def langaufun(x, par):
'''
Fit parameters:
par[0]=Width (scale) parameter of Landau density
par[1]=Most Probable (MP, location) parameter of Landau density
par[2]=Total area (integral -inf to inf, normalization constant)
par[3]=Width (sigma) of convoluted Gaussian function
In the Landau distribution (represented by the CERNLIB approximation),
the maximum is located at x=-0.22278298 with the location parameter=0.
This shift is corrected within this function, so that the actual
maximum is identical to the MP parameter.
'''
# control constants
ns = 100 # number of convolution steps
sc = 5.0 # convolution extends to +-sc Gaussian sigmas
# MP shift correction
mpc = par[1] - mpshift * par[0]
xlow = x[0] - sc * par[3]
xupp = x[0] + sc * par[3]
step = (xupp - xlow) / ns
sumup = 0
for i in range(1, ns / 2):
xx = xlow + (i - 0.5) * step
fland = TMath.Landau(xx, mpc, par[0]) / par[0]
sumup += fland * TMath.Gaus(x[0], xx, par[3])
xx = xupp - (i - .5) * step
fland = TMath.Landau(xx, mpc, par[0]) / par[0]
sumup += fland * TMath.Gaus(x[0], xx, par[3])
return par[2] * step * sumup * invsq2pi / par[3]
def langaufun(x, par):
"""Convoluted Landau and Gaussian Fitting Function
source: https://root.cern.ch/root/html/tutorials/fit/langaus.C.html
translated to python by Benjamin Rottler ([email protected])
parameters:
par[0] = Width (scale) parameter of Landau density
par[1] = Most Probable (MP, location) parameter of Landau density
par[2] = Total area (integral -inf to inf, normalization constant)
par[3] = Width (sigma) of convoluted Gaussian function
In the Landau distribution (represented by the CERNLIB approximation),
the maximum is located at x=-0.22278298 with the location parameter=0.
This shift is corrected within this function, so that the actual
maximum is identical to the MP parameter.
"""
# numeric constants
invsq2pi = (2 * pi)**(-1 / 2)
mpshift = -0.22278298 # Landau maximum location
# control constants
np = 500 # number of convolution steps
sc = 5 # convolution extends to +-sc Guassion sigmas
# mp shift correction
mpc = par[1] - mpshift * par[0]
# range of convolution integral
xlow, xupp = x[0] - sc * par[3], x[0] + sc * par[3]
# Convolution integral of Landau and Gaussion by sum
i = 1
step = (xupp - xlow) / np
s = 0
while i <= np / 2:
xx = xlow + (i - 0.5) * step
fland = TMath.Landau(xx, mpc, par[0]) / par[0]
s += fland * TMath.Gaus(x[0], xx, par[3])
xx = xupp - (i - 0.5) * step
fland = TMath.Landau(xx, mpc, par[0]) / par[0]
s += fland * TMath.Gaus(x[0], xx, par[3])
i += 1
return (par[2] * step * s * invsq2pi / par[3])
def DeltaDeltaR(tau_4vec, lep_4vec, MET_2vec):
"""
Calculate the difference in dR between the expected dR (from Landau function) and measured dR
between tau and lepton
"""
visTauLep = tau_4vec + lep_4vec
MET_4Vec = TLorentzVector()
MET_4Vec.SetPtEtaPhiM(MET_2vec.Mod(), 0, MET_2vec.Phi(), 0)
TauLep = visTauLep + MET_4Vec
TauLepPt = TauLep.Pt() / 1000
expecteddR = 18.5279 * TMath.Landau(TauLepPt, -14.8407, 67.7441)
dR = tau_4vec.DeltaR(lep_4vec)
return abs(dR - expecteddR), dR, TauLepPt
def ApplyTheFakeRate(x, p, parametrization):
if parametrization == 'Jet':
Land = p[2] * TMath.Landau(x, p[3], p[4])
Pol0 = p[0] + p[1] * x
return Land + Pol0
elif parametrization == 'Lepton':
if x > 250: x = 250
Land = p[0] + p[1] * pow(x, 1) + p[2] * pow(x, 2) + p[3] * pow(
x, 3) + p[4] * pow(x, 4)
# Land = p[2] * TMath.Landau(x, p[3], p[4])
# Pol0 = p[0]
# return Land + Pol0
return Land
else:
raise Exception("Not a valid parametrization")
def _FIT_Jet(x, p):
Land = p[2] * TMath.Landau(x[0], p[3], p[4])
Pol0 = p[0] + p[1] * x[0]
return Land + Pol0
def _FIT_Jet_Function(x, p):
Land = p[2] * TMath.Landau(x, p[3], p[4])
Pol0 = p[0]+p[1]*x
return Land + Pol0
def NoisePlusLandauGaus(x, par):
#p_noise comes from a template histogram and is normalized to 1.0
p_noise = 0
if (x[0] >= 0 and x[0] < 2):
p_noise = 0.0219891
elif (x[0] >= 2 and x[0] < 4):
p_noise = 0.120234
elif (x[0] >= 4 and x[0] < 6):
p_noise = 0.201533
elif (x[0] >= 6 and x[0] < 8):
p_noise = 0.208594
elif (x[0] >= 8 and x[0] < 10):
p_noise = 0.150293
elif (x[0] >= 10 and x[0] < 12):
p_noise = 0.103087
elif (x[0] >= 12 and x[0] < 14):
p_noise = 0.0691951
elif (x[0] >= 14 and x[0] < 16):
p_noise = 0.0490216
elif (x[0] >= 16 and x[0] < 18):
p_noise = 0.0344967
elif (x[0] >= 18 and x[0] < 20):
p_noise = 0.0217874
elif (x[0] >= 20 and x[0] < 22):
p_noise = 0.0117006
elif (x[0] >= 22 and x[0] < 24):
p_noise = 0.00484164
else:
p_noise = 0.003228
#p_landau = TMath.Landau(x[0],par[2],par[3],False)
invsq2pi = 0.3989422804014
# (2 pi)^(-1/2)
mpshift = -0.22278298
# Landau maximum location
np = 500.0
# number of convolution steps
sc = 5.0
# convolution extends to +-sc Gaussian sigmas
#integral result
sum = 0.0
#MP shift correction
mpc = par[2] - mpshift * par[3]
#Range of convolution integral
xlow = x[0] - sc * par[4]
xupp = x[0] + sc * par[4]
step = (xupp - xlow) / np
#Convolution integral of Landau and Gaussian by sum
for i in range(1, int(np / 2) + 1):
xx = xlow + (i - .5) * step
fland = TMath.Landau(xx, mpc, par[3]) / par[3]
sum += fland * TMath.Gaus(x[0], xx, par[4])
xx = xupp - (i - .5) * step
fland = TMath.Landau(xx, mpc, par[3]) / par[3]
sum += fland * TMath.Gaus(x[0], xx, par[4])
p_landauGaus = step * sum * invsq2pi / par[4]
return par[0] * ((1 - par[1]) * p_noise + par[1] * p_landauGaus)
def _FIT_Lepton_Function(x, p):
Land = p[2] * TMath.Landau(x, p[3], p[4])
# Pol0 = p[0]+p[1]*x
Pol0 = p[0] + p[1]
return Land + Pol0
