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""" distances.py
Module containing several functions to compute spike distances
Copyright 2014, Mario Mulansky <mario.mulansky@gmx.net>
Distributed under the BSD License
"""
import numpy as np
import threading
from pyspike import PieceWiseConstFunc, PieceWiseLinFunc
############################################################
# isi_distance
############################################################
def isi_distance(spikes1, spikes2):
""" Computes the isi-distance profile S_isi(t) of the two given spike
trains. Retruns the profile as a PieceWiseConstFunc object. The S_isi
values are defined in the interval [0,1). 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.
Args:
- spikes1, spikes2: ordered arrays of spike times with auxiliary spikes.
Returns:
- PieceWiseConstFunc describing the isi-distance.
"""
# 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!"
# cython implementation
from cython_distance import isi_distance_cython
times, values = isi_distance_cython(spikes1, spikes2)
return PieceWiseConstFunc(times, values)
############################################################
# spike_distance
############################################################
def spike_distance(spikes1, spikes2):
""" Computes the spike-distance profile S_spike(t) of the two given spike
trains. Returns the profile as a PieceWiseLinFunc object. The S_spike
values are defined in the interval [0,1). 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.
Args:
- spikes1, spikes2: ordered arrays of spike times with auxiliary spikes.
Returns:
- PieceWiseLinFunc describing the spike-distance.
"""
# 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!"
# cython implementation
from cython_distance import spike_distance_cython
times, y_starts, y_ends = spike_distance_cython(spikes1, spikes2)
return PieceWiseLinFunc(times, y_starts, y_ends)
############################################################
# multi_distance
############################################################
def multi_distance(spike_trains, pair_distance_func, indices=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:
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
"""
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 indices for j in indices[i+1:]]
# start with first pair
(i, j) = pairs[0]
average_dist = pair_distance_func(spike_trains[i], spike_trains[j])
for (i, j) in pairs[1:]:
current_dist = pair_distance_func(spike_trains[i], spike_trains[j])
average_dist.add(current_dist) # add to the average
average_dist.mul_scalar(1.0/len(pairs)) # normalize
return average_dist
############################################################
# multi_distance_par
############################################################
def multi_distance_par(spike_trains, pair_distance_func, indices=None):
""" parallel implementation of the multi-distance. Not currently used as
it does not improve the performance.
"""
num_threads = 2
lock = threading.Lock()
def run(spike_trains, index_pairs, average_dist):
(i, j) = index_pairs[0]
# print(i,j)
this_avrg = pair_distance_func(spike_trains[i], spike_trains[j])
for (i, j) in index_pairs[1:]:
# print(i,j)
current_dist = pair_distance_func(spike_trains[i], spike_trains[j])
this_avrg.add(current_dist)
with lock:
average_dist.add(this_avrg)
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 indices for j in indices[i+1:]]
num_pairs = len(pairs)
# start with first pair
(i, j) = pairs[0]
average_dist = pair_distance_func(spike_trains[i], spike_trains[j])
# remove the one we already computed
pairs = pairs[1:]
# distribute the rest into num_threads pieces
clustered_pairs = [pairs[n::num_threads] for n in xrange(num_threads)]
threads = []
for pairs in clustered_pairs:
t = threading.Thread(target=run, args=(spike_trains, pairs,
average_dist))
threads.append(t)
t.start()
for t in threads:
t.join()
average_dist.mul_scalar(1.0/num_pairs) # normalize
return average_dist
############################################################
# isi_distance_multi
############################################################
def isi_distance_multi(spike_trains, indices=None):
""" computes the multi-variate isi-distance for a set of spike-trains. That
is the average isi-distance of all pairs of spike-trains:
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
- indices: list of indices defining which spike trains to use,
if None all given spike trains are used (default=None)
Returns:
- A PieceWiseConstFunc representing the averaged isi distance S
"""
return multi_distance(spike_trains, isi_distance, indices)
############################################################
# spike_distance_multi
############################################################
def spike_distance_multi(spike_trains, indices=None):
""" computes the multi-variate spike-distance for a set of spike-trains.
That is the average spike-distance of all pairs of spike-trains:
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
- indices: list of indices defining which spike-trains to use,
if None all given spike trains are used (default=None)
Returns:
- A PieceWiseLinFunc representing the averaged spike distance S
"""
return multi_distance(spike_trains, spike_distance, indices)
def isi_distance_matrix(spike_trains, indices=None):
""" Computes the average isi-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 isi-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 indices for j in indices[i+1:]]
distance_matrix = np.zeros((len(indices), len(indices)))
for i, j in pairs:
d = isi_distance(spike_trains[i], spike_trains[j]).avrg()
distance_matrix[i, j] = d
distance_matrix[j, i] = d
return distance_matrix
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