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
|
#cython: boundscheck=False
#cython: wraparound=False
#cython: cdivision=True
"""
cython_distances.pyx
cython implementation of the isi- and spike-distance
Note: using cython memoryviews (e.g. double[:]) instead of ndarray objects
improves the performance of spike_distance by a factor of 10!
Copyright 2014, Mario Mulansky <mario.mulansky@gmx.net>
Distributed under the BSD License
"""
"""
To test whether things can be optimized: remove all yellow stuff
in the html output::
cython -a cython_distance.pyx
which gives::
cython_distance.html
"""
import numpy as np
cimport numpy as np
from libc.math cimport fabs
from libc.math cimport fmax
from libc.math cimport fmin
DTYPE = np.float
ctypedef np.float_t DTYPE_t
############################################################
# isi_distance_cython
############################################################
def isi_distance_cython(double[:] s1, double[:] s2,
double t_start, double t_end):
cdef double[:] spike_events
cdef double[:] isi_values
cdef int index1, index2, index
cdef int N1, N2
cdef double nu1, nu2
N1 = len(s1)
N2 = len(s2)
spike_events = np.empty(N1+N2+2)
# the values have one entry less as they are defined at the intervals
isi_values = np.empty(N1+N2+1)
# first x-value of the profile
spike_events[0] = t_start
# first interspike interval - check if a spike exists at the start time
if s1[0] > t_start:
# edge correction
nu1 = fmax(s1[0]-t_start, s1[1]-s1[0])
index1 = -1
else:
nu1 = s1[1]-s1[0]
index1 = 0
if s2[0] > t_start:
# edge correction
nu2 = fmax(s2[0]-t_start, s2[1]-s2[0])
index2 = -1
else:
nu2 = s2[1]-s2[0]
index2 = 0
isi_values[0] = fabs(nu1-nu2)/fmax(nu1, nu2)
index = 1
with nogil: # release the interpreter to allow multithreading
while index1+index2 < N1+N2-2:
# check which spike is next, only if there are spikes left in 1
# next spike in 1 is earlier, or there are no spikes left in 2
if (index1 < N1-1) and ((index2 == N2-1) or
(s1[index1+1] < s2[index2+1])):
index1 += 1
spike_events[index] = s1[index1]
if index1 < N1-1:
nu1 = s1[index1+1]-s1[index1]
else:
# edge correction
nu1 = fmax(t_end-s1[index1], nu1)
elif (index2 < N2-1) and ((index1 == N1-1) or
(s1[index1+1] > s2[index2+1])):
index2 += 1
spike_events[index] = s2[index2]
if index2 < N2-1:
nu2 = s2[index2+1]-s2[index2]
else:
# edge correction
nu2 = fmax(t_end-s2[index2], nu2)
else: # s1[index1+1] == s2[index2+1]
index1 += 1
index2 += 1
spike_events[index] = s1[index1]
if index1 < N1-1:
nu1 = s1[index1+1]-s1[index1]
else:
# edge correction
nu1 = fmax(t_end-s1[index1], nu1)
if index2 < N2-1:
nu2 = s2[index2+1]-s2[index2]
else:
# edge correction
nu2 = fmax(t_end-s2[index2], nu2)
# compute the corresponding isi-distance
isi_values[index] = fabs(nu1 - nu2) / fmax(nu1, nu2)
index += 1
# the last event is the interval end
if spike_events[index-1] == t_end:
index -= 1
else:
spike_events[index] = t_end
# end nogil
return spike_events[:index+1], isi_values[:index]
############################################################
# get_min_dist_cython
############################################################
cdef inline double get_min_dist_cython(double spike_time,
double[:] spike_train,
# use memory view to ensure inlining
# np.ndarray[DTYPE_t,ndim=1] spike_train,
int N,
int start_index,
double t_start, double t_end) nogil:
""" Returns the minimal distance |spike_time - spike_train[i]|
with i>=start_index.
"""
cdef double d, d_temp
# start with the distance to the start time
d = fabs(spike_time - t_start)
if start_index < 0:
start_index = 0
while start_index < N:
d_temp = fabs(spike_time - spike_train[start_index])
if d_temp > d:
return d
else:
d = d_temp
start_index += 1
# finally, check the distance to end time
d_temp = fabs(t_end - spike_time)
if d_temp > d:
return d
else:
return d_temp
############################################################
# isi_avrg_cython
############################################################
cdef inline double isi_avrg_cython(double isi1, double isi2) nogil:
return 0.5*(isi1+isi2)*(isi1+isi2)
# alternative definition to obtain <S> ~ 0.5 for Poisson spikes
# return 0.5*(isi1*isi1+isi2*isi2)
############################################################
# spike_distance_cython
############################################################
def spike_distance_cython(double[:] t1, double[:] t2,
double t_start, double t_end):
cdef double[:] spike_events
cdef double[:] y_starts
cdef double[:] y_ends
cdef int N1, N2, index1, index2, index
cdef double t_p1, t_f1, t_p2, t_f2, dt_p1, dt_p2, dt_f1, dt_f2
cdef double isi1, isi2, s1, s2
N1 = len(t1)
N2 = len(t2)
spike_events = np.empty(N1+N2+2)
y_starts = np.empty(len(spike_events)-1)
y_ends = np.empty(len(spike_events)-1)
with nogil: # release the interpreter to allow multithreading
spike_events[0] = t_start
t_p1 = t_start
t_p2 = t_start
if t1[0] > t_start:
# dt_p1 = t2[0]-t_start
t_f1 = t1[0]
dt_f1 = get_min_dist_cython(t_f1, t2, N2, 0, t_start, t_end)
isi1 = fmax(t_f1-t_start, t1[1]-t1[0])
dt_p1 = dt_f1
s1 = dt_p1*(t_f1-t_start)/isi1
index1 = -1
else:
t_f1 = t1[1]
dt_f1 = get_min_dist_cython(t_f1, t2, N2, 0, t_start, t_end)
dt_p1 = 0.0
isi1 = t1[1]-t1[0]
s1 = dt_p1
index1 = 0
if t2[0] > t_start:
# dt_p1 = t2[0]-t_start
t_f2 = t2[0]
dt_f2 = get_min_dist_cython(t_f2, t1, N1, 0, t_start, t_end)
dt_p2 = dt_f2
isi2 = fmax(t_f2-t_start, t2[1]-t2[0])
s2 = dt_p2*(t_f2-t_start)/isi2
index2 = -1
else:
t_f2 = t2[1]
dt_f2 = get_min_dist_cython(t_f2, t1, N1, 0, t_start, t_end)
dt_p2 = 0.0
isi2 = t2[1]-t2[0]
s2 = dt_p2
index2 = 0
y_starts[0] = (s1*isi2 + s2*isi1) / isi_avrg_cython(isi1, isi2)
index = 1
while index1+index2 < N1+N2-2:
# print(index, index1, index2)
if (index1 < N1-1) and (t_f1 < t_f2 or index2 == N2-1):
index1 += 1
# first calculate the previous interval end value
s1 = dt_f1*(t_f1-t_p1) / isi1
# the previous time now was the following time before:
dt_p1 = dt_f1
t_p1 = t_f1 # t_p1 contains the current time point
# get the next time
if index1 < N1-1:
t_f1 = t1[index1+1]
else:
t_f1 = t_end
spike_events[index] = t_p1
s2 = (dt_p2*(t_f2-t_p1) + dt_f2*(t_p1-t_p2)) / isi2
y_ends[index-1] = (s1*isi2 + s2*isi1)/isi_avrg_cython(isi1,
isi2)
# now the next interval start value
if index1 < N1-1:
dt_f1 = get_min_dist_cython(t_f1, t2, N2, index2,
t_start, t_end)
isi1 = t_f1-t_p1
s1 = dt_p1
else:
dt_f1 = dt_p1
isi1 = fmax(t_end-t1[N1-1], t1[N1-1]-t1[N1-2])
# s1 needs adjustment due to change of isi1
s1 = dt_p1*(t_end-t1[N1-1])/isi1
# s2 is the same as above, thus we can compute y2 immediately
y_starts[index] = (s1*isi2 + s2*isi1)/isi_avrg_cython(isi1,
isi2)
elif (index2 < N2-1) and (t_f1 > t_f2 or index1 == N1-1):
index2 += 1
# first calculate the previous interval end value
s2 = dt_f2*(t_f2-t_p2) / isi2
# the previous time now was the following time before:
dt_p2 = dt_f2
t_p2 = t_f2 # t_p2 contains the current time point
# get the next time
if index2 < N2-1:
t_f2 = t2[index2+1]
else:
t_f2 = t_end
spike_events[index] = t_p2
s1 = (dt_p1*(t_f1-t_p2) + dt_f1*(t_p2-t_p1)) / isi1
y_ends[index-1] = (s1*isi2 + s2*isi1) / isi_avrg_cython(isi1,
isi2)
# now the next interval start value
if index2 < N2-1:
dt_f2 = get_min_dist_cython(t_f2, t1, N1, index1,
t_start, t_end)
isi2 = t_f2-t_p2
s2 = dt_p2
else:
dt_f2 = dt_p2
isi2 = fmax(t_end-t2[N2-1], t2[N2-1]-t2[N2-2])
# s2 needs adjustment due to change of isi2
s2 = dt_p2*(t_end-t2[N2-1])/isi2
# s2 is the same as above, thus we can compute y2 immediately
y_starts[index] = (s1*isi2 + s2*isi1)/isi_avrg_cython(isi1, isi2)
else: # t_f1 == t_f2 - generate only one event
index1 += 1
index2 += 1
t_p1 = t_f1
t_p2 = t_f2
dt_p1 = 0.0
dt_p2 = 0.0
spike_events[index] = t_f1
y_ends[index-1] = 0.0
y_starts[index] = 0.0
if index1 < N1-1:
t_f1 = t1[index1+1]
dt_f1 = get_min_dist_cython(t_f1, t2, N2, index2,
t_start, t_end)
isi1 = t_f1 - t_p1
else:
t_f1 = t_end
dt_f1 = dt_p1
isi1 = fmax(t_end-t1[N1-1], t1[N1-1]-t1[N1-2])
if index2 < N2-1:
t_f2 = t2[index2+1]
dt_f2 = get_min_dist_cython(t_f2, t1, N1, index1,
t_start, t_end)
isi2 = t_f2 - t_p2
else:
t_f2 = t_end
dt_f2 = dt_p2
isi2 = fmax(t_end-t2[N2-1], t2[N2-1]-t2[N2-2])
index += 1
# the last event is the interval end
if spike_events[index-1] == t_end:
index -= 1
else:
spike_events[index] = t_end
# the ending value of the last interval
isi1 = max(t_end-t1[N1-1], t1[N1-1]-t1[N1-2])
isi2 = max(t_end-t2[N2-1], t2[N2-1]-t2[N2-2])
s1 = dt_f1*(t_end-t1[N1-1])/isi1
s2 = dt_f2*(t_end-t2[N2-1])/isi2
y_ends[index-1] = (s1*isi2 + s2*isi1) / isi_avrg_cython(isi1, isi2)
# end nogil
# 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]
############################################################
# coincidence_python
############################################################
cdef inline double get_tau(double[:] spikes1, double[:] spikes2,
int i, int j, double max_tau):
cdef double m = 1E100 # some huge number
cdef int N1 = spikes1.shape[0]-1 # len(spikes1)-1
cdef int N2 = spikes2.shape[0]-1 # len(spikes2)-1
if i < N1 and i > -1:
m = fmin(m, spikes1[i+1]-spikes1[i])
if j < N2 and j > -1:
m = fmin(m, spikes2[j+1]-spikes2[j])
if i > 0:
m = fmin(m, spikes1[i]-spikes1[i-1])
if j > 0:
m = fmin(m, spikes2[j]-spikes2[j-1])
m *= 0.5
if max_tau > 0.0:
m = fmin(m, max_tau)
return m
############################################################
# coincidence_cython
############################################################
def coincidence_cython(double[:] spikes1, double[:] spikes2,
double t_start, double t_end, double max_tau):
cdef int N1 = len(spikes1)
cdef int N2 = len(spikes2)
cdef int i = -1
cdef int j = -1
cdef int n = 0
cdef double[:] st = np.zeros(N1 + N2 + 2) # spike times
cdef double[:] c = np.zeros(N1 + N2 + 2) # coincidences
cdef double[:] mp = np.ones(N1 + N2 + 2) # multiplicity
cdef double tau
while i + j < N1 + N2 - 2:
if (i < N1-1) and (j == N2-1 or spikes1[i+1] < spikes2[j+1]):
i += 1
n += 1
tau = get_tau(spikes1, spikes2, i, j, max_tau)
st[n] = spikes1[i]
if j > -1 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 (j < N2-1) and (i == N1-1 or spikes1[i+1] > spikes2[j+1]):
j += 1
n += 1
tau = get_tau(spikes1, spikes2, i, j, max_tau)
st[n] = spikes2[j]
if i > -1 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
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] = t_start
st[len(st)-1] = t_end
c[0] = c[1]
c[len(c)-1] = c[len(c)-2]
mp[0] = mp[1]
mp[len(mp)-1] = mp[len(mp)-2]
return st, c, mp
|