Fitting Basics in CERN ROOT (PyROOT): Gaussian Fit

1️⃣ Importing ROOT

import ROOT

2️⃣ Creating and Filling the Histogram

ROOT.gRandom.SetSeed(12345)  # reproducible example
h = ROOT.TH1F("h", "Gaussian Example; X; Counts", 60, -4.0, 4.0)

for _ in range(12000):
    h.Fill(ROOT.gRandom.Gaus(0.0, 1.0))

• ROOT.gRandom.SetSeed(12345): sets the random-number seed so you always get the same random data. Useful for tutorials.
• TH1F: creates a 1D histogram with:
  • "h" — internal name of the histogram
  • "Gaussian Example; X; Counts" — title and axis labels (before semicolon = title, after = X and Y labels)
  • 60 — number of bins
  • -4.0, 4.0 — x-axis range
• for _ in range(12000): ...: fills the histogram 12,000 times with random Gaussian values.
• ROOT.gRandom.Gaus(0.0, 1.0): generates a random number from a Gaussian distribution with mean = 0 and sigma = 1.

3️⃣ Getting Basic Statistics from the Histogram

print("Histogram mean (approx):", round(h.GetMean(), 3))
print("Histogram RMS (approx):", round(h.GetRMS(), 3))

• h.GetMean(): calculates the mean value based on the filled histogram.
• h.GetRMS(): gives the RMS (root mean square), which is related to the width of the distribution.
• round(..., 3): rounds the numbers to 3 decimal places to make the output cleaner.

4️⃣ Creating the Canvas and Drawing the Histogram

c = ROOT.gROOT.FindObject("c")
if not c:
    c = ROOT.TCanvas("c", "Gaussian Fit Demo", 900, 650)

h.SetLineColor(ROOT.kBlue + 1)
h.SetLineWidth(2)
h.SetFillColor(ROOT.kAzure - 9)
h.SetFillStyle(3004)
h.Draw()

• gROOT.FindObject("c"): if a canvas named "c" already exists (e.g., from a previous run), reuse it.
• Otherwise, TCanvas("c", "Gaussian Fit Demo", 900, 650) creates a new window of size 900×650 pixels.
• SetLineColor, SetFillColor, SetFillStyle: change how the histogram looks (line color, fill color, pattern).
• h.Draw(): actually draws the histogram on the current canvas.

5️⃣ Fitting a Gaussian to the Histogram

fit_result = h.Fit("gaus", "S Q")  # "S"=store result, "Q"=quiet (no spam)

f = h.GetFunction("gaus")
amp   = f.GetParameter(0); amp_err   = f.GetParError(0)
mean  = f.GetParameter(1); mean_err  = f.GetParError(1)
sigma = f.GetParameter(2); sigma_err = f.GetParError(2)

• h.Fit("gaus", "S Q"):
  • "gaus" — tells ROOT to use its built-in Gaussian function.
  • "S" — store the fit result in a TFitResultPtr object (fit_result).
  • "Q" — quiet mode (do not print a long fit report to the terminal).
• h.GetFunction("gaus"): gets the fitted function object (a TF1).
• GetParameter(i): returns parameter i:
  • 0 → amplitude (height of the peak)
  • 1 → mean (μ), position of the peak
  • 2 → sigma (σ), width of the peak
• GetParError(i): gives the uncertainty (error) on parameter i.

6️⃣ Checking Fit Quality: Chi2/NDF

print(f"Chi2/NDF   = {fit_result.Chi2():.1f} / {fit_result.Ndf()}")

• fit_result.Chi2(): the χ² value of the fit.
• fit_result.Ndf(): number of degrees of freedom.
• Chi2/NDF near ~1 often indicates a reasonable fit (but always check the plot visually).

7️⃣ Saving the Plot as an Image

c.SaveAs("gaussian_fit.png")
print("Saved: gaussian_fit.png")

• SaveAs("gaussian_fit.png"): saves whatever is currently drawn on the canvas to a PNG file.
• You can also use other formats: .pdf, .root, .jpg, etc.

8️⃣ Saving the Histogram and Fit to a ROOT File

out = ROOT.TFile("gaussian_fit_output.root", "RECREATE")
h.Write()
f.Write("gaus_fit")
out.Close()

• TFile("gaussian_fit_output.root", "RECREATE"): opens a ROOT file in “recreate” mode (overwrite if it exists).
• h.Write(): stores the histogram inside the ROOT file.
• f.Write("gaus_fit"): stores the fitted function with the name "gaus_fit".
• out.Close(): closes the file and writes everything to disk.