Fitter problem with pol1 when the slope is negative and x-error bars> y-error bars bug? in PyROOT

Newbie
1

got this for several data sets, was able to reproduce with this sample data:

import ROOT
import numpy
y=numpy.array([5,3,1.0])
xerr=numpy.array([1,1,1.0])
x=numpy.array([1,2,3.0])
yerr=numpy.array([0.1,0.2,0.7])
a=ROOT.TGraphErrors(len(x),x,y,xerr,yerr)
a.Fit("pol1")`

OUTPUT:

 FCN=2.00003 FROM MIGRAD    STATUS=CONVERGED     245 CALLS         246 TOTAL
                     EDM=1.28797e-009    STRATEGY= 1  ERROR MATRIX UNCERTAINTY  25.5 per cent
  EXT PARAMETER                                   STEP         FIRST
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE
   1  p0         -5.00789e+005  1.66517e+007 -4.29583e+005 -1.79607e-009
   2  p1          2.50387e+005  8.32551e+006  2.14780e+005 -3.71990e-009
<ROOT.TFitResultPtr object at 0x0D22F2B8>

as you can see, the fit parameters are BS… giving initial guesses does nothing.

ROOT Version: 5.34.38, 5.34.30, 5.34.22, 5.30.06, all 32bit versions, with python 2.7.18+numpy
Platform: windows

3

@assosiation ,

Happy to see that you are enjoying yourself with ROOT.

Below a script based on this.

{
   auto c1 = new TCanvas("c1","A Simple Graph with error bars",200,10,700,500);
   c1->SetFillColor(42);
   c1->SetGrid();
   c1->GetFrame()->SetFillColor(21);
   c1->GetFrame()->SetBorderSize(12);
   const Int_t n = 3;
   Double_t x[n]  = {-0.22, 0.05, 0.25};
   //Double_t y[n]  = {1,2.9,5.6};
   Double_t y[n]  = {-1,-2.9,-5.6};
   Double_t ex[n] = {.05,.1,.07};
   Double_t ey[n] = {.8,.7,.6};
   auto gr = new TGraphErrors(n,x,y,ex,ey);
   gr->SetTitle("TGraphErrors Example");
   gr->SetMarkerColor(4);
   gr->SetMarkerStyle(21);
   gr->Fit("pol1");
   gr->Draw("AP");
}

By flipping the sign on y, you can have your positive and negative slope. Either way, smooth sailing :wink:

But making the x-errors larger than the y-errors gives an error matrix that is not positive
definite. Realize that although a pol1, the moment x-errors are supplied the fit becomes
non-linear (and start depending on starting values).

Let’s see if in case of number of degrees of freedom = 1 (3 data points, two fit paramters)
something can ne done.

1 Like
4

Thank you for the clarification about the error matrix, didn’t think about that! For the NSF of 1, I only created the example code like that, noticed the problem on a reasonable data set, tried to reproduce with mage up numbers. Well, will think of the ways to solve this by making slope positive or flipping the access.
Been using root for a while now but every time I find something like this feel myself a newbie again, bwahaha

5

As I wrote earlier, the moment you introduce errors in x, a fit becomes always
non-linear and starting values matter. The error in a data point is calculated
as ey_new^2 = ey^2 + (dy/dx * ex)^2 and dy/dx will depend on the values of
the function parameter.

I can not find anymore after the generalization of the fitting code where this
happens, @moneta will know.

Anyhow, your problem will be solved by doing first a fit without errors in x, and using
this fit result as input into the final fit with errors in x:

   gr->Fit("pol1","EX0");
   gr->Fit("pol1");
1 Like