PyROOT Exercise 2: Graphs and Fits

Exercise

Write a python macro ExerciseGraph.py.

1. Create a graph with symmetric errors and 5 points.
2. Set the following points: (1.0, 2.1), (2.0, 2.9), (3.0, 4.05), (4.0, 5.2), (5.0, 5.95)
3. Set the errors on x to 0.0 and the errors on y to 0.1 (all at once).
4. Draw the graph including the axes and error bars.
5. Create a one dimensional function f(x) = ax + b and fit it to the graph.

Bonus questions:

1. Programatically obtain the two parameters a and b and their estimated uncertainties.

Solution

import ROOT
%jsroot on

Welcome to JupyROOT 6.28/00

from ROOT import TCanvas, TF1, TGraphErrors

canvas = TCanvas("canvas", "", 800, 600)

graph = TGraphErrors(5)
graph.SetPoint(0, 1.0, 2.1)
graph.SetPoint(1, 2.0, 2.9)
graph.SetPoint(2, 3.0, 4.05)
graph.SetPoint(3, 4.0, 5.2)
graph.SetPoint(4, 5.0, 5.95)
for i in range(5):
  graph.SetPointError(i, 0, 0.1)

funct = TF1("funct", "[0] * x + [1]", 0, 6)
graph.Fit("funct")

graph.Draw()
funct.Draw("same")
canvas.Draw()

print(f"a = {funct.GetParameter(0):.6f} +/- {funct.GetParError(0):.6f}")
print(f"b = {funct.GetParameter(1):.6f} +/- {funct.GetParError(1):.6f}")

a = 1.000000 +/- 0.031623
b = 1.040000 +/- 0.104881
 FCN=5.7 FROM MIGRAD    STATUS=CONVERGED      33 CALLS          34 TOTAL
                     EDM=2.71359e-21    STRATEGY= 1      ERROR MATRIX ACCURATE 
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  p0           1.00000e+00   3.16228e-02   1.70422e-05  -2.08465e-09
   2  p1           1.04000e+00   1.04881e-01   5.65226e-05  -1.21781e-09

Last update: 06 March 2023