Re: integral using TF1

Hi Shamin,

Some possible pointers :

1. Your histogram is too coarsely binned comapred to the structure you want to fit .
2. Calculate the integral of the expression as a function of par[0] and par[1] You know the errors in the pars (and could also get their correlation) . Now it is a straightforward error-propagation exercise to ge the error in the integral . Maybe the answer is well inside the error .
3. You are fitting the histogram points NOT the function integral; if point 1) is ok, one would expect also a correct (see 2)) integral . However, you could re-parametrize your function expression such that it guarantees that the function integral equals the histogram sum .

Eddy

• "Shamim, Mansoora" <shamimm_at_phys.ksu.edu> wrote:
  >
  >
  > Hi,
  > I am trying to fit a simple exponential function to my histogram.
  > Please see the macro.
  > Fit range is between 40, 55.
  > Total entries in my histogram are 1743. After fitting the function
  > when I calculate the integral of teh function between 40 and 55 using
  > TF1 it turns out to be 1821.71.
  > Does anyone have any idea what I am doing wrong.
  > Thanks for help
  > Mansoora
  >
  >
  > Double_t fitf(Double_t *x, Double_t *par)
  > {
  >
  > Double_t fitval = TMath::Exp(par[0]+x[0]*par[1]);
  >
  > return fitval;
  > }
  > void myfit()
  > {
  > TFile *f = new TFile("sumdata_all.root");
  >
  > TCanvas *c1 = new TCanvas("c1","the fit canvas",500,400);
  >
  > TH1F *hpx = (TH1F*)f->Get("allbmet");
  >
  > // Creates a Root function based on function fitf above
  > TF1 *func = new TF1("fitf",fitf,40,55,2);
  >
  > // Sets initial values and parameter names
  > // func->SetParameters(0,0);
  >
  >
  > func->SetParNames("Constant","slope");
  >
  > // Fit histogram in range defined by function
  > hpx->Fit(func,"r");
  >
  >
  > // Gets integral of function between fit limits
  > printf("Integral of function = %g\n",func->Integral(40,55));
  > printf("Integral of function = %g\n",hpx->Integral(40,55));
  > }
  >
  >
  > The output is the following
  >
  > FCN=4.40737 FROM MIGRAD STATUS=CONVERGED 490 CALLS 491
  > TOTAL
  > EDM=9.42813e-12 STRATEGY= 1 ERROR MATRIX
  > ACCURATE
  > EXT PARAMETER STEP FIRST
  > NO. NAME VALUE ERROR SIZE
  > DERIVATIVE
  > 1 Constant 9.38380e+00 4.56946e-01 4.39444e-05
  > 5.63492e-05
  > 2 slope -9.83892e-02 1.01634e-02 9.77412e-07
  > 2.15489e-03
  > Integral of function = 1821.71
  > Integral of histogram = 64
  >
  >