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mk3_calibration.py
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#!/usr/bin/env python
import numpy as np
import pickle
import itertools
import pylab
import os
from scipy.optimize import minimize
def get_rotation_matrix(axis, angle):
rads = np.radians(angle)
cosa = np.cos(rads)
sina = np.sin(rads)
I = np.diag([1]*3)
rotation_matrix = I * cosa + axis['mT'] * (1-cosa) + axis['mC'] * sina
return rotation_matrix
def get_axis(direction, position):
axis = {}
d = np.array(direction)
p = np.array(position)
axis['direction'] = d
axis['position'] = p
axis['mT'] = get_mT(direction)
axis['mC'] = get_mC(direction)
return axis
def get_mC(direction):
mC = np.array([[ 0.0, -direction[2], direction[1]],
[ direction[2], 0.0, -direction[0]],
[-direction[1], direction[0], 0.0]])
return mC
def get_mT(direction):
mT = np.outer(direction, direction)
return mT
def get_shift(kappa_axis, phi_axis, kappa1, phi1, x, kappa2, phi2):
tk = kappa_axis['position']
tp = phi_axis['position']
Rk2 = get_rotation_matrix(kappa_axis, kappa2)
Rk1 = get_rotation_matrix(kappa_axis, -kappa1)
Rp = get_rotation_matrix(phi_axis, phi2-phi1)
a = tk - np.dot(Rk1, (tk-x))
b = tp - np.dot(Rp, (tp-a))
shift = tk - np.dot(Rk2, (tk-b))
return shift
def get_align_vector(t1, t2, kappa, phi, kappa_axis, phi_axis, align_direction):
t1 = np.array(t1)
t2 = np.array(t2)
x = t1 - t2
Rk = get_rotation_matrix(kappa_axis, -kappa)
Rp = get_rotation_matrix(phi_axis, -phi)
x = np.dot(Rp, np.dot(Rk, x))/np.linalg.norm(x)
c = np.dot(phi_axis['direction'], x)
if c < 0.:
c = -c
x = -x
cos2a = pow(np.dot(kappa_axis[direction], align_direction), 2)
d = (c - cos2a)/(1 - cos2a)
if abs(d) > 1.:
new_kappa = 180.
else:
new_kappa = np.degrees(np.arccos(d))
Rk = get_rotation_matrix(kappa_axis, new_kappa)
pp = np.dot(Rk, phi_axis['direction'])
xp = np.dot(Rk, x)
d1 = align_direction - c*pp
d2 = xp - c*pp
new_phi = np.degrees(np.arccos(np.dot(d1, d2)/np.linalg.norm(d1)/np.linalg.norm(d2)))
newaxis = {}
newaxis['mT'] = get_mT(pp)
newaxis['mC'] = get_mC(pp)
Rp = get_rotation_matrix(newaxis, new_phi)
d = np.abs(np.dot(align_direction, np.dot(Rp, xp)))
check = np.abs(np.dot(align_direction, np.dot(xp, Rp)))
if check > d:
new_phi = -new_phi
shift = get_shift(kappa_axis, phi_axis, kappa, phi, 0.5*(t1 + t2), new_kappa, new_phi)
align_vector = new_kappa, new_phi, shift
return align_vector
def shift_error(parameters, x0, kappa, phi, observation):
#kappa_direction = np.array(list(parameters[: 2]) + [-0.913545])
#kappa_position = parameters[2: 5]
#phi_direction = parameters[5: 8]
#phi_position = parameters[8:]
kappa_direction = parameters[:3] #[0.29636375, 0.29377944, -0.913545]
kappa_position = parameters[3: 6]
phi_direction = parameters[6: 9] #[0, 0, -1]
phi_position = parameters[9:]
kappa_axis = get_axis(kappa_direction, kappa_position)
phi_axis = get_axis(phi_direction, phi_position)
model = np.array([get_shift(kappa_axis, phi_axis, 0., 0., x0, k, p) for k, p in zip(kappa, phi)])
error = np.sum((model-observation)**2)
return error
def main():
import optparse
import random
parser = optparse.OptionParser()
parser.add_option('-r', '--results', default='MK3/mkc.pickle', type=str)
options, args = parser.parse_args()
#kappa_axis = get_axis([0.282543, 0.2925819, -0.913545], [-0.499986, -0.2591313, 0.484796])
kappa_axis = get_axis([0.28579375, 0.29825935, -0.91069766], [0.06054262, -0.17344149, -0.39538791])
#phi_axis = get_axis([0, 0, -1], [-0.316151, -0.039378, 0.4179955])
phi_axis = get_axis([0, 0, -1], [0.22284277, -0.03217082, -2.03321131])
align_direction = np.array([0, 0, -1])
# x = [cx, cy, ay]
#print('get_shift(kappa, phi, 0, 0., np.array([0.1, 0.5, 0.3]), 15., 25.)')
#print(get_shift(kappa, phi, 0, 0., np.array([0.1, 0.5, 0.3]), 15., 25.))
mkc = pickle.load(open(options.results, 'rb'))
mkc = list(mkc)
mkc.sort(key=lambda x: (x[-2], x[-1]))
mkc = np.array(mkc)
observation = mkc[:, [3, 4, 1]]
kappas = mkc[:, -2]
phis = mkc[:, -1]
x0 = mkc[0, [3, 4, 1]]
#initial_parameters = [-0.30655466, -0.3570731, 0.52893628, -0.0942107, 0.15449601, 0.36023525]
#initial_parameters = [0.29636375, 0.29377944, -0.499986, -0.2591313, 0.484796, 0, 0, -1, -0.316151, -0.039378, 0.4179955]
initial_parameters = [0.282543, 0.2925819, -0.913545, -0.499986, -0.2591313, 0.484796, 0, 0, -1, -0.316151, -0.039378, 0.4179955]
initial_parameters = [0.28579375, 0.29825935, -0.91069766,
0.06054262, -0.17344149, -0.39538791,
#0.04804586, -0.00507483, -1.01343307,
0, 0, -1,
0.22284277, -0.03217082, -2.03321131]
#initial_parameters = [random.random() for k in range(12)]
#initial_parameters = [ 0.31377822, 0.30374482, -0.913545, -0.47170958, -0.66398839, 0.37447831, 0, 0, -1, -0.02065501, -0.15673108, 0.40641754]
#initial_parameters =[random.random() for k in range(11)] # [-0.30655466, -0.3570731, 0.52893628, -0.0942107, 0.15449601, 0.36023525]
fit = minimize(shift_error, initial_parameters, args=(x0, kappas, phis, observation))
parameters = fit.x
print('fit results')
print(list(parameters))
#parameters = np.array([ 0.29636375, 0.29377944, -0.90992064, -0.30655466, -0.3570731, 0.52893628, 0.03149443, 0.03216924, -0.99469729, -0.01467116, -0.08069945, 0.46818622])
#kappa_direction = np.array(list(parameters[: 2]) + [-0.913545])
#kappa_position = parameters[2: 5]
#phi_direction = parameters[5: 8]
#phi_position = parameters[8:]
kappa_direction = parameters[: 3]
kappa_position = parameters[3: 6]
phi_direction = parameters[6: 9]
phi_position = parameters[9:]
print('kappa_direction=%s' % str(list(kappa_direction)))
print('kappa_position=%s' % str(list(kappa_position)))
print('phi_direction=%s' % str(list(phi_direction)))
print('phi_position=%s' % str(list(phi_position)))
kappa_axis = get_axis(kappa_direction, kappa_position)
phi_axis = get_axis(phi_direction, phi_position)
#kp = list(zip(kappas, phis))
#kp.sort()
shifts = np.array([get_shift(kappa_axis, phi_axis, 0., 0., x0, kappa, phi) for kappa, phi in zip(kappas, phis)])
kappas_model = np.linspace(0, 240, 49)
phis_model = np.linspace(0, 360, 73)
shifts_model = np.array([get_shift(kappa_axis, phi_axis, 0., 0., x0, kappa, phi) for kappa, phi in zip(kappas_model, phis_model)])
print('model errors')
print('cx, cy, ay')
print(np.mean(np.abs(shifts - observation), axis=0))
print('standard deviations')
print(np.std(shifts - observation, axis=0))
pylab.figure(figsize=(16, 9))
pylab.plot(shifts[:,0], 'o-', label='cx model')
pylab.plot(shifts[:,1], 'o-', label='cy model')
pylab.plot(shifts[:,2], 'o-', label='ay model')
pylab.plot(mkc[:, 3], 'o', label='cx experiment')
pylab.plot(mkc[:, 4], 'o', label='cy experiment')
pylab.plot(mkc[:, 1], 'o', label='ay experiment')
pylab.title(os.path.basename(options.results.replace('.pickle', '')))
pylab.legend()
pylab.savefig(options.results.replace('.pickle', '.png'))
pylab.show()
if __name__ == '__main__':
main()