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
|
# Module containing functions to compute multivariate spike train order
# Copyright 2015, Mario Mulansky <mario.mulansky@gmx.net>
# Distributed under the BSD License
from __future__ import absolute_import
import numpy as np
from math import exp
from functools import partial
import pyspike
from pyspike import DiscreteFunc
from pyspike.generic import _generic_profile_multi
############################################################
# spike_train_order_profile
############################################################
def spike_train_order_profile(spike_train1, spike_train2, max_tau=None):
""" Computes the spike delay asymmetry profile A(t) of the two given
spike trains. Returns the profile as a DiscreteFunction object.
:param spike_train1: First spike train.
:type spike_train1: :class:`pyspike.SpikeTrain`
:param spike_train2: Second spike train.
:type spike_train2: :class:`pyspike.SpikeTrain`
:param max_tau: Maximum coincidence window size. If 0 or `None`, the
coincidence window has no upper bound.
:returns: The spike-distance profile :math:`S_{sync}(t)`.
:rtype: :class:`pyspike.function.DiscreteFunction`
"""
# check whether the spike trains are defined for the same interval
assert spike_train1.t_start == spike_train2.t_start, \
"Given spike trains are not defined on the same interval!"
assert spike_train1.t_end == spike_train2.t_end, \
"Given spike trains are not defined on the same interval!"
# cython implementation
try:
from .cython.cython_directionality import \
spike_train_order_profile_cython as \
spike_train_order_profile_impl
except ImportError:
# raise NotImplementedError()
if not(pyspike.disable_backend_warning):
print("Warning: spike_distance_cython not found. Make sure that \
PySpike is installed by running\n 'python setup.py build_ext --inplace'!\n \
Falling back to slow python backend.")
# use python backend
from .cython.directionality_python_backend import \
spike_train_order_python as spike_train_order_profile_impl
if max_tau is None:
max_tau = 0.0
times, coincidences, multiplicity \
= spike_train_order_profile_impl(spike_train1.spikes,
spike_train2.spikes,
spike_train1.t_start,
spike_train1.t_end,
max_tau)
return DiscreteFunc(times, coincidences, multiplicity)
############################################################
# spike_train_order
############################################################
def spike_train_order(spike_train1, spike_train2, normalize=True,
interval=None, max_tau=None):
""" Computes the overall spike delay asymmetry value for two spike trains.
"""
if interval is None:
# distance over the whole interval is requested: use specific function
# for optimal performance
try:
from .cython.cython_directionality import \
spike_train_order_cython as spike_train_order_impl
if max_tau is None:
max_tau = 0.0
c, mp = spike_train_order_impl(spike_train1.spikes,
spike_train2.spikes,
spike_train1.t_start,
spike_train1.t_end,
max_tau)
except ImportError:
# Cython backend not available: fall back to profile averaging
c, mp = spike_train_order_profile(spike_train1, spike_train2,
max_tau).integral(interval)
if normalize:
return 1.0*c/mp
else:
return c
else:
# some specific interval is provided: not yet implemented
raise NotImplementedError()
############################################################
# spike_train_order_profile_multi
############################################################
def spike_train_order_profile_multi(spike_trains, indices=None,
max_tau=None):
""" Computes the multi-variate spike delay asymmetry profile for a set of
spike trains. For each spike in the set of spike trains, the multi-variate
profile is defined as the sum of asymmetry values divided by the number of
spike trains pairs involving the spike train of containing this spike,
which is the number of spike trains minus one (N-1).
:param spike_trains: list of :class:`pyspike.SpikeTrain`
:param indices: list of indices defining which spike trains to use,
if None all given spike trains are used (default=None)
:type indices: list or None
:param max_tau: Maximum coincidence window size. If 0 or `None`, the
coincidence window has no upper bound.
:returns: The multi-variate spike sync profile :math:`<S_{sync}>(t)`
:rtype: :class:`pyspike.function.DiscreteFunction`
"""
prof_func = partial(spike_train_order_profile, max_tau=max_tau)
average_prof, M = _generic_profile_multi(spike_trains, prof_func,
indices)
# average_dist.mul_scalar(1.0/M) # no normalization here!
return average_prof
############################################################
# spike_train_order_matrix
############################################################
def spike_train_order_matrix(spike_trains, normalize=True, indices=None,
interval=None, max_tau=None):
""" Computes the spike delay asymmetry matrix for the given spike trains.
"""
if indices is None:
indices = np.arange(len(spike_trains))
indices = np.array(indices)
# check validity of indices
assert (indices < len(spike_trains)).all() and (indices >= 0).all(), \
"Invalid index list."
# generate a list of possible index pairs
pairs = [(indices[i], j) for i in range(len(indices))
for j in indices[i+1:]]
distance_matrix = np.zeros((len(indices), len(indices)))
for i, j in pairs:
d = spike_train_order(spike_trains[i], spike_trains[j], normalize,
interval, max_tau=max_tau)
distance_matrix[i, j] = d
distance_matrix[j, i] = -d
return distance_matrix
############################################################
# spike_order_values
############################################################
def spike_order_values(spike_trains, indices=None,
interval=None, max_tau=None):
""" Computes the spike train symmetry value for each spike in each spike
train.
"""
if indices is None:
indices = np.arange(len(spike_trains))
indices = np.array(indices)
# check validity of indices
assert (indices < len(spike_trains)).all() and (indices >= 0).all(), \
"Invalid index list."
# list of arrays for reulting asymmetry values
asymmetry_list = [np.zeros_like(st.spikes) for st in spike_trains]
# generate a list of possible index pairs
pairs = [(indices[i], j) for i in range(len(indices))
for j in indices[i+1:]]
# cython implementation
try:
from .cython.cython_directionality import \
spike_order_values_cython as spike_order_values_impl
except ImportError:
raise NotImplementedError()
# if not(pyspike.disable_backend_warning):
# print("Warning: spike_distance_cython not found. Make sure that \
# PySpike is installed by running\n 'python setup.py build_ext --inplace'!\n \
# Falling back to slow python backend.")
# # use python backend
# from .cython.python_backend import coincidence_python \
# as coincidence_profile_impl
if max_tau is None:
max_tau = 0.0
for i, j in pairs:
a1, a2 = spike_order_values_impl(spike_trains[i].spikes,
spike_trains[j].spikes,
spike_trains[i].t_start,
spike_trains[i].t_end,
max_tau)
asymmetry_list[i] += a1
asymmetry_list[j] += a2
for a in asymmetry_list:
a /= len(spike_trains)-1
return asymmetry_list
############################################################
# optimal_asymmetry_order_from_matrix
############################################################
def optimal_spike_train_order_from_matrix(D, full_output=False):
""" finds the best sorting via simulated annealing.
Returns the optimal permutation p and A value.
Internal function, don't call directly! Use optimal_asymmetry_order
instead.
"""
N = len(D)
A = np.sum(np.triu(D, 0))
p = np.arange(N)
T = 2*np.max(D) # starting temperature
T_end = 1E-5 * T # final temperature
alpha = 0.9 # cooling factor
total_iter = 0
while T > T_end:
iterations = 0
succ_iter = 0
while iterations < 100*N and succ_iter < 10*N:
# exchange two rows and cols
ind1 = np.random.randint(N-1)
delta_A = -2*D[p[ind1], p[ind1+1]]
if delta_A > 0.0 or exp(delta_A/T) > np.random.random():
# swap indices
p[ind1], p[ind1+1] = p[ind1+1], p[ind1]
A += delta_A
succ_iter += 1
iterations += 1
total_iter += iterations
T *= alpha # cool down
if succ_iter == 0:
break
if full_output:
return p, A, total_iter
else:
return p, A
############################################################
# optimal_spike_train_order
############################################################
def optimal_spike_train_order(spike_trains, indices=None, interval=None,
max_tau=None, full_output=False):
""" finds the best sorting of the given spike trains via simulated
annealing.
Returns the optimal permutation p and A value.
"""
D = spike_train_order_matrix(spike_trains, indices, interval, max_tau)
return optimal_spike_train_order_from_matrix(D, full_output)
############################################################
# permutate_matrix
############################################################
def permutate_matrix(D, p):
N = len(D)
D_p = np.empty_like(D)
for n in range(N):
for m in range(N):
D_p[n, m] = D[p[n], p[m]]
return D_p
|
