Rf 3 0 9_Ndimplot

Multidimensional models: making 2/3 dimensional plots of pdfs and datasets

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 Monday, January 17, 2022 at 09:59 AM.

In [ ]:
import ROOT

Create 2D model and dataset

Create observables

In [ ]:
x = ROOT.RooRealVar("x", "x", -5, 5)
y = ROOT.RooRealVar("y", "y", -5, 5)

Create parameters

In [ ]:
a0 = ROOT.RooRealVar("a0", "a0", -3.5, -5, 5)
a1 = ROOT.RooRealVar("a1", "a1", -1.5, -1, 1)
sigma = ROOT.RooRealVar("sigma", "width of gaussian", 1.5)

Create interpreted function f(y) = a0 - a1sqrt(10abs(y))

In [ ]:
fy = ROOT.RooFormulaVar("fy", "a0-a1*sqrt(10*abs(y))", [y, a0, a1])

Create gauss(x,f(y),s)

In [ ]:
model = ROOT.RooGaussian("model", "Gaussian with shifting mean", x, fy, sigma)

Sample dataset from gauss(x,y)

In [ ]:
data = model.generate({x, y}, 10000)

Make 2D plots of data and model

Create and fill ROOT 2D histogram (20x20 bins) with contents of dataset hh_data = data.createHistogram("hh_data",x, ROOT.RooFit.Binning(20), ROOT.RooFit.YVar(y, ROOT.RooFit.Binning(20))) hh_data = data.createHistogram("x,y", 20, 20) # does not work, see https://root.cern.ch/phpBB3/viewtopic.php?t=16648

In [ ]:
hh_data = ROOT.RooAbsData.createHistogram(data, "x,y", x, Binning=20, YVar=dict(var=y, Binning=20))

Create and fill ROOT 2D histogram (50x50 bins) with sampling of pdf hh_pdf = model.createHistogram("hh_model",x, ROOT.RooFit.Binning(50), ROOT.RooFit.YVar(y, ROOT.RooFit.Binning(50)))

In [ ]:
hh_pdf = model.createHistogram("x,y", 50, 50)
hh_pdf.SetLineColor(ROOT.kBlue)

Create 3D model and dataset

Create observables

In [ ]:
z = ROOT.RooRealVar("z", "z", -5, 5)

gz = ROOT.RooGaussian("gz", "gz", z, ROOT.RooFit.RooConst(0), ROOT.RooFit.RooConst(2))
model3 = ROOT.RooProdPdf("model3", "model3", [model, gz])

data3 = model3.generate({x, y, z}, 10000)

Make 3D plots of data and model

Create and fill ROOT 2D histogram (8x8x8 bins) with contents of dataset hh_data3 = data3.createHistogram("hh_data3", x, ROOT.RooFit.Binning(8), ROOT.RooFit.YVar(y, ROOT.RooFit.Binning(8)), ROOT.RooFit.ZVar(z, ROOT.RooFit.Binning(8)))

In [ ]:
hh_data3 = ROOT.RooAbsData.createHistogram(
    data3,
    "hh_data3",
    x,
    Binning=8,
    YVar=dict(var=y, Binning=8),
    ZVar=dict(var=z, Binning=8),
)

Create and fill ROOT 2D histogram (20x20x20 bins) with sampling of pdf

In [ ]:
hh_pdf3 = model3.createHistogram(
    "hh_model3",
    x,
    Binning=20,
    YVar=dict(var=y, Binning=20),
    ZVar=dict(var=z, Binning=20),
)
hh_pdf3.SetFillColor(ROOT.kBlue)

c1 = ROOT.TCanvas("rf309_2dimplot", "rf309_2dimplot", 800, 800)
c1.Divide(2, 2)
c1.cd(1)
ROOT.gPad.SetLeftMargin(0.15)
hh_data.GetZaxis().SetTitleOffset(1.4)
hh_data.Draw("lego")
c1.cd(2)
ROOT.gPad.SetLeftMargin(0.20)
hh_pdf.GetZaxis().SetTitleOffset(2.5)
hh_pdf.Draw("surf")
c1.cd(3)
ROOT.gPad.SetLeftMargin(0.15)
hh_data.GetZaxis().SetTitleOffset(1.4)
hh_data.Draw("box")
c1.cd(4)
ROOT.gPad.SetLeftMargin(0.15)
hh_pdf.GetZaxis().SetTitleOffset(2.5)
hh_pdf.Draw("cont3")
c1.SaveAs("rf309_2dimplot.png")

c2 = ROOT.TCanvas("rf309_3dimplot", "rf309_3dimplot", 800, 400)
c2.Divide(2)
c2.cd(1)
ROOT.gPad.SetLeftMargin(0.15)
hh_data3.GetZaxis().SetTitleOffset(1.4)
hh_data3.Draw("lego")
c2.cd(2)
ROOT.gPad.SetLeftMargin(0.15)
hh_pdf3.GetZaxis().SetTitleOffset(1.4)
hh_pdf3.Draw("iso")
c2.SaveAs("rf309_3dimplot.png")

Draw all canvases

In [ ]:
from ROOT import gROOT 
gROOT.GetListOfCanvases().Draw()