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
)
# Create kernel PDF from the generated sample
kde = BinnedKernelDensity("KernelPDF",
phsp, # Phase space
ntuple, # Input ntuple
"x","y", # Variables to use
200,200, # Numbers of bins
0.4, 0.4,# Kernel widths
poly, # Approximation PDF (0 for flat approximation)
50000 # Sample size for MC convolution (0 for binned convolution)
)
# 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")
canvas.Print("TwoDimPolyPdf.png")
#outfile.Close()
