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, April 17, 2024 at 11:17 AM.
import ROOT
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)
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(Title="d(Gauss)/dx")
Plot gauss in frame (i.e. in x)
gauss.plotOn(xframe)
<cppyy.gbl.RooPlot object at 0x9911d60>
Plot derivatives in same frame
dgdx.plotOn(xframe, LineColor="m")
d2gdx2.plotOn(xframe, LineColor="r")
d3gdx3.plotOn(xframe, LineColor="kOrange")
<cppyy.gbl.RooPlot object at 0x9911d60>
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(Title="d(Gauss)/d(sigma)", Range=(0.0, 2.0))
Plot gauss in frame (i.e. in x)
gauss.plotOn(sframe)
<cppyy.gbl.RooPlot object at 0x9bb4ea0>
[#1] INFO:NumericIntegration -- RooRealIntegral::init(gauss_Int[sigma]) using numeric integrator RooIntegrator1D to calculate Int(sigma)
Plot derivatives in same frame
dgds.plotOn(sframe, LineColor="m")
d2gds2.plotOn(sframe, LineColor="r")
d3gds3.plotOn(sframe, LineColor="kOrange")
<cppyy.gbl.RooPlot object at 0x9bb4ea0>
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")
Info in <TCanvas::Print>: png file rf111_derivatives.png has been created
Draw all canvases
from ROOT import gROOT
gROOT.GetListOfCanvases().Draw()