def LinearFit():
from ConstrainedFit import clsq
xabs= [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0 ]
data= [ 1.1, 1.9, 2.9, 4.1, 5.1, 6.1, 6.9, 7.9, 9.1 ]
errors= [ 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1 ]
covm= clsq.covmFromErrors( errors )
upar= [ 0.1, 1.1 ]
upnames= { 0: "a", 1: "b" }
def linearConstrFun( mpar, upar, xv ):
constraints= []
for mparval, xval in zip( mpar, xv ):
constraints.append( upar[0]+upar[1]*xval - mparval )
return constraints
solver= clsq.clsqSolver( data, covm, upar, linearConstrFun,
uparnames=upnames, args=(xabs,) )
print "Constraints before solution"
print solver.getConstraints()
solver.solve()
ca= clsq.clsqAnalysis( solver )
ca.printResults()
return
def LinearFit():
from ConstrainedFit import clsq
xabs= [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0 ]
data= [ 1.1, 1.9, 2.9, 4.1, 5.1, 6.1, 6.9, 7.9, 9.1 ]
errors= [ 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1 ]
covm= clsq.covmFromErrors( errors )
upar= [ 0.1, 1.1 ]
upnames= { 0: "a", 1: "b" }
def linearConstrFun( mpar, upar, xv ):
constraints= []
for mparval, xval in zip( mpar, xv ):
constraints.append( upar[0]+upar[1]*xval - mparval )
return constraints
solver= clsq.clsqSolver( data, covm, upar, linearConstrFun,
uparnames=upnames, args=(xabs,) )
print( "Constraints before solution" )
print( solver.getConstraints() )
solver.solve()
ca= clsq.clsqAnalysis( solver )
ca.printResults()
return
def Triangle( opt="" ):
from ConstrainedFit import clsq
from math import sqrt, tan
data= [ 10.0, 7.0, 9.0, 1.0 ]
errors= [ 0.05, 0.2, 0.2, 0.02 ]
covm= clsq.covmFromErrors( errors )
mpnames= { 0: "a", 1: "b", 2: "c", 3: "gamma" }
upar= [ 30.0 ]
upnames= { 0: "A" }
def triangleConstrFun( mpar, upar ):
a= mpar[0]
b= mpar[1]
c= mpar[2]
gamma= mpar[3]
aa= upar[0]
p= (a+b+c)/2.0
s= sqrt( p*(p-a)*(p-b)*(p-c) )
return [ tan(gamma/2.0)-s/(p*(p-c)), aa-s ]
solver= clsq.clsqSolver( data, covm, upar, triangleConstrFun,
uparnames=upnames, mparnames=mpnames )
print( "Constraints before solution" )
print( solver.getConstraints() )
lBlobel= False
lCorr= False
lResidual= True
if "b" in opt:
lBlobel= True
if "corr" in opt:
lCorr= True
if "r" in opt:
lResidual= False
solver.solve( lBlobel=lBlobel, lResidual=lResidual )
ca= clsq.clsqAnalysis( solver )
ca.printResults( corr=lCorr )
if "m" in opt:
_doMinosAll( solver )
if "cont" in opt:
_doProfile2d( solver, ipar1=0, type1="u", ipar2=1, type2="m" )
print( "Profile A" )
par= clsq.createClsqPar( 0, "u", solver )
results= ca.profile( par )
print( results )
return solver
def Triangle( opt="" ):
from ConstrainedFit import clsq
from math import sqrt, tan
data= [ 10.0, 7.0, 9.0, 1.0 ]
errors= [ 0.05, 0.2, 0.2, 0.02 ]
covm= clsq.covmFromErrors( errors )
mpnames= { 0: "a", 1: "b", 2: "c", 3: "gamma" }
upar= [ 30.0 ]
upnames= { 0: "A" }
def triangleConstrFun( mpar, upar ):
a= mpar[0]
b= mpar[1]
c= mpar[2]
gamma= mpar[3]
aa= upar[0]
p= (a+b+c)/2.0
s= sqrt( p*(p-a)*(p-b)*(p-c) )
return [ tan(gamma/2.0)-s/(p*(p-c)), aa-s ]
solver= clsq.clsqSolver( data, covm, upar, triangleConstrFun,
uparnames=upnames, mparnames=mpnames )
print "Constraints before solution"
print solver.getConstraints()
lBlobel= False
lCorr= False
if "b" in opt:
lBlobel= True
if "corr" in opt:
lCorr= True
solver.solve( lBlobel=lBlobel )
ca= clsq.clsqAnalysis( solver )
ca.printResults( corr=lCorr )
if "m" in opt:
_doMinosAll( solver )
if "cont" in opt:
_doProfile2d( solver, ipar1=0, type1="u", ipar2=1, type2="m" )
print "Profile A"
par= clsq.createClsqPar( 0, "u", solver )
results= ca.profile( par )
print results
return solver
def Branchingratios( opt="m" ):
from ConstrainedFit import clsq
data= [ 0.265, 0.28, 0.37, 0.166, 0.42, 0.5, 0.20, 0.16,
0.72, 0.6, 0.37, 0.64, 0.45, 0.028, 10.0, 7.5 ]
errors= [ 0.014, 0.05, 0.06, 0.013, 0.15, 0.2, 0.08, 0.08,
0.15, 0.4, 0.16, 0.40, 0.45, 0.009, 5.0, 2.5 ]
# Error scale factor a la Blobel lecture:
if "e" in opt:
print "Apply scaling *2.8 of error[13]"
errors[13]= errors[13]*2.8
covm= clsq.covmFromErrors( errors )
upar= [ 0.33, 0.36, 0.16, 0.09, 0.055 ]
upnames= { 0: "B1", 1: "B2", 2: "B3", 3: "B4", 4: "B5" }
def brConstrFun( mpar, upar ):
constraints= []
x= []
for i in range( 5 ):
x.append( upar[i] )
for i in range( 5, 21 ):
x.append( mpar[i-5] )
constraints.append( x[0]+x[1]+x[2]+x[3]+x[4]-1.0 )
constraints.append( x[3]-x[5]*x[0] )
constraints.append( x[3]-x[6]*x[0] )
constraints.append( x[3]-x[7]*x[0] )
constraints.append( x[3]-(x[1]+x[2])*x[8] )
constraints.append( x[3]-(x[1]+x[2])*x[9] )
constraints.append( x[3]-(x[1]+x[2])*x[10] )
constraints.append( x[3]-(x[1]+x[2])*x[11] )
constraints.append( x[3]-(x[1]+x[2])*x[12] )
constraints.append( x[1]-(x[1]+x[2])*x[13] )
constraints.append( x[1]-(x[1]+x[2])*x[14] )
constraints.append( x[0]-(x[1]+x[2])*x[15] )
constraints.append( x[0]-(x[1]+x[2])*x[16] )
constraints.append( 3.0*x[4]-x[0]*x[17] )
constraints.append( x[3]-x[18] )
constraints.append( (x[1]+x[2])-x[4]*x[19] )
constraints.append( (x[1]+x[2])-x[4]*x[20] )
return constraints
solver= clsq.clsqSolver( data, covm, upar, brConstrFun, epsilon=0.00001,
uparnames=upnames )
print "Constraints before solution"
print solver.getConstraints()
lBlobel= False
if "b" in opt:
lBlobel= True
solver.solve( lBlobel=lBlobel )
lcov= False
lcorr= False
if "corr" in opt:
lcov= True
lcorr= True
ca= clsq.clsqAnalysis( solver )
ca.printResults( cov=lcov, corr=lcorr )
if "m" in opt:
_doMinosAll( solver, "u" )
if "cont" in opt:
_doProfile2d( solver, ipar1=0, type1="u", ipar2=1, type2="u" )
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 Branchingratios( opt="m" ):
from ConstrainedFit import clsq
data= [ 0.265, 0.28, 0.37, 0.166, 0.42, 0.5, 0.20, 0.16,
0.72, 0.6, 0.37, 0.64, 0.45, 0.028, 10.0, 7.5 ]
errors= [ 0.014, 0.05, 0.06, 0.013, 0.15, 0.2, 0.08, 0.08,
0.15, 0.4, 0.16, 0.40, 0.45, 0.009, 5.0, 2.5 ]
# Error scale factor a la Blobel lecture:
if "e" in opt:
print( "Apply scaling *2.8 of error[13]" )
errors[13]= errors[13]*2.8
covm= clsq.covmFromErrors( errors )
# PDG values as start values, last number is 5.5%, not 0.55 as in br.txt
upar= [ 0.33, 0.36, 0.16, 0.09, 0.055 ]
upnames= { 0: "B1", 1: "B2", 2: "B3", 3: "B4", 4: "B5" }
def brConstrFun( mpar, upar ):
constraints= []
x= []
for i in range( 5 ):
x.append( upar[i] )
for i in range( 5, 21 ):
x.append( mpar[i-5] )
constraints.append( x[0]+x[1]+x[2]+x[3]+x[4]-1.0 )
constraints.append( x[3]-x[5]*x[0] )
constraints.append( x[3]-x[6]*x[0] )
constraints.append( x[3]-x[7]*x[0] )
constraints.append( x[3]-(x[1]+x[2])*x[8] )
constraints.append( x[3]-(x[1]+x[2])*x[9] )
constraints.append( x[3]-(x[1]+x[2])*x[10] )
constraints.append( x[3]-(x[1]+x[2])*x[11] )
constraints.append( x[3]-(x[1]+x[2])*x[12] )
constraints.append( x[1]-(x[1]+x[2])*x[13] )
constraints.append( x[1]-(x[1]+x[2])*x[14] )
constraints.append( x[0]-(x[1]+x[2])*x[15] )
constraints.append( x[0]-(x[1]+x[2])*x[16] )
constraints.append( 3.0*x[4]-x[0]*x[17] )
constraints.append( x[3]-x[18] )
constraints.append( (x[1]+x[2])-x[4]*x[19] )
constraints.append( (x[1]+x[2])-x[4]*x[20] )
return constraints
solver= clsq.clsqSolver( data, covm, upar, brConstrFun, epsilon=0.00001,
uparnames=upnames )
print( "Constraints before solution" )
print( solver.getConstraints() )
lBlobel= False
if "b" in opt:
lBlobel= True
lResidual= False
if "r" in opt:
lResidual= True
solver.solve( lBlobel=lBlobel, lResidual=lResidual )
lcov= False
lcorr= False
if "corr" in opt:
lcov= True
lcorr= True
ca= clsq.clsqAnalysis( solver )
ca.printResults( cov=lcov, corr=lcorr )
if "m" in opt:
_doMinosAll( solver, "u" )
if "cont" in opt:
_doProfile2d( solver, ipar1=0, type1="u", ipar2=1, type2="u" )
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