Basic functionality: interpreted functions and pdfs
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 Tuesday, March 19, 2024 at 07:14 PM.
import ROOT
Declare observable x
x = ROOT.RooRealVar("x", "x", -20, 20)
ROOT.To construct a proper pdf, the formula expression is explicitly normalized internally by dividing it by a numeric integral of the expression over x in the range [-20,20]
alpha = ROOT.RooRealVar("alpha", "alpha", 5, 0.1, 10)
genpdf = ROOT.RooGenericPdf("genpdf", "genpdf", "(1+0.1*abs(x)+sin(sqrt(abs(x*alpha+0.1))))", [x, alpha])
Generate a toy dataset from the interpreted pdf
data = genpdf.generate({x}, 10000)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(genpdf_Int[x]) using numeric integrator RooIntegrator1D to calculate Int(x) [#1] INFO:NumericIntegration -- RooRealIntegral::init(genpdf_Int[x]) using numeric integrator RooIntegrator1D to calculate Int(x)
Fit the interpreted pdf to the generated data
genpdf.fitTo(data, PrintLevel=-1)
<cppyy.gbl.RooFitResult object at 0x(nil)>
[#1] INFO:Fitting -- RooAbsPdf::fitTo(genpdf_over_genpdf_Int[x]) fixing normalization set for coefficient determination to observables in data [#1] INFO:Fitting -- using CPU computation library compiled with -mavx2 [#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_genpdf_over_genpdf_Int[x]_genpdfData) Summation contains a RooNLLVar, using its error level [#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: activating const optimization [#1] INFO:NumericIntegration -- RooRealIntegral::init(genpdf_Int[x]) using numeric integrator RooIntegrator1D to calculate Int(x) [#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: deactivating const optimization
Make a plot of the data and the pdf overlaid
xframe = x.frame(Title="Interpreted expression pdf")
data.plotOn(xframe)
genpdf.plotOn(xframe)
<cppyy.gbl.RooPlot object at 0xb054560>
[#1] INFO:NumericIntegration -- RooRealIntegral::init(genpdf_Int[x]) using numeric integrator RooIntegrator1D to calculate Int(x)
Construct parameter mean2 and sigma
mean2 = ROOT.RooRealVar("mean2", "mean^2", 10, 0, 200)
sigma = ROOT.RooRealVar("sigma", "sigma", 3, 0.1, 10)
Construct interpreted function mean = sqrt(mean^2)
mean = ROOT.RooFormulaVar("mean", "mean", "sqrt(mean2)", [mean2])
Construct a gaussian g2(x,sqrt(mean2),sigma)
g2 = ROOT.RooGaussian("g2", "h2", x, mean, sigma)
Construct a separate gaussian g1(x,10,3) to generate a toy Gaussian dataset with mean 10 and width 3
g1 = ROOT.RooGaussian("g1", "g1", x, 10, 3)
data2 = g1.generate({x}, 1000)
Fit g2 to data from g1
r = g2.fitTo(data2, Save=True, PrintLevel=-1) # ROOT.RooFitResult
r.Print()
[#1] INFO:Fitting -- RooAbsPdf::fitTo(g2_over_g2_Int[x]) fixing normalization set for coefficient determination to observables in data [#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_g2_over_g2_Int[x]_g1Data) Summation contains a RooNLLVar, using its error level [#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: activating const optimization [#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: deactivating const optimization RooFitResult: minimized FCN value: 2551.39, estimated distance to minimum: 4.39288e-06 covariance matrix quality: Full, accurate covariance matrix Status : MINIMIZE=0 HESSE=0 Floating Parameter FinalValue +/- Error -------------------- -------------------------- mean2 1.0010e+02 +/- 1.98e+00 sigma 3.1172e+00 +/- 7.12e-02
Plot data on frame and overlay projection of g2
xframe2 = x.frame(Title="Tailored Gaussian pdf")
data2.plotOn(xframe2)
g2.plotOn(xframe2)
<cppyy.gbl.RooPlot object at 0xb37fd80>
Draw all frames on a canvas
c = ROOT.TCanvas("rf103_interprfuncs", "rf103_interprfuncs", 800, 400)
c.Divide(2)
c.cd(1)
ROOT.gPad.SetLeftMargin(0.15)
xframe.GetYaxis().SetTitleOffset(1.4)
xframe.Draw()
c.cd(2)
ROOT.gPad.SetLeftMargin(0.15)
xframe2.GetYaxis().SetTitleOffset(1.4)
xframe2.Draw()
c.SaveAs("rf103_interprfuncs.png")
Info in <TCanvas::Print>: png file rf103_interprfuncs.png has been created
Draw all canvases
from ROOT import gROOT
gROOT.GetListOfCanvases().Draw()