def PoissonLikelihood( opt="" ):
from ConstrainedFit import clhood
from ConstrainedFit import clsq
from scipy.special import gammaln
from scipy.stats import poisson, norm
from math import log
# Data, two counts, errors not needed(!):
data= [ 9.0, 16.0 ]
# errors= [ 3.0, 4.0 ]
mpnames= { 0: "count 1", 1: "count 2" }
# Fit variable is parameter of poisson distribution:
upar= [ 12.0 ]
upnames= { 0: "mu" }
# Likelihood is sum of log(poisson) for each data point:
def lfun( mpar ):
result= 0.0
for datum, parval in zip( data, mpar ):
parval= parval.item()
result-= log( poisson.pmf( datum, parval ) )
# Calculated log(poisson):
# result-= datum*log( parval ) - gammaln( datum+1.0 ) - parval
return result
# Constraints force poisson distribution with same parameter
# for every data point:
def constrFun( mpar, upar ):
return [ mpar[0] - upar[0],
mpar[1] - upar[0] ]
solver= clhood.clhoodSolver( data, upar, lfun, constrFun,
uparnames=upnames, mparnames=mpnames )
print "Constraints before solution"
print solver.getConstraints()
lBlobel=False
lPrint= False
lCorr= False
if "b" in opt:
lBlobel= True
if "p" in opt:
lPrint= True
if "c" in opt:
lCorr= True
solver.solve( lBlobel=lBlobel, lpr=lPrint )
ca= clsq.clsqAnalysis( solver )
ca.printResults( corr=lCorr )
return
def GaussLikelihood( opt="" ):
from ConstrainedFit import clhood, clsq
from scipy.stats import norm
from math import log
# Data and errors:
xabs= [ 1.0, 2.0, 3.0, 4.0, 5.0 ]
data= [ 1.1, 1.9, 2.9, 4.1, 5.1 ]
errors= [ 0.1, 0.1, 0.1, 0.1, 0.1 ]
# Linear function (straight line) parameters:
upar= [ 0.0, 1.0 ]
upnames= { 0: "a", 1: "b" }
# Likelihood is sum of log(Gauss) for each data point:
def lfun( mpar ):
result= 0.0
for datum, parval, error in zip( data, mpar, errors ):
parval= parval.item()
result-= log( norm.pdf( datum, parval, error ) )
# result+= 0.5*((datum-parval)/error)**2
return result
# Constraints force linear function for each data point:
def constrFun( mpar, upar ):
constraints= []
for xval, parval in zip( xabs, mpar ):
constraints.append( upar[0] + upar[1]*xval - parval )
return constraints
# Configure options:
lBlobel=False
lPrint= False
lCorr= False
if "b" in opt:
lBlobel= True
if "p" in opt:
lPrint= True
if "c" in opt:
lCorr= True
# Solution using constrained log(likelihood) minimisation:
print "\nMax likelihood constrained fit"
solver= clhood.clhoodSolver( data, upar, lfun, constrFun, uparnames=upnames )
print "Constraints before solution"
print solver.getConstraints()
solver.solve( lBlobel=lBlobel, lpr=lPrint )
ca= clsq.clsqAnalysis( solver )
ca.printResults( corr=lCorr )
# Solution using constrained least squares:
print "\nLeast squares constrained fit"
covm= clsq.covmFromErrors( errors )
solver= clsq.clsqSolver( data, covm, upar, constrFun, uparnames=upnames )
print "Constraints before solution"
print solver.getConstraints()
solver.solve( lBlobel=lBlobel, lpr=lPrint )
ca= clsq.clsqAnalysis( solver )
ca.printResults( corr=lCorr )
return
def GaussLikelihood( opt="" ):
from ConstrainedFit import clhood, clsq
from scipy.stats import norm
from math import log
# Data and errors:
xabs= [ 1.0, 2.0, 3.0, 4.0, 5.0 ]
data= [ 1.1, 1.9, 2.9, 4.1, 5.1 ]
errors= [ 0.1, 0.1, 0.1, 0.1, 0.1 ]
# Linear function (straight line) parameters:
upar= [ 0.0, 1.0 ]
upnames= { 0: "a", 1: "b" }
# Likelihood is sum of log(Gauss) for each data point:
def lfun( mpar ):
result= 0.0
for datum, parval, error in zip( data, mpar, errors ):
parval= parval.item()
result-= log( norm.pdf( datum, parval, error ) )
# result+= 0.5*((datum-parval)/error)**2
return result
# Constraints force linear function for each data point:
def constrFun( mpar, upar ):
constraints= []
for xval, parval in zip( xabs, mpar ):
constraints.append( upar[0] + upar[1]*xval - parval )
return constraints
# Configure options:
lBlobel=False
lPrint= False
lCorr= False
if "b" in opt:
lBlobel= True
if "p" in opt:
lPrint= True
if "c" in opt:
lCorr= True
# Solution using constrained log(likelihood) minimisation:
print( "\nMax likelihood constrained fit" )
solver= clhood.clhoodSolver( data, upar, lfun, constrFun, uparnames=upnames )
print( "Constraints before solution" )
print( solver.getConstraints() )
solver.solve( lBlobel=lBlobel, lpr=lPrint )
ca= clsq.clsqAnalysis( solver )
ca.printResults( corr=lCorr )
# Solution using constrained least squares:
print( "\nLeast squares constrained fit" )
covm= clsq.covmFromErrors( errors )
solver= clsq.clsqSolver( data, covm, upar, constrFun, uparnames=upnames )
print( "Constraints before solution" )
print( solver.getConstraints() )
solver.solve( lBlobel=lBlobel, lpr=lPrint )
ca= clsq.clsqAnalysis( solver )
ca.printResults( corr=lCorr )
return
def PoissonLikelihood( opt="" ):
from ConstrainedFit import clhood
from ConstrainedFit import clsq
from scipy.special import gammaln
from scipy.stats import poisson
from math import log
# Data, two counts, errors not needed(!):
data= [ 9.0, 16.0 ]
# errors= [ 3.0, 4.0 ]
mpnames= { 0: "count 1", 1: "count 2" }
# Fit variable is parameter of poisson distribution:
upar= [ 12.0 ]
upnames= { 0: "mu" }
# Likelihood is sum of log(poisson) for each data point:
def lfun( mpar ):
result= 0.0
for datum, parval in zip( data, mpar ):
parval= parval.item()
result-= poisson.logpmf( datum, parval )
# Calculated log(poisson):
# result-= datum*log( parval ) - gammaln( datum+1.0 ) - parval
return result
# Constraints force poisson distribution with same parameter
# for every data point:
def constrFun( mpar, upar ):
return [ mpar[0] - upar[0],
mpar[1] - upar[0] ]
solver= clhood.clhoodSolver( data, upar, lfun, constrFun,
uparnames=upnames, mparnames=mpnames )
print( "Constraints before solution" )
print( solver.getConstraints() )
lBlobel=False
lPrint= False
lCorr= False
if "b" in opt:
lBlobel= True
if "p" in opt:
lPrint= True
if "c" in opt:
lCorr= True
solver.solve( lBlobel=lBlobel, lpr=lPrint )
ca= clsq.clsqAnalysis( solver )
ca.printResults( corr=lCorr )
# Minuit fit of the two count likelihood, corresponds
# to max L solution
from AverageTools import minuitSolver
def fcn( n, grad, fval, par, ipar ):
mu= par[0]
lsum= 0.0
for datum in data:
lsum-= poisson.logpmf( datum, mu )
# Calculated log(poisson):
# lsum-= datum*log( mu ) - gammaln( datum+1.0 ) - mu
fval.value= lsum
return
par= [ 12.0 ]
parerr= [ 1.0 ]
parname= [ "mu" ]
ndof= 1
solver= minuitSolver.minuitSolver( fcn, par, parerr, parname, ndof )
solver.minuitCommand( "SET ERRDEF 0.5" )
solver.solve()
solver.printResults()
return
