combinedFit¶

Combined (simultaneous) fit of two histogram with separate functions and some common parameters

See http://root.cern.ch/phpBB3//viewtopic.php?f=3&t=11740#p50908 for a modified version working with Fumili or GSLMultiFit

N.B. this macro must be compiled with ACliC

Author: Lorenzo Moneta
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Monday, March 27, 2023 at 09:46 AM.

In [ ]:

%%cpp -d

#include <Fit/Fitter.h>
#include <Fit/BinData.h>
#include <Fit/Chi2FCN.h>
#include <TH1.h>
#include <Math/WrappedMultiTF1.h>
#include <HFitInterface.h>
#include <TCanvas.h>
#include <TStyle.h>

definition of shared parameter background function

In [ ]:

int iparB[2] = {
   0, // exp amplitude in B histo
   2  // exp common parameter
};
%%cpp -d

signal + background function

In [ ]:

int iparSB[5] = {
   1, // exp amplitude in S+B histo
   2, // exp common parameter
   3, // Gaussian amplitude
   4, // Gaussian mean
   5  // Gaussian sigma
};
%%cpp -d

Create the GlobalCHi2 structure

In [ ]:

struct GlobalChi2 {
   GlobalChi2(ROOT::Math::IMultiGenFunction &f1, ROOT::Math::IMultiGenFunction &f2) : fChi2_1(&f1), fChi2_2(&f2) {}

   // parameter vector is first background (in common 1 and 2)
   // and then is signal (only in 2)
   double operator()(const double *par) const
   {
      double p1[2];
      for (int i = 0; i < 2; ++i)
         p1[i] = par[iparB[i]];

      double p2[5];
      for (int i = 0; i < 5; ++i)
         p2[i] = par[iparSB[i]];

      return (*fChi2_1)(p1) + (*fChi2_2)(p2);
   }

   const ROOT::Math::IMultiGenFunction *fChi2_1;
   const ROOT::Math::IMultiGenFunction *fChi2_2;
};

In [ ]:

TH1D *hB = new TH1D("hB", "histo B", 100, 0, 100);
TH1D *hSB = new TH1D("hSB", "histo S+B", 100, 0, 100);

TF1 *fB = new TF1("fB", "expo", 0, 100);
fB->SetParameters(1, -0.05);
hB->FillRandom("fB");

TF1 *fS = new TF1("fS", "gaus", 0, 100);
fS->SetParameters(1, 30, 5);

hSB->FillRandom("fB", 2000);
hSB->FillRandom("fS", 1000);

perform now global fit

In [ ]:

TF1 *fSB = new TF1("fSB", "expo + gaus(2)", 0, 100);

ROOT::Math::WrappedMultiTF1 wfB(*fB, 1);
ROOT::Math::WrappedMultiTF1 wfSB(*fSB, 1);

ROOT::Fit::DataOptions opt;
ROOT::Fit::DataRange rangeB;

set the data range

In [ ]:

rangeB.SetRange(10, 90);
ROOT::Fit::BinData dataB(opt, rangeB);
ROOT::Fit::FillData(dataB, hB);

ROOT::Fit::DataRange rangeSB;
rangeSB.SetRange(10, 50);
ROOT::Fit::BinData dataSB(opt, rangeSB);
ROOT::Fit::FillData(dataSB, hSB);

ROOT::Fit::Chi2Function chi2_B(dataB, wfB);
ROOT::Fit::Chi2Function chi2_SB(dataSB, wfSB);

GlobalChi2 globalChi2(chi2_B, chi2_SB);

ROOT::Fit::Fitter fitter;

const int Npar = 6;
double par0[Npar] = {5, 5, -0.1, 100, 30, 10};

create before the parameter settings in order to fix or set range on them

In [ ]:

fitter.Config().SetParamsSettings(6, par0);

fix 5-th parameter

In [ ]:

fitter.Config().ParSettings(4).Fix();

set limits on the third and 4-th parameter

In [ ]:

fitter.Config().ParSettings(2).SetLimits(-10, -1.E-4);
fitter.Config().ParSettings(3).SetLimits(0, 10000);
fitter.Config().ParSettings(3).SetStepSize(5);

fitter.Config().MinimizerOptions().SetPrintLevel(0);
fitter.Config().SetMinimizer("Minuit2", "Migrad");

fit FCN function directly (specify optionally data size and flag to indicate that is a chi2 fit)

In [ ]:

fitter.FitFCN(6, globalChi2, 0, dataB.Size() + dataSB.Size(), true);
ROOT::Fit::FitResult result = fitter.Result();
result.Print(std::cout);

TCanvas *c1 = new TCanvas("Simfit", "Simultaneous fit of two histograms", 10, 10, 700, 700);
c1->Divide(1, 2);
c1->cd(1);
gStyle->SetOptFit(1111);

fB->SetFitResult(result, iparB);
fB->SetRange(rangeB().first, rangeB().second);
fB->SetLineColor(kBlue);
hB->GetListOfFunctions()->Add(fB);
hB->Draw();

c1->cd(2);
fSB->SetFitResult(result, iparSB);
fSB->SetRange(rangeSB().first, rangeSB().second);
fSB->SetLineColor(kRed);
hSB->GetListOfFunctions()->Add(fSB);
hSB->Draw();

Draw all canvases

In [ ]:

gROOT->GetListOfCanvases()->Draw()