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
|
"""
Generic functions to compute multi-variate profiles and distance matrices.
Copyright 2015, Mario Mulansky <mario.mulansky@gmx.net>
Distributed under the BSD License
"""
from __future__ import division
import numpy as np
############################################################
# _generic_profile_multi
############################################################
def _generic_profile_multi(spike_trains, pair_distance_func, indices=None):
""" Internal implementation detail, don't call this function directly,
use isi_profile_multi or spike_profile_multi instead.
Computes the multi-variate distance for a set of spike-trains using the
pair_dist_func to compute pair-wise distances. That is it computes the
average distance of all pairs of spike-trains:
:math:`S(t) = 2/((N(N-1)) sum_{<i,j>} S_{i,j}`,
where the sum goes over all pairs <i,j>.
Args:
- spike_trains: list of spike trains
- pair_distance_func: function computing the distance of two spike trains
- indices: list of indices defining which spike trains to use,
if None all given spike trains are used (default=None)
Returns:
- The averaged multi-variate distance of all pairs
"""
def divide_and_conquer(pairs1, pairs2):
""" recursive calls by splitting the two lists in half.
"""
L1 = len(pairs1)
if L1 > 1:
dist_prof1 = divide_and_conquer(pairs1[:L1//2],
pairs1[L1//2:])
else:
dist_prof1 = pair_distance_func(spike_trains[pairs1[0][0]],
spike_trains[pairs1[0][1]])
L2 = len(pairs2)
if L2 > 1:
dist_prof2 = divide_and_conquer(pairs2[:L2//2],
pairs2[L2//2:])
else:
dist_prof2 = pair_distance_func(spike_trains[pairs2[0][0]],
spike_trains[pairs2[0][1]])
dist_prof1.add(dist_prof2)
return dist_prof1
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:]]
L = len(pairs)
if L > 1:
# recursive iteration through the list of pairs to get average profile
avrg_dist = divide_and_conquer(pairs[:len(pairs)//2],
pairs[len(pairs)//2:])
else:
avrg_dist = pair_distance_func(spike_trains[pairs[0][0]],
spike_trains[pairs[0][1]])
return avrg_dist, L
############################################################
# _generic_distance_multi
############################################################
def _generic_distance_multi(spike_trains, pair_distance_func,
indices=None, interval=None):
""" Internal implementation detail, don't call this function directly,
use isi_distance_multi or spike_distance_multi instead.
Computes the multi-variate distance for a set of spike-trains using the
pair_dist_func to compute pair-wise distances. That is it computes the
average distance of all pairs of spike-trains:
:math:`S(t) = 2/((N(N-1)) sum_{<i,j>} D_{i,j}`,
where the sum goes over all pairs <i,j>.
Args:
- spike_trains: list of spike trains
- pair_distance_func: function computing the distance of two spike trains
- indices: list of indices defining which spike trains to use,
if None all given spike trains are used (default=None)
Returns:
- The averaged multi-variate distance of all pairs
"""
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:]]
avrg_dist = 0.0
for (i, j) in pairs:
avrg_dist += pair_distance_func(spike_trains[i], spike_trains[j],
interval)
return avrg_dist/len(pairs)
############################################################
# generic_distance_matrix
############################################################
def _generic_distance_matrix(spike_trains, dist_function,
indices=None, interval=None):
""" Internal implementation detail. Don't use this function directly.
Instead use isi_distance_matrix or spike_distance_matrix.
Computes the time averaged distance of all pairs of spike-trains.
Args:
- spike_trains: list of spike trains
- indices: list of indices defining which spike-trains to use
if None all given spike-trains are used (default=None)
Return:
- a 2D array of size len(indices)*len(indices) containing the average
pair-wise distance
"""
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 = [(i, j) for i in range(len(indices))
for j in range(i+1, len(indices))]
distance_matrix = np.zeros((len(indices), len(indices)))
for i, j in pairs:
d = dist_function(spike_trains[indices[i]], spike_trains[indices[j]],
interval)
distance_matrix[i, j] = d
distance_matrix[j, i] = d
return distance_matrix
|
