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Revision 25487 - (download) (as text) (annotate)
Mon Sep 22 12:44:13 2008 UTC (6 years, 4 months ago) by moneta
File size: 32042 byte(s)
Import changes from math development branch, in particular a re-implementation of 
fitting methods for the histogram and graph objects. 

NOTE: Since some files are removed, a  make clean-hist is needed in order to be able 
to compile hist after an svn update. 

 
The implementation of TH1::Fit, TGraph::Fit, TGraph2D::Fit and TMultiGraph::Fit is 
done in a common function implemented in HFitImpl.cxx (HFit::Fit). 

In addition the file HFitInterface.h define ROOT::Fit::FitObject functions passing 
option directly via Foption class and not by a string. They are used by the FitPanel.

Remove previously existing files THistFitInterface.cxx (and *.h) and 
TGraphFitInterface.cxx (and *.h). The code is now in the  HFitInterface.cxx (and *.h) 
files. 

Use plugin manager directly to open the Fit Panel. Do not pass anymore via the THistPainter. 
Changes in TH1::FitPanel, TGraph::FitPanel. 
Add FitPanel() method for TGraph2D and TMultiGraph. 

Add new class TBackCompFitter, providing a backward compatible implementation of 
TVirtualFitter using the new fitting class. It is constructed from the fitter class 
and can be used to retrieve the fit information (result and configuration) via the 
TVirtualFitter API from FitConfig and FitResult. A static istance is created after 
calling the Fit method.   
  
Other changes are:  


TGraph: 
  - when creating a graph from an histogram, don't use the same name. 
  Otherwise it will conflict later with histogram created internally by the TGraph. 

TH2: 
     add protected method TH2::DoFitSlices and TH2::DoProfile as common implementations
     for (FitSlicesX,FitSclicesY) and (ProfileX, ProfileY).
     pass the global statistics in DoProjection when range is (1,NBIN)

TBinimialEfficiencyFit: 
     add possibility to set verbose option, and set different precision and 
     max iterations for minimizing.

// @(#)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 "TMultiGraph.h"
#include "TGraph.h"
#include "TH1.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 <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
Use <tt>TMultiGraph::Add</tt> to add a new graph to the list.
The TMultiGraph owns the objects in the list.
Drawing options are the same as for TGraph.
<p>
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>
The drawing option for each TGraph may be specified as an optional
second argument of the Add function.
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>.
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.

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

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

   TGraph *gr;
   gr = (TGraph*)graphlist->First();
   fGraphs->Add(gr,chopt);
   for(Int_t i = 1; i < graphlist->GetSize(); i++){
      gr = (TGraph*)graphlist->After(gr);
      fGraphs->Add(gr,chopt);
   }
}


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

   Draw("alp");
   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 TGraph::PainGraph
   //
   //  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 drawin the TMultiGraph.

   AppendPad(option);
}


//______________________________________________________________________________
Int_t 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);
}


//______________________________________________________________________________
Int_t 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 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.
   //
   //   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

   return DoFit(f1,option,goption,rxmin,rxmax);  // implemented in HFitImpl.cxx

}

//______________________________________________________________________________
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();
      py=g->GetY();
      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;
}


//______________________________________________________________________________
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.

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


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

   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

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

   char *l;
   static char chopt[33];
   Int_t nch = strlen(option);
   Int_t i;
   for (i=0;i<nch;i++) chopt[i] = toupper(option[i]);
   chopt[nch] = 0;
   TGraph *g;

   l = strstr(chopt,"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;

      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();
            if (nch) {
               xtitle = new char[nch+1];
               strcpy(xtitle,fHistogram->GetXaxis()->GetTitle());
            }
            nch = strlen(fHistogram->GetYaxis()->GetTitle());
            if (nch) {
               ytitle = new char[nch+1];
               strcpy(ytitle,fHistogram->GetYaxis()->GetTitle());
            }
            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();
         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);
      }
      fHistogram->Paint("0");
   }

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

      while (lnk) {
         obj = lnk->GetObject();
         if (strlen(lnk->GetOption())) obj->Paint(lnk->GetOption());
         else                          obj->Paint(chopt);
         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::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 mulitple 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(ostream &out, Option_t *option /*= ""*/)
{
   // Save primitive as a C++ statement(s) on output stream out

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

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