def convertEffWeightsToMoments( Weights, **kwargs ) :
verb = kwargs.pop( 'Verbose', True )
pols = [ '0 0', 'para para', 'perp perp', '0 para', '0 perp', 'para perp', 'S S', '0 S', 'para S', 'perp S' ]
wNames = kwargs.pop( 'WeightNames'
, { '0 0' : 'Re_ang_A0_A0', 'para para' : 'Re_ang_Apar_Apar', 'perp perp' : 'Re_ang_Aperp_Aperp'
, '0 para' : 'Re_ang_A0_Apar', '0 perp' : 'Im_ang_A0_Aperp', 'para perp' : 'Im_ang_Apar_Aperp'
, 'S S' : 'Re_ang_AS_AS', '0 S' : 'Re_ang_A0_AS', 'para S' : 'Re_ang_Apar_AS', 'perp S' : 'Im_ang_Aperp_AS'
}
)
pref = kwargs.pop('WeightNamesPrefix', '')
if pref:
for wNam in wNames.keys(): wNames[wNam] = pref + '_' + wNames[wNam]
for pol in pols :
assert pol in wNames.keys()\
, 'P2VV - ERROR: convertEffWeightsToMoments(): polarization "%s" not found in weight names dictionary' % pol
assert wNames[pol] in Weights.keys()\
, 'P2VV - ERROR: convertEffWeightsToMoments(): weight "%s" not found in weights dictionary' % wNames[pol]
momNames = [ 'p2vvab_0000', 'p2vvab_0020', 'p2vvab_0022'
, 'p2vvab_0021', 'p2vvab_002m1', 'p2vvab_002m2'
, 'p2vvab_1000', 'p2vvab_1021', 'p2vvab_102m1'
, 'p2vvab_2000'
]
# convert weights to moments
from math import sqrt, pi
coef = lambda name : Weights[ wNames[name] ][0]
moms = { }
moms['p2vvab_0000'] = 1. / 3. * ( coef('0 0') + coef('para para') + coef('perp perp') )
moms['p2vvab_0020'] = 1. / 3. * sqrt(5.) * ( coef('0 0') + coef('para para') + coef('perp perp') - 3. * coef('S S') )
moms['p2vvab_0022'] = -sqrt(5. / 3.) * ( coef('para para') - coef('perp perp') )
moms['p2vvab_2000'] = 5. / 2. * ( coef('0 0') - coef('S S') )
moms['p2vvab_0021'] = - 8. / 3. * sqrt( 5. / 2. ) / pi * coef('para S')
moms['p2vvab_002m1'] = - 8. / 3. * sqrt( 5. / 2. ) / pi * -coef('perp S')
moms['p2vvab_002m2'] = sqrt( 5. / 3. ) * -coef('para perp')
moms['p2vvab_1000'] = 1. / 2. * sqrt(3.) * coef('0 S')
moms['p2vvab_1021'] = -32. / 3. * sqrt( 5. / 6. ) / pi * coef('0 para')
moms['p2vvab_102m1'] = +32. / 3. * sqrt( 5. / 6. ) / pi * -coef('0 perp')
# match the general moments coefficients format
for name in momNames : moms[name] = ( moms[name], 0., 0. )
# get scale factor for moment coefficient
scale = kwargs.pop( 'Scale', 1. )
if verb or kwargs.pop( 'PrintMoments', verb ) :
# print moments to screen
printMoments( BasisFuncNames = momNames, Moments = moms, Scale = scale )
if kwargs.get( 'OutputFilePath', '' ) :
# write the moments to a file
writeMoments( kwargs.pop('OutputFilePath'), BasisFuncNames = momNames, Moments = moms, Scale = scale, Verbose = verb )
# check if there are remaining keyword arguments
assert len(kwargs) == 0, 'P2VV - ERROR: convertEffWeightsToMoments(): unused keyword arguments: %s' % kwargs
def normalizeMoments( momentsFileOrig, momentsFileNorm, normMoment = 'Re_ang_A0_A0', printMoms = True ):
# moment containers
funcNames = [ ]
moments = { }
correlations = { }
# read moments
print 'input moments:'
from P2VV.Utilities.DataMoments import readMoments, printMoments
readMoments( momentsFileOrig, BasisFuncNames = funcNames, Moments = moments, Correlations = correlations, ProcessAll = True )
if printMoms: printMoments( BasisFuncNames = funcNames, Moments = moments, Correlations = correlations )
# calculate moments with new normalization
from math import sqrt
valNorm = moments[normMoment][0]
errNorm = moments[normMoment][1]
momsNew = { }
corrsNew = { }
# moments value and error
for name in funcNames :
valNew = moments[name][0] / valNorm
err = moments[name][1]
corrNorm = correlations[name][normMoment]
varNew = ( err**2 + valNew**2 * errNorm**2 - 2. * valNew * err * errNorm * corrNorm ) / valNorm**2
momsNew[name] = ( valNew, sqrt(varNew), ( sqrt( valNew**2 / varNew ) ) if varNew != 0. else 0. if valNew == 0. else float('inf') )
corrsNew[name] = { }
# moments correlations
for name0 in funcNames :
for name1 in funcNames :
valsNew = ( momsNew[name0][0], momsNew[name1][0] )
errsNew = ( momsNew[name0][1], momsNew[name1][1] )
errs = ( moments[name0][1], moments[name1][1] )
corr01 = correlations[name0][name1]
corr0Norm = correlations[name0][normMoment]
corr1Norm = correlations[name1][normMoment]
corr01New = ( errs[0] * errs[1] * corr01 + valsNew[0] * valsNew[1] * errNorm**2\
- valsNew[1] * errs[0] * errNorm * corr0Norm - valsNew[0] * errs[1] * errNorm * corr1Norm ) / valNorm**2
if abs( errsNew[0] ) > 1.e-10 and abs( errsNew[1] ) > 1.e-10 :
corr01New /= errsNew[0] * errsNew[1]
elif abs( corr01New ) < 1.e-10 and name0 == normMoment and name1 == normMoment :
corr01New = 1.
elif abs( corr01New ) < 1.e-10 and ( name0 == normMoment or name1 == normMoment ) :
corr01New = 0.
else :
corr01New = -999.
corrsNew[name0][name1] = corr01New
corrsNew[name1][name0] = corr01New
print 'output moments:'
from P2VV.Utilities.DataMoments import writeMoments
writeMoments( momentsFileNorm, BasisFuncNames = funcNames, Moments = momsNew, Correlations = corrsNew )
if printMoms: printMoments( BasisFuncNames = funcNames, Moments = momsNew, Correlations = corrsNew )
def write( self, filePath = 'moments', **kwargs ) :
writeMoments( filePath, BasisFuncNames = self._basisFuncNames, Moments = self._coefficients, Correlations = self._correlations,
**kwargs )
def combineMoments( momentsFilesIn, momentsFileOut, prefix = '', printMoms = True):
funcNames = [ 'Re_ang_A0_A0', 'Re_ang_Apar_Apar', 'Re_ang_Aperp_Aperp'
, 'Im_ang_Apar_Aperp', 'Re_ang_A0_Apar', 'Im_ang_A0_Aperp'
, 'Re_ang_AS_AS', 'Re_ang_Apar_AS', 'Im_ang_Aperp_AS', 'Re_ang_A0_AS' ]
if prefix:
funcNamesWPF = []
for name in funcNames: funcNamesWPF += [prefix + '_' + name]
funcNames = funcNamesWPF
# moment containers
moments = [ ]
correlations = [ ]
# read moments
from P2VV.Utilities.DataMoments import readMoments, printMoments
for momsFile in momentsFilesIn :
moments.append( { } )
correlations.append( { } )
readMoments( momsFile, BasisFuncNames = funcNames, Moments = moments[-1], Correlations = correlations[-1] )
if printMoms: printMoments( BasisFuncNames = funcNames, Moments = moments[-1], Correlations = correlations[-1] )
# combine moments
from ROOT import TMatrixD
combNames = [ name for name in funcNames if moments[0][name][1] > 0. ]
momVec = TMatrixD( len(combNames), 1 )
covMat = TMatrixD( len(combNames), len(combNames) )
for moms, corrs in zip( moments, correlations ) :
mom = TMatrixD( len(combNames), 1 )
cov = TMatrixD( len(combNames), len(combNames) )
for it1, name1 in enumerate(combNames) :
mom[it1][0] = moms[name1][0]
for it2, name2 in enumerate(combNames) :
cov[it1][it2] = moms[name1][1] * moms[name2][1] * corrs[name1][name2]
cov.Invert()
momVec += cov * mom
covMat += cov
covMat.Invert()
momVec = covMat * momVec
momsNew = { }
corrsNew = { }
for name in funcNames :
if moments[0][name][1] > 0. : continue
momsNew[name] = moments[0][name]
corrsNew[name] = correlations[0][name]
from math import sqrt
for it1, name1 in enumerate(combNames) :
val = momVec[it1][0]
err = sqrt( covMat[it1][it1] )
momsNew[name1] = ( val, err, abs( val / err ) )
corrsNew[name1] = { }
for name in funcNames :
if moments[0][name][1] > 0. : continue
corrsNew[name1][name] = correlations[0][name1][name]
for it2, name2 in enumerate(combNames) :
corrsNew[name1][name2] = covMat[it1][it2] / err / sqrt( covMat[it2][it2] )
# write combined moments to file
from P2VV.Utilities.DataMoments import writeMoments
writeMoments( momentsFileOut, BasisFuncNames = funcNames, Moments = momsNew, Correlations = corrsNew )
if printMoms: printMoments( BasisFuncNames = funcNames, Moments = momsNew, Correlations = corrsNew )
varNew = ( err**2 + valNew**2 * errNorm**2 - 2. * valNew * err * errNorm * corrNorm ) / valNorm**2
momsNew[name] = ( valNew, sqrt(varNew), ( sqrt( valNew**2 / varNew ) ) if varNew != 0. else 0. if valNew == 0. else float('inf') )
corrsNew[name] = { }
# moments correlations
for name0 in funcNames :
for name1 in funcNames :
valsNew = ( momsNew[name0][0], momsNew[name1][0] )
errsNew = ( momsNew[name0][1], momsNew[name1][1] )
errs = ( moments[name0][1], moments[name1][1] )
corr01 = correlations[name0][name1]
corr0Norm = correlations[name0][normMoment]
corr1Norm = correlations[name1][normMoment]
corr01New = ( errs[0] * errs[1] * corr01 + valsNew[0] * valsNew[1] * errNorm**2\
- valsNew[1] * errs[0] * errNorm * corr0Norm - valsNew[0] * errs[1] * errNorm * corr1Norm ) / valNorm**2
if abs( errsNew[0] ) > 1.e-10 and abs( errsNew[1] ) > 1.e-10 :
corr01New /= errsNew[0] * errsNew[1]
elif abs( corr01New ) < 1.e-10 and name0 == normMoment and name1 == normMoment :
corr01New = 1.
elif abs( corr01New ) < 1.e-10 and ( name0 == normMoment or name1 == normMoment ) :
corr01New = 0.
else :
corr01New = -999.
corrsNew[name0][name1] = corr01New
corrsNew[name1][name0] = corr01New
print 'output moments:'
from P2VV.Utilities.DataMoments import writeMoments
writeMoments( momentsFileNorm, BasisFuncNames = funcNames, Moments = momsNew, Correlations = corrsNew )
printMoments( BasisFuncNames = funcNames, Moments = momsNew, Correlations = corrsNew )
