from ROOT import DalitzPhaseSpace, BinnedKernelDensity, FactorisedDensity, FormulaDensity
from ROOT import BinnedDensity, AdaptiveKernelDensity, PolynomialDensity
from ROOT import TFile, TNtuple, TCanvas, TH1F, TH2F, TText
# Define masses of initial ("d") and final state particles ("a,b,c") for the Dalitz phase space.
md = 1.8646 # D0
ma = 0.497 # KS0
mb = 0.139 # Pi
mc = 0.139 # Pi
# Define Dalitz phase space for D0->KsPiPi decay
# The phase space is defined in x=m^2(ab), y=m^2(ac) variables
phsp = DalitzPhaseSpace("PhspDalitz", md, ma, mb, mc)
# Create a true PDF over this phase space, polynomial of power 4 in x and y
truepdf = FormulaDensity("TruePDF", phsp, "sqrt(1.-0.1*(x-1.3)^4)*(1.+2.*exp(-y))")
outfile = TFile.Open("DalitzPdf.root", "RECREATE")
ntuple = TNtuple("ntuple", "2D NTuple", "x:y")
# Generate 50000 toys according to the "true" PDF
truepdf.generate(ntuple, 25000)
# Create an approximation PDF, polynomial of power 3
poly = PolynomialDensity("PolyPDF",
phsp, # Phase space
2, # Power of the polynomial
ntuple, # Input ntuple
"x","y", # Ntuple variables
50000 # Sample size for MC integration
)
#
# It also uses FormulaDensity to describe the true PDF in a parametrised way.
from ROOT import gSystem, gStyle
gSystem.Load("../lib/libMeerkat.so")
from ROOT import OneDimPhaseSpace, FormulaDensity
from ROOT import BinnedKernelDensity, BinnedDensity, AdaptiveKernelDensity
from ROOT import TFile, TNtuple, TCanvas, TH1F, TText
# Define 1D phase space for a variable in range (-1, 1)
phsp = OneDimPhaseSpace("Phsp1D", -1., 1.)
# Create a "true" PDF over this phase space in a parametrised way
formula = FormulaDensity("FormulaPDF", phsp, "(1. + 4.*exp(-x*x/2/0.1/0.1))*( abs(x)<1 )")
outfile = TFile("OneDimAdaptiveKernel.root", "RECREATE")
ntuple = TNtuple("ntuple", "1D NTuple", "x")
# Generate toys according to the "true" PDF
formula.generate(ntuple, 10000)
# Create kernel PDF from the generate sample
kde = BinnedKernelDensity("KernelPDF",
phsp, # Phase space
ntuple, # Input ntuple
"x", # Variable to use
1000, # Number of bins
0.1, # Kernel width
0, # Approximation PDF (0 for flat approximation)
gSystem.Load("../lib/libMeerkat.so")
from ROOT import OneDimPhaseSpace, ParametricPhaseSpace, FormulaDensity, PolynomialDensity
from ROOT import TFile, TNtuple, TCanvas, TH2F, TText
# First create the 1D phase space for variable x
xphsp = OneDimPhaseSpace("PhspX", -1., 1.)
# Now create the parametric phase space for (x,y) where limits on variable y are functions of x
phsp = ParametricPhaseSpace("PhspParam", xphsp, "-sqrt(1-x^2)", "sqrt(1-x^2)", -1., 1.)
outfile = TFile("TwoDimPolyPdf.root", "RECREATE")
ntuple = TNtuple("ntuple", "2D NTuple", "x:y")
# True PDF
true_pdf = FormulaDensity("TruePDF", phsp, "1.+0.1*x-0.4*x^2-0.8*y^2")
# Generate 10000 toys according to the true PDF
true_pdf.generate(ntuple, 50000)
poly = PolynomialDensity("PolyPDF", phsp, 4, ntuple, "x", "y", 100000)
poly_hist = TH2F("poly", "Polynomial PDF", 200, -1.1, 1.1, 200, -1.1, 1.1)
poly.project(poly_hist)
poly_hist.Write()
gStyle.SetOptStat(0)
canvas = TCanvas("canvas", "TwoDimPolyPdf", 400, 400)
poly_hist.Draw("zcol")
from ROOT import gSystem, gStyle
gSystem.Load("../lib/libMeerkat.so")
from ROOT import OneDimPhaseSpace, ParametricPhaseSpace, BinnedKernelDensity, FormulaDensity
from ROOT import TFile, TNtuple, TCanvas, TH1F, TH2F, TText
# First create the 1D phase space for variable x
xphsp = OneDimPhaseSpace("PhspX", -1., 1.)
# Now create the parametric phase space for (x,y) where limits on variable y are functions of x
phsp = ParametricPhaseSpace("PhspParam", xphsp, "-sqrt(1-x^2)", "sqrt(1-x^2)", -1., 1.)
# Create a uniform PDF over this phase space
# Sum of a polynomial shape and a Gaussian peak with correlation between x and y
truepdf = FormulaDensity("TruePDF", phsp, "1.-0.8*x^2-0.8*y^2+exp(-(x-y)^2/2./(0.4)^2-(x+y)^2/2./(0.8)^2)")
# Create an approximation PDF over this phase space
# Just a polymonial shape. It will mostly be used to approximate the PDF
# at the edges of the phase space.
approxpdf = FormulaDensity("TruePDF", phsp, "1.-0.8*x^2-0.8*y^2")
outfile = TFile("ParamPhsp.root", "RECREATE")
ntuple = TNtuple("ntuple", "2D NTuple", "x:y")
# Generate 50000 toys according to the "true" PDF
truepdf.generate(ntuple, 50000)
# Create kernel PDF from the generated sample. Use polynomial shape as an approximation PDF
kde = BinnedKernelDensity("KernelPDF",
phsp, # Phase space
