def generate_binned_kd(self, bandwidth, pdf_seed=None):
"""Wrapper method of `BinnedKernelDensity` constructor for N-dimensional
kernel PDF with binned interpolation from the sample of points in an
NTuple with weight.
Parameters
----------
bandwidth : list floats
List of kernel widths.
pdf_seed : KernelDensity | None
PDF seed for the approximation PDF.
Returns
-------
binned_kernel : BinnedKernelDensity
BinnedKernelDensity instance.
"""
if pdf_seed is None:
pdf_seed = 0
args = []
args.extend([
"BinnedKernelDensity",
self.space, # Phase space.
self.tree # Input NTuple.
])
args.extend(self.model.vars) # Variables to use.
args.append("weight") # Weights.
args.extend(self.model.nbins) # Numbers of bins.
args.extend(bandwidth) # Kernel widths.
args.extend([
pdf_seed, # Approximation PDF (0 for flat approximation).
0
]) # Sample size for MC convolution (0 for binned convolution)
self.binned_kernel = BinnedKernelDensity(*args)
return self.binned_kernel
rnd = TRandom3()
for i in range(0, 10000) :
x = rnd.Rndm()*2.-1.
w = x*x
ntuple.Fill(x, w)
uniform_hist.Fill(x, w)
ntuple.Write()
# Create kernel PDF from the generated sample
# If the number of variables passed to the constructor is larger by 1 than the phase
# space dimensionality, the last variables is considered as the weight
kde = BinnedKernelDensity("KernelPDF",
phsp,
ntuple, # Input ntuple
"x", # Variable to use
"w", # Weight variable
1000, # Number of bins
0.1, # Kernel width
0, # Approximation PDF (0 for flat approximation)
100000 # Sample size for MC convolution (0 for binned convolution)
)
# Write binned PDF into a file
kde.writeToFile("WeightedTuple_bins.root")
# That's it. Now fill some control histograms and plot them.
kernel_hist = TH1F("kernel", "Kernel PDF", 200, -1.5, 1.5)
kde.project(kernel_hist)
uniform_hist.Write()
kernel_hist.Write()
# 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)
)
# Write binned PDF into a file
kde.writeToFile("DalitzPdf_bins.root")
# That's it. Now fill some histograms and show the results.
true_hist = TH2F("true", "True PDF", 100, phsp.lowerLimit(0), phsp.upperLimit(0),
100, phsp.lowerLimit(1), phsp.upperLimit(1))
poly_hist = TH2F("poly", "Polynomial PDF", 100, phsp.lowerLimit(0), phsp.upperLimit(0),
100, phsp.lowerLimit(1), phsp.upperLimit(1))
kernel_hist = TH2F("kernel", "Kernel PDF", 100, phsp.lowerLimit(0), phsp.upperLimit(0),
# Create a uniform PDF over this phase space
uniform = UniformDensity("UniformPDF", phsp)
outfile = TFile("OneDimPdf.root", "RECREATE")
ntuple = TNtuple("ntuple", "1D NTuple", "x")
# Generate 10000 toys according to the uniform PDF
uniform.generate(ntuple, 10000)
# Create kernel PDF from the generate sample
kde = BinnedKernelDensity("KernelPDF",
phsp,
ntuple, # Input ntuple
"x", # Variable to use
1000, # Number of bins
0.2, # Kernel width
0, # Approximation PDF (0 for flat approximation)
100000 # Sample size for MC convolution (0 for binned convolution)
)
# Write binned PDF into a file
kde.writeToFile("OneDimPdfBins.root")
uniform_hist = TH1F("unform", "PDF", 200, -1.5, 1.5)
kernel_hist = TH1F("kernel", "Kernel PDF", 200, -1.5, 1.5)
uniform.project(uniform_hist)
kde.project(kernel_hist)
gStyle.SetOptStat(0)
def __init__(self, args):
self.kde_norm = 1.0
self.kde = None
self.args = args
self.approx_pdf = 0
if args.pdf_seed:
self.approx_pdf = args.pdf_seed
for i in range(args.ndim):
self.kde_norm *= args.variables[i].range[1] - args.variables[
i].range[0]
self.kde_norm = self.kde_norm**(-1)
# fixed bw kde
if not args.adaptive:
if args.ndim == 1:
print ""
print "... constructing 1 dim. KDE (fixed bandwith)"
print ""
kde = BinnedKernelDensity(
"KernelPDF",
args.space, # Phase space
args.tree, # Input ntuple
args.var_names[0], # Variables to use
"weight", # weights
args.nbins[0], # Numbers of bins
args.bws[0], # Kernel widths
self.
approx_pdf, # Approximation PDF (0 for flat approximation)
args.mc_conv
) # Sample size for MC convolution (0 for binned convolution)
self.kde = kde
elif args.ndim == 2:
print ""
print "... constructing 2 dim. KDE (fixed bandwith)"
print ""
kde = BinnedKernelDensity(
"KernelPDF",
args.space, # Phase space
args.tree, # Input ntuple
args.var_names[0],
args.var_names[1], # Variables to use
"weight", # weights
args.nbins[0],
args.nbins[1], # Numbers of bins
args.bws[0],
args.bws[1], # Kernel widths
self.
approx_pdf, # Approximation PDF (0 for flat approximation)
args.mc_conv
) # Sample size for MC convolution (0 for binned convolution)
self.kde = kde
elif args.ndim == 3:
print ""
print "... constructing 3 dim. KDE (fixed bandwith)"
print ""
kde = BinnedKernelDensity(
"KernelPDF",
args.space, # Phase space
args.tree, # Input ntuple
args.var_names[0],
args.var_names[1],
args.var_names[2], # Variables to use
"weight", # weights
args.nbins[0],
args.nbins[1],
args.nbins[2], # Numbers of bins
args.bws[0],
args.bws[1],
args.bws[2], # Kernel widths
self.
approx_pdf, # Approximation PDF (0 for flat approximation)
args.mc_conv
) # Sample size for MC convolution (0 for binned convolution)
self.kde = kde
elif args.ndim == 4:
print ""
print "... constructing 4 dim. KDE (fixed bandwith)"
print ""
kde = BinnedKernelDensity(
"KernelPDF",
args.space, # Phase space
args.tree, # Input ntuple
args.var_names[0],
args.var_names[1],
args.var_names[2],
args.var_names[3], # Variables to use
"weight", # weights
args.nbins[0],
args.nbins[1],
args.nbins[2],
args.nbins[3], # Numbers of bins
args.bws[0],
args.bws[1],
args.bws[2],
args.bws[3], # Kernel widths
self.
approx_pdf, # Approximation PDF (0 for flat approximation)
args.mc_conv
) # Sample size for MC convolution (0 for binned convolution)
self.kde = kde
# adaptive bw kde
else:
if not self.approx_pdf:
print "please provide a seed for the KDE. exiting..."
sys.exit(1)
if args.ndim == 1:
print ""
print "... constructing 1 dim. KDE (adaptive bandwith)"
print ""
kde_adapt = AdaptiveKernelDensity(
"KernelPDF",
args.space, # Phase space
args.tree, # Input ntuple
args.var_names[0], # Variables to use
"w", # weights
args.nbins[0], # Numbers of bins
args.bws[0], # Kernel widths
self.approx_pdf, # PDF for width scaling
0, # Approximation PDF (0 for flat approximation)
args.mc_conv
) # Sample size for MC convolution (0 for binned convolution)
self.kde = kde_adapt
elif args.ndim == 2:
print ""
print "... constructing 2 dim. KDE (adaptive bandwith)"
print ""
kde_adapt = AdaptiveKernelDensity(
"KernelPDF",
args.space, # Phase space
args.tree,
args.var_names[0],
args.var_names[1], # Variables to use
"weight", # weights
args.nbins[0],
args.nbins[1], # Numbers of bins
args.bws[0],
args.bws[1], # Kernel widths
self.approx_pdf, # PDF for width scaling
0, # Approximation PDF (0 for flat approximation)
args.mc_conv
) # Sample size for MC convolution (0 for binned convolution)
self.kde = kde_adapt
elif args.ndim == 3:
print ""
print "... constructing 3 dim. KDE (adaptive bandwith)"
print ""
kde_adapt = AdaptiveKernelDensity(
"KernelPDF",
args.space, # Phase space
args.tree, # Input ntuple
args.var_names[0],
args.var_names[1],
args.var_names[2], # Variables to use
"weight", # weights
args.nbins[0],
args.nbins[1],
args.nbins[2], # Numbers of bins
args.bws[0],
args.bws[1],
args.bws[2], # Kernel widths
self.approx_pdf, # PDF for width scaling
0, # Approximation PDF (0 for flat approximation)
args.mc_conv
) # Sample size for MC convolution (0 for binned convolution)
self.kde = kde_adapt
elif args.ndim == 4:
print ""
print "... constructing 4 dim. KDE (adaptive bandwith)"
print ""
kde_adapt = AdaptiveKernelDensity(
"KernelPDF",
args.space, # Phase space
args.tree, # Input ntuple
args.var_names[0],
args.var_names[1],
args.var_names[2],
args.var_names[3], # Variables to use
"weight", # weights
args.nbins[0],
args.nbins[1],
args.nbins[2],
args.nbins[3], # Numbers of bins
args.bws[0],
args.bws[1],
args.bws[2],
args.bws[3], # Kernel widths
self.approx_pdf, # PDF for width scaling
0, # Approximation PDF (0 for flat approximation)
args.mc_conv
) # Sample size for MC convolution (0 for binned convolution)
self.kde = kde_adapt
# 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)
100000 # Sample size for MC convolution (0 for binned convolution)
)
# Create adaptive kernel PDF with the kernel width depending on the binned PDF
kde_adaptive = AdaptiveKernelDensity("AdaptivePDF",
phsp, # Phase space
ntuple, # Input ntuple
"x", # Variable to use
1000, # Number of bins
0.1, # Initial kernel width
kde, # PDF for width scaling
0, # Approximation PDF (0 for flat approximation)
100000 # Sample size for MC convolution (0 for binned convolution)
# 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
ntuple, # Input ntuple
"x","y", # Variables to use
200,200, # Numbers of bins
0.2, 0.2, # Kernel widths
approxpdf, # Approximation PDF (0 for flat approximation)
100000 # Sample size for MC convolution (0 for binned convolution)
)
# Write binned PDF into a file
kde.writeToFile("ParamPhsp_bins.root")
# That's it. Now fill some histograms and show the results.
true_hist = TH2F("true", "True PDF", 100, phsp.lowerLimit(0), phsp.upperLimit(0),
100, phsp.lowerLimit(1), phsp.upperLimit(1))
kernel_hist = TH2F("kernel", "Kernel PDF", 100, phsp.lowerLimit(0), phsp.upperLimit(0),
100, phsp.lowerLimit(1), phsp.upperLimit(1))