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
|
"""
Module containing several functions to compute the ISI profiles and distances
Copyright 2014-2015, Mario Mulansky <mario.mulansky@gmx.net>
Distributed under the BSD License
"""
from pyspike import PieceWiseConstFunc
from pyspike.generic import _generic_profile_multi, _generic_distance_matrix
############################################################
# isi_profile
############################################################
def isi_profile(spikes1, spikes2):
""" Computes the isi-distance profile :math:`S_{isi}(t)` of the two given
spike trains. Retruns the profile as a PieceWiseConstFunc object. The S_isi
values are defined positive S_isi(t)>=0. 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.
:param spikes1: ordered array of spike times with auxiliary spikes.
:param spikes2: ordered array of spike times with auxiliary spikes.
:returns: The isi-distance profile :math:`S_{isi}(t)`
:rtype: :class:`pyspike.function.PieceWiseConstFunc`
"""
# 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!"
# load cython implementation
try:
from cython.cython_distance import isi_distance_cython \
as isi_distance_impl
except ImportError:
print("Warning: isi_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 isi_distance_python \
as isi_distance_impl
times, values = isi_distance_impl(spikes1, spikes2)
return PieceWiseConstFunc(times, values)
############################################################
# isi_distance
############################################################
def isi_distance(spikes1, spikes2, interval=None):
""" Computes the isi-distance I of the given spike trains. The
isi-distance is the integral over the isi distance profile
:math:`S_{isi}(t)`:
.. math:: I = \int_{T_0}^{T_1} S_{isi}(t) dt.
:param spikes1: ordered array of spike times with auxiliary spikes.
:param spikes2: ordered array of spike times with auxiliary spikes.
:param interval: averaging interval given as a pair of floats (T0, T1),
if None the average over the whole function is computed.
:type interval: Pair of floats or None.
:returns: The isi-distance I.
:rtype: double
"""
return isi_profile(spikes1, spikes2).avrg(interval)
############################################################
# isi_profile_multi
############################################################
def isi_profile_multi(spike_trains, indices=None):
""" computes the multi-variate isi distance profile for a set of spike
trains. That is the average isi-distance of all pairs of spike-trains:
S_isi(t) = 2/((N(N-1)) sum_{<i,j>} S_{isi}^{i,j},
where the sum goes over all pairs <i,j>
:param spike_trains: list of spike trains
:param indices: list of indices defining which spike trains to use,
if None all given spike trains are used (default=None)
:type state: list or None
:returns: The averaged isi profile :math:`<S_{isi}>(t)`
:rtype: :class:`pyspike.function.PieceWiseConstFunc`
"""
average_dist, M = _generic_profile_multi(spike_trains, isi_profile,
indices)
average_dist.mul_scalar(1.0/M) # normalize
return average_dist
############################################################
# isi_distance_multi
############################################################
def isi_distance_multi(spike_trains, indices=None, interval=None):
""" computes the multi-variate isi-distance for a set of spike-trains.
That is the time average of the multi-variate spike profile:
I = \int_0^T 2/((N(N-1)) sum_{<i,j>} S_{isi}^{i,j},
where the sum goes over all pairs <i,j>
:param spike_trains: list of spike trains
:param indices: list of indices defining which spike trains to use,
if None all given spike trains are used (default=None)
:param interval: averaging interval given as a pair of floats, if None
the average over the whole function is computed.
:type interval: Pair of floats or None.
:returns: The time-averaged isi distance :math:`I`
:rtype: double
"""
return isi_profile_multi(spike_trains, indices).avrg(interval)
############################################################
# isi_distance_matrix
############################################################
def isi_distance_matrix(spike_trains, indices=None, interval=None):
""" Computes the time averaged isi-distance of all pairs of spike-trains.
:param spike_trains: list of spike trains
: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 interval: averaging interval given as a pair of floats, if None
the average over the whole function is computed.
:type interval: Pair of floats or None.
:returns: 2D array with the pair wise time average isi distances
:math:`I_{ij}`
:rtype: np.array
"""
return _generic_distance_matrix(spike_trains, isi_distance,
indices, interval)
|
