Rf 1 1 1_Derivatives¶

Basic functionality: numerical 1st, and 3rd order derivatives w.r.t. observables and parameters

pdf = gauss(x,m,s)

Author: Clemens Lange, Wouter Verkerke (C++ version)
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Wednesday, January 19, 2022 at 10:12 AM.

In [ ]:
import ROOT

Set up model¶

Declare variables x,mean, with associated name, title, value and allowed range

In [ ]:
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

In [ ]:
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

In [ ]:
dgdx = gauss.derivative(x, 1)

Second and third derivative of normalized gauss(x) w.r.t. observable x

In [ ]:
d2gdx2 = gauss.derivative(x, 2)
d3gdx3 = gauss.derivative(x, 3)

Construct plot frame in 'x'

In [ ]:
xframe = x.frame(Title="d(Gauss)/dx")

Plot gauss in frame (i.e. in x)

In [ ]:
gauss.plotOn(xframe)

Plot derivatives in same frame

In [ ]:
dgdx.plotOn(xframe, LineColor="m")
d2gdx2.plotOn(xframe, LineColor="r")
d3gdx3.plotOn(xframe, LineColor="kOrange")

Create and plot derivatives w.r.t. sigma¶

Derivative of normalized gauss(x) w.r.t. parameter sigma

In [ ]:
dgds = gauss.derivative(sigma, 1)

Second and third derivative of normalized gauss(x) w.r.t. parameter sigma

In [ ]:
d2gds2 = gauss.derivative(sigma, 2)
d3gds3 = gauss.derivative(sigma, 3)

Construct plot frame in 'sigma'

In [ ]:
sframe = sigma.frame(Title="d(Gauss)/d(sigma)", Range=(0.0, 2.0))

Plot gauss in frame (i.e. in x)

In [ ]:
gauss.plotOn(sframe)

Plot derivatives in same frame

In [ ]:
dgds.plotOn(sframe, LineColor="m")
d2gds2.plotOn(sframe, LineColor="r")
d3gds3.plotOn(sframe, LineColor="kOrange")

Draw all frames on a canvas

In [ ]:
c = ROOT.TCanvas("rf111_derivatives", "rf111_derivatives", 800, 400)
c.Divide(2)
c.cd(1)
xframe.GetYaxis().SetTitleOffset(1.6)
xframe.Draw()
c.cd(2)