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
|
#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
DTYPE = np.float
ctypedef np.float_t DTYPE_t
############################################################
# isi_distance_cython
############################################################
def isi_distance_cython(double[:] s1,
double[:] s2):
cdef double[:] spike_events
cdef double[:] isi_values
cdef int index1, index2, index
cdef int N1, N2
cdef double nu1, nu2
N1 = len(s1)-1
N2 = len(s2)-1
nu1 = s1[1]-s1[0]
nu2 = s2[1]-s2[0]
spike_events = np.empty(N1+N2)
spike_events[0] = s1[0]
# the values have one entry less - the number of intervals between events
isi_values = np.empty(N1+N2-1)
with nogil: # release the interpreter to allow multithreading
isi_values[0] = fabs(nu1-nu2)/fmax(nu1, nu2)
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 >= N1:
break
spike_events[index] = s1[index1]
nu1 = s1[index1+1]-s1[index1]
elif s1[index1+1] > s2[index2+1]:
index2 += 1
if index2 >= N2:
break
spike_events[index] = s2[index2]
nu2 = s2[index2+1]-s2[index2]
else: # s1[index1+1] == s2[index2+1]
index1 += 1
index2 += 1
if (index1 >= N1) or (index2 >= N2):
break
spike_events[index] = s1[index1]
nu1 = s1[index1+1]-s1[index1]
nu2 = s2[index2+1]-s2[index2]
# compute the corresponding isi-distance
isi_values[index] = fabs(nu1 - nu2) / fmax(nu1, nu2)
index += 1
# the last event is the interval end
spike_events[index] = s1[N1]
# 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=0) nogil:
""" Returns the minimal distance |spike_time - spike_train[i]|
with i>=start_index.
"""
cdef double d, d_temp
d = fabs(spike_time - spike_train[start_index])
start_index += 1
while start_index < N:
d_temp = fabs(spike_time - spike_train[start_index])
if d_temp > d:
break
else:
d = d_temp
start_index += 1
return d
############################################################
# spike_distance_cython
############################################################
def spike_distance_cython(double[:] t1,
double[:] t2):
cdef double[:] spike_events
cdef double[:] y_starts
cdef double[:] y_ends
cdef int N1, N2, index1, index2, index
cdef double dt_p1, dt_p2, dt_f1, dt_f2, isi1, isi2, s1, s2
N1 = len(t1)
N2 = len(t2)
spike_events = np.empty(N1+N2-2)
spike_events[0] = t1[0]
y_starts = np.empty(len(spike_events)-1)
y_ends = np.empty(len(spike_events)-1)
with nogil: # release the interpreter to allow multithreading
index1 = 0
index2 = 0
index = 1
dt_p1 = 0.0
dt_f1 = get_min_dist_cython(t1[1], t2, N2, 0)
dt_p2 = 0.0
dt_f2 = get_min_dist_cython(t2[1], t1, N1, 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 >= N1:
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)/(0.5*(isi1+isi2)*(isi1+isi2))
# now the next interval start value
dt_f1 = get_min_dist_cython(t1[index1+1], t2, N2, 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)/(0.5*(isi1+isi2)*(isi1+isi2))
elif t1[index1+1] > t2[index2+1]:
index2 += 1
if index2+1 >= N2:
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) / (0.5*(isi1+isi2)*(isi1+isi2))
# now the next interval start value
dt_f2 = get_min_dist_cython(t2[index2+1], t1, N1, 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)/(0.5*(isi1+isi2)*(isi1+isi2))
else: # t1[index1+1] == t2[index2+1] - generate only one event
index1 += 1
index2 += 1
if (index1+1 >= N1) or (index2+1 >= N2):
break
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_cython(t1[index1+1], t2, N2, index2)
dt_f2 = get_min_dist_cython(t2[index2+1], t1, N1, 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[N1-1]
# the ending value of the last interval
isi1 = max(t1[N1-1]-t1[N1-2], t1[N1-2]-t1[N1-3])
isi2 = max(t2[N2-1]-t2[N2-2], t2[N2-2]-t2[N2-3])
s1 = dt_p1*(t1[N1-1]-t1[N1-2])/isi1
s2 = dt_p2*(t2[N2-1]-t2[N2-2])/isi2
y_ends[index-1] = (s1*isi2 + s2*isi1) / (0.5*(isi1+isi2)*(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]
|
