def SignalShape(x, par):
'''
:param x: x[0]: x position
x[1]: y position
:param par: par[0]: number of peaks
par[1]: mean bkg signal
par[2]: peak height in percent of bkg
par[3]: peak1 x position
par[4]: peak1 y position
par[5]: peak1 sigma in x
par[6]: peak1 sigma in y
...
par[3+4*n]: peakn x position
par[4+4*n]: peakn y position
par[5+4*n]: peakn sigma in x
par[6+4*n]: peakn sigma in y
:return:
'''
norm = par[1] * par[2]
result = par[1]
if par[1] == 0:
norm = 1
for i in range(int(par[0])):
result += norm * TMath.Gaus(x[0], par[3 + 4 * i], par[5 + 4 * i]) * TMath.Gaus(x[1], par[4 + 4 * i], par[6 + 4 * i])
return result
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 ManualHitDistribution(x, par):
'''
Probability density function for hit distribution based on
6 2d gaussian in a rectangular pattern. The PDF is NOT
normalized to 1
:param x: array, x[0]: x position, x[1]: y position
:param par: parameter array;
:return:
'''
result = 0.1 # bkg
norm = 1.
sigma = 0.04
for i in range(len(par) / 2):
result += norm * TMath.Gaus(x[0], par[2 * i], sigma) * TMath.Gaus(x[1], par[2 * i + 1], sigma)
return result
def DoubleGaus(x, par):
'''
Sum of two Gaussian functions with same mean and different sigma
Parameters
----------
- x: function variable
- par: function parameters
par[0]: normalisation
par[1]: mean
par[2]: first sigma
par[3]: second sigma
par[4]: fraction of integral in second Gaussian
'''
firstGaus = TMath.Gaus(x[0], par[1], par[2], True)
secondGaus = TMath.Gaus(x[0], par[1], par[3], True)
return par[0] * ((1 - par[4]) * firstGaus + par[4] * secondGaus)
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 DoublePeakSingleGaus(x, par):
'''
Sum of two Gaussian functions with different mean and sigma
Parameters
----------
- x: function variable
- par: function parameters
par[0]: normalisation first peak
par[1]: mean first peak
par[2]: sigma first peak
par[3]: normalisation second peak
par[4]: mean second peak
par[5]: sigma second peak
'''
firstGaus = par[0] * TMath.Gaus(x[0], par[1], par[2], True)
secondGaus = par[3] * TMath.Gaus(x[0], par[4], par[5], True)
return firstGaus + secondGaus
def ffunc_DDPIPI(x, par):
''' function for correlated breit wigner: e+e- --> pipiDD with convoluted Gaussian function'''
sum = 0.
X = x[0]
sigma_gaus = 1.6 * 0.001
xlow = X - 5. * sigma_gaus
xup = X + 5. * sigma_gaus
step = (xup - xlow) / 100.
for i in range(1, 50):
xx = xlow + (i - 0.5) * step
ffun = func_DDPIPI(xx, par)
sum += ffun * TMath.Gaus(X, xx, sigma_gaus)
xx = xup - +(i - 0.5) * step
ffun = func_DDPIPI(xx, par)
sum += ffun * TMath.Gaus(X, xx, sigma_gaus)
return sum * step * GeV_2_sigma / sigma_gaus
def DoublePeakDoubleGaus(x, par):
'''
Sum of a double Gaussian function and a single Gaussian function
Parameters
----------
- x: function variable
- par: function parameters
par[0]: normalisation first peak
par[1]: mean first peak
par[2]: first sigma first peak
par[3]: second sigma first peak
par[4]: fraction of integral in second Gaussian first peak
par[5]: normalisation second peak
par[6]: mean second peak
par[7]: sigma second peak
'''
firstGaus = TMath.Gaus(x[0], par[1], par[2], True)
secondGaus = TMath.Gaus(x[0], par[1], par[3], True)
thirdGaus = par[5] * TMath.Gaus(x[0], par[6], par[7], True)
return par[0] * (
(1 - par[4]) * firstGaus + par[4] * secondGaus) + thirdGaus
def SingleGaus(x, par):
'''
Gaussian function
Parameters
----------
- x: function variable
- par: function parameters
par[0]: normalisation
par[1]: mean
par[2]: sigma
'''
return par[0] * TMath.Gaus(x[0], par[1], par[2], True)
def __call__(self, x, par):
out = 0
t = (x[0] - par[1]) / par[2]
if (par[0] < 0): t = -t
absAlpha = TMath.Abs(par[3])
if (t >= -absAlpha):
out = par[0] * TMath.Exp(-0.5 * t * t)
else:
a = TMath.Power(par[4] / absAlpha, par[4]) * TMath.Exp(
-0.5 * absAlpha * absAlpha)
b = par[4] / absAlpha - absAlpha
out = par[0] * (a / TMath.Power(b - t, par[4]))
out = out + par[5] * TMath.Gaus(x[0], par[1], par[6])
return out
def myFitFunc(x=None, par=None):
return par[0] * TMath.Gaus(x[0], par[1], par[2], kFALSE)
def __call__(self, x, par):
out = par[0] * (1 - par[1] * x[0]) * (x[0]**(
-par[2])) + par[3] * TMath.Gaus(x[0], par[4], par[5])
return out
def __call__(self, x, par):
x1 = par[0] * TMath.Power(x[0] - 60, -par[1])
x2 = TMath.Exp(-1.0 * (TMath.Power(par[2] * (x[0] - 60), 2)))
out = x1 * x2 + par[3] * TMath.Gaus(x[0], par[4], par[5])
return out
def __call__(self, x, par):
x1 = par[0] * TMath.Power(x[0], -par[1])
x2 = TMath.Exp(-par[2] * x[0])
out = x1 * x2 + par[3] * TMath.Gaus(x[0], par[4], par[5])
return out
def __call__(self, x, par):
out = (par[0] *
TMath.Gaus(x[0], par[1], par[2])) + par[3] * (x[0]**-par[4])
return out
def __call__(self, x, par):
x1 = par[0] * TMath.Power(x[0], -par[1])
x2 = TMath.Exp(-par[2] * x[0])
x3 = TMath.Exp(-par[3] * x[0] * x[0])
return x1 * x2 * x3 + par[4] * TMath.Gaus(x[0], par[5], par[6])
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 __call__( self, x, par ):
out=par[0] * TMath.Gaus(x[0],par[1],par[2])
return out;
sys.exit()
FONLLVar = ['central', 'min', 'max']
hPromptD0, hPromptLcpK0s, hPromptLcpKpi, hPromptLcpiL = ({}
for _ in range(4))
inFile = TFile.Open(args.inFileName)
for var in FONLLVar:
hPromptD0[var] = inFile.Get(f'hD0Kpipred_{var}')
hPromptD0[var].Scale(1. / args.BRD0)
hPromptLcpK0s[var] = inFile.Get(f'hLcK0sppred_{var}')
hPromptLcpKpi[var] = inFile.Get(f'hLcpkpipred_{var}')
for iPt in range(1, hPromptD0['central'].GetNbinsX() + 1):
for var in FONLLVar:
pT = hPromptD0[var].GetBinCenter(iPt)
crossSec = hPromptD0[var].GetBinContent(iPt)
factor = 0.11 + 4.68735e-01 * TMath.Gaus(
pT, 1, 4.90037) # parametrised from 5.02 TeV measurement
hPromptLcpK0s[var].SetBinContent(iPt,
factor * crossSec * args.BRpK0s)
hPromptLcpKpi[var].SetBinContent(iPt,
factor * crossSec * args.BRpKpi)
outFileName = args.inFileName.replace('.root', '_Mod.root')
os.system(f'cp {args.inFileName} {outFileName}')
outFile = TFile.Open(outFileName, 'update')
for var in FONLLVar:
hPromptLcpK0s[var].Write(hPromptLcpK0s[var].GetName(),
TObject.kOverwrite)
hPromptLcpKpi[var].Write(hPromptLcpKpi[var].GetName(),
TObject.kOverwrite)
outFile.Close()
def func_DDPIPI(x, par):
''' function for correlated breit wigner: e+e- --> DDpipi '''
xx = x[0]
return par[0] * pow(xx, -2) * TMath.Exp(
-1 * par[1] * (xx - 4.015)) + par[2] * TMath.Gaus(xx, par[3], par[4])
def AddToField(X, B, S0, Sigma, Integral):
"Add gaussian to field"
for i in range(len(X)):
B[i] += Integral * TMath.Gaus(X[i], S0, Sigma, True)
