// @(#)root/hist:$Id$
// Author: Rene Brun   12/10/2000

/*************************************************************************
 * 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 "TROOT.h"
#include "TEnv.h"
#include "TBrowser.h"
#include "TMultiGraph.h"
#include "TGraph.h"
#include "TH1.h"
#include "TH2.h"
#include "TPolyLine3D.h"
#include "TVirtualPad.h"
#include "Riostream.h"
#include "TVirtualFitter.h"
#include "TPluginManager.h"
#include "TClass.h"
#include "TMath.h"
#include "TSystem.h"
#include <stdlib.h>

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

#include <ctype.h>

extern void H1LeastSquareSeqnd(Int_t n, Double_t *a, Int_t idim, Int_t &ifail, Int_t k, Double_t *b);

ClassImp(TMultiGraph)


//______________________________________________________________________________
/* Begin_Html
<center><h2>TMultiGraph class</h2></center>

A TMultiGraph is a collection of TGraph (or derived) objects. It allows to
manipulate a set of graphs as a single entity. In particular, when drawn,
the X and Y axis ranges are automatically computed such as all the graphs
will be visible.
<p>
<tt>TMultiGraph::Add</tt> should be used to add a new graph to the list.
<p>
The TMultiGraph owns the objects in the list.
<p>
The drawing options are the same as for TGraph.
Like for TGraph, the painting is performed thanks to the
<a href="http://root.cern.ch/root/html/TGraphPainter.html">TGraphPainter</a>
class. All details about the various painting options are given in
<a href="http://root.cern.ch/root/html/TGraphPainter.html">this class</a>.
Example:
<pre>
     TGraph *gr1 = new TGraph(...
     TGraphErrors *gr2 = new TGraphErrors(...
     TMultiGraph *mg = new TMultiGraph();
     mg->Add(gr1,"lp");
     mg->Add(gr2,"cp");
     mg->Draw("a");
</pre>
A special option <tt>3D</tt> allows to draw the graphs in a 3D space. See the
following example:
End_Html
Begin_Macro(source)
{
   c0 = new TCanvas("c1","multigraph L3",200,10,700,500);
   c0->SetFrameFillColor(30);

   TMultiGraph *mg = new TMultiGraph();

   TGraph *gr1 = new TGraph(); gr1->SetLineColor(kBlue);
   TGraph *gr2 = new TGraph(); gr2->SetLineColor(kRed);
   TGraph *gr3 = new TGraph(); gr3->SetLineColor(kGreen);
   TGraph *gr4 = new TGraph(); gr4->SetLineColor(kOrange);

   Double_t dx = 6.28/100;
   Double_t x  = -3.14;

   for (int i=0; i<=100; i++) {
      x = x+dx;
      gr1->SetPoint(i,x,2.*TMath::Sin(x));
      gr2->SetPoint(i,x,TMath::Cos(x));
      gr3->SetPoint(i,x,TMath::Cos(x*x));
      gr4->SetPoint(i,x,TMath::Cos(x*x*x));
   }

   mg->Add(gr4); gr4->SetTitle("Cos(x*x*x)"); gr4->SetLineWidth(3);
   mg->Add(gr3); gr3->SetTitle("Cos(x*x)")  ; gr3->SetLineWidth(3);
   mg->Add(gr2); gr2->SetTitle("Cos(x)")    ; gr2->SetLineWidth(3);
   mg->Add(gr1); gr1->SetTitle("2*Sin(x)")  ; gr1->SetLineWidth(3);

   mg->Draw("a fb l3d");
   return c0;
}
End_Macro
Begin_Html
<p>
The number of graphs in a multigraph can be retrieve with:
<pre>
mg->GetListOfGraphs()->GetSize();
</pre>
<p>
The drawing option for each TGraph may be specified as an optional
second argument of the <tt>Add</tt> function.
<p>
If a draw option is specified, it will be used to draw the graph,
otherwise the graph will be drawn with the option specified in
<tt>TMultiGraph::Draw</tt>.
<p>
The following example shows how to fit a TMultiGraph.
End_Html
Begin_Macro(source)
{
   TCanvas *c1 = new TCanvas("c1","c1",600,400);

   Double_t px1[2] = {2.,4.};
   Double_t dx1[2] = {0.1,0.1};
   Double_t py1[2] = {2.1,4.0};
   Double_t dy1[2] = {0.3,0.2};

   Double_t px2[2] = {3.,5.};
   Double_t dx2[2] = {0.1,0.1};
   Double_t py2[2] = {3.2,4.8};
   Double_t dy2[2] = {0.3,0.2};

   gStyle->SetOptFit(0001);

   TGraphErrors *g1 = new TGraphErrors(2,px1,py1,dx1,dy1);
   g1->SetMarkerStyle(21);
   g1->SetMarkerColor(2);

   TGraphErrors *g2 = new TGraphErrors(2,px2,py2,dx2,dy2);
   g2->SetMarkerStyle(22);
   g2->SetMarkerColor(3);

   TMultiGraph *g = new TMultiGraph();
   g->Add(g1);
   g->Add(g2);

   g->Draw("AP");

   g->Fit("pol1","FQ");
   return c1;
}
End_Macro
Begin_Html
<p>
The axis titles can be modified the following way:
<p>
<pre>
   [...]
   TMultiGraph *mg = new TMultiGraph;
   mg->SetTitle("title;xaxis title; yaxis title");
   mg->Add(g1);
   mg->Add(g2);
   mg->Draw("apl");
</pre>
<p>
When the graphs in a TMultiGraph are fitted, the fit parameters boxes
overlap. The following example shows how to make them all visible.

End_Html
Begin_Macro(source)
../../../tutorials/graphs/multigraph.C
End_Macro
Begin_Html

<p>
The axis limits can be changed the like for TGraph. The same methods apply on
the multigraph.
Note the two differents ways to change limits on X and Y axis.

End_Html
Begin_Macro(source)
{
   TCanvas *c2 = new TCanvas("c2","c2",600,400);

   TGraph *g[3];
   Double_t x[10] = {0,1,2,3,4,5,6,7,8,9};
   Double_t y[10] = {1,2,3,4,5,5,4,3,2,1};
   TMultiGraph *mg = new TMultiGraph();
   for (int i=0; i<3; i++) {
      g[i] = new TGraph(10, x, y);
      g[i]->SetMarkerStyle(20);
      g[i]->SetMarkerColor(i+2);
      for (int j=0; j<10; j++) y[j] = y[j]-1;
      mg->Add(g[i]);
   }
   mg->Draw("APL");
   mg->GetXaxis()->SetTitle("E_{#gamma} (GeV)");
   mg->GetYaxis()->SetTitle("Coefficients");

   // Change the axis limits
   gPad->Modified();
   mg->GetXaxis()->SetLimits(1.5,7.5);
   mg->SetMinimum(0.);
   mg->SetMaximum(10.);

   return c2;
}
End_Macro
Begin_Html
<p>
The method <a href="http://root.cern.ch/root/html/TPad.html#TPad:BuildLegend">
<tt>TPad::BuildLegend</tt></a> is able to extract the graphs inside a
multigraph. The following example demonstrate this.

End_Html
Begin_Macro(source)
{
   TCanvas *c3 = new TCanvas("c3","c3",600, 400);

   TMultiGraph * mg = new TMultiGraph("mg","mg");

   const Int_t size = 10;

   double px[size];
   double py1[size];
   double py2[size];
   double py3[size];

   for ( int i = 0; i <  size ; ++i ) {
      px[i] = i;
      py1[i] = size - i;
      py2[i] = size - 0.5 * i;
      py3[i] = size - 0.6 * i;
   }

   TGraph * gr1 = new TGraph( size, px, py1 );
   gr1->SetName("gr1");
   gr1->SetTitle("graph 1");
   gr1->SetMarkerStyle(21);
   gr1->SetDrawOption("AP");
   gr1->SetLineColor(2);
   gr1->SetLineWidth(4);
   gr1->SetFillStyle(0);

   TGraph * gr2 = new TGraph( size, px, py2 );
   gr2->SetName("gr2");
   gr2->SetTitle("graph 2");
   gr2->SetMarkerStyle(22);
   gr2->SetMarkerColor(2);
   gr2->SetDrawOption("P");
   gr2->SetLineColor(3);
   gr2->SetLineWidth(4);
   gr2->SetFillStyle(0);

   TGraph * gr3 = new TGraph( size, px, py3 );
   gr3->SetName("gr3");
   gr3->SetTitle("graph 3");
   gr3->SetMarkerStyle(23);
   gr3->SetLineColor(4);
   gr3->SetLineWidth(4);
   gr3->SetFillStyle(0);

   mg->Add( gr1 );
   mg->Add( gr2 );

   gr3->Draw("ALP");
   mg->Draw("LP");
   c3->BuildLegend();

   return c3;
}
End_Macro
Begin_Html


End_Html */


//______________________________________________________________________________
TMultiGraph::TMultiGraph(): TNamed()
{
   // TMultiGraph default constructor.

   fGraphs    = 0;
   fFunctions = 0;
   fHistogram = 0;
   fMaximum   = -1111;
   fMinimum   = -1111;
}


//______________________________________________________________________________
TMultiGraph::TMultiGraph(const char *name, const char *title)
       : TNamed(name,title)
{
   // Constructor with name and title.

   fGraphs    = 0;
   fFunctions = 0;
   fHistogram = 0;
   fMaximum   = -1111;
   fMinimum   = -1111;
}


//______________________________________________________________________________
TMultiGraph::TMultiGraph(const TMultiGraph& mg) :
  TNamed (mg),
  fGraphs(mg.fGraphs),
  fFunctions(mg.fFunctions),
  fHistogram(mg.fHistogram),
  fMaximum(mg.fMaximum),
  fMinimum(mg.fMinimum)
{
   // Copy constructor.
}


//______________________________________________________________________________
TMultiGraph& TMultiGraph::operator=(const TMultiGraph& mg)
{
   // Assignement operator.

   if (this!=&mg) {
      TNamed::operator=(mg);
      fGraphs=mg.fGraphs;
      fFunctions=mg.fFunctions;
      fHistogram=mg.fHistogram;
      fMaximum=mg.fMaximum;
      fMinimum=mg.fMinimum;
   }
   return *this;
}


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

   if (!fGraphs) return;
   TGraph *g;
   TIter   next(fGraphs);
   while ((g = (TGraph*) next())) {
      g->ResetBit(kMustCleanup);
   }
   fGraphs->Delete();
   delete fGraphs;
   fGraphs = 0;
   delete fHistogram;
   fHistogram = 0;
   if (fFunctions) {
      fFunctions->SetBit(kInvalidObject);
      //special logic to support the case where the same object is
      //added multiple times in fFunctions.
      //This case happens when the same object is added with different
      //drawing modes
      TObject *obj;
      while ((obj  = fFunctions->First())) {
         while (fFunctions->Remove(obj)) { }
         delete obj;
      }
      delete fFunctions;
   }
}


//______________________________________________________________________________
void TMultiGraph::Add(TGraph *graph, Option_t *chopt)
{
   // Add a new graph to the list of graphs.
   // Note that the graph is now owned by the TMultigraph.
   // Deleting the TMultiGraph object will automatically delete the graphs.
   // You should not delete the graphs when the TMultigraph is still active.

   if (!fGraphs) fGraphs = new TList();
   graph->SetBit(kMustCleanup);
   fGraphs->Add(graph,chopt);
}


//______________________________________________________________________________
void TMultiGraph::Add(TMultiGraph *multigraph, Option_t *chopt)
{
   // Add all the graphs in "multigraph" to the list of graphs.
   // If "chopt" is defined all the graphs in "multigraph" will be added with
   // the "chopt" option.
   // If "chopt" is undefined each graph will be added with the option it had
   // in "multigraph".

   TList *graphlist = multigraph->GetListOfGraphs();
   if (!graphlist) return;

   if (!fGraphs) fGraphs = new TList();

   TObjOptLink *lnk = (TObjOptLink*)graphlist->FirstLink();
   TObject *obj = 0;

   while (lnk) {
      obj = lnk->GetObject();
      if (!strlen(chopt)) fGraphs->Add(obj,lnk->GetOption());
      else                fGraphs->Add(obj,chopt);
      lnk = (TObjOptLink*)lnk->Next();
   }
}


//______________________________________________________________________________
void TMultiGraph::Browse(TBrowser *b)
{
   // Browse multigraph.

   TString opt = gEnv->GetValue("TGraph.BrowseOption", "");
   if (opt.IsNull()) {
      opt = b ? b->GetDrawOption() : "alp";
      opt = (opt == "") ? "alp" : opt.Data();
   }
   Draw(opt.Data());
   gPad->Update();
}


//______________________________________________________________________________
Int_t TMultiGraph::DistancetoPrimitive(Int_t px, Int_t py)
{
   // Compute distance from point px,py to each graph.

   // Are we on the axis?
   const Int_t kMaxDiff = 10;
   Int_t distance = 9999;
   if (fHistogram) {
      distance = fHistogram->DistancetoPrimitive(px,py);
      if (distance <= 0) return distance;
   }

   // Loop on the list of graphs
   if (!fGraphs) return distance;
   TGraph *g;
   TIter   next(fGraphs);
   while ((g = (TGraph*) next())) {
      Int_t dist = g->DistancetoPrimitive(px,py);
      if (dist <= 0) return 0;
      if (dist < kMaxDiff) {gPad->SetSelected(g); return dist;}
   }
   return distance;
}


//______________________________________________________________________________
void TMultiGraph::Draw(Option_t *option)
{
   // Draw this multigraph with its current attributes.
   //
   //   Options to draw a graph are described in TGraphPainter.
   //
   //  The drawing option for each TGraph may be specified as an optional
   //  second argument of the Add function. You can use GetGraphDrawOption
   //  to return this option.
   //  If a draw option is specified, it will be used to draw the graph,
   //  otherwise the graph will be drawn with the option specified in
   //  TMultiGraph::Draw. Use GetDrawOption to return the option specified
   //  when drawing the TMultiGraph.

   TString opt = option;
   opt.ToLower();

   if (gPad) {
      if (!gPad->IsEditable()) gROOT->MakeDefCanvas();
      if (opt.Contains("a")) gPad->Clear();
   }
   AppendPad(option);
}


//______________________________________________________________________________
TFitResultPtr TMultiGraph::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 TF1::Fit(TF1 *f1...

   char *linear;
   linear= (char*)strstr(fname, "++");
   TF1 *f1=0;
   if (linear)
      f1=new TF1(fname, fname, xmin, xmax);
   else {
      f1 = (TF1*)gROOT->GetFunction(fname);
      if (!f1) { Printf("Unknown function: %s",fname); return -1; }
   }

   return Fit(f1,option,"",xmin,xmax);
}


//______________________________________________________________________________
TFitResultPtr TMultiGraph::Fit(TF1 *f1, Option_t *option, Option_t *goption, Axis_t rxmin, Axis_t rxmax)
{
   // Fit this multigraph with function f1.
   //
   //   In this function all graphs of the multigraph are fitted simultaneously
   //
   //   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.
   //
   //   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 a chi2 fitting function is used for fitting the TGraphs's.
   //   The function is implemented in FitUtil::EvaluateChi2.
   //   In case of TGraphErrors 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);
   //
   //  Access to the fit result
   //  ========================
   //  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->Parameter(0); // retrieve the value for the parameter 0
   //     Double_t err0   = r->ParError(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.
   //
   //
   //   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

   // internal multigraph fitting methods
   Foption_t fitOption;
   ROOT::Fit::FitOptionsMake(ROOT::Fit::kGraph,option,fitOption);

   // create range and minimizer options with default values
   ROOT::Fit::DataRange range(rxmin,rxmax);
   ROOT::Math::MinimizerOptions minOption;
   return ROOT::Fit::FitObject(this, f1 , fitOption , minOption, goption, range);

}

//______________________________________________________________________________
void TMultiGraph::FitPanel()
{
   // Display a panel with all histogram fit options.
   // See class TFitPanel 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");
}

//______________________________________________________________________________
Option_t *TMultiGraph::GetGraphDrawOption(const TGraph *gr) const
{
   // Return the draw option for the TGraph gr in this TMultiGraph.
   // The return option is the one specified when calling TMultiGraph::Add(gr,option).

   if (!fGraphs || !gr) return "";
   TListIter next(fGraphs);
   TObject *obj;
   while ((obj = next())) {
      if (obj == (TObject*)gr) return next.GetOption();
   }
   return "";
}


//______________________________________________________________________________
void TMultiGraph::InitGaus(Double_t xmin, Double_t xmax)
{
   // Compute Initial values of parameters for a gaussian.

   Double_t allcha, sumx, sumx2, x, val, rms, mean;
   Int_t bin;
   const Double_t sqrtpi = 2.506628;

   // Compute mean value and RMS of the graph in the given range
   Int_t np = 0;
   allcha = sumx = sumx2 = 0;
   TGraph *g;
   TIter next(fGraphs);
   Double_t *px, *py;
   Int_t npp; //number of points in each graph
   while ((g = (TGraph*) next())) {
      px=g->GetX();
      py=g->GetY();
      npp=g->GetN();
      for (bin=0; bin<npp; bin++) {
         x=px[bin];
         if (x<xmin || x>xmax) continue;
         np++;
         val=py[bin];
         sumx+=val*x;
         sumx2+=val*x*x;
         allcha+=val;
      }
   }
   if (np == 0 || allcha == 0) return;
   mean = sumx/allcha;
   rms  = TMath::Sqrt(sumx2/allcha - mean*mean);

   Double_t binwidx = TMath::Abs((xmax-xmin)/np);
   if (rms == 0) rms = 1;
   TVirtualFitter *grFitter = TVirtualFitter::GetFitter();
   TF1 *f1 = (TF1*)grFitter->GetUserFunc();
   f1->SetParameter(0,binwidx*allcha/(sqrtpi*rms));
   f1->SetParameter(1,mean);
   f1->SetParameter(2,rms);
   f1->SetParLimits(2,0,10*rms);
}


//______________________________________________________________________________
void TMultiGraph::InitExpo(Double_t xmin, Double_t xmax)
{
   // Compute Initial values of parameters for an exponential.

   Double_t constant, slope;
   Int_t ifail;

   LeastSquareLinearFit(-1, constant, slope, ifail, xmin, xmax);

   TVirtualFitter *grFitter = TVirtualFitter::GetFitter();
   TF1 *f1 = (TF1*)grFitter->GetUserFunc();
   f1->SetParameter(0,constant);
   f1->SetParameter(1,slope);
}


//______________________________________________________________________________
void TMultiGraph::InitPolynom(Double_t xmin, Double_t xmax)
{
   // Compute Initial values of parameters for a polynom.

   Double_t fitpar[25];

   TVirtualFitter *grFitter = TVirtualFitter::GetFitter();
   TF1 *f1 = (TF1*)grFitter->GetUserFunc();
   Int_t npar   = f1->GetNpar();

   LeastSquareFit(npar, fitpar, xmin, xmax);

   for (Int_t i=0;i<npar;i++) f1->SetParameter(i, fitpar[i]);
}


//______________________________________________________________________________
void TMultiGraph::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

   const Double_t zero = 0.;
   const Double_t one = 1.;
   const Int_t idim = 20;

   Double_t  b[400]        /* was [20][20] */;
   Int_t i, k, l, ifail, bin;
   Double_t power;
   Double_t da[20], xk, yk;


   //count the total number of points to fit
   TGraph *g;
   TIter next(fGraphs);
   Double_t *px, *py;
   Int_t n=0;
   Int_t npp;
   while ((g = (TGraph*) next())) {
      px=g->GetX();
      npp=g->GetN();
      for (bin=0; bin<npp; bin++) {
         xk=px[bin];
         if (xk < xmin || xk > xmax) continue;
         n++;
      }
   }
   if (m <= 2) {
      LeastSquareLinearFit(n, a[0], a[1], ifail, xmin, xmax);
      return;
   }
   if (m > idim || m > n) return;
   da[0] = zero;
   for (l = 2; l <= m; ++l) {
      b[l-1]           = zero;
      b[m + l*20 - 21] = zero;
      da[l-1]          = zero;
   }
   Int_t np = 0;

   next.Reset();
   while ((g = (TGraph*) next())) {
      px=g->GetX();
      py=g->GetY();
      npp=g->GetN();

      for (k = 0; k <= npp; ++k) {
         xk     = px[k];
         if (xk < xmin || xk > xmax) continue;
         np++;
         yk     = py[k];
         power  = one;
         da[0] += yk;
         for (l = 2; l <= m; ++l) {
            power   *= xk;
            b[l-1]  += power;
            da[l-1] += power*yk;
         }
         for (l = 2; l <= m; ++l) {
            power            *= xk;
            b[m + l*20 - 21] += power;
         }
      }
   }
   b[0]  = Double_t(np);
   for (i = 3; i <= m; ++i) {
      for (k = i; k <= m; ++k) {
         b[k - 1 + (i-1)*20 - 21] = b[k + (i-2)*20 - 21];
      }
   }
   H1LeastSquareSeqnd(m, b, idim, ifail, 1, da);

   if (ifail < 0) {
      //a[0] = fY[0];
      py=((TGraph *)fGraphs->First())->GetY();
      a[0]=py[0];
      for (i=1; i<m; ++i) a[i] = 0;
      return;
   }
   for (i=0; i<m; ++i) a[i] = da[i];
}


//______________________________________________________________________________
void TMultiGraph::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

   Double_t xbar, ybar, x2bar;
   Int_t i;
   Double_t xybar;
   Double_t fn, xk, yk;
   Double_t det;

   ifail = -2;
   xbar  = ybar = x2bar = xybar = 0;
   Int_t np = 0;
   TGraph *g;
   TIter next(fGraphs);
   Double_t *px, *py;
   Int_t npp;
   while ((g = (TGraph*) next())) {
      px=g->GetX();
      py=g->GetY();
      npp=g->GetN();
      for (i = 0; i < npp; ++i) {
         xk = px[i];
         if (xk < xmin || xk > xmax) continue;
         np++;
         yk = py[i];
         if (ndata < 0) {
            if (yk <= 0) yk = 1e-9;
            yk = TMath::Log(yk);
         }
         xbar  += xk;
         ybar  += yk;
         x2bar += xk*xk;
         xybar += xk*yk;
      }
   }
   fn    = Double_t(np);
   det   = fn*x2bar - xbar*xbar;
   ifail = -1;
   if (det <= 0) {
      if (fn > 0) a0 = ybar/fn;
      else        a0 = 0;
      a1 = 0;
      return;
   }
   ifail = 0;
   a0 = (x2bar*ybar - xbar*xybar) / det;
   a1 = (fn*xybar - xbar*ybar) / det;
}


//______________________________________________________________________________
Int_t TMultiGraph::IsInside(Double_t x, Double_t y) const
{
   // Return 1 if the point (x,y) is inside one of the graphs 0 otherwise.

   Int_t in = 0;
   if (!fGraphs) return in;
   TGraph *g;
   TIter next(fGraphs);
   while ((g = (TGraph*) next())) {
      in = g->IsInside(x, y);
      if (in) return in;
   }
   return in;
}


//______________________________________________________________________________
TH1F *TMultiGraph::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 TMultiGraph::Draw. Return fHistogram
   //    2- user had called TPad::DrawFrame. return pointer to hframe histogram

   if (fHistogram) return fHistogram;
   if (!gPad) return 0;
   gPad->Modified();
   gPad->Update();
   if (fHistogram) return fHistogram;
   TH1F *h1 = (TH1F*)gPad->FindObject("hframe");
   return h1;
}


//______________________________________________________________________________
TF1 *TMultiGraph::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.

   if (!fFunctions) return 0;
   return (TF1*)fFunctions->FindObject(name);
}

//______________________________________________________________________________
TList *TMultiGraph::GetListOfFunctions()
{
   // Return pointer to list of functions.
   // If pointer is null create the list

   if (!fFunctions) fFunctions = new TList();
   return fFunctions;
}


//______________________________________________________________________________
TAxis *TMultiGraph::GetXaxis() const
{
   // Get x axis of the graph.
   // This method returns a valid axis only after the TMultigraph has been drawn.

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


//______________________________________________________________________________
TAxis *TMultiGraph::GetYaxis() const
{
   // Get y axis of the graph.
   // This method returns a valid axis only after the TMultigraph has been drawn.

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


//______________________________________________________________________________
void TMultiGraph::Paint(Option_t *option)
{
   // Paint all the graphs of this multigraph.

   const TPickerStackGuard pushGuard(this);

   if (!fGraphs) return;
   if (fGraphs->GetSize() == 0) return;

   char *l;
   Int_t nch = strlen(option);

   TString chopt = option;
   chopt.ToUpper();

   l = (char*)strstr(chopt.Data(),"3D");
   if (l) {
      l = (char*)strstr(chopt.Data(),"L");
      if (l) PaintPolyLine3D(chopt.Data());
      return;
   }

   l = (char*)strstr(chopt.Data(),"PADS");
   if (l) {
      chopt.ReplaceAll("PADS","");
      PaintPads(chopt.Data());
      return;
   }

   TGraph *g;

   l = (char*)strstr(chopt.Data(),"A");
   if (l) {
      *l = ' ';
      TIter   next(fGraphs);
      Int_t npt = 100;
      Double_t maximum, minimum, rwxmin, rwxmax, rwymin, rwymax, uxmin, uxmax, dx, dy;
      rwxmin    = gPad->GetUxmin();
      rwxmax    = gPad->GetUxmax();
      rwymin    = gPad->GetUymin();
      rwymax    = gPad->GetUymax();
      char *xtitle = 0;
      char *ytitle = 0;
      Int_t firstx = 0;
      Int_t lastx  = 0;
      Bool_t timedisplay = kFALSE;
      char *timeformat = 0;

      if (fHistogram) {
         //cleanup in case of a previous unzoom
         if (fHistogram->GetMinimum() >= fHistogram->GetMaximum()) {
            nch = strlen(fHistogram->GetXaxis()->GetTitle());
            firstx = fHistogram->GetXaxis()->GetFirst();
            lastx  = fHistogram->GetXaxis()->GetLast();
            timedisplay = fHistogram->GetXaxis()->GetTimeDisplay();
            if (nch) {
               xtitle = new char[nch+1];
               strlcpy(xtitle,fHistogram->GetXaxis()->GetTitle(),nch+1);
            }
            nch = strlen(fHistogram->GetYaxis()->GetTitle());
            if (nch) {
               ytitle = new char[nch+1];
               strlcpy(ytitle,fHistogram->GetYaxis()->GetTitle(),nch+1);
            }
            nch = strlen(fHistogram->GetXaxis()->GetTimeFormat());
            if (nch) {
              timeformat = new char[nch+1];
              strlcpy(timeformat,fHistogram->GetXaxis()->GetTimeFormat(),nch+1);
            }
            delete fHistogram;
            fHistogram = 0;
         }
      }
      if (fHistogram) {
         minimum = fHistogram->GetYaxis()->GetXmin();
         maximum = fHistogram->GetYaxis()->GetXmax();
         uxmin   = gPad->PadtoX(rwxmin);
         uxmax   = gPad->PadtoX(rwxmax);
      } else {
         g = (TGraph*) next();
         if (g) g->ComputeRange(rwxmin, rwymin, rwxmax, rwymax);
         while ((g = (TGraph*) next())) {
            Double_t rx1,ry1,rx2,ry2;
            g->ComputeRange(rx1, ry1, rx2, ry2);
            if (rx1 < rwxmin) rwxmin = rx1;
            if (ry1 < rwymin) rwymin = ry1;
            if (rx2 > rwxmax) rwxmax = rx2;
            if (ry2 > rwymax) rwymax = ry2;
            if (g->GetN() > npt) npt = g->GetN();
         }
         if (rwxmin == rwxmax) rwxmax += 1.;
         if (rwymin == rwymax) rwymax += 1.;
         dx = 0.05*(rwxmax-rwxmin);
         dy = 0.05*(rwymax-rwymin);
         uxmin    = rwxmin - dx;
         uxmax    = rwxmax + dx;
         if (gPad->GetLogy()) {
            if (rwymin <= 0) rwymin = 0.001*rwymax;
            minimum = rwymin/(1+0.5*TMath::Log10(rwymax/rwymin));
            maximum = rwymax*(1+0.2*TMath::Log10(rwymax/rwymin));
         } else {
            minimum  = rwymin - dy;
            maximum  = rwymax + dy;
         }
         if (minimum < 0 && rwymin >= 0) minimum = 0;
         if (maximum > 0 && rwymax <= 0) maximum = 0;
      }

      if (fMinimum != -1111) rwymin = minimum = fMinimum;
      if (fMaximum != -1111) rwymax = maximum = fMaximum;
      if (uxmin < 0 && rwxmin >= 0) {
         if (gPad->GetLogx()) uxmin = 0.9*rwxmin;
         //else                 uxmin = 0;
      }
      if (uxmax > 0 && rwxmax <= 0) {
         if (gPad->GetLogx()) uxmax = 1.1*rwxmax;
         //else                 uxmax = 0;
      }
      if (minimum < 0 && rwymin >= 0) {
         if (gPad->GetLogy()) minimum = 0.9*rwymin;
         //else                minimum = 0;
      }
      if (maximum > 0 && rwymax <= 0) {
         if (gPad->GetLogy()) maximum = 1.1*rwymax;
         //else                maximum = 0;
      }
      if (minimum <= 0 && gPad->GetLogy()) minimum = 0.001*maximum;
      if (uxmin <= 0 && gPad->GetLogx()) {
         if (uxmax > 1000) uxmin = 1;
         else              uxmin = 0.001*uxmax;
      }
      rwymin = minimum;
      rwymax = maximum;
      if (fHistogram) {
         fHistogram->GetYaxis()->SetLimits(rwymin,rwymax);
      }

      // Create a temporary histogram to draw the axis
      if (!fHistogram) {
         // the graph is created with at least as many channels as there are points
         // to permit zooming on the full range
         rwxmin = uxmin;
         rwxmax = uxmax;
         fHistogram = new TH1F(GetName(),GetTitle(),npt,rwxmin,rwxmax);
         if (!fHistogram) return;
         fHistogram->SetMinimum(rwymin);
         fHistogram->SetBit(TH1::kNoStats);
         fHistogram->SetMaximum(rwymax);
         fHistogram->GetYaxis()->SetLimits(rwymin,rwymax);
         fHistogram->SetDirectory(0);
         if (xtitle) {fHistogram->GetXaxis()->SetTitle(xtitle); delete [] xtitle;}
         if (ytitle) {fHistogram->GetYaxis()->SetTitle(ytitle); delete [] ytitle;}
         if (firstx != lastx) fHistogram->GetXaxis()->SetRange(firstx,lastx);
         if (timedisplay) {fHistogram->GetXaxis()->SetTimeDisplay(timedisplay);}
         if (timeformat) {fHistogram->GetXaxis()->SetTimeFormat(timeformat); delete [] timeformat;}
      }
      fHistogram->Paint("0");
   }

   TGraph *gfit = 0;
   if (fGraphs) {
      TObjOptLink *lnk = (TObjOptLink*)fGraphs->FirstLink();
      TObject *obj = 0;

      chopt.ReplaceAll("A","");

      while (lnk) {

         obj = lnk->GetObject();

         gPad->PushSelectableObject(obj);

         if (!gPad->PadInHighlightMode() || (gPad->PadInHighlightMode() && obj == gPad->GetSelected())) {
            TString opt = lnk->GetOption();
            if (!opt.IsWhitespace())
               obj->Paint(opt.ReplaceAll("A","").Data());
            else {
               if (!chopt.IsWhitespace()) obj->Paint(chopt.Data());
               else                       obj->Paint("L");
            }
         }

         lnk = (TObjOptLink*)lnk->Next();
      }

      gfit = (TGraph*)obj; // pick one TGraph in the list to paint the fit parameters.
   }

   TObject *f;
   TF1 *fit = 0;
   if (fFunctions) {
      TIter   next(fFunctions);
      while ((f = (TObject*) next())) {
         if (f->InheritsFrom(TF1::Class())) {
            if (f->TestBit(TF1::kNotDraw) == 0) f->Paint("lsame");
            fit = (TF1*)f;
         } else  {
            f->Paint();
         }
      }
   }

   if (fit) gfit->PaintStats(fit);
}


//______________________________________________________________________________
void TMultiGraph::PaintPads(Option_t *option)
{
   // Divides the active pad and draws all Graphs in the Multigraph separately.

   TIter next(fGraphs);
   Int_t neededPads = fGraphs->GetSize();
   Int_t existingPads = 0;
   TString opt = (TString)option;

   TVirtualPad *curPad = gPad;
   TObject *obj;
   TIter nextPad(curPad->GetListOfPrimitives());

   while ((obj = nextPad())) {
      if (obj->InheritsFrom(TVirtualPad::Class())) existingPads++;
   }
   if (existingPads < neededPads) {
      curPad->Clear();
      Int_t nx = (Int_t)TMath::Sqrt((Double_t)neededPads);
      if (nx*nx < neededPads) nx++;
      Int_t ny = nx;
      if (((nx*ny)-nx) >= neededPads) ny--;
      curPad->Divide(nx,ny);
   }
   Int_t i = 0;
   TGraph *g;

   TObjOptLink *lnk = (TObjOptLink*)fGraphs->FirstLink();
   obj = 0;

   while (lnk) {
      g = (TGraph*)lnk->GetObject();
      i++;
      curPad->cd(i);
      TString apopt = lnk->GetOption();
      if (strlen(apopt)) {
         g->Draw((apopt.Append("A")).Data());
      } else {
         if (strlen(opt)) g->Draw(opt.Append("A"));
         else             g->Draw("LA");
      }
      lnk = (TObjOptLink*)lnk->Next();
   }

   curPad->cd();
}


//______________________________________________________________________________
void TMultiGraph::PaintPolyLine3D(Option_t *option)
{
   // Paint all the graphs of this multigraph as 3D lines.

   Int_t i, npt=0;
   char *l;
   Double_t rwxmin=0., rwxmax=0., rwymin=0., rwymax=0.;
   TIter next(fGraphs);
   TGraph *g;

   g = (TGraph*) next();
   if (g) {
      g->ComputeRange(rwxmin, rwymin, rwxmax, rwymax);
      npt = g->GetN();
   }

   while ((g = (TGraph*) next())) {
      Double_t rx1,ry1,rx2,ry2;
      g->ComputeRange(rx1, ry1, rx2, ry2);
      if (rx1 < rwxmin) rwxmin = rx1;
      if (ry1 < rwymin) rwymin = ry1;
      if (rx2 > rwxmax) rwxmax = rx2;
      if (ry2 > rwymax) rwymax = ry2;
      if (g->GetN() > npt) npt = g->GetN();
   }

   Int_t ndiv = fGraphs->GetSize();
   TH2F* frame = new TH2F("frame","", ndiv, 0., (Double_t)(ndiv),
                                      10, rwxmin, rwxmax);

   TAxis *Xaxis = frame->GetXaxis();
   Xaxis->SetNdivisions(-ndiv);
   next.Reset();
   for (i=ndiv; i>=1; i--) {
      g = (TGraph*) next();
      Xaxis->SetBinLabel(i, g->GetTitle());
   }

   frame->SetStats(kFALSE);
   frame->SetMinimum(rwymin);
   frame->SetMaximum(rwymax);

   l = (char*)strstr(option,"A");
   if (l) frame->Paint("lego0,fb,bb");
   l = (char*)strstr(option,"BB");
   if (!l) frame->Paint("lego0,fb,a,same");

   Double_t *x, *y;
   Double_t xyz1[3], xyz2[3];

   next.Reset();
   Int_t j = ndiv;
   while ((g = (TGraph*) next())) {
      npt = g->GetN();
      x   = g->GetX();
      y   = g->GetY();
      gPad->SetLineColor(g->GetLineColor());
      gPad->SetLineWidth(g->GetLineWidth());
      gPad->SetLineStyle(g->GetLineStyle());
      gPad->TAttLine::Modify();
      for (i=0; i<npt-1; i++) {
         xyz1[0] = j-0.5;
         xyz1[1] = x[i];
         xyz1[2] = y[i];
         xyz2[0] = j-0.5;
         xyz2[1] = x[i+1];
         xyz2[2] = y[i+1];
         gPad->PaintLine3D(xyz1, xyz2);
      }
      j--;
   }

   l = (char*)strstr(option,"FB");
   if (!l) frame->Paint("lego0,bb,a,same");
   delete frame;
}


//______________________________________________________________________________
void TMultiGraph::Print(Option_t *option) const
{
   // Print the list of graphs.

   TGraph *g;
   if (fGraphs) {
      TIter   next(fGraphs);
      while ((g = (TGraph*) next())) {
         g->Print(option);
      }
   }
}


//______________________________________________________________________________
void TMultiGraph::RecursiveRemove(TObject *obj)
{
   // Recursively remove this object from a list. Typically implemented
   // by classes that can contain multiple references to a same object.

   if (!fGraphs) return;
   TObject *objr = fGraphs->Remove(obj);
   if (!objr) return;
   delete fHistogram; fHistogram = 0;
   if (gPad) gPad->Modified();
}


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

   char quote = '"';
   out<<"   "<<std::endl;
   if (gROOT->ClassSaved(TMultiGraph::Class())) {
      out<<"   ";
   } else {
      out<<"   TMultiGraph *";
   }
   out<<"multigraph = new TMultiGraph();"<<std::endl;
   out<<"   multigraph->SetName("<<quote<<GetName()<<quote<<");"<<std::endl;
   out<<"   multigraph->SetTitle("<<quote<<GetTitle()<<quote<<");"<<std::endl;

   if (fGraphs) {
      TObjOptLink *lnk = (TObjOptLink*)fGraphs->FirstLink();
      TObject *g;

      while (lnk) {
         g = lnk->GetObject();
         g->SavePrimitive(out, Form("multigraph%s",lnk->GetOption()));
         lnk = (TObjOptLink*)lnk->Next();
      }
   }
   const char *l = strstr(option,"th2poly");
   if (l) {
      out<<"   "<<l+7<<"->AddBin(multigraph);"<<std::endl;
   } else {
      out<<"   multigraph->Draw(" <<quote<<option<<quote<<");"<<std::endl;
   }
   TAxis *xaxis = GetXaxis();
   TAxis *yaxis = GetYaxis();

   if (xaxis) xaxis->SaveAttributes(out, "multigraph","->GetXaxis()");
   if (yaxis) yaxis->SaveAttributes(out, "multigraph","->GetYaxis()");
}


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

   fMaximum = maximum;
   if (fHistogram)  fHistogram->SetMaximum(maximum);
}


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

   fMinimum = minimum;
   if (fHistogram) fHistogram->SetMinimum(minimum);
}