1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
|
""" 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 isi_distance(spikes1, spikes2, T_end, T_start=0.0):
""" Computes the instantaneous isi-distance S_isi (t) of the two given
spike trains.
Args:
- spikes1, spikes2: ordered arrays of spike times.
- T_end: end time of the observation interval.
- T_start: begin of the observation interval (default=0.0).
Returns:
- PieceWiseConstFunc describing the isi-distance.
"""
# add spikes at the beginning and end of the interval
s1 = np.empty(len(spikes1)+2)
s1[0] = T_start
s1[-1] = T_end
s1[1:-1] = spikes1
s2 = np.empty(len(spikes2)+2)
s2[0] = T_start
s2[-1] = T_end
s2[1:-1] = 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] = T_start
# 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] = T_end
# 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, T_end, T_start=0.0):
""" Computes the instantaneous spike-distance S_spike (t) of the two given
spike trains.
Args:
- spikes1, spikes2: ordered arrays of spike times.
- T_end: end time of the observation interval.
- T_start: begin of the observation interval (default=0.0).
Returns:
- PieceWiseLinFunc describing the spike-distance.
"""
# add spikes at the beginning and end of the interval
t1 = np.empty(len(spikes1)+2)
t1[0] = T_start
t1[-1] = T_end
t1[1:-1] = spikes1
t2 = np.empty(len(spikes2)+2)
t2[0] = T_start
t2[-1] = T_end
t2[1:-1] = spikes2
spike_events = np.empty(len(t1)+len(t2)-2)
spike_events[0] = T_start
spike_events[-1] = T_end
y_starts = np.empty(len(spike_events)-1)
y_starts[0] = 0.0
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 = t1[1]-t1[0]
isi2 = t2[1]-t2[0]
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)
else:
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)
index += 1
return PieceWiseLinFunc(spike_events, y_starts, y_ends)
|
