Detailed Description

Fitting multiple functions to different ranges of a 1-D histogram Example showing how to fit in a sub-range of an histogram An histogram is created and filled with the bin contents and errors defined in the table below.

3 gaussians are fitted in sub-ranges of this histogram. A new function (a sum of 3 gaussians) is fitted on another subrange Note that when fitting simple functions, such as gaussians, the initial values of parameters are automatically computed by ROOT. In the more complicated case of the sum of 3 gaussians, the initial values of parameters must be given. In this particular case, the initial values are taken from the result of the individual fits.

 
 FCN=0.0848003 FROM MIGRAD    STATUS=CONVERGED     105 CALLS         106 TOTAL
                     EDM=1.77382e-07    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  Constant     4.96664e+00   2.83221e+00   4.26889e-04   1.67619e-04
   2  Mean         9.54663e+01   1.23905e+01   7.53972e-04  -2.63161e-04
   3  Sigma        6.82779e+00   7.49131e+00   5.87496e-05   3.68521e-03
 FCN=0.0771026 FROM MIGRAD    STATUS=CONVERGED      72 CALLS          73 TOTAL
                     EDM=2.00364e-07    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  Constant     5.96312e+00   1.14355e+00   4.82019e-04   1.52951e-04
   2  Mean         1.00467e+02   1.53372e+00   3.74926e-04   6.69980e-04
   3  Sigma        3.54806e+00   1.16899e+00   3.22077e-05   3.86167e-03
 FCN=0.0087702 FROM MIGRAD    STATUS=CONVERGED      93 CALLS          94 TOTAL
                     EDM=5.57239e-07    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  Constant     9.12665e-01   4.37176e-01   1.46528e-04   2.91010e-04
   2  Mean         1.16309e+02   8.37408e+00   3.57386e-03  -3.17966e-05
   3  Sigma        8.38413e+00   1.84577e+01   4.99414e-04  -4.98793e-04
 FCN=0.312817 FROM MIGRAD    STATUS=CONVERGED     515 CALLS         516 TOTAL
                     EDM=1.73245e-07    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  p0           4.91145e+00   1.41387e+00   3.61239e-04  -3.22790e-04
   2  p1           9.44525e+01   3.71612e+00   5.60861e-04  -6.78941e-05
   3  p2           5.94796e+00   2.41732e+00   4.25396e-04   2.68176e-05
   4  p3           3.22134e+00   3.11650e+00   5.86729e-04  -1.82620e-04
   5  p4           1.01663e+02   1.67863e+00   5.56527e-04   3.95769e-04
   6  p5           2.48454e+00   1.91461e+00   3.85832e-04   7.23818e-05
   7  p6           9.11463e-01   3.68235e-01   1.45489e-04   5.77239e-04
   8  p7           1.17582e+02   5.06329e+00   2.01798e-03  -8.25382e-05
   9  p8           7.58627e+00   8.76000e+00   2.12468e-03   2.02614e-05

 
#include "TH1.h"
#include "TF1.h"
 
void multifit() {
   const Int_t np = 49;
   Float_t x[np] = {1.913521, 1.953769, 2.347435, 2.883654, 3.493567,
                    4.047560, 4.337210, 4.364347, 4.563004, 5.054247,
                    5.194183, 5.380521, 5.303213, 5.384578, 5.563983,
                    5.728500, 5.685752, 5.080029, 4.251809, 3.372246,
                    2.207432, 1.227541, 0.8597788,0.8220503,0.8046592,
                    0.7684097,0.7469761,0.8019787,0.8362375,0.8744895,
                    0.9143721,0.9462768,0.9285364,0.8954604,0.8410891,
                    0.7853871,0.7100883,0.6938808,0.7363682,0.7032954,
                    0.6029015,0.5600163,0.7477068,1.188785, 1.938228,
                    2.602717, 3.472962, 4.465014, 5.177035};
 
   TH1F *h = new TH1F("h","Example of several fits in subranges",np,85,134);
   h->SetMaximum(7);
 
   for (int i=0;i<np;i++) {
      h->SetBinContent(i+1,x[i]);
   }
 
   Double_t par[9];
   TF1 *g1    = new TF1("g1","gaus",85,95);
   TF1 *g2    = new TF1("g2","gaus",98,108);
   TF1 *g3    = new TF1("g3","gaus",110,121);
   TF1 *total = new TF1("total","gaus(0)+gaus(3)+gaus(6)",85,125);
   total->SetLineColor(2);
   h->Fit(g1,"R");
   h->Fit(g2,"R+");
   h->Fit(g3,"R+");
   g1->GetParameters(&par[0]);
   g2->GetParameters(&par[3]);
   g3->GetParameters(&par[6]);
   total->SetParameters(par);
   h->Fit(total,"R+");
}
 

Author: Rene Brun

Definition in file multifit.C.