rf604_constraints.py

## \ingroup tutorial_roofit_main

## \notebook -nodraw

## Likelihood and minimization: fitting with constraints

##

## \macro_code

## \macro_output

##

## \date February 2018

## \authors Clemens Lange, Wouter Verkerke (C++ version)

import ROOT

# Create model and dataset

# ----------------------------------------------

# 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 = f*gauss + (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)

# Create constraint pdf

# -----------------------------------------

# 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)

# Method 1 - add internal constraint to model

# -------------------------------------------------------------------------------------

# 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)

# Fit modelc with constraint term on parameter f

r2 = modelc.fitTo(d, Constrain={f}, Save=True, PrintLevel=-1)

# Method 2 - specify external constraint when fitting

# ------------------------------------------------------------------------------------------

# 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)

# 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")