def example1():
#
np.random.seed(47117)
nTry = 1000 #: number of tries
nLayer = 5 #: number of detector layers
print " Gbltst $Rev$ ", nTry, nLayer
start = time.clock()
# track direction
sinLambda = 0.3
cosLambda = math.sqrt(1.0 - sinLambda**2)
sinPhi = 0.
cosPhi = math.sqrt(1.0 - sinPhi**2)
# Curvilinear system: track direction T, U = Z x T / |Z x T|, V = T x U
tuvDir = np.array([[cosLambda * cosPhi, cosLambda * sinPhi, sinLambda], \
[-sinPhi, cosPhi, 0.], \
[-sinLambda * cosPhi, -sinLambda * sinPhi, cosLambda]])
# measurement resolution
measErr = np.array([0.001, 0.001]) # 10 mu
measPrec = 1.0 / measErr**2
# scattering error
scatErr = 0.001 # 1 mrad
# RMS of CurviLinear track parameters (Q/P, slopes, offsets)
clErr = np.array([0.001, -0.1, 0.2, -0.15, 0.25])
# precision matrix for external seed (in local system)
locSeed = None
seedLabel = 0 # label of point with seed
if seedLabel != 0:
print " external seed at label ", seedLabel
#
bfac = 0.2998 # Bz*c for Bz=1
step = 1.5 / cosLambda # constant steps in RPhi
#
Chi2Sum = 0.
NdfSum = 0
LostSum = 0.
#
binaryFile = open("milleBinaryISN.dat", "wb")
#
for iTry in range(nTry):
# generate (CurviLinear) track parameters
clNorm = np.random.normal(0., 1., 5)
clPar = clErr * clNorm
# covariance matrix
clCov = np.eye(5)
for i in range(5):
clCov[i, i] = clErr[i]**2
# arclength
s = 0.
# point-to-point jacobian (from previous point)
jacPointToPoint = np.eye(5)
# additional (local or global) derivatives
addDer = np.array([[1.0], [0.0]])
labGlobal = np.array([[4711], [4711]])
# create trajectory
traj = GblTrajectory(bfac != 0.)
# at previous point: transformation from local to curvilinear system
oldL2c = np.eye(5)
for iLayer in range(nLayer):
#print " layer ", iLayer
# measurement directions (J,K) from stereo angle
sinStereo = (0. if iLayer % 2 == 0 else 0.1)
cosStereo = math.sqrt(1.0 - sinStereo**2)
# measurement system: I, J ,K
ijkDir = np.array([[1., 0., 0.], \
[0., cosStereo, sinStereo], \
[0., -sinStereo, cosStereo]])
# local system: measurement or curvilinear
#local = gblMeasSystem(ijkDir, tuvDir)
local = gblCurviSystem(ijkDir, tuvDir)
# projections
proL2m = local.getTransLocalToMeas()
proL2c = local.getTransLocalToCurvi()
proC2l = np.linalg.inv(proL2c)
# projection curvilinear to measurement directions
proC2m = local.getTransCurviToMeas()
# measurement - prediction in measurement system with error
measNorm = np.random.normal(0., 1., 2)
meas = np.dot(proC2m, clPar[3:5]) + measErr * measNorm
# jacobian is calculated in curvilinear system and transformed
jac = np.dot(proC2l, np.dot(jacPointToPoint, oldL2c))
# point with (independent) measurements (in measurement system)
point = GblPoint(jac)
point.addMeasurement([proL2m, meas, measPrec])
# additional local parameters?
# point.addLocals(addDer)
# additional global parameters?
point.addGlobals(labGlobal, addDer)
addDer = -addDer # locDer flips sign every measurement
# add point to trajectory
iLabel = traj.addPoint(point)
if iLabel == abs(seedLabel):
clSeed = np.linalg.inv(clCov)
locSeed = np.dot(proL2c, np.dot(clSeed, proL2c.T))
# propagate to scatterer
jacPointToPoint = gblSimpleJacobian(step, cosLambda, bfac)
clPar = np.dot(jacPointToPoint, clPar)
clCov = np.dot(jacPointToPoint, np.dot(clCov, jacPointToPoint.T))
s += step
if (iLayer < nLayer - 1):
scat = np.array([0., 0.])
# point with scatterer
jac = np.dot(proC2l, np.dot(jacPointToPoint, proL2c))
point = GblPoint(jac)
if scatErr > 0:
scatP = local.getScatPrecision(scatErr)
point.addScatterer([scat, scatP])
iLabel = traj.addPoint(point)
if iLabel == abs(seedLabel):
clSeed = np.linalg.inv(clCov)
locSeed = np.dot(proL2c, np.dot(clSeed, proL2c.T))
# scatter a little
scatNorm = np.random.normal(0., 1., 2)
clPar[1:3] = clPar[1:3] + scatErr * scatNorm
# propagate to next measurement layer
clPar = np.dot(jacPointToPoint, clPar)
clCov = np.dot(jacPointToPoint, np.dot(clCov,
jacPointToPoint.T))
s += step
oldL2c = proL2c
# add external seed
if locSeed is not None:
traj.addExternalSeed(seedLabel, locSeed)
# fit trajectory
Chi2, Ndf, Lost = traj.fit()
print " Record, Chi2, Ndf, Lost", iTry, Chi2, Ndf, Lost
# dump trajectory
#traj.printPoints()
#traj.printData()
# write to MP binary file
# traj.milleOut(binaryFile)
# sum up
Chi2Sum += Chi2
NdfSum += Ndf
LostSum += Lost
# get corrections and covariance matrix at points
if (iTry == 0):
for i in range(1, nLayer + 1):
locPar, locCov = traj.getResults(-i)
print " >Point ", i
print " locPar ", locPar
#print " locCov ", locCov
locPar, locCov = traj.getResults(i)
print " Point> ", i
print " locPar ", locPar
#print " locCov ", locCov
# check residuals
for i in range(traj.getNumPoints()):
numData, aResiduals, aMeasErr, aResErr, aDownWeight = traj.getMeasResults(
i + 1)
for j in range(numData):
print " measRes ", i, j, aResiduals[j], aMeasErr[
j], aResErr[j], aDownWeight[j]
numData, aResiduals, aMeasErr, aResErr, aDownWeight = traj.getScatResults(
i + 1)
for j in range(numData):
print " scatRes ", i, j, aResiduals[j], aMeasErr[
j], aResErr[j], aDownWeight[j]
#
end = time.clock()
print " Time [s] ", end - start
print " Chi2Sum/NdfSum ", Chi2Sum / NdfSum
print " LostSum/nTry ", LostSum / nTry
def example1():
#
np.random.seed(47117)
nTry = 1000 #: number of tries
nLayer = 5 #: number of detector layers
print " Gbltst $Rev: 95 $ ", nTry, nLayer
start = time.clock()
# track direction
sinLambda = 0.3
cosLambda = math.sqrt(1.0 - sinLambda ** 2)
sinPhi = 0.
cosPhi = math.sqrt(1.0 - sinPhi ** 2)
# Curvilinear system: track direction T, U = Z x T / |Z x T|, V = T x U
tuvDir = np.array([[cosLambda * cosPhi, cosLambda * sinPhi, sinLambda], \
[-sinPhi, cosPhi, 0.], \
[-sinLambda * cosPhi, -sinLambda * sinPhi, cosLambda]])
# measurement resolution
measErr = np.array([ 0.001, 0.001]) # 10 mu
measPrec = 1.0 / measErr ** 2
# scattering error
scatErr = 0.001 # 1 mread
# RMS of CurviLinear track parameters (Q/P, slopes, offsets)
clErr = np.array([0.001, -0.1, 0.2, -0.15, 0.25])
# precision matrix for external seed (in local system)
locSeed = None
seedLabel = 0 # label of point with seed
if seedLabel != 0:
print " external seed at label ", seedLabel
#
bfac = 0.2998 # Bz*c for Bz=1
step = 1.5 / cosLambda # constant steps in RPhi
#
Chi2Sum = 0.
NdfSum = 0
LostSum = 0.
#
binaryFile = open("milleBinaryISN.dat", "wb")
#
for iTry in range(nTry):
# generate (CurviLinear) track parameters
clNorm = np.random.normal(0., 1., 5)
clPar = clErr * clNorm
# covariance matrix
clCov = np.eye(5)
for i in range(5):
clCov[i, i] = clErr[i] ** 2
# arclength
s = 0.
# point-to-point jacobian (from previous point)
jacPointToPoint = np.eye(5)
# additional (local or global) derivatives
addDer = np.array([[1.0], [0.0]])
labGlobal = np.array([[4711], [4711]])
# create trajectory
traj = GblTrajectory(bfac != 0.)
# at previous point: transformation from local to curvilinear system
oldL2c = np.eye(5)
for iLayer in range(nLayer):
#print " layer ", iLayer
# measurement directions (J,K) from stereo angle
sinStereo = (0. if iLayer % 2 == 0 else 0.1)
cosStereo = math.sqrt(1.0 - sinStereo ** 2)
# measurement system: I, J ,K
ijkDir = np.array([[1., 0., 0.], \
[0., cosStereo, sinStereo], \
[0., -sinStereo, cosStereo]])
# local system: measurement or curvilinear
#local = gblMeasSystem(ijkDir, tuvDir)
local = gblCurviSystem(ijkDir, tuvDir)
# projections
proL2m = local.getTransLocalToMeas()
proL2c = local.getTransLocalToCurvi()
proC2l = np.linalg.inv(proL2c)
# projection curvilinear to measurement directions
proC2m = local.getTransCurviToMeas()
# measurement - prediction in measurement system with error
measNorm = np.random.normal(0., 1., 2)
meas = np.dot(proC2m, clPar[3:5]) + measErr * measNorm
# jacobian is calculated in curvilinear system and transformed
jac = np.dot(proC2l, np.dot(jacPointToPoint, oldL2c))
# point with (independent) measurements (in measurement system)
point = GblPoint(jac)
point.addMeasurement([proL2m, meas, measPrec])
# additional local parameters?
# point.addLocals(addDer)
# additional global parameters?
point.addGlobals(labGlobal, addDer)
addDer = -addDer # locDer flips sign every measurement
# add point to trajectory
iLabel = traj.addPoint(point)
if iLabel == abs(seedLabel):
clSeed = np.linalg.inv(clCov)
locSeed = np.dot(proL2c, np.dot(clSeed, proL2c.T))
# propagate to scatterer
jacPointToPoint = gblSimpleJacobian(step, cosLambda, bfac)
clPar = np.dot(jacPointToPoint, clPar)
clCov = np.dot(jacPointToPoint, np.dot(clCov, jacPointToPoint.T))
s += step
if (iLayer < nLayer - 1):
scat = np.array([0., 0.])
# point with scatterer
jac = np.dot(proC2l, np.dot(jacPointToPoint, proL2c))
point = GblPoint(jac)
scatP = local.getScatPrecision(scatErr)
point.addScatterer([scat, scatP])
iLabel = traj.addPoint(point)
if iLabel == abs(seedLabel):
clSeed = np.linalg.inv(clCov)
locSeed = np.dot(proL2c, np.dot(clSeed, proL2c.T))
# scatter a little
scatNorm = np.random.normal(0., 1., 2)
clPar[1:3] = clPar[1:3] + scatErr * scatNorm
# propagate to next measurement layer
clPar = np.dot(jacPointToPoint, clPar)
clCov = np.dot(jacPointToPoint, np.dot(clCov, jacPointToPoint.T))
s += step
oldL2c = proL2c
# add external seed
if locSeed is not None:
traj.addExternalSeed(seedLabel, locSeed)
# dump trajectory
# traj.dump()
# fit trajectory
Chi2, Ndf, Lost = traj.fit()
print " Record, Chi2, Ndf, Lost", iTry, Chi2, Ndf, Lost
# write to MP binary file
# traj.milleOut(binaryFile)
# sum up
Chi2Sum += Chi2
NdfSum += Ndf
LostSum += Lost
# get corrections and covariance matrix at points
if (iTry == 0):
for i in range(1, nLayer + 1):
locPar, locCov = traj.getResults(-i)
print " >Point ", i
print " locPar ", locPar
#print " locCov ", locCov
locPar, locCov = traj.getResults(i)
print " Point> ", i
print " locPar ", locPar
#print " locCov ", locCov
# check residuals
for i in range(traj.getNumPoints()):
numData, aResiduals, aMeasErr, aResErr, aDownWeight = traj.getMeasResults(i + 1)
for j in range(numData):
print " measRes " , i, j, aResiduals[j], aMeasErr[j], aResErr[j], aDownWeight[j]
numData, aResiduals, aMeasErr, aResErr, aDownWeight = traj.getScatResults(i + 1)
for j in range(numData):
print " scatRes " , i, j, aResiduals[j], aMeasErr[j], aResErr[j], aDownWeight[j]
#
end = time.clock()
print " Time [s] ", end - start
print " Chi2Sum/NdfSum ", Chi2Sum / NdfSum
print " LostSum/nTry ", LostSum / nTry
def example1():
'''
Create points on initial trajectory, create trajectory from points,
fit and write trajectory to MP-II binary file,
get track parameter corrections and covariance matrix at points.
Equidistant measurement layers and thin scatterers, propagation
with simple jacobian (quadratic in arc length differences).
Curvilinear system (U,V,T) as local coordinate system.
'''
def gblSimpleJacobian(ds, cosl, bfac):
'''
Simple jacobian: quadratic in arc length difference.
@param ds: arc length difference
@type ds: float
@param cosl: cos(lambda)
@type cosl: float
@param bfac: Bz*c
@type bfac: float
@return: jacobian to move by 'ds' on trajectory
@rtype: matrix(float)
'''
jac = np.eye(5)
jac[1, 0] = -bfac * ds * cosl
jac[3, 0] = -0.5 * bfac * ds * ds * cosl
jac[3, 1] = ds
jac[4, 2] = ds
return jac
#
np.random.seed(47117)
nTry = 1000 #: number of tries
nLayer = 5 #: number of detector layers
print " Gbltst $Rev: 234 $ ", nTry, nLayer
start = time.clock()
# track direction
sinLambda = 0.3
cosLambda = math.sqrt(1.0 - sinLambda ** 2)
sinPhi = 0.
cosPhi = math.sqrt(1.0 - sinPhi ** 2)
# tDir = np.array([cosLambda * cosPhi, cosLambda * sinPhi, sinLambda])
# U = Z x T / |Z x T|, V = T x U
uvDir = np.array([[-sinPhi, cosPhi, 0.], \
[-sinLambda * cosPhi, -sinLambda * sinPhi, cosLambda]])
# measurement resolution
measErr = np.array([ 0.001, 0.001]) # 10 mu
measPrec = 1.0 / measErr ** 2
# scattering error
scatErr = np.array([ 0.001, 0.001]) # 1 mread
scatPrec = 1.0 / scatErr ** 2
# RMS of CurviLinear track parameters (Q/P, slopes, offsets)
clErr = np.array([0.001, -0.1, 0.2, -0.15, 0.25])
clSeed = None
seedLabel = 0 # label of point with seed
if seedLabel != 0:
print " external seed at label ", seedLabel
#
bfac = 0.2998 # Bz*c for Bz=1
step = 1.5 / cosLambda # constant steps in RPhi
#
Chi2Sum = 0.
NdfSum = 0
LostSum = 0.
#
binaryFile = open("milleBinaryISN.dat", "wb")
#
for iTry in range(nTry):
# generate (CurviLinear) track parameters
clNorm = np.random.normal(0., 1., 5)
clPar = clErr * clNorm
# covariance matrix
clCov = np.eye(5)
for i in range(5):
clCov[i, i] = clErr[i] ** 2
# arclength
s = 0.
sPoint = []
# point-to-point jacobian (from previous point)
jacPointToPoint = np.eye(5)
# additional (local or global) derivatives
addDer = np.array([[1.0], [0.0]])
labGlobal = np.array([[4711], [4711]])
# create trajectory
traj = GblTrajectory(bfac != 0.)
for iLayer in range(nLayer):
# measurement directions
sinStereo = (0. if iLayer % 2 == 0 else 0.5)
cosStereo = math.sqrt(1.0 - sinStereo ** 2)
mDir = np.array([[sinStereo, cosStereo, 0.0], [0., 0, 1.]])
# projection measurement to local (curvilinear uv) directions (duv/dm)
proM2l = np.dot(uvDir, mDir.T)
# projection local (uv) to measurement directions (dm/duv)
proL2m = np.linalg.inv(proM2l)
# measurement - prediction in measurement system with error
measNorm = np.random.normal(0., 1., 2)
meas = np.dot(proL2m, clPar[3:5]) + measErr * measNorm
# point with measurement
point = GblPoint(jacPointToPoint)
point.addMeasurement([proL2m, meas, measPrec])
# additional local parameters?
# point.addLocals(addDer)
# additional global parameters?
point.addGlobals(labGlobal, addDer)
addDer = -addDer # locDer flips sign every measurement
# add point to trajectory
iLabel = traj.addPoint(point)
sPoint.append(s)
if iLabel == abs(seedLabel):
clSeed = np.linalg.inv(clCov)
# propagate to scatterer
jacPointToPoint = gblSimpleJacobian(step, cosLambda, bfac)
clPar = np.dot(jacPointToPoint, clPar)
clCov = np.dot(jacPointToPoint, np.dot(clCov, jacPointToPoint.T))
s += step
if (iLayer < nLayer - 1):
scat = np.array([0., 0.])
# point with scatterer
point = GblPoint(jacPointToPoint)
point.addScatterer([scat, scatPrec])
iLabel = traj.addPoint(point)
sPoint.append(s)
if iLabel == abs(seedLabel):
clSeed = np.linalg.inv(clCov)
# scatter a little
scatNorm = np.random.normal(0., 1., 2)
clPar[1:3] = clPar[1:3] + scatErr * scatNorm
# propagate to next measurement layer
clPar = np.dot(jacPointToPoint, clPar)
clCov = np.dot(jacPointToPoint, np.dot(clCov, jacPointToPoint.T))
s += step
# add external seed
if clSeed is not None:
traj.addExternalSeed(seedLabel, clSeed)
# dump trajectory
# traj.dump()
# fit trajectory
Chi2, Ndf, Lost = traj.fit()
print " Record, Chi2, Ndf, Lost", iTry, Chi2, Ndf, Lost
# write to MP binary file
# traj.milleOut(binaryFile)
# sum up
Chi2Sum += Chi2
NdfSum += Ndf
LostSum += Lost
# get corrections and covariance matrix at points
if (iTry == 0):
for i in range(1, 1):
locPar, locCov = traj.getResults(i)
print " Point< ", i
print " locPar ", locPar
print " locCov ", locCov
locPar, locCov = traj.getResults(-i)
print " Point> ", i
print " locPar ", locPar
print " locCov ", locCov
#
end = time.clock()
print " Time [s] ", end - start
print " Chi2Sum/NdfSum ", Chi2Sum / NdfSum
print " LostSum/nTry ", LostSum / nTry
