def addHistToTGraphPoisson(self, h, g, w=1.):
for i in range(0, g.GetN()):
# shifted by +1, i.e. over/underflow
err = h.GetBinError(i + 1)
y = h.GetBinContent(i + 1)
binWidth = h.GetBinWidth(i + 1)
# From https://twiki.cern.ch/twiki/bin/view/CMS/PoissonErrorBars
alpha = 1. - 0.6827
n = int(
round(y * binWidth /
w)) # Round is necessary due to, well, rounding errors
l = Math.gamma_quantile(alpha / 2., n, 1.) if n != 0. else 0.
u = Math.gamma_quantile_c(alpha, n + 1, 1) if n != 0. else 0.
g.SetPointEYlow(
i,
math.sqrt(((n - l) / binWidth * w)**2 + g.GetErrorYlow(i)**2))
g.SetPointEYhigh(
i,
math.sqrt(((u - n) / binWidth * w)**2 + g.GetErrorYhigh(i)**2))
gx = Double(0.)
gy = Double(0.)
g.GetPoint(i, gx, gy)
g.SetPoint(i, gx, y + gy)
def __init__( self, process_list, sf = None, df = None ):
self.__processes = process_list
if sf and df:
self.__sf = sf
self.__df = df
alpha = 1 - 0.6827
self.__sfCRGraph = TGraphAsymmErrors(self.__sf)
self.__dfCRGraph = TGraphAsymmErrors(self.__df)
for g in [self.__sfCRGraph, self.__dfCRGraph]:
for i in range(g.GetN()):
N = g.GetY()[i]
LowErr = 0 if N == 0 else Math.gamma_quantile(alpha/2, N, 1.)
UpErr = Math.gamma_quantile_c(alpha/2, N+1, 1.) # recommended by StatComm (1.8)
# Math.gamma_quantile_c(alpha, N+1, 1.) # gives 1.2, strictly 68% one-sided
g.SetPointEYlow(i, N-LowErr)
g.SetPointEYhigh(i, UpErr-N)
for p in self.__processes:
if p.name() in ['nonpromptSF', 'nonpromptDF']:
nom, low, high = [], [], []
for ib in range(p.nominal().GetXaxis().GetNbins()):
if p.name() in ['nonpromptDF']: hnp = self.__dfCRGraph
else: hnp = self.__sfCRGraph
npcr = hnp.GetY()[ib]
npcrErrLow = hnp.GetEYlow()[ib]
npcrErrHigh = hnp.GetEYhigh()[ib]
np = p.nominal().GetBinContent(ib+1)
npErr = p.nominal().GetBinError(ib+1)
alpha = np/npcr if npcr > 0 else npErr
nom.append(npcr*alpha)
low.append(npcrErrLow*alpha)
high.append(npcrErrHigh*alpha)
hnom = p.nominal().Clone()
for ib in range(hnom.GetXaxis().GetNbins()):
hnom.SetBinContent(ib+1, nom[ib])
npGraph = TGraphAsymmErrors(hnom)
for ib in range(hnom.GetXaxis().GetNbins()):
npGraph.SetPointEYlow(ib, low[ib])
npGraph.SetPointEYhigh(ib, high[ib])
if p.name() in ['nonpromptDF']:
self.__dfGraph = npGraph
else:
self.__sfGraph = npGraph
self.__uncertainties = set()
for p in self.__processes:
self.__uncertainties = self.__uncertainties.union( set( p.uncertaintySources() ) )
def calculatePoissonErrors(n, confidenceInterval=0.6827):
## Calcultes the Poisson error for a given numer
# n number of entries
# confidenceInterval probability covered inside the error band
from ROOT import Math
n = round(n)
invIntegral = (1. - confidenceInterval) / 2.
lo = Math.gamma_quantile(invIntegral, n, 1.) if n != 0 else 0.
hi = Math.gamma_quantile_c(invIntegral, n + 1, 1.)
return n - lo, hi - n
def createTGraphPoisson(self, h, w=1.):
self.tfile.cd()
g = TGraphAsymmErrors(h)
for i in range(0, g.GetN()):
y = h.GetBinContent(i+1)
binWidth = h.GetBinWidth(i+1)
# From https://twiki.cern.ch/twiki/bin/view/CMS/PoissonErrorBars
alpha = 1. - 0.6827
n = int(round(y*binWidth/w)) # Round is necessary due to, well, rounding errors
l = Math.gamma_quantile(alpha/2., n, 1.) if n != 0. else 0.
u = Math.gamma_quantile_c(alpha, n+1, 1)
# print y*binWidth/w, n, y, u, l
g.SetPointEYlow(i, (n-l)/binWidth*w)
g.SetPointEYhigh(i, (u-n)/binWidth*w)
return g
def createTGraphPoisson(self, h, w=1.):
self.tfile.cd()
g = TGraphAsymmErrors(h)
for i in range(0, g.GetN()):
y = h.GetBinContent(i + 1)
binWidth = h.GetBinWidth(i + 1)
# From https://twiki.cern.ch/twiki/bin/view/CMS/PoissonErrorBars
alpha = 1. - 0.6827
n = int(
round(y * binWidth /
w)) # Round is necessary due to, well, rounding errors
l = Math.gamma_quantile(alpha / 2., n, 1.) if n != 0. else 0.
u = Math.gamma_quantile_c(alpha, n + 1, 1)
# print y*binWidth/w, n, y, u, l
g.SetPointEYlow(i, (n - l) / binWidth * w)
g.SetPointEYhigh(i, (u - n) / binWidth * w)
return g
def addHistToTGraphPoisson(self, h, g, w=1.):
for i in range(0, g.GetN()):
# shifted by +1, i.e. over/underflow
err = h.GetBinError(i+1)
y = h.GetBinContent(i+1)
binWidth = h.GetBinWidth(i+1)
# From https://twiki.cern.ch/twiki/bin/view/CMS/PoissonErrorBars
alpha = 1. - 0.6827
n = int(round(y*binWidth/w)) # Round is necessary due to, well, rounding errors
l = Math.gamma_quantile(alpha/2., n, 1.) if n != 0. else 0.
u = Math.gamma_quantile_c(alpha, n+1, 1) if n != 0. else 0.
g.SetPointEYlow(i, math.sqrt(((n-l)/binWidth*w)**2 + g.GetErrorYlow(i)**2))
g.SetPointEYhigh(i, math.sqrt(((u-n)/binWidth*w)**2 + g.GetErrorYhigh(i)**2))
gx = Double(0.)
gy = Double(0.)
g.GetPoint(i, gx, gy)
g.SetPoint(i, gx, y + gy)
Nzj = zmumuj_data.Get('TotEvts').GetVal()*ztautauj.Get('NormEvts').GetVal()/zmumuj.Get('NormEvts').GetVal()
#Nwt = (Nevts - (Nqcd + Nzj))*(wtOttbar/(1+wtOttbar))
Nwt = powheg_predictions.Get("Wt_dr_xsec").GetVal() * L * totaleff_wt
Nsig = Nevts - Nqcd - Nzj - Nwt
Nbkg = Nqcd + Nzj + Nwt
acc = TFile("/user2/sfarry/workspaces/top/tuples/ttbar_acc.root")
A = acc.Get('acc').GetVal()
A_err = acc.Get('acc_err').GetVal()
xsec = Nsig * A / (totaleff * L )
from math import floor
#poisson uncertainties
alpha = 1 - 0.68268942
Nwt_err_lo = Nwt - Math.gamma_quantile(alpha/2.0, floor(Nwt),1)
Nzj_err_lo = Nzj - Math.gamma_quantile(alpha/2.0, floor(Nzj),1)
Nqcd_err_lo = Nqcd - Math.gamma_quantile(alpha/2.0, floor(Nqcd),1)
Nbkg_err_lo = Nbkg - Math.gamma_quantile(alpha/2.0, floor(Nbkg),1)
Nwt_err_hi = Math.gamma_quantile_c(alpha/2.0, floor(Nwt)+1,1) - Nwt
Nzj_err_hi = Math.gamma_quantile_c(alpha/2.0, floor(Nzj)+1,1) - Nzj
Nqcd_err_hi = Math.gamma_quantile_c(alpha/2.0, floor(Nqcd)+1,1) - Nqcd
Nbkg_err_hi = Math.gamma_quantile_c(alpha/2.0, floor(Nbkg)+1,1) - Nbkg
stat_err = xsec / sqrt(Nevts)
syst_err = xsec * sqrt(pow(totaleff_err / totaleff, 2) + pow(A_err / A, 2) + pow(Nbkg_err_hi/(Nevts - Nbkg),2))
lumi_err = xsec * 0.039
print "Number of selected events: %f +/- %f" %(Nevts, sqrt(Nevts))
print "Same sign background : %f + %f - %f" %(Nqcd, Nqcd_err_hi, Nqcd_err_lo)
def __call__(self, population, signalYield, signalSample, backgroundYield,
backgroundSample):
# Histogram holders
signalHistogram = TH1F('signalHistogram', 'signal', self.nbins, 0, 1)
backgroundHistogram = TH1F('backgroundHistogram', 'background',
self.nbins, 0, 1)
# Loop over the chromosomes in the population
for genome in population:
# Reset histograms
signalHistogram.Reset()
backgroundHistogram.Reset()
# Get a nn describe by the chromosome (feed foreward)
net = nn.create_ffphenotype(genome)
# Loop over the events creating signal histogram
for event in signalSample:
# Extract variables and weight
variables = event[1:]
weight = event[0]
# Not strictly necessary in feedforward nets
net.flush()
# Net output
output = net.sactivate(variables)[0]
# Filling histograms
signalHistogram.Fill(output, weight)
# Signal overall normalization scale
signalScale = signalYield / len(signalSample)
# Loop over the events creating background histogram
for event in backgroundSample:
# Extract variables and weight
variables = event[1:]
weight = event[0]
# Not strictly necessary in feedforward nets
net.flush()
# Net output
output = net.sactivate(variables)[0]
# Filling histograms
backgroundHistogram.Fill(output, weight)
# Background overall normalization scale
backgroundScale = backgroundYield / len(backgroundSample)
# Random generators
rcount = TRandom3(int(random.uniform(0, 65535)))
rsignal = TRandom3(int(random.uniform(0, 65535)))
rbackground = TRandom3(int(random.uniform(0, 65535)))
zscore = 0.
sqweight = 0.
# Computing weighted z-score
for bin in xrange(1, signalHistogram.GetNbinsX() + 1):
newz = 0.
oldz = 0.
# Computing the zvalue per bin
for point in xrange(1, self.mpoints + 1):
# Sample background
background = Math.gamma_quantile(
rbackground.Uniform(),
(backgroundHistogram.GetBinContent(bin) /
backgroundScale) + 1., backgroundScale)
# Background larger that zero
if background > 0.:
# Sampling signal
signal = Math.gamma_quantile(
rsignal.Uniform(),
(signalHistogram.GetBinContent(bin) / signalScale)
+ 1., signalScale)
# Sampling count
count = rcount.Poisson(signal + background)
# Computing pvalue
pvalue = Math.poisson_cdf_c(
count, background) + Math.poisson_pdf(
count, background)
# Computing zvalue
zvalue = self.minz
if pvalue < 1.0:
zvalue = Math.normal_quantile_c(pvalue, 1)
# zvalue iterative average
newz = (zvalue + (point - 1) * oldz) / point
# Computing relative difference
error = math.fabs((newz - oldz) / newz)
# Convergency criteria
if error < self.error: break
# Updating oldz
oldz = newz
if point == self.mpoints:
self.message(
'Warning reach maximum number of integration %s points.'
% point)
weight = self.weight(signalHistogram.GetBinCenter(bin))
zscore = zscore + weight * newz
sqweight = sqweight + weight**2
# Fitness function is zscore transform back to 1 - pvalue
# Set the fitness value to the chomosome
genome.fitness = 1. - Math.normal_cdf_c(
zscore / Math.sqrt(sqweight))
def __call__(self, population, signalYield, signalSample, backgroundYield, backgroundSample):
# Histogram holders
signalHistogram = TH1F('signalHistogram', 'signal', self.nbins, 0, 1)
backgroundHistogram = TH1F('backgroundHistogram', 'background', self.nbins, 0, 1)
# Loop over the chromosomes in the population
for genome in population:
# Reset histograms
signalHistogram.Reset()
backgroundHistogram.Reset()
# Get a nn describe by the chromosome (feed foreward)
net = nn.create_ffphenotype(genome)
# Loop over the events creating signal histogram
for event in signalSample:
# Extract variables and weight
variables = event[1:]
weight = event[0]
# Not strictly necessary in feedforward nets
net.flush()
# Net output
output = net.sactivate(variables)[0]
# Filling histograms
signalHistogram.Fill(output, weight)
# Signal overall normalization scale
signalScale = signalYield/len(signalSample)
# Loop over the events creating background histogram
for event in backgroundSample:
# Extract variables and weight
variables = event[1:]
weight = event[0]
# Not strictly necessary in feedforward nets
net.flush()
# Net output
output = net.sactivate(variables)[0]
# Filling histograms
backgroundHistogram.Fill(output, weight)
# Background overall normalization scale
backgroundScale = backgroundYield/len(backgroundSample)
# Random generators
rcount = TRandom3(int(random.uniform(0,65535)))
rsignal = TRandom3(int(random.uniform(0,65535)))
rbackground = TRandom3(int(random.uniform(0,65535)))
zscore = 0.; sqweight = 0.
# Computing weighted z-score
for bin in xrange(1,signalHistogram.GetNbinsX()+1):
newz = 0.; oldz = 0.
# Computing the zvalue per bin
for point in xrange(1,self.mpoints+1):
# Sample background
background = Math.gamma_quantile(rbackground.Uniform(),
(backgroundHistogram.GetBinContent(bin)/backgroundScale)+1., backgroundScale
)
# Background larger that zero
if background > 0.:
# Sampling signal
signal = Math.gamma_quantile(rsignal.Uniform(),
(signalHistogram.GetBinContent(bin)/signalScale)+1., signalScale
)
# Sampling count
count = rcount.Poisson(signal+background)
# Computing pvalue
pvalue = Math.poisson_cdf_c(count,background) + Math.poisson_pdf(count,background)
# Computing zvalue
zvalue = self.minz
if pvalue < 1.0: zvalue = Math.normal_quantile_c(pvalue,1)
# zvalue iterative average
newz = (zvalue + (point - 1)*oldz)/point
# Computing relative difference
error = math.fabs((newz - oldz)/newz)
# Convergency criteria
if error < self.error: break
# Updating oldz
oldz = newz
if point == self.mpoints:
self.message('Warning reach maximum number of integration %s points.' % point)
weight = self.weight(signalHistogram.GetBinCenter(bin))
zscore = zscore + weight * newz
sqweight = sqweight + weight**2
# Fitness function is zscore transform back to 1 - pvalue
# Set the fitness value to the chomosome
genome.fitness = 1. - Math.normal_cdf_c(zscore/Math.sqrt(sqweight))
