Hi
could someone please tell me if there is a way to simultaneously fit multiple functions to multiple graphs?
To be more explicit I have several functions f_i which have some common parameters shared amongst them and I would like to fit these to different graphs, is there a way to fit these? I am not an expert at C so if you could try to be explicit in how I would implement this that would be much appreciated.
thanks
Mark
So I have an updated status to this post. I have managed to perform a simultaneous fit for multiple graphs,
the issue I am now facing is that the fitted parameters have very large errors even though the fit seems to be very good, and I would like to know how to resolve this issue. The way I have performed this fit is quite simple it is a modified version of the tutorial combinedFit.C it is as follows:
//+ 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: L. Moneta - Dec 2010
#include "Fit/Fitter.h"
#include "Fit/BinData.h"
#include "Fit/Chi2FCN.h"
#include "TH1.h"
#include "TF1.h"
#include "TList.h"
#include "Math/WrappedMultiTF1.h"
#include "HFitInterface.h"
#include "TCanvas.h"
#include "TStyle.h"
#include "TMath.h"
#include "TGraph.h"
#include "TRandom.h"
// definition of shared parameter
// background function
int iparB1[2] = { 0, // exp amplitude in B histo
2 // exp common parameter
};
// signal + background function
int iparB2[2] = { 1, // exp amplitude in S+B histo
2, // exp common parameter
};
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[iparB1[i] ];
double p2[2];
for (int i = 0; i < 2; ++i) p2[i] = par[iparB2[i] ];
return (*fChi2_1)(p1) + (*fChi2_2)(p2);
}
const ROOT::Math::IMultiGenFunction * fChi2_1;
const ROOT::Math::IMultiGenFunction * fChi2_2;
};
double myfunc1(double *x, double *par){
float xx =x[0];
double f = TMath::Exp(par[0]+par[1]*xx);
return f;
}
double myfunc2(double *x, double *par){
float xx =x[0];
double f = TMath::Exp(par[0]+par[1]*xx);
return f;
}
double myfunction1(double *x, double *par){
double constant = 2.0;
float xx =x[0];
double f = TMath::Exp(constant*par[0]+par[1]*xx);
return f;
}
double myfunction2(double *x, double *par){
float constant = 2.0;
float xx =x[0];
double f = TMath::Exp(constant*par[0]+par[1]*xx);
return f;
}
void combinedFit(){
int nd = 200;
double rnd1,x, rnd2,xp[nd],y1[nd],y2[nd];
double e = 0.1;
TRandom r1,r2;
x = (double) 100.0/nd;
//TH1D * hB1 = new TH1D("hB1","histo B1",100,0,100);
//TH1D * hB2 = new TH1D("hB2","histo B2",100, 0,100);
TF1 * fB1 = new TF1("fB1",myfunc1,0,100,2);
TF1 * fB2 = new TF1("fB2",myfunc2,0,100,2);
fB1->SetParameters(1,-0.05);
fB2->SetParameters(1,-0.05);
//hB1->FillRandom("fB1",2000);
//hB2->FillRandom("fB1",2000);
for (Int_t i=0; i<nd; i++) {
rnd1 = r1.Uniform(-e,e); // Generate a random number in [-e,e]
rnd2 = r2.Uniform(-e,e); // Generate a random number in [-e,e]
y1[i] = fB1->Eval(x*i)*(1+rnd1);
y2[i] = fB2->Eval(x*i)*(1+rnd2);
xp[i] = x*i;
//cout<< rnd2<<" "<<xp[i] <<" " << y2[i]<<endl;
}
TGraph *gb1 = new TGraph(nd,xp,y1);
TGraph *gb2 = new TGraph(nd,xp,y2);
TF1 * ffitB1 = new TF1("ffitB1",myfunction1,0,100,2);
TF1 * ffitB2 = new TF1("ffitB2",myfunction2,0,100,2);
ROOT::Math::WrappedMultiTF1 wfB1(*ffitB1,1);
ROOT::Math::WrappedMultiTF1 wfB2(*ffitB2,1);
ROOT::Fit::DataOptions opt;
ROOT::Fit::DataRange rangeB1;
ROOT::Fit::DataRange rangeB2;
// set the data range
rangeB1.SetRange(0,100);
rangeB2.SetRange(0,100);
ROOT::Fit::BinData dataB1(opt,rangeB1);
ROOT::Fit::BinData dataB2(opt,rangeB2);
ROOT::Fit::FillData(dataB1, gb1);
ROOT::Fit::FillData(dataB2, gb2);
ROOT::Fit::Chi2Function chi2_B1(dataB1, wfB1);
ROOT::Fit::Chi2Function chi2_B2(dataB2, wfB2);
GlobalChi2 globalChi2(chi2_B1, chi2_B2);
ROOT::Fit::Fitter fitter;
const int Npar = 3;
double par0[Npar] = {50,50,-0.1};
// create before the parameter settings in order to fix or set range on them
fitter.Config().SetParamsSettings(3,par0);
// fix 5-th parameter
//fitter.Config().ParSettings(4).Fix();
// set limits on the third and 4-th parameter
//fitter.Config().ParSettings(2).SetLimits(-10,-1.E-4);
//fitter.Config().ParSettings(2).SetLimits(0,10000);
//fitter.Config().ParSettings(3).SetStepSize(5);
fitter.Config().MinimizerOptions().SetPrintLevel(0);
fitter.Config().SetMinimizer("Minuit","Minimize");
// fit FCN function directly
// (specify optionally data size and flag to indicate that is a chi2 fit)
fitter.FitFCN(3,globalChi2,0,dataB1.Size()+dataB2.Size(),true);
ROOT::Fit::FitResult result = fitter.Result();
result.Print(std::cout);
TCanvas * c1 = new TCanvas("Simfit","Simultaneous fit of two graphs",
10,10,700,700);
c1->Divide(1,2);
c1->cd(1);
gStyle->SetOptFit(1111);
ffitB1->SetFitResult(result, iparB1);
ffitB1->SetRange(rangeB1().first, rangeB1().second);
ffitB1->SetLineColor(kBlue);
gb1->GetListOfFunctions()->Add(ffitB1);
gb1->Draw("alp");
//
c1->cd(2);
ffitB2->SetFitResult( result, iparB2);
ffitB2->SetRange(rangeB2().first, rangeB2().second);
ffitB2->SetLineColor(kRed);
gb2->GetListOfFunctions()->Add(ffitB2);
gb2->Draw("alp");
}This is essentially how the fit is performed in my actual code though the functions I am fitting are slightly more complicated unfortunately this piece of code does not have the problem of large errors I can post my actual code but it is more complicated and not very well written…
Is there a reason why the errors minuit give are large and is there any way of minimizing them?
Hello, I was following your example for the simultaneous fitting of two TGraphs and it is working fine. But as you also pointed out that it results into large errors of common parameters. Did you found any solution for this issue?
-Neeraj
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