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rf604_constraints.py
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1 ## \file
2 ## \ingroup tutorial_roofit
3 ## \notebook -nodraw
4 ##
5 ## Likelihood and minimization: fitting with constraints
6 ##
7 ## \macro_code
8 ##
9 ## \date February 2018
10 ## \authors Clemens Lange, Wouter Verkerke (C++ version)
11 
12 from __future__ import print_function
13 import ROOT
14 
15 
16 # Create model and dataset
17 # ----------------------------------------------
18 
19 # Construct a Gaussian p.d.f
20 x = ROOT.RooRealVar("x", "x", -10, 10)
21 
22 m = ROOT.RooRealVar("m", "m", 0, -10, 10)
23 s = ROOT.RooRealVar("s", "s", 2, 0.1, 10)
24 gauss = ROOT.RooGaussian("gauss", "gauss(x,m,s)", x, m, s)
25 
26 # Construct a flat p.d.f (polynomial of 0th order)
27 poly = ROOT.RooPolynomial("poly", "poly(x)", x)
28 
29 # model = f*gauss + (1-f)*poly
30 f = ROOT.RooRealVar("f", "f", 0.5, 0., 1.)
31 model = ROOT.RooAddPdf(
32  "model",
33  "model",
34  ROOT.RooArgList(
35  gauss,
36  poly),
37  ROOT.RooArgList(f))
38 
39 # Generate small dataset for use in fitting below
40 d = model.generate(ROOT.RooArgSet(x), 50)
41 
42 # Create constraint pdf
43 # -----------------------------------------
44 
45 # Construct Gaussian constraint p.d.f on parameter f at 0.8 with
46 # resolution of 0.1
47 fconstraint = ROOT.RooGaussian(
48  "fconstraint",
49  "fconstraint",
50  f,
51  ROOT.RooFit.RooConst(0.8),
52  ROOT.RooFit.RooConst(0.1))
53 
54 # Method 1 - add internal constraint to model
55 # -------------------------------------------------------------------------------------
56 
57 # Multiply constraint term with regular p.d.f using ROOT.RooProdPdf
58 # Specify in fitTo() that internal constraints on parameter f should be
59 # used
60 
61 # Multiply constraint with p.d.f
62 modelc = ROOT.RooProdPdf(
63  "modelc", "model with constraint", ROOT.RooArgList(model, fconstraint))
64 
65 # Fit model (without use of constraint term)
66 r1 = model.fitTo(d, ROOT.RooFit.Save())
67 
68 # Fit modelc with constraint term on parameter f
69 r2 = modelc.fitTo(
70  d,
71  ROOT.RooFit.Constrain(
72  ROOT.RooArgSet(f)),
73  ROOT.RooFit.Save())
74 
75 # Method 2 - specify external constraint when fitting
76 # ------------------------------------------------------------------------------------------
77 
78 # Construct another Gaussian constraint p.d.f on parameter f at 0.8 with
79 # resolution of 0.1
80 fconstext = ROOT.RooGaussian("fconstext", "fconstext", f, ROOT.RooFit.RooConst(
81  0.2), ROOT.RooFit.RooConst(0.1))
82 
83 # Fit with external constraint
84 r3 = model.fitTo(d, ROOT.RooFit.ExternalConstraints(
85  ROOT.RooArgSet(fconstext)), ROOT.RooFit.Save())
86 
87 # Print the fit results
88 print("fit result without constraint (data generated at f=0.5)")
89 r1.Print("v")
90 print("fit result with internal constraint (data generated at f=0.5, is f=0.8+/-0.2)")
91 r2.Print("v")
92 print("fit result with (another) external constraint (data generated at f=0.5, is f=0.2+/-0.1)")
93 r3.Print("v")