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rf313_paramranges.py
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1 ## \file
2 ## \ingroup tutorial_roofit
3 ## \notebook
4 ## Multidimensional models: working with parameterized ranges to define non-rectangular
5 ## regions for fitting and integration
6 ##
7 ## \macro_code
8 ##
9 ## \date February 2018
10 ## \authors Clemens Lange, Wouter Verkerke (C++ version)
11 
12 import ROOT
13 
14 
15 # Create 3D pdf
16 # -------------------------
17 
18 # Define observable (x,y,z)
19 x = ROOT.RooRealVar("x", "x", 0, 10)
20 y = ROOT.RooRealVar("y", "y", 0, 10)
21 z = ROOT.RooRealVar("z", "z", 0, 10)
22 
23 # Define 3 dimensional pdf
24 z0 = ROOT.RooRealVar("z0", "z0", -0.1, 1)
25 px = ROOT.RooPolynomial(
26  "px", "px", x, ROOT.RooArgList(
27  ROOT.RooFit.RooConst(0)))
28 py = ROOT.RooPolynomial(
29  "py", "py", y, ROOT.RooArgList(
30  ROOT.RooFit.RooConst(0)))
31 pz = ROOT.RooPolynomial("pz", "pz", z, ROOT.RooArgList(z0))
32 pxyz = ROOT.RooProdPdf("pxyz", "pxyz", ROOT.RooArgList(px, py, pz))
33 
34 # Defined non-rectangular region R in (x, y, z)
35 # -------------------------------------------------------------------------------------
36 
37 #
38 # R = Z[0 - 0.1*Y^2] * Y[0.1*X - 0.9*X] * X[0 - 10]
39 #
40 
41 # Construct range parameterized in "R" in y [ 0.1*x, 0.9*x ]
42 ylo = ROOT.RooFormulaVar("ylo", "0.1*x", ROOT.RooArgList(x))
43 yhi = ROOT.RooFormulaVar("yhi", "0.9*x", ROOT.RooArgList(x))
44 y.setRange("R", ylo, yhi)
45 
46 # Construct parameterized ranged "R" in z [ 0, 0.1*y^2 ]
47 zlo = ROOT.RooFormulaVar("zlo", "0.0*y", ROOT.RooArgList(y))
48 zhi = ROOT.RooFormulaVar("zhi", "0.1*y*y", ROOT.RooArgList(y))
49 z.setRange("R", zlo, zhi)
50 
51 # Calculate integral of normalized pdf in R
52 # ----------------------------------------------------------------------------------
53 
54 # Create integral over normalized pdf model over x,y, in "R" region
55 intPdf = pxyz.createIntegral(ROOT.RooArgSet(
56  x, y, z), ROOT.RooArgSet(x, y, z), "R")
57 
58 # Plot value of integral as function of pdf parameter z0
59 frame = z0.frame(ROOT.RooFit.Title(
60  "Integral of pxyz over x,y, in region R"))
61 intPdf.plotOn(frame)
62 
63 c = ROOT.TCanvas("rf313_paramranges", "rf313_paramranges", 600, 600)
64 ROOT.gPad.SetLeftMargin(0.15)
65 frame.GetYaxis().SetTitleOffset(1.6)
66 frame.Draw()
67 
68 c.SaveAs("rf313_paramranges.png")