FittingDemo.C File Reference

Detailed Description

Example for fitting signal/background.

This example can be executed with:

root > .x FittingDemo.C  (using the CINT interpreter)
root > .x FittingDemo.C+ (using the native complier via ACLIC)

Processing /mnt/build/workspace/root-makedoc-v608/rootspi/rdoc/src/v6-08-00-patches/tutorials/fit/FittingDemo.C...
 FCN=58.9284 FROM MIGRAD    STATUS=CONVERGED     618 CALLS         619 TOTAL
                     EDM=1.54329e-09    STRATEGY= 1  ERROR MATRIX UNCERTAINTY   1.2 per cent
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  p0          -8.64715e-01   8.87889e-01   3.02210e-05  -3.15277e-06
   2  p1           4.58434e+01   2.64076e+00   6.35729e-04   1.78463e-05
   3  p2          -1.33214e+01   9.77307e-01  -1.31737e-04   3.73302e-05
   4  p3           1.38074e+01   2.20785e+00  -1.29864e-03  -9.22424e-06
   5  p4           1.72308e-01   3.72077e-02  -5.22394e-06  -1.45631e-03
   6  p5           9.87281e-01   1.13098e-02   2.92804e-06  -3.44378e-04
 **********
 **   10 **SET NOGRAD
 **********
 PARAMETER DEFINITIONS:
    NO.   NAME         VALUE      STEP SIZE      LIMITS
     1 p0          -8.64715e-01  8.87889e-01     no limits
     2 p1           4.58434e+01  2.64076e+00     no limits
     3 p2          -1.33214e+01  9.77307e-01     no limits
     4 p3           1.38074e+01  2.20785e+00     no limits
     5 p4           2.00000e-01  3.72077e-02     no limits
     6 p5           1.00000e+00  1.13098e-02     no limits
 **********
 **   11 **SET ERR           1
 **********
 **********
 **   12 **SET PRINT           2
 **********
 **********
 **   13 **SET STR           1
 **********
 NOW USING STRATEGY  1: TRY TO BALANCE SPEED AGAINST RELIABILITY
 **********
 **   14 **MIGRAD        1780        0.01
 **********
 FIRST CALL TO USER FUNCTION AT NEW START POINT, WITH IFLAG=4.
 START MIGRAD MINIMIZATION.  STRATEGY  1.  CONVERGENCE WHEN EDM .LT. 1.00e-05
 FCN=60.858 FROM MIGRAD    STATUS=INITIATE       22 CALLS          23 TOTAL
                     EDM= unknown      STRATEGY= 1      NO ERROR MATRIX       
  EXT PARAMETER               CURRENT GUESS       STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  p0          -8.64715e-01   8.87889e-01   8.87889e-01   4.29214e-01
   2  p1           4.58434e+01   2.64076e+00   2.64076e+00   4.53155e-01
   3  p2          -1.33214e+01   9.77307e-01   9.77307e-01   8.11696e-01
   4  p3           1.38074e+01   2.20785e+00   2.20785e+00  -6.67494e-01
   5  p4           2.00000e-01   3.72077e-02   3.72077e-02   5.35278e+01
   6  p5           1.00000e+00   1.13098e-02   1.13098e-02   1.53279e+02
NO ERROR MATRIX       
 FCN=59.0986 FROM MIGRAD    STATUS=PROGRESS       39 CALLS          40 TOTAL
                     EDM=0.770568    STRATEGY= 1      NO ERROR MATRIX       
  EXT PARAMETER               CURRENT GUESS       STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  p0          -9.13550e-01   8.87889e-01  -4.88344e-02  -1.02740e-01
   2  p1           4.58158e+01   2.64076e+00  -2.75905e-02  -4.11668e-01
   3  p2          -1.33297e+01   9.77307e-01  -8.26649e-03  -1.43164e+00
   4  p3           1.43059e+01   2.20785e+00   4.98560e-01   3.34033e-01
   5  p4           1.76669e-01   3.72077e-02  -2.33314e-02  -5.66279e+00
   6  p5           9.90624e-01   1.13098e-02  -9.37641e-03   5.09250e+01
 MIGRAD MINIMIZATION HAS CONVERGED.
 MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
   START COVARIANCE MATRIX CALCULATION.
 EIGENVALUES OF SECOND-DERIVATIVE MATRIX:
         1.2685e-02  2.6097e-01  6.2144e-01  1.0079e+00  1.5369e+00  2.5601e+00
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY
 FCN=58.9284 FROM HESSE     STATUS=OK             40 CALLS         164 TOTAL
                     EDM=2.83537e-05    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  p0          -8.62472e-01   8.91793e-01   2.08429e-03   4.68256e-04
   2  p1           4.58294e+01   2.64212e+00   1.52471e-03  -1.63791e-03
   3  p2          -1.33163e+01   9.76930e-01   6.23584e-04   6.32364e-03
   4  p3           1.38135e+01   2.17742e+00   5.05443e-03  -2.23116e-04
   5  p4           1.72389e-01   3.58301e-02   9.43447e-05   1.89644e-02
   6  p5           9.87280e-01   1.12690e-02   4.24065e-05  -7.70600e-02
 PARAMETER  CORRELATION COEFFICIENTS  
       NO.  GLOBAL      1      2      3      4      5      6
        1  0.78593   1.000 -0.512  0.400 -0.082 -0.117  0.042
        2  0.98828  -0.512  1.000 -0.978 -0.526 -0.391 -0.061
        3  0.98564   0.400 -0.978  1.000  0.545  0.410  0.053
        4  0.78922  -0.082 -0.526  0.545  1.000  0.710  0.071
        5  0.71738  -0.117 -0.391  0.410  0.710  1.000  0.070
        6  0.09369   0.042 -0.061  0.053  0.071  0.070  1.000
 FCN=58.9284 FROM MIGRAD    STATUS=PROGRESS      176 CALLS         177 TOTAL
                     EDM=6.09404e-13    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  p0          -8.64713e-01   8.91793e-01  -2.24105e-03   1.85566e-07
   2  p1           4.58434e+01   2.64212e+00   1.39273e-02  -9.90056e-09
   3  p2          -1.33214e+01   9.76930e-01  -5.15131e-03   2.02571e-07
   4  p3           1.38074e+01   2.17742e+00  -6.03314e-03   7.41648e-07
   5  p4           1.72309e-01   3.58301e-02  -7.96940e-05  -2.58628e-05
   6  p5           9.87281e-01   1.12690e-02   1.37418e-06  -8.42700e-05
 MIGRAD MINIMIZATION HAS CONVERGED.
 FCN=58.9284 FROM MIGRAD    STATUS=CONVERGED     176 CALLS         177 TOTAL
                     EDM=6.09404e-13    STRATEGY= 1  ERROR MATRIX UNCERTAINTY   0.0 per cent
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  p0          -8.64713e-01   8.91794e-01  -2.24105e-03   1.85566e-07
   2  p1           4.58434e+01   2.64221e+00   1.39273e-02  -9.90056e-09
   3  p2          -1.33214e+01   9.76963e-01  -5.15131e-03   2.02571e-07
   4  p3           1.38074e+01   2.17751e+00  -6.03314e-03   7.41648e-07
   5  p4           1.72309e-01   3.58302e-02  -7.96940e-05  -2.58628e-05
   6  p5           9.87281e-01   1.12690e-02   1.37418e-06  -8.42700e-05
 EXTERNAL ERROR MATRIX.    NDIM=  25    NPAR=  6    ERR DEF=1
  7.953e-01 -1.205e+00  3.484e-01 -1.594e-01 -3.729e-03  4.227e-04 
 -1.205e+00  6.981e+00 -2.525e+00 -3.027e+00 -3.704e-02 -1.812e-03 
  3.484e-01 -2.525e+00  9.545e-01  1.159e+00  1.434e-02  5.871e-04 
 -1.594e-01 -3.027e+00  1.159e+00  4.742e+00  5.537e-02  1.737e-03 
 -3.729e-03 -3.704e-02  1.434e-02  5.537e-02  1.284e-03  2.833e-05 
  4.227e-04 -1.812e-03  5.871e-04  1.737e-03  2.833e-05  1.270e-04 
 PARAMETER  CORRELATION COEFFICIENTS  
       NO.  GLOBAL      1      2      3      4      5      6
        1  0.78593   1.000 -0.512  0.400 -0.082 -0.117  0.042
        2  0.98828  -0.512  1.000 -0.978 -0.526 -0.391 -0.061
        3  0.98564   0.400 -0.978  1.000  0.545  0.410  0.053
        4  0.78924  -0.082 -0.526  0.545  1.000  0.710  0.071
        5  0.71738  -0.117 -0.391  0.410  0.710  1.000  0.070
        6  0.09364   0.042 -0.061  0.053  0.071  0.070  1.000
 EXTERNAL ERROR MATRIX.    NDIM=   6    NPAR=  6    ERR DEF=1
  7.953e-01 -1.205e+00  3.484e-01 -1.594e-01 -3.729e-03  4.227e-04 
 -1.205e+00  6.981e+00 -2.525e+00 -3.027e+00 -3.704e-02 -1.812e-03 
  3.484e-01 -2.525e+00  9.545e-01  1.159e+00  1.434e-02  5.871e-04 
 -1.594e-01 -3.027e+00  1.159e+00  4.742e+00  5.537e-02  1.737e-03 
 -3.729e-03 -3.704e-02  1.434e-02  5.537e-02  1.284e-03  2.833e-05 
  4.227e-04 -1.812e-03  5.871e-04  1.737e-03  2.833e-05  1.270e-04 
 FCN=58.9284 FROM MIGRAD    STATUS=CONVERGED     176 CALLS         177 TOTAL
                     EDM=6.09404e-13    STRATEGY= 1  ERROR MATRIX UNCERTAINTY   0.0 per cent
  EXT PARAMETER                  PARABOLIC         MINOS ERRORS        
  NO.   NAME      VALUE            ERROR      NEGATIVE      POSITIVE   
   1  p0          -8.64713e-01   8.91794e-01                            
   2  p1           4.58434e+01   2.64221e+00                            
   3  p2          -1.33214e+01   9.76963e-01                            
   4  p3           1.38074e+01   2.17751e+00                            
   5  p4           1.72309e-01   3.58302e-02                            
   6  p5           9.87281e-01   1.12690e-02                            

#include "TH1.h"
#include "TMath.h"
#include "TF1.h"
#include "TLegend.h"
#include "TCanvas.h"

// Quadratic background function
Double_t background(Double_t *x, Double_t *par) {
   return par[0] + par[1]*x[0] + par[2]*x[0]*x[0];
}


// Lorenzian Peak function
Double_t lorentzianPeak(Double_t *x, Double_t *par) {
  return (0.5*par[0]*par[1]/TMath::Pi()) /
    TMath::Max( 1.e-10,(x[0]-par[2])*(x[0]-par[2])
   + .25*par[1]*par[1]);
}

// Sum of background and peak function
Double_t fitFunction(Double_t *x, Double_t *par) {
  return background(x,par) + lorentzianPeak(x,&par[3]);
}

void FittingDemo() {
 //Bevington Exercise by Peter Malzacher, modified by Rene Brun

   const int nBins = 60;

   Double_t data[nBins] = { 6, 1,10,12, 6,13,23,22,15,21,
                           23,26,36,25,27,35,40,44,66,81,
                           75,57,48,45,46,41,35,36,53,32,
                           40,37,38,31,36,44,42,37,32,32,
                           43,44,35,33,33,39,29,41,32,44,
                           26,39,29,35,32,21,21,15,25,15};
   TCanvas *c1 = new TCanvas("c1","Fitting Demo",10,10,700,500);
   c1->SetFillColor(33);
   c1->SetFrameFillColor(41);
   c1->SetGrid();

   TH1F *histo = new TH1F("histo",
      "Lorentzian Peak on Quadratic Background",60,0,3);
   histo->SetMarkerStyle(21);
   histo->SetMarkerSize(0.8);
   histo->SetStats(0);

   for(int i=0; i < nBins;  i++) histo->SetBinContent(i+1,data[i]);

   // create a TF1 with the range from 0 to 3 and 6 parameters
   TF1 *fitFcn = new TF1("fitFcn",fitFunction,0,3,6);
   fitFcn->SetNpx(500);
   fitFcn->SetLineWidth(4);
   fitFcn->SetLineColor(kMagenta);

   // first try without starting values for the parameters
   // This defaults to 1 for each param.
   // this results in an ok fit for the polynomial function
   // however the non-linear part (lorenzian) does not
   // respond well.
   fitFcn->SetParameters(1,1,1,1,1,1);
   histo->Fit("fitFcn","0");

   // second try: set start values for some parameters
   fitFcn->SetParameter(4,0.2); // width
   fitFcn->SetParameter(5,1);   // peak

   histo->Fit("fitFcn","V+","ep");

   // improve the picture:
   TF1 *backFcn = new TF1("backFcn",background,0,3,3);
   backFcn->SetLineColor(kRed);
   TF1 *signalFcn = new TF1("signalFcn",lorentzianPeak,0,3,3);
   signalFcn->SetLineColor(kBlue);
   signalFcn->SetNpx(500);
   Double_t par[6];

   // writes the fit results into the par array
   fitFcn->GetParameters(par);

   backFcn->SetParameters(par);
   backFcn->Draw("same");

   signalFcn->SetParameters(&par[3]);
   signalFcn->Draw("same");

   // draw the legend
   TLegend *legend=new TLegend(0.6,0.65,0.88,0.85);
   legend->SetTextFont(72);
   legend->SetTextSize(0.04);
   legend->AddEntry(histo,"Data","lpe");
   legend->AddEntry(backFcn,"Background fit","l");
   legend->AddEntry(signalFcn,"Signal fit","l");
   legend->AddEntry(fitFcn,"Global Fit","l");
   legend->Draw();

}

Author

Rene Brun

Definition in file FittingDemo.C.