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""" distances.py
Module containing several functions to compute spike distances
Copyright 2014, Mario Mulansky <mario.mulansky@gmx.net>
"""
import numpy as np
from pyspike import PieceWiseConstFunc, PieceWiseLinFunc
def add_auxiliary_spikes( spike_train, T_end , T_start=0.0):
""" Adds spikes at the beginning (T_start) and end (T_end) of the
observation interval.
Args:
- spike_train: ordered array of spike times
- T_end: end time of the observation interval
- T_start: start time of the observation interval (default 0.0)
Returns:
- spike train with additional spikes at T_start and T_end.
"""
assert spike_train[0] >= T_start, \
"Spike train has events before the given start time"
assert spike_train[-1] <= T_end, \
"Spike train has events after the given end time"
if spike_train[0] != T_start:
spike_train = np.insert(spike_train, 0, T_start)
if spike_train[-1] != T_end:
spike_train = np.append(spike_train, T_end)
return spike_train
def isi_distance(spikes1, spikes2):
""" Computes the instantaneous isi-distance S_isi (t) of the two given
spike trains. The spike trains are expected to have auxiliary spikes at the
beginning and end of the interval. Use the function add_auxiliary_spikes to
add those spikes to the spike train.
Args:
- spikes1, spikes2: ordered arrays of spike times with auxiliary spikes.
Returns:
- PieceWiseConstFunc describing the isi-distance.
"""
# check for auxiliary spikes - first and last spikes should be identical
assert spikes1[0]==spikes2[0], \
"Given spike trains seems not to have auxiliary spikes!"
assert spikes1[-1]==spikes2[-1], \
"Given spike trains seems not to have auxiliary spikes!"
# shorter names
s1 = spikes1
s2 = spikes2
# compute the interspike interval
nu1 = s1[1:]-s1[:-1]
nu2 = s2[1:]-s2[:-1]
# compute the isi-distance
spike_events = np.empty(len(nu1)+len(nu2))
spike_events[0] = s1[0]
# the values have one entry less - the number of intervals between events
isi_values = np.empty(len(spike_events)-1)
# add the distance of the first events
# isi_values[0] = nu1[0]/nu2[0] - 1.0 if nu1[0] <= nu2[0] \
# else 1.0 - nu2[0]/nu1[0]
isi_values[0] = (nu1[0]-nu2[0])/max(nu1[0],nu2[0])
index1 = 0
index2 = 0
index = 1
while True:
# check which spike is next - from s1 or s2
if s1[index1+1] < s2[index2+1]:
index1 += 1
# break condition relies on existence of spikes at T_end
if index1 >= len(nu1):
break
spike_events[index] = s1[index1]
elif s1[index1+1] > s2[index2+1]:
index2 += 1
if index2 >= len(nu2):
break
spike_events[index] = s2[index2]
else: # s1[index1+1] == s2[index2+1]
index1 += 1
index2 += 1
if (index1 >= len(nu1)) or (index2 >= len(nu2)):
break
spike_events[index] = s1[index1]
# compute the corresponding isi-distance
isi_values[index] = (nu1[index1]-nu2[index2]) / \
max(nu1[index1], nu2[index2])
index += 1
# the last event is the interval end
spike_events[index] = s1[-1]
# use only the data added above
# could be less than original length due to equal spike times
return PieceWiseConstFunc(spike_events[:index+1], isi_values[:index])
def get_min_dist(spike_time, spike_train, start_index=0):
""" Returns the minimal distance |spike_time - spike_train[i]|
with i>=start_index.
"""
d = abs(spike_time - spike_train[start_index])
start_index += 1
while start_index < len(spike_train):
d_temp = abs(spike_time - spike_train[start_index])
if d_temp > d:
break
else:
d = d_temp
start_index += 1
return d
def spike_distance(spikes1, spikes2):
""" Computes the instantaneous spike-distance S_spike (t) of the two given
spike trains. The spike trains are expected to have auxiliary spikes at the
beginning and end of the interval. Use the function add_auxiliary_spikes to
add those spikes to the spike train.
Args:
- spikes1, spikes2: ordered arrays of spike times with auxiliary spikes.
Returns:
- PieceWiseLinFunc describing the spike-distance.
"""
# check for auxiliary spikes - first and last spikes should be identical
assert spikes1[0]==spikes2[0], \
"Given spike trains seems not to have auxiliary spikes!"
assert spikes1[-1]==spikes2[-1], \
"Given spike trains seems not to have auxiliary spikes!"
# shorter variables
t1 = spikes1
t2 = spikes2
spike_events = np.empty(len(t1)+len(t2)-2)
spike_events[0] = t1[0]
y_starts = np.empty(len(spike_events)-1)
y_ends = np.empty(len(spike_events)-1)
index1 = 0
index2 = 0
index = 1
dt_p1 = 0.0
dt_f1 = get_min_dist(t1[1], t2, 0)
dt_p2 = 0.0
dt_f2 = get_min_dist(t2[1], t1, 0)
isi1 = max(t1[1]-t1[0], t1[2]-t1[1])
isi2 = max(t2[1]-t2[0], t2[2]-t2[1])
s1 = dt_f1*(t1[1]-t1[0])/isi1
s2 = dt_f2*(t2[1]-t2[0])/isi2
y_starts[0] = (s1*isi2 + s2*isi1) / ((isi1+isi2)**2/2)
while True:
# print(index, index1, index2)
if t1[index1+1] < t2[index2+1]:
index1 += 1
# break condition relies on existence of spikes at T_end
if index1+1 >= len(t1):
break
spike_events[index] = t1[index1]
# first calculate the previous interval end value
dt_p1 = dt_f1 # the previous time now was the following time before
s1 = dt_p1
s2 = (dt_p2*(t2[index2+1]-t1[index1]) + dt_f2*(t1[index1]-t2[index2])) / isi2
y_ends[index-1] = (s1*isi2 + s2*isi1) / ((isi1+isi2)**2/2)
# now the next interval start value
dt_f1 = get_min_dist(t1[index1+1], t2, index2)
isi1 = t1[index1+1]-t1[index1]
# s2 is the same as above, thus we can compute y2 immediately
y_starts[index] = (s1*isi2 + s2*isi1) / ((isi1+isi2)**2/2)
elif t1[index1+1] > t2[index2+1]:
index2 += 1
if index2+1 >= len(t2):
break
spike_events[index] = t2[index2]
# first calculate the previous interval end value
dt_p2 = dt_f2 # the previous time now was the following time before
s1 = (dt_p1*(t1[index1+1]-t2[index2]) + dt_f1*(t2[index2]-t1[index1])) / isi1
s2 = dt_p2
y_ends[index-1] = (s1*isi2 + s2*isi1) / ((isi1+isi2)**2/2)
# now the next interval start value
dt_f2 = get_min_dist(t2[index2+1], t1, index1)
#s2 = dt_f2
isi2 = t2[index2+1]-t2[index2]
# s2 is the same as above, thus we can compute y2 immediately
y_starts[index] = (s1*isi2 + s2*isi1) / ((isi1+isi2)**2/2)
else: # t1[index1+1] == t2[index2+1] - generate only one event
index1 += 1
index2 += 1
if (index1+1 >= len(t1)) or (index2+1 >= len(t2)):
break
assert dt_f2 == 0.0
assert dt_f1 == 0.0
spike_events[index] = t1[index1]
y_ends[index-1] = 0.0
y_starts[index] = 0.0
dt_p1 = 0.0
dt_p2 = 0.0
dt_f1 = get_min_dist(t1[index1+1], t2, index2)
dt_f2 = get_min_dist(t2[index2+1], t1, index1)
isi1 = t1[index1+1]-t1[index1]
isi2 = t2[index2+1]-t2[index2]
index += 1
# the last event is the interval end
spike_events[index] = t1[-1]
# the ending value of the last interval
isi1 = max(t1[-1]-t1[-2], t1[-2]-t1[-3])
isi2 = max(t2[-1]-t2[-2], t2[-2]-t2[-3])
s1 = dt_p1*(t1[-1]-t1[-2])/isi1
s2 = dt_p2*(t2[-1]-t2[-2])/isi2
y_ends[index-1] = (s1*isi2 + s2*isi1) / ((isi1+isi2)**2/2)
# use only the data added above
# could be less than original length due to equal spike times
return PieceWiseLinFunc(spike_events[:index+1],
y_starts[:index], y_ends[:index])
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