rf705_linearmorph.py

## \ingroup tutorial_roofit_main

## \notebook

## 'SPECIAL PDFS' RooFit tutorial macro #705

##

## Linear interpolation between p.d.f shapes using the 'Alex Read' algorithm

##

## \macro_image

## \macro_code

## \macro_output

##

## \date February 2018

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

import ROOT

# Create end point pdf shapes

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

# Observable

x = ROOT.RooRealVar("x", "x", -20, 20)

# Lower end point shape: a Gaussian

g1mean = ROOT.RooRealVar("g1mean", "g1mean", -10)

g1 = ROOT.RooGaussian("g1", "g1", x, g1mean, 2.0)

# Upper end point shape: a Polynomial

g2 = ROOT.RooPolynomial("g2", "g2", x, [-0.03, -0.001])

# Create interpolating pdf

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

# Create interpolation variable

alpha = ROOT.RooRealVar("alpha", "alpha", 0, 1.0)

# Specify sampling density on observable and interpolation variable

x.setBins(1000, "cache")

alpha.setBins(50, "cache")

# Construct interpolating pdf in (x,a) represent g1(x) at a=a_min

# and g2(x) at a=a_max

lmorph = ROOT.RooIntegralMorph("lmorph", "lmorph", g1, g2, x, alpha)

# Plot interpolating pdf aat various alphas a l p h a

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

# Show end points as blue curves

frame1 = x.frame()

g1.plotOn(frame1)

g2.plotOn(frame1)

# Show interpolated shapes in red

alpha.setVal(0.125)

lmorph.plotOn(frame1, LineColor="r")

alpha.setVal(0.25)

lmorph.plotOn(frame1, LineColor="r")

alpha.setVal(0.375)

lmorph.plotOn(frame1, LineColor="r")

alpha.setVal(0.50)

lmorph.plotOn(frame1, LineColor="r")

alpha.setVal(0.625)

lmorph.plotOn(frame1, LineColor="r")

alpha.setVal(0.75)

lmorph.plotOn(frame1, LineColor="r")

alpha.setVal(0.875)

lmorph.plotOn(frame1, LineColor="r")

alpha.setVal(0.95)

lmorph.plotOn(frame1, LineColor="r")

# Show 2D distribution of pdf(x,alpha)

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

# Create 2D histogram

hh = lmorph.createHistogram("hh", x, Binning=40, YVar=dict(var=alpha, Binning=40))

hh.SetLineColor("kBlue")

# Fit pdf to dataset with alpha=0.8

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

# Generate a toy dataset alpha = 0.8

alpha.setVal(0.8)

data = lmorph.generate({x}, 1000)

# Fit pdf to toy data

lmorph.setCacheAlpha(True)

lmorph.fitTo(data, Verbose=True, PrintLevel=-1)

# Plot fitted pdf and data overlaid

frame2 = x.frame(Bins=100)

data.plotOn(frame2)

lmorph.plotOn(frame2)

# Scan -log(L) vs alpha

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

# Show scan -log(L) of dataset w.r.t alpha

frame3 = alpha.frame(Bins=100, Range=(0.1, 0.9))

# Make 2D pdf of histogram

nll = lmorph.createNLL(data)

nll.plotOn(frame3, ShiftToZero=True)

lmorph.setCacheAlpha(False)

c = ROOT.TCanvas("rf705_linearmorph", "rf705_linearmorph", 800, 800)

c.Divide(2, 2)

c.cd(1)

ROOT.gPad.SetLeftMargin(0.15)

frame1.GetYaxis().SetTitleOffset(1.6)

frame1.Draw()

c.cd(2)

ROOT.gPad.SetLeftMargin(0.20)

hh.GetZaxis().SetTitleOffset(2.5)

hh.Draw("surf")

c.cd(3)

ROOT.gPad.SetLeftMargin(0.15)

frame3.GetYaxis().SetTitleOffset(1.4)

frame3.Draw()

c.cd(4)

ROOT.gPad.SetLeftMargin(0.15)

frame2.GetYaxis().SetTitleOffset(1.4)

frame2.Draw()

c.SaveAs("rf705_linearmorph.png")