Likelihood and minimization: fitting with constraints
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 07:16 PM.
from __future__ import print_function
import ROOT
Construct a Gaussian pdf
x = ROOT.RooRealVar("x", "x", -10, 10)
m = ROOT.RooRealVar("m", "m", 0, -10, 10)
s = ROOT.RooRealVar("s", "s", 2, 0.1, 10)
gauss = ROOT.RooGaussian("gauss", "gauss(x,m,s)", x, m, s)
Construct a flat pdf (polynomial of 0th order)
poly = ROOT.RooPolynomial("poly", "poly(x)", x)
model = fgauss + (1-f)poly
f = ROOT.RooRealVar("f", "f", 0.5, 0.0, 1.0)
model = ROOT.RooAddPdf("model", "model", [gauss, poly], [f])
Generate small dataset for use in fitting below
d = model.generate({x}, 50)
Construct Gaussian constraint pdf on parameter f at 0.8 with resolution of 0.1
fconstraint = ROOT.RooGaussian("fconstraint", "fconstraint", f, 0.8, 0.1)
Multiply constraint term with regular pdf using ROOT.RooProdPdf Specify in fitTo() that internal constraints on parameter f should be used
Multiply constraint with pdf
modelc = ROOT.RooProdPdf("modelc", "model with constraint", [model, fconstraint])
Fit model (without use of constraint term)
r1 = model.fitTo(d, Save=True, PrintLevel=-1)
[#1] INFO:Fitting -- RooAbsPdf::fitTo(model) 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_model_modelData) Summation contains a RooNLLVar, using its error level [#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: activating const optimization [#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: deactivating const optimization
Fit modelc with constraint term on parameter f
r2 = modelc.fitTo(d, Constrain={f}, Save=True, PrintLevel=-1)
[#1] INFO:Minimization -- Including the following constraint terms in minimization: (fconstraint) [#1] INFO:Minimization -- The global observables are not defined , normalize constraints with respect to the parameters (f) [#1] INFO:Fitting -- RooAbsPdf::fitTo(modelc) fixing normalization set for coefficient determination to observables in data [#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_modelc_modelData) Summation contains a RooNLLVar, using its error level [#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: activating const optimization [#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: deactivating const optimization
Construct another Gaussian constraint pdf on parameter f at 0.8 with resolution of 0.1
fconstext = ROOT.RooGaussian("fconstext", "fconstext", f, 0.2, 0.1)
Fit with external constraint
r3 = model.fitTo(d, ExternalConstraints={fconstext}, Save=True, PrintLevel=-1)
[#1] INFO:Minimization -- Including the following constraint terms in minimization: (fconstext) [#1] INFO:Minimization -- The global observables are not defined , normalize constraints with respect to the parameters (f,m,s) [#1] INFO:Fitting -- RooAbsPdf::fitTo(model) fixing normalization set for coefficient determination to observables in data [#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_model_modelData) Summation contains a RooNLLVar, using its error level [#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: activating const optimization [#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: deactivating const optimization
Print the fit results
print("fit result without constraint (data generated at f=0.5)")
r1.Print("v")
print("fit result with internal constraint (data generated at f=0.5, is f=0.8+/-0.2)")
r2.Print("v")
print("fit result with (another) external constraint (data generated at f=0.5, is f=0.2+/-0.1)")
r3.Print("v")
fit result without constraint (data generated at f=0.5) fit result with internal constraint (data generated at f=0.5, is f=0.8+/-0.2) fit result with (another) external constraint (data generated at f=0.5, is f=0.2+/-0.1) RooFitResult: minimized FCN value: 134.849, estimated distance to minimum: 2.11658e-05 covariance matrix quality: Full, accurate covariance matrix Status : MINIMIZE=0 HESSE=0 Floating Parameter InitialValue FinalValue +/- Error GblCorr. -------------------- ------------ -------------------------- -------- f 5.0000e-01 6.4987e-01 +/- 1.21e-01 <none> m 0.0000e+00 7.1824e-01 +/- 4.97e-01 <none> s 2.0000e+00 2.1880e+00 +/- 4.61e-01 <none> RooFitResult: minimized FCN value: 133.901, estimated distance to minimum: 5.96672e-06 covariance matrix quality: Full, accurate covariance matrix Status : MINIMIZE=0 HESSE=0 Floating Parameter InitialValue FinalValue +/- Error GblCorr. -------------------- ------------ -------------------------- -------- f 6.4987e-01 7.3784e-01 +/- 7.53e-02 <none> m 7.1824e-01 6.6350e-01 +/- 5.04e-01 <none> s 2.1880e+00 2.3885e+00 +/- 4.95e-01 <none> RooFitResult: minimized FCN value: 137.195, estimated distance to minimum: 0.000153955 covariance matrix quality: Full, accurate covariance matrix Status : MINIMIZE=0 HESSE=0 Floating Parameter InitialValue FinalValue +/- Error GblCorr. -------------------- ------------ -------------------------- -------- f 7.3784e-01 3.6215e-01 +/- 8.17e-02 <none> m 6.6350e-01 7.0071e-01 +/- 5.88e-01 <none> s 2.3885e+00 1.6987e+00 +/- 4.78e-01 <none>