def binder(positions, orientations, bl, m=4, method='ball', margin=0):
"""Calculate the binder cumulant, given positions and orientations.
bl: the binder length scale, such that
B(bl) = 1 - .333 * S4 / S2^2
where SN are <phibl^N> averaged over each block/cluster of size bl in frame.
"""
if margin:
if margin < ss:
margin *= ss
center = 0.5*(positions.max(0) + positions.min(0))
dmask = d < d.max() - margin
positions = positions[dmask]
orientations = orientations[dmask]
if 'neigh' in method or 'ball' in method:
tree = KDTree(positions)
balls = tree.query_ball_tree(tree, bl)
balls, ball_mask = helpy.pad_uneven(balls, 0, True, int)
ball_orient = orientations[balls]
ball_orient[ball_mask] = np.nan
phis = np.nanmean(np.exp(m*ball_orient*1j), 1)
phi2 = np.dot(phis, phis) / len(phis)
phiphi = phis*phis
phi4 = np.dot(phiphi, phiphi) / len(phiphi)
return 1 - phi4 / (3*phi2*phi2)
else: # elif method=='block':
raise ValueError("method {} not implemented".format(method))
def binder(positions, orientations, bl, m=4, method='ball', margin=0):
""" Calculate the binder cumulant for a frame, given positions and orientations.
bl: the binder length scale, such that
B(bl) = 1 - .333 * S4 / S2^2
where SN are <phibl^N> averaged over each block/cluster of size bl in frame.
"""
if margin:
if margin < ss:
margin *= ss
center = 0.5*(positions.max(0) + positions.min(0))
dmask = d < d.max() - margin
positions = positions[dmask]
orientations = orientations[dmask]
if 'neigh' in method or 'ball' in method:
tree = cKDTree(positions)
balls = tree.query_ball_tree(tree, bl)
balls, ball_mask = helpy.pad_uneven(balls, 0, True, int)
ball_orient = orientations[balls]
ball_orient[~ball_mask] = np.nan
phis = np.nanmean(np.exp(m*ball_orient*1j), 1)
phi2 = np.dot(phis, phis) / len(phis)
phiphi = phis*phis
phi4 = np.dot(phiphi, phiphi) / len(phiphi)
return 1 - phi4 / (3*phi2*phi2)
else:
raise ValueError, "method {} not implemented".format(method)
#elif method=='block':
left, right, bottom, top = (positions[:,0].min(), positions[:,0].max(),
positions[:,1].min(), positions[:,1].max())
xbins, ybins = np.arange(left, right + bl, bl), np.arange(bottom, top + bl, bl)
blocks = np.rollaxis(np.indices((xbins.size, ybins.size)), 0, 3)
block_ind = np.column_stack([
np.digitize(positions[:,0], xbins),
np.digitize(positions[:,1], ybins)])
def binder(positions, orientations, bl, m=4, method='ball', margin=0):
"""Calculate the binder cumulant, given positions and orientations.
bl: the binder length scale, such that
B(bl) = 1 - .333 * S4 / S2^2
where SN are <phibl^N> averaged over each block/cluster of size bl in frame.
"""
if margin:
if margin < ss:
margin *= ss
center = 0.5 * (positions.max(0) + positions.min(0))
dmask = d < d.max() - margin
positions = positions[dmask]
orientations = orientations[dmask]
if 'neigh' in method or 'ball' in method:
tree = KDTree(positions)
balls = tree.query_ball_tree(tree, bl)
balls, ball_mask = helpy.pad_uneven(balls, 0, True, int)
ball_orient = orientations[balls]
ball_orient[ball_mask] = np.nan
phis = np.nanmean(np.exp(m * ball_orient * 1j), 1)
phi2 = np.dot(phis, phis) / len(phis)
phiphi = phis * phis
phi4 = np.dot(phiphi, phiphi) / len(phiphi)
return 1 - phi4 / (3 * phi2 * phi2)
else: # elif method=='block':
raise ValueError("method {} not implemented".format(method))
def pair_angles(positions, neighborhood=None, ang_type='absolute', margin=0, dub=2*ss):
""" do something with the angles a given particle makes with its neighbors
`ang_type` can be 'relative', 'delta', or 'absolute'
`neighborhood` may be:
an integer (probably 4, 6, or 8), giving that many nearest neighbors,
or None (which gives voronoi)
`margin` is the width of excluded boundary margin
`dub` is the distance upper bound (won't use pairs farther apart)
"""
if neighborhood is None or str(neighborhood).lower() in ['voronoi', 'delauney']:
#method = 'voronoi'
tess = Delaunay(positions)
neighbors = get_neighbors(tess, xrange(tess.npoints))
neighbors, nmask = helpy.pad_uneven(neighbors, 0, True, int)
elif isinstance(neighborhood, int):
#method = 'nearest'
tree = cKDTree(positions)
# tree.query(P, N) returns query particle and N-1 neighbors
distances, neighbors = tree.query(positions, 1 + neighborhood,
distance_upper_bound=dub)
assert np.allclose(distances[:,0], 0), "distance to self not zero"
distances = distances[:,1:]
assert np.allclose(neighbors[:,0], np.arange(tree.n)), "first neighbor not self"
neighbors = neighbors[:,1:]
nmask = np.isfinite(distances)
neighbors[~nmask] = np.where(~nmask)[0]
dx, dy = (positions[neighbors] - positions[:, None, :]).T
angles = np.arctan2(dy, dx).T % tau
assert angles.shape == neighbors.shape
if ang_type == 'relative':
# subtract off angle to nearest neighbor
angles -= angles[:, 0, None] # None to keep dims
elif ang_type == 'delta':
# sort by angle then take diff
angles[~nmask] = np.inf
angles.sort(-1)
angles -= np.roll(angles, 1, -1)
nmask = np.all(nmask, 1)
elif ang_type != 'absolute':
raise ValueError, "unknown ang_type {}".format(ang_type)
angles[~nmask] = np.nan
if margin:
if margin < ss: margin *= ss
center = 0.5*(positions.max(0) + positions.min(0))
d = helpy.dist(positions, center) # distances to center
dmask = d < d.max() - margin
assert np.allclose(len(dmask), map(len, [angles, nmask]))
angles = angles[dmask]
nmask = nmask[dmask]
return (angles % tau, nmask) + ((dmask,) if margin else ())
sys.stdout.flush()
cos = np.cos(o)
sin = np.sin(o)
coscorr = corr.autocorr(cos, cumulant=False, norm=False)
sincorr = corr.autocorr(sin, cumulant=False, norm=False)
coscorrs.append(coscorr)
sincorrs.append(sincorr)
else:
coscorrs = [ corr.autocorr(np.cos(trackset['o']), cumulant=False, norm=False)
for trackset in tracksets.values() ]
sincorrs = [ corr.autocorr(np.sin(trackset['o']), cumulant=False, norm=False)
for trackset in tracksets.values() ]
# Gather all the track correlations and average them
allcorr = coscorrs + sincorrs
allcorr = helpy.pad_uneven(allcorr, np.nan)
tcorr = np.arange(allcorr.shape[1])/fps
meancorr = np.nanmean(allcorr, 0)
added = np.sum(np.isfinite(allcorr), 0)
errcorr = np.nanstd(allcorr, 0)/np.sqrt(added - 1)
sigma = errcorr + 1e-5*np.nanstd(errcorr) # add something small to prevent 0
if args.verbose:
print "Merged nn corrs"
# Fit to exponential decay
tmax = int(50*args.zoom)
fmax = np.searchsorted(tcorr, tmax)
fitform = lambda s, DR: 0.5*np.exp(-DR*s)
fitstr = r"$\frac{1}{2}e^{-D_R t}$"
p0 = [1]
try:
def neighborhoods(positions, voronoi=False, size=None, reach=None,
tess=None, tree=None):
"""Build a list of lists or padded array of neighborhoods around each point
select neighbors by any combination of three basic choices:
Voronoi/Delaunay, distance/ball, count/nearest/number
parameters
positions : array with shape (N, 2) or fields 'x' and 'y'
voronoi : whether to require pairs to be voronoi or delaunay neighbors
size : maximum size for each neighborhood excluding center/self
reach : maximum distance to search (exclusive). scalar for distance/ball
for other criteria, it may be an array of distances or a str such as
'[min|max|mean]*{factor}' where the function is of neighbor distances
tess, tree : optionally provide spatial.Delaunay or spatial.KDTree instance
returns
neighbors : list of lists (or padded array) with shape (npoints, size)
neighbors[i] gives indices in positions to neighbors of positions[i]
i.e., the coordinates for all neighbors of positions[i] are given by
positions[neighbors[i]], with shape (size, 2)
mask : True if not a real neighbor
distances : distance to the neighbor, only calculated if needed.
"""
try:
fewest, most = size
except TypeError:
fewest, most = None, size
need_dist = True
filter_reach = reach is not None
try:
dub = float(reach)
filter_reach = False
except (TypeError, ValueError):
dub = np.inf
if voronoi:
tess = tess or Delaunay(positions)
neighbors = get_neighbors(tess, 'all')
elif most is not None:
tree = tree or KDTree(positions)
distances, neighbors = tree.query(
positions, np.max(most)+1, distance_upper_bound=dub)
distances, neighbors = distances[:, 1:], neighbors[:, 1:] # remove self
mask = np.isinf(distances)
neighbors[mask] = np.where(mask)[0]
need_dist = False
elif reach is None:
raise ValueError("No limits on neighborhood selection applied")
else:
tree = tree or KDTree(positions)
neighbors = tree.query_ball_tree(tree, dub)
for i in xrange(len(neighbors)):
neighbors[i].remove(i) # remove self
if need_dist:
ix = np.arange(len(positions))[:, None]
neighbors, mask = helpy.pad_uneven(neighbors, ix, True, int)
distances = distance.cdist(positions, positions)[ix, neighbors]
distances[mask] = np.inf
sort = distances.argsort(1)
distances, neighbors = distances[ix, sort], neighbors[ix, sort]
if isinstance(reach, basestring):
fun, fact = reach.split('*') if '*' in reach else (reach, 1)
ix = np.arange(len(positions))
fun = {'mean': np.nanmean, 'min': np.nanmin, 'max': np.nanmax,
'median': np.nanmedian}[fun]
fact = float(fact)
reach = fun(np.where(mask, np.nan, distances), 1, keepdims=True)*fact
if filter_reach:
mask[distances >= reach] = True
distances[mask] = np.inf
if fewest is not None:
mask[(~mask).sum(1) < fewest] = True
if np.iterable(most):
extra = np.clip(mask.shape[1] - most, 0, None)
i = np.where(extra)
extra = extra[i]
i = np.repeat(i[0], extra)
j = mask.shape[1] - np.concatenate(map(range, extra)) - 1
mask[i, j] = True
most = most.max()
return neighbors[:, :most], mask[:, :most], distances[:, :most]
def neighborhoods(positions,
voronoi=False,
size=None,
reach=None,
tess=None,
tree=None):
"""Build a list of lists or padded array of neighborhoods around each point
select neighbors by any combination of three basic choices:
Voronoi/Delaunay, distance/ball, count/nearest/number
parameters
positions : array with shape (N, 2) or fields 'x' and 'y'
voronoi : whether to require pairs to be voronoi or delaunay neighbors
size : maximum size for each neighborhood excluding center/self
reach : maximum distance to search (exclusive). scalar for distance/ball
for other criteria, it may be an array of distances or a str such as
'[min|max|mean]*{factor}' where the function is of neighbor distances
tess, tree : optionally provide spatial.Delaunay or spatial.KDTree instance
returns
neighbors : list of lists (or padded array) with shape (npoints, size)
neighbors[i] gives indices in positions to neighbors of positions[i]
i.e., the coordinates for all neighbors of positions[i] are given by
positions[neighbors[i]], with shape (size, 2)
mask : True if not a real neighbor
distances : distance to the neighbor, only calculated if needed.
"""
try:
fewest, most = size
except TypeError:
fewest, most = None, size
need_dist = True
filter_reach = reach is not None
try:
dub = float(reach)
filter_reach = False
except (TypeError, ValueError):
dub = np.inf
if voronoi:
tess = tess or Delaunay(positions)
neighbors = get_neighbors(tess, 'all')
elif most is not None:
tree = tree or KDTree(positions)
distances, neighbors = tree.query(positions,
np.max(most) + 1,
distance_upper_bound=dub)
distances, neighbors = distances[:, 1:], neighbors[:,
1:] # remove self
mask = np.isinf(distances)
neighbors[mask] = np.where(mask)[0]
need_dist = False
elif reach is None:
raise ValueError("No limits on neighborhood selection applied")
else:
tree = tree or KDTree(positions)
neighbors = tree.query_ball_tree(tree, dub)
for i in xrange(len(neighbors)):
neighbors[i].remove(i) # remove self
if need_dist:
ix = np.arange(len(positions))[:, None]
neighbors, mask = helpy.pad_uneven(neighbors, ix, True, int)
distances = distance.cdist(positions, positions)[ix, neighbors]
distances[mask] = np.inf
sort = distances.argsort(1)
distances, neighbors = distances[ix, sort], neighbors[ix, sort]
if isinstance(reach, basestring):
fun, fact = reach.split('*') if '*' in reach else (reach, 1)
ix = np.arange(len(positions))
fun = {
'mean': np.nanmean,
'min': np.nanmin,
'max': np.nanmax,
'median': np.nanmedian
}[fun]
fact = float(fact)
reach = fun(np.where(mask, np.nan, distances), 1, keepdims=True) * fact
if filter_reach:
mask[distances >= reach] = True
distances[mask] = np.inf
if fewest is not None:
mask[(~mask).sum(1) < fewest] = True
if np.iterable(most):
extra = np.clip(mask.shape[1] - most, 0, None)
i = np.where(extra)
extra = extra[i]
i = np.repeat(i[0], extra)
j = mask.shape[1] - np.concatenate(map(range, extra)) - 1
mask[i, j] = True
most = most.max()
return neighbors[:, :most], mask[:, :most], distances[:, :most]
if __name__=='__main__' and args.nn:
# Calculate the <nn> correlation for all the tracks in a given dataset
# TODO: fix this to combine multiple datasets (more than one prefix)
data, trackids, odata, omask = helpy.load_data(prefix, True, False)
tracksets, otracksets = helpy.load_tracksets(data, trackids, odata, omask,
min_length=args.stub)
coscorrs = [ corr.autocorr(np.cos(otrackset), cumulant=False, norm=False)
for otrackset in otracksets.values() ]
sincorrs = [ corr.autocorr(np.sin(otrackset), cumulant=False, norm=False)
for otrackset in otracksets.values() ]
# Gather all the track correlations and average them
allcorr = coscorrs + sincorrs
allcorr = helpy.pad_uneven(allcorr, np.nan)
tcorr = np.arange(allcorr.shape[1])/fps
meancorr = np.nanmean(allcorr, 0)
errcorr = np.nanstd(allcorr, 0)/sqrt(len(allcorr))
if verbose:
print "Merged nn corrs"
# Fit to exponential decay
tmax = 50
fmax = np.searchsorted(tcorr, tmax)
fitform = lambda *args, **kwargs: 0.5*corr.exp_decay(*args, **kwargs)
popt, pcov = curve_fit(fitform, tcorr[:fmax], meancorr[:fmax],
p0=[1], sigma=errcorr[:fmax].mean() + errcorr[:fmax])
D_R = 1/popt[0]
print 'D_R: {:.4f}'.format(D_R)