fit2dHist.C: + Example to fit two histograms at the same time via TVirtualFitter

//
//+   Example to fit two histograms at the same time via TVirtualFitter
//
// To execute this tutorial, you can do:
//
// root > .x fit2dHist.C  (executing via CINT, slow)
//   or
// root > .x fit2dHist.C+     (executing via ACLIC , fast, with Minuit)
// root > .x fit2dHist.C+(2)  (executing via ACLIC , fast, with Minuit2)
//   or using the option to fit independently the 2 histos
// root > .x fit2dHist.C+(10) (via ACLIC, fast, independent fits with Minuit)
// root > .x fit2dHist.C+(12) (via ACLIC, fast, independent fits with Minuit2)
//
// Note that you can also execute this script in batch with eg,
//  root -b -q "fit2dHist.C+(12)"
//
// or execute interactively from the shell
//  root fit2dHist.C+
//  root "fit2dHist.C+(12)"
//
// Authors: Lorenzo Moneta, Rene Brun 18/01/2006   

#include "TH2D.h"
#include "TF2.h"
#include "TCanvas.h"
#include "TStyle.h"
#include "TRandom3.h"
#include "TVirtualFitter.h"
#include "TList.h"

#include <iostream>
  
double gauss2D(double *x, double *par) {
   double z1 = double((x[0]-par[1])/par[2]);
   double z2 = double((x[1]-par[3])/par[4]);
   return par[0]*exp(-0.5*(z1*z1+z2*z2));
}   
double my2Dfunc(double *x, double *par) {
   return gauss2D(x,&par[0]) + gauss2D(x,&par[5]);
}


// data need to be globals to be visible by fcn 
TRandom3 rndm; 
TH2D *h1, *h2;
Int_t npfits;

void myFcn(Int_t & /*nPar*/, Double_t * /*grad*/ , Double_t &fval, Double_t *p, Int_t /*iflag */  )
{
  TAxis *xaxis1  = h1->GetXaxis();
  TAxis *yaxis1  = h1->GetYaxis();
  TAxis *xaxis2  = h2->GetXaxis();
  TAxis *yaxis2  = h2->GetYaxis();

  int nbinX1 = h1->GetNbinsX(); 
  int nbinY1 = h1->GetNbinsY(); 
  int nbinX2 = h2->GetNbinsX(); 
  int nbinY2 = h2->GetNbinsY(); 

  double chi2 = 0; 
  double x[2]; 
  double tmp;
  npfits = 0;
  for (int ix = 1; ix <= nbinX1; ++ix) { 
    x[0] = xaxis1->GetBinCenter(ix);
    for (int iy = 1; iy <= nbinY1; ++iy) { 
      if ( h1->GetBinError(ix,iy) > 0 ) { 
        x[1] = yaxis1->GetBinCenter(iy);
        tmp = (h1->GetBinContent(ix,iy) - my2Dfunc(x,p))/h1->GetBinError(ix,iy);
        chi2 += tmp*tmp; 
        npfits++;
      }
    }
  }
  for (int ix = 1; ix <= nbinX2; ++ix) { 
     x[0] = xaxis2->GetBinCenter(ix);
    for (int iy = 1; iy <= nbinY2; ++iy) { 
      if ( h2->GetBinError(ix,iy) > 0 ) { 
        x[1] = yaxis2->GetBinCenter(iy);
        tmp = (h2->GetBinContent(ix,iy) - my2Dfunc(x,p))/h2->GetBinError(ix,iy);
        chi2 += tmp*tmp; 
        npfits++;
      }
    }
  }
  fval = chi2; 
}

void FillHisto(TH2D * h, int n, double * p) { 


  const double mx1 = p[1]; 
  const double my1 = p[3]; 
  const double sx1 = p[2]; 
  const double sy1 = p[4]; 
  const double mx2 = p[6]; 
  const double my2 = p[8]; 
  const double sx2 = p[7]; 
  const double sy2 = p[9]; 
  //const double w1 = p[0]*sx1*sy1/(p[5]*sx2*sy2); 
  const double w1 = 0.5; 

  double x, y; 
  for (int i = 0; i < n; ++i) {
    // generate randoms with larger gaussians
    rndm.Rannor(x,y);

    double r = rndm.Rndm(1);
    if (r < w1) { 
      x = x*sx1 + mx1; 
      y = y*sy1 + my1; 
    }
    else { 
      x = x*sx2 + mx2; 
      y = y*sy2 + my2; 
    }      
    h->Fill(x,y);
     
  }
}
      
  


int fit2dHist(int option=1) { 

  // create two histograms 

  int nbx1 = 50;
  int nby1 = 50;
  int nbx2 = 50;
  int nby2 = 50;
  double xlow1 = 0.; 
  double ylow1 = 0.; 
  double xup1 = 10.; 
  double yup1 = 10.; 
  double xlow2 = 5.; 
  double ylow2 = 5.; 
  double xup2 = 20.; 
  double yup2 = 20.; 

  h1 = new TH2D("h1","core",nbx1,xlow1,xup1,nby1,ylow1,yup1);
  h2 = new TH2D("h2","tails",nbx2,xlow2,xup2,nby2,ylow2,yup2);

  double iniParams[10] = { 100, 6., 2., 7., 3, 100, 12., 3., 11., 2. };
  // create fit function
  TF2 * func = new TF2("func",my2Dfunc,xlow2,xup2,ylow2,yup2, 10);
  func->SetParameters(iniParams);

  // fill Histos
  int n1 = 1000000;
  int n2 = 1000000; 
  FillHisto(h1,n1,iniParams);
  FillHisto(h2,n2,iniParams);

  // scale histograms to same heights (for fitting)
  double dx1 = (xup1-xlow1)/double(nbx1); 
  double dy1 = (yup1-ylow1)/double(nby1);
  double dx2 = (xup2-xlow2)/double(nbx2);
  double dy2 = (yup2-ylow2)/double(nby2);
  // scale histo 2 to scale of 1 
  h2->Sumw2();
  h2->Scale(  ( double(n1) * dx1 * dy1 )  / ( double(n2) * dx2 * dy2 ) );

  bool global = false;
  if (option > 10) global = true;
  if (global) { 
    // fill data structure for fit (coordinates + values + errors) 
    std::cout << "Do global fit" << std::endl;
    // fit now all the function together

    //The default minimizer is Minuit, you can also try Minuit2
    if (option%10 == 2) TVirtualFitter::SetDefaultFitter("Minuit2");
    else                TVirtualFitter::SetDefaultFitter("Minuit");
    TVirtualFitter * minuit = TVirtualFitter::Fitter(0,10);
    for (int i = 0; i < 10; ++i) {  
      minuit->SetParameter(i, func->GetParName(i), func->GetParameter(i), 0.01, 0,0);
    }
    minuit->SetFCN(myFcn);

    double arglist[100];
    arglist[0] = 0;
    // set print level
    minuit->ExecuteCommand("SET PRINT",arglist,2);

    // minimize
    arglist[0] = 5000; // number of function calls
    arglist[1] = 0.01; // tolerance
    minuit->ExecuteCommand("MIGRAD",arglist,2);

    //get result
    double minParams[10];
    double parErrors[10];
    for (int i = 0; i < 10; ++i) {  
      minParams[i] = minuit->GetParameter(i);
      parErrors[i] = minuit->GetParError(i);
    }
    double chi2, edm, errdef; 
    int nvpar, nparx;
    minuit->GetStats(chi2,edm,errdef,nvpar,nparx);

    func->SetParameters(minParams);
    func->SetParErrors(parErrors);
    func->SetChisquare(chi2);
    int ndf = npfits-nvpar;
    func->SetNDF(ndf);

    // add to list of functions
    h1->GetListOfFunctions()->Add(func);
    h2->GetListOfFunctions()->Add(func);
  }
  else {     
    // fit independently
    h1->Fit(func);
    h2->Fit(func);
  }	     

  // Create a new canvas.
  TCanvas * c1 = new TCanvas("c1","Two HIstogram Fit example",100,10,900,800);
  c1->Divide(2,2);
  gStyle->SetOptFit();
  gStyle->SetStatY(0.6);

  c1->cd(1);
  h1->Draw();
  func->SetRange(xlow1,ylow1,xup1,yup1);
  func->DrawCopy("cont1 same");
  c1->cd(2);
  h1->Draw("lego");
  func->DrawCopy("surf1 same");
  c1->cd(3);
  func->SetRange(xlow2,ylow2,xup2,yup2);
  h2->Draw();
  func->DrawCopy("cont1 same");
  c1->cd(4);
  h2->Draw("lego");
  gPad->SetLogz();
  func->Draw("surf1 same");

  return 0; 
}