def motion_model(particle_poses, speed_command, odom_pose, odom_pose_prev, dt):
"""Apply motion model and return updated array of particle_poses.
Parameters
----------
particle_poses: an M x 3 array of particle_poses where M is the
number of particles. Each pose is (x, y, theta) where x and y are
in metres and theta is in radians.
speed_command: a two element array of the current commanded speed
vector, (v, omega), where v is the forward speed in m/s and omega
is the angular speed in rad/s.
odom_pose: the current local odometry pose (x, y, theta).
odom_pose_prev: the previous local odometry pose (x, y, theta).
dt is the time step (s).
Returns
-------
An M x 3 array of updated particle_poses.
"""
M = particle_poses.shape[0]
# Robot Trajectory between poses.
trajectory = arctan2((odom_pose[1] - odom_pose_prev[1]), (odom_pose[0] - odom_pose_prev[0]))
# Pose variables.
d = sqrt(((odom_pose[1] - odom_pose_prev[1]) ** 2) + ((odom_pose[0] - odom_pose_prev[0]) ** 2))
phi_1_local = angle_difference(odom_pose_prev[2], trajectory)
phi_2_local = angle_difference(odom_pose[2], trajectory)
# Calculate difference between poses.
difference_x = d * cos(odom_pose[2] + phi_1_local) # First column is x.
difference_y = d * sin(odom_pose[2] + phi_1_local) # Second column is y.
difference_theta = wraptopi(phi_1_local + phi_2_local) # Third colum is theta.
# Assign gaussian noise values.
mu_x = 0
sigma_x = 0.01
mu_y = 0
sigma_y = 0.008
mu_theta = 0
sigma_theta = 0.0007
# Update particle poses.
for m in range(M):
particle_poses[m, 0] += difference_x + mu_x + randn() * sigma_x # First column is x.
particle_poses[m, 1] += difference_y + mu_y + randn() * sigma_y # Second column is y.
particle_poses[m, 2] = wraptopi((particle_poses[m, 2] + difference_theta) + mu_theta + randn() * sigma_theta) # Third colum is theta.
return particle_poses
def predict_angles(pdb_path, resolution, A):
"""
Predict the tilt angle at which each reflection will be observed. Here a positive
tilt angle corresponds to images with a +y coordinate. Reflections that lie in the
missing wedge are excluded.
Inputs:
-------
pdb_path: path to reference PDB file
resolution: high-resolution limit of structure factors
A: crystal setting matrix
Outputs:
--------
hkl_t: dict with keys as Millers and values as tilt angles
"""
# predict coordinates of all reflections in reciprocal pixels
sg_symbol, sg_no, cell, cs = cctbx_utils.unit_cell_info(pdb_path)
hkl = np.array(
miller.build_set(crystal_symmetry=cs,
anomalous_flag=True,
d_min=resolution).expand_to_p1().indices())
qvecs = np.inner(A, np.squeeze(hkl)).T
# predict tilt angle from associated coordinates
t = np.rad2deg(np.arctan2(qvecs[:, 1], qvecs[:, 0]))
t[(t > 90) & (t <= 180)] = utils.wraptopi(t[(t > 90) & (t < 180)] +
180.0) # shift q2 to q4
t[(t >= -180) & (t <= -90)] += 180.0 # shift q3 to q1
# generate a dict with keys as Millers and values as tilt angles
hkl_t = OrderedDict((tuple(key), val) for key, val in zip(hkl, t))
return hkl_t
def add_phase_errors(hklp, sigma, friedels_same=True):
"""
Add phase errors drawn from a normal distribution, N(mu, sigma), to the data
in hklp. Parameters and data should be in degrees. Note that mu is set to 0,
as this corresponds to a global phase shift.
Inputs:
-------
hklp: dict whose keys are Millers and values are phases in degrees
sigma: standard deviation of error normal distribution
friedels_same: force phase relationship between Friedel mates, boolean
Outputs:
--------
hklp_error: dict whose keys are Millers and values are phases with errors
"""
# draw errors from a normal distribution and add to phases
errors = sigma * np.random.randn(len(hklp.keys()))
p_errors = utils.wraptopi(np.array(hklp.values()) + errors)
hklp_error = OrderedDict(
(key, val) for key, val in zip(hklp.keys(), p_errors))
# force phase relationship between Friedel mates
if friedels_same is True:
for key in hklp_error:
fkey = (-1 * key[0], -1 * key[1], -1 * key[2])
if fkey in hklp_error.keys():
hklp_error[fkey] = -1 * hklp_error[key]
return hklp_error
def initial_errors(hklp, refp, shifts):
"""
Compute the starting phase errors to reference; output metrics are sigma
of the normal distribution and mean of phase errors to reference.
Inputs:
-------
hklp: dict with Millers as keys and values as phases
refp: dict with Millers as keys and values as reference phases
shifts: fractional shifts that reposition hklp on reference phase origin
Outputs:
--------
sigma: variance of normal distribution fit to phase residuals to reference
m_error: mean of phase residuals to reference
"""
# shift phases back to reference origin
hkl, p = np.array(hklp.keys()), np.array(hklp.values())
p_unshift = utils.wraptopi(p + 360 * np.dot(hkl, shifts).ravel())
# remove Friedel mates from the shifted phases and compute error metrics
hkl_sel = utils.remove_Friedels(hklp.keys())
hklp_unshift = OrderedDict((key, val)
for key, val in zip(hklp.keys(), p_unshift)
if key in hkl_sel)
sigma, m_error = utils.residual_phase_distribution(refp, hklp_unshift)
return sigma, m_error
def transition(self, v, omega, dt=0.1):
from numpy import sin, cos
hp = self.heading
if omega == 0.0:
self.x += v * cos(hp) * dt
self.y += v * sin(hp) * dt
else:
self.x += -v / omega * sin(hp) + v / omega * sin(hp + omega * dt)
self.y += v / omega * cos(hp) - v / omega * cos(hp + omega * dt)
self.heading = wraptopi(hp + omega * dt)
def test_wraptopi():
"""
Confirming that utils.wraptopi yields same results as Matlab's wrapTo180 function,
except that former wraps to domain [-180,180) rather than [-180,180] as in Matlab.
See: https://www.mathworks.com/help/map/ref/wrapto180.html for more details.
"""
x = np.array([-400, -190, -180, -175, 175, 180, 190, 380]).astype(float)
xw = np.array([-40, 170, -180, -175, 175, 180, -170, 20]).astype(float)
xw[xw == 180] = -180
yw = utils.wraptopi(x)
np.testing.assert_array_almost_equal(yw, xw)
return
def motion_model(poses, command_prev, odom_pose, odom_pose_prev):
"""Apply motion model and return updated array of poses.
Parameters
----------
poses: an M x 3 array of robot poses where M is the number of
particles. Each pose is (x, y, theta) where x and y are in metres
and theta is in radians.
command: a two element array of the current commanded speed
vector, (v, omega), where v is the forward speed in m/s and omega
is the angular speed in rad/s.
odom_pose: the current local odometry pose (x, y, theta).
odom_pose_prev: the previous local odometry pose (x, y, theta).
Returns
-------
An M x 3 array of updated poses.
"""
M = poses.shape[0]
# For each particle calculate its predicted pose plus some
# additive error to represent the process noise.
# Odometry model pose change parameterisation
phi_1 = np.arctan2((odom_pose[1] - odom_pose_prev[1]),
(odom_pose[0] - odom_pose_prev[0])) - odom_pose_prev[2],
phi_2 = wraptopi(odom_pose[2] - odom_pose_prev[2] - phi_1)
distance = np.sqrt((odom_pose[1] - odom_pose_prev[1])**2 +
(odom_pose[0] - odom_pose_prev[0])**2)
# Adding randomly sampled noise as s
mu, sigma = 0, 0.02 # mean and standard deviation
s = np.random.normal(mu, sigma, len(poses))
# Updating poses
poses[:,
0] = poses[:, 0] + distance * np.cos(poses[:, 2] +
phi_1) + s #odom_pose_prev[2]
poses[:,
1] = poses[:, 1] + distance * np.sin(poses[:, 2] +
phi_1) + s #odom_pose_prev[2]
poses[:, 2] = poses[:, 2] + phi_1 + phi_2 + s
return poses
def test_average_phases():
"""
Confirming that mean of circular data is correctly computed by utils.average_phases.
Comparison is to scipy.stats.circmean function, but this doesn't have the option of
computing the weighted mean.
"""
p_vals = (np.random.rand(10) - 0.5) * 360.0
p_ref = scipy.stats.circmean(np.deg2rad(p_vals),
low=-1 * np.pi,
high=np.pi)
p_ref = utils.wraptopi(np.array(np.rad2deg(p_ref)))
p_est = utils.average_phases(p_vals)
np.testing.assert_allclose(p_ref, p_est)
return
def test_std_phases():
"""
Compare utils.std_phases to the output of scipy.stats.circmean. Note that the results
diverge when the phases are randomly distributed over the unit circle, but match well
when the range is not too large. Here it's checked that for phases randomly drawn from
a domain of 45 degrees, the two functions match to within 1%.
"""
p_domain = 45.0
p_vals = (np.random.rand(10) - 0.5) * p_domain + np.random.randint(
-180, 180)
p_vals = utils.wraptopi(p_vals)
p_ref = np.rad2deg(scipy.stats.circstd(np.deg2rad(p_vals)))
p_est = utils.std_phases(p_vals)
assert np.abs(p_est - p_ref) / p_ref * 100.0 < 1.0
return
def test_reduce_crystals():
import ProcessCrystals as proc
# set up paths and default values
pdb_path, res = "./reference/pdb_files/4bfh.pdb", 3.0
sg_symbol, sg_no, cell, cs = cctbx_utils.unit_cell_info(pdb_path)
refI, refp = cctbx_utils.reference_sf(pdb_path,
res,
expand_to_p1=True,
table='electron')
refI_mod = OrderedDict((key, np.array([val])) for key, val in refI.items())
refp_mod = OrderedDict((key, np.array([val])) for key, val in refp.items())
# check that reduced phases are internally consistent
rc = proc.ReduceCrystals(refI_mod, refp_mod, cell, sg_symbol)
p_asu = rc.reduce_phases(weighted=True)
rc.reduce_intensities()
eq = np.array([np.allclose(v, v[0]) for v in p_asu.values()])
assert all([
np.allclose(np.around(p_asu.values()[i]) % 180, 0)
for i in np.where(eq == False)[0]
])
# check that reduced phases and intensities match reference
hkl_asu = list(
cs.build_miller_set(anomalous_flag=False, d_min=res).indices())
assert np.allclose(
utils.wraptopi(
np.array([rc.data['PHIB'][hkl] - refp[hkl] for hkl in hkl_asu])),
0)
assert np.allclose(
np.array([rc.data['IMEAN'][hkl] - refI[hkl] for hkl in hkl_asu]), 0)
# check that shifting phases from origin leads to loss of symmetry-expected relationships
rc.shift_phases(np.random.random(3))
p_asu = rc.reduce_phases(weighted=True)
eq = np.array([np.allclose(v, v[0]) for v in p_asu.values()])
assert not all([
np.allclose(np.around(p_asu.values()[i]) % 180, 0)
for i in np.where(eq == False)[0]
])
return
def predict_angles(specs_path, pdb_path, resolution, A):
"""
Predict the tilt angle at which each reflection will be observed. Here a positive
tilt angle corresponds to images with a +y coordinate. Reflections that lie in the
missing wedge are excluded.
Inputs:
-------
specs_path: dict specifying details of data collection strategy
pdb_path: path to reference PDB file
resolution: high-resolution limit of structure factors
A: crystal setting matrix
Outputs:
--------
hkl_t: dict with keys as Millers and values as tilt angles
"""
# load information about collection strategy
specs = pickle.load(open(specs_path))
# predict coordinates of all reflections in reciprocal pixels
sg_symbol, sg_no, cell, cs = cctbx_utils.unit_cell_info(pdb_path)
hkl = np.array(
miller.build_set(crystal_symmetry=cs,
anomalous_flag=True,
d_min=resolution).expand_to_p1().indices())
qvecs = np.inner(A, np.squeeze(hkl)).T
xyz = qvecs * 1.0 / specs['mag'] * specs['px_size']
# predict tilt angle from associated coordinates
t = np.rad2deg(np.arctan2(xyz[:, 1], xyz[:, 0]))
t[(t > 90) & (t <= 180)] = utils.wraptopi(t[(t > 90) & (t < 180)] +
180.0) # shift q2 to q4
t[(t >= -180) & (t <= -90)] += 180.0 # shift q3 to q1
# retain reflections not in missing wedge region
max_angle = specs['angle'] + 0.5 * specs['increment']
valid_idx = np.where((t > -1 * max_angle) & (t < max_angle))[0]
t, hkl = t[valid_idx], hkl[valid_idx]
print "Retained %i reflection outside missing wedge" % (len(hkl))
# generate a dict with keys as Millers and values as tilt angles
hkl_t = OrderedDict((tuple(key), val) for key, val in zip(hkl, t))
return hkl_t
def add_random_phase_shift(hklp):
"""
Introduce a random phase shift, at most one unit cell length along each axis.
Inputs:
-------
hklp: dict whose keys are Millers and values are phases in degrees
Outputs:
--------
hklp_shifted: dict whose keys are Millers and values are shifted phases
fshifts: fractional shifts by which origin was translated
"""
fshifts = np.array([random.random() for i in range(3)])
hkl, p = np.array(hklp.keys()), np.array(hklp.values())
p_shifted = utils.wraptopi(p - 360 * np.dot(hkl, fshifts).ravel())
hklp_shifted = OrderedDict(
(tuple(key), val) for key, val in zip(hkl, p_shifted))
return hklp_shifted, fshifts
def __init__(self, x=0, y=0, heading=pi / 2):
self.x = x
self.y = y
self.heading = wraptopi(heading)