'''

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

'''

Read trajectory from MP-II binary file and refit.

'''

#

binaryFile = open("milleBinaryISN.dat", "rb")

nRec = 0

maxRec = 10 #: maximum number of records to read

Chi2Sum = 0.

NdfSum = 0

LostSum = 0.

start = time.clock()

try:

while(nRec < maxRec):

# create trajectory

traj = GblTrajectory(0)

# read from file

traj.milleIn(binaryFile) # get data blocks from file

nRec += 1

# fit trajectory

Chi2, Ndf, Lost = traj.fit()

print " Record, Chi2, Ndf, Lost", nRec, Chi2, Ndf, Lost

# sum up

Chi2Sum += Chi2

NdfSum += Ndf

LostSum += Lost

except EOFError:

pass

print " records read ", nRec

end = time.clock()

print " Time [s] ", end - start

print " Chi2Sum/NdfSum ", Chi2Sum / NdfSum

'''

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.

Detector arrangement according to HPS test setup 2012, B=0.

'''

def gblSimpleJacobian(ds, cosl, bfac):

'''

Simple jacobian: quadratic in arc length difference (parabola instead of circle),

assuming constant magnetic field in Z direction.

@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 = 10 #: number of detector layers

# positions (perpendicular to detector plane)

positions = [88., 95., 188., 195., 288., 295., 488., 495., 688., 695.]

# stereo angles

angles = [0., 0.005, 0., 0.005, 0., 0.005, 0., 0.01, 0., 0.01 ]

# misalignment in measurement direction

deltaU = [0., 0., 0.0, 0.00, 0., 0., 0., 0., 0., 0.]

print " GblHpsTest $Rev: 234 $ ", nTry, nLayer

start = time.clock()

# track direction: in x direction

sinLambda = 0.

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([ 0.006, 0.006]) # 6 mu

measPrec = 1.0 / measErr ** 2

measPrec[1] = 0.0 # only 1D measurement (perpendicular to strip direction)

# scattering error

scatErr = np.array([ 0.000070, 0.000070]) # 70 micro-rad

scatPrec = 1.0 / scatErr ** 2

# RMS of track parameters

clErr = np.array([0.001, 0.05, 0.05, 1., 1.])

clSeed = np.eye(5)

for i in range(5):

clSeed[i, i] = 1.0 / clErr[i] ** 2

#

bfac = 0.#2998 # Bz*c for Bz=1 (units:MeV, T, mm)

#

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

# 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):

# step

step = positions[iLayer] / cosLambda - s

prop = np.array([[1., step], [0., 1.]])

#print " layer ", iLayer, step, varMs

# measurement directions (in YZ plane: perpendicular/parallel to strip direction)

sinStereo = angles[iLayer]

cosStereo = math.sqrt(1.0 - sinStereo ** 2)

mDir = np.array([[0., sinStereo, cosStereo], [0., cosStereo, -sinStereo]])

# 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

meas[0] += deltaU[iLayer] # misalignment

# point with measurement

#measPrec[0] = 1.0 / (varMs[0][0] + measErr[0] * measErr[0])

point = GblPoint(jacPointToPoint)

point.addMeasurement([proL2m, meas, measPrec])

# point with scatterer

scat = np.array([0., 0.])

point.addScatterer([scat, scatPrec])

# scatter a little

scatNorm = np.random.normal(0., 1., 2)

clPar[1:3] = clPar[1:3] + scatErr * scatNorm

# additional global parameters?

addDer = np.array([[1.0], [0.0]])

labGlobal = np.array([[11101 + iLayer], [0]])

point.addGlobals(labGlobal, addDer)

# add point to trajectory

iLabel = traj.addPoint(point)

sPoint.append(s)

# propagate to scatterer

jacPointToPoint = gblSimpleJacobian(step, cosLambda, bfac)

clPar = np.dot(jacPointToPoint, clPar)

s += step

# add external seed

# traj.addExternalSeed(1, 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

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