fit2dHist.C

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/// \file
/// \ingroup tutorial_fit
/// \notebook
///
/// Example to fit two histograms at the same time via TVirtualFitter
///
/// To execute this tutorial, you can do:
///
/// ~~~{.cpp}
/// root > .x fit2dHist.C  (executing via CINT, slow)
/// ~~~
///
///   or
/// ~~~{.cpp}
/// 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
/// ~~~{.cpp}
/// 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,
/// ~~~{.cpp}
///  root -b -q "fit2dHist.C+(12)"
/// ~~~
///
/// or execute interactively from the shell
/// ~~~{.cpp}
///  root fit2dHist.C+
///  root "fit2dHist.C+(12)"
/// ~~~
///
/// \macro_image
/// \macro_output
/// \macro_code
///
/// \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;
}