rf705_linearmorph.py File Reference

Detailed Description

'SPECIAL PDFS' RooFit tutorial macro #705

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

 
 
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(ROOT.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")

[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x831fe20 with pdf g1_MORPH_g2_CACHE_Obs[x]_NORM_x for nset (x) with code 0
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x831fe20 with pdf g1_MORPH_g2_CACHE_Obs[x]_NORM_x for nset (x) with code 0
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x831fe20 with pdf g1_MORPH_g2_CACHE_Obs[x]_NORM_x for nset (x) with code 0
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x831fe20 with pdf g1_MORPH_g2_CACHE_Obs[x]_NORM_x for nset (x) with code 0
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x831fe20 with pdf g1_MORPH_g2_CACHE_Obs[x]_NORM_x for nset (x) with code 0
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x831fe20 with pdf g1_MORPH_g2_CACHE_Obs[x]_NORM_x for nset (x) with code 0
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x831fe20 with pdf g1_MORPH_g2_CACHE_Obs[x]_NORM_x for nset (x) with code 0
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x831fe20 with pdf g1_MORPH_g2_CACHE_Obs[x]_NORM_x for nset (x) with code 0
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x81b7aa0 with pdf g1_MORPH_g2_CACHE_Obs[x]_NORM_x_alpha for nset (x,alpha) with code 0 from preexisting content.
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x8756b70 with pdf g1_MORPH_g2_CACHE_Obs[x]_NORM_x for nset (x) with code 0
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x8763160 with pdf g1_MORPH_g2_CACHE_Obs[x]_NORM_x for nset (x) with code 0 from preexisting content.
[#0] PROGRESS:Eval -- RooIntegralMorph::fillCacheObject(lmorph) filling multi-dimensional cache..................................................
 
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x88f04a0 with pdf g1_MORPH_g2_CACHE_Obs[alpha,x]_NORM_x for nset (x) with code 0
[#1] INFO:Fitting -- RooAbsPdf::fitTo(lmorph_over_lmorph_Int[x]) 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_lmorph_over_lmorph_Int[x]_lmorphData) Summation contains a RooNLLVar, using its error level
[#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: activating const optimization
[#0] WARNING:Minimization -- RooAbsMinimizerFcn::synchronize: WARNING: no initial error estimate available for alpha: using 0.1
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x895a6a0 with pdf g1_MORPH_g2_CACHE_Obs[alpha,x] for nset () with code 1 from preexisting content.
 
prevFCN = 9770.913047  alpha=0.807, 
prevFCN = 9770.181345  alpha=0.7929, 
prevFCN = 9772.015076  alpha=0.8008, 
prevFCN = 9770.800603  alpha=0.7992, 
prevFCN = 9770.785966  alpha=0.8001, 
prevFCN = 9770.896896  alpha=0.7999, 
prevFCN = 9770.682007  
prevFCN = 9770.682007  alpha=0.7994, 
prevFCN = 9770.748743  alpha=0.7997, 
prevFCN = 9770.712263  alpha=0.8004, 
prevFCN = 9770.849353  alpha=0.8002, 
prevFCN = 9770.888877  alpha=0.8, 
prevFCN = 9770.908995  alpha=0.8, 
prevFCN = 9770.671799  alpha=0.8, 
prevFCN = 9770.909805  alpha=0.8, 
prevFCN = 9770.667124  alpha=0.8, 
prevFCN = 9770.910615  alpha=0.8, 
prevFCN = 9770.91254  alpha=0.8, 
prevFCN = 9770.912239  alpha=0.8, 
prevFCN = 9770.669355  alpha=0.8, 
prevFCN = 9770.666818  alpha=0.8, 
prevFCN = 9770.66743  alpha=0.8, 
prevFCN = 9770.91141  alpha=0.8, 
prevFCN = 9770.670187  alpha=0.8, 
prevFCN = 9770.668617  alpha=0.8, 
prevFCN = 9770.667852  alpha=0.8, 
prevFCN = 9770.667479  alpha=0.8, 
prevFCN = 9770.667297  alpha=0.8, 
prevFCN = 9770.667208  alpha=0.8, 
prevFCN = 9770.667165  alpha=0.8, 
prevFCN = 9770.667144  alpha=0.8, 
prevFCN = 9770.667134  alpha=0.8, 
prevFCN = 9770.667129  alpha=0.8, 
prevFCN = 9770.667126  alpha=0.8, 
prevFCN = 9770.667124  alpha=0.8, 
prevFCN = 9770.91141  alpha=0.8, 
prevFCN = 9770.670187  alpha=0.8, 
prevFCN = 9770.666827  alpha=0.8, 
prevFCN = 9770.667421  alpha=0.8, 
prevFCN = 9770.667064  alpha=0.8, 
prevFCN = 9770.667183  alpha=0.8, 
prevFCN = 9770.667124  alpha=0.8, 
prevFCN = 9770.667064  alpha=0.8, 
prevFCN = 9770.667183  alpha=0.8, 
prevFCN = 9770.66653  alpha=0.8, 
prevFCN = 9770.667718  alpha=0.8, 
prevFCN = 9770.667005  alpha=0.8, 
prevFCN = 9770.667243  alpha=0.8, [#1] INFO:Minimization -- RooAbsMinimizerFcn::setOptimizeConst: deactivating const optimization
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x8fa6060 with pdf g1_MORPH_g2_CACHE_Obs[alpha,x]_NORM_x for nset (x) with code 0 from preexisting content.
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x8fa7c40 with pdf g1_MORPH_g2_CACHE_Obs[alpha,x]_NORM_x for nset (x) with code 0 from preexisting content.
[#1] INFO:Fitting -- RooAbsPdf::fitTo(lmorph_over_lmorph_Int[x]) fixing normalization set for coefficient determination to observables in data
[#1] INFO:Caching -- RooAbsCachedPdf::getCache(lmorph) creating new cache 0x800f740 with pdf g1_MORPH_g2_CACHE_Obs[alpha,x] for nset () with code 1 from preexisting content.

Date

February 2018

Authors

Clemens Lange, Wouter Verkerke (C version)

Definition in file rf705_linearmorph.py.