TwoHistoFit2D.C

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/// \file
/// \ingroup tutorial_fit
/// \notebook
/// Example to fit two histograms at the same time.
///
/// \macro_image
/// \macro_output
/// \macro_code
///
/// \author Rene Brun

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

#include <vector>
#include <map>
#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) {
   double *p1 = &par[0];
   double *p2 = &par[5];
   return gauss2D(x,p1) + gauss2D(x,p2);
}



// data need to be globals to be visible by fcn

std::vector<std::pair<double, double> > coords;
std::vector<double > values;
std::vector<double > errors;

void myFcn(Int_t & /*nPar*/, Double_t * /*grad*/ , Double_t &fval, Double_t *p, Int_t /*iflag */  )
{
  int n = coords.size();
  double chi2 = 0;
  double tmp,x[2];
  for (int i = 0; i <n; ++i ) {
    x[0] = coords[i].first;
    x[1] = coords[i].second;
    tmp = ( values[i] - my2Dfunc(x,p))/errors[i];
    chi2 += tmp*tmp;
  }
  fval = chi2;
}
TRandom3 rndm;
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 TwoHistoFit2D(bool global = true) {

  // 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.;

  TH2D * h1 = new TH2D("h1","core",nbx1,xlow1,xup1,nby1,ylow1,yup1);
  TH2D * 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 = 50000;
  int n2 = 50000;
  //  h1->FillRandom("func", n1);
  //h2->FillRandom("func",n2);
  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);
//   h1->Sumw2();
//   h1->Scale( 1.0 / ( n1 * dx1 * dy1 ) );
  // scale histo 2 to scale of 1
  h2->Sumw2();
  h2->Scale(  ( double(n1) * dx1 * dy1 )  / ( double(n2) * dx2 * dy2 ) );


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

    // fill data structure for fit (coordinates + values + errors)
    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();

  /// reset data structure
  coords = std::vector<std::pair<double,double> >();
  values = std::vector<double>();
  errors = std::vector<double>();


  for (int ix = 1; ix <= nbinX1; ++ix) {
    for (int iy = 1; iy <= nbinY1; ++iy) {
      if ( h1->GetBinContent(ix,iy) > 0 ) {
         coords.push_back( std::make_pair(xaxis1->GetBinCenter(ix), yaxis1->GetBinCenter(iy) ) );
         values.push_back( h1->GetBinContent(ix,iy) );
         errors.push_back( h1->GetBinError(ix,iy) );
      }
    }
  }
  for (int ix = 1; ix <= nbinX2; ++ix) {
    for (int iy = 1; iy <= nbinY2; ++iy) {
      if ( h2->GetBinContent(ix,iy) > 0 ) {
         coords.push_back( std::make_pair(xaxis2->GetBinCenter(ix), yaxis2->GetBinCenter(iy) ) );
         values.push_back( h2->GetBinContent(ix,iy) );
         errors.push_back( h2->GetBinError(ix,iy) );
      }
    }
  }

  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 = coords.size()-nvpar;
  func->SetNDF(ndf);

  std::cout << "Chi2 Fit = " << chi2 << " ndf = " << ndf << "  " << func->GetNDF() << std::endl;

  // 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;
}