Re: Fitting Basics

From: Rene Brun (Rene.Brun@cern.ch)
Date: Wed Nov 10 1999 - 22:47:58 MET 

Hi Philip,
I suggest you read the HOWTOs
  http://root.cern.ch/root/HowtoFit.html

You will find below an example of macro doing something 
somehow similar to what you want/

You can call Minuit commands (eg to follow your example)

   gMinuit->Command("FIX 2 3");
   gMinuit->Command("MINi");
   gMinuit->Command("IMProve");

// example of macro fitting background + signal
// -STEP 1: Generates theoretical function
// -STEP 2: Generates an histogram by sampling the function
// -STEP 3: estimates background parameters
// -STEP 4: estimates signal parameters
// -STEP 5: Combined fit of background + signal
//
   Double_t kTH = -0.5;

Double_t Background(Double_t *x, Double_t *par)
// The background function
{
   Double_t arg = 0;
   if (par[2]) arg = (x[0] - par[1])/par[2];

   Double_t val = par[0]*TMath::Exp(kTH*arg*arg)*x[0]*x[0];
   return val;
}

Double_t Signal(Double_t *x, Double_t *par)
// The signal function: a gaussian
{
   Double_t arg = 0;
   if (par[2]) arg = (x[0] - par[1])/par[2];

   Double_t sig = par[0]*TMath::Exp(-0.5*arg*arg);
   return sig;
}

Double_t Total(Double_t *x, Double_t *par)
// Combined background + signal
{
   Double_t tot = Background(x,par) + Signal(x,&par[3]);
   return tot;
}

void backsig()
{
   // the control function
   
   //STEP 1: Generates theoretical function
   Int_t npar = 6;
   Double_t params[6] = {100,3,1,350,6,0.5};
   TF1 *theory = new TF1("theory",Total,0,10,npar);
   theory->SetParameters(params);
   
   //STEP 2: Generates an histogram by sampling the theory function
   TH1F *Data = new TH1F("Data","Data sampled from theory",100,0,10);
   Data->FillRandom("theory",10000);
   
   //STEP 3: Estimates background parameters using a gaussian
   Data->Fit("gaus","q0");
   
   //STEP 4: Subtract estimated background to original data
   // Creates a temporary histogram and fit a gaussian
   TH1F *htemp = (TH1F*)Data->Clone();
   htemp->Reset();
   TF1 *eback = Data->GetFunction("gaus");
   for (Int_t bin=1;bin<=100;bin++) {
      Float_t x = Data->GetBinCenter(bin);
      Double_t fval = eback->Eval(x);
      Double_t diff = TMath::Abs(fval - Data->GetBinContent(bin));
      htemp->Fill(x,diff);
   }
   htemp->Fit("gaus","q0");
   TF1 *esig = htemp->GetFunction("gaus");
   
   //STEP 5: Fit background + signal
   eback->GetParameters(&params[0]);
   esig->GetParameters(&params[3]);
   Data->Fit("theory");
}

Rene Brun


On Wed, 10 Nov 1999, Philip M Borawski wrote:

> Please excuse my newbiness here, but I have some very basic questions on
> fitting signal plus background interactivley.  
> 
> First question, is there a way to set parameters to predefined functions
> (gaus for instance)?  
> 
> Next, is there a way to interactivley optimize the fit of this 'first
> guess'?
> 
> This is motivated by common fitting methods in PAW.  For
> instance to fit signal+background in PAW one would (for example) do
> somthing like:
> 
> ve/cr p(7) r 120 1.860 .015 1 1 1 1
> h/fit 222 g+p3 m 7 p
> 
> and then inside minuit
> 
> fix 2,3
> mini
> impre
> 
> Is there an anolog to this method in ROOT?
> 
> Any examples or comments would be greatly appreciated.
> 
> Thank you in advance
> 
> 
> Philip Borawski
> University of Texas at Dallas
> SLAC/BaBar Collaboration
> 
> 
> 
> 
>

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