import numpy as np
import param
from holoviews import Store, Options, Layout, HoloMap, Histogram, Dimension
from holoviews.operation import TreeOperation
[docs]class WeightIsotropy(TreeOperation):
"""
Computes a histogram of azimuths between the positional
preferences of pre- and post-synaptic neurons weighted
by the connection strength and normalized relative to
the orientation preference.
Useful for determining whether lateral connection are
anisotropic along the axis of preferred orientation.
"""
num_bins = param.Integer(default=20, doc="""
Number of bins in the histogram.""")
roi = param.NumericTuple(default=(-0.5, -0.5, 0.5, 0.5), doc="""
Region of interest supplied as a four-tuple of the
form (left, bottom, right, top)""")
projections = param.List(default=[], doc="""
List of tuples of the form (sheet, projection).""")
@classmethod
def _last(cls, obj):
return obj.last if isinstance(obj, HoloMap) else obj
def _process(self, tree, key=None):
layout = Layout()
for s, p in self.p.projections:
# Get last element
orelmnt = self._last(tree.OrientationPreference[s])
xelmnt = self._last(tree.XPreference[s])
yelmnt = self._last(tree.YPreference[s])
# If any preference has not been supplied skip analysis
if any(not o for o in [orelmnt, xelmnt, yelmnt]):
return Layout()
# Flatten preferences
xpref_arr = xelmnt.data.flat
ypref_arr = yelmnt.data.flat
# Iterate over CFs in ROI
l, b, r, t = self.p.roi
lat_weights = tree.CFs[p]
azimuths, weights = [], []
for key, cf in lat_weights[l:r, b:t].items():
# Get preferences for a particular unit
unit_angle, unit_x, unit_y = orelmnt[key], xelmnt[key], yelmnt[key]
weight_arr = cf.situated.data.flat
weight = weight_arr[weight_arr>0]
xpref = xpref_arr[weight_arr>0]
ypref = ypref_arr[weight_arr>0]
# Compute x/y-preference differences between
# pre- and post-synaptic neurons
dx = unit_x - xpref
dy = unit_y - ypref
# Compute angle between position preferences
# of the pre- and post-synaptic neurons
# Correcting for preferred orientation
conn_angle = np.arctan2(dy, dx)
conn_angle[conn_angle<0] += 2*np.pi
delta = conn_angle - unit_angle
delta2 = conn_angle - (unit_angle + np.pi)
delta = np.hstack([delta, delta2])
delta[delta<0] += 2*np.pi
weight = np.hstack([weight, weight])
azimuths.append(delta)
weights.append(weight)
# Combine azimuths and weights for all CFs
azimuths = np.concatenate(azimuths)
weights = np.concatenate(weights)
# Compute histogram
bins, edges = np.histogram(azimuths, range=(0, 2*np.pi),
bins=self.p.num_bins, weights=weights, normed=True)
# Construct Elements
label =' '.join([s, p])
histogram = Histogram(bins, edges, group="Weight Isotropy",
kdims=[Dimension('Azimuth')], label=label)
layout.WeightIsotropy['_'.join([s, p])] = histogram
return layout
[docs]def circular_dist(a, b, period):
"""
Returns the distance between a and b (scalars) in a domain with `period` period.
"""
return np.minimum(np.abs(a - b), period - np.abs(a - b))
[docs]class WeightDistribution(TreeOperation):
"""
Computes histogram of the difference in feature
preference between pre- and post-synaptic neurons
weighted by the connection strength between them.
"""
feature = param.String(default='Orientation', doc="""
Feature to compute the distribution over""")
num_bins = param.Integer(default=10, doc="""
Number of histogram bins.""")
normalized = param.Boolean(default=False, doc="""
Whether to normalize the histogram""")
projections = param.List(default=[], doc="""
List of tuples of the form (sheet, projection).""")
weighted = param.Boolean(default=True)
def _process(self, tree, key=None):
preferences = tree[self.p.feature+'Preference']
layout = Layout()
for s, p in self.p.projections:
if s not in preferences:
continue
featurepref = preferences[s]
if isinstance(featurepref, HoloMap):
featurepref = featurepref.last
feature = featurepref.value_dimensions[0]
feature_arr = featurepref.data.flat
cfs = tree.CFs[p]
deltas, weights = [], []
for k, cf in cfs.items():
preferred = featurepref[k]
weight_arr = cf.situated.data.flat
feature_slice = feature_arr[weight_arr>0]
weight_slice = weight_arr[weight_arr>0]
if feature.cyclic:
feature_delta = circular_dist(preferred, feature_slice, feature.range[1])
else:
feature_delta = np.abs(feature_slice-preferred)
deltas.append(feature_delta)
weights.append(weight_slice)
deltas = np.concatenate(deltas)
weights = np.concatenate(weights)
bin_range = (0, feature.range[1]/2.) if feature.cyclic else None
bins, edges = np.histogram(deltas, range=bin_range, bins=self.p.num_bins,
weights=weights, normed=self.p.normalized)
# Construct Elements
label = ' '.join([s,p])
group = '%s Weight Distribution' % self.p.feature
histogram = Histogram(bins, edges, group=group, label=label,
kdims=[' '.join([self.p.feature, 'Difference'])],
vdims=['Weight'])
layout.WeightDistribution['_'.join([s,p])] = histogram
return layout
options = Store.options(backend='matplotlib')
options.Histogram.Weight_Isotropy = Options('plot', projection='polar', show_grid=True)
