TF1::IntegralError fails

ROOT
1

Hi,

I have problems to get a reasonable IntegralError for some fits and fit functions. Sometimes the function seems to return reasonable numbers, sometimes it returns crap. Here is a code example

void testinterr(bool add=false)
{
  gRandom->SetSeed(1);
  
  TH1F *h1 = new TH1F("h1","",100,0.98,1.1);
  TF1 *f1 = new TF1("f1","[0]*(x>[1])*(x<[3])*(abs(x-[1]))^[2]*(abs(x-[3]))^[4]",0.98,1.1);

  f1->SetParameters(10,0.988,0.5,4,2);
  h1->FillRandom("f1",10000);
  
  if (add) {
    // with these lines in I get Err = 0
    f1->SetParameters(10,0.988,0.8,4,2);
    h1->FillRandom("f1",3000);
  }
  
  h1->Fit("f1","");
  TFitResultPtr pfit = h1->Fit("f1","ms");
  
  double n  = f1->Integral(1,1.04);
  double dn = f1->IntegralError(1,1.04,pfit->GetParams(), pfit->GetCovarianceMatrix().GetMatrixArray());
  
  cout <<n<<" +- "<<dn<<endl;
}

which gives in my case

root [0] .x testinterr.C(0)
Info in <TCanvas::MakeDefCanvas>:  created default TCanvas with name c1
 FCN=64.9812 FROM HESSE     STATUS=NOT POSDEF     33 CALLS         336 TOTAL
                     EDM=4.81713e-08    STRATEGY= 1      ERR MATRIX NOT POS-DEF
  EXT PARAMETER                APPROXIMATE        STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  p0           2.50059e+00   3.25677e-01   9.95067e-05  -2.09580e-03
   2  p1           9.87771e-01   3.57446e-05   4.71006e-07   4.91257e+00
   3  p2           4.78138e-01   1.44689e-02   1.35182e-05   1.60692e-02
   4  p3           3.63503e+02   5.37157e+01   1.63897e-02  -8.33421e-06
   5  p4           8.80006e-01   2.22002e-02   6.75196e-06  -3.26871e-02
3.39934 +- 0.0443608

and

root [1] .x testinterr.C(1)
Warning in <TROOT::Append>: Replacing existing TH1: h1 (Potential memory leak).
Warning in <Fit>: Abnormal termination of minimization.
 FCN=80.6087 FROM MIGRAD    STATUS=CALL LIMIT   1631 CALLS        1632 TOTAL
                     EDM=0.000483126    STRATEGY= 1  ERROR MATRIX UNCERTAINTY  39.0 per cent
  EXT PARAMETER                APPROXIMATE        STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  p0           7.19014e+00   2.31244e+00   4.12053e-02  -4.37627e-01
   2  p1           9.87753e-01   5.17554e-05   4.37660e-07   1.18930e+02
   3  p2           5.47573e-01   1.46104e-02   5.23733e-05   9.36261e+00
   4  p3           1.35637e+01   5.08601e+00   8.97266e-02  -4.60816e-01
   5  p4           1.81669e+00   4.26753e-01  -7.46502e-03  -7.92311e+00
4.26503 +- 0

The first error looks fine I guess, but in the second case, err = 0 is obviously wrong. The fit output prints “Warning in <Fit>: Abnormal termination of minimization.” in the second case, perhaps this is connected to the problem.

Does somebody know what’s going wrong, and how to fix it? I would like to use this rather complicated function to describe a phase space border background shape (of a phi(1020)) and have no good idea how to alternatively estimate the error of the integral. Other functions (except polynomials as it seems) show a similar behavior anyways, so replacing the function didn’t help until now. Polys unfortunately don’t fit sufficiently well.

Best and thanks,
Klaus

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ROOT Version: 6.24-04
Platform: Not Provided
Compiler: Not Provided

2

I think @moneta can help you.

3

One of the problems is that, before fitting, you need to:

  // set reasonable initial parameters values
  f1->SetParameter(0, f1->GetParameter(0) / f1->Integral(h1->GetXaxis()->GetXmin(), h1->GetXaxis()->GetXmax()) * h1->Integral() * h1->GetBinWidth(1));
4

Why that?

5
6

Unfortunately this doesn’t help, I still get 0 as error.

7

When your fit fails, do not expect anything useful.

If you are interested in the integral between 1.0 and 1.04, then use, e.g.:

h1->Fit("pol4", "L", "", 0.995, 1.095)
TF1 *f1 = h1->GetFunction("pol4");
8

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