rf111_derivatives.py

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## \file
## \ingroup tutorial_roofit
## \notebook
## Basic functionality: numerical 1st, and 3rd order derivatives w.r.t. observables and parameters
##
## ```
## pdf = gauss(x,m,s)
## ```
##
## \macro_code
##
## \date February 2018
## \authors Clemens Lange, Wouter Verkerke (C++ version)
 
import ROOT
 
# Set up model
# ---------------------
 
# Declare variables x,mean, with associated name, title, value and allowed
# range
x = ROOT.RooRealVar("x", "x", -10, 10)
mean = ROOT.RooRealVar("mean", "mean of gaussian", 1, -10, 10)
sigma = ROOT.RooRealVar("sigma", "width of gaussian", 1, 0.1, 10)
 
# Build gaussian pdf in terms of x, and sigma
gauss = ROOT.RooGaussian("gauss", "gaussian PDF", x, mean, sigma)
 
# Create and plot derivatives w.r.t. x
# ----------------------------------------------------------------------
 
# Derivative of normalized gauss(x) w.r.t. observable x
dgdx = gauss.derivative(x, 1)
 
# Second and third derivative of normalized gauss(x) w.r.t. observable x
d2gdx2 = gauss.derivative(x, 2)
d3gdx3 = gauss.derivative(x, 3)
 
# Construct plot frame in 'x'
xframe = x.frame(ROOT.RooFit.Title("d(Gauss)/dx"))
 
# Plot gauss in frame (i.e. in x)
gauss.plotOn(xframe)
 
# Plot derivatives in same frame
dgdx.plotOn(xframe, ROOT.RooFit.LineColor(ROOT.kMagenta))
d2gdx2.plotOn(xframe, ROOT.RooFit.LineColor(ROOT.kRed))
d3gdx3.plotOn(xframe, ROOT.RooFit.LineColor(ROOT.kOrange))
 
# Create and plot derivatives w.r.t. sigma
# ------------------------------------------------------------------------------
 
# Derivative of normalized gauss(x) w.r.t. parameter sigma
dgds = gauss.derivative(sigma, 1)
 
# Second and third derivative of normalized gauss(x) w.r.t. parameter sigma
d2gds2 = gauss.derivative(sigma, 2)
d3gds3 = gauss.derivative(sigma, 3)
 
# Construct plot frame in 'sigma'
sframe = sigma.frame(ROOT.RooFit.Title(
    "d(Gauss)/d(sigma)"), ROOT.RooFit.Range(0., 2.))
 
# Plot gauss in frame (i.e. in x)
gauss.plotOn(sframe)
 
# Plot derivatives in same frame
dgds.plotOn(sframe, ROOT.RooFit.LineColor(ROOT.kMagenta))
d2gds2.plotOn(sframe, ROOT.RooFit.LineColor(ROOT.kRed))
d3gds3.plotOn(sframe, ROOT.RooFit.LineColor(ROOT.kOrange))
 
# Draw all frames on a canvas
c = ROOT.TCanvas("rf111_derivatives", "rf111_derivatives", 800, 400)
c.Divide(2)
c.cd(1)
ROOT.gPad.SetLeftMargin(0.15)
xframe.GetYaxis().SetTitleOffset(1.6)
xframe.Draw()
c.cd(2)
ROOT.gPad.SetLeftMargin(0.15)
sframe.GetYaxis().SetTitleOffset(1.6)
sframe.Draw()
 
c.SaveAs("rf111_derivatives.png")