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KalmanNEXT.py
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KalmanNEXT.py
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import Array
from math import *
from KalmanFilter import KalmanFilter, KalmanData
from Physics import Constants, NEXT, K2P
from numpy import loadtxt
from scipy.interpolate import interp1d
from scipy.integrate import quad as integrate
def Beta( p, m = Constants.me ):
'''
Return the beta value for a given momentum.
'''
return p / sqrt( p**2 + m**2 )
def thetaMS( p, x, Q = 1 ):
'''
Return the angle of multiple scattering for a certain momentum p in MeV/c and a number of radiation lengths x.
'''
return 13.6 / ( Beta(p) * p ) * Q * sqrt( x ) * ( 1.0 + 0.038 * log( x ) )
_Eloss_data = loadtxt('/Users/Gonzalo/github/PyKalman/KalmanFilter/xe_estopping_power_NIST.dat')
_ds, _dEds = zip(*_Eloss_data)
_Eloss = interp1d( (0,) + _ds, (_dEds[0],) + _dEds, kind = 'cubic' )
class NEXTKF(KalmanFilter):
'''
State = ( x - dz tanx, y - dz tany, tanx, tany, E )
'''
xyresolution = 0.1 # cm
Eresolution = 0.5 # MeV
xyres2 = xyresolution**2
Eres2 = Eresolution**2
def __init__( self, P = 15., T = 27. ):
KalmanFilter.__init__( self, name = 'NEXT Kalman Filter' )
self.gas = NEXT( P, T )
def TransportMatrix( self, index0, index1 ):
This = self.Track.GetNode(index0)
Other = self.Track.GetNode(index1)
state = This.Pstate.State if This.status < 2 else This.Fstate.State
tx = state[2]
ty = state[3]
dz = Other.running - This.running
ds = abs(dz) * ( tx**2 + ty**2 + 1 ) ** 0.5
F = Array.Identity( self.Sdim )
F[-1][-1] = self.Eloss( state[-1], ds )
return F
def MeasurementMatrix( self, index0, index1 ):
dz = self.Track.GetNode(index1).running - self.Track.GetNode(index0).running
return Array.Matrix( [ 1., 0., dz, 0., 0. ],
[ 0., 1., 0., dz, 0. ],
[ 0., 0., 0., 0., 1. ])
def MultipleScatteringMatrix( self, index0, index1 ):
This = self.Track.GetNode(index0)
Other = self.Track.GetNode(index1)
z0 = This.running
z02 = z0**2;
z1 = Other.running
L = abs( z1 - z0 ) / self.gas.x0 * 0.1
dx, dy, tx, ty, e = This.Pstate.State
theta02 = thetaMS( K2P(e) , L )**2
factor = theta02 * ( 1 + tx**2 + ty**2 )
p33 = factor * ( 1 + tx**2 )
p44 = factor * ( 1 + ty**2 )
p34 = factor * tx * ty
return Array.Matrix( [ z02 * p33, z02 * p34, -z0 * p33, -z0 * p34, 0. ],
[ z02 * p34, z02 * p44, -z0 * p34, -z0 * p44, 0. ],
[ -z0 * p33, -z0 * p34, p33, p34, 0. ],
[ -z0 * p34, -z0 * p44, p34, p44, 0. ],
[ 0., 0., 0., 0., self.Eres2 ])
def NoiseMatrix( self, index ):
V = Array.Identity(self.Mdim) * self.xyres2
V[-1][-1] = self.Eres2
return V
def Eloss( self, e0, ds ):
return _Eloss( e0 ) * ds
class KFNEXT(KalmanFilter):
'''
State = ( x, y, tanx, tany, E )
'''
xyresolution = 0.1 # cm
# Eresolution = 0.01 #/ 2.458 # MeV
Eresolution = 0.01 * 2.458**0.5 #/ 2.458 # MeV
xyres2 = xyresolution**2
Eres2 = Eresolution**2
def __init__( self, P = 15., T = 27. ):
KalmanFilter.__init__( self, name = 'NEXT Kalman Filter' )
self.gas = NEXT( P, T )
def SetMeasurements( self, runs, hits ):
KalmanFilter.SetMeasurements( self, runs, hits )
totalE = sum( hit.State[-1] for hit in hits )
for i,hit in enumerate(hits):
self.Track.GetNode(i).ParticleEnergy = totalE
totalE -= hit.State[-1]
def TransportMatrix( self, index0, index1 ):
This = self.Track.GetNode(index0)
Other = self.Track.GetNode(index1)
state = This.Pstate.State if This.status < 2 else This.Fstate.State
tx = state[2]
ty = state[3]
dz = Other.running - This.running
ds = abs(dz) * ( tx**2 + ty**2 + 1 ) ** 0.5
F = Array.Identity( self.Sdim )
F[0][2] = dz
F[1][3] = dz
F[-1][-1] = self.Eloss( This.ParticleEnergy, ds ) / This.hit.State[-1]
return F
def MeasurementMatrix( self, index0, index1 ):
return Array.Matrix( [ 1., 0., 0., 0., 0. ],
[ 0., 1., 0., 0., 0. ],
[ 0., 0., 0., 0., 1. ])
def MultipleScatteringMatrix( self, index0, index1 ):
This = self.Track.GetNode(index0)
Other = self.Track.GetNode(index1)
dx, dy, tx, ty, e = This.Pstate.State
z0 = This.running
z02 = z0**2;
z1 = Other.running
dz = z1 - z0
ds = abs(dz) * ( tx**2 + ty**2 + 1 ) ** 0.5
L = ds / self.gas.x0
theta02 = thetaMS( K2P(This.ParticleEnergy) , L )**2
factor = theta02 * ( 1 + tx**2 + ty**2 )
p33 = factor * ( 1 + tx**2 )
p44 = factor * ( 1 + ty**2 )
p34 = factor * tx * ty
state = This.Pstate.State if This.status < 2 else This.Fstate.State
self.Eres2 = self.Eresolution**2 / state[-1]
return Array.Matrix( [ z02 * p33/3, z02 * p34/3, -z0 * p33/2, -z0 * p34/2, 0. ],
[ z02 * p34/3, z02 * p44/3, -z0 * p34/2, -z0 * p44/2, 0. ],
[ -z0 * p33/2, -z0 * p34/2, p33 , p34 , 0. ],
[ -z0 * p34/2, -z0 * p44/2, p34 , p44 , 0. ],
[ 0., 0., 0., 0. , self.Eres2 ])# * 10.
def NoiseMatrix( self, index ):
V = Array.Identity(self.Mdim) * self.xyres2
V[-1][-1] = self.Eresolution**2 / self.Track.GetNode(index).hit.State[-1]
return V
def Eloss( self, e0, ds ):
return _Eloss( e0 ) * ds
#class KFNEXT(KalmanFilter):
# '''
# State = ( x, y, tanx, tany, E )
# '''
#
# xyresolution = 0.1 # cm
# Eresolution = 0.5 # MeV
#
# xyres2 = xyresolution**2
# Eres2 = Eresolution**2
#
# def __init__( self, P = 15., T = 27. ): # MeV
# KalmanFilter.__init__( self, name = 'NEXT Kalman Filter' )
# self.gas = NEXT( P, T )
#
# def TransportMatrix( self, index0, index1 ):
# F = Array.Identity( self.Sdim )
# F[0][2] = F[1][3] = dz
# Prev = self.Track.GetNode(index0)
# This = self.Track.GetNode(index1)
# s = Prev.Fstate.Vector
# dz = (This.running - Prev.running)**2 * ( 1 + s[2]**2 +s[3]**2 ) * thetaMS( p, L )**2
#
# p3p3 = dz#...
#
# return
#
# def MeasurementMatrix( self, index0, index1 ):
# dz = self.Track.GetNode(index1).running - self.Track.GetNode(index0).running
# dz = - dz
# return Array.Matrix( [ 1., 0., dz, 0., 0. ],
# [ 0., 1., 0., dz, 0. ],
# [ 0., 0., 0., 0., 1. ])
#
# def MultipleScatteringMatrix( self, index ):
# z0 = self.Track.GetNode(index).running
# z02 = z0**2;
# edep = self.this_hit[-1]
# try:
# L = abs( self.Track.GetNode(index+1).running - z0 ) / self.gas.x0
# except:
# L = 1e3
#
# x0, y0, tx, ty, p = self.Pstate.State
# theta02 = thetaMS( p , L )**2
#
# factor = theta02 * ( 1 + tx**2 + ty**2 )
# p33 = factor * ( 1 + tx**2 )
# p44 = factor * ( 1 + ty**2 )
# p34 = factor * tx * ty
#
# return Array.Matrix( [ z02 * p33, z02 * p34, -z0 * p33, -z0 * p34 ],
# [ z02 * p34, z02 * p44, -z0 * p34, -z0 * p44 ],
# [ -z0 * p33, -z0 * p34, p33, p34 ],
# [ -z0 * p34, -z0 * p44, p34, p44 ])
#
# def NoiseMatrix( self, index ):
# return Array.Identity(2) * xyresolution**2
#
class TrigoKF( KalmanFilter ):
'''
State = ( x, y, tantheta, tanphi )
'''
Ndim = 4
xyresolution = 0.1 # cm
def __init__( self ):
KalmanFilter.__init__( self, name = 'Trigo Kalman Filter' )
def TransportMatrix( self, index ):
z = self.Track.GetNode(index).running
return Array.Matrix( [ 1., 0., z , 0. ],
[ 0., 1., z , 0. ],
[ 0., 0., 1., 0. ],
[ 0., 0., 0., 1. ])
def MeasurementMatrix( self, index ):
return Array.Matrix( [ 1., 0., 0., 0. ],
[ 0., 1., 0., 0. ])
def MultipleScatteringMatrix( self, index ):
return Array.Identity(4) * 1e-12
def NoiseMatrix( self, index ):
return Array.Identity(2) * self.xyresolution**2
if __name__ == '__main__':
import ROOT
R = ROOT.TRandom3(0)
V = Array.Identity(2) * 0.01
Nhits = 500
hits = [ Array.Vector( sin(0.01*i) + R.Gaus(0,.1), -cos(0.1*i) + R.Gaus(0,.1) ) for i in range(Nhits) ]
runnings = map( float, range(Nhits) )
measurements = [ KalmanData( h, V ) for h in hits ]
istate = Array.Vector( hits[0][0], hits[0][1], 0., 0. )
istate = Array.Vector( 0., 0., 0., 0. )
icvmatrix = Array.Identity(4) * 2
nextkf = NEXTKF()
nextkf = TrigoKF()
nextkf.SetMeasurements( runnings, measurements )
nextkf.SetInitialState( KalmanData( istate, icvmatrix ) )
track = nextkf.Fit()
p = track.Plot()
p3 = track.Plot3D()
cchi = ROOT.TCanvas()
chi2 = ROOT.TGraph()
chi2.SetMarkerStyle(20)
for i in range(Nhits):
chi2.SetPoint(i,i,track.GetNode(i).chi2)
chi2.Draw('AP')
raw_input()