHistogram; fHistogram = 0;}
}


//______________________________________________________________________________
void TGraph2D::SetPoint(Int_t n, Double_t x, Double_t y, Double_t z)
{
   // Sets point number n.
   // If n is greater than the current size, the arrays are automatically
   // extended.

   if (n < 0) return;

   if (!fX || !fY || !fZ || n >= fSize) {
   // re-allocate the object
      Int_t newN = TMath::Max(2*fSize,n+1);
      Double_t *savex = new Double_t [newN];
      Double_t *savey = new Double_t [newN];
      Double_t *savez = new Double_t [newN];
      if (fX && fSize) {
         memcpy(savex,fX,fSize*sizeof(Double_t));
         memset(&savex[fSize],0,(newN-fSize)*sizeof(Double_t));
         delete [] fX;
      }
      if (fY && fSize) {
         memcpy(savey,fY,fSize*sizeof(Double_t));
         memset(&savey[fSize],0,(newN-fSize)*sizeof(Double_t));
         delete [] fY;
      }
      if (fZ && fSize) {
         memcpy(savez,fZ,fSize*sizeof(Double_t));
         memset(&savez[fSize],0,(newN-fSize)*sizeof(Double_t));
         delete [] fZ;
      }
      fX    = savex;
      fY    = savey;
      fZ    = savez;
      fSize = newN;
   }
   fX[n]    = x;
   fY[n]    = y;
   fZ[n]    = z;
   fNpoints = TMath::Max(fNpoints,n+1);
}


//______________________________________________________________________________
void TGraph2D::SetTitle(const char* title)
{
   // Sets graph title

   fTitle = title;
   if (fHistogram) fHistogram->SetTitle(title);
}


//_______________________________________________________________________
void TGraph2D::Streamer(TBuffer &b)
{
   // Stream a class object

   if (b.IsReading()) {
      UInt_t R__s, R__c;
      Version_t R__v = b.ReadVersion(&R__s, &R__c);
      b.ReadClassBuffer(TGraph2D::Class(), this, R__v, R__s, R__c);

      ResetBit(kMustCleanup);
   } else {
      b.WriteClassBuffer(TGraph2D::Class(),this);
   }
}

---