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
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
|
""" python_backend.py
Collection of python functions that can be used instead of the cython
implementation.
Copyright 2014, Mario Mulansky <mario.mulansky@gmx.net>
Distributed under the BSD License
"""
import numpy as np
############################################################
# isi_distance_python
############################################################
def isi_distance_python(s1, s2):
""" Plain Python implementation of the isi distance.
"""
# 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] = abs(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] = abs(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 spike_events[:index + 1], isi_values[:index]
############################################################
# get_min_dist
############################################################
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
############################################################
# spike_distance_python
############################################################
def spike_distance_python(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 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 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 spike_events[:index+1], y_starts[:index], y_ends[:index]
############################################################
# cumulative_sync_python
############################################################
def cumulative_sync_python(spikes1, spikes2):
def get_tau(spikes1, spikes2, i, j):
return 0.5*min([spikes1[i]-spikes1[i-1], spikes1[i+1]-spikes1[i],
spikes2[j]-spikes2[j-1], spikes2[j+1]-spikes2[j]])
N1 = len(spikes1)
N2 = len(spikes2)
i = 0
j = 0
n = 0
st = np.zeros(N1 + N2 - 2)
c = np.zeros(N1 + N2 - 3)
c[0] = 0
st[0] = 0
while n < N1 + N2:
if spikes1[i+1] < spikes2[j+1]:
i += 1
n += 1
tau = get_tau(spikes1, spikes2, i, j)
st[n] = spikes1[i]
if spikes1[i]-spikes2[j] > tau:
c[n] = c[n-1]
else:
c[n] = c[n-1]+1
elif spikes1[i+1] > spikes2[j+1]:
j += 1
n += 1
tau = get_tau(spikes1, spikes2, i, j)
st[n] = spikes2[j]
if spikes2[j]-spikes1[i] > tau:
c[n] = c[n-1]
else:
c[n] = c[n-1]+1
else: # spikes1[i+1] = spikes2[j+1]
j += 1
i += 1
if i == N1-1 or j == N2-1:
break
n += 1
st[n] = spikes1[i]
c[n] = c[n-1]
n += 1
st[n] = spikes1[i]
c[n] = c[n-1]+1
c[0] = 0
st[0] = spikes1[0]
st[-1] = spikes1[-1]
return st, c
############################################################
# coincidence_python
############################################################
def coincidence_python(spikes1, spikes2):
def get_tau(spikes1, spikes2, i, j):
m = 1E100 # some huge number
if i < len(spikes1)-2:
m = min(m, spikes1[i+1]-spikes1[i])
if j < len(spikes2)-2:
m = min(m, spikes2[j+1]-spikes2[j])
if i > 1:
m = min(m, spikes1[i]-spikes1[i-1])
if j > 1:
m = min(m, spikes2[j]-spikes2[j-1])
return 0.5*m
N1 = len(spikes1)
N2 = len(spikes2)
i = 0
j = 0
n = 0
st = np.zeros(N1 + N2 - 2) # spike times
c = np.zeros(N1 + N2 - 2) # coincidences
mp = np.ones(N1 + N2 - 2) # multiplicity
while n < N1 + N2 - 2:
if spikes1[i+1] < spikes2[j+1]:
i += 1
n += 1
tau = get_tau(spikes1, spikes2, i, j)
st[n] = spikes1[i]
if j > 0 and spikes1[i]-spikes2[j] < tau:
# coincidence between the current spike and the previous spike
# both get marked with 1
c[n] = 1
c[n-1] = 1
elif spikes1[i+1] > spikes2[j+1]:
j += 1
n += 1
tau = get_tau(spikes1, spikes2, i, j)
st[n] = spikes2[j]
if i > 0 and spikes2[j]-spikes1[i] < tau:
# coincidence between the current spike and the previous spike
# both get marked with 1
c[n] = 1
c[n-1] = 1
else: # spikes1[i+1] = spikes2[j+1]
# advance in both spike trains
j += 1
i += 1
if i == N1-1 or j == N2-1:
break
n += 1
# add only one event, but with coincidence 2 and multiplicity 2
st[n] = spikes1[i]
c[n] = 2
mp[n] = 2
st = st[:n+2]
c = c[:n+2]
mp = mp[:n+2]
st[0] = spikes1[0]
st[-1] = spikes1[-1]
c[0] = c[1]
c[-1] = c[-2]
mp[0] = mp[1]
mp[-1] = mp[-2]
return st, c, mp
############################################################
# add_piece_wise_const_python
############################################################
def add_piece_wise_const_python(x1, y1, x2, y2):
x_new = np.empty(len(x1) + len(x2))
y_new = np.empty(len(x_new)-1)
x_new[0] = x1[0]
y_new[0] = y1[0] + y2[0]
index1 = 0
index2 = 0
index = 0
while (index1+1 < len(y1)) and (index2+1 < len(y2)):
index += 1
# print(index1+1, x1[index1+1], y1[index1+1], x_new[index])
if x1[index1+1] < x2[index2+1]:
index1 += 1
x_new[index] = x1[index1]
elif x1[index1+1] > x2[index2+1]:
index2 += 1
x_new[index] = x2[index2]
else: # x1[index1+1] == x2[index2+1]:
index1 += 1
index2 += 1
x_new[index] = x1[index1]
y_new[index] = y1[index1] + y2[index2]
# one array reached the end -> copy the contents of the other to the end
if index1+1 < len(y1):
x_new[index+1:index+1+len(x1)-index1-1] = x1[index1+1:]
y_new[index+1:index+1+len(y1)-index1-1] = y1[index1+1:] + y2[-1]
index += len(x1)-index1-2
elif index2+1 < len(y2):
x_new[index+1:index+1+len(x2)-index2-1] = x2[index2+1:]
y_new[index+1:index+1+len(y2)-index2-1] = y2[index2+1:] + y1[-1]
index += len(x2)-index2-2
else: # both arrays reached the end simultaneously
# only the last x-value missing
x_new[index+1] = x1[-1]
# the last value is again the end of the interval
# x_new[index+1] = x1[-1]
# only use the data that was actually filled
return x_new[:index+2], y_new[:index+1]
############################################################
# add_multiple_value_sequence_python
############################################################
def add_multiple_value_sequence_python(x1, y1, mp1, x2, y2, mp2):
x_new = np.empty(len(x1) + len(x2))
y_new = np.empty_like(x_new)
mp_new = np.empty_like(x_new)
x_new[0] = x1[0]
index1 = 0
index2 = 0
index = 0
while (index1+1 < len(y1)) and (index2+1 < len(y2)):
if x1[index1+1] < x2[index2+1]:
index1 += 1
index += 1
x_new[index] = x1[index1]
y_new[index] = y1[index1]
mp_new[index] = mp1[index1]
elif x1[index1+1] > x2[index2+1]:
index2 += 1
index += 1
x_new[index] = x2[index2]
y_new[index] = y2[index2]
mp_new[index] = mp2[index2]
else: # x1[index1+1] == x2[index2+1]
index1 += 1
index2 += 1
index += 1
x_new[index] = x1[index1]
y_new[index] = y1[index1] + y2[index2]
mp_new[index] = mp1[index1] + mp2[index2]
# one array reached the end -> copy the contents of the other to the end
if index1+1 < len(y1):
x_new[index+1:index+1+len(x1)-index1-1] = x1[index1+1:]
y_new[index+1:index+1+len(x1)-index1-1] = y1[index1+1:]
mp_new[index+1:index+1+len(x1)-index1-1] = mp1[index1+1:]
index += len(x1)-index1-1
elif index2+1 < len(y2):
x_new[index+1:index+1+len(x2)-index2-1] = x2[index2+1:]
y_new[index+1:index+1+len(x2)-index2-1] = y2[index2+1:]
mp_new[index+1:index+1+len(x2)-index2-1] = mp2[index2+1:]
index += len(x2)-index2-1
# else: # both arrays reached the end simultaneously
# x_new[index+1] = x1[-1]
# y_new[index+1] = y1[-1] + y2[-1]
# mp_new[index+1] = mp1[-1] + mp2[-1]
y_new[0] = y_new[1]
mp_new[0] = mp_new[1]
# the last value is again the end of the interval
# only use the data that was actually filled
return x_new[:index+1], y_new[:index+1], mp_new[:index+1]
############################################################
# add_piece_lin_const_python
############################################################
def add_piece_wise_lin_python(x1, y11, y12, x2, y21, y22):
x_new = np.empty(len(x1) + len(x2))
y1_new = np.empty(len(x_new)-1)
y2_new = np.empty_like(y1_new)
x_new[0] = x1[0]
y1_new[0] = y11[0] + y21[0]
index1 = 0 # index for self
index2 = 0 # index for f
index = 0 # index for new
while (index1+1 < len(y11)) and (index2+1 < len(y21)):
# print(index1+1, x1[index1+1], self.y[index1+1], x_new[index])
if x1[index1+1] < x2[index2+1]:
# first compute the end value of the previous interval
# linear interpolation of the interval
y = y21[index2] + (y22[index2]-y21[index2]) * \
(x1[index1+1]-x2[index2]) / (x2[index2+1]-x2[index2])
y2_new[index] = y12[index1] + y
index1 += 1
index += 1
x_new[index] = x1[index1]
# and the starting value for the next interval
y1_new[index] = y11[index1] + y
elif x1[index1+1] > x2[index2+1]:
# first compute the end value of the previous interval
# linear interpolation of the interval
y = y11[index1] + (y12[index1]-y11[index1]) * \
(x2[index2+1]-x1[index1]) / \
(x1[index1+1]-x1[index1])
y2_new[index] = y22[index2] + y
index2 += 1
index += 1
x_new[index] = x2[index2]
# and the starting value for the next interval
y1_new[index] = y21[index2] + y
else: # x1[index1+1] == x2[index2+1]:
y2_new[index] = y12[index1] + y22[index2]
index1 += 1
index2 += 1
index += 1
x_new[index] = x1[index1]
y1_new[index] = y11[index1] + y21[index2]
# one array reached the end -> copy the contents of the other to the end
if index1+1 < len(y11):
# compute the linear interpolations values
y = y21[index2] + (y22[index2]-y21[index2]) * \
(x1[index1+1:-1]-x2[index2]) / (x2[index2+1]-x2[index2])
x_new[index+1:index+1+len(x1)-index1-1] = x1[index1+1:]
y1_new[index+1:index+1+len(y11)-index1-1] = y11[index1+1:]+y
y2_new[index:index+len(y12)-index1-1] = y12[index1:-1] + y
index += len(x1)-index1-2
elif index2+1 < len(y21):
# compute the linear interpolations values
y = y11[index1] + (y12[index1]-y11[index1]) * \
(x2[index2+1:-1]-x1[index1]) / \
(x1[index1+1]-x1[index1])
x_new[index+1:index+1+len(x2)-index2-1] = x2[index2+1:]
y1_new[index+1:index+1+len(y21)-index2-1] = y21[index2+1:] + y
y2_new[index:index+len(y22)-index2-1] = y22[index2:-1] + y
index += len(x2)-index2-2
else: # both arrays reached the end simultaneously
# only the last x-value missing
x_new[index+1] = x1[-1]
# finally, the end value for the last interval
y2_new[index] = y12[-1]+y22[-1]
# only use the data that was actually filled
return x_new[:index+2], y1_new[:index+1], y2_new[:index+1]
|